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Hafner-Bomholt-the 3d electrodynamic wave simulator-1993-17

1. vertical direction iterate and show the scalar potential 2 2D Laplace 5 point operator electrostatics Solve problems of 2D electrostatics Define electrodes and dielectric domains as outlined in the previous subsection iterate and show the scalar potential 3 3D Laplace 7 point operator electrostatics Like algorithm 2 but for solving 3D problems Thus a 3D grid is required i e the number of levels should be bigger than one 4 2D Laplace 5 point operator electrostatics simplified algorithm permittivity ignored Like algorithm 2 but a simplified algorithm is used where the new values of an iteration are stored on the same array as the old values Moreover the permittivity is ignored i e it is assumed that free space is everywhere outside the electrodes 5 2D Laplace 9 point operator electrostatics permittivity ignored Like algo rithm 2 but a more complicated 9 point operator is used Moreover the per mittivity is ignored i e it is assumed that free space is everywhere outside the electrodes 6 2D life The famous game 2D life There are different variants of 2D life that can be characterized by four integer numbers i j k l A living cell value 1 stays alive when i up to j of its eight neighbors are alive otherwise it dies A dead cell is reanimated when k up to l of its eight neighbors are alive otherwise it remains dead The four integers are compressed to a single integer number
2. part type 1 m0 1 00000E 00 Figure 17 8 Desk of the 3D MMP plot program showing the time average of the Poynting vector for a plane wave incident on a plate of finite thickness with a circular aperture plane fictitious boundary in the center of the aperture Unfortunately the errors cannot really be reduced with this more complicated model To decide whether model 26 is preferable or not you have to work with finer discretiza tions with more unknowns 17 9 3 Optimizations Ring Multipoles Connections Model 27 When a model is not very accurate but the number of unknowns is so large that it can not be increased anymore you can try to modify the MMP expansions and the matching points for getting better results or at least for getting more information Changing the origins and orders of multipoles is quite easy with the editor Maybe you mistrust the normal expansion in the domain containing the aperture In this case replace it by some multipoles Also the editor provides some features for generating 3D multipoles you better start with a modification of the 2D model used for generating the 3D model However you certainly get more experience trying both approaches for obtaining a use ful set of multipoles Incidentally when you automatically generate multipoles for the infinite domains you get multipoles far away from the aperture as well if you have gen erated matching points far away from the aperture Remove these m
3. Ey z at Feap e The system in a point 41 E12 at Tht Figure A 1 Coordinate systems used in the 3D MMP main program Conversions of the coordinates al al at of a vector in a system with Os basis Y1 2 1 2 E to the coordinates a2 a2 a2 in the basis Xo 2 7 7 2 7 is done by az az ay te ay at a z and in the reverse direction by Az az a tj of A 2 a az 281 tij is a 3 by 3 orthogonal matrix with t11 t21 t31 being the coordinates of in Xy t12 t22 t32 those of and t13 t23 t33 those of For position vectors the change in origin vectors exp and Py must additionally be taken into account A 2 2 Cylindrical and Spherical Coordinates Many expansions are evaluated in curvilinear systems of coordinates like circular cylin drical coordinates p y z or spherical coordinates r y and are subsequently transformed to Cartesian coordinates x y z y Figure A 2 Non Cartesian coordinate systems The relations between the coordinates in figure A 2 is r xu y 2 x rsinvcosp pcosp p x y y rsindsinp psing yp arctan y x z rcosv Y arctan p z The angles y and Y are hardly ever needed explicitly cf section B 4 A vector with coordinates ar a9 ap in the basis p p is converted to coordinates ax dy a7 1 in the basis y z by ay ay COS p sin ay
4. 114 115 116 117 S Kiener The MMP method applied to EMC in Proc of the IEEE EMC Nagoya Sept 1989 G Lucca and P Leuchtmann Lignes conducteurs multiples avec retour la terre Une m thode g n rale pour le calcul des imp dances et admittances dans le cas des problemes de CEM basse fr quence in Proc 5 me colloque international en langue francaise sur la compatibilit lectromagn tique Evian Sept 1989 S Kiener La m thode MMP appliqu e la CEM in Proc 5 me colloque inter national en langue francaise sur la compatibilit lectromagn tique Evian Sept 1989 Ch Hafner MMP programs for fast computations of electrodynamic fields on small machines in Proc GAMNI SMAI Conference on Approximation and Nu merical Methods for the Solution of Maxwell Equations Paris Dec 1989 H Baggenstos and P Leuchtmann Numerische Berechnung elektromagnetischer Felder mittels MMP Programmen Elektrie vol 44 pp 165 169 May 1990 N Kuster and Q Balzano SAR approximation in the near field of sources using free space H field values in Proc of the 12th Annual Meeting of the Bioelectro magnetic Society San Antonio Texas June 1990 M Reite L Higgs N Kuster J Lebet and B Pasche Sleep inducing effects of low energy emission therapy in Proc of the 12th Annual Meeting of the Bioelec tromagnetic Society San Antonio Texas June 1990
5. P Regli Ch Hafner and N Kuster Animated electromagnetic field represen tation in Proc of the XXIIIrd General Assembly of the International Union of Radio Science URSI Prague Aug 1990 N Kuster and R A Tell SAR approximation in the near field of reradiating structures using free H field values in Proc of the XXIIIrd General Assembly of the International Union of Radio Science URSI Prague Aug 1990 S Kiener Eddy currents in bodies with sharp edges IEEE Trans on Magnetics vol 26 pp 482 485 march 1990 Ch Hafner and S Kiener Introduction to the MMP codes and to the GMT in Short Course on Numerical Techniques for Electromagnetics Lausanne Mar 1990 Ch Hafner Transputers for computational electromagnetics in Proc IEEE MTT Workshop on new developments in numerical modelling of microwave and millimeter wave structures Dallas May 1990 Ch Hafner Graphic input output programs for the 3D MMP code on PC s in Proc IEEE AP S and URSI Int Symposium Dallas May 1990 J Li and S Kiener On the solution of periodical structures with GMT in Proc IEEE AP s Int Symposium Dallas pp 610 613 May 1990 334 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 S Kiener Introduction la TMG et aux codes MMP Revue de Physique Ap pliqu e vol 25 pp 73
6. 78 to the zero routines n called by subroutine nullen in file ANS F They write the respective parameters along with the labels to standard output The include file MMPAR SRC is an abridged version of COMM SRC and contains only those variables which are needed by MMP_PAR 13 9 2 Fourier Transform mmp_fan and mmp_f3d The Fourier transform which produces a file MMP_FOU FRQ from MMP_FOU TIM can be found in MMP_FAN F The inverse transform which produces time value plot files MMP_Tyy xxx for the 3D graphic plot program from the files MMP_Pyy xxx is in file MMP_F3D SRC Both are rather straightforward implementations of the formulas in section 12 3 13 10 Modification of the Source Adding Expansions One of the most likely modifications of the 3D MMP source code is the addition of custom expansion routines for special purposes For this usually three subroutines are needed the names are chosen as an example only auser The expansion subroutine cf section 13 3 2 nuser A dummy expansion routine which computes the number of parameters of the expansion cf section 13 3 2 muser A dummy expansion routine for parameter labeling with the MMP_PAR utility cf section 13 9 A good example are the routines for the plane wave aplwv file ANS F nplwv file ANS F and mplwv file MMPAR SRC A simpler case is the routine for the rectangular waveguide modes aquad file ANS F which does not consider symmetries and always ha
7. nBox number of boxes kBox number of actual box nBoxT total number of texts and variables contained in all boxes kBoxT actual box text and box variable BoxTxt i texts contained in the boxes up to 20 characters BoxRea i real values contained in the boxes BoxInt i integer values contained in the boxes IBox j k information of box number k j 1 horizontal pixel coordinate of lower left corner 320 jPull 1 mx my Rmx Rmy iButt iscreen imeta idevi iwidth iheight 2 vertical pixel coordinate of lower left corner 3 horizontal pixel coordinate of upper right corner 4 vertical pixel coordinate of upper right corner 5 length of text area in characters 6 length of variable area in characters 7 offset for corresponding texts and variables BoxTxt IBox 7 k 1 is the first text of box number k 8 number of lines texts and variables The box is active on bright if IBox j k lt 0 9 actual line number contains information on the lines of a box that have to be displayed if the box is pulled up or down jPul1 1 0 do not show line number 1 pixel coordinates of the mouse cursor real 2D coordinates of the mouse cursor status of the mouse button no button pressed button 1 pressed button 2 pressed buttons 1 and 2 pressed button 3 pressed output device adress screen output device adress meta file actual output device adress equal to iscreen or imeta width of output device in pix
8. A more detailed description is given in the user s guide to the 3D MMP main program see chapter 10 and in the description of the regular actions Change values with the first count up and second count down mouse button in the value area of this box except the values Ncon Nint Nfpt that are modified with add and delete commands Box 13 Additional Real Data Type pull down input output ang 1 angle used for rotation and for the generation of a torus or object 2 area of biggest influence for special blowing types fac 1 blowing factor 2 factor used for the generation of a cylinder torus or object aspect ratio of the two tangent vectors of the matching points R rq real part of frequency for 3D MMP main program Ifrq imaginary part of frequency for 3D MMP main program len length of the sides of a cylinder or object to be generated Vmet size of the vertical side of a window in a meta file Vmet maximum radial distance of points for the generation of an object Change values with the first count up and second count down mouse button in the value area of this box Rfrq and Ifrq are used in the 3D MMP program The remaining values in this box are used within the editor only Box 14 Integer Data of Expansions Type pull down input output Exp _dom domain number Exp _IE1 expansion type Exp _IE2 expansion parameter Exp _IE3 expansion parameter Exp _IE4 expansion parameter Exp _IE
9. Although you do not have to know them all by heart you should try them and get familiar with the ones you like most Look at the errors obtained in the matching points and you see that large errors 237 occur above all in relatively rough models for saving computation time and when the distance between two multipoles is relatively large When you use only 3 multipoles on the positive Y axis in our example put them at the locations Y 0 04 Y 0 12 and Y 0 2 This is much easier to do with a text editor than with the graphic 3D MMP editor Nonetheless you can do this with the following procedure Assume that your pole is at the position 0 1325 on the Y axis and you want to put it at the position 0 12 First you do not know that its actual position is 0 1325 and measuring on the screen is not recommended If the item selected in the item box is pole you can click the second mouse button when the mouse cursor is on the pole The coordinates of the pole are displayed in the boxes x y z Thus you can simply read the actual position Click the pole and it becomes active when it was inactive before Before you try to move the pole make sure that only the pole to be moved is active Afterwards you can run 3D move pole and answer both questions move__elements_OK_ set_new_vector _YES in the affirmative You are asked set_start_point____ Instead of setting the start po
10. Here the value 0 is appropriate A multipole should now be generated in the center of the arc Before you proceed save the data with 2D write file Now you can try other 2D commands such as 2D lt check pole etc Reload the 2D arc with 2D read file to get back the reasonable data discretized above in case you make a mistake Needless to say the number in the item box file has to be identical with the one used for writing the file Answer the question add_2D_objects_____ in the negative by clicking the question box with the second button and answer the question replace_2D_objects_ in the affirmative by clicking the box with the first button The mouse cursor disappears and reading 2D _data_file is displayed You can continue as soon as the mouse cursor is visible again Now it is time to start the 3D construction of the sphere A sphere can be generated by rotating the arc defined above around the Y axis with an angle of 360 degrees This value is already predefined in the additional real data box ang Thus you can run the command 3D generate torus as soon as you are sure that the second real parameter fac of the command is appropriate In most cases the value 1 0 is most reasonable because this results in square matching points Answer the question set_axis_ey______ in the affirmative First you see some l
11. I N Bronstein and K A Semendjajew Taschenbuch der Mathematik Erg nzende Kapitel Thun und Frankfurt am Main Verlag Harri Deutsch 2nd ed 1981 A Bjork and G Dahlquist Numerische Methoden R Oldenbourg Verlag 1972 G J Burke and A J Poggio Numerical Electromagnetics Code NEC Method of Moments San Diego Naval Ocean Systems Center 1981 K Simonyi Theoretische Elektrotechnik VEB Deutscher Verlag der Wis senschaften 1980 C Miller Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen Springer Verlag 1957 L W Kantorowitsch and G P Akilow Funktionalanalysis In Normierten R umen Berlin Akademie Verlag 1964 V V Varadan and V K Varadan Acoustic Electromagnetic and Elastic Wave Scattering Focus on the T Matriz Approach Pergamon Press 1979 E Stiefel and A F ssler Gruppentheoretische Methoden und ihre Anwendungen Teubner Stuttgart 1979 J Singer On the equivalence of Galerkin and Raleigh Ritz methods Journal of the Royal Aeronautical Society vol 66 p 592 Sept 1962 T K Sarkar A note on the choice weighting functions on the Method of Mo ments IEEE Transactions on Antennas and Propagation vol 33 pp 436 441 Apr 1985 T K Sarkar A R Djordjevi and E Arvas On the choice of expansion and weighting functions in the numerical solution of operator equations EEE Trans actions on Antennas and Propagation vol 33 pp
12. Syracuse June 1988 N Kuster and Q Balzano The near and farfield simulation of radios held by man calculated with the MMP method in URSI Radio Science Meeting Syracuse June 1988 P Leuchtmann A completely automated procedure for the choice of functions in the MMP method in Proc of the International Conference on Computational Methods in Flow Analysis Okayama pp 71 78 June 1988 Ch Hafner Revolutionen und Revolution re der Physik ETH Bulletin July 1988 Ch Hafner On the comparison of numerical methods ACES Journal and Newsletter vol 3 no 2 1988 Ch Hafner Revolutionen und Revolution re der Physik Schweizer Ingenieur und Architekt vol 106 Dec 1988 Ch Hafner Numerical field calculations on PC s IEEE AP S Newsletter Dec 1988 S Kiener Grundlagen zum induktiven Heizen eines Kochgef sses Bulletin SEV VSE vol 79 no 9 pp 458 461 1988 N Kuster and Ch Hafner Numerische Methoden zur Berechnung der Feld verteilung im menschlichen K rper verursacht durch k rpernahe Funkger te in Proceeding der Jahrestagung des Fachverbandes ftir Strahlenschutz Nichtion isierende Strahlung K ln Nov 1988 P Leuchtmann and G L Solbiati Generalized coupling theory A computer adapted theory for solving interference problems in Proceedings of the 4th Sym posium on Electromagnetic Compatibility Z rich Mar 1989 L Bomholt an
13. Therefore the maximum number of elements of the matrix share on the main transputer ncam in file comm inc has to be redefined to a fixed smaller size ncam maximum number of elements of the matrix share R on the root transputer The maximum size of the updating rows kmm and the maximum number of matrix ele ments mami in the programs chi and chl is defined in file par src kmm maximum number of columns of the matrix A mami maximum number of elements of the matrix shares R to Ry in pro grams chi and chl Standard parameters are set in comment lines for transputers with different sizes of memory The CONVERT utility can be used as indicated in the previous subsection cor converting CH1 SRC and CHL SRC into CH1 F and CHL F respectively After compilation and linking the programs have to be configured for a particular size and arrangement of the pipeline when the 3L parallel FORTRAN compiler is used A detailed description of configuring the similar 2D MMP code for the Microway QUAD PUTER can be found in 4 Moreover sample configuration files extension CFG for 274 the Microway QUADPUTER are included For this board the conversion compilation linking and configuration is done automatically in 3LF DOS BAT 275 21 Running the 3D MMP Programs 21 1 Required Data and Auxiliary Files For starting the 3D MMP editor and the 3D MMP plot program some data files must be present Above all the data concerning the windows and b
14. Z rich Mar 1991 P Leuchtmann and F Bomholt On the modelling of electromagnetic field of emc test arrangements with the mmp code in 8th Annual Review of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Mon terey Mar 1992 P Regli Automatic Expansion Setting for the 3D MMP Code in 8th Annual Re view of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Monterey Mar 1992 C Hafner and N Kuster Iterative and Block Iterative Solutions of Overdeter mined Systems of Equations in the MMP code in 8th Annual Review of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Mon terey Mar 1992 336 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 C Hafner FD Schemes Particles Cellular Automata and other Exotic Features of the 3D MMP Graphics in 8th Annual Review of Progress in Applied Computa tional Electromagnetics ACES Conference Proceedings Monterey Mar 1992 J Li The MMP Applied to the Scattering Problem of the Periodically Fluctuated Lossy Dielectric Surface and Periodical Grating Embedded in Dielectric Layer in Proc IEEE AP S and URSI Int Symposium Chicago July 1992 I N Bronstein and K A Semendjajew Taschenbuch der Mathematik Thun und Frankfurt am Main Verlag Harri Deutsch 20st ed 1981
15. after As a conse quence the matching points are no longer attached to the expansion and can be manipulated separately Moreover the matching points are saved in the input file Although this gives you more flexibility there is a drawback too when manip ulating the wire you have to make sure that you change both the wire and the corresponding matching points 2 Adjust all matching points with the command 3D adjust points after setting the boundary conditions you want to have matched For example select the stan dard values 0 and 1 in the boxes MPt E1 3 and MPt H1 3 respectively which means that all useful conditions are matched automatically 3 Save all 3D data on a file MMP_3DI 021 and leave the editor 241 4 Copy the parameters computed in the previous model on the parameter file MMP_PAR 021 with the DOS command 5 Run the main program and compute the errors without computing the parameters again Do not select task 1 in the main menu You obtain much larger errors than in model 20 This warns you that the result is not so good as you might have believed Looking at the errors in the dummy matching points of model 20 you notice that the errors in these points are considerably larger than in the other points In fact the wire is not thin enough to allow an accurate computation with the thin wire approximation Of course you can now com
16. from the Options menu Note that you might be asked to insert some of the original Windows disks if you do that For more information see your Windows manual The assignment of colors and fill patterns to graphic elements and their states is done in the desk files MMP_E3D DSK and MMP_P3D DSK In the MMP 3D plot program it is also possible to assign colors and fill patterns of most of the graphic elements interactively For changing the colors or the color palette you can modify the desk file with any text editor Since the graphic programs do not run when the desk files are corrupt be careful when you do this In the default desks of the 3D MMP graphic programs 16 colors are used When a driver with more colors is used this results in more memory requirement than necessary As a result there might not be enough memory left on your PC to start the program or to display pull and hint boxes When you are working with drivers with less than 16 colors 92 colors will be simulated with fill patterns To avoid interference of the fill patterns in the MMP programs with the fill patterns for simulating colors you can replace all color numbers in the desk files by numbers that do not exceed the maximum color number of your driver Of course you can do this interactively in the 3D MMP plot program 14 7 Generating Hardcopies and Meta Files The 3D MMP editor as well as the 3D MMP plot program enable you to generate hardcopies of the desk and
17. number of particle iterations before a new picture is drawn number of field iterations before a new picture is drawn type of iterative procedure see hint box for more information additional information for some iterative procedures number of pictures of a movie generated with generate pic f or move part representation of the trail of particles see hint box for more informa tion Box 35 Domain Real Data Type pull down input output real part of relative permittivity imaginary part of relative permittivity real part of relative permeability imaginary part of relative permeability real part of conductivity imaginary part of conductivity Use the command show dom to display the values of a certain With adjust dom domain domain in this box the values in this box are copied on the corresponding values of the 16 7 Selecting Appropriate Field Representations The plot program allows to represent many different types of field in very different ways Thus many parameters have to be selected in such a way that an appropriate repre sentation is found In this section the various possibilities are outlined in a tutorial style Pictures are usually generated with the command show pic f When you run this procedure immediately after having started the plot program you obtain a message 192 indicating that the field is constant
18. you should set the following data iter fiel 0 Re_Om 1 0 angle 0 0 tim 0 0 iter part 10 dt 0 1 Note that it is important to set the number of field iterations to zero Otherwise the FD algorithm would be applied iter fiel times the new field would be drawn and the particle would be moved in each time step Although the FD algorithm computes a static field the program adds a harmonic time dependence with the angular frequency Re_Om I e the results are used as low frequency approximations When you select a low frequency you will see how the charge oscillates between the electrodes Depending on many parameters the charge can come very close to the electrodes It even can move through the electrodes because the electrodes are not solid bodies in this implementation It is up to you to refine the FD model to introduce different dielectrics to study the boundary conditions the solution as a function of the number of iterations etc Note that several FD schemes for electrostatics are implemented in the plot program For example you can compare the 5 point approximation of the 2D Laplacian operator with its 9 point approximation 17 16 Finite Differences Time Domain Model 34 The Finite Differences Time Domain FDTD algorithm based in the plot program is based on a leap frog scheme In this scheme the different components of the fiel
19. 315 F Overview of the Graphics Source F 1 Source Files of the 3D MMP Graphics Package The files of the 3D MMP graphics package are contained self extracting files on the distribution diskette see chapter refdiskcont F 2 Elementary MMP Graphic Subroutines Beside standard FORTRAN subroutines the graphic MMP codes call a small set of elementary graphic functions that can be simulated by most of the well known graphic packages Many of them affect only a part of the MMP features Thus useful codes can be achieved even if only a subset of the elementary graphic functions is simulated or if some of these functions are not completely simulated All elementary graphic functions are integer functions and return the value 0 if no error occurred A short description is given below An example is the module MMP_GEM that simulates the elementary graphic functions by subroutines and functions of the GEMVDI FORTRAN interface and by some DOS calls Another example is given in the modules MMP_WIW and MMP_WI8 that simulate the elementary graphic functions by subroutines and functions of Microsoft Windows The syntax of the elementary graphic functions is mgxxxx where xxxx is a string of four characters mgopen itype ihsize ivsize mname idev iwid ihgh itwd ithg Open workstation This function is essential If no meta files shall or can be generated it is sufficient to simulate the part that opens the screen as graphic workstation In this case m
20. Scaling Integrals 2 a 10 8 RlotS 5 4 8 os amp xo a ah ay at eee tal at bE me AA A kk 10 8 1 Plots on Grids Regular Plots 0 o 10 8 2 Plots on Sets of Points General Plots 10 8 3 Plots on Matching Points Extended Error Files 11 Output 11 1 Parameters 0 o he ee ea EN Be ee ee ed 11 2 Residual Errors ea bh ee ets ee ce Bo a ok BS ee E a RN TS Integrals a m mea da Ha el eee aah at Goh D4 de Med 4 TA ANRIGUS S 4a 25 we lta Sth wae duals Ble es ee de ete om Sot ae 11 5 Screen and Output File o o e 11 6 Warnings and Error Messages e e ee 36 36 40 40 41 42 44 44 45 46 46 46 12 Utilities 12 1 12 2 12 3 Program Start 2 45 42 Be heh a Es Se eA a Geo Parameter Labeling a rue 4 a oes oS BL A Fourier Transform mit dun 40 e Oa EG a eo Se ot AAA 13 Functional Overview of the 3D MMP Main Program 13 1 13 2 13 3 13 4 13 5 13 6 13 7 13 8 13 9 A Short Overview aaau Main Program and Main Procedures o oo Rows and Expansions p ena a e E o e E ee T33 Routine zeile cou naro Gae e e e e a a E a a a OR ot 13 32 Expansions e a a id A OE a 13 3 9 Connections oo todas 4b ese Be eo Ge eA e a ate 13 34 Constraints moco RY ee ee A Aa eee Symmetries syd bP Be Be A tok ek Sede RS ht Input and Output Initializations 2 0 0 0 2 02000 IS ssl API 4 te shag A e d
21. The errors are now very small In fact they are considerably smaller than in model 1 with 150 MHz Increasing the frequency with by a factor of 2 is essentially the same as increasing the diameter of the sphere by a factor of 2 or the surface of the sphere by the square of 2 i e 4 This has been done in step 3 above In model 2 there are 64 matching points whereas there are only 16 matching points in model 1 If you compare the parameter files MMP_PAR 002 and MMP_PAR 001 you see that there are a little bit less than four times as much parameters in the second model This is an effect of rounding in the procedure that determines the orders of the multipoles However there are about 4 times as many equations with about four times as many unknowns Thus the computation time is expected to be about 64 times as long 224 17 3 Ideally Conducting Sphere with Dipole Excita tion 17 3 1 The Basic Model Models 3 5 In this model the incident plane wave shall be replaced by a dipole on the negative X axis for example in the distance 1 m from the center of the sphere A dipole is the lowest order multipole in electrodynamics so delete the plane wave and to add an appropriate dipole IE1 6 302 3 0 1 0 0 Of course the dipole must be oriented in such a way that the symmetry is the same as the symmetry of the plane wave Since the field of the dipole is infinite at its location X overflow problems can occur when the field is computed on or
22. The matching points defining the surface of the wire antenna are neither contained in the input file MMP_3DI 024 nor in the connection file MMP_C23 024 Moreover no matching points for wires in a connection are generated in the main program Thus the 244 3D show points 1 generating_meta_file lso meta 5 clear EXIT ang 3 000E 01 M_ 126 Domain 1 MPt nMat 126 Exp dom 1 Win Wink 2 Wx11 1 0008 00 ix11 323 Er 1 00008 00 wgt 1 000E 00 sel 0 000E 00 Win h 1 0 01 7 5008 01 y 0 0008 00 2 1 0308 00 Figure 17 6 Desk of the 3D MMP plot program showing the time average of the Poynting vector field for an active thin wire fead at the center illuminating an ideally conducting sphere Computation with result of model 23 introduced as connection surface of the wire antenna is not known in the main program and the corresponding boundary conditions are not matched Because of the singularity of the field on the wire you have either to select the window data in such a way that there is no coincidence of grid points with the axis of the wire or to introduce a set of dummy matching points around the wire as outlined in model 3 5 More complicated models containing both thin wires and MMP expansions have been used in 41 17 9 Apertures in Plates 17 9 1 A Simple Model Model 25 It is well known that apertures in ideally conducting thin plates can be computed w
23. a Windows interface has not yet been written In addition to the compilers indicated above the 3D MMP programs have been running and tested with the following compilers that are no longer supported for several reasons e Ryan McFarland FORTRAN version 2 11 This compiler generates relatively fast codes for XT and AT compatibles with numeric coprocessors A GEMVDI interface for this compiler is included in the 2D MMP package 4 Neither older nor newer versions have been tested Because of the 640kbytes memory limit of this compiler it is no longer supported Microsoft FORTRAN for XT and AT compatibles This compiler is not supported because the form of the include statement is different from all other compilers Moreover its handling is relatively complicated and the resulting code is not faster than the one generated by Ryan McFarland FORTRAN Older versions of Microsoft FORTRAN are even unable to compile the 2D MMP codes No MMP graphic interfaces are available for this compiler Microway NDP 486 compiler version 3 1 for 486 or 386 based PCs with 80387 coprocessor and extended memory Weitek 1167 or 3167 floating point accelerators are supported as well as virtual memory The compiler runs either with the PharLap tools DOS extender Assembler Virtual memory manager etc or with the NDP tools It is important to note that the GEMVDI interface does not run with the NDP tools So far an appropriate interface could not be generated beca
24. call MStop ja if ja EQ 1 return call copVRonI kFPt 0 do 1 1 1 nlev do 1 i 1 nhor do 1 k 1 nver Note that the subroutine dspper displays the amount of work that has already been performed in the question information box when iteration is performed The subroutine MStop tests whether the user is pressing a mouse button and returns the value ja 1 if this is the case The subroutine copVRonI copies the field of the previous iteration that was stored in VR on the old field vector VI of the actual iteration In the loops the number of the actual field point kFPt and its four neighbors in horizontal kFPtmx and kFPtpx and vertical kFPtmy and kFPtpy direction are computed first kFPt kFPt 1 if iFPt kFPt 1t 1 goto 1 kFPtmx kFPt nver kFPtpx kFPt nver kFPtmy kFPt 1 kFPtpy kFPt 1 211 The if statement jumps to the end of the loop if the domain number iFPt of the actual field point is zero or less I e the field in points with domain numbers 0 or less is left unchanged After this four if statements define what has to be done when the field point is on the left right lower or upper boundary respectively These are the boundary conditions of the algorithm Note that the function getEpsR gets the real part of the permittivity of the field point After the boundary conditions the main algorithm the five point star operator is defined E getEpsR kFPt Emx getEpsR kFPtmx Epx getEpsR kFPtpx Emy getEpsR kFPtmy Epy g
25. color numbers of the different objects 1 3D vector arrow plane n component transverse part 3D vector triangle shadow grid filling numbers of the different objects 3D vector arrow plane n component transverse part 3D vector triangle shadow grid NON AUN NOUO BRAUNE 324 G Limitations of the Compiled Version The 3D MMP codes are essentially limited by parameters defined in different parameter statements Most of these statements are contained in include files For the compiled version of the 3D MMP codes the most important parameters are listed below If some of them are too small for one of your models you have to compile the corresponding pro gram after adjusting the the corresponding parameters with an appropriate FORTRAN compiler Probably you will require either more than 4Mbytes RAM or a compiler with a virtual memory manager and a sufficiently large hard disk when you considerably increase some of the parameters G 1 Main Program ngebm 50 maximum number of domains nmatm 2000 maximum number of matching points nentm 200 maximum number of expansions including excitations nordm 100 maximum order of an expansion nkolm 500 maximum number of columns of the system matrix nkolcm 1500 maximum number of columns including connections nloesm 8 maximum number of symmetry components nrekm 10 maximum recursion depth for nested connections nnbedm 1 maximum numb
26. concern was the influence of insulators and deformations of transmission lines In order to guarantee reliable and accurate results the technique was closely related with analytical methods used by G Mie in 1900 A Sommerfeld and many others As soon as several numerical problems had been eliminated the code turned out to be efficient and useful for many other applications as well Thus it was natural to widen the range of applications and to study the technique in detail Beside codes for electro and magnetostatics a 3D MMP code for electromagnetic scattering was written by G Klaus on a CDC 6500 In those days the relatively poor machines and weak financial support forced us to very carefully implement the codes Although this certainly was a big handicap it turned out to be helpful as soon a we got our first personal computer The first aim was to write a PC version of the 2D MMP code for students Since CDC FORTRAN was completely incompatible with all other FORTRAN compilers the codes had to be rewritten entirely This gave us the opportunity to design more flexible and portable codes and to take advantage of the graphic capabilities of PCs Finally the codes turned out to be efficient accurate reliable and useful not only for students and teaching electromagnetics but also for a large range of scientific applications This encouraged us to implement a PC version of the 3D MMP code as well The 3D code was entirely rewritten and many
27. error_in wind _ data will indicate this Since material properties must be known for computing fields like the energy densities this command reads the first part of the corresponding input file MMP_3DI xxx Thus some of the messages indicated in the description of read input might occur as well When you did not store the material properties in the input file MMP_3DI xxx you should read the correct input file immediately after reading MMP_Pyy xxx Note that this occurs above all when you use the Fourier feature of the 3D MMP code read____ mmp_t Read the information contained in the 3D time dependent plot files MMP_Tyy xxx Anal ogous to read mmp p see above with the following differences 1 The information concerning the location of the field points is not contained in this file It is assumed to be on the file MMP_Pyy 000 2 The material properties are assumed to be on the input file MMP_3DI 000 rather than 165 on MMP_3DI xxx because MMP_Tyy xxx files usually are generated by the Fourier transform program Thus it is strongly recommended to use the problem number 000 when the Fourier transform is applied To avoid mixing of data belonging to different problems working on separate directories is helpful read____ input Read a 3D MMP input file MMP_3DI xxx Select the extension number xxx in the item box These data are used above all for displaying the matching poin
28. file ZYLC F the spherical functions file SPHF F and the matrix routines file CHOL F 73 13 2 Main Program and Main Procedures The main program mmpal11 reads the options from the command line UNIX version only or through questions from standard input It also arranges for the input files to be read and the output to be written It performs a loop over the frequencies and branches into the main subroutines mmp computation of parameters resa11 computation of errors intega evaluation of integrals pltp00 pltp50 plot routines or user Subroutine user is a frame intended for custom extensions Fit it to your needs The parameters are computed in routine mmp successively for each symmetry compo nent of the problem There is a main loop over the symmetry components with inner loops over the matching points and the constraints For each of the matching points and constraints the rows are computed routines zeile nbedz weighted routine gew and updated routine update Routine factor is called for the Cholesky factorization and solve for the back substitution After computation of all parameters the result can be scaled by calling routine norm The errors in the field points the assessment for the field the error in percent and the values of the constraints are computed in resall This routine directly writes the error file MMP_ERR xxx resall mainly calls routine resid for the computation of the residuals in a single match
29. fill aaaa and color aaaa boxes are not used for vector representations When you look at the pictures you have seen so far you will note that the size of the elements is scaled automatically When you want to increase the size of the elements you simply have to increase the field scaling factor in the box f sc Even if you select a large factor no field vector will point outside the square of the corresponding field point The length of all elements is limited When the length would be bigger than the limit it is set equal to the limit When you have selected the fill pattern 2 the element is filled with a pattern indicating the strength Completely filled dark vectors exceed the limit considerably whereas not filled bright vectors are either shorter or not much larger than the limit It can be reasonable to invert the filling of one or several elements For doing that select the value 3 instead of 2 Also you can suppress the automatic filling that indicates the strength of the field by choosing different numbers this is not reasonable in most cases Thus you will usually have 2 3 and 4 in most cases 4 turns off all elements with two exceptions il1 _plane_ and fill _grid__ The latter is not used in vector representations i e if you have selected the box gt on the top line However for these elements the fill pattern 4 means that instead of indi
30. i9 0 1 pole representation turned off on set computation of average O time dependent values 1 time average set representation type 0 show grid lines 1 show vector representation set fillings i1 3D arrow line i2 plane rectangle around field point length of sides equal to dis tance from neighbors i3 n component of vector square around field point area propor tional to strength of n component i4 transverse part triangle with field point in center of short line area proportional to strength of transverse part i5 3D arrow triangle with field point in center of short line area proportional to strength of vector i6 shadow of 3D arrow triangle on plane i7 grid quadrangles The effects of the different fillings are outlined in the description of box number 8 199 setcol il setscl ri setlev il setaut setlig r1 3 i1 reapyy tl reatyy its reapf2 14 1 reapt2 i1 i reaerr il 7 5 3 2 2 3 set colors see setfil Usually color numbers 0 background up to 15 are reasonable for monochrome monitors only numbers 0 and 1 should be used The colors depend on the definition in the desk files and on the screen drivers If negative numbers are given the absolute value defines the color and the framing of the border of the corresponding element is suppressed set scaling factors r1 field vector scaling r2 error scaling r3 normal vector scaling on
31. matrix ill conditioned matrix not positive definite These warning and error messages can occur when Cholesky factorization is used Try solving the problem with orthogonal transformations less rows than columns Not enough equations have been specified Try less expansion functions or more match ing points or boundary conditions check scaling factors se2 Warning that the scaling factors s are smaller than sklein 2d problem without plane wave excitation Warning that a 2D problem iprob 200 299 is without a plane wave excitation There fore the propagation constants y of the 2D expansions cannot be initialized to the exci tation and the values for y defined in the input file are used Errors in the Basic Packages In rare cases errors can occur in the basic packages e g during evaluation of com plex functions or Bessel functions These error messages are implemented with ordinary FORTRAN STOP statements and therefore cannot be found in the output file 70 12 Utilities 12 1 Program Start After preparing the required data files you can start the 3D MMP utilities exactly like the main program Under Windows you can double click the corresponding icon For more information see section 9 2 12 2 Parameter Labeling The MMP_PAR program labels parameter and connection files in order to simplify their interpretation and modification It reads from MMP_PAR xxx and writes to MMP_PAL xxx where xxx is a number specified
32. pull down input output Con w weight of a constraint Win h distance height between levels of a standard plot To display the values in this box perform the commands show constrain and show window respectively Change the values with the first count up and second count down mouse but ton in the value area of this box and perform the commands adjust constrain and adjust window respectively 151 16 3D Graphic Plot Program 16 1 Program Start To run the 3D MMP graphic plot program under Windows you can double click the corresponding item After this you sometimes might obtain error messages issued by Windows Since these messages are not issued by the 3D MMP program you have to consult your Windows manual for more information Note that the working directory is defined as command line parameter The predefined working directory is subdirectory EX3D of the directory MMP3D i e the place where the example input files are stored If you want to work on a different directory you can click the icon of the 3D MMP plot program once select Properties in the menu File of the Windows Program Manager and modify the Command Line according to your needs Instead of this you can use any of the features provided by Windows for running an application for example you can select Run in the menu File of the Windows Program Manager If the gra
33. the program will first check the file MMP_DIR zzz As soon as an error is detected the error number and the number of the corresponding line is displayed in the information box and no movie is generated If no error has been detected the pictures are generated within the window that has been clicked As all time consuming processes you can abort the generation of a movie If this is done all sequences that have been completed before can be viewed as usual The initial directives of the first sequence may be incomplete I e it is not necessary that the first picture is determined uniquely by these directives In this case you can select the representation data file etc of the first picture before generating a movie For example if the file MMP_DIR 120 contains the following lines seq 1 203 setphi 18 0 enddir 1 parts 20 pictures incphi 18 0 enddir end selecting generate movie 11 120 will generate movie number 11 that shows the time dependence of the actual picture with the actual parameters representation etc in 20 pictures The initial directive setphi will set the phase of the first picture to zero If this directive is omitted the phase defined in the line angle of the additional real data box is used instead If the representation scaling or any other parameter is inconvenient this can be changed before generate movie 11 120 is repeated In this case you are asked w
34. y 5 500 01 z 0 000E 00 Figure 15 2 Desk of the 3D MMP editor program showing the matching points of an arc 2D show____ vect axis Show the 2D lines and arcs in form of vectors see fig 15 3 2D show____ window___ See 3D constructions 2D show____ pole_____ Activate the 2D expansion with the number selected in the item box inactivate all other 2D expansions The additional data of the expansion is displayed in the corresponding boxes Note that the same boxes are used for 3D and 2D expansions since the latter are used to generate the former NO_such_2D_pole____ indicates that the item number is outside the range of expansions that have been defined 102 2DJadd Jare a generating_meta_file Jio meta 2 clear EXIT ang 3 6008 02 M_ 5 Domain 1 Met M el 10 Exp _ dom 1 Con pt 1 y yr 7 wxli 1 0005 00 ixil 6 Er 1 0000 00 wgt 1 000E 00 se1 0 000E 00 Con w 0 0E 00 k 0 0008 00 y 5 5008 01 2 0 000E 00 Figure 15 3 Desk of the 3D MMP editor program showing an arc in form of a vector 2D show____ domain___ Activate the 2D expansions lines and arcs belonging to the domain with the number selected in the item box inactivate all others The additional data of the domain is displayed in the corresponding boxes NO_such_domain_____ indicates that the item number is outside the range of expansions that have
35. 0 00000E 00 00 jpart type 1 mos 1 01 1 00000E 00 Figure 17 4 Desk of the 3D MMP plot program showing the time average of the Poynting vector field for a plane wave incident on a thin wire refined model with spherical endings multipoles near the endings matching points are pushed away from the ending When the digit is 9 no matching point is generated for the corresponding segment see fig 17 5 17 8 Using Connections Model 24 As soon as you have a model of an antenna you certainly are interested in solving the problem of a body illuminated by this antenna for example the ideally conducting sphere of model 2 illuminated by the wire antenna of model 23 see fig 17 6 The resulting model has only two symmetry planes whereas model 2 has three of them Thus you have to generate a new model of the sphere with twice as many matching points and unknowns as model 2 l e the computation time that is to be expected is considerably larger When the distance between the antenna and the scatterer is not very small the influence of the scattered field on the antenna can be neglected i e you can assume that the parameters computed in model 23 are a good approximation of the parameters of the antenna computed here The MMP feature called connections allows to introduce parameters known from a previous computation As a consequence the number of unknowns can be reduced This is very agreeable for problems with a large number of
36. 00000E 00 ESTATE tim 0 00000E 00 part type i 1 mo 1 000008 00 Figure 16 6 Desk of the 3D MMP plot program showing the time average of the Poynting vector for a plane wave incident on a lossy sphere with reduced drawing depth rotated window plane manager representation turned on 16 5 Summary of Regular Actions 16 5 1 show____ show pic f This is the most important regular action that is used most frequently It simply generates a picture in the window that is clicked for starting the action Before this is done the following steps are important and affect the picture that will be shown 1 Read the data to be shown with the corresponding read commands 2 Select the size location and orientation of the window plane For doing this several commands adjust wind move wind etc are available 3 Select the field type the field components the representation to be used etc in the boxes on the right hand side of the first line 4 Select the scaling factors the fill patterns and the colors to be used for the different parts of a representation in the pull down boxes below the first line 162 As soon as you have started show pic f you will be asked compute_new_scaling Usually you will answer in the affirmative except when you want to be sure that the same scaling as for the previous picture is used which is impo
37. 1 returns previous length function produce orthogonal system from two vectors v and U2 WS SYS Wwe at clear complex vector back substitution on trapezoidal matrix share update a vector to a trapezoidal matrix determine Givens rotations 308 d2abs function absolute value of a complex number cpngad add a row to normal equations cdppfa Cholesky factorization cddotc dot product of two complex vectors cdppco Cholesky factorization with estimation of condition number cdscal product of a real factor and a complex vector cdasum function sum of the absolute values of a complex vector cdaxpy complex scalar times vector plus vector cdabs1 function R z S z File SPHF F bessel spherical Bessel functions jn z yn 2 AD AD 2 forn 0 N jn auxiliary routine for spherical Bessel functions jn z rekup upward recurrence of spherical Bessel functions brekdn downward recurrence of spherical Bessel functions sicom trigonometric functions ps my form 0 M legenm associated Legendre functions PM x for n M N vkfnor scaling factor Smn for 3D solutions File ZYLC F chi cylindrical Hankel functions H z for n 0 N ch2 cylindrical Hankel functions H z for n 0 N ci modified cylindrical Bessel functions I z for n 0 N cj cylindrical Bessel functions J 2 for n 0 N ck modified cylindrical Hankel functions Kn z for n 0 N cy cylindrical Neumann functions Y 2 for n 0
38. 10 0 blowin 1 21 202 setphi 0 0 enddir 1 parts 10 pictures incphi 18 0 enddir seg 2 setphi 45 0 enddir 2 parts 4 pictures inclev enddir end 16 8 3 Generating the Movie After writing a file MMP_DIR zzz make sure that there is enough space left on the disk used to store the pictures It has already been mentioned that this depends on the size of the window the resolution of the screen driver and of the number of colors To test the size of a picture file MMP_Fyy xxx one can save a single picture Clicking one of the windows with the first mouse button when write pic f yy xxx has been selected in the first three boxes of the top line will write the picture file MMP_Fyy xxx with the corresponding information file MMP_Iyy xxx Of course saving a large number of pictures leads to an alternative way of generating movies It should be mentioned that the information file MMP_Iyy xxx does not contain all information contained in the file MMP_Iyy 000 that is required for showing a movie Thus a slight modification of MMP_Iyy 000 is necessary This is not explained here because generating a movie picture by picture is cumbersome anyway To generate a movie select generate movie yy zzz in the first three boxes of the top line where yy is the movie number and zzz is the extension number of the file MMP_DIR zzz that contains the directives When one of the windows is clicked with the first mouse button
39. 300 gt 7 g gt 1 1 gt 9 9 gt 200 gt 6 f gt 2 2 gt 10 gt 100 gt 5 e gt 3 3 gt 20 gt 50 gt 4 d gt 4 4 gt 50 amp gt 20 gt 3 gt 5 5 gt 100 gt 10 j gt 2 b gt 6 6 gt 200 gt 9 i gt 1 a gt 7 7 gt 300 67 If possible i e depending on the compiler the output is appended to the output file already present If msfil 0 the output file is not opened unless an error occurs see the following section 11 6 Warnings and Error Messages Error and warning messages are issued if something occurs which does not allow the execution to continue or if something looks suspicious Only the most common errors are trapped there are still lots of ways left for malicious or unskilled users to crash the program An error message is fatal and stops execution It looks like 999 MMP ERROR in routine ininp ERROR error opening input file Sometimes only warnings are issued and execution is continued 999 MMP ERROR in routine factor WARNING matrix ill conditioned The messages are in any case written to the output file which is opened if necessary If the screen output is enabled they will also be issued there The following is a list of the error and warning messages that can occur Errors at Startup error reading program options wrong task option wrong method option wrong plot option wrong frequency option A wrong pro
40. 5c 2 5d are derived from 2 5a 2 5b For investigation of the propagation of electromagnetic waves it is usually assumed that the sources generating a field are outside the domain considered For such domains the Maxwell equations are homogeneous and the Helmholtz equations A R E A h H 2 6a 2 6b can be derived k w pe is the wave number of the medium An additional condition which is necessary to guarantee the physical relevance of the solutions to 2 5 and 2 6 as well as the uniqueness of the solution of 2 1 is the radiation condition It can be looked upon as a boundary condition for infinity and limits the asymptotic behavior of the fields For 3D problems it is lim 240 ikf r 0 2 7 and for 2D problems Of p _ z Jim VA iks p 0 2 8 f stands here for any of the field components The radiation condition states that all sources of the field are within a finite distance of the origin However it is not satisfied for some idealized solutions like the plane wave Inhomogeneous space is divided into several homogeneous domains D each of which is characterized by 2 4 with u e and 0 Applying 2 5 to the boundary 0D leads 18 to the boundary conditions ixE x 2 9a il EB i lB So 2 9b nx E xH a 2 9c R m gt pd 2 9d So is a surface charge on the boundary and Ay is a surface current along the boundary 2 3 Choices for the 3D MMP Code The 3D MMP co
41. 622 Aug 1985 Ch Hafner and G Klaus Application of the multiple multipole MMP method to electrodynamics COMPEL The International Journal for Computation in Electrical and Electronic Engineering vol 4 no 3 1985 Ch Hafner MMP calculations of guided waves in Proc IGTE Graz pp 63 70 Oct 1985 Ch Hafner Die MMP Methode Archiv f r Elektrotechnik vol 69 pp 321 325 1986 G Klaus S Kiener and F Bomholt Applications of the MMP method to field calculations near bodies with apertures in Proc of the 7th Symposium on Elec tromagnetic Compatibility Z rich Mar 1987 331 74 75 76 TT 78 79 80 81 82 83 84 85 86 87 88 N Kuster SAR and E H Poynting vector fields in human models caused by antennas placed close to the body calculated with the MMP method in Proc of the 9th Annual Meeting of the Bioelectromagnetic Society Portland June 1987 Ch Hafner Numerische Berechnung elektromagnetischer Felder Springer Verlag 1987 P Leuchtmann Automatic choice of MMP functions in dynamic problems in URSI Radio Science Meeting Syracuse June 1988 Ch Hafner Numerical field calculation with MMP programs on PC s in URSI Radio Science Meeting Syracuse June 1988 S Kiener and G Klaus Calculation of the electromagnetic field at edges with the MMP method in URSI Radio Science Meeting
42. 9 PS my C 13c C 13d C 13e C 13f C 14a C 14b C 14c C 14d C 14e C 14f Solution Symmetry to x 0 Symmetry to y 0 Symmetry to z 0 m odd m even m odd m even m n odd m n even Ecmn odd even even even odd even Esmn even odd odd odd odd even Hemn even odd odd odd even odd Hsmn odd even even even even odd The different modes mn are scaled to equal radiated power with o j1 1 2n 1 n m m0 C 15a Snir mn n 1 2 n m de and 1 1 2n 1 i E n n 1 2 ey kG 190 290 respectively The magnetic modes are additionally scaled with the inverse of the wave impedance The whole expansion can be scaled with ssca section 10 5 A complete expansion is the combination y Cif Sscal tontos 20 F ise FEW i N N m 0 n max 1 m E s AA J daso A For 8D multipoles choose bm AD for 3D normal expansions bm jm A complete expansion C 16 rotated around any axis through its origin can be represented exactly by the functions of the unrotated expansion C 4 Rectangular Waveguide 2 Zs oe y Figure C 1 Rectangular Waveguide Rectangular waveguide modes are solutions of the Helmholtz equations in a Cartesian coordinate system for lossless domains 0 e with ideally conducting boundaries at x 0 x a y 0 and y b They can be seen as superpositions of plane waves The transverse wave numbers for the x and y di
43. E 2 The input format is the same for all expansions ient integer number for identification in input and output programs not significant to the MMP program ig number of the domain in which the expansion is valid iel type of the expansion ie2 ie6 integer parameters sel se2 real parameters cegam complex parameter xe ze origin of the expansion Terp Xex Zex v1 orientation xey zey va orientation Some of the parameters are ignored by certain expansions and some will be initialized The values can afterwards be found in the parameter file s MMP_PAR xxx The types and the parameters of the expansions are described below The vectors v and Vz for the orientation need not be normalized nor orthogonal The orthonormal right handed coordinate system z y z of the expansion is obtained from U1 V as follows Zan Ut gt BX U2 ee ot Boe erx a ez 75 37 ey Ez X ex 01 01 x Va When symmetries are used the expansions may be on either side of a symmetry plane In case an expansion is lying in one or more symmetry planes attention has to be paid to its proper orientation One of the vectors r or has to be perpendicular to each plane otherwise there will be no saving in the number of parameters The various expansion types are distinguished by the parameter ie1 In this version the following types are implemented the parameters not mentioned will be ignored e Connection Connections are a very
44. H dA 7 J We dV 8 Ur dV 9 Sp av 10 Sp dv 11 SP AV Integrals are computed as a Riemann sum ipts DIFF AO 10 1 i e the values for the integral are a sum over the values in the integral points In analogy to the matching points integral points are defined by a location and two vectors xint yint zint coordinates of the integral point 62 xintt1 yintt1 zintt1 v xintt2 yintt2 zintt2 Uz For the line integral the line element d will be v for a surface integral the surface element dA AF will be 0 x Ya and for a volume integral the volume element dV AV will be 7 The domain of the integral points is determined with the automatic procedure There fore be careful with integrals close to boundaries For constraints only integral types 1 2 4 and 5 may be used Otherwise the param eters of the problem do not appear linearly within the constraint which does not make sense Other integrals are in a block preceded by the scaling directive inorm and the number of integrals nint If inorm is zero no scaling of the result is done If it is not equal to zero the first of the integrals in the following block is used as a scaling integral i e the parameters are scaled in such a way that the integral is equal to 1 The remaining integrals are evaluated and the corresponding values are written to the integral file MMP_INT xxx The number of constraints is limited to nnbedm the total number
45. IEEE AP S International Symposium San Jose June 1989 Ch Hafner MMP a program package based on the Generalized Multipole Tech nique GMT in IEEE AP S International Symposium San Jose June 1989 Ch Hafner Computations of electromagnetic fields by the MMP method in URSI International Symposium on Electromagnetic Theory Stockholm pp 141 143 Aug 1989 S Kiener The GMT applied to antenna problems in Proc of the ISAP Tokyo Aug 1989 Ch Hafner and S Kiener Parallel computations of 3 D electromagnetic fields on transputers in Proc of the ISAP Tokyo Aug 1989 S Kiener Scattering on bodies with edges in Proc of the 2nd International Symposium on Antennas and EM Theory Shanghai Sept 1989 Ch Hafner and L Bomholt Calculation of electromagnetic fields on personal computers and workstations in Proc of the 2nd International Symposium on Antennas and EM Theory Shanghai Sept 1989 Ch Hafner Computation of electromagnetic fields on transputers by the MMP method in IEEE Transactions on Magnetics vol 26 Tokyo pp 823 826 Mar 1989 7th COMPUMAG Conference Sept 1989 S Kiener Eddy currents in bodies with sharp edges by the MMP method in IEEE Transactions on Magnetics vol 26 Tokyo pp 482 485 Mar 1989 7th COMPUMAG Conference Sept 1989 333 104 105 106 107 108 109 110 111 112 113
46. If the file is present reading MMP_PLT xxx is displayed reading If no 2D plot file is found or when errors occur during reading this is indicated with error_opening file_ and error_reading file too_many_poles____ too_many_match _pts wrong_f pt number_ respectively The last three messages indicate that there is not enough memory in the 3D MMP plot program for storing the poles expansions matching points or field points read____ part Read the particle file MMP_PRT xxx with the number xxx selected in the item box and replace the actual particles by the particles defined in this file During reading reading _particles__ is displayed When the file is not present or when it is corrupt ERROR_read_particle is displayed When there is not enough memory left for saving the part of the screen behind the particles this is indicated by ERROR_set_particle_ 16 5 3 write _ write___ pic f Save the actual pixel information of the window that has been clicked for starting the action The file MMP_Fyy xxx will contain the pixel data and MMP_Iyy xxx will contain the corresponding information on the size and location of the window Select yy in the item box and xxx in the file extension box If one of the files required cannot be opened for example because not enough memory is available on the disk error_opening file is displayed write___ wind Write window file MMP_WIN
47. It is favorably formed by subsequently summing up the exterior products of the rows M N A A gt Y A 5 4 j 1 Li 1 Positive definite matrices can be factorized into triangular matrices using the Cholesky factorization A A X X 5 5 where X is upper triangular The vector of unknowns c can be found by successively solving the triangular systems X z A b 5 6 and Xc z 5 7 using forward and backward substitution respectively As already stated in section 2 3 it is easier to use the augmented system A d A b 0 5 8 with the Cholesky factor ip 5 9 z is the same vector as in 5 6 and can be used to calculate c with only one single back ward substitution 5 7 p is the norm of the residual vector and serves as an immediate measure for the quality of the solution For large M and N the formulation of the complex normal equations 5 3 needs MN 2 times 8 FLOPS the Cholesky factorization requires N 6 times 8 FLOPS and the back substitution needs N 2 times 8 FLOPS A FLOP is one floating operation usually an addition or a multiplication The matrix A A is equivalent to the one obtained with the projection or error method However practice shows that it has very poor numerical properties Its condition number is the square of the one of A Although solving the least squares problem with the normal equations is the fastest method it also is numerically the worst and it is only feasible for rath
48. MMP_WIN xxx file number xxx increase time step and read corresponding plot file Note reset to time step 000 if file not found increase frequency number and read corresponding plot file Note reset to frequency number 000 if file not found increase phase of time harmonic field difference of phase in degrees increase level number set level 1 if maximum number exceeded increase distance of eye above window plane see seteye difference of eye distance decrease time step and read corresponding plot file Note reset to time step 000 if time step number negative decrease frequency number and read corresponding plot file Note reset to frequency number 000 if frequency number negative decrease phase of time harmonic field difference of phase in degrees decrease level number set maximum level if level number lt 1 decrease distance of eye above window plane see seteye difference of eye distance blow window limits blow factor is r1 i Note after i1 pictures the total blow factor is r1 shrink window limits shrink factor is r1 4 Note after i1 pictures the total shrink factor is r1 move shift window limits 201 r1 2 local Cartesian coordinates ty Yw of shift vector movpln move shift origin of window plane r1 3 global 3D Cartesian coordinates of shift vector rotpln rotate window plane around current axis ri angle in degrees invaxi invert direction of the axis invpln invert window plane invert
49. N cir1 cya01 auxiliary routines File COMPL F cdinv2 complex inversion 22 1 21 rcopc2 copy real variable to complex variable z x caddc2 complex additions 23 21 Za cchas2 change sign of complex variable z z cminr2 complex variable minus real variable z2 21 czero2 clear complex variable z 0 ccopy2 copy complex variable to complex variable z2 21 rmalc2 product of real and complex variable z 127 cmalc2 complex product 23 2122 cminc2 complex subtraction 23 21 Za rminc2 real variable minus complex variable z2 x 21 cdivc2 complex division 23 21 22 cdivr2 divide complex variable by real variable 22 21 x rdivc2 divide real variable by complex variable z2 1 21 cdabs2 function absolute value of a complex number z 309 cdmsq2 function square of absolute value of a complex number z 2 z cdsqr2 complex square 22 27 cdsqrt2 complex square root 22 y 21 cdexp2 complex exponential function z2 e cdlog2 complex logarithm z2 log 21 cdcosi2 complex sine and cosine z2 cos z1 23 sin 21 cdcos2 complex cosine z2 cos 21 cdsin2 complex sine za sin 2 datan2c function replaces intrinsic function datan2 E 2 Parameters and Variables in File COMM SRC COMM INC For the parameters and variables in the program FORTRAN implicit notation is used Integer parameters and variables start with the letters i to n real variables with the letter
50. Save the 3D data on the file MMP_3DI 000 with 3D write file Afterwards you can play with the other 3D features of the editor Finally leave the editor either with EXIT or QUIT As soon as you have finished your editor session you can double click the icon for running the main program This program runs in text mode First you have to specify what has to be dome In most cases it is convenient to select the tasks 124 When you read the comment for task 4 you might wonder whether you did define a plot window or not In fact a default plot window identical with the first screen window has been generated automatically by the editor If you don t like this window exit the 3D MMP main program now by selecting task O EXIT and return to the editor for adjusting the plot window Otherwise select the proper task the method 1 frequency 1 and input file number 0 The program will display some data of interest indicating the progress errors etc Upon termination of the 3D MMP main program you can enter the 3D MMP plot program by double clicking the corresponding icon Maybe you consider the errors displayed by the main program to be too large and you want to improve your model with the editor without running the plot program for saving time For unexperienced users this is certainly not recommended because the relative errors in the matching points can be misleading If you intend to generate a movie in the fo
51. The Art of Scientific Computing Cambridge University Press 1986 I Gradshteyn and I M Rhyzhik Table of Integrals Series and Products Academic Press 4th ed 1965 M Abramowitz and I A Stegun Handbook of Mathematical Functions Dover Publications 1965 D E Amos Algorithm 644 a portable package for Bessel functions of a complex argument and nonnegative order ACM Transactions on Mathematical Software vol 12 pp 265 273 Sept 1986 Ch Hafner Bestimmung der dielektrischen Eigenschaften der Ummantelung eines Kabels mit Hilfe eines Optimierungsprogrammes Bulletin SEV VSE vol 69 Dec 1978 Ch Hafner Ausbreitung schneller Impulse auf PVC isolierten Netzkabeln Bul letin SEV VSE vol 70 pp 137 141 Feb 1979 G Klaus and W Blumer Potenzreihen und asymptotische Entwicklungen fiir Besselfunktionen der Ordnung 0 und 1 und deren Kreuzprodukte fiir die Berech nung von Spannungs und Stromantworten in NEMP geschtitzten Kabeln tech rep Forschungsinstitut fiir milit rische Bautechnik FMB Z rich 1980 R Ballisti G Klaus and P A Neukomm The influence of the human body on the radiation characteristics of small body mounted antennas especially in the resonance region from 50 to 200 Mhz in Proc of the 4th Symposium on Electromagnetic Compatibility Z rich Mar 1981 P A Neukomm G Klaus and R Ballisti Polarisation transmission effect of the human body and its
52. To affirm any question and to remove any message after a process has been terminated i e when the box is active click this box with the first mouse button To answer in the negative click this box with the second mouse button When you want to abort the actual process instead of 84 answering the question click the Esc box on the right hand side of the question box When the message ready_for_action__ is displayed you can start the regular action defined in the first three boxes of the top line by clicking the question information box Last Top Line Box Exit or Quit The last box of the top line is a special action box used to leave the 3D MMP graphic programs either without saving data QUIT or with saving data EXIT 14 4 Windows The graphic data is displayed in windows In the 3D MMP graphic programs it is possible to have several windows at the same time This makes the construction of 3D models much easier Essentially two different types of windows are handled screen windows and plot win dows Screen windows are the windows that are visible for you during a session whereas the plot windows are used by the 3D MMP main program for generation standard plot files Screen windows correspond to windows known from typical Windows applications Although their outfit is simpler they are much more complex objects than usual windows see below Both screen and plot windows con
53. Type active inactive M show matching points and errors in matching points Tf this box is active the matching points are shown In activate this box with mouse button 1 or 2 If an error file has been read after reading the input file the errors in the matching points are represented as well If an input file has been read after reading an error file errors will not be shown Box 24 Poles and Other Expansions Type active inactive P If this box is active the expansions are shown In activate this box with mouse button 1 or 2 Box 25 Time Dependent Fields Time Average of Fields Type roll show time dependent fields show time average of fields Click the first or second mouse button in this box for changing the line number When time dependent fields are selected in this box the field at a certain time are shown Instead of the time t the phase wt is used for time harmonic fields The phase value in degrees is selected in the additional real data box angle Note that the time average is reasonable for the scalar energy and power densities in the time harmonic case with real w only For complex frequencies the imaginary part S w is ignored and a picture is nonetheless drawn In the case of time harmonic vector fields the absolute values of the complex components is drawn instead of the time average that would be zero Box 26 Representation with Vectors Grid Lines Type pull down input gt use ve
54. When all expansions have been inserted to cup it is updated to the matrix ca cup3 and cup2 need to hold only one expansion the length of which is indicated by last For simplicity s sake these arrays have the same length nkolm as the updating rows cup which contain all expansions The current length of the rows in cup is indicated by the global variable nkol 13 3 3 Connections Connections require evaluation of a previously solved MMP problem and therefore can be seen as a recursive feature especially if they are nested conn calls entsym for evaluation for nested connections entsym again calls conn Recursive calls of subroutines are not standard FORTRAN However no local vari ables of the subroutines involved into the recursion are used on different levels at the 75 same time All important variables are saved on a stack The maximum recursion depth is determined by parameter nrekm This approach should work even on compilers which do not support recursive calls conn considers symmetries i e only the symmetry adapted components of the con nection are evaluated The parameters for the connections are stored in the array cpic which has a length of nkolcm The connection and its expansions are stored in the same array as the ordinary expansions If a connection is used multiply within the same problem the parameters and expansions are stored just once 13 3 4 Constraints Constraints are formed as integrals for each
55. a Qrnt P 2 ajes cos b sin 7 y 12 2 The last term occurs only if N is even The a and b are computed from the a and b and the phasors f R f 13 f by a aR f 1 3 F 12 3a bi aS f UR F 12 3b II The purpose of the MMP_FAN and the MMP_F3D utilities is to facilitate the use of the Fourier transform with the multiple frequency option of the 3D MMP main program The time data x of the time dependence as well as the period T and the number of plot pictures npict is found in file MMP_FOU TIM The Fourier analysis is made by MMP_FAN which computes the Fourier coefficients a9 2 41 An 1 An 2 and the angular frequencies w from the x and T Thus a frequency file MMP_FOU FRQ is generated MMP_F3D performs the inverse transform for MMP_Pyy xxx plot files It produces a series of npict time value plot files MMP_Tyy xxx with xxx ranging from tmin to tmax These files can be visualized with the 3D MMP graphic plot program Since the MMP_Pyy xxx files contain potentials when the file identification number is 1291 all plot files read by MMP_F3D must have the same file identification number Otherwise the program is stopped Note that the plot files MMP_Tyy xxx will contain the potentials when the file identification number of MMP_Pyy 000 is 1291 The plot program reads the file identifi cation number and additional plot data that is not contained in the time dependent files in the fil
56. a NEG Hyg NN by minimizing the error function 7 in some way This system can then be solved by known methods of linear algebra 1 2 Error Method In the error method a functional of the error function 7 shall be minimized F n min 1 8 One possibility is the square norm of the error function 7 within the function space spanned by the fk wn n dr min 1 9 OD Wr is a positive real weighting function This choice has the advantage that it will lead to linear expressions for the c Derivation by the real and imaginary parts of the complex parameters leads to 2 wn L fi ndr 0 j 1 N 1 10 oD or more explicitly N Sal wli Lhar f Wwn L fj hdr j hoss N 1 11 a 0D aD In matrix notation this is lajilnlei bln 9 1 N 1 12 13 1 3 Projection Method In the projection method sometimes also referred to as the moment method the error function 7 is orthogonalized relative to a function space spanned by testing functions ts j 1 M defined on the boundary For this purpose an inner product is needed which we can define as where Wm r is a positive real weighting function that is omitted in most formulations The equations are obtained by m t 0 j 1 M 1 14 or N Da Wm L fi dr Wmt hdr j 1 M 1 15 fal 9D oD in matrix notation Usually as many testing functions t as unknowns c are used M N If M gt N an overdetermined system of equations results which
57. a pole does not define an expansion function and can be eliminated Instead you can increase the maximum order of the pole poles_are_dependent The pole is too close to the poles that are connected graphically with this pole Slight dependences can be tolerated but in general it is recommended to remove dependences by moving one of the dependent poles number_out_of_range The number of the pole that should be tested is either less than 1 or bigger then the maximum number of poles 15 6 10 2D adjust__ Adjust additional data of active elements For safety reasons you are asked adjust_elements_OK_ when you try to delete any element If this question is answered in the negative nothing is deleted and process_aborted____ is displayed 110 2D adjust__ line___ Adjust the additional matching point data of active lines and arcs i e replace the data of the active elements by the data previously selected in the corresponding matching point data boxes After the adjustment all elements are inactive 2D adjust__ arc______ Identical with 2D adjust line see above 2D adjust__ window___ See 3D constructions 2D adjust__ pole_____ Adjust data of active expansions This is done analogously as with the lines and arcs see above Moreover the checking routine allows to adjust multipoles automatically according to the implemented rules For th
58. a single matching point has do be adjusted the 3D show command can be used first to activate the desired matching point Thus if the question adjust_ALL_points_ is answered in the negative only the active matching points are adjusted 3D adjust__ vect axis Adjust the vector respectively axis that is used in several 3D constructions Since all its data can be represented graphically there is no additional data in any box l e this command is different from the other 3D adjust commands For graphical construc tions it is helpful to use the same planes in the first two windows and to perform the constructions in these windows only even if several windows have been added If you did forget to reset the planes in the first two windows XY plane in window 1 and XZ plane in window 2 you have the chance to do this by answering the question reset _planes_1 2__ in the affirmative If the second question set_axis_manually_ is answered in the negative one of the default axes is set when the question set_axis_M _xxxx_ is answered in the affirmative Otherwise the vector respectively axis is left unchanged and axis_not_changed___ is displayed As one can see from the question above the number of the default axis to be used is contained in the box M 1 is the X axis 2 the Y axis 3 the Z axis 1 the X axis 2 the Y axis 3 the Z axis Thus this number has to be selected before the co
59. advantages Symmetries are also an easy way of introducing perfectly conducting infinite planes into a model The mathematical tool needed for treatment of symmetries is group theory A com plete and understandable description of its application on boundary value and eigenvalue problems is given in 35 36 37 38 39 in this section only the consequences are outlined A linear symmetry transformation in n dimensional space is represented by a n by n matrix D The various symmetry transformations which are applicable on a given geometry can be seen as representations of the elements s of a group G They are consequently written as D s A matrix A has the symmetry of the group G if D s A AD s Vs EG 7 1 For the matrix equation in a boundary value problem Ac b equation 7 1 means that a symmetry transformation of the boundary values b is equiv alent to the same transformation of the result c Group theory shows that a transformation T can be found which transforms A into a block diagonal matrix A fig 7 1 The number and the size of the blocks is determined by the group G The transformations T are tabulated for the most common symmetry groups As a consequence the boundary value problem splits up into K smaller symmetry adapted ones which can be solved separately at a lower overall expense Note that it is not necessary for the boundary conditions to be symmetric Ac b AxCk bk k 1 K 7 2 The Az usually have a bette
60. an appropriate 2D input file MMP_2D1 xxx either with a text editor or with a special program Automatic generation of relatively simple 3D objects out of 2D objects In the current version a 3D cylinder a 3D torus or a more general 3D object can be generated i e a 2D object can be translated along a vector it can be rotated around an axis or it can be generated by a combined transformation consisting of 1 a translation along an axis 2 a rotation around the same axis and 3 a translation perpendicular to the axis at the same time Of course additional subroutines can be implemented in order to generate more complicated 3D objects but this is not necessary in most cases Combination of different 3D objects in order to create more complicated objects with the command 3D add objects In the current version of the 3D MMP editor only two 3D objects can be handled at a time This does not limit the complexity of the objects because up to one thousand different 3D objects can be stored on different files If two objects are to be combined to a new one one often wants to eliminate some parts of the two objects for example the points of object 1 inside object 2 This can easily be done with the commands 3D generate parts and 3D delete parts Check of the existing 3D poles deleting of dependent poles adjustment of poles with too high or too low orders or degrees This is very important when 3D
61. an input file is read in Since the origin of a plot window is always in the center of the rectangle used for computing the plot data the origin of a screen window that has been generated from the data of a plot window is in the center of the rectangle on the screen as well even if the plot window had been generated using the data of a screen window with origin outside the center 85 14 4 1 Screen Windows The outfit of a 3D MMP screen window is much simpler than the outfit of windows in typical Windows applications A screen window consists of a rectangle and can have a horizontal and a vertical line through the point in the center It has no title no scroll bars no menu list etc It is used for displaying graphic elements without texts Usually in all screen windows the same objects are shown with a different point of view i e the structure and contents of all screen windows essentially is identical Screen windows can be overlapping but this is not desirable in most cases because one usually wants to see different views of a 3D object in the different windows at the same time If two screen windows are overlapping the graphic objects in the second window overwrite the contents of the first one whereas in typical Windows applications one of the windows is in the foreground and the other one is in the background i e partially invisible In Windows usually only one window is active whereas all 3D MMP screen windows can be active at
62. and now picture is drawn In fact the field is zero everywhere Obviously you should get a more interesting field first If you have already created a plot file with the main program you can read this file now Otherwise you can generate a field with one of the iterative procedures i e the command generate pic f see section 16 9 But for testing purpose you can obtain a non zero field more simply with the command clear pic f 3 This allows to generate a random field on a regular grid covering the actual window plane The predefined size of the grid is ten by ten grid lines and one level only When you want to obtain a different grid you should modify the corresponding parameters in the first box below the top line on the right hand side of the screen the distance between the levels in the box d_1ev and run clear pic f 3 again Since drawing a picture with many field points is time consuming it is reasonable to work here with a relatively small number of grid lines When you have a high resolution monitor you probably see that the width of all lines is more than one pixels In this case you can reduce the unit line width in the box linew Like many other boxes you do not see it directly and you have to search it when you are not familiar with program it hides behind rx_11 After having obtained a picture with the command show pic f you
63. application in Proc of the 6th International Symposium on Biotelemetry Leuven Belgium June 1981 Ch Hafner and R Ballisti Electromagnetic waves on cylindrical structures calcu lated by the method of moments and by the point matching technique in IEEE AP S International Symposium Los Angeles June 1981 Ch Hafner and P Leuchtmann Group and representation theory of finite groups and its application to field computation problems with symmetrical boundaries in IEEE AP S International Symposium Los Angeles June 1981 R Ballisti Ch Hafner and P Leuchtmann Application of the representation theory of finite groups to field computation problems with symmetrical bound aries IEEE Transactions on Magnetics vol 18 no 2 pp 584 587 1982 3rd COMPUMAG Conference Sept 1981 G Klaus R Ballisti and P A Neukomm Body mounted antennas Nearfield computations on lossy dielectric bodies in Proc of the 7th International Sympo sium on Biotelemetry Stanford June 1982 330 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 Ch Hafner and R Ballisti The multiple multipole method MMP COMPEL The International Journal for Computation in Electrical and Electronic Engineer ing vol 2 no 1 1983 R Ballisti and Ch Hafner The multiple multipole method MMP in electro and magnetostatic problems IEEE Transact
64. are chosen to satisfy 1 2 exactly 1 3 is approximated The general solution of 1 2 has the form f fo gt chs 1 5 k where fo is the particular solution of the inhomogeneous problem Lf g and the fx are solutions of the homogeneous problem Lf 0 From the fx the basis functions f can be chosen SOLA h Lfypt nah n 1 6 n is an error function representing the difference between the exact and the ap proximate solution on the boundary fo and h merge to a new inhomogeneity h In the following only h is used e Domain method or seminumerical method It is analogous to the boundary method but the roles of the boundary and the domain are interchanged The basis 12 functions satisfy 1 3 exactly and equation 1 2 approximately By analogy to the boundary method this leads to DLs g C 1 7 Formally the domain method and the boundary method are analogous e Purely numerical method The basis functions satisfy neither 1 2 nor 1 3 For complicated or nonlinear operators this might be of interest but it is not con sidered here For our purposes the boundary method is the most efficient one as only equation 1 3 for the boundary remains to be solved Therefore for numerical treatment only the boundary has to be discretized In the following various conceptually different approaches for determining the coefficients are compared All aim at setting up a linear system of equations a jillc b
65. been defined Generate add a new line Before its execution select the additional data belonging to the line in the corresponding boxes Note that the same boxes are used for 3D matching points and 2D lines and arcs since the latter are used to generate the former If the maximum number of lines and arcs is exceeded too_many_elements_ 103 is displayed Otherwise set_start_point_winl indicates that you are expected to define the start point of the line within the first window Click the first mouse button in the first window and release it at the position where you want to put the start point The actual coordinates w and Yw of the cursor are displayed in the first two boxes of the bottom line as long as the button is pressed Afterwards set_end_point_win1_ tells you to define the end point of the line within the first window Generate add a new arc Before its execution select the additional data belonging to the arc in the corresponding boxes Note that the same boxes are used for 3D matching points and 2D lines and arcs since the latter are used to generate the former If the maximum number of lines and arcs is exceeded the message too_many_elements_ is displayed Otherwise set_center_in win1_ indicates that you are expected to define the center of the arc within the first window Click the first mouse button in the first window and release it at the position where you want to put the center The act
66. between matrix shares in parallel version weights of the rows norm of residual vector inverse of condition number cf 31 Rows for Expansions cup2 cup3 Parameters npar cpi Field Values cf rows for symmetry adapted expansions in entsym rows for expansions in entnr number of parameters in c parameter vectors c variable for field values Auxiliaries for Expansions rho r rinv thsin thcos phisin phicos asi aco aleg pfakt skalf cbes ckap ckap2 crkap cigr ceigz cka ciomu cioeps czie letm lete radius p radius r 1 r sin Y cos Y sin p Cos Y cos mp for m 0 M sin mo for m 0 M P cos 9 or PM cos 9 for n M scaling factors scaling factors Bn Kp or bn kr for n 0 N transverse wave number k2 pK iy p el N 7 wave number k IW or twup iwe or iwe p Zi logicals for E transversal magnetic or H transversal electric modes 314 Auxiliaries for Complex Computations chhi chh3 ci auxiliaries for complex computations eed Additional Variables for Parallel Version tlant nproc npro ikol ma nzeile 116 size of the share of R on root processor 0 lt tiant lt 1 number of processors in pipeline number of actual processor number of rows of matrix share on the processor number of elements of matrix share on the processor number of rows that have been updated for communication between transputers
67. button you are asked whether you really want to abort the process abort_process _ _YES If you answer in the affirmative the process is aborted immediately and the message process_aborted__ is displayed Otherwise the process is continued Button 1 left If you press the first mouse button when the cursor is near the lower left corner of the actual window selected in the corresponding item box you can move the window to any location on the screen by moving the mouse and releasing the button at the desired position When you do this make sure that the entire window is on the screen If you press the first mouse button when the cursor is near the upper right corner of the actual window selected in the corresponding item box you can change the size of the window on the screen by moving the mouse and releasing the button at the desired position If you press the first mouse button when the cursor is near the left side of the actual window selected in the corresponding item box you can blow the window to any desired size on the screen by moving the mouse horizontally and releasing the button at the desired position When you do this make sure that the entire window is on the screen Note that the aspect ratio of the window remains unchanged If you press the first mouse button when the cursor is inside the actual window selected in the corresponding item box you can select a rectangular area In the editor all points of a selecte
68. by a plane wave The 3D MMP modeling of active antennas is very similar You can easily modify model 22 to obtain an active wire antenna Obviously you need to delete above all the expansion defining the incident wave A soon as this has been done the new excitation is defined by the last parameter of the last expansion i e essentially the current at the end of the thin wire expansion when this is your last expansion Usually an active wire antenna is fed in the center To achieve this simply invert the thin wire expansion The boundary conditions should not be matched near the feed point Of course you can separate the matching points attached to the wire as indicated above and delete the points near the feed point But there is a much simpler procedure When the matching points for a wire are generated automatically the number ie6 in the box Exp IE6 is used for pushing the matching points away from the start and end point of the wire The first digit of this two digit number concerns the first segment and the second digit concerns the last segment of the wire The larger the digit the more the 242 gt 0 EXIT generate meta _ 161 22 computing S field noj e a s fiela1 xlylel ue metav 8 0008 02 111 3Darrow 2 depth 3 0008 02 IER 1 000008 00 fvz__0 000008 00 total FPt 225 k 0 00000E 00 ly 0 00000E 00 r z 0 00000E 00 Weg ae ETT A iter part Z tim
69. by the user The format of the output is essentially the same as that of the input The format for the labels is the following conn 1 Jj connection 7 wire c i thin wire expansion C 1 2Qdec i m 2D expansion C 6 des i m 2D expansion C 6 2dhe i m 2D expansion C 7 2dhs i m 2D expansion C 7 Q2dtc i m 2D expansion C 9 2dts i m 2D expansion C 9 3dec i m n 3D expansion C 11 or C 12 des i m n 3D expansion C 11 3dhc i m n 3D expansion C 13 or C 14 3dhs i m n 3D expansion C 13 rect wg i rectangular waveguide mode C 17 or C 18 circ wg 1 circular waveguide mode C 19 or C 20 pl wave i plane wave C 21 evane i evanescent plane wave C 22 evan h i evanescent plane wave C 23 1 is the identification number ient from file MMP_3DI xxx 12 3 Fourier Transform The Fourier transform allows computations of arbitrary non sinusoidal periodic time dependencies by determining the Fourier series computing the MMP problem for each of the harmonic frequencies and recombining the results with the inverse Fourier transform The Fourier coefficients a and b of a periodic function x t with period T sampled with N equidistant values x x kT N for k 0 1 N 1 are N 1 2 2rkl W gt Zk COS 2 k 0 12 1a 71 N 1 2 nk b 2 a sin e 12 1b forl 1 n and n N 1 2 if N is odd and n N 2 if N is even The inverse transform after determination of the results f is n al 21 lt
70. can modify the values in this box with the first count up and second count down mouse button and perform the com mand adjust wind afterwards Before you do this it is a good idea to perform show wind This makes sure that you have all actual data of the window in the box Box 6 Exit or Quit Program Type roll special action EXIT exit program ask questions for saving data before leaving QUIT quit program without saving data Leave program when the first mouse button is pressed in this box The contents EXIT or QUIT of this box is changed with the second mouse button Box 7 Integer Field Point Data Type pull down output actual _FPt number of the actual field point total FPt number of field points FPt_dom iF domain number of the actual field point in the built in iterative pro cedures this value can have a different meaning Select the desired field point clicking the second mouse button when the cursor is near this point Box 8 Fill Patterns of Field Representations Type pull down input output fi11 3Darrow fill pattern of 3D vector represented by an arrow fill plane fill pattern of plane in field point fill _z comp fill pattern of n component perpendicular to plane fill _T comp fill pattern of tangential components fi11 3Dtria fill pattern of 3D vector represented by a triangle fi11 _shadow fill pattern of shadow of 3D vector triangle fill grid fill pattern of gr
71. cannot be solved without admitting a residual error in 1 14 Typical choices of testing functions are the values of the expansion functions f on the boundary Galerkin s choice of testing functions or Galerkin s method or subsectional functions especially piecewise constant or linear functions and Dirac delta functions On one hand appropriate smooth testing functions lead to better results than simple testing functions On the other hand smooth testing functions are usually more difficult to obtain and their scalar products are more difficult to evaluate There are smooth testing functions leading to bad results as well Needless to say that such functions have to be avoided Incidentally similar statements hold for basis functions 1 4 Generalized Point Matching Method In the point matching method the error function 7 is set to zero in single points rj Qj 1 M n irj 0 G 1 M 1 17 or se Se wpL fl wph 1 M 1 18 i 1 where w r is a positive real weighting function In matrix notation lajilplci b p FH 1 2 Mi aN 1 19 The simple case M N is also known as collocation The more general case M gt N is here denoted as generalized point matching It leads to an overdetermined system of 14 equations A solution can be found when a residual error n n r in the matching point r is allowed The most common method for solving the equations is the least squares technique which mi
72. check raina n See ek ee PE ee ea 127 15 10 3D ad justi ie 2 ee WS ee AS bee A Rae eN 129 15 7 113D gensrate e Weak ed tet hee Le weed She d 133 15 112 3D read esca etl A eee ee ee ale Ga oe SO 140 1b 713 3D writes ck oun ae eee Wb eR a OO a oe 141 15 38 Summary of Boxes sic aoe ae A BG eee GO ee a Oe 142 16 3D Graphic Plot Program 152 t61 Program Start dde RR A Aa 152 16 2 Program EXit ro ade ee e e a e Vena Apes 152 163 ACIONS 3 a IA A a AA e BOS eee 153 16 3 1 Regular Actions e eee 153 16 3 2 Window Actions aaa aaa 154 16 3 3 Special Actions m si ia E A eed 155 16 4 Graphic Representations ee 155 16 4 1 Regular and General PlotS o 155 16 4 2 Visualizing Electromagnetic Fields 156 16 4 3 Representation of Fields 0 157 16 4 4 Geometric Data and Mismatching Data Errors 159 16 4 5 Projections and Hiding o 160 16 5 Summary of Regular Actions o e e 162 T6 De1 Sh a A A AA a Ge de 162 16 522 reada T sema AAA A aR eae 164 A a AAA ae eh li ay ee a ee a i 168 16 04 penerate ua tdi ok Bee A eh Qe eae N 169 1675 5 Add oa da Boe ane Geek Y 171 Ode Stent A en a els Oy Pee ee Gh de A eg 173 TOKT MOVE e Lye db dot fe Dd ad b Oak ee Be ds 173 16 5 8 Totates 2 2 aa a dow Ab Soe a OR oR Aa eye ke 175 167529 DIM od Aden ei a ee ate Uh Un Seg Se howe 175 LOD LO inverti are yak I
73. compare the parameter files for computations with different frequencies and especially the parameter file MMP_PAR 000 of model 0 without symmetries with the parameter file MMP_PAR 001 of model 1 with symmetries In MMP_PAR 000 there is one block of 59 parameters Most of them are very small With an infinitely accurate computation you would get exactly zero for these parameters The remaining 16 non zero parameters correspond to the 17 parameters in the two blocks of MMP_PAR 001 To understand the difference of the numbers of non zero parameters note that because of the symmetry decomposition the parameters for the incident plane wave occur twice i e once in each block of MMP_PAR 001 Obviously the non zero parameters in both files are not identical due to numerical inaccuracies Of course model 1 with the reduced number of parameters is expected to be more accurate To verify this you can improve the discretization as indicated below 223 17 2 3 Changing the Discretization Model 2 You have probably noticed that the results become more and more inaccurate when the frequency is increased in model 0 or 1 For example when a frequency of 300 MHz the diameter of the sphere is one wavelength is assumed in model 1 you get 100 percent errors in some matching points To get more accurate results the discretization has to be improved by increasing the number of matching points and the orders of the multipole Although the latter is relat
74. conditions to be satisfied in order to get a system of equations On the boundary OD between domains D and D the boundary conditions are is a vector normal to the surface Between two general domains there are supposed to be no unknown surface charges or currents therefore 0 and s 0 In the coordinate system 1 812 of a matching point this leads to the six equations eE En 4 1 En El 4 1b Ev Et 4 1c iH pHi 4 1d Hy H 4 1e Hi Hh 4 1 The equations for the normal components are dependent of those for the tangential components and only four linearly independent conditions remain But the linear depen dence is lost again when a residual error in the boundary conditions is admitted In this case it is better to explicitly use all of the boundary conditions in order to distribute the error more evenly among the components of the field 4 2 Perfectly Conducting Surfaces Within perfectly conducting domains the field is zero No expansion has to be made for those domains which are therefore not domains in the MMP sense Because of the surface currents and charges the conditions to be satisfied on the boundary of a perfectly conducting domain reduce to Ej 9 4 2a Ej 0 4 2b uH 0 4 2c Again 4 2c is dependent of 4 2a 4 2b Those equations of 4 1 which have been omitted can serve to determine the unknown electric surface charge and current 25 4 3 Imperfectly Con
75. coordinates t2 component of the real part of the magnetic field in the field point local coordinates t2 component of the imaginary part of the magnetic field in the field point local coordinates t2 component of the real part of the vector potential in the field point local coordinates t2 component of the imaginary part of the vector potential in the field point local coordinates Analogous to box 27 Box 29 n Component of Field in Field Point Type output VZ EZR EZI HZR HZI AZR AZI VR VI_ n i e Zw component of the field shown in the field point local coor dinates n component of the real part of the electric field in the field point local coordinates n component of the imaginary part of the electric field in the field point local coordinates n component of the real part of the magnetic field in the field point local coordinates n component of the imaginary part of the magnetic field in the field point local coordinates n component of the real part of the vector potential in the field point local coordinates n component of the imaginary part of the vector potential in the field point local coordinates real part of the scalar potential in the field point local coordinates imaginary part of the scalar potential in the field point local coordi nates Analogous to box 27 Box 30 Colors of Field Representations Type pull down input output color 3Darr color of 3D
76. corners including end points lxya array containing pixel coordinates of the corners lxya 0 1xya 1 pixel coordinates of first point lxya 2 1xya 3 pixel coordinates of second point lcol color number lwid width of line in pixels larr type of end of polyline 0 usual 1 arrow mgfill idev lcor lxya lcol 1fil lbor Draw filled polygon This function is essential In the graphic MMP programs filled polygons with color numbers 0 15 and different widths are drawn If fewer colors are available the color numbers 2 15 can be replaced by an available number For example on a monochrome output device one can replace 2 15 simply by 1 The different fillings 1fil can be replaced by different intensities of a color especially if 256 colors are available idev device address lcor number of corners lxya array containing pixel coordinates of the corners lxya 0 1xya 1 pixel coordinates of first point lxya 2 lxya 3 pixel coordinates of second point lcol color number 1fil fill type 0 not filled 8 completely filled lbor 0 do not show border 1 show border mgrect idev 1xul lyul lwid 1hgt 1c01 1fi1 1bor Draw filled rectangle This function can be simulated by mgfi11 if necessary idev device address 1xul horizontal pixel coordinate of upper left corner lyul vertical pixel coordinate of upper left corner lwid pixel width of rectangle lhgt pixel length of rectangle lcol color number 1fil fill type 0 not
77. direction of second tangent vector iterat iterate the field perform generate pic f Note that all essential actions performed during a session are reported in file MMP_P3D LOG The information contained in this file is very helpful when you are not sure how to select the values for the directives outlined above It should be mentioned that the directives setaaa reaaaa and invaaa where aaa is a string with three characters are used essentially as initial directives and make not much sense within the definition of a set of pictures with one exception When a new plot file is read with the directives inctim dectim incfrq decfrq the input file containing the material properties should be read immediately afterwards with the directive rea3di in the case of inctim and dectim when the corresponding input file number is not 000 and in the case of incfrq and decfrq when the corresponding input file number is not equal to the frequency number Incidentally when a time dependent plot file MMP_Tyy xxx is read the information concerning the location of the field points is not contained in this file It is assumed to be on the file MMP_Pyy 000 Thus it is convenient to work always with problem number 000 in such cases i e when the Fourier transform is applied As an example a typical form of MMP_DIR zzz is the following seq 1 setrep 111211100 setvec 0 setlev 0 reapyy 001 setlev 1 setaxi 0 0 0 0 0 0 1 0 1 0 1 0 rotpln
78. el number of matching points per element 2D line or arc MPt __ actual matching point number MPt nMat number of matching points When a matching point is in activated with the second mouse button in a window or with the show points command the corresponding values are displayed in this box 149 Change the values with the first count up and second count down mouse button in the value area of this box and perform the command adjust points Exceptions e MPt _ __ is changed either when a matching point is in activated with the second mouse button in a window or with the show points command e MPt nMat is changed with add points delete points and similar com mands Since objects and parts of objects contain matching points as well the corresponding commands with object or part instead of points affect the values in this box as well Box 20 Integer Data of Domains Type pull down input output Domain _ actual domain number Domain M number of domains Although you can change the values of this box with the first count up and second count down mouse button in the value area this does not affect the corresponding internal values To effectively change the actual domain number use show domain and to change the number of domains use add d
79. excitation f encounters an obstacle of finite extension mostly which has propagation properties different from surrounding space fig 2 1 This results in the obstacle producing a scattered field f which can be found by solving the boundary value problem D f d 2 1 for an inhomogeneity d caused by f Often the total field f resulting from the scattering process is of interest For linear problems this is the superposition of the incident and the scattered wave pa fFe Pe 2 2 In the following section we will have a look at the field equations underlying electro magnetic waves Figure 2 1 Scattering problem An incident wave f encounters an obstacle a scattered wave f results 2 2 Field Equations Electromagnetic theory is based on Mazxwell s equations 3 a 1E B 2 3 cur om 2 3a bo a curl H jo jo 5D 2 3b ot 17 div D po pe 2 3c div B 0 2 3d where additional dependencies are given by the constitutive relations For linear homo geneous and isotropic media they are B p 2 4a D cE 2 4b jc o 2 4c Harmonic time dependence is used and time dependent quantities are represented as phasors f the time value can be obtained by f t R fe This yields the complex time harmonic Maxwell equations curl E iw 2 5a curl de 0 iwe E Te iwe E 2 5b dive p 2 5c div y 0 2 5d where 2
80. files files and if necessary the corresponding geometry file MMP_PLT GEO These files are generated by the 2D MMP code and are described in the corresponding manual 4 D 11 Particle Files MMP_PRT xxx The 3D graphic plot program MMP_P3D is able to move particles The data of the particles can be stored in the particle fieles nprt number of particles it is ic particle type size on screen color X y Z position 300 VX VY VZ velocity n q f mass electric charge friction coefficient D 12 Fourier Time Value File MMP FOU TIM The parameters in brackets starting time ending time number of pictures are not used by the mmp_fan program but only by the inverse transform mmp_f3d t0 nt tmin tmax npict period number of sampling values starting time ending time number of pictures ft Sampled time values D 13 Fourier Frequency File MMP_FOU FRQ The parameters in brackets basic frequency Fourier coefficients are not used by the 3D MMP main program They are produced by the Fourier transform MMP_FAN and are used for the inverse Fourier transform MMP_F3D Note that unlike in the input file MMP_3DI xxx these are angular frequencies The number of frequencies no is limited to the parameter nfreqm defined in COMM SRC no omega0 number of frequencies basic frequency comei ak bk no 1 complex angular frequencies Fourier coefficients D 14 Editor Desk File MMP_E3D DSK Initial data concerning windows bo
81. filled 8 completely filled lbor 0 do not show border 1 show border mgtext idev string lstr lxtx lytx 1c01 Draw text string 317 This function is essential at least on the screen In order to get a useful representation of the boxes in the graphic MMP programs a font with 80 characters on a line of the screen should be used The color number is not important at all because black on white text is completely sufficient Proportional fonts are not recommended because this makes the input of data in boxes very difficult The correct width and height of a character must be given in the function mgopen idev device address string character string with 1 up to 80 characters lstr length of string number of characters 1xtx horizontal pixel coordinate of lower left of text string lytx vertical pixel coordinate of lower left of text string lcol color number mgsetc idev 1lcol lred 1lgreen lblue Set color composition red green blue This function is not very important and can be replaced by a dummy routine It is used to fix the colors of the screen only idev device address screen only lcol color number lred red intensity 0 1000 of color lgreen green intensity 0 1000 of color lblue blue intensity 0 1000 of color function mgcurs idev Define cursor form and display cursor for the first time This function is essential because the MMP graphic routines are handled entirely by a mouse It is called only
82. grid when the tangent vectors defining the plot plane are not orthogonal In order to reduce the number of input data the limits of the window plane are defined by the lengths of the horizontal and vertical tangent vectors and the origin of a plot window is always in the center of the rectangle The main consequence is the following One has two approaches to shift a plot window in the 3D MMP graphic programs one can shift the origin in 3D space or one can shift the limits which is equivalent to shifting the origin within the plane The latter is agreeable in most cases but it results in a plot window with a displaced origin that is no longer in the center of the rectangle When the data of a plot window are stored in the file MMP_E3D xxx the editor performs the transformation required Since the limits of the window plane are not stored they are lost When an input file MMP_E3D xxx is read by the editor the limits are recomputed from the tangent vectors and the origin is set in the center of the rectangle Thus when you prefer to work with an origin in the lower left corner of the window you can do that in the editor But when you leave the editor compute the plot file and enter the 88 plot program you will get an origin in the center and different limits when you read the window data from MMP_3DI xxx Nonetheless you will have the same locations of the objects in the plot program as in the editor This problem can be avoided when a screen
83. improved Thus it is good to have an error representation in the editor as well 3D read file_____ Read 3D input file MMP_3DI xxx Select the extension number xxx in the item box In the 3D MMP editor the input files are not only used for defining a model that can be computed with the 3D MMP main program but also for saving the matching points and expansions of a 3D object This is important because only two objects can be handled at a time If the question 140 read ALL_3D_data__ is answered in the affirmative the data in the file will overwrite all actual data i e the actual matching points expansions etc are lost If two objects are defined in the input file you will obtain two objects If you answer in the negative the matching points and expansions defined in the file are used to create a new object If two objects have been defined in the input file they will be combined to a new object If no object has been defined before this command is executed object number one is created If one object exists object number two is created Finally if two object are already defined the question replace_object _YES is asked and object number two is replaced if this is answered in the affirmative Other wise the process is aborted with the message 3D_data_not_read__ The message reading _3D_data_file is displayed as long as the corresponding file is read The following messages indicate that either object number o
84. in creased A most simple but not very accurate step by step procedure is used Thus relatively small time steps are required for obtaining accurate results In addition to the time the phase angle is increased with the increment dt times Re_Om when the field is time harmonic I e it is implicitly assumed that the frequency is not complex When you reduce the time step the movement of the particles probably turns out to be very slow In this case you can increase the number iter part The particles will be moved iter part times before their new location is displayed on the screen When the particle movement is too fast you can increase the delay delay that does not affect the computation itself Note that the time step dt can be negative Moving a particle back and forth is useful for checking the accuracy When the field is computed iteratively you can mix both the iteration of the field and the movement of the particle by selecting positive number in the boxes iter field and iter part respectively When you iterate the field you probably want to see not only the particles but also the actual field Since this is time consuming you will prefer to generate a movie by selecting the number of pictures in the box ipic mov The generation of the movie is ident
85. in the item box can either be added to the existing 2D elements or be used to replace the existing 2D elements Thus the questions add_2D_objects_____ replace_2D_objects_ are asked If both questions are answered in the negative nothing is read and 2D_data_not_read__ is displayed Otherwise reading 2D_data_file indicates that the program is reading data The following errors can occur too_many_expansions too_many_elements__ The number of elements exceeds the maximum number allowed no_2D_data_found__ The data file MMP_2DI xxx is missing Make sure that you did select the correct item number xxx and that the file you want to read is in the working directory 112 15 6 13 2D write____ Write data to files 2D write____ window__ See 3D constructions 2D write____ file____ Save the data of the current 2D lines arcs and expansions on a 2D file MMP_2DI xxx Select xxx in the item box If this file already exists you are asked overwrite_2D_file__ If this question is answered in the negative the file is not written and 2D_data_not_saved_ is displayed Otherwise saving _2D_data_file indicates that the 2D data are being saved 15 7 Summary of 3D Actions 15 7 1 3D show____ Show 3D elements and display the corresponding additional data Note that the latter makes no sense when several elements with different additional data are shown at the same time with this command 3D show____
86. in the color and fill box during a session D 15 Plot Program Desk File MMP_P3D DSK Initial data concerning windows boxes colors etc in the 3D MMP plot program This file is searched first on the current directory then on the directory MMP of the current drive and finally on the directory MMP of drive C If it is missing the program cannot be started 302 nWin number of windows iWin1 6 x and y coordinates of lower left corner x and y coordinates of upper right corner resolution in x and y direction invisible grid lines nBox number of Boxes iBox1 5 x and y coordinates of lower left corner length of text area in characters length of variable area in characters number of lines contained in the box if negative the initial status of the box is active bright and the absolute value indicates the number of lines BoxInt BoxRea initial integer and real value of the current line BoxTxt initial text area of the current line The following line is repeated 16 times for the colors 0 15 irgb1 3 red green blue intensity of corresponding color icolr color of windows and inactive boxes icolv color of active boxes icolb color of the axis and vector icolb color of the axis and vector icolmat 1 1 colors for matching points icolerr 0 9 colors for errors ifilmat 1 1 fill patterns for matching points ifilerr 0 9 fill patterns for errors vlight 1 3 global Cartesian coordinates of light vector Coordinates x and y
87. in the vicinity of the dipole To avoid this you can generate a small sphere of dummy matching points boundary condition 0 weights 0 around the dipole This has another drawback another dummy sphere is implicitly generated around the point X because of the symmetry operations This does not affect the computation of the parameters and errors at all but you get a kind of a black hole around the points X and X i e little spheres where the field is not computed at all The first one is desired and avoids overflows For small dummy spheres this is not an important drawback When you want to move the dipole to another location on the X axis you have to move the corresponding dummy matching points as well For simplifying this the 3D MMP editor allows to move an object consisting of several expansions and matching points The number of objects is limited to two objects This is no problem here because we only have two objects 1 the sphere with the corresponding expansions and 2 the dummy sphere with the excitation For learning how to deal with more objects we store the conducting sphere with its multipole and the dipole with its dummy matching points on two separate files MMP_3DI 003 and MMP_3DI 004 The data of these files describe only a part of the whole model To get an input file that can be processed by the main program proceed as follows 1 Start the editor and read first all data of file MMP_3DI 003 with the command 3D read fil
88. is I a cos kz b sin kz ci C 5 The field contributions of the constant current have to be obtained by numerical integra tion This expansion has been presented in 41 In practice the simpler expansion C 4 performs in practically all cases as well Therefore the continuous charge expansions are not included in this release C 2 Cylindrical Solutions The field components for the electric transverse magnetic solutions of order n and degree m in the point p y z are in polar coordinates Egm _ Y Ep p MPa m Kp SS KpBm 1 Kp sin mp en C 6a Elm iy Ep PROL Sn mp el yz C 6b c EPS K Bm Kp a mg e7 C 6c ES m iwe sin oo HE mBalnp Smee C 64 Elm iwe HES EE n Bn Kp KB mes sp amg e C 6e c HES ZA C 6f gsm mb Kp Sin my ey C 7a BESO Bl 0B nap ame eo 0 19 ES 9 C 7c HE S VB sp KPBmes ip Smee C 7d 287 mp er C 7e HE i si HS sm 5 mBm Kp AN c HES k Bm Kp y RD ez C 7f The solutions have the following symmetries Solution Symmetry to x 0 Symmetry to y 0 m odd m even m odd m even Ecm odd even even even Esm even odd odd odd Hem even odd odd odd Hsm odd even even even The whole expansion can be scaled with Seca section 10 5 magnetic modes are additionally scaled with the inverse of the wave impedance A complete expansion of order M is the combination
89. its output All graphic elements can be graphically manipu lated the programs are fully mouse operated and require no keyboard input except for generating hardcopies Although 3D MMP graphics run under Windows and GEM the graphic elements are different from the typical graphic elements known from typical Windows applications Above all you work on a desk consisting of at least one window and several boxes i e you have essentially only two graphic elements Windows are used to show and manipulate data that can be represented graphically whereas boxes are used to display and change other data types texts integer and real values The layout of 81 the desk can be adapted to your wishes and possibilities e g for monitors of different resolution The initial size and location of windows and boxes as well as most of the initial values contained in the boxes are defined in the corresponding desk files with the extension DSK A three button mouse is recommended but two buttons are sufficient for all essential actions Pressing the third button is identical with pressing the first and second mouse button at the same time but the latter is difficult because one has a good chance to press one of the buttons a little bit earlier which will start an action that is not intended To avoid this problem a short delay has been built in when the second mouse button is pressed Thus to simulate the third button on a two button mouse you should press
90. kind order m spherical Bessel functions jn Yn AD or po spherical Bessel function order n spherical Neumann function order n spherical Hankel function of the first kind order n spherical Hankel function of the second kind order n associated Legendre function P cos 9 P cos 0 sin Y cos my or sinmy respectively real and imaginary part of a complex number A 1 3 Differential Operators general symbol for a field function f fine fi scattered incident and total field D general operator 279 L D D div curl grad linear operators domain domain i boundary of D boundary between D and D divergence curl gradient A 1 4 Matrices and Vectors aji A A X X R R R RN ci e b b S Smn Sscal Wk zn A system matrix augmented system matrix cf equation 2 14 Cholesky factor Cholesky factor of the augmented matrix triangular matrix for updating augmented triangular matrix shares of R in the parallel version vectors of unknowns vectors of excitation scaling factors for the expansion functions extra weight of the boundary conditions in matching point k conjugate complex number adjoint conjugate transposed matrix or vec tor A 1 5 Electromagnetic Fields Phasors may be brought to special attention by underlining f w The time value can be calculated by f t R f w e 2 ri Je Pe S SU D by O E 4 SP PEL EWE Pj electric f
91. lead to acceptable results Some typical results are shown in figures 16 4 16 6 and 16 5 17 4 3 Surface Impedance Boundary Conditions Model 13 A well known method that is helpful for computing the field outside the lossy dielectric sphere consists in using surface impedance boundary conditions see section 4 3 A simplified expansion for the inner domain is already implicit to these conditions so you don t need the normal expansion from model 12 anymore and can delete it Although now zero field results in domain 2 the domain itself must not be deleted because the corresponding material properties are used in the formulation of the surface impedance conditions To replace the usual boundary conditions by surface boundary conditions adjust the corresponding matching points with the values 11000 and 0 in the boxes MPt E1 3 and MPt H1 3 In order to reduce the errors the orders of the remaining multipole in the center of the sphere can be increased For doing that diminish the overdiscretization factor in the additional integer data box over and run the command 3D adjust pole with the automatic determination of the maximum order and degree When you select less than 1 in the box over the overdetermination is nonetheless set equal to 1 In most cases this avoids an underdetermined system of equations that would lead to an error in the main program Note that usually three boundary c
92. matching points r4 grid line scaling r5 factor for logarithmic iso lines 1 or less for linear iso lines set level number level number i1 0 for all levels set autoscaling for next picture only set light vector direction global Cartesian components i1 gt 0 show negative shadows read complex frequency dependent plot file MMP_Pyy xxx ii file number yy i2 frequency number xxx i3 use window defined in MMP_Pyy xxx if i3 gt 0 read real time dependent plot file MMP_Tyy xxx This directive is equivalent to settim with i1 gt 1 i1 file number yy i2 time step number xxx i3 use window defined in MMP_Pyy xxx if i3 gt 0 read 2D frequency dependent plot file MMP_PLF xxx or MMP_DAT PLT i1 frequency number xxx read MMP_DAT PLT if MMP_PLF xxx missing i2 use window defined in plot file if i2 gt 0 read 2D time dependent plot file MMP_PLT xxx and MMP_PLT GEO i1 time step number xxx i2 use window defined in plot file if i2 gt 0 read error file MMP_ERR xxx i1 frequency number xxx i2 perform symmetry operations if i2 gt 0 200 rea3di i1 i2 reawin il inctim incfrq incphi ri inclev inceye ri dectim decfrq decphi ri declev deceye ri blowin r1 i1 shrwin r1 i1 movwin i3 use matching points with domain number i3 as field points if i3 gt 1 read 3D input file MMP_3DI xxx i1 frequency number xxx i2 perform symmetry operations if i2 gt 0 read window file
93. moved You can move the origin of the window plane if you answer the question move _window_plane__ in the affirmative This requires the definition of a 3D vector or axis You can either use the vector respectively axis that has previously been defined and answer the question set_new_vector axis in the negative or you can adjust the axis now and answer the question in the affirmative The steps required to adjust the axis are indicated in the explanation of adjust axis Needless to say that the message window_NOT_defined_ indicates that the window that you are trying to move does not exist If you decide not to move the window plane you can move the window limits instead For doing this a 2D vector in the window plane is required and you are asked set_from to_vector_ Now you have to press the first mouse button when the cursor is at the start point of the vector and release it when the cursor is at the end point move____ part Move the particle selected in the item box When the particle number is out of range all particles are moved Since this is reasonable in most cases you usually will select the item number 0 Before you start this command you have to define some particles with either add part or read part Otherwise the process is aborted with the message NO_particles_______ T When there is not enough memory left for saving the part of the screen behind the particles this is indicated by ER
94. movies 16 9 Iterative Procedures The 3D MMP plot program includes some iterative algorithms for generating electro magnetic and other fields The algorithms in the actual version are relatively simple and have been designed for educational purpose and for testing rather than for solving scien tific problems Nonetheless the program is prepared for more sophisticated algorithms It is expected that users having an appropriate FORTRAN compiler are able to easily implement their own algorithms Before an iteration is started with the command generate pic f the initial field and the parameters of the iterative procedure have to be defined After the iteration a 206 picture of the resulting field is automatically shown Thus the desired representation of the field has to be selected exactly as when show pic f is started see section 16 7 16 9 1 Initializing the Field The initial field required for iterative algorithms depends on the algorithm and on the application Some algorithms like the computation of the Mandelbrot and Julia set sim ply require a zero field on regular grid Such a field is generated with the command clear pic f 0 Note that you have to select the number of grid lines before you start this command and that the field will cover the actual screen window plane Of course you can run the Mandelbrot and Julia algorithms when you have a non zero field and look w
95. movies it is sufficient for slide shows For storing a slide i e a single picture the command write pic f is used The corresponding pixel information is written on a file MMP_Fyy xxx where yy is the slide show number that is selected in the item box and xxx is the picture number selected in the file extension box The file MMP_Fyy xxx has exactly the same form as the MMP _Fyy xxx files of a movie For this reason the command write pic f can be used for exchanging pictures of a movie or even for generating movies in a very time consuming way The most important difference between movies and slide shows is the following Only one information file MMP_Iyy 000 is generated for a movie whereas an information file MMP_Iyy xxx is generated for each picture of the slide show The movie information file MMP_Iyy 000 contains some additional information on the structure of the movie that is missing in the slide information files MMP_Iyy xxx For showing a picture of a slide show the corresponding numbers yy and xxx have to be selected in the item and in the file extension box before the command read pic f is executed Note that the program will read the movie information file MMP_Iyy 000 when the slide information file MMP_Iyy xxx is missing This allows to show any picture of a movie separately Moreover if you are familiar with directive files for movies you might prefer generating slide shows like
96. new features were added 17 After completion of the second version graphic input and output programs were designed the code was entirely revised once more and some minor additional features were introduced according to the experience of the users The actual version of the 3D MMP code for electromagnetic scattering on PCs is assumed to be reliable user friendly portable and a powerful and interesting alternative to many other codes for numerical electromagnetics Although one cannot expect that the code is completely free of errors we hope very much that we did detect and eliminate all major bugs In 1989 the name Generalized Multipole Technique GMT was introduced in agree ment with most of the scientists who had written codes based on similar techniques like MMP 1 Because of the close relation to analytic solutions GMT is most powerful when high accuracy and reliability of the results is required above all for computations in the close nearfield and on the surface of scatterers Compared with other numerical techniques GMT is similar to the Method of Moments MoM It is certainly superior to MoM if lossy media are present because GMT is a true boundary method requiring the discretization of the boundaries only whereas MoM codes require the entire discretization of lossy bodies The MMP code is the most elaborated implementation of GMT with a large number of important additional features for widening its range of applications and fo
97. number always is selected in the item box movie When such a movie does already exist you are asked overwrite _movie____ If you do not want to overwrite the existing movie answer in the negative and the process is aborted with the message movie_not_generated For a more detailed description see section 16 9 generate movie Generate a movie by executing a directives file MMP_DIR xxx containing the directives for generating the movie see section 16 8 Select the movie number yy in the item box and the extension number xxx of the directives file MMP_DIR xxx in the file extension box In addition to the files MMP_Fyy zzz containing the pixel information of the dif ferent pictures an ASCII file MMP_Iyy 000 containing the information on the size and location of the window and some additional data concerning the structure of the movie is generated In order to avoid overwriting existing movies the program checks whether the file MMP_Iyy 000 does already exist If so overwrite_0K_ _ _YES is asked When this question is answered in the negative the process is aborted and movie_not_generated is displayed Note that the files MMP_Fyy zzz are used for slide shows as well see section 16 8 7 Since the corresponding information files have the extension number zzz rather than 000 the program does not detect these files and will overwrite them Overwriting slide shows can be avoided when different numbers yy are used fo
98. of 5 ci fi S gal aos a yz fE de 2 M y ie i bm E Cm Z7 f Hem 4 if C 8 m 1 For 2D multipoles choose Bm HY for 2D normal expansions By Jm A complete expansion C 8 rotated around its z axis can be represented exactly by the functions of the unrotated expansion For the special case where y k and thus 0 only the simple transverse elec tromagnetic or TEM case exists This case is only possible in a configuration with a single not simply connected domain The electric and magnetic field components can be used separately for electro or magnetostatics The solutions are directly converted to Cartesian coordinates Cm 1 ESTE mt ae m 1 p e C 9a T m 1 sin ikz E TETT cos m 1 e C 9b c EST lt p C 9e T m 1_1 sin ikz HA Z mF cos m 1 pe C 9d T m 1_1 cos ikz Hy Z mal sin m l pe C 9e c Hos 9 C 9f The solutions have the following symmetries 288 Solution Symmetry to x 0 Symmetry to y 0 m odd m even m odd m even Tem odd even even even Tsm even odd odd odd The whole expansion can be scaled with sca section 10 5 A TEM multipole of order M is the combination M XO ifi Sscal fore Y am FO bm om C 10 i m 1 A complete expansion C 10 rotated around its z axis can be represented exactly by the functions of the unrotated expansion C 3 Spherical Solutions The spherical solutions in
99. of doing that 1 select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data 2 press the first mouse button within a window and release it as soon as the cursor is at the position where you want to have the projection of the point on the actual window plane In order to define the location of the point completely you are asked to set the height of the point above the plane in the next step set_height_above_pln i e you are expected to give the height of the point above the window plane Only a vertical movement of the cursor will affect this value The actual height is displayed in the second box of the bottom line as long as the mouse button is pressed down If you did use method 1 to discretize the start point set_end_point_data_ indicates that you are expected to give the coordinates of the end point in the same way Le select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data If you did use method 2 to discretize the start point set_end_point______ indicates that you are expected to discretize the end point of the wire in the same way 116 as the start point Of course you will be asked set_height_above_pln afterwards if you apply method 2 If the numbers in the boxes Exp IE2 and Exp IE5 are bigger than 0 the match ing points corresp
100. of expansion functions fig 2 2 Usually more than just one domain is used The formalism described in chapter 1 can easily be adapted by making the single expansion functions valid in only one domain The expansion functions for domain D are a f in Dj and on Djk 2 12 0 in Dp j k and the boundary conditions are enforced on all 0ODjx Other equations than the boundary conditions can be added to the overdetermined system of equations 19 E 7 x Es y E 4 Ne Mle x Sais E he a x x NN ca 5 Xx A A A x Y 7 N f AN Figure 2 2 MMP model of a scattering problem The x s denote origins of multipoles or other expansions the L s matching points The system of equations is azi p cs bj p gj 1 M i 1 N 2 13 The number of equations M ranges between 2 to 10 times the number of unknowns N depending on the type of the problem and the quality of the model The system is solved by a direct orthogonal method which yields a least squares result Bearing 2 11 and 2 2 in mind and with regard to chapter 5 2 13 is favorably written in the augmented form aj 05 0 j 1 M i 1 N 2 14 All expansions including the excitation can be treated in the same way Once the unknowns c have been determined the residual errors on the boundary and the field values can be evaluated in arbitrary points The results are usually presented as error distributions on the surface and as plo
101. one has not only to select the corresponding item in the item box but also the number of the constraint integral or set of field points If this number is incorrect one of the messages NO_constraint_ xxx_ NO_integral_ xxx__ NO_field_pt set_ xxx is displayed When a 3D point is clicked with the second mouse button its global coordinates are displayed in the boxes of the bottom line Note that activating points defining constraints integrals or sets of field points is not important because these points cannot be manipulated graphically like matching points and expansions A different representation is used for showing active and inactive objects Usually thick lines are used for active elements Note that the width of thin lines wLin can be modified in the box containing the real window data If this value is too big you will get too thick lines If it is too small thick lines for representing active elements will have the same width as thin lines for representing inactive elements The appropriate line width is device dependent i e it depends on your output device Moreover different colors and fillings can be used if desired The fillings and colors of the objects are defined in the desk file MMP_E3D DSK Especially in 3D constructions with a large number of objects it can be difficult to select a special object Such problems can be overcome either by choosing an appropriate window plane or with the regular action
102. ortho File CHOL F cpchcl cpchsl cpchud crotg2 handle warnings and errors initializations immediately after start of program initializations prior to a computation various initializations initialize constants initialize domains initialize expansions initialize connections initialize output control initialize message levels read input file read expansion logical read connection read matching point read constraints generate matching points for wires read integral head read plot block skip an integral in the input file read single integral points read parameter file write parameter file integer function for automatic determination of the domain of a point function distance to next matching point for 2D expansions function distance to next matching point for 3D expansions coordinate transformation A 1 for real vectors coordinate transformation A 2 for real vectors coordinate transformation A 1 for complex vectors coordinate transformation A 2 for complex vectors coordinate transformation A 1 for an expansion coordinate transformation A 2 for an expansion coordinate transformation A 3 for an expansion coordinate transformation A 4 for an expansion vector product t x Y for real vectors vector product u x Y for complex vectors function dot product w v of real vectors dot product u Y of a real and a complex vector scale a vector to length 1 function scale a vector to length
103. p R k z 2 _ os R2 sin A C 1a TAN j 2 z ie AAA sin IS Ariwe R Recast he R2 sin M2 C 1b 2 1 21 R 2 22 Ip er HS pp R B cosh 22 sin Be C10 grz with the abbreviation R vVp z 2 The thin wire expansion is even about both x 0 and y 0 A straight wire with a more arbitrary parameterized current distribution can be obtained by joining N short segments i of length 1 lt m 2Rk with a current I a cos kz b sinkz zi being the local coordinate on the segment i The continuity conditions for the current are h a Q1 COS kl bi sin kl a2 a2 COS kl ba sin kl Q3 C 2 Q COS kl b sin kl Qi 1 an cos kly by sin kly Ie J and Ie are the currents at the beginning and the end of the wire respectively The b can be eliminated _ i Si kl i cot kl C 3 1 286 Thus the expansion for a long wire with N segments of length l is s s h 9 cot kl i FO O cotkli Ie N A f 10 f go gt ai fi a kli Ja toghla sin kly 94 with pos standing for one of ES J To BAS 1 or HSS Io It is implemented for a wire of length L made of N segments of equal length l l L N The charge distribution on this wire is not continuous This can have negative in fluence if matching points are very close to segment joints A thin wire expansion with continuous charge can be produced if the current on a segment
104. particle file included in this package with read part 32 In this file two electrons and a positive particle consisting of two protons are contained These particle form a very large atom that is relatively stable You should set dt 1 0E 3 or less and iter part 10 or more before you move these particles You can slightly modify the initial conditions with adjust part for getting a more stable solutions If you have found an absolutely stable atom with three or more particles please send the corresponding data to the authors Before you run move part with new initial conditions you always should save the data on a particle file with write part When you want to reset the particles you can do this with read part whenever you want Instead of trying to get stable atoms you can try to get stable systems of uncharged planets Although this is more simple it certainly is not trivial above all when you have planets moving around two stars of similar size 258 17 15 Finite Differences Model 33 The most simple iterative algorithm of computational electromagnetics is certainly the Finite Difference FD procedure for 2D electrostatics based on the five point star oper ator This algorithm is one of the algorithms implemented in the plot program It has the number iter type 2 Before you run any iterative algorithm
105. point and its reflection If the field is only defined in a domain which is not intersected by a symmetry plane it is also possible to obtain the even or odd field in the reflected domain by PUEP HP and f P f P 7 4 In the 3D MMP code there is no difference made between domains which are or are not intersected therefore 7 3 is always used For electromagnetic vector fields additional dependencies between the components have to be taken into account Because Maxwell s equations are invariant with respect to reflections about a plane the components must transform either like Bit P Hi P H P HP E P E P ASP A 2 or like Ei P P Ai P Hi P 7 6 E P E P Hy P H P 37 x x Ji ij E d j C x J y te x al x x a al 4 ae y B Figure 7 2 MMP model of a symmetric boundary value problem with one plane of symmetry Watch the different discretization in A and B It is never necessary to put matching points onto symmetry planes due to the duality of the electric and magnetic field The index 1 stands for the com ponent of a vector perpendicular to the plane for the one parallel to the plane For the 3D MMP code an electromagnetic field is defined to be even about a plane if 7 5 is true and odd if 7 6 holds On the symmetry plane itself for an even field E 0 and A 0 7 7 is valid and for an odd field El
106. potentials and not alway requires all field data Moreover one can define material properties in the plot program that can be stored in the plot file as well To distinguish the different plot formats a different file identification 1291 number is used The following format is used for plots on grids yy 00 49 The list of the field points goes through vertical rows starting with the bottom left point and ending with the top right point The field values are given in global coordinates The lines in brackets are contained in files with the identification number 1291 only 32 or 1291 file identification number ireare ireaim ireaeh ireaap ifi avphtent numbers ixs iys izs symmetry numbers ndom number of domains rdom1 6 material properties of domains xplu yplu zplu left bottom corner of rectangular plot window Xpru ypru zpru right bottom corner xplo yplo zplo left top corner nhor nver nlev ndom sdplt number of points hor and vert levels domain number distance between levels ig domain of field point cex cey cez E chx chy chz cax cay caz complex vector potential cv complex scalar potential In general plot files the coordinate system of each field point is specified by Y and Up However the field values are given in global coordinates 42 or 1291 file identification number ireare ireaim ireaeh ireaap ifi avphtent numbers ixs iys izs symmetry numbers ndom number of domains rdom1 6 materia
107. scaling is based on the maximum of the field you probably get undesired scaling factors For avoiding this you should perform first as many iterations as required for moving the maximum of the pulse inside the window without generating a movie set ipic mov 0 iter fiel 30 run generate pic f and answer both questions in the affirmative and start the movie from this position set ipic mov 50 iter fiel 10 run generate pic f and answer both questions in the negative Needless to say a monochrome screen driver makes the movie faster and less memory consuming 262 Part V Installation Configuration and Running 263 18 Hardware Requirements 18 1 Ordinary PCs An XT compatible PC is sufficient to run small 3D MMP versions when an appropriate compiler is applied For example all models in the tutorial can be computed on an simple XT with 640kbytes memory numeric coprocessor 8087 20Mbytes hard disk But in general 3D computations is a too big business for XTs and ATs with 80286 processors Le a 386 or a 486 machine is strongly recommended Since a large number of floating point operations has to be performed a 80387 numeric coprocessor must be installed in the 386 PC It should be mentioned that the 80287 coprocessor used in ATs is not faster than the 8087 in XTs i e it is not worth talking about this coprocessor Howe
108. sel se2 iel ie2 ie3 ie4 ie5 ie6 sel se2 311 expansion corresponding to a 3D multipole with IE1 301 radial function 1 Bessel 2 Neumann 3 Hankel 1 4 Hankel 2 maximum order and degree n 1 IE3 m 0 E3 not used in the actual implementation not used in the actual implementation not used in the actual implementation radius of the ring not used in the actual implementation 312 expansion corresponding to a 3D multipole with IE1 302 radial function 1 Bessel 2 Neumann 3 Hankel 1 4 Hankel 2 minimum order maximum order minimum degree maximum degree radius of the ring not used in the actual implementation 313 expansion like expansion IE1 312 but TM field only radial function 1 Bessel 2 Neumann 3 Hankel 1 4 Hankel 2 minimum order maximum order minimum degree maximum degree radius of the ring not used in the actual implementation 314 expansion like expansion IE1 312 but TE field only radial function 1 Bessel 2 Neumann 3 Hankel 1 4 Hankel 2 minimum order maximum order minimum degree maximum degree radius of the ring not used in the actual implementation e Rectangular waveguide mode Emn C 17 or Hmn C 18 mode numbers m and n propagating in the e direction The origin of the expansion is one of the edges of the waveguide iel ie2 ie3 ie4 sel se2 501 1 Emn 2 Hmn m in E direction n in direction width a in amp direction width b in e direction cega
109. set of elementary graphics functions that can be simulated with all useful graphic systems Unfortunately many of the graphic libraries for PCs are not useful These routines are used in the 3D MMP graphic programs only e System dependent routines like time routines routines for reading command line parameters and communication routines for networks These routines can be omit ted if they are not available To simulate the elementary graphics functions one has to write an appropriate inter face to the graphic library or system that is to be used In the 3D MMP package for PCs an interface to Microsoft Windows 3 for Watcom FORTRAN is included In addition interfaces to the GEMVDI routines of GEM a product of Digital Research Inc for several compilers and a Windows 3 interface for Micro Way NDP 860 FORTRAN are available upon request Time routines are available in almost all compilers They are used above all for benchmarks Moreover command line parameters can be helpful for simplifying the call of a program This feature is used in the UNIX version of the 3D MMP main program and in the Windows version Finally communication routines are used when one wants to work in a network of different machines or on a transputer network All of these special routines are only called in the module MAIN SRC of the 3D MMP main program When they are not available or cannot be simulated by other routines they can be replaced by dummy routines This w
110. show that is described below 15 4 Actions 15 4 1 Regular Actions In the 3D MMP editor regular actions consist of the dimension an action and of an item To start such an action the question information box box 4 on the top line has to be clicked with the mouse button 1 when ready_for_action__ is displayed Not all regular actions are performed directly In many cases you are asked some questions either for safety reasons or to specify the regular action Usually some param eters used during the process to be performed have to be defined in the corresponding 97 boxes before the regular action is started If this has been done the dimension of the construction and action to be performed should be selected with the first or second mouse button in the corresponding boxes The item should be selected afterwards because the items that can be selected depend on the dimension and on the action The correspond ing information is contained in the file MMP_E3D ACT The program tries to read this file when the item box is clicked the first time If this file is missing the message error_reading ACT is displayed in the question information box As a consequence all items are displayed when the item box is clicked with the first or second mouse button This and the se lection of the action or of the dimension after the selection of the item allows to select a regular action that has not been implemented If yo
111. simulations of electromagnetic fields in Proc PIERS Symposium Boston July 1991 N Kuster Absorption Mechanism Extraction in the Close Near Field of Antennas by Numerical Computations in Proc PIERS Symposium Boston July 1991 N Kuster A Mixed Direct Iterative LS Procedure for Large Full Matrices and Its Physical Interpretation in Proc PIERS Symposium Boston July 1991 N Kuster C Hafner and L Bomholt 3D MMP Software Package for PCs in Proc of the 13th Annual Meeting of the Bioelectromagnetic Society Salt Lake City Utah June 1991 M Reite L Higgs J P Lebet A Barbault C Rossel N Kuster and B Pasche Low Energy Emission Therapy LEET influences Sleep and Blood Pressure Pa rameters in Healty Volunteers in Proc of the World Federation of Sleep Research Societies Meeting Cannes Sept 1991 N Kuster Absorption im Nahfeld aktiver Antennen und passiver resonanter Strukturen oberhalb 300 MHz Strahlenschutz fu r Mensch und Umwelt Band I Verlag TUV Rheinland pp 487 492 1991 P Leuchtmann H Ryser and B Szentkuti Conducted versus Radiated Tests Numerical Field Simulation and Measured Data in Proc of the 9th Symposium on Electromagnetic Compatibility Zurich pp 59 64 Mar 1991 S Kiener and F Bomholt The GMT and the MMP codes Applications to EMC the Babinet Theorem in Proc of the 9th Symposium on Electromagnetic Com patibility
112. single column They are computed in nbedz The integral points are treated the same way as field points ignr is called to determine the domain and zeile to compute the rows The integral contribution of each column of cup is computed by routine intval and summed up into a row cnbed which is finally updated Constraints need to be evaluated for each of the usually more than one symmetry components of the problem The integral points and the orientation are therefore stored in arrays which limits the number of constraints to nnbedm and the total number of integral points within them to nnbptn 13 4 Symmetries The implementation of symmetries can be looked at separately The reflective symmetries about X 0 Y 0 and Z 0 which are to be considered are specified in the input file as is1 is2 and is3 and are stored in the array is The loop over the symmetry components of the problem is controlled by routines inisym and nexsym the current symmetry is stored in array isa Those symmetries which can be considered for matching and field points in the sym metry planes are taken care of in routine setisp The zero and non zero components of the field are marked in array isp setisp also determines which symmetry decomposi tion 7 3 has to be made array isszp in a field or matching point depending on its location and orientation Expansions which are not symmetry adapted are symmetrized in entsym Subroutine setise finds out from th
113. sinz B 1 nt E 8 13 For large arguments z gt n the spherical Bessel functions behave like 1 jn 2 gt sin z Z B 14 z 2 1 Yn z gt cos z gt B 15 z B 3 Associated Legendre Functions The associated Legendre functions P x and Q x are solutions of the differential equation d w x dw x m 1 a a 2x a F n n 1 z Both functions are real valued for real valued arguments Q x has singularities for x 1 and therefore will not be used The Legendre functions are easiest to calculate by recurrence The stable relations w x 0 B 16 Pra V1 22 2n 1 P x B 17a Pr a 2n 1 2P 2 B 17b P Ol xP 1 m P a B 17e 284 allow to compute all P x from the starting value Po a 1 B 18 In the expressions for the spherical expansions for m gt 0 the term P7 cos 0 sin appears To avoid divisions by zero during the evaluation it is better to introduce the functions P cos Y P cos Y sind B 19 which are regular in these places Relations B 17 are valid for P as well The starting value is Pi 1 B 20 P x is even with respect to x 0 if m n is even and it is odd if m n is odd B 4 Harmonic Functions The harmonic functions c y are solutions of the harmonic differential equation Pe p de m c p 0 B 21 Orthogonal bases for solutions are the trigonometric functions cos m and sin my or alte
114. size and location of the window The movie is shown at the location indicated in this file and not a the current location of one of the windows 16 8 2 Directive Files Before a movie can be generated with the command generate movie you have to write an appropriate file MMP_DIR zzz that contains the directives necessary for generating the sequences Simple movies with only one sequence can be generated automatically during iterative procedures with the commands generate pic f or move part No directive file is required in this case The structure of the directive files is the following To indicate the begin of a sequence the command seq has to be given on one line of the file MMP_DIR zzz The program reads only the first three characters of this line The remaining information in brackets is ignored by the program A sequence consists of a packet of initial directives that have to be performed before a loop for drawing and storing pictures is started All directives consist of name with six characters on a line Most of the directives require some additional integer or real data that have to be given on a separate line after the name The directives that have been implemented are described below The last directive of a packet is enddir without any additional data After the end of the initial directives the program expects the number il sets 197 that indicates the number of sets
115. stated rules always imagine the whole problem which consists of the discretized part and its reflections and avoid dependencies between a multipole and its reflected counterpart as between ordinary multipoles Make sure that the multipoles and normal expansions on a symmetry plane are properly oriented i e that always one of the basis vectors of their coordinate system Ey z is perpendicular to a symmetry plane Otherwise no reduction of the num ber of parameters will take place for these expansions The 3D MMP graphic editor automatically adjusts the orientation of expansions upon request Normal expansions need to be on the intersection of all symmetry planes because the reflected expansion can cause dependencies Matching points on the symmetry planes are not necessary and even inefficient as shown in chapter 7 45 8 7 2D Problems For 2D problems the rules for discretization and for setting poles are analogous to the 3D case 2D poles have a less local behavior logarithmic for zero orders and small arguments 1 Kp instead of 1 kr for large arguments and therefore are more exposed to the danger of dependencies On the other hand in 2D more complex models can be solved either with the 2D MMP package 4 that handles scattering and eigenvalue problems or with 3D MMP for scattering The excitation of a 2D scattering problem is often a plane wave which is oriented in such a way that it is either transverse electric or trans
116. that it enters only At or A respectively In the wrong matrix it will produce a zero column and the matrix will become singular Each plane of symmetry in which a multipole or normal expansion lies leads to a reduction of the number of its parameters by a factor of 2 But if the expansion is not properly oriented all functions are symmetrized and the expansion will enter both At and A with the full number of coefficients Because normal expansions must not be used multiply their origin has always to be on the intersection of all symmetry planes The matching points can be treated by analogy In a point and in its reflected coun terpart the values of a symmetric field are identical to a possible change of sign This results in the same equations for both points and by consequence only one has to be considered In a point on a symmetry plane several of the components are zero because of 7 7 and 7 8 and the symmetrization of the remaining components is simplified Note that it is never necessary to put a matching point on a symmetry plane cf fig 7 2 Zero rows in an overdetermined system of equations do no harm but waste computing time during updating Field points are in contrast to the matching points often lying on symmetry planes The reason is that the field is easier to interpret there due to the reduced number of non zero components However the consideration of these symmetries does not save much computational time as evalua
117. the harddisk is sufficient Last but not least the input output devices are important for graphics For 3D applications a high resolution color monitor is desirable but a monochrome monitor might be sufficient for the beginning Only 16 colors are used in the actual version of 3D MMP graphics for PCs I e more than 16 colors are not helpful Although several screen drivers for Microsoft Windows with 256 colors are available the color representation of most Windows screen drivers is worse than the one of GEM because most of the colors usually are simulated by mixing of 16 predefined colors and because the color palette of these 16 colors cannot be adjusted like in GEM However the compiled 3D MMP version included in this package runs under Windows 3 GEM versions are available upon request The 3D MMP editor and plot programs are handled entirely with a mouse A mouse with at least 2 buttons is required but 3 buttons are recommended Note that some mouse drivers of Microsoft Windows ignore the third button of a mouse In this case the third button can be simulating by pressing button 1 immediately after button 2 To get hard copies of the pictures on the screen meta files can be generated Windows itself does not include any feature for printing meta files but there are many Windows applications for example Microsoft Word for Windows that allow to read and print meta files 18 2 Transputer Add On Boards An interesting alternative for user
118. the window plane The tangential vectors are represented by simple triangles the normal components by squares in the plane of the field point A cross on the squares indicates negative values of the normal components In addition the 3D vectors can be represented in form of triangles as well Although one has a little bit more information in a triangle than in an arrow this is not really sufficient for the imagination Here one can turn on some light The shadows of the 3D triangles on the planes in the matching points have been found very helpful Unfortunately computing the shadows of a large number of objects is very time consuming especially for general plots For this reason a simplified procedure is applied that computes the shadows on infinite planes in the field points i e triangular shadows of the 3D triangles are shown even if these shadows are much longer than the size of the rectangles representing the field points For regular plots one has no difficulty to adjust the direction of the light incidence in such a way that the shadows look nice Another problem is caused by the fact that 3D arrows can be behind the plane in the field point When the plane is not invisible or transparent such arrows become invisible Similarly the shadow can become invisible Introducing a negative light source generating a negative shadow on the opposite side of the plane is an unconventional solution that requires some experience In the
119. to a certain extent nonlinear magnetic hysteresis losses Ideally conducting domains are identified by the number 0 This domain is default and must not be specified in the input file Imperfectly conducting domains with surface impedance boundary conditions are specified as ordinary domains Ideally and imper fectly conducting domains are not domains in the MMP sense i e the field within the domains is assumed to be equal to zero therefore no expansions must be made for these domains 10 5 Expansions and Excitations The expansions are specified as a list and will be inserted into the columns of the ma trix A in that same order The sequence of the functions within an expansion follows from the expressions in appendix C The excitations are simply the last of the basis functions Excitations usually are expansions with only one parameter e g plane waves or connections For multiple excitations this is necessary whereas for single excitations 54 any expansion can be used The number of excitations is specified in the first line of the input file behind the problem type number If it is omitted a single excitation is assumed Note that multiple excitations are incompatible with the Givens factorization method and with the multiple input file feature The maximum number of expansions including those within connections see below and excitations is limited to nentm the maximum number of parameters to nkolm see sections 20 3 2 and
120. to be pressed when the cursor is in the text area This will cause the line number to be increased or decreased Usually such boxes are used instead of pull boxes if only a few lines are contained Special Action Boxes Special action boxes are 1 single line boxes that cause a special action to be performed when the first or the second mouse button is pressed while the cursor is in the text area 2 a variant of selection boxes that cause a special action to be performed when the first mouse button is pressed while the cursor is in the text area To select the line displayed in the second case only the second mouse button can be used The most important box of this type is the EXIT QUIT box Hint Boxes A hint box is displayed in the center of the screen as long as the third first and second mouse button is pressed in a box on the condition that the hint files MMP_E3D xxx are correctly installed and can be read by the editor and that the program has enough memory for saving the part of the screen used to display the hint box A hint box contains some information on the actual line of the corresponding box The content of a hint box is read from the hint file MMP_E3D xxx or MMP_P3D xxx where xxx is the number of the box that has been clicked Hint files are searched first on the current directory then on MMP and finally on C MMP If the appropriate hint file is not found no hint box is shown Although the hint feature is muc
121. to show the grid lines and to deform the grid lines according to the strength of the field in the field points which leads to a very simple but impressive representation of the field e The locations of the field points can be computed and need not to be read and stored The advantage of a general plot is its generality that allows for example the visualization of the field on the surface of a body In the actual version of the 3D MMP plot program three different representations have been implemented e a general vector representation that contains several elements discussed below e a simple grid representation that can be applied to regular plots only e a grid representation with iso lines that can be applied to regular plots only In addition to the 3D plot files the 3D MMP plot program allows to read regular 2D plot files generated with the 2D MMP code 4 Of course the program is able to read both frequency dependent complex and time dependent real 2D and 3D plot files Moreover one can read and display the field in the matching points stored in general error files 155 16 4 2 Visualizing Electromagnetic Fields A 3D vector field is a complicated object that is hard to visualize especially on monitors with a limited resolution It is well known that one has at least two vector fields in electrodynamics The 3D MMP plot program allows to show up to three vector fields at a time but this is certainly too much for the imagina
122. try now the transparent mode i e the fill pattern 1 However in most cases you will prefer to display only one level at a time Note that the movie feature see section 16 8 allows to generate a movie where the field in all levels is shown successively When you have a nice picture you probably want to print it on your printer For doing that you can generate a meta file by simply running generate meta Before you do this you should select the size of the picture i e the length of the vertical side of the window in the box metav Often you want to have the content of the window only i e you want to suppress the boxes of the desk in the meta file by selecting the value O in the box meta_boxes_ Finally you should remember that your printer probably has a higher resolution than your screen Thus you can reduce the unit line width in the box linew before you generate a meta file The plot program allows to generate several meta files with different numbers that are selected in the item box Unfortunately Windows does not include an output program that allows to print a meta file Thus you need a Windows application that is able to read and print meta files For example Microsoft Word for Windows is such an application The MMP meta files usually are larger than 64kbytes and cannot be read by Word For this reason the plot program writes the meta file on the Windows clipboard as well From there Word can read large MMP meta
123. unknowns Here another consequence is much more important The 243 generate meta _ computing S field ixo E x s ie141 x y m e gt 0 ExT lcolor 3Darr 1 depth 6 000E 01 IER 1 00000E 00 x 0 00000E 00 y 0 00000E 00 z 0 00000E 00 iter part 1 lcim 0 00000E 00 tim 00E 00 part type 1 Figure 17 5 Desk of the 3D MMP plot program showing the time average of the Poynting vector field for an active thin wire fead at the center refined model with spherical endings multipoles near the endings scatterer without the antenna has more symmetry planes that can be used to reduce the number of matching points and unknowns Therefore you can essentially use model 2 For introducing the parameters of model 23 in a new model 24 proceed as follows 1 4 Copy the resulting data on MMP_3DI 024 Copy the parameter file MMP_PAR 023 on a connection file for example MMP_C23 024 with the DOS command copy Replace the incident plane wave in the 3D input file MMP_3DI 002 of model 2 by a connection with the number 23 according to MMP_C23 024 Move the origin of the connection to the place where you want to have the wire antenna more precisely the origin of the global coordinate system used in model 23 Note that the tangent vectors of the connection should point in X and Y direction and not in Y and Z direction like the incident plane wave
124. which should be about the same for all expansion functions However its definition is not quite clear It can be a global one like total radiated power or a local one like the size of the field values in the closest matching point which for multipoles depends mainly on their distance from its origin A practical reason for scaling is the interpretation of the resulting parameters c The convergence of the parameters within a single multipole can show whether the highest order is sufficient and one may want to compare different expansions by the size of their parameters Practice has shown that it is usually unnecessary to scale the columns for numerical reasons Furthermore the influence of the actual model and of the choice and location of the expansions on the condition of the matrix is dominant The numerical accuracy of the parameters plays only a minor role as the size of the residual errors gives a good control over the solution However the advantages for interpretation have been leading to the scaling of the expansions as currently implemented In the 3D MMP code scaling is done between electric and magnetic modes and between different orders and degrees within a single multipole or normal expansion For some expansion types an extra scaling factor can be specified chapter 10 and appendix C 24 4 Equations 4 1 Boundary Conditions After having the appropriate basis of expansion functions for the field we shall discuss the
125. window number in the corresponding item box and press the first mouse button when the cursor is near the lower left corner of the window Move the cursor and release the button when the window is at the desired location Make sure that the entire window is on the screen Note that the size of the window is fixed during this action Adjusting the Size of a Screen Window When you want to adjust the physical size a screen window select the window number in the corresponding item box and press the first mouse button when the cursor is near the upper right corner of the window Move the cursor and release the button when the corner is at the desired location Note that the lower left corner is fixed during this action Blowing a Screen Window When you want to blow a screen window i e adjust the physical size a screen window without changing the aspect ratio of the horizontal and vertical sides select the window number in the corresponding item box and press the first mouse button when the cursor is near the right hand side of the window Move the cursor and release the button when the window has the desired size Note that both the lower left corner and the aspect ratio of the horizontal and vertical sides are fixed during this action In Activating a Field Point Click the second mouse button when the cursor is near the point to be in activated Note that the data of this point will be displayed in the corresponding boxes Adjusting a Se
126. wire_____ Activate either all wires or only those with numbers n1 up to n2 If n2 lt n1 n2 is set to ni n1 has to be defined in the item box and n2 in the additional integer data box M If n1 is less than 1 or bigger than the number of wires that have been defined all wires are inactivated Otherwise activate_all_wires_ is asked 3D show____ points___ Activate either all points or only those with numbers n1 up to n2 If n2 lt n1 n2 is set to ni n1 has to be defined in the item box and n2 in the additional integer data box M If n1 is less than 1 or bigger than the number of points that have been defined all points are inactivated Otherwise activate_all_points is asked 3D show____ vect axis Show actual vector respectively axis that is used for different 3D constructions 113 3D show____ window___ Show window plane Before execution select the number of the window to be shown in the item box If no such window exists window NOT _defined_ is displayed Otherwise the window plane is shown graphically with a vector pointing at the origin of the plane and two vectors starting a the origin and pointing in the direction of the two tangent vectors Moreover all window data are displayed in the corresponding boxes 3D show____ parts____ Show parts of two objects With two objects you can in general distinguish four parts e the part of obje
127. with the x component and y component proportional to the electric and magnetic energy density respectively So far you do not see any vector at all although you have selected the vector rep resentation in the box gt O In fact all but one of the various objects of the vector representation are turned off To turn them on you have to modify the corresponding fill patterns in the box fill aaaa where aaaa indicates the element Of course you can turn all elements on now replace the values 4 in these boxes for example by 2 or by any value bigger than 4 and run show pic f again In most cases you will prefer not to display all elements at the same time When you do not know the meaning of the values in the fill aaaa boxes you can click the box with the third mouse button and you will get some information in a hint box Maybe you do not like the colors of the elements In this case you can select different colors in the corresponding color aaaa box Note that negative color numbers are used to suppress the drawing of the border of the corresponding element However it is certainly worth trying several different values 193 in the boxes fill aaaa and color aaaa and running show pic f again and again for getting experience Note that the last lines of the
128. works in Newton s world and the results are accurate for sufficiently small distances between the particle The particles in the plot program are characterized by the location Cartesian co ordinates in the boxes x y z the velocity Cartesian coordinates in the boxes vx vy vz the mass m0 the electric charge qe and a friction con stant fr In addition the following integer constants are used 1 The particle type 212 part type is 0 for realistic particles If this value is not zero one obtains a pseudo particle that simply follows the lines of the actual field For more information on this parameter see the corresponding hint box 2 The size part size of the particle on the screen which has no influence on the movement When a particle is outside the window this value becomes negative 3 The color part col of the particle on the screen If the field is defined on a regular grid and when a particle is outside the grid this value becomes negative and the particle will not be moved anymore 4 The trail of the particle is defined in the box part rep When this value is negative the actual time is fixed which is reasonable for drawing field lines For more information on this parameter see the corresponding hint box The friction is a f
129. xxx Select the extension number xxx in the item box When a file with the number selected in the item box does already exist you are asked overwrite_wind file 168 If this question is answered in the negative the actual window data are not saved and process_aborted__ is displayed Otherwise writing window_file is displayed during writing and window_file_saved__ afterwards If the file cannot be opened cannot_open_file__ is displayed In most cases this indicates that the disk is full write___ mmp_p Save the actual field data in the regular plot file MMP_Pyy xxx with the numbers yy and xxx selected in the item and file extension box respectively This command allows you to save the entire electromagnetic field with scalar and vector potentials or some parts only For deciding what has to be saved you are asked the following questions save_real_parts____ save_imagin _parts_ save_E H_ fields____ save_vect potential save_scal potential You can answer all questions in the affirmative for saving all data but you might prefer to answer several questions in the negative for reducing the size of the plot file write___ part Save the data of the actual particles in the particle file MMP_PRT xxx with the number xxx selected in the item box If no particles have been defined the process is stopped with the message NO_particles defined If a particle file MMP_PRT xxx does already exist you are a
130. you can proceed as indicated in the first ten examples for finding a more efficient model 17 4 2 Lossy Dielectric Sphere Model 12 Let us consider the same model as model 11 but with a lossy dielectric Because we want to keep the computation time small we reduce the frequency to 150 MHz instead of 230 increasing the number of matching points and maximum orders and we accept relatively large errors here and in the following examples If you are curious about more accurate results it is up to you to improve the models Introducing losses in the dielectric is very simple 1 Select the domain number 2 in the item box and execute the command 3D show domain l 2 Adjust the relative permittivity the relative permeability p and the conduc tivity in the boxes Er Ur and Sr 3 Run 3D adjust domain 4 Save the data on file MMP_3DI 012 and leave the editor The results depend very much on the size of the conductivity For large conductivities the fields outside the sphere tend to the fields of the ideally conducting sphere as expected It is important to note that non spherical problems with large conductivities can be very difficult to handle because of the mathematical behavior of the normal expansions used inside the bodies severe cancellations occur Fortunately in most of these cases the idealized models with ideal instead of good conductors
131. you have to define the geometry of the problem you want to compute Let us start with two rectangular electrodes on the potential 1 and 1 in free space Since all field points are to be assumed in free space after clear pic f O you have to adjust the domain numbers and scalar potentials of the field points in side the electrodes For doing this set the appropriate values in the field point data boxes i e VR 1 0 in the box containing the Z component for the first electrode and FPt_dom iF O Now press the first mouse button down when the cursor is at the lower left corner of the first electrode move the cursor to the upper right corner of the first electrode and release the button Although the electrode is not visible it already is there To verify this select V field2 and run show pic f after having selected the desired representation To define the second electrode proceed exactly as for the first one but change the potential to VR_ 1 0 Before you start the FD iteration you have to set the number of iterations to be performed for example iter fiel 20 and the field representation in the top line and in the four uppermost boxes below the top line This is necessary because generate pic f does not only iterate the field It also draws the final field When you are working in color mode the iso lin
132. you install 3D MMP read the file READ ME on the distribution diskette This file contains the latest information on the installation procedure the disk contents and on modifications that are not documented in this manual 20 1 Installation of Source and Auxiliary Files Some programs of the 3D MMP package use auxiliary files or read data from several auxiliary data files These files are searched first in the actual directory afterwards in the directory MMP of the current drive and finally in the directory C MMP Thus it is most convenient to install the corresponding files on C MMP or if you have not enogh space on drive C on X MMP where X is any drive The installation program INSTALL BAT automatically generates appropriate directories and copies the source and auxiliary files on the correct directories For running INSTALL BAT insert the 3D MMP distribution disk in your floppy drive exit Windows or click the DOS icon if you are in Windows INSTALL BAT runs under DOS and type INSTALL A X Enter where A is the source floppy drive and X is the destination hard disk drive 20 2 Installation of Windows It is assumed that you have installed Microsoft Windows version 3 0 or newer on your 386 with numeric coprocessor or on your 486 When you want to use the Watcom version of 3D MMP Windows should run in enhanced mode After having installed 3D MMP it will be convenient to start a Windows session and to add a new program group accord
133. 0 cf section 7 2 2 symmetry about this plane only the even symmetry component of the problem is considered EZ 0 Ej 4 0 cf section 7 2 3 symmetry about this plane both the odd and the even symmetry com ponents of the problem are considered Examples 3 3 0 scattering at an object which is symmetric about X 0 and Y 0 but not about Z 0 for a general orientation of the excitation 130 scattering at the same object the excitation is a plane wave polarized with E in the X direction H in the Z direction and propagation in the Y direction 120 scattering at the same object the excitation is a plane wave polarized with E in the X direction H in the Y direction and propagation in the Z direction Symmetries can also be used to introduce infinite perfectly conducting planes at X 0 Y 0 or Z 0 is1 is2 or is3 equal to 1 For definitions of the symmetries and the impacts on expansions matching points and field points see chapter 7 and the following sections 10 4 Domains Each domain is identified by an integer number igeb between 0 and ngebm The domain numbers do not have to be in sequence The properties of a general domain are declared by relative constant of permittivity cer r the relative constant of permeability cur ur and by the conductivity csig a Note that all three constants are complex a generalization that allows for some popular models of loss mechanisms such as polarization losses and
134. 0 and AY 0 7 8 is valid As a result the problem Ac b with respect to one reflective plane splits up into an even and an odd problem Atct bt and A c b A and A can be set up directly and each have only approximately half the number of parameters and equations of A The field is evaluated by summing up the symmetry components N 1 N 1 Te anr Mah 7 9 i 1 t 1 Above considerations can be superposed for three orthogonal planes of symmetry The inhomogeneity and the solution split up into eight symmetry adapted components Pa PR Le A LS 8 A eto jak ae 7 10 b bttt 4 btt 4 btt 4 ES btt bt bt b7 7 11 38 and the whole problem divides into the eight parts Atttett btt ARCH htt At ct bt At et ht ee ear eg N 7 12 A te b Die ee h Each of these symmetry adapted matrices has only one eighth of the number of rows and columns of the original problem For impact of the symmetry on the problem imagine that an MMP model is symmetric fig 7 2 A nonsymmetric expansion can be symmetrized with 7 3b and 7 3c An expansion and its reflected counterpart produce the same symmetrized functions so only one of them has to be considered Expansions with origins on the symmetry plane needs special treatment If it is properly oriented it can already be even or odd about the plane and consequently adapted to one of the symmetries It is important
135. 07 138 Dec 1981 P Leuchtmann Optimal location for matching points for wire modelling with MMP Applied Computational Electromagnetics ACES journal vol 6 pp 21 37 Dec 1991 P Leuchtmann and L Bomholt Thin wire feature for the MMP code in 6th Annual Review of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Monterey pp 233 240 Mar 1990 P Leuchtmann New expansion functions for long structures in the MMP code in 7th Annual Review of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Monterey pp 198 202 Mar 1991 J Zheng A new expansion function of gmt the ringpole in 7th Annual Re view of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Monterey pp 170 173 Mar 1991 Ch Hafner Multiple Multipole MMP computations of guided waves and waveg uide discontinuities Int J of Numerical Modelling vol 3 pp 247 257 1990 P Regli Ch Hafner and N Kuster Graphic output routines of the MMP program package on PC s and SUN workstations in 5th Annual Review of Progress in Applied Computational Electromagnetics ACES Conference Proceed ings Monterey Mar 1989 329 46 47 48 49 50 51 52 53 54 55 56 57 58 W H Press B P Flannery S A Teukolsky and W T Vetterling Numerical Recipes
136. 1 00000E 00 Figure 17 7 Desk of the 3D MMP editor program showing two different views of a circular slot in a plate of finite thickness The fictitious boundary is visible near the center of the right window Looking at the model 25 either with the editor or the plot program you may notice that its visualization is already quite difficult This is a good reason for trying the different features offered by the 3D MMP graphic programs 17 9 2 A More Fictitious Model Model 26 The multipoles in model 25 have to be placed in a sufficient distance from the fictitious boundary i e from the center of the aperture You might believe that this is the reason for the inaccurate results When you want to move the multipoles closer to the center of the aperture you can introduce for example two spherical fictitious boundaries on both sides of the aperture Thus you get three domains In the domains on both sides of the plate you can use similar expansions as in model 25 with origins of the multipoles in the center of the aperture Since the additional domain in between has almost spherical shape you can introduce a normal expansion 247 f A T f generate meta 19 ls 25 computing S field 4 no fe H s field1 Fxlylz se l gt 0 EXIT sequ M 37 langle 3 000E 01 lcolor 3Darr 1 ER 1 00000E 00 vy_ 0 000008 00 9 50000E 01 K ii z 0 00000E 00 o iter part 1 A
137. 3 in enhanced mode Although Digital Research s GEM does not seem to survive the next years it still is an interesting alternative for those who prefer working under DOS without Windows and for those who are familiar with 2D MMP Several GEM versions of 3D MMP are available upon request In addition several graphic packages for FORTRAN compilers on PCs have been tested by the authors HALO 88 NDP GREX etc The experience with these packages were not encouraging or even bad The GEM and Windows interfaces written by H U Gerber are considered to be most appropriate for our purpose 19 3 Compilers The compiled version of the 3D MMP code included in this package has been compiled with the Watcom 386 FORTRAN compiler version 8 5 for 386 or 486 based PCs This compiler does support a large number of DOS extenders including the DOS extender of Microsoft Windows 3 0 The 3D MMP code version 3 3 includes a graphic interface for Windows A GEMVDI interface for this compiler has not yet been written However this compiler is certainly the best choice for running FORTRAN codes under Windows Note that you should apply all actual Watcom patches when you want to compile 3D MMP with this compiler Moreover the 3D MMP package contains some include files WIN FI that replace the corresponding include files of Watcom because 3D MMP does not work properly with the original Watcom include files In addition to Watcom interfaces and auxiliaries for compiling
138. 3D MMP with the following compilers are available upon request e Lahey F77L3 EM 32 version 4 0 for 486 and 386 PCs with numeric coprocessor and extended memory This compiler allows to bind the OS386 DOS extender and generates excellent warnings and error messages It is actively supported by the 3D MMP package but older versions have not been tested Weitek 1167 or 3167 floating point accelerators are supported as well as virtual memory It has to be mentioned that the cheaper Lahey compilers for XT and AT compatibles have not been tested A GEMVDI interface is included in the 3D MMP package Microway NDP 860 compiler version 4 0 for the Micro Way i860 number smasher To run codes on the i860 Micro Way has included the files RUN860 EXE and RUN860P EXE when the GREX library is used Instead of Micro Way s alien file servers the MMP servers RUN860H EXE and RUN860W EXE should be used for running graphic codes with the GEMVDI interface or codes under Microsoft Win dows respectively RUN860H EXE can be used for running all non graphic MMP programs as well 269 e 3L Parallel FORTRAN compiler versions 2 0 and 2 1 for transputers and transputer networks The batch files included in the 3D MMP package are appropriate for version 2 1 and require a slight modification when version 2 0 is used The GEMVDI interface works with both versions but no movies can be generated Since it is not recommended to run graphics on add on boards with transputers
139. 5 expansion parameter Exp _IE6 expansion parameter Exp __ _ number of the actual expansion Exp nExp number of expansions For the meaning of the expansion data see section 10 5 147 When an expansion is in activated with the second mouse button in a window or with the show pole command the corresponding values are displayed in this box Change the values with the first count up and second count down mouse button in the value area of this box and perform the command adjust pole Exceptions e Exp __ _ is changed either when an expansion is in activated with the second mouse button in a window or with the show pole command e Exp nExp is changed with add pole delete pole and similar commands Since a wire is a special expansion the corresponding commands with wire instead of pole affect the values in this box as well Since objects and parts of objects contain expansions as well the corresponding com mands with object or part instead of pole affect the values in this box as well Box 15 Question Information YES Start Box Type text output response The content of this box is overwritten during program execution It is used to dis play messages give instructions ask questions and to answer these questions in the affirmative When a question is asked in this box the p
140. 7 749 july 1990 S Kiener C Hafner and L Bomholt The mmp codes a 2d and 3d package implemented on PC s in Proc ANTEM Wimnipeg Canada Aug 1990 S Kiener Pr sentation des codes MMP comparaisons et combinations avec d autres m thodes in Proc JINA 90 Nice Nov 1990 S Kiener RCS of perfect conducting or coated bodies computed by the MMP codes in Proc Workshop JINA 90 Nice Nov 1990 S Kiener Les limites du modele de Maxwell applications aux discontinuit s ge ometriques r solues par les codes MMP PhD thesis Diss ETH Nr 9336 Zurich 1990 Ch Hafner On the relationship between the MoM and the GMT IEEE AP S Magazine vol 32 Dec 1990 Ch Hafner and N Kuster Computations of electromagnetic fields by the multi ple multipole method Generalized Multipole Technique Radio Science vol 26 pp 291 297 Jan 1991 P Leuchtmann and Ch Hafner Ersetzt das Feldberechnungsprogramm den EMV Spezialisten Technische Rundschau vol 83 pp 48 51 Mar 1991 Ch Hafner On the implementation of FE and GTD concepts in the MMP code Archiv fiir Elektronik und Ubertragungstechnik vol 45 Sept 1991 Ch Hafner The MMP code for computational electromagnetics on personal com puters SIAM J Sci Stat Comp vol no 1991 Ch Hafner L Bomholt and P Regli Simulation of electrodynamic fields on small computers Seymour Cray Wett
141. 988 996 Sept 1985 A R Djordjevi and T K Sarkar A theorem on the Moment Methods IEEE Transactions on Antennas and Propagation vol 35 pp 353 355 Mar 1987 A Ludwig A comparison of spherical wave voundary value matching versus inte gral equation scattering solutions for a perfecly conducting body IEEE Transac tions on Antennas and Propagation vol 34 pp 857 865 July 1986 337 164 M F Iskander A Lakhtakia and C H Durney A new procedure for improving 165 166 167 168 169 170 171 172 173 the solution stability and extending the frequency range of the EBCM IEEE Transactions on Antennas and Propagation vol 31 pp 317 324 Mar 1983 P C Waterman Matrix formulation of electromagnetic scattering Proceedings of the IEEE vol 53 pp 805 812 Nov 1965 R L Branham Jr Are orthogonal transformations worthwhile for least squares problems SIGNUM Newsletter vol 22 pp 14 19 Jan 1987 R F Harrington Matrix methods for field problems Proceedings of the IEEE vol 55 pp 136 149 Feb 1967 D S Jones A critique of the variational method in scattering problems IRE Transactions vol AP 4 no 4 pp 297 301 1956 T B A Senior Diffraction by an imperfectly conducting half plane at oblique incidence Applied Scientific Research B vol 8 pp 35 61 1959 T B A Senior Impedance boundary conditions for sta
142. Books 1990 G Klaus 3 D Streufeldberechnungen mit Hilfe der MMP Methode PhD thesis Diss ETH Nr 7792 1985 P Leuchtmann Automatisierung der Funktionenwahl bei der MMP Methode PhD thesis Diss ETH Nr 8301 1987 J Sroka H Baggenstos and R Ballisti On the coupling of the Generalized Multipole Technique with the Finite Element Method in IEEE Transactions on Magnetics vol 26 Tokyo pp 658 661 Mar 1990 7th COMPUMAG Confer ence Sept 1989 N Kuster G Klaus and Q Balzano The SAR and field simulation of radios held by man calculated with the MMP method in Proc of the 10th Annual Meeting of the Bioelectromagnetic Society Stamford June 1988 Ch Hafner and R Ballisti Electromagnetic field calculations on PC s and work stations using the MMP method IEEE Transactions on Magnetics vol 25 pp 2828 2830 July 1989 Third Biennial IEEE Conference on Electromagnetic Field Computation Ch Hafner and L Bomholt Implementation and performance of MMP programs on transputers in 5th Annual Review of Progress in Applied Computational Elec tromagnetics ACES Conference Proceedings Monterey Mar 1989 N Kuster and R Ballisti MMP method simulation of antennae with scatter ing objects in the closer nearfield IEEE Transactions on Magnetics vol 25 pp 2881 2883 July 1989 Third Biennial IEEE Conference on Electromagnetic Field Computation N Kuster and R Tell A dos
143. Cholesky frequency 1 single frequency 2 multiple frequency Fourier transform input file number xxx xxx lt 0 input files xxx 0 nome Fourier Tr XXX gt 0 single input file xxx The first two lines are suppressed when a single processor is used Otherwise xxx indicates the number of processors that have been found Usually the working directory is the current directory and aaaaa is a blank string Since Microsoft Windows does not allow running an application from any directory the Windows version of the 3D MMP codes allow to add the path of the working directory to the command line In this case aaaaa is equal to this string and indicates where the program looks for input files and writes output files On PCs the following questions have to be answered interactively on UNIX systems the options can also be entered on the command line tasks This option specifies what the program shall do The various tasks can be combined and put into a single integer number e g 124 for a computation of the parameters subsequent calculation of the errors and of a plot In multiple frequency runs see below these choices will be executed for each of the frequencies i e 124 for the first frequency 124 for the second frequency and so on Upon completion the program will restart and be ready again for new tasks until you explicitly exit with option 0 The exit option can also be used with the other task options e g as 1240 In the cas
144. E Awe a eee OO Bee ee A 176 TO OI Tadjustes is Fake GS oh hee pa 176 LOIT clear co ay tie ae i a is e ta a ct es a 179 16 6 Summary of Boxes 2 0 0 2 eee 180 16 7 Selecting Appropriate Field Representations 192 16 8 Movies and Slide Shows 2 2 20 0 00000000000 000 2 196 16 8 1 Introduction s ecs ae naea ee ee RD ee eee 196 16 8 2 Directive Files lt lt aa 197 16 8 3 Generating the Movie o 00000 203 16 8 4 Movies with Several Windows 00 0 204 16 8 5 Error Messages e atea cor ee a Ra a Et ee T g 205 16 8 6 Starting and Stopping a Movie o o 205 16 8 6 Slide SHOWS 0d re ato e Yee EE ea a Se Boe 206 16 9 Iterative Procedures ee ee ee 206 16 9 1 Initializing the Field 0 o 207 16 9 2 Defining and Starting an Iteration 207 16 9 3 Writing New Algorithms o a 210 16 10Moving Particles and Field Lines o o 212 IV Tutorial 215 17 Tutorial 216 17 1 Introduction aea a de a ee wee a 216 17 2 Ideally Conducting Sphere with Plane Wave Excitation 217 17 2 1 Your First MMP Problem Model 0 217 17 2 2 Introducing Symmetries Model 1 0 o o o o 221 17 2 3 Changing the Discretization Model 2 224 17 3 Ideally Conducting Sphere with Dipole Excitation 225 17 3 1 The Basic M
145. EG Vind Kp sin my e C 19b p EFD k Jm Kp cos mo e C 19c s 1 HE E nJm xp sin my e7 C 19d p 292 a HE E mm 150 504 m31 Kp cos mp e C 19c P HEmn 0 C 19f For the magnetic transverse electric modes Hmn m gt 0 and n gt 1 K a po 1 ann is the n th zero of E Im Kp Elim m6 sin my e C 20a purer EE m4 rp kpJm 1 5p cos mo e C 20b EE 0 C 20c Aen gt mJ rp kp Jm i Kp cos my e C 20d ny mom sin my e C 20e H Hmm k J xp cos my et C 20f Symmetries are the same as for the 2D expansions Ecm and Hem but are not implemented The magnetic modes are scaled with the inverse of the wave impedance C 6 Plane Wave The plane wave expansion is mostly used as excitation E e C 21a Hg E C 21b It is odd with respect to x 0 and even to y 0 The expansion can be scaled with sca section 10 5 C 7 Evanescent Plane Wave The evanescent plane wave is a solution in Cartesian coordinates more general than the plane wave The electric mode is BE eilkyytke2 C 22a H Ez ilkyythe2 C 22b wp HE Y uva C 22c wp 293 and the magnetic mode E _ he gilkyythe2 C 23a WE El Es gilkyythe2 C 23b WE HOD eilbuuthe2 C 23c ky is the y component on the complex wave vector and can be specified the longitudinal component k is obtained from k k2 k For ky 0 th
146. If a file MMP_Iyy xxx is missing the infor mation is assumed to be in the file MMP_Iyy 000 Only one file MMP_Iyy 000 is generated for a movie yy whereas a MMP_Iyy xxx is generated for each slide single picture of a slide show yy The parameters in brackets are missing in the information files for slides nPic nSeq number of pictures number of sequences of a movie ix0 iy0 width height pixel coordinates of lower left corner width and height in pixels il n number of pictures in the different sequences movies only 304 D 21 Picture File MMP Fyy xxx Pixel information of picture part of the screen xxx of a movie or slide show yy The corresponding information files MMP_Iyy xxx are described below D 22 Windows Meta Files MMP_Eyy WMF and MMP Pyy WMF Windows meta files with graphic data generated by the 3D MMP editor and the 3D MMP plot program respectively They contain graphic data that can be reprocuced on any ouput device with full resolution using an appropriate Windows application D 23 Main Program Log File MMP_M3D LOG The amount of output on the log file of the main program depends on the value of iof in the input file The contents of the output file are described in chapter 11 D 24 Editor Log File MMP_E3D LOG Data on the actions that have been performed during a 3D MMP editor session The current version of the 3D MMP editor writes no data on this file D 25 Plot Program Log File MMP_P3D LOG Data on the ac
147. Move active expansions 15 7 6 3D blow____ Perform different deformations on the expansions or matching points As many of them require some experience before they are helpful it is certainly a good idea to store the 3D write file before executing points or expansions including wires and objects the procedure is the following the distance of the matching points or expansions from objects with the command 3D blow e a given point i e the start point of the axis that can be defined with e the axis For matching 3D adjust vect axis e the plane of the current window i e the window that is clicked in order to start the action is multiplied with a function that depends on the blowing type and on a quantity called blowing distance Thus in addition to the blowing factor that is selected in the box and ang Currently the following types are implemented where f is the blowing factor box Type Blow Function o 1 14 1 e 2 1 4 E De 0 3 f r 4 1 x fac d an additional parameter box ang fac the blowing type and the blowing distance have to be selected in the boxes M and r the distance of the matching points or expansions from the point axis or plane 124 respectively For the types 1 and 2 d is the blowing distance When r is larger than d th
148. ROR_set_particle_ Note that you have not only to select the data defining the representation of the field but also the data defining the iterative procedure i e the values in the boxes tim dt Tmx iter aaaa etc When iter fiel is bigger than 0 the field will be iterated exactly as in the command generate pic f Electrically charged particles are not only affected by the interactions gravitation and Coulomb force between the particles but also by the given field If the number ipic mov is bigger than 1 a movie with as many pictures as indicated in this box is generated automatically The movie number is selected in the item box movie When such a movie does already exist you are asked overwrite movie____ If you do not want to overwrite the existing movie answer in the negative and the process is aborted with the message movie_not_generated When you do not generate a movie the process does not stop as long as one of the particles is inside the window and you have to stop the process manually by keeping the first mouse button pressed down If a regular grid is given the field is interpolated between the grid lines Since the interpolation fails if a particle is outside the grid a 174 particle is no longer moved as soon as it is outside the grid This is important when you want to study the interaction o
149. The 3D Electrodynamic Wave Simulator 3D MMP Software and User s Guide Christian Hafner Lars Henning Bomholt 1993 Contents Preface I Theory 1 Theory of Trial Methods 1 1 Boundary and Domain Methods o e e 1 2 Error Method lt a A a e a ee N 133 Projection Method ur a Ble 8 a ue A 1 4 Generalized Point Matching Method o o 1 5 Comparison of the Methods 00002000004 2 Fundamentals of 3D MMP 2 1 Scattering Problems ieee 3 40 e0 se4 dor wie ed laa ae a s 2 2 Field Equations cs lala oi Ge ee PG ee Oe AO eS G 2 3 Choices for the 3D MMP Code 0 0 00 4 3 Expansion Functions 3 1 General Remarks 2 2 2 20 sa ee a ke a ee a 3 2 Solutions by Separation of the Helmholtz Equations 3 3 Solutions by Integration 2 00 00 0000000000008 OA CONNECHIONS 2 cused SR Ye has A SS eee ee ee Re ee 3 5 A de Based Cols GO ade eect ok the dS kG ae as 4 Equations 4 1 Boundary Conditions 0 0 0 0 000000000 4 2 Perfectly Conducting Surfaces 2 ee 4 3 Imperfectly Conducting Surfaces o a 4A Constraints co a n A les ok E a a a 4 5 Weighting or E eases da Se hee Ah A 5 Solving the System of Equations 5 1 General Remarks 022 ee ee 5 2 Solution with Normal Equations e o 5 3 Solution with Orthogonal Transformations o DL Exact EQUabiONS a a Ae ee Me tad 9 9 Par
150. Thun und Frankfurt am Main Van Nostrand Reinhold Company New York 3rd ed 1985 L Collatz Numerische Behandlung von Differentialgleichungen Springer Verlag 1951 R F Harrington Field Computation by Moment Methods New York Macmillan Company 1951 T K Sarkar A note on the variational method Raleigh Ritz Galerkin s Method and the method of least squares Radio Science vol 18 pp 1207 1224 Nov 1983 T K Sarkar From Reaction Concept to Conjugate Gradient Have we made any progress IEEE AP S Newsletter vol 31 pp 6 12 Aug 1989 J A Stratton Electromagnetic Theory McGraw Hill 1941 J D Jackson Classical Electrodynamics John Wiley amp Sons 1962 D S Jones Acoustic and Electromagnetic Waves Oxford University Press 1986 P Moon and D E Spencer Field Theory Handbook Springer Verlag 2nd ed 1988 I N Vekua New Methods for Solving Elliptic Equations North Holland Publishing Company Amsterdam John Wiley amp Sons New York 1967 Y Leviathan and A Boag Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model IEEE Transactions on Antennas and Propagation vol 35 pp 1119 1127 Oct 1987 Y Leviathan A Boag and A Boag Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies theory and numerical solution IEEE Transactions on Antennas
151. ____ Generate 3D multipoles automatically or semi automatically Select the type of the pro cedure to be performed in the item box the desired overdetermination in the additional integer data box over and the domain number in the box Domain t The restriction of the procedure on one domain only is advantageous in complex cases If the type of the pole setting procedure is 0 the curvature of the object in all active matching point is evaluated and a pole is set according to the curvature The maximum orders of a multipole depend on the number of the correlated matching points and on the overdetermination of the system of equations The latter has to be selected in the additional integer information box over before the command is executed Afterwards the pole is tested If errors are detected the pole is deleted Note that poles that have been defined earlier can be deleted as well if they do not pass the testing procedure Thus if you want to set poles that violate the rules you have to do this after running the automatic pole setting procedure If the type is bigger than 0 one pole is generated for each active matching point that is not yet correlated with an existing pole like when the type is 0 but the distance of the pole from the matching point is not computed from the curvature but from the size of the tangent vectors in the matching point and from the type number The larger the type number the larger the distance be
152. a wire expansion type 101 Note appropriate matching points can be generated directly when a wire is added with the command 3D add wire 3D generate parts____ Generate parts of two objects With two objects you can in general distinguish four parts e the part of object 1 inside object 2 e the part of object 1 outside object 2 e the part of object 2 inside object 1 e the part of object 2 outside object 1 3D generate object Generate a 3D object by 1 translating a 2D construction along an axis 2 rotating it around the axis and 3 translating each point in the direction perpendicular to the axis This command uses the matching points and expansions of the actual 2D construction the axis and four real values that have to be selected in the boxes ang len drad and fac It 1 translates all 2D matching points and expansions along the axis up to a maximum distance len 2 rotates all 2D matching points and expansions around the axis with a maximum angle ang 3 translates each matching point and expansion perpendicular to the axis up to a maximum distance drad The ratio of the lengths of the tangent vectors of the matching points is defined by fac Moreover multipoles that are located near the axis are moved on the axis Since you might have forgotten to adjust the axi
153. ack side Moreover it can fail in special cases when the boundary is not smooth enough In such cases you should add dummy matching points with zero weight pole_order_too_big_ The order of the pole should be reduced Instead one can reduce the overdetermination in the box over If this is done all poles should be adjusted according to the new value of over pole_order_too_small The number of orders is zero Such a pole does not define an expansion function and can be eliminated Instead one can increase the maximum order of the pole poles_are_dependent The pole is too close to the poles that are connected graphically with this pole Slight dependences can be tolerated but in general it is recommended to try to remove depen dences by moving one of the dependent poles number_out_of_range The number of the pole that should be tested is either less than 1 or bigger than the maximum number of poles I e no such pole has yet been defined 15 7 10 3D adjust__ Adjust data of 3D elements For safety reasons you are asked adjust_elements_OK_ when you try to adjust anything Answering this question in the negative will abort the process with the message process_aborted____ Most of the 3D adjust commands are used to change adjust the additional real and integer data of 3D elements for example the domain number of an expansion The actual data are displayed in the corres
154. actual version of the 3D MMP plot 3D vectors can be represented with the following elements in each field point see fig 16 2 e an arrow representation with length proportional to vector e a rectangle indicating the field plane with fill pattern indicating the length of the field vector if desired a triangle representing the tangential part of the vector in the plane of the field point e a square representing the normal component of the vector with respect to the plane of the field point e a 3D triangle representing the 3D vector the shadow of the 3D triangle 157 Of course it is convenient to use different colors for the different elements Unfortunately colors reduce the speed of movies too much on todays PCs f T I F z i generate meta _ 2 2 computing H field _ iNo E H fieldl Ely Tz mM p gt 0J EXIT at Ae part type 1 Figure 16 2 Desk of the 3D MMP plot program showing some test points All repre sentation types and the manager representation see below are turned on Near the center one can see two field points with 3D arrows shadow quadrangle for the normal component and triangle for the tangential part of the vector In most of the other points one cannot see all these elements The values of fields in different points can vary considerably As a consequence one has either some very small elements representing the small vectors or very large elemen
155. ad of performing steps 3 4 and 5 adjust the number of matching points and continue with step 6 Of course the 2D construction of a single arc with a single multipole is not time consuming Thus saving and restoring 2D data does not save as much time here as in the case of more complicated constructions Maybe you would like to visualize the scattered field only This requires a slight modification of the parameter file MMP_PAR 001 and a recomputation of the plot file task 4 in the main program To modify the parameter file you can use any text editor For getting some more information you might prefer to run the parameter labeling program first As you can see when you are editing MMP_PAL 001 some information has been added to the lines of the blocks containing the parameters Because of the symmetry number is1 3 there are two parameter blocks Both contain the incident plane wave in the bottom line The corresponding complex number pairs are 1 0 0 0 If you replace the values 1 0 by 0 0 you virtually eliminate the incident plane waves and get the scattered field only when you run the main program with the modified parameter file Finally copy back the modified parameter file to MMP_PAR 001 Since you know that the parameter of the incident wave is on the bottom lines of the parameter blocks you can also modify MMP_PAR 001 directly without running the parameter labeling program before If you want to get some more insight in the 3D MMP code
156. ain number defined in the box F pt dom is used for all field points when it is positive In this case the domain numbers defined in the different field points are ignored in the 3D MMP main program i e the questions above are irrelevant Both the number of general plot files i e sets of field points and the number of field points per set are defined in the include file MMP_E3D INC If the corresponding values are exceeded one of the messages too_many_field_pts_ too_many_points___ is displayed and the process is aborted Note that the matching points required to generate a set of field points are not deleted automatically when this command is executed If they have solely been created for generating a set of field points you have to delete them Since general plots are a memory consuming feature at least the number of sets of field points usually is quite small in the editor In the main program the field points need not to be stored For this reason the number of general plots is quite large i e 50 in the main program Essentially the same holds for constraints and integrals 3D generate integrals Generate integrals from a set of matching points An integral essentially consists of a type and of one or several integral points The geometric data defining a integral point is exactly the same as the one defining a matching point In order to simplify the code integral points cannot be manipulated like m
157. aling factors 2 stop the command as soon as the drawing starts 3 Set the level number 1 and run show pic f without new scaling factors If you answer the question compute_new_scaling in the negative the field computed in the upper levels remains unchanged and can be used by the procedure that moves the pseudo particles 4 Save the background with write pic f 257 Note that move part 1 moves the first particle only This allows to watch the drawing of the different lines separately For drawing all lines at the same time the particle number must be out of range i e less than 1 or bigger than the total number of particles 17 14 Electric Charges Model 32 After having used pseudo particles you probably want to see how realistic particles might behave The particles implemented in the plot program can have a mass and an electrical charge Moreover you can define a friction constant for each particle and you can characterize the particles by different colors on the screen The particle data including the position and velocity are contained in the two boxes near the bottom of the desk You have to define them before you add a particle with add part Note that only non relativistic particles have been implemented in the actual version of the plot program I e the mass is a constant and the interaction between the particle has no time delay it is computed fr
158. allelizatione 0 it a A Gp A E a A ae oe ee 6 Evaluation of Results 6 1 Residuals and Errors a a a aa 6 22 Pield o p a E Bote Sd A id aa E ey 6 3 Integrals tass ag 2 de a sd a SA G a aTi A 7 Symmetries 7 1 Boundary Value Problems and Symmetry o 7 2 Reflective Symmetries in the 3D MMP Code 8 Modeling and Validation 8 1 General Remarks e 8 2 Discretizing the Boundary e 8 3 Multipolesi odo sos rr a 2 Eee es 8 4 Normal Expansions 0 000 eee ee A A NN 8 6 Symmetries E FAA he Ga E DT 221 Problems ads a es ae ee Ge daa dl oe ee ee 8 8 Validation 3 2 ans Sone ee OR Be ee ae PS PS Ae eee 8 9 Improving a Model odio ae eR ee ee A ad II User s Guide of the Main Program 9 Running the Main Program 951 Introductions n si 2 pe a eas Pe bie Oo Ra Ae OE Re ey 92 Programi Start ud ti dd de RO ee ae 10 Input 10 1 General Remarks o 0 0002 cee eee eee 10 2 Coordinates and Geometric Tolerances o o 10 3 General Data sc sacra a nth od ee A Rae Ge GAS ok 10 3 Type f Problem oiee eA vane A A Ee aes 10 3 2 Output on Screen and Output File 10 33 Frequency eii ee o al A ee 10 3 4 Symmetries sosna aa a e e a A ee 104 DOMAains x bos ce a a a a ad 3 10 5 Expansions and Excitations 0 0 002000022 eee 10 6 Matehing Points x costa Sai hae ee le ew ee a BS ee ees 10 7 Constraints
159. ally represented and manipulated graphically Thus graphical constructions are included in the 3D adjust window command For graphical constructions it is helpful to use the same planes in the first two windows and to perform the constructions in these windows only even if several windows have been added If you did forget to reset the planes in the first two windows XY plane in window 1 and XZ plane in window 2 you have the 131 chance to do this by answering the question reset_planes_1 2__ in the affirmative If a screen window with the number selected in the item box exists the question adjust_corners_____ is displayed This allows to adjust the lower left and upper right corners of the screen window i e its physical size This can either be done by the values in the boxes ix11 iyll ixur and iyur or by a manual discretization of the corners If the question set_corners_manual If you answer this question in the affirmative you will have to set the lower left and the upper right corner of the window manually by pressing one of the mouse buttons when the cursor is at the desired location of the lower left corner and releasing it when the cursor is at the desired location of the upper right corner According to that adjust_window_corn is displayed If you do not want to set the corners manually the information in the integer data boxes ix11 iy11 etc is used If
160. and subsequently use the solution within the disturbed problem than modeling and computing the whole disturbed problem e Successive Improvement The error in a problem can be minimized in one ore more subsequent computations using previous results as excitation An advantage 23 is that there are no direct dependencies between expansions at the various levels of iteration as might be the case if all would be used at the same time e Splitting Problems Many problems can be split up into several almost inde pendent parts The parts may have a higher symmetry than the problem as a whole 3 5 Scaling The range of numbers which is used by a particular expansion depends on the unit system on the type of the expansion and its mathematical functions and on the way it is used within a model In order to compensate for this an expansion function f may be scaled with a scaling factor s fi gt sf 3 5 which is equivalent with a column scaling of aji There are several reasons for doing this From the numerical point of view scaling influences the condition number of the matrix and therefore the accuracy of the solution However no general scaling technique based on the values of the matrix elements alone is known to improve the condition number in all cases In our implementation an additional difficulty is that not the entire matrix aji is known at a time cf chapter 5 A common way out is to scale for a physical significance
161. and Propagation vol 36 pp 1722 1734 Dec 1988 328 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 T B A Senior Impedance boundary conditions for imperfectly conducting sur faces Applied Scientific Research B vol 8 pp 418 436 1960 J J Dongarra C B Moler J R Bunch and G W Stewart LINPACK User s Guide SIAM 1979 G H Golub and C F Van Loan Matriz Computations Johns Hopkins University Press 2nd ed 1989 C L Lawson and R J Hanson Solving Least Squares Problems Prentice Hall 1974 Ch Hafner Parallel computation of electromagnetic fields on transputers IEEE AP S Newsletter pp 6 12 Oct 1989 A Fassler Application of Group Theory to the Method of Finite Elements for Solving Boundary Value Problems PhD thesis Diss ETH Nr 5696 1976 P Leuchtmann Group theoretical symmetry considerations by the application of the method of images Archiv fiir Elektronik und Ubertragungstechnik vol 36 pp 124 128 Mar 1982 E Stiefel and A Fassler Gruppentheoretische Methoden und ihre Anwendung Stuttgart B G Teubner 1976 Ch Hafner and P Leuchtmann Gruppentheoretische Ausniitzung von Symme trien Teil 1 Scientia Electrica vol 27 pp 75 100 Sept 1981 Ch Hafner R Ballisti and P Leuchtmann Gruppentheoretische Ausntitzung von Symmetrien Teil 2 Scientia Electrica vol 27 pp 1
162. and a normal expansion for the coating in the center Although you can try using different matching point distributions for the inner and outer boundary of the coating and different maximum orders and degrees for the multipole and for the normal expansion Since there are already many parameters in this model you should at least start with the same number of matching points for both boundaries of the coating and with identical maximum orders and degrees for all multipoles and normal expansions In this case you don t need to start with a 2D construction instead simply proceed as follows 1 Read a 3D model with a single sphere for example model 14 2 Add a domain 3 for the coating and adjust the material properties of domain 1 space outside the coating and domain 2 inside the sphere 3 Adjust the data of all matching points of the sphere the domain 1 must be replaced by 3 because the sphere is now surrounded by the coating rather than by free space 4 Copy the matching points of the sphere on themselves with the command 3D copy points You now have two objects with an identical set of matching points 5 Blow the object 2 with the desired factor for example 1 2 The blow command con sists of several different procedures that can change the geometric shape of an ob ject Here only the most simple one is used I e you can start 3D blow object as soon as you have selected the blow factor 1 2 in
163. and field values is negligible compared to the time needed for determining the unknowns 6 1 Residuals and Errors The error distribution on the boundary is an important aspect in estimating the quality of the result see chapter 8 More useful than looking at the residuals of the field components is to introduce one single error value py for a matching point k on 0D as an indicator for the mismatching in this point It is the average of the residuals defined by the boundary conditions 4 9 1 le Et El a 2 Pr 6 f Ter T z Ej H z Ej ij 6 1 pH HP i j i Aa Ss zzy MAL y Jer at Hi Hi pin F and for perfectly conducting surfaces with the boundary conditions 4 10 respectively 1 4 12 i 2 12 pe 5 Bisl Zeal z 203 6 2 Tk For surface impedance boundary conditions the error is 2_1 i i i i Pk gt Es Zj Hio F Eve a Z H 1 6 3 Tk In points with reduced boundary conditions only the matched components are averaged Note that the weight wz defined in 4 8 does not affect the error value Otherwise a denser discretization would reduce the error due to the smaller surface elements If the original matrix a s is not stored for saving memory the rows have to be re computed In addition to the original matching points the error may also be determined between them However in case of overdetermined systems of equations the err
164. and inplot for the regular plot window Single field points section 10 8 and integral points with the exception of those in constraints section 10 7 are not read in at the start of the program but as required by the corresponding subroutines Therefore their number is not limited On the other hand if those points are used several times during a run the file position in the input file has to be reset inpar and outpar read and write parameter files A group of LOGICAL variables linpin to lefpin controls which parts of the input and parameter file have already been read 13 5 2 Output Messages about the progress of the program are written by messag to the screen and to the output file The messages are coded with the FORTRAN parameters ms in file comm inc The array of logical variables mslev controls whether routine messag shall be called depending on the amount of output defined by msscr and msfil in the input file Errors and warning messages are processed by mmperr Depending on the param eter ierloc the message is treated either as a warning only upon which execution is continued or as a fatal error upon which execution is stopped The output file MMP_M3D LOG is opened by messag or mmperr as soon as needed If possible the output of successive runs is appended to old output files in order to keep information on previous runs Other output such as writing MMP_ERR xxx MMP_INT xxx and the plot files is done by the respective
165. and your Windows manual 216 17 2 Ideally Conducting Sphere with Plane Wave Ex citation 17 2 1 Your First MMP Problem Model 0 The most simple case is the ideally conducting sphere see fig 15 1 because this allows to reduce the number of boundary conditions and because there is only one domain with a non zero field outside the sphere To generate an appropriate 3D MMP input data file it is most convenient to invoke the 3D MMP editor by double clicking the corresponding icon As soon as you have done this the graphic screen should appear In the center of the screen a hint box should give you some more information If this hint box is missing the corresponding hint file is missing or the real memory is not sufficient for storing the pixel information of the desk behind the hint box Although this is not a serious problem it might indicate that you should try running the code with another screen driver The hint box is removed as soon as any of the mouse buttons is clicked The program initializes now some parameters and displays ready_with_defaults in the box near the center of the top line Now you can move the cursor with the mouse to any location of the screen It is most reasonable to do the following steps now although an experienced user might omit some of them 1 Check the predefined values in the additional real and integer data boxes ang 3 600E 02 and M 5 For doing this move the cursor in the text a
166. answered in the positive the window plane can be adjusted The construction is the same as in the add wind command If the question adjust _window_data_ is answered in the positive the data contained in the different window data boxes is entered It is strongly recommended to use the command show wind before the data in the boxes are adjusted Otherwise there is a good chance that you forget to modify some of the values appropriately and get unexpected results Moreover the command write wind is certainly helpful for unexperienced users Needless to say that no_such window ____ indicates that no plot window with the number selected in the item box exists 178 adjust__part Adjust the data of the particle selected in the item box If the number is out of range NO_such_particle___ is displayed Otherwise you are asked set_r v_manually___ and you can continue as described in the add part command adjust__dom _ Adjust the data of the domain selected in the item box If the number is out of range NO_such_domain_____ is displayed 16 5 12 clear__ clear__ pic f Clear the field values and set new values depending on the value selected in the item box You are asked keep_old_grid____ If you answer in the positive the number of grid lines and levels the domain numbers and the actual time are left unchange
167. art it as any Windows application For more information see the 3D MMP user s guides and your Windows manual Note that the input and output files except the hint and desk files of the 3D MMP programs are stored on the directory given as command line parameter When no com mand line parameter is specified they are stored on the same directory as the MMP programs themselves which is certainly not convenient When you want to change the directory for storing the data files you will have to change properties of the MMP icons according to your Windows manual Note that the procedure of moving the icon of a data file on the icon of the application is not useful because the MMP programs use several data files at the same time Moreover the file handling of the actual MMP version is different from the one of typical Windows applications The MMP programs do not allow to change the directory or to search files 276 If you have a transputer board inyour PC and if you have compiled 3D MMP with with 3L parallel FORTRAN you can run the resulting code with the afserver delivered with 3L parallel FORTRAN under DOS For running the main program type AFSERVER C MMP3D 3LF MMP _M34 B4 0 1 provided that you store the compiled parallel version on the directory C MMP3D 3LF Note that the alien file server AFSERVER EXE is delivered with the 3L FORTRAN com piler The switch o 1 causes the code to run slower but it is necessary when the on
168. ary of the domain of this pole Check the domain numbers of the pole and of the lines and arcs defining the boundary pole_inside_dom_xx_ A pole is inside the domain This is only reasonable if this pole is used to simulate a small antenna for example a dipole in the domain Otherwise adjust the domain number of the pole or of the lines and arcs defining the boundary of this domain Note that the automatic detection of the domain number used in the MMP programs requires oriented boundaries first domain number of lines and arcs on the left hand side and second domain number on the right hand side of these elements Moreover it can fail in special cases when the boundary is not smooth enough In such cases dummy matching points may have to be added pole_near_sym plane A symmetry plane has been defined at least one of the symmetry numbers is1 is3 is not equal to zero and the origin of the pole is close to but not within this plane This may cause numerical dependences with its symmetric counterpart cf 8 6 To avoid this move the pole away from the symmetry plane or exactly on the symmetry plane Note that this is done automatically when a 3D element is generated out of a 2D construction pole_order_too_big_ Reduce the order of the pole or the value of the overdetermination in the box over If you do the latter all poles should be adjusted according to the new value of over pole_order_too_small The number of orders is zero Such
169. asked rotate_elements_OK_ when you try to delete any element If this question is answered in the negative nothing is deleted and process_aborted____ is displayed 107 Before execution set the angle of rotation in the additional real data box angle in degrees set_center_in win1_ tells you to define the start point within the first window by pressing the first mouse button and releasing it when the cursor is at the position of the center The coordinates Ly and Yw Of the cursor are displayed in the first two boxes of the bottom line 2D rotate_ line_____ Rotate active lines and arcs 2D rotate__ arc______ Identical with 2D rotate line see above 2D rotate__ window___ See 3D constructions 2D rotate__ object___ Simultaneously perform 2D rotate line see above and 2D rotate pole see be low 2D rotate__ pole_____ Rotate active expansions 15 6 8 2D invert__ Invert active elements i e change directions For safety reasons you are asked invert_elements_OK_ when you try to invert any element If this question is answered in the negative nothing is deleted and process_aborted____ is displayed 2D invert line__ Invert the direction of active lines and arcs Since the domain number one defined in the box MPt domi is on the left hand side and domain number two defi
170. atching points Instead the matching points of one or both objects can be used to generate a set of integral points for generating an integral If such a set does already exist when the command 3D generate integrals is executed you can either add the matching points to the existing integral points or replace the existing integral points by the matching points Thus you are asked first add_to_existing pts Answering this question in the negative will cause the question replace_exist _pts_ If this question is answered in the negative as well nothing is done and process_aborted___ is displayed In order to decide whether the matching points of the first the second or both objects shall be used to generate the field points of an integral the questions use_objects_1 2___ use_object_1_only__ use_object_2_only__ are asked If all three questions are answered in the negative nothing is done and process_aborted___ is displayed Both the maximum number of integrals and the maximum number of field points per integral are defined in the include file MMP_E3D INC Since integrals are a time and memory consuming feature of the MMP code both numbers usually are quite small If they are exceeded one of the messages too_many_integrals_ 139 too_many_points___ us displayed and the process is aborted Note that the matching points required to generate a set of field points are not deleted automatically when this command is exec
171. ate a model with the 3D MMP editor that is much too large for being computed with the compiled version of the main program included in this package For computing such models a 386 or 486 usually is too slow But you easily can transfer the input files generated on your PC to a bigger machine where you can compile and run a larger version of the main program Instead of this you might prefer to use appropriate add on boards for your PC G 5 Graphic Plot Program mmat 5000 maximum number of matching points mpol 1000 maximum number of expansions mdom 100 maximum number of domains mwind 50 maximum number of plot windows mfpt 10000 maximum number of field points mprt 100 maximum number of particles Note that the number of particles can be limited to less than mPrt 100 by the graphic system because the space on the screen occupied by each particle must be saved on a bit map 326 Bibliography 12 13 A Ludwig A new technique for numerical electromagnetics IEEE AP S Newsletter vol 31 pp 40 41 Feb 1989 Ch Hafner Beitr ge zur Berechnung der Ausbreitung elektromagnetischer Wellen in zylindrischen Strukturen mit Hilfe des Point Matching Verfahrens PhD the sis Diss ETH Nr 6683 1980 Ch Hafner The Generalized Multipole Technique for Computational Electromag netics Artech House Books 1990 Ch Hafner 2 D MMP Two Dimensional Multiple Multipole Analysis Software and User s Manual Artech House
172. atically defining the domain numbers of all field points Thus you can use the 3D MMP editor for generating an appropriate model When you want to compare the FDTD solution with an MMP solution you already have such a model But there are some difficulties to recognize 1 The incident wave in the FDTD algorithm always travels in X direction whereas the incident wave of 3D MMP can travel in any direction in model 29 Y direction 2 The incident wave of 3D MMP can be much more general than in the FDTD algorithm of the plot program Thus a comparison is impossible in some cases 3 The Fourier programs of the 3D MMP package handle repeated pulses whereas the FDTD procedure works with a single pulse only I e one can expect a good agreement when the time difference between the pulses is much bigger than the duration of the pulses This can cause a large number of plot files and a large computation time on for the MMP model 4 The time dependence in the FDTD algorithm is less general than in the Fourier feature For model 29 a sin pulse is a good approximation 5 A large number of matching points can be required in the MMP model for obtaining a sufficient accuracy of the high frequency components This will cause the command clear pic f 2 to be very time consuming when a fine grid is used In order to avoid the difficulties 1 and 5 mentioned above you should modify the model 29 with the editor 1 Read the input file 29 with 3D r
173. ave been written by H U Gerber Without his assistance the 3D MMP graphics certainly would mot look not so nice 10 Part I Theory 1 Theory of Trial Methods 1 1 Boundary and Domain Methods In this chapter some methods for the solution of inhomogeneous functional equations common in electromagnetic field computation are derived and compared A functional equation can be written in operator notation as Dif d 1 1 where D is a general differential operator f the unknown function and d the inhomo geneity It is assumed that equation 1 1 has a unique solution furthermore that D is linear and that space is explicitly divided into homogeneous domains and their bound aries The method is formulated here for only one domain D with boundary OD and for a complex valued scalar function f However it can easily be expanded onto multiple domains The operator equation splits up into Lf g in D 1 2 Lf h on OD The analytical solution of 1 1 or both 1 2 and 1 3 respectively is usually only possible for very simple geometries otherwise only approximate methods can be used In the trial method the unknown function f is approximated by a linear combination of a finite set of basis or expansion functions f ES fo Y afi 1 4 where the coefficients or parameters c have to be determined There are several methods depending on the choice of the expansion functions e Boundary method or semianalytical method The basis functions
174. ave to be passed on down the pipeline Parallel speedup does not depend quite linearly on the number of processors The proces sors towards the end of the pipeline are unemployed until R is sufficiently filled optimum parallelism is reached only after N rows have been updated For larger problems where it is important after all exploitation gets better Back substitution is not parallelized but only takes very little time It starts on the last processor in the pipeline and propagates on to the upper ones A big advantage of this approach is that it can easily be adapted to pipelines with an arbitrary number of transputers without changes in the program s structure There fore the hardware can be adapted to the problem size For larger problems additional processors can be attached to the pipeline which give it more memory as well as more computational power Evaluation of errors and field values chapter 6 is not parallelized and is done on the root processor As this processor also has to hold the large part of the program as well as the rest of the data it is favorable to use a processor with more memory and possibly more computational power than the others 33 6 Evaluation of Results Once the unknown parameters have been determined it is easy to evaluate the residual error of the boundary conditions or the components of the field in arbitrary points on the boundary For common problems the computational time for error
175. basis functions are needed This is somewhat simplified by the fact that the scope of numerical field computation is only quantifying largely known problems and not discovering new effects though it has to be admitted that even simple electromagnetic problems can produce stunningly complex results The loss of completeness is not as severe as it might seem because the functions in everyday problems are usually better behaved than those in a mathematician s imagination Singularities mostly enter through idealizations in the modeling process and can be disarmed Another criterion for the choice of expansion functions is that of user friendliness and implementation A few types of expansion functions should be flexible enough to be used for a wide range of problems and they should also be fast to compute Therefore closed form solutions with functions that can easily be evaluated are preferable 3 2 Solutions by Separation of the Helmholtz Equa tions Separation of 2 6a or 2 6b and a deduction of closed form expressions is possible in several coordinate systems 26 Expansions of a field in an infinite series of free space solutions in circular cylindrical and spherical coordinates are very common in analytical approaches Due to the high symmetries of the respective coordinate systems they are very flexible and the mathe matical functions within them can be obtained numerically at a low computational cost through recurrence relations In
176. be performed and start regular actions by clicking this box with the first or second mouse button Box 16 Escape Box Type fixed text response Esc This box is used to escape a process instead of answering a question asked in box 15 The content of this box is fixed Box 17 First Field Type of Field Set Type dependent roll active inactive E E DE We IDE electric energy density pe Pe R w S E E electric power loss density in lossy dielectrics J Je o D D cE In activate this box with mouse button 1 or 2 Only active field types are shown The line number of this box is changed when the line number of box 14 is changed For the field sets see box 14 Note the scalar fields we and pe are copied on the tl component when a vector representation is used When the material properties are complex the fields we Je D are computed in the time harmonic case only 186 Box 18 Second Field Type of Field Set Type dependent roll active inactive H H BH Wm BH magnetic energy density pm Pm w S u H magnetic power loss density in lossy magnetics Ho ex _ surface current on ideal conductors B B pH Analogous to box 17 For the field sets see box 14 Note the scalar fields wm and pm are copied on the t2 component when a vector representation is used The vector fields are not shown when box 17 is active When the material properties are complex the fields wm and B are computed in the time harmo
177. been aborted because the integral to be deleted does not exist 15 7 4 3D copy Copy 3D objects For safety reasons you are asked copy___elements_OK_ when you try to copy anything Answering this question in the negative will abort the process with the message process_aborted____ All 3D copy commands are used to generate a copy of the original items at a different location Thus a vector that points from the original location to the destination is required This vector is used for several regular actions and can be manipulated with 3D adjust vect axis If you did forget to set the vector appropriately you get the chance to do that when you answer the question set_new_vector _YES in the positive In this case a simplified 3D adjust vect axis procedure is performed before the 3D copy command is executed you have to set the start and end point of the vector respectively axis during this procedure 3D copy____ wire_____ Copy active wires 3D copy points ___ Copy active matching points 3D copy____ object___ Copy object number 1 to object number 2 Since object number 2 is overwritten the question overwrite_obj 2_O0K_ is asked when object 2 does already exist If this question is answered in the negative the process is aborted and object_NOT_copied_ is displayed 122 3D copy pole_____ Cop
178. ber of matching points and the number of unknowns quadruple so mem r 16 Smem Topu gt 64 Topu This shows that modeling in 3D is intrinsically much more difficult and critical than in 2D and also is the reason why 3D problems usually look much simpler than 2D 40 ones Given the multipoles as expansion functions which are most efficient for surfaces following coordinate surfaces it makes clear why 3D MMP models mostly have rather round shapes It also shows that for optimizing a model it is more important to find a minimal base of expansion functions i e to set the multipoles optimally than to minimize the number of matching points In the first steps of modeling the matching points should be rather too dense because the model is easier to improve by changing the order of the expansions alone 8 2 Discretizing the Boundary The boundary is discretized as an unordered set of matching points each of which repre sents conditions 4 9 4 10 or 4 11 A part of the boundary belongs to each matching point It is represented by a rectangular surface element fig 8 1 Figure 8 1 Discretization of a surface with matching points each of which is represented by a rectangular surface element The expansion functions for the field are sampled on the matching points which should be dense enough to avoid aliasing not only of the incident field but also of the multipole expansions The subsequent setting of the multipoles is base
179. bewerb Ergebnisse 1990 pp 10 11 feb 1991 S Kiener and F Bomholt The GMT and the MMP code Applications to EMC the Babinet theorem in Proc of the 9th Symposium on Electromagnetic Compat ibility Z rich pp 481 486 Mar 1991 P Leuchtmann On the modelling of the electromagnetic field of EMC test ar rangements with the MMP code in Proc of the 9th Symposium on Electromag netic Compatibility Z rich pp 487 492 Mar 1991 Ch Hafner MMP solutions of scattering at large bodies in Proc IEEE AP S and URSI Int Symposium London Ontario June 1991 Ch Hafner On the numerical solutions of eigenvalue problems in Proc IEEE AP S and URSI Int Symposium London Ontario June 1991 J Li The MMP Applied to the Scattering Problem of the Periodical Array in Proc IEEE AP S and URSI Int Symposium London Ontario June 1991 335 134 135 136 137 138 139 140 141 142 143 144 145 146 147 Ch Hafner Justification of classical transmission line computations by numerical solutions of eigenvalue problems in Proc PIERS Symposium Boston July 1991 Ch Hafner MMP solutions of scattering at large bodies in Proc PIERS Sym posium Boston July 1991 Ch Hafner Animated 3D graphics for electromagnetic fields on PC s in Proc PIERS Sympostum Boston July 1991 Ch Hafner Scientific and educational MMP
180. bject visible by reducing the drawing depth or by moving the screen window plane The objects to be shown are divided into several slices parallel to the window plane The slices in the back are displayed first and the slices in the front are displayed after wards This leads to a hiding that is the better the more slices are used On the other hand the computation time is increased with the number of slices In the editor the number of slices is fixed to a reasonable value 40 whereas it can be adjusted in the plot program 14 4 2 Plot Windows Plot windows are handled like screen windows but they do not have a physical size on the screen i e the integer data of the corners are not required Since regular plots are computed in the 3D MMP main program on a rectangular grid one has something like the invisible grid lines of the screen windows in the plot windows as well Since regular field plots can be computed on a regular 3D grid by the 3D MMP main program one generally has several levels above the window plane where the field will be computed For this purpose two additional numbers are required 1 the number of levels and the distance between levels The levels in the plot windows correspond to the slices in the screen windows used for hiding Thus one has similar additional data for plot and screen windows with a different meaning For reasons of flexibility the 3D MMP main program allows to compute the field on a non rectangular
181. bject will be displayed in the corresponding boxes e Button 2 is used to count down digits in the value part of boxes e Button 2 is used in the text area of boxes 1 to display all lines of a pull box and to select the line of a pull box to be displayed when the button is released 2 to decrease the line number of a roll or selection box 3 to in activate a single line box 4 to change the contents of special action boxes containing more than a single line 5 to start an action of special action boxes containing only a single line 6 to answer questions asked in box number 4 of the top line e When a movie is shown in the plot program button 2 is used to terminate the actual sequence and to start the next sequence 91 Button 3 middle or right e Clicked in a box button 3 causes a hint box to appear see above provided that the corresponding hint file can be read Otherwise the following message is displayed cannot_show_hint_box e When a movie is shown in the plot program it is stopped when button 3 is pressed down Note that Button 3 can be simulated on a two button mouse by pressing down button 1 immediately after button 2 When you are working under Microsoft Windows the third button of your mouse might be inactive because the Windows mouse driver ignores it In this case you can simulate button three as indicated above but you probably will prefer installing a better mouse driver 14 6 Colors and Fill Patterns Mo
182. button one immediately after button two The physical location of the buttons on the mouse depends on the mouse Button 1 usually is the left button button 2 is either the right or the middle button in most cases and button 3 is the remaining button 2D show line 0 generating meta file Jino meta 1 clear EXIT f ang 3 600E 02 M_ 5 Domain a Juet domi 0 Exp dom 1 con pt 1 Wx11 1 0008 00 ix11 6 Ex 1 00008 00 wgt 1 000E 00 se1_0 000E 00 Con w 0 08 00 x 0 000E 00 y 0 000 00 0 0008 00 Figure 14 1 Desk of the MMP 3D editor 143 Boxes Boxes are used for entering and displaying data for choosing actions performing actions and for providing information and help I e Boxes play the role of very different graphic elements known from typical Windows applications Pull down menus buttons alert boxes dialog boxes input boxes etc 82 In general a box contains of several lines but only one of the lines is usually displayed in order to reduce the area occupied by the box on the screen Each line consists of a text area on the left hand side and of a value area that contains an integer or a real value Either the text area or the value area can be missing All digits within the value area of a box are increased or decreased when button 1 or 2 is clicked while the cursor is on the digit Similarly signs of real values can be changed To change th
183. buttons After this the hint box will disappear and the program expects that one of the mouse buttons is pressed The standard editor desk consists of two windows and of 23 boxes see fig 15 1 The number of boxes is fixed defined in the file MMP_E3D DSK but you can increase the number of windows 15 2 Program Exit Most of the boxes are used to read and display data or to define actions to be performed The most important exception is the last box of the top line that is used to leave the program There are two alternatives to leave the program that can be selected with the second mouse button in this box If the content of this box is QUIT the program is terminated without saving any data when the box is clicked with the first mouse button If the content of this box is EXIT the program saves the data of the current windows in the file MMP_WIN 000 the 2D data in MMP_E2D 000 and the 3D data in MMP_E3D 000 If one of these files does already exist you are asked overwrite_wind file overwrite_2D_file__ overwrite_3D_file__ Answering in the negative has the effect that the corresponding data are not saved Otherwise the data is saved and the corresponding messages writing window file saving 2D data file saving 3D_data file are displayed 94 3D show object 0 generating meta file No meta 0 clear EXIT f 7 T ang 3 600E 02 M 5 Domain 1 Met domi 0 Exp dom 1 Con p
184. c elements on Repeat the picture com mand show pict and watch the additional squares triangles and vectors indicating the field vectors and its components Most users will prefer playing with the plot program instead of reading the manual In order to help them hint boxes can be invoked with the third mouse button Problems can occur above all because of over and underflows or when the program writes outside the screen area The latter can be the case when a window is moved blown adjusted or added As you can see for reasons of simplicity arrows near the border of the window are not clipped Thus the windows should be placed in a sufficient distance from the borders of the screen When the program writes outside the screen area a large number of lines covers the screen In this case one can clear the screen with the command clear wind 0 and continue either after disabling the arrow representation select 4 or less in the fill vector box or after moving or resizing commands adjust or blow the windows Over or underflow problems can occur because the plot program uses single precision whereas the 3D MMP main program uses double precision throughout As a consequence the values in the files generated by the main program can be too large for the plot program Usually an error results during reading and the plot program displays an error message for example error_in field00003 indicating t
185. cating large values with different fillings the elements always are completely filled but different colors are used to indicate the strength This allows to obtain a much better quality of the pictures provided that the screen driver and the graphic interface allows the plot program to set the color palette appropriately Note that the color composition red green blue of the 16 colors used in the plot program is defined in the desk file Since the default colors of Windows are not appropriate here a palette starting with white black dark blue red yellow is defined in the desk file Unfortunately some screen drivers do either not allow to change the color composition at all or only with very rough steps Moreover Windows screen drivers often generate different colors by mixing predefined colors which is not very nice However you can modify the color composition in the desk file with a text editor when you do not like the actual colors or when you do not obtain 16 different colors in the range mentioned above because your screen driver does not allow that Be careful because the plot program does not run when the desk file is corrupt Two alternative color palettes are added at the end of the desk file for giving an idea how this can look like Note that the program does not read this information Now it is time to look at the remaining boxes of the top line When you turn the boxes M and P on the matching points and expansions po
186. ce the 3D MMP main program can generate error files containing the field values on both sides of the boundaries as well the program can read a part of these data like a general plot file with field points identical with the matching points This allows to show the field in the matching points when the question use_M pts_as_F pts_ is answered in the affirmative If you want to use this feature you have to select first the domain number of the field points in the additional integer data box sequ M 166 because displaying the fields on both sides of a matching points would result in over loaded plots This feature is used above all for showing the field on the surface of ideal conductors When the domain number 0 is selected in the box sequ M the values in the matching points on all ideal conductors are read Since you might have forgotten to select the domain number you are asked set_domain _ _0___ When this answer is answered in the negative the question set_domain _ _xxxx where xxxx is the domain number selected in the sequ M box is displayed This is the second opportunity to abort the read error command by answering in the nega tive error_file_not_read indicates this Otherwise the program tries reading the error file and displays reading _MMP_ERR xxx during reading The error messages MMP_ERR xxx_missing error_in pointyyyyy indicate that no error file with t
187. ching point check colors for errors colors for matching points icolBed 1 1 colors for constraints icolInt 1 1 colors for integrals icolFPt 1 1 colors for field points general plots ifilobj 2 2 fill patterns for 3D objects ifilpar 4 4 fill patterns for parts of 3D objects ifildom 2 2 fill patterns for domains ifilchk 4 4 fill patterns for matching point check ifilerr 0 9 fill patterns for errors ifilmat 1 1 fill patterns for matching points ifilBed 1 1 fill patterns for constraints ifilInt 1 1 fill patterns for integrals ifilFPt 1 1 fill patterns for field points general plots Coordinates x and y in device independent 1000 by 1000 integer coordinate system with lower left corner 0 0 and upper right corner 1000 1000 Depending on the box type real or integer parameter one of the two initial values BoxInt and BoxRea is treated as a dummy The array elements of the colors and fill patterns above have the following meaning e A positive index indicates the front side and a negative index indicates the back side of the corresponding element e index 0 is sometimes used when other elements are shown For example when the command show pole is performed matching points are shown with the color icolmat 0 and the fill pattern ifilmat 0 The color numbers and the fill patterns are essentially the same as described in the 3D MMP plot program where they can be selected
188. chip RAM is too small A command line parameter indicating the working directory is not provided because under DOS the working directory is always the directory where you are when you start a program I e when you want to work in the subdirectory MMP3D EX3D use the DOS command CD MMP3D EX3D before you run 3D MMP Note that only the main program has been parallelized The quadputer version 4 processors has the name MMP_M34 B4 whereas MMP_M3D B4 is used for the single processor version of the main program 277 Part VI Appendices 278 A Symbols and Coordinate Systems A 1 Notation The MKSA system is used throughout All variables may be complex unless explicitly denoted A 1 1 Mathematical and Physical Constants oene e NNR A FE Q v 1 frequency angular frequency w 2r f speed of light c 1 ey wavelength c f complex permittivity el conductivity permeability wave number k wpe w ue iwpo transverse wave number propagation constant or longitudinal wave number y k k wave impedance in a medium Z y p e wave impedance in free space Z y Ho o a iw 2 A 1 2 Mathematical Functions Bm Jm Ym HY AY bn Jn Yn hP cylindrical Bessel functions of integer order Jm Ym Ho or HP cylindrical Bessel function order m cylindrical Neumann function order m cylindrical Hankel function of the first kind order m cylindrical Hankel function of the second
189. cially for animation F 5 T Ta I i generate meta _ Sj 4 computing Wm field E No DE BH jE energy 2 y z Mie 8 EXIT sequ M cg metav 8 000E 02 Maa alee aa jfill grid o lcolor grid _ 11 A frx_11 5 500E 01 ix low left 19 ER 1 00000E 00 vy_ 0 00000E 00 vz 0 00000E 00 total FPt 900 x 9 50000E 01 y 5 00000 01 iter part 1 tim 0 00000E 00 part type a m0 1 00000E 00 Figure 16 3 Desk of the 3D MMP plot program showing the energy density for a pulsed plane wave incident on a cylindrical lens representation with deformed grid lines iso lines and fill patterns The model and other representations can be found in the last example of the tutorial To select an appropriate representation for a given field several boxes are provided in the 3D MMP plot program To get familiar with the MMP features it is strongly recommended to start with simple cases with a relatively low number of about 100 field points When a special representation is found that is considered to be most beautiful or best suited for common applications the initial values in the desk file can be modified in such a way that this representation is the default 16 4 4 Geometric Data and Mismatching Data Errors When the field in the field points is shown some additional information is required for your orientation The most natural way is to show the matching points on the boundarie
190. code where one does not work with overdetermined systems of equations more than one matching point is needed per segment According to 40 two matching points per segments are sufficient and their optimal positions can be estimated from simple formulae that have been implemented in the 3D MMP code Additional dummy matching points around the wire are usually necessary for the automatic detection of domains At open ends of the wire the last matching point should have a distance of 1 3 to 1 2 segment lengths from the end Otherwise the high error values near the end which are caused by the very high field values will bring about a too small current on the wire see above and 41 The current at the end has to be left freely floating If several wires are joined or if wires are joined to surfaces the boundary conditions are sufficient to guarantee good continuity also in these places Tests have shown that it is not even necessary to use the continuity conditions C 2 for thin wires the residual errors on the boundary may even get smaller due to the higher number of parameters 8 6 Symmetries When reflective symmetries are used cf chapter 7 only one half of the model with respect to each plane of symmetries has to be used These are the expansions and the matching points in the principal domain which has been defined as the positive half space in regard of each symmetry plane e g X gt 0 for a symmetry about X 0 To apply the above
191. cond count down mouse button in the value area of this box and perform the command adjust pole Since a wire is a special expansion the corresponding commands with wire instead of pole affect the values in this box as well Since objects and parts of objects contain expansions as well the corresponding com mands with object or part instead of pole affect the values in this box as well Box 18 Real Data of Matching Points Type input output wgt user defined weight of the matching point affects all boundary condi tions When a matching point is in activated with the second mouse button in a window or with the show points command the corresponding values are displayed in this box Change the values with the first count up and second count down mouse button in the value area of this box and perform the command adjust points Since objects and parts of objects contain matching points as well the corresponding commands with object or part instead of points affect the values in this box as well Box 19 Integer Data of Matching Points Type pull down input output MPt dom1 first domain number MPt dom2 second domain number MPt E1 3 boundary conditions concerning the electric field MPt H1 3 boundary conditions concerning the magnetic field MPt M
192. cos y cos Y ay sin y A 3a dy ar sin p sin Y ay sin y cos a cos p A 3b az ar cos ay sin A 3c A vector with coordinates a ay az in the basis is converted to coordinates ax dy az in the basis j z by Ay Ap COS P ay SIN Y A 4a Ay Ap SiN Y ay cosy A 4b Gz Az A 4c 282 B Functions The different functions needed for the solution of the Helmholtz equations 2 6a or 2 6b in Cartesian polar and spherical coordinates have similar qualities The differential equations they satisfy are of second order One of the most important properties for us is that values for different orders of the functions can easily be obtained by recurrence Only the most important properties are presented here Additional information on the functions and their computation can be found in 46 47 48 and for the Bessel functions especially in 49 and 2 B 1 Cylindrical Bessel Functions Cylindrical Bessel functions or Bessel functions B z of integer order n and a complex argument z are solutions to the differential equation 2 PB z dB z Z p2 Ti 2 de 2 n B z 0 B 1 Solutions are the Bessel function of the first kind J z and the Bessel function of the second kind or Neumann function Y z As an alternative basis the Hankel functions of the first and second kind H z and H z may also be used The relations between the solutions are
193. ct 1 inside object 2 e the part of object 1 outside object 2 e the part of object 2 inside object 1 e the part of object 2 outside object 1 If the parts have not been computed yet see 3D generate parts this can be done now Since the computation of the part numbers of all matching points can be time consuming the question compute_new_parts_ is asked If the parts have already been computed it can be answered in the negative The representation of the parts depends on the number n selected in the item box and of the corresponding fillings and colors defined in the desk file If n is 0 the parts are shown with different fillings and colors provided that the standard desk file is used For n 1 2 3 4 only the corresponding part is shown with its color and filling whereas the matching points of the other parts are shown in transparent mode 3D show____ object___ Show objects If the number n of the item box is 0 both objects are shown with different fillings and colors defined in the desk file For n 1 2 only the corresponding object is shown with its color and filling whereas the matching points of the other object is shown in transparent mode 3D show____ pole_____ Activate either all expansions or only those with numbers n1 up to n2 If n2 lt n1 n2 is set to n1 n1 has to be defined in the item box and n2 in the additional integer data box M If n1 is less than 1 or bigger than the numbe
194. ctor representation number of fill patterns or colors 188 use grid line representation without iso lines number of fill patterns or colors ss use grid line representation with iso lines number of iso lines Note Each line contains a number that affects the representation The number of fill patterns or colors is the maximum number of colors when the corresponding value in box number 8 is 4 Otherwise it is the maximum number of fill patterns The maximum number of fill patterns in the present version is 8 Since the color number 0 is the background color it is reasonable to select 15 or less colors for a color monitor with 16 colors when the value in box 8 is 4 When you have selected for example 20 iso lines in the third line of this box and 4 in the last line of box 8 you might prefer to select 10 colors in the second line You will get two iso lines per colors i e you will have one iso line on the border of an area characterized by a certain color and exactly one iso line inside such an area If you select 15 colors instead you will have areas with one or two iso lines inside When you do not remember how many fill patterns or colors you have and when you want to select the maximum number set the number 0 In this case the program will select the number automatically Box 27 tl Component of Field in Field Point Type pull down input output vx tl i e 2 component of field shown in the field point local coo
195. d 10 6 Matching Points The geometry of the scattering objects is entered as a list of matching points their maximum number is limited by nmatm see sections 20 3 2 and E 2 In the 3D MMP main program matching points are used for several purposes e For the formulation of the equations e For the evaluation of the errors e For the automatic detection of the domain of a field point Matching points are defined by the following data imat integer number for identification in input and output programs not significant to the MMP program igi number of domain D 60 ig2 number of domain D ir boundary conditions see below sgp additional weight w r XpX Zpx location Tpt of matching point xpti zpt2 v orientation xpti zpt2 gt orientation The vectors y and V for the orientation need not be normalized nor orthogonal The orthonormal right handed coordinate system 41 2 is obtained from U1 v2 as follows E z P U1 X U2 U1 En Cih a o The area s of the surface element associated with the matching point cf 4 8 yields A t2 En X Ct 01 x Va Sk i 01 x Va For automatic detection of the domain cf chapter 6 the normal vector has to point from domain D into domain D If no matching points are given in the input file the number of the domain of all field and integral points will be set equal to 1 When symmetries are used the matching points may be on either side
196. d Otherwise a new grid is created with n horiz _ horizontal grid lines n vertic _ vertical grid lines on n levels__ levels with a distance d_lev between the levels and the actual time tim is reset to zero If the item number is gt 1 the domain numbers in all field points are replaced by the numbers computed with the automatic procedure In this case an input file should be read first because the matching point data are required in this procedure If the item number is equal to 1 all field values are set equal to the domain numbers This is useful for testing only If the item number is equal to 0 all field values are set equal to 0 This is useful for many iterative procedures If the item number is equal to 1 all field vectors are set equal to the position vector This is useful for testing and for some iterative procedures like the Newton and Julia algorithms If the item number is equal to 2 all field values are set equal to a random number between 0 and 1 If the item number is lt 2 all field values are set equal to a random number between 1 and 1 In order to avoid unintended actions you are asked whether you really want to set the corresponding field values I e one of the following questions is asked set_domain numbers_ set_field FieldPt 179 set_field to_zero_ set_field position_ set_random_ 0 1 set_ra
197. d This is not considered to be a drawback because such excitations are dangerous anyway and require a good knowledge of the code for avoiding unexpected or undesired results Instead of adding new expansions with the command add the commands copy rotate etc might be useful For example when you want to have several plane waves incident from different directions you can start with one plane wave generate a second one with copy 7 rotate it around an appropriate axis and so on 4 Adjust the number of excitations in the box nexc Note that the editor does not test this number and accepts numbers that will cause errors in the main program This is especially important when you have a large number of excitations For getting started it is certainly reasonable to use only two excitations 5 Save the data on an input file and exit the editor When you run the main program for computing the parameters plot files etc the matrix will be updated only once Thus although several data files will be written like when a Fourier series is computed the computation time will remain moderate As soon as the main program has computed all plot files you can start the plot program and read the data It is important to note that the input file number is identical with the plot file extension number when a single excitation is defined in the input file 253 generate
198. d cnbed file identification number number of matching points error field in bordering domains percentage error number of constraints values of constraints In addition to the values contained in the standard error file the extended or general error file created by task 6 of the main program contains the complex fields on both sides of all matching points 6 nmat ip sperr fvali fval2 sperrp cex1 cey1 cezl chx1 chy1 chz1 cex2 cey2 cez2 chx2 chy2 chz2 nnbed cnbed file identification number number of matching points error field in bordering domains percentage error E on the first side of the matching point H on the first side of the matching point E on the second side of the matching point H on the second side of the matching point number of constraints values of constraints 298 D 7 Integral File MMP_INT xxx This file contains the values of the integrals of the input file nint number of integrals cint values of integrals D 8 Complex 3D Plot File MMP_Pyy xxx For yy 00 49 plots are produced on regular grids for yy 50 99 in arbitrary field points see chapter 10 and file MMP_3DI xxx in this chapter Since the plot program can compute electromagnetic fields on regular grids with iterative algorithms it can write regular plot files as well In these files the scalar and vector potentials can be added or some parts of the electromagnetic field can be omitted because the plot program sometimes works with
199. d Ch Hafner A MMP program for computations of 3D electromag netic fields on PC s in 5th Annual Review of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Monterey Mar 1989 332 89 90 91 92 93 94 95 96 97 100 101 102 103 Ch Hafner Feldberechnungen mit Personal Computern Grundlagen und Er fahrungen Bulletin SEV VSE vol 80 no 9 pp 505 508 1989 B Pasche J P Lebet A Barbault C Rossel and N Kuster Electroencephalo graphic changes and blood pressure lowering effect of low energy emission therapy in Proc of the 11th Annual Meeting of the Bioelectromagnetic Society Tucson June 1989 N Kuster Internal check routine of the MMP program packages for model vali dation in JEEE AP S International Symposium San Jose June 1989 Electro magnetic Modeling Software Workshop P Leuchtmann The construction of practically useful fast converging expansions for the GMT in IEEE AP S International Symposium San Jose June 1989 N Kuster Computations of 3 D problems of high complexity with GMT in IEEE AP S International Symposium San Jose June 1989 S Kiener Bodies with sharp edges Calculation of near and farfields in IEEE AP S International Symposium San Jose June 1989 Ch Hafner Parallel computations of electromagnetic fields on PC s using trans puters in
200. d are computed in different points For saving memory six of these points are virtually con centrated in one point where the field is stored and displayed by the plot program In usual FDTD codes absorbing boundary conditions are implemented on the borders of the grid These conditions reduce the non physical reflections of waves travelling across the border In the plot program simpler boundary conditions are implemented that do not absorb the energy of waves but have the advantage that 1D 2D and 3D problems can be computed with one and the same algorithm The incident wave in the FDTD algorithm of the plot program always is a plane wave incident from the right border and travelling in X direction Its polarization is either parallel or perpendicular to the XY plane and its time dependence has the form sin wt within the time interval from 0 to Tmx Outside the time interval the field of the incident wave is zero Although the FDTD program in the plot program is very simple it can be used for comparing the results of the 3D MMP main program with a completely different method above all when the Fourier transform has been applied like in model 29 You can generate the FDTD model of a 2D lens like you did generate the FD model 33 Since the lens has a circular boundary this turns out to be cumbersome The command 260 clear pic f 2 allows to use the data of the matching points stored in a 3D MMP input file for autom
201. d item matching points expansions etc visible in the rectangle will become active In the plot program all values of all field points visible in the rectangle will be set to the field values defined in the corresponding boxes While entering geometric data requested by the program during execution of a regular action such as setting a point the coordinates of the actual location on the 90 invisible grid will be displayed in the coordinate boxes as long as the first mouse button is pressed down while the cursor is in the window The data are entered when the button is released e Button 1 is used to count up digits in the value part of boxes e Button 1 is used in the text area of boxes 1 to display all lines of a pull box and to select the line of a pull box to be displayed when the button is released 2 to increase the line number of a roll or selection box 3 to in activate a single line box 4 to start an action 5 to answer questions asked in box number 4 of the top line 6 to remove messages in box number 4 of the top line e When a movie is shown in the plot program it is paused as long as button 1 is pressed down Button 2 right or middle e Button 2 is used in the window to select and deselect certain graphic 3D objects Usually only the object displayed in the item box is affected Furthermore depend ing on the type of the object the location in global coordinates and the additional real and integer data of the o
202. d on the dis cretization Thus the matching point distribution should be denser where more accuracy is required Watch out for points near edges corners or ends of thin wires In these regions the field is locally very high but has little influence on the overall solution The boundary conditions have very high numerical values in these places because of the high field With the least squares algorithm the error in these points is unnecessarily reduced at the expense of the error in other matching points This can have a global influence on the solution which is then likely to produce a too small scattered field It is therefore advisable to keep the matching points away from these singularities or to round off the boundary where possible The error tends even to get higher in places where the curvature has a discontinuity although the boundary itself remains smooth Domains of a geometrically complicated shape can be subdivided with fictitious boundaries into several more simply shaped domains all of which have the same elec tromagnetic properties cf fig 8 2 On the fictitious boundary i e within the original 41 Figure 8 2 Geometrically complex domains can be subdivided with fictitious boundaries domain an error is allowed Expansions may be found more easily and sometimes nor mal expansions can be used see below In addition to enforcing boundary conditions in the 3D MMP main program the matching points are used for comp
203. d points for generating a general plot file If such a set does already exist when the command 3D generate field pts is executed you can either add the matching points to the existing field points or replace the existing field points by the matching points Thus you are asked first add_to_existing pts Answering this question in the negative will cause the question replace_exist _pts_ If you answer this question in the negative as well nothing is done and process_aborted___ is displayed In order to decide whether the matching points of the first the second or both objects shall be used to generate the set of field points the questions use_objects_1 2___ use_object_1_only__ use_object_2_only__ are asked If you answer all three questions in the negative nothing is done and process_aborted___ is displayed The domain number of a field point can be determined automatically in the MMP main program In some special cases for example when a field point is between two matching points you might wish to turn this feature off non zero value in the box F pt dom and determine the number of the domain of the field points manually Since two different domains belong to every matching point either the first or the second domain number can used to fix the domain number of the field point to be generated 138 For this reason the questions use_MP_domain_ _1__ use_MP_domain_ _2__ are asked Note that the dom
204. da O HP B 2 Ya 00 H B 3 2 The values for a fixed argument z and different orders n can be obtained by recurrence Bal By 1 z Bny1 2 B 4 Depending on the the function and the argument z either upward or downward recur rence is stable For upward recurrence the starting values By and B must be obtained by evaluation of series continued fractions Wronskians or asymptotic expansions If downward recurrence is stable one can start with values B 0 and B 1 1 or ap proximations for high orders and subsequently normalize the values with expressions for series of Bessel functions Miller s algorithm 49 2 For large arguments z gt n the cylindrical Bessel functions behave like Jale 2 cos z gt 2 B 5 Y 2 O sin z gt y B 6 283 B 2 Spherical Bessel Functions Spherical Bessel functions b z are solutions of the differential equation d b z db z 2 a de ae dz The connection to the cylindrical Bessel functions is T n 2 Y Z Brzo B 8 and the recurrence relations are 2n 1 z2 n n 1 b z 0 B 7 bn z dn 1 2 dn 1 2 B 9 Depending on the function and the argument z either upward or downward recurrence is stable The starting or scaling values bo z and b z can be obtained with elementary functions e g sin Z jo z 7 B 10 sinz cosz j B 11 jua 2 B 11 COS z yo z gt B 12 cosz
205. de helps solve electromagnetic scattering problems with harmonic time dependence within piecewise linear homogeneous and isotropic domains 2 4 without j 0 Po 0 S 0 0 Using the trial method formalism of impressed sources j chapter 1 operator equation 1 2 can be identified with the Helmholtz equations 2 6 and equation 1 3 corresponds to the boundary conditions 2 9 In the MMP programs the field itself is the primary quantity and is expanded directly The basis functions f are the complex vector valued functions s138 aw where 7 is a point in three dimensional space Usually closed form solutions of Maxwell s equations are used mostly multipole solutions in cylindrical and spherical coordinates 2D and 3D multipoles The excitation f is itself a solution of the Helmholtz equations and therefore of the same type as the expansion functions As a consequence the inhomogeneity can be written as h LfNy1 2 11 The equations are obtained with the generalized point matching technique The ex pansion functions are matched in discrete matching points on the boundary As long as the boundary is relatively smooth the functions behave well on it and its discretization is within limits independent of the choice of the origins of the expansions A model of a scattering problem consists therefore apart from additional data like media properties frequency etc of a set of matching points and a set
206. diff O tot 0 scaling factor 2 00E 00 residuals 16 MP time diff O tot 0 constraints 0 integrals 1 time diff 1 tot 1 integral 2 9 942558E 01 1 210919E 03 plotting 625 FP time diff O tot 1 3D MMP END time diff 10 tot 11 Besides the actual size of the problem and the CPU time the following interesting quantities can be found in the output file resnor norm of the residual vector 7 which is a direct and fast indicator for the quality of the solution cf chapters 5 8 rcond LINPACK condition number estimator for the condition of 4 4 only for Cholesky factorization which is about the inverse of the condition number a warning message is issued if it is less than working precision i e if 1 0d0 rcond 1 0d0 The rows and matrices can be displayed graphically values 3 or 4 for msscr and msfil respectively e g for the rows 1235679 213253637697 81224678 113253647597 90123456001122334465 0234689 213233638698 90234579 213243547597 90122256001032435475a gfecba23213043457697 9g8ffcb003113143546687 8hgfedcb001021325464 jihgedcabaa00203344658jihhfdcbbba00213244668 jihgfeccbbaa001123d EARTE baa00003355668 baa00112244667 dcbba0011224 ba012457bab11232455677ba002456baa11223445668ccaa123cbbaa0011324d The following symbols are used to denote the size z of the elements logio z Symbol log z Symbol logio z Symbol logio z Symbol lt 300 gt 8 h gt 0 0 gt 8 8 gt
207. dinate system Another useful approach of deriving scalars from vectors comes from the energy con cept The 3D MMP plot program allows to represent energy and power loss densities Both the electric and the magnetic field densities we and Wm can be shown separately as well as the total energy density w and the power loss densities pe Pm Pj pe according to the dielectric magnetic and Ohmic losses due to the imaginary part of the permittivity the imaginary part of the permeability and the real part of the conductivity The 3D MMP main program computes above all time harmonic fields Although it is possible to represent such fields with complex values this is certainly not a user friendly approach In many cases the time average of the field is of interest Of course the 3D MMP plot program allows to show time averages but it does not represent complex fields directly _It is important to note that the time average of the time harmonic vector fields D H B j is zero The plot program will show the absolute values of the complex constants instead Moreover the time average for complex frequencies is not defined In this case the plot program ignores the imaginary part of the frequency and displays the resulting value that corresponds to the value of the envelope at the time t 0 The flexible concept used in the actual implementation allows to show fields that are hard to understand or even meaningless Although this software package is
208. ditor are identical with those used in the 3D MMP plot program read____ mmp_p Read the information contained in the 3D frequency dependent plot files MMP_Pyy xxx Select yy in the item box and xxx in the file extension box Reading the data of all levels planes above the window plane of a regular plot file can be time consuming You can decide whether you want to try reading all levels or one level only by selecting the corresponding level number in the additional integer data box level level 0 stands for all levels If the level number is not zero you are asked read_all_levels____ If you answer in the affirmative the level number is set to zero and all levels are read When a regular plot window is read the window information contained in this file can be used to modify the data of the actual window For this reason the question use_plot_window____ is asked Above all when you have a large plot file with many levels the memory might be insufficient for storing all data at a time If this is the case too_many_f _points_ is displayed If the level number selected is not present in the plot file level_missing ____ is displayed When the plot file selected is missing itself MMP_Pyy xxx_missing is displayed Otherwise reading MMP_Pyy xxx indicates that the field is being read If errors are detected during reading one of the messages error_in_pointxxxxx error_in fieldxxxxx
209. do this the type of the element has to be selected in the item box and the second mouse button has to be clicked when the cursor is near the center point of the corresponding element except for 2D lines where the cursor should be near the start point Alternatively a group of elements can be activated at the same time with the first mouse button in the actual window In this case the number of the actual window has 96 to be selected first in the corresponding fifth line of the item box Note that window 1 is used when the selected value is out of range Afterwards the type of the element to be activated has to be selected in the item box Finally a rectangle is selected with the first mouse button in the window Two diagonal corners of the rectangle are defined by the cursor positions where the button has been pressed and released As long as the button is pressed down the actual rectangle is displayed Note that only visible points are activated i e points outside the drawing depth are not affected When an element is activated or inactivated with the second mouse button its real and integer data are displayed in the corresponding boxes Since different elements are characterized by different data the data displayed are left unchanged when a group of elements is selected with the first button even if the group consists of exactly one element To activate or inactivate points defining constraints integrals or sets of field points
210. domain Before its execution select the material properties ur r and o in the corresponding boxes Er Ei Ur Ui Sr Si Note that all material properties are complex in the 3D MMP code although real values will be assumed in most cases For this reason the default values of the imaginary parts in the boxes Ei Ui Si are zero If the maximum number of expansions is exceeded the message too_many_domains__ is displayed Note that domain number 0 is used for all ideal conductors and has not to be defined Moreover domain number 1 is predefined as free space If the data of domain number 1 are not appropriate the regular action 2D adjust domain has to be performed 15 6 3 2D delete _ Delete elements For safety reasons you are asked delete_elements_OK_ when you try to delete any element If this question is answered in the negative nothing is deleted the process is aborted and process_aborted____ is displayed 2D delete_ line_____ Delete both active lines and ares 2D delete__ arc______ Identical with 2D delete line see above 2D delete__ window See 3D constructions 2D delete__ object___ Delete active lines arcs and poles 2D delete__ pole_____ Delete active poles 105 2D delete__ domain __ Delete the doma
211. ducting Surfaces The surfaces of domains with a high refractive index can be modeled with surface im pedance boundary conditions 30 The field within the refractive domain D is locally approximated by vertically entering plane waves explicit expansions for the field within the domain are not made Like the perfectly conducting domains these are not domains in the MMP sense The surface impedance boundary conditions are n n Zje x 4 3 Zi 4 p5 Es is the wave impedance of the refractive domain In the coordinate system of the matching point the equations are En Z His 4 4a Ei Zj Hin 4 4b For validity it is necessary to make sure that the waves entering in a place do not exit again in another place on the boundary As a consequence the boundary must satisfy a condition 2 5 lt R 4 5 WHjTj where is the penetration depth or skin depth and R the smallest radius of curvature at a point of the boundary or the smallest thickness of the domain In practice this means that surface impedance boundary conditions are only applicable on surfaces of well conducting domains usually denoted as imperfectly conducting surfaces For Zj approaching zero which is the case for a high permittivity j or a high con ductivity o the surface impedance boundary conditions turn into those for perfectly conducting surfaces 4 2a 4 2b For a detailed deduction see e g 30 4 4 Constraints The approximatio
212. e answering the question read ALL_3D data__ in the affirmative 2 Read the matching point and expansion data of file MMP_3DI 004 only answering the question read_ALL_3D_data__ in the negative As a consequence the data of MMP_3DI 003 remain unchanged and the dipole with its dummy matching points in file MMP_3DI 004 is read in as object 2 3 Move the second object to the desired location with the command 3D move object Note that you have to select the object number i e 2 in the item box If you consider the dummy sphere to be either too large or too small you can use the 3D blow object command to change this Since this command allows to deform the objects in various manners it is recommended to read the manual and to get some experience first 225 4 Save all data on a new 3D input file MMP_3D1 005 quit the editor run the main program and so on 17 3 2 Adding Multipoles Model 6 Working with the previous models you probably have noticed that the errors are large when the dipole is near the surface of the sphere To get more accurate results you can try to move the multipole out of the center of the sphere towards the dipole As you know from electrostatics there is a mirror point of the dipole inside the sphere If the multipole would be moved to this point the rules for getting useful MMP expansions are violated To avoid this the matching point density on the sph
213. e maximum number of variables associated with a directive maximum number of sequences of a movie maximum number of pictures of a movie maximum number of parts of a sequence in a movie Important Variables nDom kDom E U S UI nMat kMat iMat pMat hMat err nPol kPol number of domains number of the actual domain real part of relative permittivities of the domains real part of relative permeabilities of the domains conductivities of the domains imaginary part of relative permeabilities of the domains number of matching points number of the actual matching point domain numbers of the matching point planes defining the matching points height of the matching points above the window plane errors in the matching points number of expansions poles number of the actual expansion pole 323 iPol rPol pPol hPol nFPt kFPt pFPt hFPt vFPt EXR EXI irgb icol ifil HZR HZ1 integer information of the expansions poles real information of the expansions poles planes defining the expansions poles height of the expansions poles above the window plane number of field points number of the actual field point planes defining the field points height of the field points above the window plane vector in the field points to be displayed R E RE RE R E 1 R E 2 R E in the field points SE SE SL SUL 1 SL 2 S in the field points red green blue intensities of the colors
214. e screen driver and on the graphic interface Box 9 Typ e of Regular Actions Type pull down show____ read____ write__ generate delete__ move____ rotate__ blow____ invert __ adjust__ clear___ show item read item write item generate item add item delete item move item rotate item blow item invert item adjust item clear item Select regular action to be performed when the first mouse button is clicked in one of the windows For more information see description of regular actions 183 Box 10 File Extension Type input output file extension number when files characterized by two numbers are used file extension number of directive file MMP_DIR for movies Select file extension number with the first count up and second count down mouse button Box 11 Items for Regular Actions Type pull down input output pic f picture or picture files MMP_Fyy xxx and MMP_Iyy xxx movie movie animation or movie files MMP_Fyy xxx and MMP_Iyy 000 axis_ axis or vector for rotations and translations light vector wind window or window file MMP_WIN xxx mmp_p 3D frequency dependent plot file MMP_Pyy xxx mmp_t 3D time dependent plot file MMP_Tyy xxx input 3D input file MMP_3DI xxx error 3D error file MMP_ERR xxx meta_ Windows meta file MMP_Pyy WMF 2Dp1f 2D frequency dependent plot file MMP_PLF xxx or MMP_DAT PLT 2Dp1t 2D time dependent plot file MMP_PLT xxx part particle or particle file MMP_PRT xxx dom _ do
215. e MMP_Pyy 000 Thus it is important to note that this file should be present when any time dependent file is opened The format of the input and output data files can be found in appendix D 72 13 Functional Overview of the 3D MMP Main Program 13 1 A Short Overview In the following a short overview of the source code is given A list of the subroutines and of the most important variables can be found in appendix E Those who show deeper interest or want to do modifications of their own will find additional information in the source code itself The subroutines have deliberately been kept small in order to isolate significant operations and improve intelligibility FORTRAN 77 makes beautiful programming i e obtaining a well structured and understandable source code a little bit difficult Furthermore in many compilers a lot of common nonstandard and even some of the standard FORTRAN features are either not or only very badly implemented Therefore as few language elements as possible are used As a consequence the program probably looks a bit clumsy but it is still or because of that very speedy and quite flexible to extensions Variables are used quite generously because almost everything sinks into insignifi cance beside the memory space used by the system matrix Even type conversions do or did not properly work in all compiler versions therefore double precision and 4 byte integer variables are used throughout wit
216. e coordinates and the location of the expansion which symmetries about xz 0 y 0 and z 0 can be considered by a symmetry adapted expansion and determines from this and from isszp the necessary symmetry decomposition This information is stored in arrays issz symmetry decomposition ise symmetries which can be considered and isnr symmetry planes A priori each expansion is assumed to be non symmetric and a full symmetry decomposition 7 3 is prepared If an expansion subroutine is able to consider these symmetries by returning only the symmetry adapted basis functions it can directly reduce the symmetry decomposition by redefining issz This is done in most of the expansions routines a The loop for the symmetrization is then controlled by array issz through routines inisz and nexsz Subroutine addsz adds up the components from rows cup3 into rows cup2 Array isd contains the signs which are necessary for the symmetrization of the various components 76 13 5 Input and Output Initializations Input output and initializations are concentrated in file ETC F 13 5 1 Input Subroutine ininp reads the input file and maps it to the variables this explains the many coincidences between symbols in the input file chapter 10 and section D 2 and the variable names section E 2 ininp calls a lot of more specialized routines as inentw for the expansion section incon for connections inmatp for matching points innbed for constraints
217. e corresponding point is almost left unchanged Windows can be blown with a constant blowing factor only Neither the type nor the blowing distance have to be specified in this case For safety reasons you are asked first blow___elements_OK_ when you try to blow anything Answering this question in the negative will abort the process with the message process_aborted____ Unless if you want to blow a window you will have to answer the questions set_blow_type_ _0__ blow_w center_point The first question is asked for safety reasons because the blowing type O is the most common one and you might have forgotten to select it If the second question is answered in the positive the objects are blown with respect to the origin of the axis Otherwise blow_w _center_axis is asked If this question is answered in the affirmative the objects are blown with respect to the axis Otherwise blow_w center_plane is asked and the objects are blown with respect to the actual plane If this question is answered in the negative the process is aborted with the message process_aborted____ Because you might have forgotten to adjust the axis that is needed in the first and second case you get the opportunity to do this when you answer the question set_new_axis______ in the affirmative 3D blow____ wire_____ Blow active wires 3D blow____ points___ Blow active matching points 3D blow____ window___ Blow the
218. e displayed when one of the boxes has been clicked with mouse button 3 The files are searched first on the current directory then on the directory MMP of the current drive and finally on the directory MMP of drive C If they are missing no hint will be displayed xxx indicates the number of the box that has been clicked The hint box number 000 is displayed at the beginning of the program lines number of lines of the current box or pull box strings number of help strings for the current line of the box string character string with up to 40 characters D 18 Window Files MMP_WIN xxx Data of the screen windows in the 3D MMP editor and the 3D MMP plot program These files are searched on the current directory only nWin number of screen windows iWin1 6 pixel coordinates of lower left corner pixel coordinates of upper right corner resolution in w and yw direction invisible grid lines rWin1 4 Ly and yy coordinates of lower left corner limits Ly and Yy coordinates of upper right corner limits pWin1 9 X Y and Z coordinate of origin of plane Fw X Y and Z coordinate of first tangent vector vi X Y and Z coordinate of second tangent vector v3 D 19 Movie Directives File MMP_DIR xxx Data necessary to generate a movie with the 3D MMP plot program For a description of the structure and language used in these files see section 16 8 2 D 20 Picture Information File MMP_Iyy xxx Data on pictures stored in MMP_Fyy xxx files
219. e evanescent plane waves degenerate into an ordinary plane waves for Sk Rk Sk Rk they degenerate into a plane wave rotated around the x axis The electric evanescent plane wave is odd with respect to x 0 the magnetic one even It can be scaled with Seca section 10 5 294 D Format of the Data Files D 1 Overview All files are ASCII files in FORTRAN list directed input format format with exception of the picture files MMP_Fyy xxx Among other things this means that the remainder of the lines following the data may be used for comments All files are read and written on the current directory In the Windows version the directory can be specified on the command line For the parameters in the input file FORTRAN implicit notation is used Unless explicitely declared integer parameters start with the letters i to n real parameters with the letters a b d to h and o to z complex parameters start with the letter c and are entered as two real numbers the first being the real part In the rest of the chapter the format is given for all files in alphabetical order Files which have the same format but different names for use in different programs are de scribed once only Indented blocks are repeated in a loop the number of times is indicated on the line preceding the block Files for the Main Program MMP_M3D The 3D MMP main program uses the following data files MMP_3DI xxx input file read only necessary to run mm
220. e fields and on the convergence of multipole expansions To start with use a simple model like MMP_3DI 002 and try some mild deformations for example select the values 1 5 1 2 2 in the boxes ang fac M respectively and blow the object with respect to the XY plane i e run 3D blow object and answer all questions you are asked in the negative except blow_w center_plane What you get is an ellipsoidal body instead of the sphere When you either increase the blow factor fac or when you apply the blow command more than once you easily get more deformed bodies and you see the errors increase considerably Obviously the simple model with a single multipole in the center may be used for slight deformations only 17 5 2 Deformations Galore Model 17 When you want to deform a body in a similar way as described above but with respect to a plane different from the XY plane you have to rotate the matching points first blow with respect to the XY plane and rotate with the negative angle In this case be aware of the fact that the value in the box ang and the axis are both used in the blow command as well as in the rotate command but with different meanings However you should try the procedure to get more experience For example 1 Apply the blow command mentioned in model 16 twice 2 Rotate the matching points with an angle of 90 degrees around t
221. e more matching points in Y direction and less matching points in p direction Moreover the automatic procedure sets different maximum orders and degrees 4 Rotate the 3D object around the Z axis with an angle of 90 degrees 5 Read the auxiliary input file MMP_3DI 004 containing the dipole with the dummy matching points and move this object to the desired location 0 6 m on the X axis 6 Add the additional multipole near the mirror point of the dipole in the conducting sphere and save the new model on file MMP_3D1 009 7 Run the main and zoom programs as before You see that you can obtain far more accurate results with about the same compu tation time as before Maybe you are able to find even better models when you modify the number of matching points on the 2D arc the factor fac the maximum orders and degrees proposed by the editor the locations of the multipoles etc With some experience you will be able to immediately generate a model like this one 17 3 6 Towards the Optimum Model 10 From the error distribution of model 9 you can see that the large errors are concentrated in an area near the dipole As mentioned earlier you should increase the matching point 228 density in this area to get better models with more balanced error distributions This can be achieved by splitting the 2D arc used for generating the sphere into two or more parts with different numbers of matching points Al
222. e new position defined by the displacement vector 15 6 5 2D move __ Move active elements to a new position 2D move executes a 2D copy with a subse quent 2D delete on the active elements at the original position For safety reasons you are asked 106 move___elements_0K_ when you try to move any element If this question is answered in the negative nothing is moved and process_aborted____ is displayed Since the procedure is essentially the same as for 2D copy a detailed description is omitted 15 6 6 2D blow____ Blow active elements i e multiply the coordinates w Yw and the size of an element by a blowing factor defined in the additional real data box fact For safety reasons you are asked blow___elements_OK_ when you try to blow any element If this question is answered in the negative nothing is blown and process_aborted____ is displayed 2D blow____ line_____ Blow active lines and arcs 2D blow____ arc______ Identical with 2D blow line see above 2D blow____ window___ See 3D constructions 2D blow____ object___ Simultaneously perform 2D blow line see above and 2D blow pole 2D blow____ pole_____ Blow active expansions 15 6 7 2D rotate_ Rotate active elements around a point For safety reasons you are
223. e oe Se ee Ae a 133022 Output e vw aos ae Mock ee dd bee ee 5 13 5 3 Initializations gee a ee lee ee ee SE Sa Boon eS Parameters and Variables 0 o e o Basic Packag s des cta ear o aa Ge a Additional Programs for Transputer Pipelines Utilities 4 12 AA rte O Be Ee ce a eri Ate seers 13 9 1 MMP_PAR Parameter Labeling Program 13 9 2 Fourier Transform mmp_fan and mmp f3d 13 10Modification of the Source Adding Expansions III User s Guide of the Graphic Interface 14 Graphics Introduction 14 1 14 2 14 3 14 4 14 5 14 6 14 7 IVETE WA dade GOP RAE Gok Be A ete Ree OE Abed R Introduction A Ls EI A ee A A Ger ee BOXES e dea n b Te a oa wer he a wie DB Gre AS eae WIndows 2 5 fo eect ht cece ee lan Oy he Bde te a ees a 14 4 1 Screen Windows aooaa a a a 144 2 Plot Windows ss ave a a A E E ine a Pa ee A Mouse Use and Actions a Colors and Fill Patterns ee Generating Hardcopies and Meta Files o 15 3D Graphic Editor 15 1 15 2 15 3 15 4 Programs Stare sd Ole E e ol AAA eB AN Program Exit bpd ok e A Ge aoe eae De of ae De Ae ape Graphic Elements and Constructions 2004 15 3 1 3D Construction and Elements 4 15 3 2 2D Construction and Elements 4 15 3 3 Activating Inactivating Representations ALCUIONS x os sy Bite wha deh eS e
224. e of multiple frequency runs the exit is performed after the last frequency run only If errors integrals or plot files have to be computed either a computation of the parameters must precede or a parameter file MMP_PAR xxx must be present If task 9 is chosen the input and parameter files are read and subroutine user is called It can be modified for various custom expansions In this version of the source 50 a version for interactive plotting with the graphic front end for UNIX workstations is shown but you are free to use subroutine user for your own needs Factorization Method This option chooses the algorithm for calculation of the parameters This is either the updating algorithm with Givens plane rotation based on the matrix A or the Cholesky factorization based on A A which is faster but numerically inferior see chapter 5 and rarely used therefore Note that the Cholesky factorization is incompatible with multiple excitations Frequency The MMP program can make computations for one or more frequencies in one run For a single frequency run the value cfreq from the input file see chapter 10 is used for the multiple frequency run the problem is computed for each of the frequencies in file MMP_FOU FRQ see appendix D Note that multiple frequencies are incompatible with multiple excitations Input File Number xxx The input and output files are numbered with an extension xxx For single frequencies with single e
225. e plot of V field2 probably is best suited with the default value fi11 grid 4 In monochrome mode you should set fi11 _grid 2 instead You will notice that you get the absolute values of the scalar potential You probably want to plot positive and negative values differently This can be done for scalar fields only In fact the potential is a scalar but the plot program treats it as a vector since it is in the second set of vector fields The resulting field has Z components only Thus you can turn off the X and Y components of the field i e you can inactivate the boxes x 259 and y When only one of the field components is turned on the plot program knows that the field is scalar and changes the scaling and representation of iso lines After having modified the field representation run show pic f When you would like to see how an electrically charged particle moves in the field you have computed with the FD algorithm you simply can add such a particle with add part and move it with move part Once more the proper choice of the time intervals dt of iter part and the properties of the particle turns out to be quite difficult Thus you might prefer to read the particle file number 33 included in this package Before you start moving the particle with move part
226. e sign of an integer value this value has to be counted down beyond zero This is necessary because integer values have a variable length whereas the length of real values is fixed Note that some of the data contained in boxes remain internally unchanged when you modify them Fore example when you change the data of a matching point displayed in the corresponding boxes it is not reasonable to change these data immediately To change the corresponding internal values something like the enter key on the keyboard is required Usually a special command has to be performed for doing this Such a command can be much more powerful than the usual enter function For example the command for adjusting the matching point data allows you to enter the data for one matching point only for all matching points at the same time or for a selected set of matching points Different kinds of boxes can be distinguished Single Line Boxes Single line boxes can be either inactive off or active on which corresponds to buttons in usual Windows applications Inactive boxes are repre sented as all other boxes whereas thick lines are drawn around active boxes and the text color is red rather than black in color mode To change the activity of such a box the first or second mouse button has to be clicked when the cursor is in the text area It should be pointed out that only some special single line boxes can be activated Pull Boxes Pull boxes contain several li
227. e surface to volume ratio of a sphere is known to be smaller than the ratio of any other body Since the surface is discretized in the MMP codes this guarantees a minimum of numerical expenditure Nonetheless you can study most of the 3D MMP features with spheres which are consequently the best suited problem to start with Note that neither spher ical symmetry nor rotational symmetry is taken into account in the 3D MMP code for personal computers Thus the procedure for non spherical bodies is essentially the same but more time consuming It is important to recognize that the input data files you are supposed to generate in this tutorial are already on the working directory i e the subdirectory EX3D of the directory MMP3D In order to avoid overwriting it is recommended to rename all files on the working directory or to copy all flies on the working directory on another directory before you start the tutorial Since colors are helpful in the 3D MMP editor it is recommended to select a color driver whenever possible Of course high resolution drivers are preferable but problems can occur because of the amount of memory required for these drivers Since only up to 16 colors are used in the actual version of the 3D MMP graphics it makes no sense to use drivers with more colors expect when you do not find an appropriate 16 color driver that allows to set the color composition For more information see the User s Guide of the Graphic Interface
228. e updated row a R is divided into N trapezoidal shares Ri Ryn of equal size which means that the updating time is about the same for each part The shares are residing on different processors cf fig 5 2 which form a pipeline structure The part of the program which produces the rows and does input and output does not have to be parallelized and can reside on the root processor This is the major portion of the code The root processor can also take a share of R however its optimum size depends on the size of the problem being solved and on the size of the pipeline Computation of the rows plus updating of this share should take the same time as updating of one of the other shares If the share is larger the rest of the pipeline has to wait for the root processor if it is smaller the processor is not fully occupied Both reduce performance The procedure for the updating on one processor 7 having a share Ri of n rows is the following 1 Get x from processor i 1 2 Update the first n columns of x into R 3 Pass the remaining modified rest of x on to processor i 1 4 Get next x go to step 1 32 R TER COI gt gt EXA NE Figure 5 2 The triangular matrix R is divided into trapezoidal parts residing on different processors in a pipeline structure The root processor holds the major not parallelized part of the program the other processors just small updating programs Only short vectors h
229. e window data is saved with the message writing window file If an error occurs when the program tries to open MMP_WIN 000 cannot_open_file__ is displayed and the process aborted 152 generate meta_ tis computing Wm field_ No DE BH JE energy ily zM P gt 0 EXIT a i ie S y or sequ M 101 EERE EERE ERECT e iT 17 THIGH l H metav 8 E 02 E E Sy 0 00000E 00 vz 0 00000E 00 Totalt FRE 300 iter part E tim 0 00000E 00 part type 1 m0 1 00000E 00 Figure 16 1 Desk of the 3D MMP plot program showing the time average of the energy density for a plane wave incident on a cylindrical lens see last example of the tutorial 16 3 Actions 16 3 1 Regular Actions Regular actions are selected above all in the first two boxes of the top line of the stan dard desk In the 3D MMP plot program regular actions or commands consist of an action and of an item To start such an action the question information box has to be clicked with the mouse button 1 or 2 Not all regular actions are performed directly In many cases you are asked some questions either for safety reasons or to specify the regular action Usually some parameters used during the regular action to be performed have to be defined in the corresponding boxes before it is started If this has been done the action to be performed should be selected with the first or second mouse button in the action box The item sh
230. ead input 29 2 Reduce the number of matching points in such a way that the shape of the lens still is well defined Near the edge you should keep every second matching point whereas you can delete about four of five matching points near the symmetry plane Note that you can activate all matching points you want to delete before you run 3D delete points 3 You can delete all expansions because they are not required in the FDTD procedure 4 Reset the window planes and rotate the remaining matching points around the Z axis with an angle of 90 degrees This can easily be done with 3D rotate object 5 With the rotation the symmetry has been changed Thus you have to adjust the symmetry numbers I e you have to exchange the contents of the boxes is1 and is2 6 Save the data on a new input file 34 with 3D write input 34 7 Exit the editor In the plot program you first can read the input file 34 Allow the program to perform the symmetry operations only one half of the lens is contained in the input file when you run read input 34 Now you should blow the plot window in such a way that the side length is about 10m Since the default length is 2m a blow factor blow 5 0 should be selected Turn the matching point representation on i e activate the box M on the top line and run show pic f for checking whether everything i
231. ed Otherwise you will have to set the plane exactly in the same way as the plane of the screen window see above 119 3D add_____ object___ Combine two objects into one As a result only one object with number one will exist but this object will contain all matching points and expansions of the original objects Since there is no way to split the resulting object into the two original ones you have to save the objects on input data files if you intend to use them later see 3D write file For safety reasons you are asked obj1i obj2 gt o0bj 1_OK_ Answering this question in the negative will abort the process with the message objects_not_added_ Add an expansion Select the additional integer and real data of the expansion to be constructed in the corresponding boxes Exp and se ReG ImG If the maxi mum number of expansions defined in the include file MMP_E3D INC is exceeded too_many_expansions is displayed and the process aborted Otherwise you have to discretize the geometric data origin and two tangent vectors exactly as described for 3D add points 3D add_____ domain___ Add a new domain Before execution select the material properties r ur and o in the corresponding boxes Er Ei Ur Ui Sr Si where the character i indicates the imaginary parts If the maximum number of expansions is
232. ed This is a good reason for trying 2D generate pole with another pole generation type Note that it does not make sense to generate more than one matching point along the axis of a 3D cylinder when only 2D expansions are present a plane wave is a special 2D expansion too Therefore choose the length of the cylinder sufficiently small To avoid that the cylinder becomes almost invisible select a reasonable length and increase the factor in the box fac in such a way that only one matching point is generated along the axis of the cylinder Before saving the model on a 3D input file adjust the data of the expansions because the procedures that generate the poles assume 3D multipoles rather than 2D multipoles Moreover it is convenient to set the problem type in the box prob to 200 This has the following consequence The propagation constant i e the Z component of all 2D expansion is set automatically equal to the value of the incident plane wave Thus you do not have to worry about the propagation constants of the 2D expansions When you would set prob 300 you would have to make sure that the propagation constants of all expansions are identical Note that prob 200 requires a construction in the XY plane 251 and a plane wave excitation which is the case here When you compute the same model with different frequencies you can see that the size of the focus o
233. ed in error file MMP_ERR xxx input file MMP_3DI xxx 3D data and MMP_2DI yyy 2D data Select item of regular action to be performed when the first mouse button is clicked in one of the windows Select item number with the first count up and second count down mouse button in the value area of this box For more information see description of regular actions Box 12 Additional Integer Data Type pull down input output M_ prob oscr ofil isti_ is2_ is3_ Ncon Nint Nfpt Inor different numbers of interest that are not stored for further use problem type for 3D MMP main program amount of screen output for 3D MMP main program amount of output on output file for 3D MMP main program symmetry with respect to plane X 0 symmetry with respect to plane Y 0 symmetry with respect to plane Z 0 number of constraints number of integrals number of general plots sets of field points scaling directive for 3D MMP main program 146 Nexc number of excitations Note that the last Nexc expansions are exci tations If multiple excitations are selected only expansions with one parameter e g plane waves and connections are allowed excitations over amount of overdetermination This number is used in the check and pole generation routines and is not stored in the input file Note The values 1 up to 4 are appropriate in most cases Most of the data in this box are transferred to the 3D MMP main program file MMP_3DI xxx
234. eguide 0 00000 eee ee 291 C 5 Circular Waveguide aoaaa ee 292 G07 Plane Wave inthe cep a a a eS 293 C 7 Evanescent Plane Wave ee 293 D Format of the Data Files 295 Dil Overview so Seid A A A 295 D 2 3D Input File MMP_3DI xxx oa caora ag ede a 0 00002 eee 296 D 3 2D Input File MMP_2DI xxx 2 2 20 0 0 0000 ee eee eee 297 D 4 Parameter Files MMP_PAR xxx MMP_PAL xxx 004 298 D 5 Connection Files MMP_CyyY XXX ee 298 D 6 Error File MMP lt ERRIXX aog oaa A A eee 298 D 7 Integral File MMP INT xxx gt aa a A a 299 D 8 Complex 3D Plot File MMP_Pyy xxXX o o 299 D 9 Real 3D Plot File MMP_Tyy xxx 300 D 10 2D Plot Files MMP_DAT PLT MMP_PLF xxx MMP_PLT XXX 300 D 11 Particle Files MMP_PRT xxx 0 e e 300 D 12 Fourier Time Value File MMP_FOU TIM 301 D 13 Fourier Frequency File MMP_FOU FRQ o 301 D 14 Editor Desk File MMP_EBD DSK o e eee 301 D 15 Plot Program Desk File MMP_P3D DSK o 302 D 16 Action Files MMP_E3D ACT and MMP_P3D ACT 303 D 17 Hint Files MMP_E3D xxx and MMP_P3D xxx 304 D 18 Window Files MMP_WIN XXX 2 aa ee 304 D 19 Movie Directives File MMP_DIR xxx 0 2 0000000004 304 D 20 Picture Information File MMP_Iyy xxx o 304 D 21 Pict
235. el coordinate of actual cursor position lycr returns vertical pixel coordinate of actual cursor position mgspix idev 1lxul lyul lwid lhgt Save pixels of a rectangular part of the screen in memory This function is used for the pull boxes on the screen only If it is replaced by a dummy routine that returns the value 1 the pull boxes are replaced by roll boxes that display one line of the box at a time only Although such boxes are less convenient they allow to run the MMP graphics correctly if mgspix and mgrpix cannot be simulated idev device address screen only 1xul horizontal pixel coordinate of upper left corner lyul vertical pixel coordinate of upper left corner lwid pixel width of rectangle lhgt pixel length of rectangle mgrpix idev 1lxul lyul lwid lhgt Restore pixels of a rectangular part of the screen from memory This function is used for the pull boxes on the screen only If it is replaced by a dummy routine that returns the value 1 the pull boxes are replaced by roll boxes that display one line of the box at a time only Although such boxes are less convenient they allow to run the MMP graphics correctly if mgspix and mgrpix cannot be simulated idev device address screen only 1xul horizontal pixel coordinate of upper left corner lyul vertical pixel coordinate of upper left corner lwid pixel width of rectangle lhgt pixel length of rectangle mgsfil idev 1lxul lyul lwid lhgt fname Save pixels of a
236. elatively slow Moreover Micro Way does not take advantage of the graphic capabilities of the i860 Consequently the 3D MMP graphics run on this board with a not exciting but acceptable speed So far Micro Way does neither support GEM nor Windows graphics Since we consider Micro Way s NDP GREX graphics library to be insufficient for our needs special interfaces with appropriate alien file servers have been written Windows and GEM versions of 3D MMP and the corresponding interfaces for Micro Way i860 FORTRAN are available upon request 18 4 Workstations Mainframes Supercomputers Since the 3D MMP main and Fourier transform programs are written in standard FOR TRAN with some very mild exceptions see next chapter they can easily be compiled on bigger machines than PCs The time consuming parts of the 3D MMP codes have been written very carefully Thus it is expected that the codes run efficiently on most machines without any modification It is assumed that it is possible to implement the 3D MMP graphics on workstations Since the graphic libraries on workstations are usually much more comfortable than the graphic libraries for PCs one can expect that it is relatively simple to simulate the elementary 3D MMP graphic functions on a workstation For SUN workstations a separate 3D MMP graphics package has been written in C by P Regli 45 16 This package takes advantage of the features available on a SUN workstation and is more comfortab
237. els height of output device in pixels BPwWNR Oo File MMP_E3D INC Important Parameters MEle MEnt MMat MPol MObj MGeb MBed MBedP MIntg MIntgP MWind MFPt MFPtP maximum number of 2D elements maximum number of 2D expansions poles maximum number of 2D 3D matching points maximum number of 3D expansions poles maximum number of 3D objects set of matching points poles maximum number of domains maximum number of constraints maximum number of points for the definition of a constraint maximum number of integrals maximum number of points for the definition of an integral maximum number of standard plot windows transferred to MMP_M3D maximum number of sets of field points general plot windows maximum number of points of a general plot window Important Variables nGeb number of domains 321 kGeb rGeb nEle kEle iEle rEle nEnt kEnt iEnt rEnt nMat nMat2 nMat3 niMat n2Mat kMat iMat rMat pMat hMat nPol nipol n2pol kPol iPol rPol pPol hPol nWind kWind iWind rWind nFPt kFPt nFPtP kFPtP iFPt iFPtP iFPta pFPt hFPt nBed number of the actual domain real information of the domains 1 real part of relative permittivities of the domains 2 real part of relative permeabilities of the domains 3 conductivities of the domains 4 imaginary part of relative permittivities of the domains 5 imaginary part of relative permeabilities of the domains number of 2D elements l
238. en it is displaying ready_for_action__ 2 When the question information box is active and displays a message remove it by clicking any mouse button 3 Select the action in the first three boxes of the top line and possible additional parameters in the other boxes 4 Click button 1 or 2 in the question information box i e box number four of the top line for starting the action Often the action is not started immediately Instead you have to answer one or several questions displayed in box number four of the top line This can be for safety reasons or to select different variants of the action Give the answers to the questions by clicking in the box 4 first button means affirmative second button means negative 89 When several screen windows are present and the window action results in time consuming drawings of 3D objects the drawing starts in the window that has been selected in the item box for handling windows and ends either when you abort the process by pressing down a mouse button or when the drawing in the last window is terminated Note that the 3D objects are not drawn in the first window when you have selected window number 2 in the corresponding item box All Buttons When a hint box is displayed it is removed when any button is clicked You can abort time consuming actions To do this keep any one of the mouse buttons pressed until the command release_mouse_button is displayed As soon as you release the
239. er of a segment should be larger than the weight of a matching point near the end The weights near the end and in the center can be selected in the boxes Exp IE3S and Exp IE4 respectively Although you probably will not get more accurate results than with two matching points per segment you should try different weightings for getting more experience However sophisticated MMP users recommend the values 1 and 7 Finally the value in the box Exp IE6 is used to change the matching point distribution an the ends of the wire Let us set this value to 0 When you count the number of matching points after completing 3D add wire you see that you already have 92 matching points 62 of them are dummy matching points that do not affect the computation time at all If you did not forget to define the incident plane wave and to select the frequency and the symmetry numbers you can already save your model leave the editor run the main program and so on But wait a second Better set the symmetry number is1 0 If you don t believe that try and read the warning issued by the main program Of course you can easily modify the weights of the matching points on the wire and look what happens The errors in the middle matching points of each segment are increased when the second weight in the box Exp IE4 is decreased At the same time the errors in the other matching points are red
240. er of of constraints nnbptm 1000 maximum number of integral points for constraints nfreqm 50 maximum number of frequencies G 2 Parameter Labelling Program nentm 1000 maximum number of expansions including excitations nkolm 2500 maximum number of columns of the system matrix nloesm 8 maximum number of symmetry components nrekm 10 maximum recursion depth for nested connections G 3 Fourier Programs 1000 maximum number of time values 1000 maximum number of frequency values G 4 Graphic Editor mele 100 maximum number of 2D elements lines and arcs ment 100 maximum number of 2D expansions mmat 5000 maximum number of matching points 325 mpol 1000 maximum number of 3D expansions mobj 2 maximum number of 3D objects mgeb 100 maximum number of domains mbed 9 maximum number of constraints mbedp 1000 maximum number of points per constraint mintg 1 maximum number of integrals mintgp 1000 maximum number of points per integral mwind 9 maximum number of screen and plot windows mfpt 1 maximum number of sets of field points mfptp 10000 maximum number of field points Note that the maximum number of 3D objects cannot be changed without major modifi cations of the entire editor program because all points of both 3D objects are stored in a single array without an index for the object number for saving memory MMat and MPol are the maximum numbers of matching points and expansions of both objects together Obviously you can gener
241. er of the rectangle and releasing the button when the cursor is near the opposite corner of the rectangle All points that are visible within this rectangle become active 15 4 3 Special Actions The most important special action is used for leaving the 3D editor see 15 2 In addition there are two more special actions that are started by clicking the corresponding box with the first mouse button Clearing the Windows Clicking the box clear with the first or second mouse button will clear all windows immediately Generating Meta Files The box meta is used to select the number xx of the meta file MMP_Exx WMF to be generated In order to create a meta file the first or second mouse button has to be pressed when the cursor is in the text area of this box If a meta file with the number xx does already exist you are asked overwrite _meta file If this question is answered in the negative no meta file is generated and NO_meta_file_gener is displayed Otherwise the program starts generating a meta file with the message generating meta_file The information written on a meta file is essentially what would be displayed on the screen if the regular action show would be performed Thus the contents of a meta file depends on the selection of the dimension in the first box of the top line and on the selection of the item in the third box of the top line Using meta files is advantageous because this allows to take advanta
242. er small problems For larger problems the matrix can numerically lose its positive definiteness during factorization and the algorithm will then come to a premature end Nevertheless this algorithm has been introduced into the 3D MMP program for small benchmark problems where numerical problems do not yet arise al 5 3 Solution with Orthogonal Transformations A much better way to solve the least squares problem is to use the QR decomposition A QR or QA R 5 10 30 to compute an upper triangular matrix R directly from A Q is unitary and therefore does not increase the condition number of A As X X R R R is equivalent with X to within a factor of et per row For practical use there are several ways of obtaining R The one fitted best to our needs is an algorithm based on Givens plane rotations A Givens transformation is the unitary M by M matrix G i j which is different from the unity matrix J only in columns and rows i and j respectively I G i j I with c s s 1 5 11 The product G i j A performs a rotation in the i j plane of A If c and s are chosen properly it can be used to selectively introduce a zero into the element ax of A c s aig _ ij 19 EA oa with ii 0 05 c a 5 and s ull gt V la l ars laij y lail ars The procedure used in the 3D MMP main program is an adaptation of a LINPACK algorithm for updating QR factorizations i e for computing the modified ma
243. erdetermination On the other hand a larger overdetermination is certainly meaningful in complicated models Moreover since it is relatively difficult to increase the matching point density of a model it is reasonable to start with a model with a relatively large number of matching points i e a large overdetermination factor over If the result turns out to be too inaccurate you only have to modify the MMP expansions in those areas where large errors are obtained whereas the matching points can be left unchanged Incidentally the computation time is proportional to the number of matching points but it is proportional to the square of the number of unknowns which is a much more severe problem In the input file MMP_3DI 010 a model generated with two 2D arcs is contained This model is just a first guess and has not been optimized at all You can see that the errors have been reduced once more Since the errors are still higher near the dipole than far away 1t is quite clear how you can go on Of course you can try to improve this model as long as you want Maybe finding a much better model is a challenge for you but the authors are getting tired of this most simple example 17 4 Using Materials 17 4 1 Dielectric Sphere Model 11 If the ideally conducting sphere that has been considered so far is replaced by an ideally dielectric sphere not much is changing at first sight and you can start in the edito
244. ere near the dipole has to be increased Although this is not very difficult you might prefer to leave the actual matching point distribution unchanged whenever possible and to change the MMP expansion only Thus you might prefer to introduce an additional mirror dipole to the multipole in the center of the sphere Provided that the results obtained without this additional pole are very inaccurate you can assume that no numerical dependences between the two poles in the sphere occur although the rules for setting multipoles are violated When you are too lazy to change the matching point distribution you are probably too lazy to compute the exact location of the mirror point too In this case you might still get too inaccurate results The most simple method for decreasing the errors is to increase the orders and degrees of the additional pole in a roughly estimated mirror point As soon as these orders and degrees are too high you will get useless results except when you introduce additional matching points near the pole but with relatively low orders and degrees you can get useful results if the dipole is not very close to the surface of the sphere It is important to note that always the last expansion function is considered to be the excitation When you simply add a new multipole near the mirror point its last expansion function becomes the excitation which is not intended There are different ways to avoid that e You can excha
245. erformed before the 3D move command is executed you have to set the start and end point of the vector respectively axis during this procedure 3D rotate_ wire_____ Rotate active wires 3D rotate__ points___ Rotate active matching point 3D rotate__ window___ Rotate the window plane If the number selected in the item box is not equal to one of the windows cannot_rotate_window is displayed and the process aborted 3D rotate__ object___ Rotate object 1 or 2 If the number selected in the item box is neither 1 nor 2 both objects are rotated 126 3D rotate__ pole_____ Rotate active expansions 15 7 8 3D invert__ Invert 3D elements For safety reasons you are asked invert_elements_OK_ when you try to invert anything Answering this question in the negative will abort the process with the message process_aborted____ 3D invert_ wire_____ Invert the direction of active wires 3D invert__ points___ Invert the direction of active matching points by inverting their second tangent vectors Va 3D invert__ vect axis Invert the direction of the vector respectively axis used in several constructions 3D invert__ window___ Invert the direction of the window plane with the number selected in the item box by inverting its second tangent vector v3 If no window with the selec
246. es because the FORTRAN compilers take about 1Mbytes of the extended memory For running the compiled 3D MMP version included in this package 4Mbytes of extended memory are required It is important to note that several FORTRAN compilers support different DOS extenders that are not necessarily compatible When the DOS high memory manager HIMEM SYS is installed it reserves extended memory Not all DOS extenders can use memory reserved by HIMEM SYS and issue an error message indicating that there is not enough memory left This forces the user to remove HIMEM SYS before an application running under such a DOS extender can be started This is quite annoying because many applications like Microsoft Windows in enhanced mode require HIMEM SYS to be installed However if you cannot run any application although you have enough extended memory try removing HIMEM SYS The compiled 3D MMP version included in this package runs under Windows 3 in enhanced mode i e it uses the extended memory manager of Windows 3 Most of the modern compilers for 386 and 486 PCs support virtual disk storage 264 Thus large problems can be computed when a sufficiently large hard disk is available Large problems are extremely time consuming on PCs Moreover the MMP matrices are dense For these reasons the compiled 3D MMP version included in this package does not use virtual disk storage and therefore runs on PCs with small harddisks l e about 10Mbytes of free memory on
247. es in Plates e 17 9 1 A Simple Model Model 25 o o o o 17 9 2 A More Fictitious Model Model 26 17 9 3 Optimizations Ring Multipoles Connections Model 27 17 10Lossy Sphere in Rectangular Waveguide Model 28 17 11Cylindrical Lens Illuminated by Pulsed Plane Wave Model 29 17 12Multiple Excitations Model 30 o o oo o 17 13Field Lines Model 31 o ooo e 17 14Electric Charges Model 32 o o o oo o e 17 15Finite Differences Model 33 o o oo o 17 16Finite Differences Time Domain Model 34 0 V Installation Configuration and Running 18 Hardware Requirements 181 Ordinary POS Ati a A RE AAA A Moves ake AG 18 2 Transputer Add On Boards e 18 3 i860 Number Smasher e 18 4 Workstations Mainframes Supercomputers 18 5 Example Configuration o o oaoa ee 19 Compilers and Systems 19 1 Introductions dc gun ee Pe aS ee Ee OA Be ae 19 2 Systems and Graphic Packages o ee 193 Compilers meca o eee ll o wie nk Ae 20 Installation and Compilation 20 1 Installation of Source and Auxiliary Files 20 2 Installation of Windows 0 00002 eee eee 20 3 Compilation 2 40 26 54 24 a ae eek eee RD EA ee 20 3 1 Standard Compilation with Supported Compilers 20 3 2 Modificat
248. esentation gt you might prefer to select a grid representation by clicking the box once You will obtain i e a grid representation without iso lines At first sight this representation looks similar to the vector represen tation when all elements except the plane are turned off but the field points now are on the corners of the squares rather than in the centers and a regular grid is required In fact to get a more useful grid representation you should do the following 1 turn the window plane in such a way that it is no longer parallel to the plane of the field points For example rotate the window with the command rotate wind around an axis with the components 1 1 1 with an angle of 30 degrees selected in the box angle You will need some experience for immediately getting an appropriate view 2 Select a grid scaling factor grids different from zero Usually 1 or a similar value is appropriate Now the grid points are no longer on the field points They are moved in a direction perpendicular to the plane of the field points in a distance proportional to the strength of the field and of the scaling factor grids When you now go back to the vector representation gt you get a 3D representation of the field that looks like the graphics preferred by managers When you look at the mountain like 3D grid and vecto
249. etEpsR kFPtpy Emx 2 0 Emx E Emx Epx 2 0 Epx E Epx Emy 2 0 Emy E Emy Epy 2 0 Epy E Epy Q Epx Emx dy2 Epy Emy dx2 VR kFPt dy2 Emx VI kFPtmx Epx VI kFPtpx 1 dx2 Emy VI kFPtmy Epy VI kFPtpy Q When the loops have been terminated the auxiliary vector VI is cleared i e reset to zero and the subroutine ends call clrVI true end Note that clearing VI is necessary because VI affects the computation of the electric field from the scalar potential 16 10 Moving Particles and Field Lines In Newton s world the movement of mass particles can be computed for all times when the location and velocity of all particles is given at a certain time Similarly the move ment of electrically charged particles can be computed It is well known that electro magnetic fields propagate with a finite speed according to Maxwell theory The synthesis of Newtons mechanics and Maxwell s electrodynamics leads to Einstein s special theory of relativity Unfortunately the location and velocity of all particles at a certain time in Einstein s world does not provide enough information for computing the movement of the particles In addition the entire field has to be known which leads to consider able problems for both modelling and the numeric code For reasons of simplicity the particle movement in the plot program ignores the time delay due to the finite speed of electromagnetic waves I e one essentially
250. etry in the Z direction 300 399 3D scattering problems Within these ranges you are free to use any values For 2D scattering problems with a plane wave excitation iprob 200 299 the propagation constants y of the 2D expansions will be initialized to the Z component of the wave vector k of the incident plane wave As a consequence for 2D problems with other excitations different problem numbers have to be used and the propagation constants have to be declared with the expansions see section 10 5 52 10 3 2 Output on Screen and Output File The amount of output on the screen and in the output file MMP_M3D LOG can be chosen with msscr screen and msfil output file A description of this output and an example is given in section 11 5 msscr Amount of Output 0 no output on screen except questions at startup 1 general output is written to the screen 2 same as msscr 1 but the current position of the program matching point number or field point number is given and the error values are shown 3 in addition to msscr 2 a graphic representation of the matrix is shown if the number of columns does not exceed 80 4 in addition to msscr 3 a graphic representation of the rows is shown if the number of columns does not exceed 80 For msfil which determines the amount of output in the output file MMP_M3D LOG the same values can be used with the exception that the current position is not written to the outp
251. ets N K K S aS E Ars Y EA Are SaN 2028 i 1 k 1 k 1 15 and the projection method 1 15 for N M gets K N K A Ana ye Are 2G S101 1 25 i l k 1 k 1 If the rg k 1 K in these two expressions are the same as the r j 1 M n 1 18 additional equivalences occur e The generalized point matching method with least squares solution 1 21 becomes equivalent to the discrete error method 1 24 if the weighting function w is chosen appropriately we Wy Arr 1 26 e The discrete projection method can be looked upon as premultiplication of the generalized point matching problem 1 19 with another M by N matrix t the elements of which are values of testing functions t at rj This is another way to obtain a system of equations with a square matrix tia lajalp les tz b p 1 27 Seen from the theory of overdetermined systems of equations the least squares method 1 21 is more common and normally produces better results The advantage of the point matching method is that the normal equations 1 21 need not to be formulated explicitly Instead 1 19 can be solved by direct methods in the least squares sense cf chapter 5 Numerically this is superior because a has a much better condition number than a 5 aji p 16 2 Fundamentals of 3D MMP 2 1 Scattering Problems In electromagnetic scattering problems one is interested in what happens when an elec tromagnetic wave incident wave or
252. exceeded too_many_domains__ is displayed and the process aborted Note that domain number 0 is used for all ideal conductors and has not to be defined Moreover domain number 1 is predefined as free space If the data of domain number 1 are not appropriate the regular action 2D adjust domain has to be performed 15 7 3 3D delete Delete 3D elements For safety reasons you are asked delete _elements_0K_ when you try to delete anything Answering this question in the negative will abort the process with the message process_aborted____ 3D delete_ wire_____ Delete active wires 3D delete points___ Delete active matching points 120 3D delete__ window___ Delete the screen or plot window with the number selected in the item box cannot_delete_window indicates that the window does not exist and cannot be deleted therefore The question delete screen wind will only be asked if more than two screen windows exist and if the corresponding screen window is defined Similarly delete_plot_window_ is asked when the corresponding plot window is defined 3D delete__ parts____ Delete the part with the number selected in the item box Before its execution the parts have to be determined I e two objects sets of matching points and expansions should exist and 3D generate parts should have been performed either directl
253. extended error file the values of the components of the electric and magnetic field are given for both sides on the boundary in addition to the error values and field assessments 11 3 Integrals The values for the integrals are shown in the integral file MMP_INT xxx on the screen and in the output file MMP_M3D LOG 11 4 Plots A variety of plots of the total field ft f 4 fi for different graphic output programs can be produced The file formats are given in appendix D for a choice consult the manuals of the graphic output programs If only the scattered field f is of interest the parameter file s have to be modified accordingly i e the parameter s for the incident field must be set to zero with a text editor 11 5 Screen and Output File Information on the run and its current position is given on the screen and in the output file The amount is controlled by msscr and by msfil cf section 10 3 2 An example of screen output msscr 1 3D MMP VERSION 3 3 date Tue Jun 18 09 02 44 1991 process 298 on black hole file number 013 max number 000 input file mmp_3di 013 read calc 16 MP complex frequency 1 50E 08 0 00E 00 time diff O tot 0 symmetry x yz 212 columns 8 constraints 0 66 normal equations factorized rcond 1 610E 09 rows 32 resnor 6 530E 03 time diff O tot 0 symmetry x y z 1 12 columns 9 constraints 0 normal equations factorized rcond 3 285E 10 rows 32 resnor 1 155E 03 time
254. f particles without an impressed field In this case you should first define a zero field on a sufficiently large and very coarse grid For a more detailed description see section 16 10 16 5 8 rotate_ rotate__ wind Rotate the window plane of the window with the number selected in the item box around the actual axis with an angle that is selected in the corresponding real data box angle For safety reasons you are asked first rotate window plane when the window exists Otherwise cannot_rotate_window is displayed Moreover the question set_new_axis______ allows to set the axis required for the rotation when you have forgotten to adjust the axis before starting rotate wind The actions required when this question is answered in the affirmative is described in the explanation of adjust axis 16 5 9 blow____ When the blow factor selected in the blow box is zero the object to be blown will collapse To avoid this factor_too_small__ is displayed and the process is aborted when the factor is less than 107 Otherwise you are asked invert_blow_factor_ This gives you the opportunity to undo a previous blow command but in most cases you will answer in the negative blow pic f To decide whether you want to blow the picture i e the window or the field values you are asked blow_field_values_ first and blow_window_______ PP after
255. f the lens depends very much on the frequency but it is difficult to realize how the waves propagate because of the multiple reflections within the lens The superposition of several time harmonic waves traveling in different directions always leads to complicated plots that are hard to understand Plots and movies which are much easier to understand are obtained with pulsed sources For doing that Fourier transform can be applied Because of numerical problems inherent in the Fourier integrals only Fourier series have been implemented in the 3D MMP code This allows to compute repeated pulses from time harmonic computations with different frequencies It is very important to recognize that several plot files MMP_Pyy xxx are used where xxx indicates the frequency number rather than the model number To avoid overwriting of files belonging to other models you should work now on a separate directory or save the files of the working directory on another directory before you compute this example Moreover you should keep in mind that when the plot program reads the time dependent files MMP_Tyy xxx it has to read parts of the files MMP_Pyy 000 and MMP_3DI 000 as well Thus you should use problem number 000 When you do not want to discretize the 2D lens yourself you should copy the input file MMP_3DI 029 contained in the 3D MMP package on MMP_3DI 000 Prepare a file MMP_FOU TIM containing the information concerning the time depen dence of the field Th
256. f the pole should be changed 8 9 Improving a Model Modeling is usually an iterative process The result of a first computation may not yet be satisfying but it can give valuable hints towards an improved model The error distribution and the field plots give a good impression of which regions are important for the solution and which are well modeled In critical regions the matching points can be placed more densely At the same time the orders of the existing poles should be augmented or more poles of smaller order be used Another possibility is to start a second computation using as excitation a connection with the solution of the previous problem New multipoles can be added in critical regions with less danger of dependencies with expansions of the previous computation than without connections 46 A third way is to increase the weight of the matching points in these regions However this reduces the accuracy in other regions In some cases it may be necessary to fix the field in some places with highly weighted matching points or to add constraints Last but not least one can introduce fictitious boundaries when the computation is considered to be much more accurate inside a domain than on its boundary Above all for complicated structures this allows to achieve a much more balanced error distribution If fictitious boundaries have been introduced moving these boundaries and varying the weights of the corresponding matching po
257. ferent Versions of Supported Com pilers Sometimes different versions of a compiler are very similar and no modification of the calling sequence is required but sometimes the installation name and switches of a compiler is changed entirely In this case the corresponding batch files XXX YYY BAT where XXX denotes the supported compiler and YYY denotes the graphic interface have to be modified according to the compiler manual When you are working with very older compiler versions you might obtain error messages In most cases this is either due to wrong switches or due to bugs in your compiler In this case you should try to get an upgrade first Otherwise you have to proceed as indicated in the next subsection 20 3 3 Modifications for Unsupported Compilers When you want to use a compiler that is not supported by the batch files you can compare the call and switches of your compiler with the calling sequences in the different batch files Since the calling of most compilers is quite similar it is expected that you will not encounter severe problems and that you are able to write appropriate batch file for your compiler according to your compiler manual The next step is slightly more difficult You have to modify the file MAIN SRC i e the compiler dependent module of the 3D MMP main program Above all you will have to introduce an appropriate time routine for your compiler in the subroutine ZEIT of MAIN SRC The comment lines in ZEIT i
258. ffirmative if the active poles shall be checked and in the negative if only the pole with the number selected in the item box has to be checked If several poles are checked it usually is impossible to read the error messages and warnings displayed during the check For this reasons after this check all poles that are considered to be incorrect are active and all other poles inactive This allows to check incorrect poles separately with the following procedure 1 Click one of the active poles to be tested with the second mouse button The pole becomes inactive and its number is displayed in the item box 2 Perform 2D lt check pole and answer both questions in the negative i e check the actual pole only 3 Read the error message and adjust or delete the pole if necessary During the check each pole that is checked is connected graphically with the correlated matching points and with all dependent poles i e poles that are too close This simplifies the detection of numerical dependences The set of expansions is considered to be correct if all matching points of a domain are correlated with exactly one pole Minor violations of these rules can be tolerated but strong violations can lead to wrong results The 109 following messages may be displayed pole_seems_to_be_OK indicates that no errors have been detected no_mat pts _found_ There are no matching points that would be required to define the bound
259. files as well Incidentally Word can convert these files for example into Postscript files Note that only one picture can be on the clipboard at the same time When you do not want to take advantage of the full resolution of your printer you can use the Windows hardcopy feature that copies the pixel information on the clipboard as well For doing this press the Print Screen button on your keyboard Note that this is the only action where the keyboard is used during a graphic MMP session For more information see your Windows manual 16 8 Movies and Slide Shows 16 8 1 Introduction For movies and slide shows the pictures on the screen are saved as pixel files and are redisplayed during the movie or slide show Therefore before a movie can be shown it has to be generated For this a command language has been designed in which the flexibility of the different representations can be fully exploited see below Simple movies can be generated automatically during iterative procedures with the commands generate pic f or move part But in most cases the command generate movie will be used A movie usually is generated in one window only even if several screen windows are 196 present The procedure for generating a movie in several windows at the same time is more complicated see below 3D MMP movies consist of one or several sequences Each sequence co
260. fining points in a continuous space whereas integers are more appropriate in discrete space The 3D space of the real world is considered to be continuous but the 2D space of your monitor is discrete The pixels of usual monitors are on a rectangular finite regular grid Although the points in 3D space defining technical applications often are on a regular grid as well the resolution of a monitor is usually insufficient to allow an exact mapping Thus one has to provide special features that allow to work on a regular grid of 3D real space that does not coincide with the pixels of the screen at all For these reasons one has to deal with different spaces different coordinate systems and different numbers Window Coordinates A plane is defined in 3D space with three vectors The first vector rz is pointing to the origin of the plane the two remaining vectors vi and v2 span the plane see fig 14 2 In the plane local 2D Cartesian coordinates x and y are used Since the vectors r vi and va are given in global 3D Cartesian coordinates X Y Z do not mix up these coordinates 86 Wxur Wyur Wxil Wyl Figure 14 2 Window Coordinates with the local coordinates w and yyw For this reason the w and yy directions of a window plane are sometimes called horizontal and vertical directions In fact these are the directions you can see when your screen is installed as usual The tangent vectors vi and va are mapped on the ho
261. first mouse button down and move the cursor along the Y axis you see that you cannot select any value because of the invisible grid of the screen As soon as you have some experience you will find that this is not a drawback As you can see in the guide the editor offers several features to set a point exactly at the desired position However let us set the start point of the arc at the position X 0 Y 0 5 by releasing the button when the cursor is at this position As expected the program requires the end point of the arc now and displays set_end_point_win1 _ in the top line Since the radius of the arc is already defined you can press the first mouse button and release it when the cursor is anywhere on the Y axis below the center of the arc Immediately afterwards the arc is displayed with an arrow at the end point You might be surprised that the arc is on the left hand side of the axis but the above definition of the arc is not unique To get the complement of the arc on the right hand side you can perform the command 2D lt check arc More important is the question whether the direction of the arc is correct or not The convention is that the first domain number selected in the box MPt dom1 is on the left hand side of the arc and the second one is on the right hand side The predefined values of MPt dom1 and MPt dom2 are 0 and 1 as you can see when you click the integer matching point data box Since d
262. flexible macro facility which allows to con catenate several expansions into one cf section 3 4 K D k 1 A connection is in most cases a solution of a previously calculated problem The parameters cz and the expansions fx are read from file MMP_Cyy xxx where yy is the parameter ie1 of the connection The format of connection files is the same as for parameter files Connections may have been calculated or created with symmetries different from that of the current problem They may be nested i e be used again within other connections to a maximum depth given by the program parameter nrekm 55 If a connection is used repeatedly within the same problem the parameters are stored just once The total number of expansions f and fk within the input file and all connections is limited to nentm the number of all parameters cz of the connections to nkolcm Multiply used connections count just once ig is ignored because a connection can be a multidomain expansion i e be valid in more than one domain Instead the domain numbers are taken from the expansion definitions at the end of the connection file Therefore make sure that the frequency and the numbers and properties of the domains with which the connection has been computed are the same as for the current problem iel 00 99 number yy of the connection file to be read ie2 initialized to first expansion number ie3 initialized to last expansion number ie4 initialized to firs
263. fmeta_ The 2 computing Wm field_ Ino DE BH jE energy xy z MIP gt 0 EXIT sequ M 101 Re_Om 1 5005 08 fill plane_ 2 icolor 3Darr 1 depth 2 000E 00 iz resolut 100 ER 1 00000E 00 vx__0 00000E 00 vy__0 00000E 00 vz__0 00000E 00__ total Fet 900 x 9 50000E 01 y 5 00000E 01 z 0 00000E 00 liter part 1 tim 0 00000E 00 AA A alist part type 1 mO 1 00000E 00 Figure 17 11 Desk of the 3D MMP plot program showing the energy density for a pulsed plane wave incident on a cylindrical lens manager representation 254 generate meta_ a 4 computing Wm field_ xo DE BHE energy x y 2 M P gt 0 EXIT SEER angle 3 000E 01 i11 3Darrow 4 color 3Darr 12 j ER 1 00000E 00 Wx 0 00000E 00 vy 0 00000E 00 vz 0 00000E 00 total _FPt 900 x 2 85000E 00 y 1 20000E 00 z 0 00000E 00 iter part 2 tim 0 00000E 00 part type E mO 1 00000E 00_ Figure 17 12 Desk of the 3D MMP plot program showing the energy density for a pulsed plane wave incident on a cylindrical lens manager representation 255 but for multiple excitations the plot file extension number is the excitation number minus one Thus you should perform read input 30 and read mmp p O 0 when you want to plot the field computed in the first window for the first excitation of model 30 When you have several excitations with different angles of incidence you probabl
264. ge of the full resolution of the output device Note that you can reduce the width of thin lines before you generate a meta file when your printer has a higher resolution than your screen For more information see 14 7 99 15 5 Summary of Model Generation In most cases the following steps are necessary to get a 3D model with the corresponding input file MMP_3DI xxx for the 3D MMP main program 1 Some general non graphic data like the frequency the symmetries and the material properties have to be defined in the corresponding boxes This should be done first because these data can be important in the following steps No regular actions are required here except for adding domains with the corresponding material properties 2D construction of boundary lines with the corresponding 2D multipoles that are intended to be used in the 3D construction of objects or of certain parts of an object The 2D multipoles can be generated automatically or semi automatically in most cases They can be omitted because the 3D multipoles can be generated in the 3D constructions but it is recommended to construct appropriate 2D multipoles because this considerably simplifies the 3D constructions in most cases In some situations the discretization of the boundaries with straight lines and arcs might be insufficient There are two ways to overcome such problems e one can implement additional elements in the MMP editor or e one can write
265. gles of incidence In this case the system matrix essentially remains unchanged and only the columns corresponding to the excitations have to be modified Thus one can save a lot of computation time if one computes the parameter sets and fields for the different excitations at the same time Like when a Fourier transform is performed the main program writes a set of parameter files error files plot files etc Thus it is reasonable to work on a separate directory when one has multiple excitations for avoiding overwriting of files of other models Instead one can copy or move the files of the other models onto another directory Since changing the working directory is cumbersome under Windows the latter is simpler To generate an appropriate input file proceed as follows 1 Generate a usual MMP model with the editor or read an already existing model for example model 18 of this tutorial 2 Define or modify the symmetry numbers in such a way that all excitations you want to add match the corresponding symmetries 3 Add as many excitations as you want to have Note that each excitation is an expansion to be added after the definition of the usual expansions and that only expansions with one parameter plane waves connections are allowed excitations when you have more than one excitation Since connections can contain any expansion this is no restriction but it makes the use of expansions with multiple parameters as excitations more complicate
266. gopen should return the value 1 when itype is equal to 1 i e if you try to generate a meta file itype 0 screen 1 meta file ihsize horizontal size of the meta file page in 1 10 mm ivsize vertical size of the meta file page in 1 10 mm mname name of the meta file character string idev returns device address is used by other mgxxxx functions iwid returns pixel width of output device ihgh returns pixel height of output device itwd returns pixel width of a character on the screen ithg returns pixel height of a character on the screen mgclos idev Close workstation This function is called only when one of the graphic MMP programs is terminated If it is not correctly implemented or even missing problems will occur when leaving the graphic MMP programs but the programs should nonetheless work correctly idev device address 316 mgplin idev lcor lxya lcol lwid larr Draw polyline This function is essential In the graphic MMP programs polylines with color numbers 0 15 and different widths are drawn If less colors are available the color numbers 2 15 can be replaced by an available number For example on a monochrome output device one can replace 2 15 simply by 1 At least two different widths lwid gt 0 of lines should be available If the line end type larr 1 that generates an arrow at the end of the line is omitted some of the graphic representations will be less nice idev device address lcor number of
267. gorithms except in the 209 FDTD and life algorithms although the resulting electric field has no physical meaning in some algorithms Nonetheless it can be useful for testing and analyzing the results 16 9 3 Writing New Algorithms All subroutines defining iterative algorithms are contained in the module MMP_P3A F When you want to add a new algorithm you have to add a new subroutine for example NewAlg a new label for example 20 in the computed goto statements in the the subroutine genField and the following lines below the computed goto 20 continue c new algorithm call NewAlg ja liniF goto 2 ja is an integer variable returned by the subroutine NewAlg that is zero if no error has been detected and if the subroutine has not been stopped by the user linif is a logical If it is true the subroutine NewAlg should initialize the field required for performing the iterations The algorithm can act on all field components that are stored in the arrays EXR EXI EYR EYI EZR EZI HXR HXI HYR HYI HZR HZI AXR AXI AYR AYI AZR AZI VR VI where E is the E field H the H field A the vector potential and V the scalar potential X Y Z indicate the Cartesian components R and I the real and imaginary parts respectively When you look at source code of the algorithms that have already been implemented you will note that the imaginary part is often used for storing the old field of the previous time step and that
268. gram option for the 3D MMP main program has been entered section 9 2 Error Opening Files error opening input file error opening error file error opening plot file error opening integral file error opening frequency file error opening output file error opening parameter file error opening connection file A file cannot be opened because it is required but not there or because there is some other problem with the file system 68 Errors due to Wrong File Format error reading general part error reading domain error reading expansion error reading matching point error reading constraint error reading scaling error reading integrals error reading integral header error reading integral point error reading plot window data error reading plot points error reading parameter file error reading connection file error reading frequency file There is an error during input from a file because of an error in the file format Note that due to the FORTRAN list directed input format an error in the input file may have occurred earlier but has not yet been noticed Too Small Version of the Program too many frequencies too many domains too many expansions too many matching points too many constraints too many constraint integral points too many plot windows too many field point sets too many columns too many parameters in connections too high order of expansion maximum recursion depth exceeded The fixed si
269. h less comfortable that the one of usual Windows applications it has some important benefits 1 It is simple and easy 2 It is very quick 3 It allows you to modify the hints you get with any text editor I e you can adapt the hints according to your needs Both in the 3D MMP editor and the 3D MMP plot program the most important boxes can be found in the top line of the desk Top Line Boxes 1 3 Definition of Regular Actions The top line of the usual MMP desk contains the most important boxes The first three boxes are used above all to define a so called regular action Regular actions are started when the first mouse button is clicked in the top line box 4 see below In the editor the first box is used to define the dimension 2D or 3D of the construction the second the action to be performed and the third the item to be manipulated In the plot program the dimension box is missing because all representations are three dimensional Thus the first box is the action box and the second box is the item box Since two numbers are required for defining a plot file a file extension box is present in the plot program in the third position of the top line This box is missing in the editor because the editor does not handle plot files Top Line Boxes 4 and 5 Dialogs The fourth box of the top line is a question information box that displays informations of interest actions that you are expected to per form and questions you have to answer
270. h memory on your disk before you start MMP_F3D Moreover when you intend to generate a movie even more disk space for storing the pictures is required When you are sure that you do not need the parameter files MMP_PAR xxx and the frequency dependent plot files MMP_Pyy xxx any longer you can delete them in order to free memory It is very important to note that MMP_Pyy 000 contains essential data that is not contained in MMP_Tyy xxx in order to reduce the size of these files Thus you can delete MMP_Pyy 001 MMP_Pyy 002 etc but you never should delete MMP_Pyy 000 unless you delete the corresponding time dependent files MMP_Tyy xxx as well The frequency dependent errors in the matching points are not 252 transformed by the program MMP_F3D Thus if you did create error files it is certainly a good idea to delete them as well before starting MMP_F3D Although the computation time required for generating movies of time dependent fields on a personal computer can be extremely large the time for generating an appro priate model is not much larger than the time for generating a time harmonic model When you already have a model working at sufficiently high frequencies the Fourier transform feature is certainly worth trying see fig 17 11 and fig 17 12 Let your PC work while having pleasant dreams 17 12 Multiple Excitations Model 30 When you study the radiation pattern of a scatterer you often want to know the field for different an
271. h the exception of some logical variables Com plex double precision numbers are nonstandard in FORTRAN 77 and consequently are implemented as a pair of real variables The basic complex operations are provided as ordinary subroutines which makes the code rather hard to read in those places where they are used a lot e g in the expansions The program grew over a longer period of time and was continuously used for ap plications Although many bugs have been detected and removed some may have been replaced by those entering through the implementation of new features and some still may be resting undetected Parts of the code e g the cylindrical Bessel functions and part of the matrix routines especially the routines for the transputer pipeline are the same as in the 2D MMP programs 4 The source code of the 3D MMP main program consists of several files The actual MMP routines are in the following files the main program and the machine dependent routines in file MAIN SRC the higher level MMP routines in file MMP F the expansions in file ANS F and utilities like input output initializations etc in file ETC F All of the MMP routines share common blocks defined in file COMM INC which is included where needed Only varying parameters are passed through the subroutine calls More general subroutine packages which can also be used independently are the double precision complex routines file COMPL F the cylindrical Bessel functions
272. h ts Pe oe A ls Sea A 15 4 1 Regular Actions e eee eee 97 15 42 Window ACtiOns 2 eoriet AA a PSS po oe 98 15 4 3 Special Actions rora ea Gnd al le goed Be ee A eee 99 15 5 Summary of Model Generation 2 2 00004 100 15 6 Summary of 2D Actions e e hie e ee 101 TSOL 12D Shows 2 0 ey eh ee oe rd Ge A e a eae a 101 15 62 2D add wel a Bee eaten ARA SEO Bey 103 T5633 2D delete 4 5 Toast p fined Bb ead bo a wine Be ds 105 15 64 2D COPY s ja Wa Oe ee baa he Oe A OR ee A 106 19 6 5 22D MOVE LES AY hg Sea ean ee Aah hs be Se ha eat 106 15 6 0 2D blow lt solve danke AA RE BR Ae heed 107 15 650 2D FOtates sey a nad dadas ek we 107 190 8 2D inverts vet a eee ee a et wots wo 108 15 6 9 2D lt check il 26 8 YL Raw eh ei dee ee le a 109 15 6 102D adjust nee oe ee ae eh ES oe eae aes 110 15 611 2D generate 26 nomor sonas aes 111 15 6 122D read doem si ea A ee ee RD a ew eee 112 15 6 132D writes A Seis eh be Bowed a Se eg a aed A 113 15 7 Summary of 3D Actions 2 2 ee 113 Lost SSD Shows ie Sa GE A a a A Bee ee 113 10 12 BD add 2 vy se ad dar dd bbe ahah ete 3 116 5 7 9 SD deletes vir oli aa A eee hae eed ee 120 10 04 3D COPY Jk aon ee ee ae ee ee Pe a A OA Get 122 ARS MOVE 2 yao 8 eee ea ee ht a ES a 123 153726 SD DLON e5 tote a ge ee en ee bee OE BEE Bay 124 Lat BD FOtate ss go ea et ya aed se wen 126 RS EN eS duds Yeas ia oS he Rit bh os a oa aida 127 15 7 9 3D lt
273. hat an error occurred while reading the third field point of the actual plot file Another source of overflows are the multiplications in the computations of energies and Poynting vectors as well as the multiplications with material properties when fields derived from E and H are computed This can cause severe errors when the command show pict is executed the program will hang and you have to restart your PC Let us return to our ideally conducting sphere When you read first the plot file MMP_P00 000 then the input file MMP_3DI 000 and finally the error file MMP_ERR 000 and activate the matching point representation in the box M you can get nice pictures of the different fields and the error distribution You can see that the time average of the Poynting field surrounds the sphere as expected and that the boundary conditions are matched quite well But it is still quite difficult to completely understand how the field propagates especially when you look at one plane only To get the field in other planes change the plot window and perhaps the resolution and the window limits as well with the editor run the 3D MMP main program without recomputing the parameters and errors and return to the plot program Of course you can try to generate a movie after writing an appropriate MMP_DIR xxx file Maybe this can help you to better understand how electromagnetic waves propagate 17 2 2 Introducing Symmetries Mode
274. hat happens But for obtaining the Mandelbrot and Julia sets you should reset the field to zero Most of the algorithms require the definition of non zero fields otherwise no inter esting results are obtained The command clear pic f I allows to generate pseudo random and other simple fields when I is different from 0 Such fields can be useful for testing and for some special algorithms In most cases a special field distribution has to be generated first Of course one can do that with an additional program that writes an appropriate plot file Usually one first will reset the field to zero and adjust it afterwards either with the command adjust pic f or with the corresponding window action see 16 3 2 For example when you want to play with the 2D or 3D life algorithms you will have to define some cells i e field points with the value 1 and all other cells should have the value 0 More realistic algorithms like the FD and FDTD procedures require the definition of material properties in the different field points as well For example in electrostatics you have 1 electrodes i e ideal conductors with a fixed scalar potential and 2 dielectrics with an unknown potential that has to be computed You can start with an initial value 0 in the dielectrics Thus you will first reset the entire field to zero and adjust the domain numbers and the values in the electrodes afterwards Note that the field in point
275. hat number xxx is available or that incorrect data are encountered in the matching point number yyyyy When symmetry planes are present the errors and the fields in the symmetric points are generated using symmetry opera tions This process is indicated with the message gen symmetric_err_ read____ 2Dp1f Read the data of frequency dependent plot files MMP_DAT PLT or MMP_PLF xxx generated with the 2D MMP programs 4 Like when reading 3D plot files you are asked use_plot_window____ Since different names are used for 2D plot files the 3D MMP plot program attempts first reading MMP_PLF xxx where xxx is the number selected in the item box If this file is present reading MMP_PLF xxx is displayed Otherwise MMP_DAT PLT is read when it is available and reading MMP_DAT PLT is displayed during reading If no 2D plot file is found or when errors occur during reading this is indicated with error_opening file_ and error_reading file_ too_many_poles____ too_many_match _pts wrong f pt number_ respectively The last three messages indicate that there is not enough memory in the 3D MMP plot program for storing the poles expansions matching points or field points 167 read 2Dp1t Read the data of time dependent plot files MMP_PLT xxx generated with the 2D MMP programs 4 Select the extension number xxx in the item box Like when reading 3D plot files you are asked use_plot_window____
276. hat the 3D MMP main program does not distinguish between matching points and expansions of different objects If you answer in the negative the questions save_object_1_only save_object_2_only_ are asked in order to determine whether object number one or two has to be saved If all questions above are answered in the negative no file is written and process_aborted____ is displayed When a file with the number selected in the item box does already exist you are asked overwrite_3D_file__ If this question is answered in the negative no file is written as well and 3D_data_not_saved_ is displayed The message saving 3D_data file is displayed during writing 15 8 Summary of Boxes In the following the contents and meaning of the different boxes is described You can obtain a similar description by clicking a box with the third mouse button A hint box will be displayed in the center of the screen on the condition that the hint files MMP_E3D xxx are correctly installed i e can be read by the editor and that the program has enough memory for saving the part of the screen used to display the hint box This box will disappear as soon as any mouse button is clicked The location of the boxes most of their text lines and most of the corresponding initial values are defined in the desk file MMP_E3D DSK This allows you to modify the corresponding data according to your needs However this should be done very carefully because the pr
277. he low level MMP routines It produces rows for matching points and field points e The rows of A which are boundary conditions in matching points have to be computed for updating and for computation of the residuals e The evaluation of field values according to 6 4 and 7 9 is done by forming first the entire rows and subsequently multiplying them with the parameter vector c 74 After some initializations zeile calls the specialized routines zmp for matching points and zfp for field points These two assemble the rows from single expansions If an expansion is relevant to a point i e made for one of the domains bordering the matching point or for the domain of a field point routine entsym is called The field components of the expansions are then inserted into the row If an expansion is not relevant routine nullen is called which inserts a block of zeroes equal to the length of the expansion into the row Routine zmp also transforms the field components to the coordinate system of the matching point and formulates the boundary conditions by calling rbed 13 3 2 Expansions Subroutine entsym symmetrizes arbitrary expansions in order to produce symmetry a dapted ones cf section 13 4 This arbitrary expansion is either routine entnr which will branch into the ordinary expansions routines or conn for connections entnr essentially makes the necessary transformation of coordinates and leaves the rest to the expansion r
278. he X axis 3 Apply the blow command with the same parameters as before twice again 234 Now your body is deformed so much that you won t get accurate results anymore even if you reduce the overdetermination To improve the results you can rotate the multipole as in model 7 Although this is helpful you always get large errors in the matching points far away from the multipole Moreover the checking routine 3D lt check points shows some active matching points at the same location indicating that these matching points are too far away from the multipole Since you get only a few active matching points you can tolerate it But you can take it as a hint that there might be a better solution Now remember the local behavior of multipoles and shift the multipole out of the origin of the global coordinate system toward the matching points with the large er rors When you shift the multipole along the positive X axis you implicitly create a second multipole on the negative X axis because of the symmetry i e you have an multiple multipole expansion instead of the single multipole expansion you had before Although mathematically educated people might worry about this procedure because they expect dependencies between the two multipoles you should at least try When you run the checking routines 3D lt check pole and 3D lt check points for dif ferent locations of the multipole on the X axis
279. he axis is copied on the light vector when the question set_light_vec axis is answered in the affirmative Since two different light types are implemented the ques tion show_negat _shadow_ is asked When this is answered in the negative only shadows of triangles 3D vec tors above the plane of the field points are shown which corresponds to a single light source Otherwise one has two light sources with rays pointing in opposite directions and shadows of triangles below the plane are shown as well adjust__ wind Adjust additional data of windows There are several additional data that can be adjusted and require an appropriate selection of the corresponding values in the window data boxes Some of these data can be manipulated graphically as well the pixel coordinates of the window corners ix_low left etc Moreover the origin and the tangent vectors defining the window planes are usually represented and manipulated graphically Thus graphical constructions are included in the adjust window command For graphical constructions it is helpful to always use the same plane in the first window and to perform the constructions in this window only even if several windows have been added If you did forget to reset the plane in the first window x y plane you have the chance to do this by answering the question reset_plane_ 1____ 7 in the affirmative If the question adjust_window_plane is
280. he dipole and to decrease the maximum degree and to increase the maximum order of the multipole in the center Moreover it has been noticed that it would be preferable to have a nonuniform distribution of the matching points on the sphere In fact the orders and degrees of a multipole essentially indicate a variation of the field with respect to the angles y and Y of the spherical coordinates defined in the origin of the multipole For this reason the automatic routine that determines the highest orders and degrees takes the matching point densities in both directions into account When decreasing the degrees of a multipole you should reduce the number of matching points in y direction as well This can be done when the factor fac is set to a value larger than 1 before the sphere is generated with the command 3D generate torus In order to increase the matching point density in Y direction you have to increase the number of matching points of the 2D arc used to generate the sphere Proceed as follows 1 Select the frequency and symmetry numbers as in the previous models 2 Generate a 2D arc with 13 matching points instead of the 10 matching points used in the previous models and generate an appropriate 2D multipole 3 Generate a sphere rotating the arc around the standard y axis with an angle of 90 degrees and a factor fac 1 6 You should get about the same number of matching points as before but you hav
281. he fillings and colors defined in the desk file In addition the matching points are shown in transparent mode 3D show____ field_pts Show one set of field points The corresponding number has to be selected in the item box If this number is either less than one or bigger than the number of sets that have been defined no_ such_field_points is displayed Otherwise the points are shown with the fillings and colors defined in the desk file In addition the matching points are shown in transparent mode 3D show____ integrals Show the points of one integral The corresponding number has to be selected in the item box If this number is either less than one or bigger than the number of integrals that have been defined no_such_integral___ is displayed Otherwise the points are shown with the fillings and colors defined in the desk file In addition the matching points are shown in transparent mode 3D show____ errors___ Show the errors in the matching points An appropriate error file has to be computed by the 3D MMP main program before this command can be executed Moreover this file has to be read first with the command 3D read errors If the error data are missing cannot_show_errors_ is displayed The errors are represented by different fillings and colors that are defined 115 in the desk file and by lines perpendicular to the matching points The lengths of these lines is
282. he item box and repeat 2D generate pole with different types until you get a reasonable 2D MMP expansion Of course you can delete or move multipoles that have been generated automatically as you like The automatic procedure doesn t set the multipoles exactly on the Y axis where you probably would like to put them This is a minor problem because the command 3D generate torus does that for you Before you start this command select ang and fac Because of the symmetry planes 90 degrees is the correct angle ang When you remember the notes on fac you probably don t know how large the factor fac should be You certainly can learn more about the MMP code when you store the 2D construction on a file and try different factors You will find that a factor larger than 1 is reasonable here The larger the factor the less matching points you obtain and the lower the maximum degrees of the multipoles The degrees of the multipoles essentially are responsible for modeling the currents flowing around the dipole Since these currents are small compared with the longitudinal currents it is reasonable to use relatively low maximum degrees In our example the factor 2 is reasonable Probably you find that the default size of the window is not appropriate for this construction The editor offers a large number of features for adjusting the window
283. he matching points are therefore not relevant In other words the reduction of the error computed in the matching points with an increased number of unknowns but a constant number of equations can be misleading The error between the matching points can even be increased so much that the error integral on the boundary is increased This effect is much more important when complicated models are considered 17 4 4 Lossy Magnetic Sphere Model 14 When you look at the material properties displayed in the boxes Er Ur etc you probably are curious about the values in the boxes Ei Ui Si Since the MMP code works with complex numbers the permeability the permittivity and the conductivity are complex although the material properties are assumed to be real in most applica tions The values in the boxes Ei Ui Si define the imaginary parts of the relative permittivity of the relative permeability and of the conductivity This allows to approx imate losses in materials It is well known that one can replace the conductivity of a lossy dielectric by an appropriate imaginary part of the permittivity But there is a little difference when the electric current and the electric displacement are considered The former is zero in a lossy dielectric with complex permittivity when the conductivity is zero Although complex material properties make life more difficult there are advantages
284. he results of the actual computation with those of the previous one For doing this several features of the plot program can be helpful e You can resize the window add a second window of the same size and display the field of both computations in the two windows e You can use the slide feature i e store different pictures on files with the write picture command and display them one after another with the read picture command 222 e You can generate meta files of different pictures After leaving the plot pro gram you can invoke a Windows application that is able to read and print Windows meta files A detailed description of the features mentioned above would turn out to be long and cumbersome but it is expected that the try and error method or the infor mation in the 3D MMP guide allow you to get familiar with the procedures very soon 11 Increase and decrease the frequency with the editor and look at the behavior of the errors and field plots for different frequencies Obviously the discretization is too rough for higher frequencies In the actual version of the editor it is impossible to increase the matching point density of a 3D object in order to get a finer discretiza tion However since it is very simple to increase the 2D matching point density with the command 2D adjust arc the 2D input file written in step 5 is helpful after entering the editor proceed as indicated above but read this file inste
285. he wave impedance The polarization and time dependence of the incident wave are selected in the box iter info The two rightmost digits i3 and i4 have the following meaning The E field points in Y direction if i4 1 Otherwise the E field points in Y direction The time dependence is T t sin wt if i3 gt 0 and T t 1 otherwise provided that 0 lt t lt To For t lt 0 and t gt Tp the incident field is set to zero on the right border To and w are selected in the boxes Tim and Re_Om respectively Note that the time is increased for every iteration with the value selected in the box dt In addition the angle y in the box angle is increased with the value in the box dt multiplied with the real part of the angular frequency Re_Om It should be mentioned that no physically reasonable results can be obtained when the source field violates the Maxwell equations or when the grid is too rough The MMP procedures that are generating a picture are very time consuming above all when you have a relatively fine grid Thus it is convenient to perform several iterations before a picture is generated This number is selected in the box iter field Moreover you probably would like to generate a movie containing a couple of pictures generated during an iteration This can be done as indicated in the previous section But there is a much simp
286. here you want to have the projection of the point on the actual window plane In order to define the location of the point completely you are asked to set the height of the point above the plane in the next step set_height_above_pln i e you are expected to give the height of the point above the window plane Only a vertical movement of the cursor will affect this value The actual height is displayed in the second box of the bottom line as long as the mouse button is pressed down If you did use method 1 to discretize the origin set_end_point_data_ indicates that you are expected to give the coordinates of the first end point in the same way I e select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data If you did use method 2 to discretize the origin set_end_point______ indicates that you are expected to discretize the end point of the first tangent vector in the same way Of course you will be asked 117 set_height_above_pln if you apply method 2 Needless to say that you are expected now to discretize the end point that defines the second tangent vector similarly set_2nd_end_point__ Of course you will have to set_height_above_pln once more if you are working with method 2 3D add_____ window___ Add screen window or plot window When this command is performed it is important to recognize that there are two different types of windows
287. hether the already existing movie shall be overwritten If this is answered in the negative no movie is generated Otherwise all files MMP_F11 xxx and MMP_I11 000 are overwritten Note that some of the directives change the values in certain boxes After the gener ation of a movie the boxes will contain the values used for drawing the final picture Usually pictures are scaled automatically in such a way that they look reasonable when all scaling factors are equal to 1 In the generation of movies this scaling has to be suppressed in order to avoid wrong relations between the values displayed in different pictures Nonetheless you might wish that the first picture of a sequence is scaled automatically especially if a new plot file is read at the beginning of the sequence The directive setaut turns the automatic scaling on After the generation of a picture of a movie the automatic scaling is always turned off 16 8 4 Movies with Several Windows In some cases you probably want to generate a movie showing several points of view or different fields in more than one window at the same time Since only the pixel information of one window is stored in the picture file the following procedure is required 1 Add as many windows as you want to have 2 Add one more window containing all other windows to be shown in the movie 3 Write the movie directive file in such a way that pictures are drawn in all windows but the last one use the directives se
288. his chapter describes the contents of MMP_3DI xxx and MMP_Cyy xxx The input file MMP_3DI xxx is usually generated by a graphic input editor For doing special things and for slight modifications editing the input file with a text editor may be more practical FORTRAN implicit notation is used for the description of the parameters in the input file Integer parameters start with the letters i to n real parameters with the letters a b d to h and o to z complex parameters start with the letter c and are entered as a pair of real numbers the first being the real part The full format of the file is given in section D 2 10 2 Coordinates and Geometric Tolerances All coordinates and vectors in the input file must be specified in the global Cartesian coordinate system x ey z For symmetry detection it has to be determined whether a component of the radius vectors 7 origin of a matching point and 7 2 origin of an expansion is equal to 0 or a component of the basis vectors of 11 2 or z Ey Ez is equal to 0 or 1 The tolerance for this is sklein and is currently 107 It can be changed in subroutine inicon in file ETC F 10 3 General Data 10 3 1 Type of Problem The program is able to solve 2D and 3D scattering problems Initializations for various problem types depend on the value of iprob Currently the following values of iprob are used iprob Problem Type 200 299 2D problems with translative symm
289. hould not be too large 3D lt check pole_____ Check multipoles either all poles of a domain only the active poles or only the pole with the number selected in the item box According to this you are asked check_ALL_poles___ and if the first question is answered in the negative check_active_poles_ If several poles are checked at a time it usually is impossible to read the error messages and warnings displayed during the check For this reason after this check all poles that are considered to be incorrect are active and all other poles inactive This allows to check all incorrect poles separately with the following procedure 1 Click one of the active poles to be tested with the second mouse button The pole becomes inactive and its number is displayed in the item box 2 Perform 3D lt check pole and answer both questions in the negative i e check the actual pole only 3 Read the error message and adjust or delete the pole if necessary During the check each pole that is checked is connected graphically with the correlated matching points and with all dependent poles i e poles that are to close This simplifies the detection of numerical dependences that should be avoided The set of expansions is considered to be correct if all matching points of a domain are correlated with exactly one pole Minor violations of these rules can be tolerated but strong violations can lead to wrong results The f
290. ht corner According to that adjust_window_corn is displayed If you do not want to set the corners manually the information in the integer data boxes ix11 iy11 etc is used In order to define the plane of the screen window you have three possibilities 1 you can set the plane manually in exactly the same way as you add a new matching point or a new expansion 2 you can set one of the default planes i e X Y X Z Y Z X Y X Z YZ 3 in the second screen window you can set a plane orthogonal to the first window plane with the same first tangent vector as the first window plane 118 According to that you are asked set_plane manually _ set_plane_M _xxxx_77 plane_orthog_plane1 Tf you answer all questions in the negative The third question is asked only if the second screen window is added the X Y plane is used The manual construction of the plane starts with set_start_point____ Le you have to define the location of the origin of the plane There are two ways of doing that 1 select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data 2 press the first mouse button within a window and release it as soon as the cursor is at the position where you want to have the projection of the point on the actual window plane In order to define the location of the o
291. ibing the incident field must have the highest number 233 Looking at the error distribution you see that the errors on the inner boundary of the coating can be considerably smaller than the errors on the outer boundary especially when the coating is lossy You are supposed to have already enough experience with the MMP code to be able to find a much more efficient model To get even more experience you can play with the material properties the maximum orders and degrees of the expansions Moreover you can change the thickness of the coating Why didn t you save the two objects you had above on separate files This would make life much easier when you have to reenter the editor and it certainly is advantageous when you make mistakes 17 5 Mutated Spheres 17 5 1 Generating an Ellipsoid Model 16 When you applied the blow command you probably became curious about the other subroutines contained in this command Of course you can load any model run the blow command with different parameters and look what happens In most cases the object you play with is deformed When you have got some experience you will be able to generate some potato like objects out of a simple sphere but you will probably not manage to exactly get a given shape like a human head or something like this Moreover you need to be careful when symmetries are present However this feature can be helpful for getting some experience with the influence of deformations on th
292. ical Generate a multipole in the center of the arc as indicated in step 6 of the construc tion of the sphere without symmetry considerations Note that it is important to select the symmetry numbers before generating poles because the pole orders and locations are affected by the symmetry of the problem Save the 2D construction on a file MMP_2DI 001 as indicated above Reduce the angle for the command 3D generate torus to 90 degrees for getting the part of the sphere in one octant only Add the incident plane wave as in step 11 of the construction of the sphere without symmetry considerations Write the new model on the 3D MMP input file MMP_3D1 001 and leave the editor Run the main program and select the same tasks 124 method 1 frequency 1 as for the sphere without symmetry considerations but select input file number 1 now The parameters are computed in two steps but the computation time for the parameters is considerably reduced whereas the computation time of the errors and of the plot file is not affected very much Since the computation time for the parameters is dominant for not very small problems symmetries should be used whenever possible although the selection of the symmetry numbers might be a prob lem for beginners Moreover the memory requirements are reduced considerably which allows to compute larger problems on the same machine when symmetries are present Run the plot program to compare t
293. ical as the one outlined in section 16 9 Particles can easily be manipulated with the commands add part del part 213 adjust part and clear part Since it can be difficult to find an appropriate set of particles you can save and restore the particle data with the commands write part and read part The movement of realistic particles with part type equal to zero depends on the actual electromagnetic field but it does not depend on the selection of the field that is displayed For example a realistic electrically charged particle with a small mass will essentially follow the electric field lines even if you have plotted the time average of the Poynting field Above all the field lines of the time average of the Poynting field seem to be very interesting For visualizing such field lines pseudo particles have been implemented that follow the lines of the actual field Such lines rarely are within a plane Thus time and memory consuming plots with a large number of grid lines and levels can be required Note that the field in all levels has to be plotted select the value 0 in the box level __ before 3D field lines can be drawn Pseudo particles are stopped if the field is zero in the actual point 214 Part IV Tutorial 215 17 Tutorial 17 1 Introduction In this tutorial the modeling and computation of s
294. id representation of scalar fields The meaning of the values in this box depends on the element In most cases the following holds 182 Box Value Representation lt 3 do not show element filling proportional to corresponding field if its value exceeds the limit invert dark bright filling proportional to corresponding field if its value exceeds the limit do not invert dark bright transparent not filled completely filled 3D vectors shown as lines with arrows are always completely filled they are not shown when the fill pattern is less than 3 For the plane in the field point additional negative fill patterns have been defined as follows Box Value Representation lt 9 do not show 3D plane 9 filing proportional to domain number of point 8 filling is 4 medium color indicates domain number of point 7 filling and color indicate domain number of point 6 filling like 3 color indicates domain number of point 5 filling like 2 color indicates domain number of point 4 filling like 8 color indicates field strength The fill pattern 4 of the grid representation has the same effect as for the plane The grid is completely filled but the color represents the strength of the field This is very useful on c olor monitors provided that the color palette can be set adequately i e as defined in the desk file Note that the setting of the color palette depends on th
295. ield intensity electric displacement magnetic field intensity magnetic induction magnetic vector potential Poynting field S Ex S E x Ae impressed current density conduction current density impressed charge density conduction charge density impressed surface current impressed surface charge electric current eletric energy density we 4 Note that the time averages overlined are only defined for real frequencies and that some of the energy and power terms become dubious for materials with complex parameters The various expansions cf chapter C are labeled with the following indices 280 Ecmn electric transverse magnetic spherical solution of order n and degree m cos my dependency Esmn same as above sin my dependency E mn same as above cosmy or sinmy dependency depending on choice in expressions Spp my and sin my Ecm electric transverse magnetic cylindrical solution of order m cos m de pendency Esm same as above sin my dependency ESm same as above cos m or sin my dependency depending on choice in ex pressions my and Sin my H same notation for magnetic transverse electric solutions A 2 Coordinate Systems and Transformations A 2 1 Cartesian Systems The expression Cartesian system is used for a coordinate system with an orthonormal right handed basis In the MMP program several of these systems are used e The global system x ey Ez e The system of an expansion
296. ile connection file integral file frequency file Message Numbers msbeg message numbers cf routine messag Input and Output Control lparin linpin lnorin lintin lpltin lefpin loutop filnam ierlev msfil msscr mslev Constants e0 u0 rz0 rco come pi sklein dklein logical true parameter file has yet to be read logical true input file has yet to be read logical true scaling integral has yet to be read cf routine norm logical true integrals have yet to be read cf routine norm logical true plot block has yet to be read logical true single field points have yet to be read logical true output file has yet to be opened string for forming file names differentiates warning messages from error messages in mmperr amount of output cf MMP_3DI xxx and subroutine messag logical array for message levels amount of output free space constant of permittivity o free space constant of permeability uy wave impedance of free space Zo speed of light current angular frequency w m 3 14159 tolerance for geometry currently 1077 tolerance for floating point numbers currently 0 Problem constants comi cfreq nome ngeb nmat array of angular frequencies w cfreq in input file number of frequencies number of domains number of matching points 311 nent nentt nkol kms nca iprob ichol Symmetries is isa nsym ise issz isd isde isdh isnr isp i
297. ill not cause the programs to work improperly 19 2 Systems and Graphic Packages On PCs above all MS DOS has been used Most of the actively supported compilers run on DOS version 3 2 or newer It seems that there are bugs in version 4 0 of MS DOS but no serious problems affecting the MMP code have been found by the authors so far However today DOS 5 0 is certainly preferable On PCs many FORTRAN compilers running under UNIX and similar systems are available But so far one cannot really see a trend to a certain system For this reason these systems are not actively supported by the 3D MMP package for PCs However the non graphic modules have been tested on SUN workstations under UNIX HELIOS is a UNIX like system for transputer networks It has been used in conjunc tion with the Meiko FORTRAN compiler Although HELIOS is considered to be quite agreeable the Meiko FORTRAN compiler is the only compiler that does cause the MMP 268 code to hang when connections are used It seems that Meiko is not interested in im proving their compiler Moreover no appropriate graphics library is available yet Thus MMP users who are already working with HELIOS can use it for running the 3D MMP main program without connections but otherwise this system is not recommended Since DOS has no useful graphics a graphic system is necessary Today Microsoft Windows 3 is widely used The compiled version of 3D MMP included in this package runs under Windows
298. imetric assesment of the significance of high intensity rf field exposure resulting from reradiating structures in Proc of the 11th Annual Meeting of the Bioelectromagnetic Society Tucson June 1989 L Bomholt and Ch Hafner Calculation of waveguide discontinuities with 2 D and 3 D MMP programs in Proc of the 2nd International Symposium on Antennas and EM Theory Shanghai Sept 1989 327 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 A C Ludwig N Kuster A Glisson and A Thal 5 1 dipole benchmark case in The ACES Collection of Canonical Problems Set 1 H A Sabbagh ed pp 34 59 Applied Computational Electromagnetics Society 1990 N Kuster 6 types of canonical problems based on one geometrical model in The ACES Collection of Canonical Problems Set 1 H A Sabbagh ed pp 60 81 Applied Computational Electromagnetics Society 1990 L Bomholt P Regli Ch Hafner and P Leuchtmann MMP 3D A package for computation of 3D electromagnetic fields on PC s and workstations in 6th Annual Review of Progress in Applied Computational Electromagnetics ACES Conference Proceedings Monterey pp 26 32 Mar 1990 L Bomholt MMP 3D A Computer Code for Electromagnetic Scattering Based on the GMT PhD thesis Diss ETH Nr 9225 1990 I N Bronshtein and K A Semendjajew Handbook of Mathematics Verlag Harri Deutsch
299. in device independent 1000 by 1000 integer coordinate system with lower left corner 0 0 and upper right corner 1000 1000 Depending on the box type real or integer parameter one of the two initial values BoxInt and BoxRea is treated as a dummy The array elements of the colors and fill patterns above have the following meaning e A positive index indicates the front side and a negative index indicates the back side of the corresponding element e the colors and fill patterns for index 0 are not used in the 3D MMP plot program The color numbers and the fill patterns above are essentially the same as the color numbers and the fill patterns of the field representations that can be selected in the color and fill box during a session D 16 Action Files MMP_E3D ACT and MMP_P3D ACT Information on the actions on items implemented in the 3D MMP editor and the 3D MMP plot program respectively These files are searched first on the current directory then on the directory MMP of the current drive and finally on the directory MMP of drive C If the searched is missing it is assumed that all actions can be applied on all items This is not a serious problem because the programs will simply display the message action not_implenm if you try to perform an action that has not been implemented 303 D 17 Hint Files MMP_E3D xxx and MMP P3D xxx Texts of the hint boxes in the 3D MMP editor and the 3D MMP plot program respectively They ar
300. in this window only If you did forget to reset the plane in the first windows x y plane you have the opportunity to do this by answering the question reset_plane_ 1____ 7 in the affirmative If the second question set_axis_manually_ is answered in the negative one of the default axes The default axis number is selected in the additional integer data box sequ M where 1 is the X axis 2 the Y axis 3 the Z axis 1 the X axis 2 the Y axis 3 the Z axis is set when the question set_axis_M _xxxx_ is answered in the affirmative Otherwise the vector respectively axis is left unchanged and axis_not_changed___ is displayed If you want to set the axis manually i e if you do not want to use one of the default axes you can set either an axis of unit length perpendicular to one of the window planes or you can set a general 3D axis The former is simpler because only one 2D point has to be given Thus if you answer the question set_perpend _axis_ in the affirmative the message set_origin____ indicates that you have to press a mouse button in one of the windows and to release it when the cursor is at the location where you want to put the origin of the axis The procedure to set a general axis is more complicated First set_start_point____ indicates that the start point of the axis or vector has to be discretized There are two ways to do that 1 select the global 3D coordinates in the three boxe
301. in with the number selected in the item box cannot_delete_dom_1 indicates that the domain number one cannot be deleted because at least one domain is necessary to get a useful model 15 6 4 2D copy __ Copy active elements For safety reasons you are asked copy___elements_OK_ when you try to copy any element If this question is answered in the negative nothing is copied and process_aborted____ is displayed Copying increases the number of elements and will not be completed if the maximum number of elements is exceeded It requires the definition of a 2D displacement vector i e the definition of a start point and of an end point set_start_point_winl tells you to define the start point within the first window by pressing the first mouse button and releasing it when the cursor is at the position of the start point The coor dinates x and Yw of the cursor are displayed in the first two boxes of the bottom line Afterwards set_end point_win1_ tells you to define the end point in the same manner as the start point 2D copy line___ Copy active lines and arcs to the new position defined by the displacement vector 2D copy arc______ Identical with 2D copy line see above 2D copy object Simultaneously perform 2D copy line see above and 2D copy pole see below 2D copy____ pole_____ Copy active expansions to th
302. ines and arcs number of the actual 2D element line or arc integer information of the 2D elements lines and arcs real information of the 2D elements lines and arcs number of 2D expansions poles number of the actual 2D expansion pole integer information of the 2D expansions poles real information of the 2D expansions poles number of matching points number of 2D and 3D matching points number of 3D matching points only number of 3D matching points of the first object number of 3D matching points of the second object number of the actual matching point integer information of the matching points real information of the matching points planes defining the matching points height of the matching points above the window plane number of expansions poles number of expansions poles of the first object number of expansions poles of the second object number of the actual expansion pole integer information of the expansions poles real information of the expansions poles planes defining the expansions poles height of the expansions poles above the window plane number of standard plot windows number of the actual standard plot window integer information of the standard plot windows real information of the standard plot windows number of sets of field points general plot windows number of the actual set of field points general plot window number of field points number of the actual field point integer
303. ines connecting the multipole in the center of the sphere with the matching points This indicates that the pole checking routine is working Afterwards the matching points are displayed To make sure that everything is correct run the checking procedures 3D lt check points and 3D lt check pole Moreover click the second mouse button when the cur sor in on the multipole to select the multipole As a consequence the actual data of the multipole is displayed in the Exp and sel boxes For the moment let s simply hope that these values are useful 219 11 To define the problem to be computed entirely you have to define the incident wave Let us try a plane wave with electric field in the Y direction and magnetic field in the Z direction A plane wave is a special expansion with the number 701 Thus set Exp IE1 to 701 and Exp dom to the domain number of the incident field i e 1 All other parameters are irrelevant for this expansion Try to perform the 3D add pole command now Note that the origin of plane wave can be anywhere Moving it in the direction of the wave vector results in a phase shift but the results remain essentially the same The first tangent vector of the plane wave expansion indicates the direction of the electric field the second tangent vector indicates the direction of the magnetic field 12
304. ines of the field that is being displayed They can be set at any position in space The command move part 0 moves all particles repeatedly in the direction of the field at the actual position Thus you get a set of field lines starting from the positions where you initially set the pseudo particles Before you do this you must compute the field within an appropriate area on a sufficiently fine grid For the models 18 and 19 it is recommended to blow the first plot window with a factor 2 to use 25 horizontal and 25 vertical grid lines and 13 levels above the X Y plane The distance between the levels should be about the same as the distance between the grid lines You can do these modifications either with the graphic editor or with any text editor When you have stored the parameters of the model you do not have to recompute them Note that the main program has to compute a quite large plot file I e it will require some time and memory 256 After having computed the plot file start the plot program and proceed as follows 1 Set level O and read the plot file with the command read mmp p O 031 provided that your model number is 31 Not that it is important to set the level number 0 before reading the plot file because otherwise only one level would be read 2 Select the E field to be shown for example the time average of the Poynting field i e and S on
305. information of the field points number of field points in the different sets of field points integer information activity of the field points planes defining the field points height of the field points above the window plane number of constraints 322 kBed kBedP iBed iBedP iBeda rBed pBed hBed nintg kIntg kIntgP iIntg iIntgP iIntga pintg hIntg number of the actual constraint number of points defining the actual constraint integer information of the constraints number of field points in the different constraints integer information activity of the points of the constraints real information of the constraints planes defining the points of the constraints height of the points of the constraints above the window plane number of integrals number of the actual integral number of points defining the actual integral integer information of the integrals number of field points in the different integrals integer information activity of the points of the integrals planes defining the points of the integrals height of the points of the integrals above the window plane File MMP_P3D INC Important Parameters MMat MPol MDom MWind MFPt MDir MInfo MPart maximum number of matching points maximum number of expansions poles maximum number of domains maximum number of standard plot windows maximum number of general plot windows sets of field points maximum number of directives for generating a movi
306. ing to your Windows manual The name of the group is up to you but MMP is used by the authors Now you should install the 3D MMP applications MMP_E3D MMP_F3D MMP_FAN MMP_M3D MMP_P3D and MMP_PAR in MMP Note 1 that the executables are in the subdirectory WIW Watcom version of the directory MMP3D on the drive X where X is the drive you have used for installing 3D MMP and 2 that you should give the path to the working direc tory as a command line parameter The working directory usually is the subdirectory EX3D of the directory MMP3D where INSTALL BAT has already installed the input files for the tutorial Note that INSTALL BAT indicates the appropriate call of the 3D MMP applications under Windows when it is terminated 20 3 Compilation 20 3 1 Standard Compilation with Supported Compilers The compilation of the 3D MMP codes depends on the hardware compiler and the installation of your compiler When your hardware configuration your compiler version corresponds to one of the standard versions given in the introduction you can use the corresponding batch file For Watcom F77 386 FORTRAN Version 8 5 WAT WIN BAT is included in this package and for 3L parallel FORTRAN Version 2 1 3LF DOS BAT can be 272 used for compiling the non graphic part on a Micro Way quadputer board and on similar transputer boards For other supported compilers appropriate batch and auxiliary files are available upon request 20 3 2 Modifications for Dif
307. ing point function fehler to compute the error from the residuals according to 6 1 6 2 6 3 and routine nbedw for the evaluation of the constraints Integrals are needed in several places for use as constraints see in the following section for scaling the solution and for evaluation of integral quantities Scaling is done by norm integrals are evaluated in routine intega Both call integ for single integrals which are computed as sums 10 1 The field components in the integral points are again computed by feldk with function ignr for the determination of the domain The addends are obtained from the field components by routine intval Plots on grids and for sets of field points are produced by the routines p1tp00 and pltp50 respectively The plot routines call function ignr for the automatic determination of the domain of a field point and routines feldfp or feldk for computation of the field values Routine feldk computes field values in a field point For each symmetry component it calls routine zeile to compute the rows and multiplies them with the parameter vector c The symmetry components are summed up Routine feldfp calls feldk and transforms the field components to the coordinate system of the field point Field points are stored in the same array as the matching points usually point nmat 1 is used 13 3 Rows and Expansions 13 3 1 Routine zeile zeile is a central subroutine of the code and stands between the high level and t
308. ing points are present you will notice that the hiding procedure of the plot program sometimes fails In order to get a better hiding you can increase the value in the box iz resolut The box to the right of P indicates that the time dependent value of the field is displayed Time harmonic fields are characterized by a complex amplitude but only a real value can be represented by the plot program In fact the complex amplitude is multiplied by e7 and the real part of this product is displayed The real part of the phase y wt in degrees is selected in the box angle When you change the value in the box angle you implicitly change the time Changing the real part of the phase instead of the time is more convenient because of the periodicity 360 degrees for time harmonic fields When you click the box 7 its content is changed to which means that the time average will be plotted when you now run show pic f Note that this makes no sense when you are working with fields that are not time harmonic The plot program automatically assumes that the fields are not time harmonic 1 when the field has been read from a real time dependent plot file and 2 when a time dependent iterative procedure FDTD has been used for generating the field Otherwise time harmonic fields are assumed Instead of selecting the vector repr
309. int graphically you can set the coordinates in the boxes y z to the actual position of the pole and click the first mouse button in one x of the windows to enter these values Note that you have to perform any action in one of these boxes before you click the window Otherwise the program uses the location of the cursor instead of the coordinates in the boxes When the values in the boxes are already correct you have to perform some dummy action in one of the boxes Afterwards you are asked to set_end_point_data_ This indicates that you now have to select the coordinates of the destination point in the boxes x y z and to click the window for entering the data 17 6 2 Lossy Fat Dipole Model 19 The procedure for modeling a lossy fat dipole see fig 17 2 is almost identical with the procedure outlined in model 12 When you use the material properties of human tissue which for this frequency has a relative permittivity of about 50 and a conductivity about 1 071m you might doubt whether a normal expansion for modeling the field inside the body still works A relatively large maximum order is required whereas the maximum degree of the normal expansion can be as low as the maximum degrees of the multipoles used to model the exterior field To keep the number of unknowns below 100 i e the limit for XT compatible PCs you have to be very caref
310. intersection of all symmetry planes even if this is not within the domain The use of normal expansions leads for many simply shaped domains to much fewer unknown parameters although its order has mostly to be very high 8 5 Thin Wires A long thin wire with arbitrary current distribution is made up of single segments C 1 cf fig 8 6 In the thin wire expansion C 4 only the continuity conditions C 2 for the current between the segments of one wire expansion are fulfilled exactly As can be seen in the analytical deduction the segments have to be shorter than a quarter of the wavelength A in practice A 10 is a good choice Moreover the length of the segments should be at least equal to the diameter of the wire The discontinuity of the charge distribution near segment junctions principally acts as a point source but is usually too small to be dangerous to nearby matching points However keep them away from such junctions if you think they might exert a bad influence on the solution Thin wire expansions are axially symmetric around their z axis Therefore only one line of matching points along the surface of the wire is needed and only the boundary con 44 IL LLLLIALLLLLLLLL LL Figure 8 6 Thin wire expansion with matching points Additional dummy matching points may be necessary for the automatic detection of the domain dition for the tangential component of E in the direction of the wire may be posed Unlike in the NEC
311. ints is helpful for getting more confidence in the results AT Part II User s Guide of the Main Program 9 Running the Main Program 9 1 Introduction The 3D MMP main program is designed for solving time harmonic 2D and 3D scattering problems for linear homogeneous and isotropic materials It is an implementation of the theory described in chapters 1 to 7 Its capabilities are Computation of the parameters c Computation of residual errors in matching points and constraints Evaluation of integral quantities Evaluation of complex amplitudes of the field f in arbitrary field points and on rectangular grids Reflective symmetries are allowed about any of the coordinate planes X 0 Y 0 and Z 0 of the global Cartesian coordinate system With the Fourier transform utility computations can also be made for nonharmonic but periodic time dependence Input and output to the 3D MMP main program is made via ASCII files Some of these files can be prepared and viewed with graphic interface programs which are described in chapters 14 to 16 The contents of the files are explained in the following chapters the file formats are listed in appendix D All files are in FORTRAN list directed input format format The programs are written in standard FORTRAN 77 and therefore use static memory allocation As a consequence the size of problems which can be computed is limited to a maximum size determined by the parameters described in sec
312. ion coordinates of point in expansion recursive index of first parameter of a connection in cpic number of parameters Matching Points imat Xp Zp xpn zpt2 sep sdp igl ig2 ir sperr fvall fval2 sperrp Constraints xnb znb xnnb znnb cnbed rnbgew nnbed inbed nbtyp nnbpt nnbpti Integrals cint rnorm xint zint xintn zintn inorm nint iint inttyp nintp identification number of matching points locations Tp orientation 11 12 weight wk surface Sk number of bodering domains boundary conditions error 6 1 6 2 6 3 estimation for field in domain 1 section 11 2 estimation for field in domain 2 section 11 2 error in percent 11 1 location of integral point vector for integral point updating vector for constraints weight of constraint number of constraints identification number of constraints type of integral in constraint number of integral points in a constraint index of first integral point in xnb etc value of integral scaling factor for problem location of integral point vector for integral point internal scaling directive number of integrals identification number of integral type of integral number of integral points in an integral Matrix Algorithms ca cup matrix updating vector 313 rc cs cxin gz cresq rcond auxiliary vector for cosines of Givens rotations auxiliary vector for sines of Givens rotations vector for passing data
313. ion of degree m gt 0 auxiliary to a2d 2D TEM expansion C 10 3D expansion C 16 3D expansion of degree m 0 n 1 N auxiliary to a3d 3D expansion of degree m gt 0 n m N auxiliary to a3d rectangular waveguide C 17 C 18 circular waveguide modes C 19 C 20 plane wave C 21 evanescent plane wave C 22 C 22 determine length of an expansion length of a connection length of a thin wire expansion length of a 2D expansion length of a 2D expansion of degree m 0 auxiliary to n2d length of a 2D expansion of degree m gt 0 auxiliary to n2d length of a 2D TEM expansion length of a 3D expansion length of a 3D expansion of degree m 0 n 1 N aux to n3d length of a 3D expansion of degree m gt 0 n m N aux to n3d length of a plane wave expansion length of a evanescent plane wave expansion integer function for symmetry detection in 2D and 3D expansions integer function for symmetry detection in 2D and 3D expansions write message to screen and to output file graphic display of rows of a matching point graphic display of the triangular matrix auxiliary function to dispz and dispm 307 mmperr init1 init2 inietc inikon inigeb inians inicon iniout inimsg ininp inentw incon inmatp innbed wiremp ininte inplot skpint inintp inpar outpar ignr snmp2d snmp3d strant stranf ctrant ctranf ztrant ztranf sphkar zylkar sxprod cxprod ssprod csprod einh reinh
314. ions for Different Versions of Supported Compilers 273 20 3 3 Modifications for Unsupported Compilers 273 20 3 4 Modifications for Different Hardware Configurations 273 20 3 5 Installation of the Parallel Code for Transputers 274 21 Running the 3D MMP Programs 276 21 1 Required Data and Auxiliary Files o 276 21 2 Running 3D MMP i 0000000 ba A eee eS 276 VI Appendices 278 A Symbols and Coordinate Systems 279 Acl Notation i et oe E EA E e aE aG 279 A 1 1 Mathematical and Physical Constants 279 A 1 2 Mathematical Functions o e 279 A 1 3 Differential Operators e 279 A 1 4 Matrices and Vectors e e 280 A 1 5 Electromagnetic Fields 2 2 oo e e 280 A 2 Coordinate Systems and Transformations 281 A 2 1 Cartesian Systems 2 2 0 0 0 eee eee ee 281 A 2 2 Cylindrical and Spherical Coordinates 282 B Functions 283 B 1 Cylindrical Bessel Functions 2 0 0 2 0 0 0200008 283 B 2 Spherical Bessel Functions e o 284 B 3 Associated Legendre Functions o 284 B 4 Harmonic Functions cs 26 6408 aaa ae a AR 285 C Expansions 286 C 1 Thin Wire Expansion 2 2 0 0 00 a a a ee 286 C2 Cylindrical Solutions ranei e064 4 ae Ee eh bg RS E 287 G 3 Spherical Solutions t enren aya ge ea ae A a Ree 289 C 4 Rectangular Wav
315. ions on Magnetics vol 19 no 6 pp 2367 2370 1983 4th COMPUMAG Conference June 1983 P Leuchtmann Automatic computation of optimum origins of the poles in the multiple multipole method MMP method IEEE Transactions on Magnetics vol 19 no 6 pp 2371 2374 1983 4th COMPUMAG Conference June 1983 Ch Hafner R Ballisti G Klaus and H Baggenstos Ein Programmpaket zur Berechnung elektromagnetischer Felder Bulletin SEV VSE vol 75 no 7 pp 381 383 1984 P Leuchtmann Uber die Berechnung von Impedanzen Bulletin SEV VSE vol 75 no 21 pp 1260 1263 1984 Ch Hafner Numerische Berechnung gef hrter Wellenausbreitung Bulletin SEV VSE vol 76 no 1 pp 15 19 1985 Ch Hafner MMP calculations of guided waves IEEE Transactions on Mag netics vol 21 pp 2310 2312 Nov 1985 5th COMPUMAG Conference June 1985 Ch Hafner A computer program for the calculation of waves on cylindrical struc tures in Proceedings of the ISAP vol 2 Kyoto Japan pp 607 610 Aug 1985 G Klaus The MMP method applied to 3 D scattering problems in Proceedings of the ISAP vol 2 Kyoto Japan pp 599 602 Aug 1985 Ch Hafner Numerical calculations of waves on cylindrical structures in Pro ceedings of the ISAE Beijing pp 72 77 Aug 1985 G Klaus 3 D nearfield calculations of waves using the MMP method in Pro ceedings of the ISAE Beijing pp 619
316. irst mouse button when the cursor is near the upper right corner of the window Move the cursor and release the button when the corner is at the desired location Note that the lower left corner is fixed during this action Blowing a Screen Window When you want to blow a screen window i e adjust the physical size a screen window without changing the aspect ratio of the horizontal and vertical sides select the window number in the corresponding item box and press the first mouse button when the cursor is near the right hand side of the window Move the cursor and release the button when 98 the window has the desired size Note that both the lower left corner and the aspect ratio of the horizontal and vertical sides are fixed during this action In Activating a Single Graphic Element Select the type of the graphic element i e make sure that this element is displayed in the item box Click the second mouse button when the cursor is near the point to be in activated Note that the data of this point will be displayed in the corresponding boxes Activating a Set of Graphic Elements Select the type of the graphic element i e make sure that this element is displayed in the item box Adjust the drawing depth appropriately Points that are in a bigger distance from the window plane will not be affected in the following Now you can select a rectangle within the window by pressing the first mouse button when the cursor is near a corn
317. is can be done with any text editor The auxiliary program MMP_FAN is a simple Fourier analysis program that computes the frequencies and Fourier coefficient of the signal in MMP_FOU TIM The corresponding values are stored in the file MMP_FOU FRQ It is recommended to check these data before starting a time consuming computation Usually the computation of the highest frequency is the most critical one If you are not sure whether your model is sufficient for the highest frequency or not first compute the solution for this frequency alone see fig 16 1 The computation of the parameter and plot files for the different frequencies with the main program is performed automatically when you select the task 14 method 1 frequency 2 Fourier transform and the input file number 29 for the model 29 considered here Especially when many frequencies have to be computed and when the plot files contain a lot of field points a huge amount of data is created and has to be stored on the disk Therefore make sure first that you have enough memory on the disk you are working on After the computation of the frequency dependent plot files MMP_Pyy xxx you have to run the inverse Fourier transform program MMP_F3D for creating the time dependent plot files MMP_Tyy xxx that can be visualized with the plot program Note that the number of these files and the time steps are defined in the first line of the file MMP_FOU TIM Once more first reassure that you have enoug
318. is reason you are asked adj _automatically_ If this question is answered in the negative the adjustment that has been explained for lines is performed Otherwise the questions adjust_ALL_poles___ adjust_active_poles are used to decide whether to adjust all poles the active poles or only the pole with the number selected in the item box Essentially the procedure is the same as in 2D lt check pole Thus the messages that can be displayed need no further ex planation The most important exception is that the orders of the poles are replaced by orders appropriate to the actual overdetermination defined in the box over 2D adjust__ domain___ Adjust the material properties of a domain Previously select the domain number in the item box and the desired complex material properties r ur and in the corresponding real data boxes Er Ei Ur Ui l Sr Si where the character i indicates the imaginary parts 9 15 6 11 2D generate This action can be applied to multipoles only 2D generate pole_____ Generate 2D multipoles automatically or semi automatically Select the type parameter of the procedure to be performed in the item box the desired overdetermination in the additional integer data box over and the domain number in the box Domain The restriction of the procedure on one domain only is advantageous in co
319. is the direction of the first tangent vector defining the plane in the field point When a field point is selected with the second mouse button this box displays the global X coordinate of the point in x direction When you are asked to input coordinates of a point to be constructed you can either discretize the point in one of the windows or you can select its Cartesian coordinates in boxes 1 to 3 To enter the values click one of the windows 180 Box 2 Y Coordinate Type input output y Analogous to box 1 for coordinates y and Y respectively Box 3 Z Coordinate Type input output Z Analogous to box 1 for coordinates Zw and Z respectively Box 4 Real Window Data Type pull down input output rx_11 lower left corner x coordinate of the window plane ry 11 lower left corner Yw coordinate of the window plane rx ur upper right corner w coordinate of the window plane ry ur upper right corner Yw coordinate of the window plane d_lev distance between levels d_eye distance of eye above window plane parallel projection is used when this value is less or equal to zero linew unit line width width of thin lines in 1 1000 of screen width depth drawing depth perpendicular to the window plane When you perform the command show wind this box displays the real data of the window selected in the item box Note that the last three values of this box are global and hold for all windows To change the rea
320. item box inactivate all other 2D elements lines and arcs If it is an arc the text in the item box is adjusted The additional data of the element is displayed in the corresponding boxes Note that the same boxes are used for 3D matching points and 2D lines and arcs since the latter are used to generate the former NO_such_element____ indicates that the item number is outside the range of lines and arcs that have been defined 2D show____ arc______ The 2D line or arc with the number selected in the item box is activated inactivate all other 2D elements lines and arcs If it is a line the text in the item box is adjusted The additional data of the element is displayed in the corresponding boxes Note that the same boxes are used for 3D matching points and 2D lines and arcs since the latter are used to generate the former NO_such_element____ indicates that the item number is outside the range of lines and arcs that have been defined 2D show____ points___ Show the 2D matching points on the lines and arcs by two lines indicating the tangent and normal direction of the boundary see fig 15 2 101 2D show points 0 generating meta file Ino meta 3 clear EXIT ang 3 6005 02 m 5 Domain 1 met M e2 10 Exp dom 1 Con pt Li Wx11 1 000 00 ix11 6 Er 1 0000E 00 wot 1 000E 00 sel 0 0005 00 con w 0 0E 00 x 0 0008 00
321. ith the Babinet theorem Essentially the scattered field consists of two parts the wave that would be reflected by the plate without the aperture and a wave caused by the aperture When the aperture is small compared with the wavelength the second part is a dipole field with origin in the aperture This is certainly encouraging for a computation with the MMP code You can expect that the wave caused by larger apertures in plates of 245 finite thickness can be modeled with a multipole in the center of the aperture or with multiple multipoles with origins in the area of the aperture When trying to generate the matching points for an MMP computation of an aperture in an infinite plate of finite thickness you become aware of the following problems e You cannot discretize an infinite boundary e You have almost no freedom to put the multipoles because they must be inside the plate Above all you cannot put a multipole in the center of the aperture The first problem can easily be overcome When the incident wave is given either as an expansion or as a connection you can use the same expansion or connection with a different direction for modeling the reflected wave generated by the plate without aperture When the corresponding parameters and the direction are computed correctly the boundary conditions hold everywhere on the plate For a perfectly conducting plane you can easily compute not only the direction but also the parameters of the reflec
322. ively simple the former is difficult in the 3D construction because no appropriate feature is present in the actual version of the editor Thus it is reasonable in most cases to improve the 2D model first To do this proceed as follows 1 The additional real and integer values e g the frequency symmetry numbers etc are not stored in the 2D file Thus you can either set these parameters manually or you can read all data of the corresponding 3D input file and delete the 3D matching points and multipoles with the command 3D delete object afterwards 2 Read the 2D input file 3 Adjust the number of matching points on the arc with the command 2D adjust points For example use twice as many i e 10 matching points Since useful results had been obtained with model 1 and a frequency of 150 MHz this seems to be reason able 4 Of course you can increase the orders of the 2D multipole manually but this is not necessary because the program automatically adjusts the orders of the 3D multipole when the command 3D generate torus is executed Note that the angle for generating the torus is not stored in the 3D input file Thus you have to change the default value of 360 degrees to 90 degrees before you generate the torus i e sphere 5 Do not forget to add the incident plane wave as you did in the two models discussed before 6 Save the new 3D model on the 3D input file MMP_3DI 002
323. l 1 When you read an input file in the plot program you are asked whether symmetry operations have to be performed or not In fact all symmetries have been ignored when the model was generated although a sphere is a very symmetric object Symmetries allow to reduce the numerical expenditure considerably 3D MMP knows up to three symmetry planes but it does not take more sophisticated symmetries into account for reasons of simplicity Since a sphere with center in the origin of the global Cartesian coordinate system is symmetric with respect to all three symmetry planes X 0 Y 0 221 and Z 0 only one eighth of the sphere needs to be discretized This can be generated by the following steps 1 10 Run the graphic editor and select the frequency as in the construction of the sphere without symmetry considerations Select the symmetry numbers is1 is2 and is3 in the additional integer data box Note that these values depend on the symmetry of the incident field For a plane wave propagating in X direction with the electric field in Y direction and the magnetic field in Z direction the correct values are is1 3 is2 1 is3 2 Generate a 2D arc with origin in the point X 0 Y 0 in the first quadrant of the XY plane Since the arc in the half plane used in the first approach was discretized with 10 matching points this time use 5 matching points only i e the predefined value The results will turn out to be almost ident
324. l data of the window modify the values in this box with the first count up and second count down mouse button and perform the command adjust wind afterwards Before you do this it is a good idea to perform show wind This makes sure that you have all actual data of the window in the box Box 5 Integer Window Data Type pull down input output ix_low left lower left corner horizontal position on the screen in pixel coordinates iy_low left lower left corner vertical position on the screen in pixel coordinates ix_up right upper right corner horizontal position on the screen in pixel coordi nates iy_up right upper right corner vertical position on the screen in pixel coordinates ix resolut horizontal resolution number of invisible grid lines iy resolut vertical resolution number of invisible grid lines iz resolut resolution perpendicular to plane levels used for hiding 181 actual wind actual screen window number Change this value with show wind n windows number of screen windows Change this value with the command ladd wind and delete wind meta_boxes_ 1 show boxes in meta files 0 omit boxes in meta files mouse_stop_ wait factor for aborting a process by clicking a mouse button When you perform the command show wind this box displays the integer data of the window selected in the item box To change the integer data of the window you
325. l parts must be arcs with exactly the same center and radius otherwise you cannot expect more accurate results When you try to start an arc at the same point where another one ends you probably are not able to do that If you do not believe it try Much better results can be obtained with the 2D rotate arc command Small or even larger areas of the surface covered by more than one matching point can be tolerated and do not or at least not considerably reduce the accuracy When you generate a sphere with a 2D model containing two different arcs one of them having the same matching point density as before the other one having a higher matching point density and proceed as in model 9 you see that the maximum orders of the multipole in the center which have been determined by the automatic pole gen eration procedure turn out to be higher than before This is due to the additional matching points near the dipole Since these points essentially correspond to the addi tional multipole near the mirror point that is generated manually the maximum orders and degrees of the multipole in the center should be reduced This can be achieved either manually or automatically when the factor for the overdetermination contained in the additional integer data box over is increased So far the default value 2 has always been used although a sphere is such an ideal object for 3D MMP that the numerical expenditure could be reduced with a smaller ov
326. l properties of domains 299 nhor nver nlev ndom sdplt number of points in first second third direction domain number distance between levels ig x y z domain coordinates of field point xt1 yt1 zt1 UL xt2 yt2 zt2 v2 cex cey cez E chx chy chz H cax cay caz complex vector potential cv complex scalar potential Note that six real numbers are used for the three complex material properties r Uy g in the plot file The file content numbers correspond to the following parts of the field 1 ireare real parts 2 ireaim imaginary parts 3 ireaeh electromagnetic field 4 ireaap vector potential 5 ireavp scalar potential When one of these integers is zero the corresponding part is omitted in the file D 9 Real 3D Plot File MMP_Tyy xxx For yy 00 49 plots are produced on grids for yy 50 99 in arbitrary field points see chapter 10 and file MMP_3DT xxx in this chapter The following format is used for both file types Note that the additional data con cerning the grid and field points are missing in this file because they can be read in the corresonding MMP_Pyy xxx file The potentials in brackets are expected to be contained in the file when the identification number of the corresonding MMP_Pyy xxx file is 1291 gt ex ey ez E hx hy hz H ax ay az vector potential v scalar potential D 10 2D Plot Files MMP_DAT PLT MMP_PLF xxx MMP_PLT xxx The 3D graphic plot program MMP_P3D is able to read 2D plot
327. le than the one described here 266 18 5 Example Configuration To give an idea of a useful configuration The actual MMP programs have been im plemented almost entirely on a portable Toshiba 5200 with a VGA driver resolution 640 480 pixels 80386 processor with 80387 coprocessor 20MHz clock 100Mbytes hard disk 4Mbytes memory DOS 3 3 Logitech Mouse with 3 buttons For solving large problems either an i860 add on board like the Micro Way i860 number smasher or a network with several IMS T800 transputers like the Micro Way Quadputer have been inserted in this machine These add on boards are usually used for running the MMP main and Fourier transform programs only because the data transfer between these boards and the host is relatively slow This is not a serious problem because the speed of the graphic 3D MMP programs on a 386 PC with 387 coprocessor is sufficient for most problems Moreover 4Mbytes of memory is sufficient for the 3D MMP graphics in most cases The 100Mbytes hard disk is fast enough for showing monochrome movies with VGA resolution 267 19 Compilers and Systems 19 1 Introduction The FORTRAN 77 standard is quite old and does not include many elements available on most of the modern machines To achieve the highest possible portability no non standard elements have been used in the 3D MMP code with three exceptions e The very helpful include statement that is available on almost all compilers e A small
328. ler than the diameter of the wire Of course it is expected that better results are obtained with shorter segments When we use the symmetry planes as for the fat dipole we have to discretize only the upper half of the dipole with a length of 0 25 m i e 10 segments should be sufficient This number is selected in the box Exp IE2 In most cases use two matching points per segment and select this number in the box Exp IE5 The matching points along a segment will be distributed according to rules given in see 40 Note that these rules do not hold when the radius of the wire is bigger than 0 6 times the length of a segment This is not an important drawback because one can easily handle short segments with three matching points Moreover multipole expansions are efficient in this case However let us try three matching points per segment although this unnecessarily increases the numerical expenditure This allows to look at some more features and you certainly are able now to try thin wire models with two matching points per segment and to compare the results Since no optimal location of the matching points is known for more than two matching points per segment the matching points are distributed uniformly MMP wizards say that in this case the matching points should be weighted with different weights and that the ratio radius length of segment should be about 1 The weight of a matching point in the cent
329. ler way select the number of pictures desired in the box ipic mov and run generate pic f The program automatically will generate a movie with the number selected in the item box movie If such a movie does already exist you will be asked overwrite_movie____ If you answer in the negative the process is stopped with the message movie_not_generated Note that you are asked compute_new_scaling as soon as you run generate pic f In most cases you will answer in the positive except when you are continuing a previous iteration and want to have the same scaling as before The plot program handles either time harmonic or non harmonic time dependent fields The type of the field depends on the iterative algorithm Obviously FDTD is of the second type For all other algorithms outlined above this is not completely clear All Laplace algorithms deal with static fields Since static fields are a good approximation for low frequency time harmonic fields the first type is assumed for all Laplace algorithms For all other algorithms the second type is set In all algorithms the scalar potential is somehow involved In the FDTD algorithm it is used for defining the amplitude of the source and plays a secondary role All other algorithms act on the scalar potential itself It is well known that one can derive the electric field from the scalar potential This is done in all al
330. les are shown in addition to the field in the field points provided that they are defined Thus you should read first an input file Usually this will be the input file that has been used in the main program for generating a plot file that has either already been read or that is read afterwards Above all when a large number of matching points is present the time required for showing the matching points and poles is quite large Thus you will not turn on M and P before you have found an appropriate field representation In the matching points a line indicating the direction of the normal vector is drawn This line is scaled with the value in the box nrm v When you do not like it set the value equal to zero If you have generated an error file with the main program you can read it after having read the input file In this case the shading and the length of the line in the matching points will indicate the errors The box error is used to change the error scaling factor 194 When you want to completely suppress the error representation read the input file again without reading the error file afterwards Very often some interesting field points are hidden behind some less interesting matching points To suppress the drawing of the points in front you can reduce the so called drawing depth in the box depth When the drawing depth is large and when many match
331. line as long as the mouse button is pressed down If you did use method 1 to discretize the start point set_end_point_data_ indicates that you are expected to give the coordinates of the end point in the same way Le select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data If you did use method 2 to discretize the start point set_end_point______ indicates that you are expected to discretize the end point in the same way as the start point Of course you will be asked set_height_above_pln afterwards if you apply method 2 3D adjust__ window___ Adjust screen and plot windows For both there are several additional values that can be adjusted and require an appropriate selection of the corresponding values in the following boxes real screen and plot window data Wx11 Wy11 etc limits integer screen window data ix11 iy11 etc corners integer plot window data Win Teal plot window data Win h Some of these values can be manipulated graphically as well by pressing the first mouse button when the cursor is near the lower left or upper right corner the pixel coordinates of the window corners ix11 iy11 ixur and iyur Moreover the origin and the tangent vectors defining the window planes are usu
332. ll matching points These data are not sufficient for plotting the field Extended error files contain the entire data of the field on both sides of all matching points I e extended error files contain similar data like general plot files and can be useful for plotting the field on the surface of a body Note that the extended error files do not contain the locations of the field points i e matching points because the these data can be found in the corresponding input files Thus no special data in the input file is required for generating extended error files Since two different field values are computed in each matching point you have to decide in the plot program which one has to be used for plotting 64 11 Output 11 1 Parameters The parameters in file MMP_PAR xxx are the coefficients c i 1 N 1 for the ex pansion functions described in appendix C The parameter file also contains information on the expansions to which they belong A parameter file can be used as a connection if the name is changed accordingly The parameters in parameter files can be labeled with the mmp_par utility section 12 2 11 2 Residual Errors The errors in the matching points and the values of the constraints are shown in the error file MMP_ERR xxx They can also appear on the screen and in the output file depending on msscr and msfil in the input file There is a block with the errors in the matching points and one with the values of the con
333. llowing plot session remember that color movies are too slow in most cases and that you first have to write a file containing the directives for the movie To load a monochrome driver you have to run Windows setup by clicking the corresponding icon in the Main window of the Program Manager and select Change System Settings from the Options menu Note that you might be asked to insert some of the original Windows disks if you do that The desk of the plot program is similar to the desk of the editor but only one window is present at the beginning As soon as you have removed the hint box some parameters are initialized and a zero field is generated This field is meaningless here It is used for the iterative features implemented in the plot program For testing the plot program and for selecting an appropriate representation you can generate a random field with the command clear pic f 3 Afterwards you can immediately run show pict What you see is the intensity representation of the random E field For representing the time average Poynting field select S instead of E and instead of the time dependent field Moreover increase the field scaling factor in the f sc box If you run show pict again Now you can set all values in the 220 fill boxes to 2 which turns all 3D graphi
334. location of the matching points and the expansion is not very critical Therefore the discretization of the boundary and the setting of expansions i e the choice of location and order can be done almost independently of each other It has been found to be the simplest way to start with the discretization of the boundary and subsequently set the multipoles A special case remain thin wires which will be treated separately In the following some simple rules for discretization and setting of expansions are given The rules are analogous for 2D and 3D models They are not strict but largely based on experience gained from using MMP They should be understood as heuristic guidelines and sometimes may be violated The more generously matching points and expansions can be used the less the model is prone to changes Before going more into details a remark about the complexity of MMP models The size of the problems which can be solved is limited by available memory and computa tional time Both depend for larger problems mostly on the size of the system matrix A with dimensions M number of rows and N number of columns Memory consumption Smem and CPU time Ty behave as Smem ox N Tepu x MN A given MMP model shall be improved by doubling the density of the matching points and the orders of the multipoles For a 2D model this results in a doubling of both M and N consequently Smem 4 Sinem Tog gt 8 Tiri For a 3D model the num
335. ly reasonable to start with the same maximum orders and degrees for the normal expansion as for the multipole in the center Thus you can simply copy this multipole and afterwards adjust the domain number and the number ie2 in the boxes Exp dom 2 and Exp IE1 1 Before doing this remember what has already been mentioned before The last function of the new expansion is considered to be the excitation which is not intended here Thus first remove the excitation and add it afterwards again When you do not want to lose the data of the incident field you can do the following 1 Copy the multipole in the center 2 Adjust the data as indicated above 3 Copy the excitation 4 Delete the original excitation Note that before an expansion is copied adjusted or deleted it should be activated whereas all other expansions should be inactive For doing this the second mouse but ton is helpful except when two expansions have the same location In this case the command 3D show pole can be used Incidentally the same holds for copying adjust ing and deleting of matching points You probably find that the results are not very accurate When working with dielectric materials keep in mind that the wavelength inside a dielectric medium is smaller than the free space wavelength This is relevant for the accuracy To increase the accuracy you have to increase the number of matching points Of course
336. m For a full expansion which is invariant to rotations about its origin Minas is equal to Ninax Sometimes properly oriented reduced poles with Mmaz lt Nmar may be more economical because they have less parameters The region of influence of such a pole is rather like a prolate spheroid The exact location of the multipoles and the choice of orders is usually not very critical at least not in generous models and several arrangements can produce N 43 good results A fully automatized pole setting program for 2D static problems which implements the above principles and is based on the matching points has already been studied in 6 Some relatively easy rules can already give a good base for subsequent hand optimization Such features are now available for 3D modeling as well and are implemented in the graphic interfaces 16 8 4 Normal Expansions Obviously many multipoles are needed around a finite domain especially in 3D Some times they can be replaced by a single normal expansion Its location is not very critical as it does not have an as local behavior as a multipole Usually the origin is chosen somewhere near the center fig 8 5 Subdividing domains with fictitious boundaries may simplify their use Figure 8 5 The poles around a domain can often be replaced by a normal expansion o Only one normal expansion may be made for a domain If symmetries are used the normal expansion has therefore to be on the
337. m initialized to propagation constant y 59 e Circular waveguide mode Emn C 19 or Hmn C 20 mode numbers m and n propagating in the direction The origin of the expansion is in the center of the waveguide There is a maximum value for m and n iel 502 ie2 1 Emn 2 Hmn ie3 radial mode number m ie4 azimuthal mode number n sel radius of the waveguide cegam initialized to propagation constant e Plane wave C 21 with E polarized into the amp direction FH into the direction and propagating into the e direction iel 701 se2 scaling factor Ssca see below e Evanescent plane wave E C 22 and H C 23 iel 702 ie2 1 E 2 H se2 scaling factor Seca see below cegam transverse component k of the wave vector The scaling radii Pscal and Tsca can be useful for scaling of the expansion They are not used in this version of the program cf section 3 5 Nevertheless they are automat ically initialized if specified as zero in the input file otherwise they remain unchanged Pscat Will be initialized to the distance from the origin of the expansion to the nearest matching point in the 2D sense i e if all matching points are projected on the plane z 0 of the expansion Tsca will be initialized to the distance in full 3D The scaling factor Ssca is a possibility to change the scaling of an expansion If specified as zero on the input file it will be initialized to 1 otherwise it remains unchange
338. main Select item of regular action to be performed when the first mouse button is clicked in one of the windows Select item number with the first count up and second count down mouse button in the value area of this box For more information see description of regular actions Box 12 Additional Integer Data Type pull down input output sequ M different numbers of interest not stored for further use level 4 _ level number of regular plots 0 all levels n horiz _ grid lines in horizontal direction n vertic grid lines in vertical direction n levels number of levels Change values with the first count up and second count down mouse button in the value area of this box Changing the last three values of this box has no effect These values are changed when a new plot file is read 184 Box 13 Additional Real Data Type pull down input output angle angle for rotations phase for time harmonic fields blow_ blowing factor delay delay for showing movies in seconds metav size of the vertical side of a window in a meta file f sc field scaling factor error error scaling factor nrm v scaling factor of normal vectors in matching points grids scaling factor of grid and normal displacement of field f log factor for logarithmic iso lines the ratio of the field values on neighbor iso lines is given by this factor For linear iso lines select 1 0 or less Re_Om real part of angular frequency Im_Om imaginary par
339. matching points should be distributed only along the wire and a few matching points per segment are most reasonable As a consequence problems occur in the automatic detection of the domain of a field point To avoid these problems additional dummy matching points have to be introduced along the wire and at the ends of the wires Thus the generation of an appropriate set of matching points for a wire is time consuming and annoying On the other hand the matching points are attached to a thin wire expansion in a very simple way For this reason an automatic procedure has been implemented that generates a helpful set of matching points directly from some parameters of the thin wire expansion cf 10 5 These matching points do not appear as ordinary matching points in the input file In addition the editor provides several features for handling wires Let us start with a plane wave incident on a thin wire see fig 17 3 with the same length of the fat dipole in model 18 This does not require any 2D construction Before 239 the command 3D add wire is started the integer and real data of the wire have to be selected in the Exp xxx and sel box respectively First of all don t forget to select the radius of the wire in the box se1 Let us start with the value 0 025 m To get useful results the length of a segment should be considerably smaller than the wavelength but it should not be much smal
340. matically for each of the points idom lt 0 or set to idom for the whole plot window 63 10 8 2 Plots on Sets of Points General Plots For the plot files MMP_Pyy xxx with yy 50 99 nwefp sets of arbitrarily oriented points is specified as nwefp number of field point sets nhor nver nlev idom sdp1t number of points in first second third direction domain number real parameter idomp domain number of the field point xefp yefp zefp coordinates of the field point xefpti yefpt1 zefpt1 v xefpt2 yefpt2 zefpt2 V2 U1 and V2 are not significant to the 3D MMP main program and are simply passed on to the plot file Each set of field points contains nhor nver nlev points The distribution of the total number of points on these three numbers and also the real value fdum may be used to structure the set of points but do not have any significance for the 3D MMP main program The domain of the field points depends on a global parameter idom and a parameter idomp of the individual field points If idom is greater or equal to zero its value overrides the value idomp which is otherwise relevant If the resulting value for the single matching point is equal or less than zero the domain is determined automatically otherwise it indicates the domain The number of plot points per set is not limited in the 3D MMP main program 10 8 3 Plots on Matching Points Extended Error Files Usual error files contain some condensed data of the field in a
341. maz scaling radius Psca1 see below scaling factor Ssca1 see below cegam propagation constant y initialized for iprob 200 299 2D problems e 2D TEM expansion C 10 with orders Min Mmaz iel ie3 ie4 sel se2 251 minimum order Minin maximum order Mmaz scaling radius Psca see below scaling factor Ssca see below e 3D expansion C 16 with orders 1 N degrees 0 M iel ie2 ie3 sel se2 301 radial function 1 j kr 2 y kr 3 h kr ah kr order N scaling radius rscai see below scaling factor Ssca see below e 3D expansion C 16 with orders Nmin Nmax and degrees Minin Mmaz iel ie2 ie3 ie4 ie5 ie6 sel se2 302 H and E modes 303 E modes only 304 H modes only radial function 1 j kr 2 y kr 3 h kr 4 40 kr minimum order Nmin maximum order Nmaz minimum degree Min maximum degree Maz scaling radius rscai see below scaling factor Seca see below e Ring multipoles have been implemented by J Zheng 43 They are multipoles distributed on a ring i e circle Since the corresponding integration is unknown it is performed numerically Ring multipoles are defined in the module RING F The center of the ring corresponds to the location of the expansion The ring is within the plane defined by the two tangent vectors of the expansion 58 iel ie2 ie3 ie4 ie5 ie6 sel se2 iel ie2 ie3 ie4 ie5 ie6 sel se2 iel ie2 ie3 ie4 ie5 ie6
342. mber r Hr O complex nent number of expansions ient ig iel 6 sel se2 cegam identification and parameters xe ye ze origin Terp of the expansion xexX yex zex vi xey yey zey U2 296 nmat imat igl ig2 ir sgp area Xp yp Zp xpt1 ypt1 zpt1 xpt2 ypt2 zpt2 nnbed iint inttyp ipts rnbgew xint yint zint xintt1 yintt1 zintt1 xintt2 yintt2 zintt2 inorm nint iint inttyp ipts xint yint zint xintt1 yintt1 zintt1 xintt2 yintt2 zintt2 nwind xplm yplm zplm xp1t1 yp1t1 zp1t1 xp1t2 yp1t2 zp1t2 nhor nver nlev idom sdplt nwefp nhor nver nlev idom sdplt idomp xefp yefp zefp xefpti yefpti zefpti xefpt2 yefpt2 zefpt2 number of matching points identification domains B C and weight location F of matching point Ui va number of constraints identification type number of points weight location of integration point direction of first tangent vector direction of second tangent vector directive for scaling of the result number of integrals identification type number of points location of integral point vi U2 number of plot windows location of window center vi U2 number of points hor and vert levels domain number distance between levels number of plot point sets number of points in first second third direction domain number distance between levels domain number location of field point vj By D 3 2D Input File MMP_2DI xxx Data of 2D constructions in the 3D MMP editor Note that these file
343. mmand is executed If you want to set the axis manually i e if you do not want to use one of the default axes you can set either an axis of unit length perpendicular to one of the window planes or you can set a general 3D axis The former is simpler because only one 2D point has to be given Thus if you answer the question set_perpend _axis_ in the affirmative the message 130 set_origin_____ indicates that you have to press a mouse button in one of the windows and to release it when the cursor is at the location where you want to put the origin of the axis The procedure to set a general axis is more complicated First set_start_point____ indicates that the start point of the axis or vector has to be discretized There are two ways of doing that 1 select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data 2 press the first mouse button within a window and release it as soon as the cursor is at the position where you want to have the projection of the point on the actual window plane In order to define the location of the point completely you are asked to set the height of the point above the plane in the next step set_height_above_pln i e you are expected to give the height of the point above the window plane Only a vertical movement of the cursor will affect this value The actual height is displayed in the second box of the bottom
344. mple check you can set the material properties of the sphere equal to the material properties of the surrounding medium The exact result of this special case with a fictitious sphere is known the reflected wave should vanish 17 11 Cylindrical Lens Illuminated by Pulsed Plane Wave Model 29 The special expansions introduced in the previous model are rather 2D than 3D expan sions In addition to waveguide modes 2D multipoles are implemented in the 3D MMP code as well This allows to compute discontinuities in waveguides of more general shape Since the 3D MMP code does not allow to solve eigenvalue problems the propagation constants of waveguide modes have to be computed for example with the 2D MMP code 4 But 2D multipoles can easily be used for solving 2D scattering problems with the 3D MMP code for example the scattering of a plane wave incident on a cylindrical dielectric lens In this case most of the work in the editor consists in the 2D construction Let us consider a simple lens consisting of an arc and a straight line The multipoles for the interior are easily generated with the command 2D generate pole When the lens is larger then the wavelength the multipoles obtained with the pole generation type O in the item box are not useful because they are too far away from the boundary Moreover the poles generated with the pole generation type 0 for the exterior are outside the allowed domain and are therefore remov
345. mplex cases If the type is 0 poles are generated according to the 2D elements lines and arcs and 111 the message generate_2D_pole ele is displayed If type is larger than 0 one pole is generated for each matching point not yet correlated with an existing pole and pole_distance_ ___xx is displayed The distance between the matching point and the corresponding pole is proportional to the type number This procedure usually generates far too many poles but in a second step deletes all poles that are incorrect according to the checking procedure Note that poles that have been defined earlier can be deleted as well when they violate one of the rules of the checking procedure If the type parameter is small a large number of low order poles is generated close to the boundary the larger it is the fewer high order poles farther away from the boundary are generated Watch out that wrong results can be obtained if the distance from a pole to the closest matching point is large compared with the wavelength This rule is not checked in the current version Thus both the selection of the type 0 when large lines or arcs are present and of large type numbers can result in multipoles that are not appropriate 15 6 12 2D read Read data from files 2D read____ window___ See 3D constructions 2D read file____ Lines arcs and expansions from the 2D file MMP_2DT xxx where xxx is to be selected
346. n fictitious boundaries No multipoles have to be set near these boundaries if they are in a sufficient distance from the discontinuity i e the sphere Needless to say that different distances and different MMP expansions have to be tried in order to validate the results z E ie generate meta_ 21 28 computing S field_ No lE 4 s field1 y z M P gt 0 EXIT sequ M 41 111 3Darrow 4 depth 1 000E 00 ER 1 000008 00 vy 0 00000E 00 z 0 00000E 00 iter part dd part type A Figure 17 10 Desk of the 3D MMP plot program showing the time average of the Poynting vector for a H01 mode in a rectangular waveguide with a lossy sphere 250 Looking at the results you find that the relative errors in some matching points are larger than 100 percent At first sight you might believe that this model is too complicated to be solved on a small machine and that more than 100 unknowns are required for a useful solution But it is important that large relative errors only occur on those parts of the boundaries where the field itself is small I e the absolute errors are small compared with maximum values of the field Moreover the absolute errors are well balanced and the field looks reasonable Nonetheless it is certainly difficult to say anything about the accuracy of the reflected and transmitted waves because systematic errors can occur in such models To get a si
347. n of the exact solution f of the problem and the admission of an error function 7 on the surface can lead to undesired effects A small local error can accumulate over the surface to a large overall error which in some cases leads to violation of laws on a larger scale A remedy is to introduce additional equations with a high weight e g in form of integrals Jusya o 4 6 imposed on a function g of the total field f In the MMP code these additional conditions are called constraints or special conditions Note that g has to be linear in the components of f so that the integral can be added to the equations as N Da ara farra o 4 7 26 As a consequence power integrals cannot be used although a discontinuity of the power flux through a boundary is a common error Constraints are only rarely used in MMP models A different technique to overcome such difficulties is to give a high weight to the boundary conditions in certain matching points in order to locally zero the error function 4 5 Weighting The weight affects the importance of an equation in an overdetermined system of equa tions Thus it is necessary to compensate for various differences which otherwise would not be relevant e In the MKSA system or SI which is used throughout in the program the electric and the magnetic field do not have the same numerical magnitude e The boundary conditions for the normal components 4 1a 4 1d are multiplied with act
348. n of the upper right corner According to that adjust_window_corn is displayed If you do not want to set the corners manually the information in the 171 corresponding integer data boxes are used In order to define the plane of the screen window you have three possibilities e you can set the plane manually e you can set one of the default panes i e X Y X Z Y Z X Y X 2 7 4 e in the second screen window you can set a plane orthogonal to the first window plane with the same first tangent vector as the first window plane According to that you are asked set_plane manually_ set_plane M _xxxx_ plane_orthog_plane1 Tf you answer all questions in the negative The third question is asked only if the second screen window is added the X Y plane is used The manual construction of the plane starts with set_start_point____ Le you have to define the location of the origin of the plane There are two ways to do that 1 select the global 3D coordinates in the three boxes containing the Cartesian coor dinates and click one of the windows when you want to enter these data 2 press the first mouse button within a window and release it as soon as the cursor is at the position where you want to have the projection of the point on the actual window plane In order to define the location of the origin completely you are asked to set its height above the plane in the next step set_height_above_pln Only a
349. n such a distance from the Y Z plane that the pole checking routine does not display the warning pole_near_sym plane which indicates that there might be a numerical dependence between the pole and its symmetric counterpart on the negative X axis To reduce these errors and to obtain a more balanced error distribution you can move the multipole on the positive X axis toward the origin X 0 When you run 3D adjust pole now and answer the question adj _automatically_ in the affirmative the pole is moved on the YZ plane for avoiding the numerical de pendence Incidentally the automatic pole generation routine would do the same when a multipole would be obtained at this location but you would see the final result only When you want to insist on the location of a multipole do not run the automatic ad justment routine when the checking procedure issues a warning Otherwise you have 235 to move the multipole back to its original location afterwards However you can obtain slightly more accurate results by moving the multipole towards the Y Z plane i e by slightly violating one of the simple rules see fig 17 1 By varying the position of the pole on the X axis you can find an optimal position causing a most balanced error dis tribution When you move the multipole from this position towards the Y Z plane you get the largest errors far away from this plane and when you move the multipole in the opposite direction you find the la
350. n the subroutine NewAlg as well There are already several subroutines in the module MMP_P3A F for clearing parts of the field For example clrVR clears the real part of the scalar potential i e it sets VR 0 in all field points Although the vector potential is read and written on plot files it is not used anywhere in the iterative procedures of the actual version of the plot program l e it is up to you to use it 210 The subroutine Lap25 in MMP_P3A F is a typical example how a subroutine defining an iterative algorithm might look like It defines a FD procedure for 2D electrostatics working on the scalar potential with a five point star operator The subroutine starts with the header that essentially is the same for all such subroutines subroutine Lap25 ja liniF c 2D Laplace scalar 5 point include mmp_grf inc include mmp_p3d inc logical liniF First the field is initialized upon request if liniF call clrVR false Then the global variables iPot 1tim ja and two variables dx2 dy2 that will often be used in the algorithm are initialized dx2 dxFPtx x 2 dy2 dyFPt 2 iPot 1 ltim false ja 0 iper 1 where dxFPt dyFPt are the distances between grid points in horizontal and vertical direction respectively Afterwards a loop over all iterations nite and loops over the all levelsnlev all horizontal grid lines nhor and all vertical grid lines nver are started do 1 it 1 nite call dspper it nite iper
351. n there is not enough memory left for saving the part of the screen behind the particles this is indicated by ERROR_set_particle_ Add a new domain too_many_domains__ indicates that the domain cannot be added because the maximum number of domains would be exceeded 16 5 6 delete_ delete__ wind Delete the window with the number selected in the item box cannot_delete_window indicates that the window does not exist or cannot be deleted because at least one window is required delete__ part Delete the particle with the number selected in the item box cannot_delete_part indicates that the particle does not exist delete__ dom _ Delete the domain with the number selected in the item box cannot_delete_dom _ indicates that the domain does not exist When too_few_domains___ indicates that there is only one domain left This domain cannot be deleted 16 5 7 move___ move____ wind A window is a relatively complicated thing One can move either the origin of the window plane with a 3D vector or the limits of the window which is equivalent to a movement 173 of the origin within the plane Finally the position of the location of a window on the screen can be moved see 16 3 2 It should be noted that the graphic objects represented in a window are virtually moved in the opposite direction if either the origin or the limits of the plane are
352. nate of velocity vector global coordinates vz z coordinate of velocity vector global coordinates Use the command show part to display the values of a certain particle in this box With adjust part the values in this box are copied on the corresponding values of the particle Box 32 Particle Integer Data Type pull down input output part type type of particle see hint box for more information part size size radius in pixels of the particle on the screen part col color used for representing the particle partic number of the actual particle data of this particle displayed in this box and in box 31 n partic number of particles Use the command show part to display the values of a certain particle in this box With adjust part the values in this box are copied on the corresponding values of the particle 191 Box 33 Iteration Real Data Type pull down input output tim dt Tmx mex qex actual time time increment for iterative procedures including particles duration of pulse used in some iterative procedures exponent of gravitation law used for particle interaction 2 0 is the physically correct value exponent of Coulomb law used for particle interaction 2 0 is the phys ically correct value Box 34 Iteration Integer Data Type pull down input output iter part iter fiel iter type iter info ipic mov part rep
353. nce in the complementary domain each of which has a pole at its center figure 8 3 The spheres are soft i e they can intersect or extend into the domain to a certain degree Once the locations of the poles are known the orders have to be determined The maximum order Nmaz and degree Minas of a multipole cf section 10 5 are bound by the overdetermination factor and the sampling theorem The overdetermination factor of the matrix A i e the quotient of the number of rows M and the number of columns N gives a lower limit for the order This factor ranges from 2 for optimized models to 10 for rather safe models with respect to the matching points A good value is about 3 which in practice means one unknown parameter per 42 Figure 8 3 The boundary is covered with spheres containing multipoles within the complementary domain associated matching point Figure 8 4 The largest angle between two matching points as seen from the origin of the multipole determines the largest possible order and degree of the multipole The sampling theorem limits the maximum order Nmaz and the maximum degree Mmaz through the largest angles which separate two neighboring matching points seen from the origin of the multipole maz in the direction and Omas in the y direction T T and Mmaz lt 8 1 a i maz Omax If the sampling theorem is violated the errors are usually very small in the matching points but large between the
354. ndicate how this might look like If you do not find an appropriate time routine for your compiler you can replace it by a dummy routine When you are working on networks of transputers or other processors you should be an advanced programmer to take advantage of the network The main module MAIN SRC and the worker programs CH1 SRC CHL SRC for transputer pipelines will give you hints how to proceed The graphic part of the 3D MMP code requires either an appropriate interface to GEMVDI Windows or an appropriate graphic library that allows to simulate the el ementary graphics functions of the 3D MMP codes This is a job for an advanced programmer as well Hints can be found in the source files and in the graphics guide 20 3 4 Modifications for Different Hardware Configurations The main code is very portable and can easily be installed on other systems The only machine dependent statements are in files MAIN SRC and for transputer pipelines only CH1 SRC and CHL SRC These statements are labeled with comments The 3D MMP graphics require a simulation of the elementary graphics functions i e a sufficient graph ics package on your system The other files should compile on all machines without alteration 273 To achieve the maximum size of the problems which can be solved with the program on a particular machine the parameters in the corresponding SRC files have to be adjusted Suggestions for parameters useful for different memory sizes
355. ndom_ 1 1 If the question is answered in the negative the desk is cleared but the field is left un changed clear___ wind Clear the window selected in the item box If the number selected is out of range the whole desk is cleared clear___ part Clear delete all particles 16 6 Summary of Boxes In the following the contents and meaning of the different boxes is described You can obtain a similar description by clicking a box with the third mouse button A hint box will be displayed in the center of the screen on the condition that the hint files MMP_P3D xxx are correctly installed and can be read by the plot program and that the program has enough memory for saving the part of the screen used to display the hint box To remove a hint box click any mouse button The location of the boxes most of their text lines and most of the corresponding initial values are defined in the desk file MMP_P3D DSK This allows you to modify the corresponding data according to your needs However this should be done very carefully because the program cannot work properly if the desk file is damaged For example if the desk file is too short the program will miss data on the file Since it is already in the graphics mode when the desk file is read it will hang The contents of the boxes of the original desk file is the following Box 1 X Coordinate Type input output x The x component in local coordinates
356. ndow number number of standard plot windows number of horizontal grid lines of the actual standard plot windows number of vertical grid lines of the actual standard plot windows number of levels perpendicular to window plane of the actual plot windows domain number of the actual standard plot window 144 When you perform the commands show constrain show field pts show integrals this box displays the real data of the selected constraint general plot or integral respec tively To change the integer data contained in this box you can modify the corresponding values with the first count up and second count down mouse button and perform the corresponding adjust command This does not apply to the actual numbers that have to be selected with the show command and to the numbers of items windows etc that have to be changed with add and delete Box 8 Exit or Quit Program Type roll special action EXIT exit program ask questions for saving data before leaving QUIT quit program without saving data Leave program when the first mouse button is pressed in this box The contents EXIT or QUIT of this box is changed with the second mouse button Box 9 Type of Regular Actions Type pull down show____ show item add_____ add item delete__ delete item copy___ copy item move____ move item blow____ blow item rotate__ rotate item in
357. ne or object number two has been created object_1_generated object_2_generated_ If either the file cannot be opened or if an error occurs when the file is read error_reading input is displayed 15 7 13 3D write _ Before saving either a window file MMP_WIN xxx or an input file MMP_3DI xxx select xxx in the item box 3D write___ window___ Write window file MMP_WIN xxx Select the extension number xxx in the item box When a file with the number selected in the item box does already exist you are asked overwrite_wind file If this question is answered in the negative the actual window data are not saved and process_aborted__ is displayed Otherwise writing window file is displayed during writing If the file cannot be opened cannot_open_file__ is displayed In most cases this indicates that the disk is full 3D write__ file_____ Write input file MMP_3DI xxx Select the extension number xxx in the item box In the 3D MMP editor the files MMP_3DI xxx are not used only for defining a model that can be computed with the 3D MMP main program but also for saving the matching points and expansions of a 3D object This is important because only two objects can be handled at a time If the question 141 save _ALL_3D_data__ is answered in the affirmative a standard input file for the 3D MMP main program is written If two objects are present the data of both will be saved on the file Note t
358. ned in the box MPt dom2 on the right hand side of the line this has the same effect as exchanging the two domain numbers 2D invert__ arc______ Identical with 2D rotate line see above 108 2D invert__ window___ See 3D constructions 15 6 9 2D lt check The meaning of this command depends on the item 2D lt check arc______ Replace active arcs by their complements To draw an arc around a center point from a start point to an end point one has two possibilities clockwise or counter clockwise If an arc is drawn by the program in the wrong direction this can be changed i e the arc can be replaced by its complement complement_act _arcs indicates that the active arcs have been replaced by their complements 2D lt check pole_____ Perform some checks on multipoles Other expansions are ignored The check of the orders of the poles depends on the overdetermination defined in the additional integer data box over The predefined value 2 is useful in most cases Values smaller than 1 or very large values are not recommended Either all poles the active poles or only the pole with the number selected in the item box can be checked Therefore you are asked first check_ALL_poles___ If this question is answered in the affirmative all poles are checked Otherwise the question check_active_poles_ has to be answered in the a
359. nes only one of which is accessible at a time in order to save space on the desk To display all lines of a pull down box the first mouse button has to be clicked in the text area of the box When the box is in the upper half of the screen it is pulled down i e the full contents are displayed in and below the box Otherwise it is pulled up As soon as the mouse button is released the line that contained the cursor an instant before is displayed and all other lines are removed If the program has not enough memory for saving the part of the screen used to display the entire contents the box is rolled i e the number of the displayed line is increased by one when the first mouse button is clicked and decreased by one when the second mouse button is clicked Note that 3D MMP pull boxes are similar to pull down menus in usual Windows applications with the following most important differences 1 In general pull boxes contain a text and a variable area whereas Windows menus contain text only 2 The representation of the line selected with the cursor is left unchanged 3 The box is pulled up rather than pulled down when it is in the lower half of the screen 4 After selecting a line the corresponding line is displayed whereas the header of the menu is displayed in typical windows applications 5 Pull boxes have no header 83 Selection Boxes To change the line displayed in a selection box either the first or the second mouse button has
360. ng the residuals of these equations sufficiently small and not increasing too much the condition number of A An extra weight of 10 usually gives good results An error estimation and numerical examples can be found in 33 5 5 Parallelization With the growing complexity of the problems one wants to solve computational time explodes Most of it is spent in the updating routine Compared to this the time for computing the rows of A is negligible Improving performance of the program therefore means in the first place improving the speed of the updating algorithm The complexity of the source code of the program behaves oppositely most of the program consists of routines for computing the functions and the rows whereas the code which performs the actual updating is only a very small part One of the most efficient ways to speed up a code is to parallelize it The approach presented here is for implementation on a coarse grained network of processors and par allelizes only the updating algorithm It has been used on transputer networks which provide high computational power at a low price They allow to build very cheap and yet extremely powerful machines which can be entirely dedicated to a task For a dis cussion of the usage of transputers for electromagnetic field calculation and the hardware currently in use see 34 A look at the updating algorithm shows that the first k rows of R are only affected by the first k columns of th
361. nge the new pole and the dipole with a text editor e You can delete the dipole add the additional pole and add the dipole again e You can make a copy of the dipole move the first of the resulting two dipoles to the location where you want to set the additional pole adjust the orders of this pole and so on 17 3 3 Optimizing the Multipole Orders Model 7 The error distribution of model 6 is not balanced Relatively large errors occur near the XZ plane To understand this be aware of the fact that the electromagnetic field does not surround the sphere like an acoustic wave would do because of the polarization and because the boundary conditions of the electric and magnetic fields on an ideal conductor are different As a consequence it is not necessarily optimal to use identical values for the maximum orders and degrees of a multipole in the center of the sphere In fact the maximum orders and degrees are determined automatically in the editor according to some simple rules that do not depend on the specific problem and excitation Since the result is reasonable but not optimal in most cases it is worth playing a little bit with 226 the maximum orders and degrees Of course you can reduce the errors by increasing the orders This is not very interesting because the computation time is increased as well But you can increase the maximum order and reduce the maximum degree of a multipole in such a way that about the same number of unknown
362. nic case only Box 19 Third Field Type of Field Set Type dependent roll active inactive S Poynting S Ex AL jE power density p jE 7 pj power density p R o E V scalar potential A vector potential Analogous to box 17 For the field sets see box 14 Note the scalar fields p and p are copied on the n component when a vector rep resentation is used When the conductivity is complex p and p are identical The vector fields and the scalar potential are not shown when box 17 or 18 is active When the material properties are complex the field p is computed in the time harmonic case only The potentials are not defined in plot files generated by the MMP main program Box 20 First Tangential t1 Component of Field Vectors Type active inactive x tl component of field vectors Activate or inactivate this box with mouse button 1 or 2 in order to switch on or off the display of the different field components Only active field components are shown This is the x component of the local coordinates in the field points i e the com ponent in direction of the first tangent vector defining the plane in the field point Box 21 Second Tangential t2 Component of Field Vectors Type active inactive y t2 component of field vectors Analogous to box 20 187 Box 22 Normal n Component of field vectors Type active inactive Zz n component of field vectors Analogous to box 20 Box 23 Matching Points and Errors
363. nimizes the sum of the squares of the residuals M S nin min 1 20 One way of doing this is to solve the normal equations ajil lajilplc aja p b p 1 21 or more explicitly N M M Soe Y LA LA la tweet hl k 1 N 1 22 i 1 j l j l Practice shows that in the collocation method the solution depends much more on the actual position of the matching points than in the generalized point matching method Although the error is exactly zero in the matching points it can oscillate widely between them Allowing a residual error in a matching point leads to a much flatter and smoother error function 7 Paradoxically a reduction of the number of expansion functions with the same set of matching points can therefore lead to much better results 1 5 Comparison of the Methods Some equivalences between the methods described above are already evident e The error method 1 11 is equivalent to a projection method with the testing functions tj Lf e The point matching method is equivalent to a projection method with Dirac delta functions as testing functions e The error method and Galerkin s method become equivalent if the f are eigen functions of A numerical implementation shows further relations The integrals in 1 11 and 1 15 usually have to be evaluated numerically They can be written as a Riemann sum of values in K points rk K i wf gdr wf g Arz 1 23 9D k 1 Thus the error method 1 11 g
364. nly because they are less common The plane wave is a solution in Cartesian coordinates and often used as excitation In addition closed form solutions already ful filling some boundary conditions can be useful e g waveguide modes for rectangular and circular waveguides Another form of special expansions is discussed in the following sections 3 3 Solutions by Integration A different approach to find solutions of the homogeneous Helmholtz equations 2 6 is to solve the inhomogeneous Maxwell equations 2 5 or the corresponding inhomogeneous Helmholtz equations for sources outside the domain considered Within the domain this solution also satisfies the homogeneous Helmholtz equations The sources can be electric currents Ye and charges Po but also their dual counterparts magnetic currents and charges which are nonphysical at least for technical applications 22 For currents the deduction is formally easiest to perform via the magnetic vector potential A H la 3 1 u It is obtained from rig H gt gt Aw E finan 3 2 where Gay eiklr r A r r TFPI is the free space Green s function From 3 2 formulas for the field quantities can be derived It is obvious that these integrations can only rarely be performed analytically In most cases one has to employ numerical methods Such expansions are appropriate in cases where multipole expansions are extremely inefficient e g for structures with a high surface v
365. not explicitly X rated we assume that people interested in 3D electromagnetic fields know what they are doing The most impressive way for studying any time dependent field is certainly the ani mated representation Although PCs are not fast enough for generating several pictures within a second they allow to read the pixel information of monochrome pictures stored 156 on a hard disk with a speed sufficient for showing movies The generation of movies is time consuming but this is considered to be one of the most attractive features of the code above all when the Fourier transform has been applied 16 4 3 Representation of Fields Field points can be treated exactly as matching points Instead of representing the errors one can represent any scalar quantity by the fill pattern and the color used for the field points For vector fields additional information is of interest When the common representation of vectors with arrows is used it is extremely difficult to recognize the component of the vector perpendicular to the window plane Instead one can indicate the tangential and normal components separately The tangential components can be shown in form of a 2D arrow whereas the normal component is a scalar that can be represented easily In the actual version of the plot program the 3D vectors are subdivided into a 2D tangential vector and the normal component with respect to the plane in the field point rather than with respect to
366. ns are required for moving the distance between two grid lines Thus for moving the incident to the center of the window about 3 3 x 50 165 iterations are required You can do this in one step by selecting iter fiel 165 and running generate pic f Allow this procedure to compute the new scaling factor when you run it the first time Otherwise the scaling factor is zero and no plot will be drawn Probably you want to see how the wave propagates You can select iter fiel 50 or even less and run generate pic f again and again for obtaining several pictures Instead of this you might prefer to generate a movie You can do this without writing movie directives For generating 50 pictures simply select ipic mov 50 The number of iterations per picture should be sufficiently small for getting a smooth movie Since movies with many pictures are memory and time consuming a compromise is necessary When you select iter fiel 10 the wave will propagate within the total number of 50 x 10 iterations over a distance that exceeds the side length of the window This allows you to see the reflections at the right border When you directly start generating a movie with iter fiel 10 i e ten itera tion per picture the first picture will be drawn at a time where the maximum of the pulse is still outside the window Since the field is scaled for the first picture only and the
367. nsists of one or several sets of pictures The maximum number of sequences mseq and the maximum number of pictures mpic of all sequences is fixed in the include file MMP_P3D INC Each picture of a movie is stored in a file with the name MMP_Fyy xxx where yy is the number of the movie and xxx is the number of the picture For this reason only 1000 pictures and 100 movies can be stored on a directory and the parameters npic and nseq should not exceed these numbers The memory required for storing one picture depends on the size of the window the resolution of the screen and on the number of colors If a VGA driver and a relatively large window is used about 25kbytes are required for monochrome pictures and about 100kbytes for pictures with 16 colors The speed of fast hard disks is sufficient to read several monochrome pictures per seconds To increase the speed of a movie one can reduce the size of the window used for generating the movie Instead one can use a graphic mode with a lower resolution To reduce the speed of a movie the delay time can be increased before the movie is shown The delay time is contained in the additional real data box that contains the angle blowing factor the size of meta files and the scaling factors as well In addition to the picture files MMP_Fyy xxx an information file MMP_Iyy 000 is re quired for showing a movie The information contained in this file concerns the number of sequences the number of pictures the
368. objects have been combined Check of the matching points This check shows whether the number of existing multipoles is sufficient or not In most cases either an automatic or a manual generation of poles is necessary This and the previous step have to be repeated until the results of both checks are satisfactory 100 7 Definition of standard plot windows It should be mentioned that the screen win dows that are visible on the screen must not be identical with the plot windows used in the 3D MMP main program Moreover the data concerning screen win dows are stored in MMP_WIN xxx files whereas the data concerning plot windows are stored in MMP_3DI xxx files 8 Definition of special expansions constraints integrals and sets of field points if required The special expansions should be generated after the check of the mul tipoles No checks for such expansions are implemented in the current version If you are not very familiar with the MMP editor it is strongly recommended to store the 3D data on a separate file before generating constraints integrals and sets of field points 15 6 Summary of 2D Actions 15 6 1 2D show____ Show 2D elements and display the corresponding additional data of the elements Note that the latter makes no sense when several elements with different additional data are shown at the same time with this command 2D show____ line____ Activate the 2D line or arc with the number selected in the
369. odel Models 3 5 o o 225 17 3 2 Adding Multipoles Model 6 o o ooo o 226 17 3 3 Optimizing the Multipole Orders Model 7 226 17 3 4 Optimizing the Matching Point Distribution Model 8 227 17 3 5 A Non Uniform Model Model 9 o o o o o o o 228 17 3 6 Towards the Optimum Model 10 o o o 228 IA Using Materials a tao e tea a PD Wl SD a GP AA eta 229 17 4 1 Dielectric Sphere Model 11 o o o oo o 229 17 4 2 Lossy Dielectric Sphere Model 12 o o o 17 4 3 Surface Impedance Boundary Conditions Model 13 17 4 4 Lossy Magnetic Sphere Model 14 o o o oo 17 4 5 Coated Sphere Model 15 o oo oo e 1 7 5 Mutated Spheres s fh a sanal k a dd a AR aN 17 5 1 Generating an Ellipsoid Model 16 o o 17 5 2 Deformations Galore Model 17 o o o o o o 176 Fats Dipoles i a6 ee rd rt a tal Das 4 17 6 1 Ideally Conducting Fat Dipole Model 18 17 6 2 Lossy Fat Dipole Model 19 o o o oo o Mae Eins Wipolese soa t i See a oy ee a Pe HE Ee Bohne 17 7 1 A Simple Thin Wire Model 20 2 0 0 0 0 0000 17 7 2 A Closer Look at the Errors Model 21 17 7 3 A Refined Model Model 22 o o o o 17 7 4 Becoming Active Model 23 o o oo o 17 8 Using Connections Model 24 o o oo o 17 9 Apertur
370. odel 3 around the Z axis with an angle of 90 degrees Instead you can load and directly modify model 7 If you prefer this keep in mind that object 1 now consists of both the conducting sphere with its multipoles and the dummy sphere with the dipole What you want to rotate are the matching points of the conducting sphere only To do this you can 1 Activate the matching points of the conducting sphere with the command 3D show points after selecting the lowest identification number of the matching points on this sphere i e 1 in the item box and the highest number 64 in the box M In case you do not remember these numbers try to find them out playing with the editor 2 Adjust the angle and the axis for the rotation Since there are several possibilities for doing that with the 3D adjust vect axis command you should try them now 3 Rotate the matching points with the command 3D rotate points In case you make a mistake you can undo the rotation by inverting the angle and running 3D rotate points again 4 Save the result on a file MMP_3DI 008 if everything is correct 227 17 3 5 A Non Uniform Model Model 9 If you have analyzed the results of the previous models carefully you have noticed that it is advantageous to rotate the conducting sphere around the Z axis with an angle of 90 degrees to introduce an additional multipole near the mirror point of t
371. of integral points in the constraints to nnbptm see sections 20 3 2 and E 2 The other integrals are limited neither in number nor in number of integral points they contain 10 8 Plots The field can be evaluated as a plot on a grid of points or as values in a set of arbitrarily oriented field points The field data for each plot window and each set of field points will be written on a file MMP_Pyy xxx with yy running from 00 to nwind 1 for the windows i e regular plot files and from 50 to 50 nwefp 1 for the field point sets i e general plot files In addition extended error files MMP_ERR xxx contain the field data on all matching points For the format of the output files see appendix D Note that all field values are given in the global Cartesian coordinate system 10 8 1 Plots on Grids Regular Plots The plot windows for regular plots on grids can be defined with the following data see also figure 14 2 nwind number of plot windows xplm yplm zplm location 7 of window center xplti yplti zplt1 horizontal tangent vector v xp1t2 yp1t2 zp1t2 vertical tangent vector Uz nhor nver nlev idom sdp1t number of points horizontally and vertically number of levels domain number level distance For each plot window the field will be plotted on a grid of nhor by nver points in nlevel planes with a distance of sdp1t in the direction of 0 x U2 Depending on the parameter idom the domain of the field points is either determined auto
372. of pictures If this number is negative the number of sets is equal to its absolute value Negative numbers of sets have the effect that the corresponding sequence will run differently when the movie is shown Usually the sequence is repeated when its final picture has been shown i e you will see the pictures 1 2 12 n gt pote When the number of sets is negative the sequence runs back and forth i e you will see the pictures 1 2 n n 1 n 2 2 1 2 The information on the line behind the integer number i1 is ignored by the program On the following lines the information concerning the different sets of pictures is expected Each set consists of a first line containing the number of pictures i2 pictures to be generated and of a packet of directives that is terminated by enddir and has exactly the same form as the packet of initial directives These directives are performed within the loop in the set After performing the directives the contents pixel information of the actual window is saved To terminate the file MMP_DIR zzz the directive end must be given In addition to seq end and enddir the following directives have been implemented drwpic draw a picture in the current window If this directive is missing it is automatically inserted when enddir is read before the picture is saved setkWi set actual window number il window number settim set time number read corresponding MMP_T
373. of the symmetry plane It is not necessary to have matching points within the symmetry planes However in these cases the normal vector has to be within the symmetry plane It is then better to orient one of the tangential vectors e or eya perpendicular to the symmetry plane because then zero rows result These can be omitted a priori and do not enter the system of equations The boundary conditions which have to be satisfied are encoded in the 8 digit integer number ir Each digit represents a boundary condition for a field component The equations referenced can be found in section 4 5 Leading zeros may be omitted For the error calculation to work properly with surface impedance boundary conditions has to point out of imperfectly conducting domains As an extension to the theory in chapter 4 not only an additional weight w r may be specified for a matching points the parameter sgp but each of ordinary boundary conditions can be weighted separately with a additional factor 27 depending on the value of the digit i If i is zero the corresponding condition is omitted Figure Component Conditions 8 Ea Gn 41a 7 By Hn 4 11b 6 E 4 9a 5 Ea 4 9b or 4 10a 4 Ep 4 9c or 4 10b 3 4 9d or 4 10c 2 Ay 4 9e 1 Hy 4 9 Examples for ir 111111 between two general domains 61 11011 between general domains only tangential components 111444 between two general domains magne
374. of your computer are given in comment lines The following SRC files are concerned COMM SRC include file for the main program PAR SRC include file for the slaves on transputer pipelines MMPAR SRC include file for the parameter labeling program MMP_E3D SRC include file for the graphic editor MMP_P3D SRC include file for the graphic plot program MMP_F3D SRC the inverse Fourier transform program itself The SRC files can be converted into include files extension INC or FORTRAN source files extension F respectively either with a text editor or automatically with the auxiliary program CONVERT For example CONVERT COMM SRC COMM INC C_SIZE_20 erases the strings C SIZE_20 from COMM SRC and writes COMM INC Note that C_SIZE_20 is appropriate for 4Mbytes memory When you are working on a PC 386 or 486 with 4Mbytes or more memory you probably will not have to adjust the parameters for the graphic programs because the default 4Mbytes C_SIZE_20 is sufficient for large problems 20 3 5 Installation of the Parallel Code for Transputers For transputers a single processor version and a version for transputer networks can be made The installation of the single processor version is completely analogous to that in the previous sections and does not need any special features For the parallel version three separate programs have to be compiled MMP_M3D CH1 and CHL Each of those programs needs only memory for a part R of the entire matrix R
375. ogram cannot work properly if the desk file is damaged For example if the desk file is too short the program will miss data on the file Since it is already in the graphics mode when the desk file is read it will hang The contents of the boxes of the original desk file is the following Box 1 X coordinate Type input output x During 2D constructions this box displays the local window coordinate x as long as the first mouse button is pressed down During 3D constructions this box displays the global coordinate in X direction as long as the first mouse button is pressed down When a 3D element is in activated with the second mouse button this box displays the global X coordinate of the object 142 When you are asked to input coordinates of a point to be constructed you can either discretize the point in one of the windows or you can select its Cartesian coordinates in the first three boxes To enter the values click one of the windows Box 2 Y coordinate Type input output y Analogous to box 1 for coordinates y and Y respectively Box 3 Z coordinate Type input output ss text for display box Analogous to box 1 for coordinates Zw and Z respectively Box 4 Real Data of Screen Windows Type pull down input output Wx11 lower left corner x coordinate of the window plane Wy11 lower left corner Yw coordinate of the window plane Wxur upper right corner x coordinate of the window plane Wyur upper right corner Y
376. oles that are located near the axis are moved on the axis Since you might have forgotten to adjust the axis and because it is convenient to use the Y axis in most cases you are asked set_vector_ey_____ If you answer this question in the affirmative the message new_axis_is_ y_axis indicates that the axis of the torus is the Y axis Otherwise the actual axis is used Although any direction of the axis can be used it should be noted that it can be very difficult to imagine the shape of the object that is generated when the axis is not within the plane of the 2D construction i e the XY plane When no 3D object is present the torus will become the first 3D object Otherwise it becomes object number two If object 2 does already exist it is overwritten when you 134 answer the question overwrite_object_2_ in the affirmative Otherwise the process is aborted i e the torus is not generated and the message object_NOT_generated is displayed In this case you can either store object 2 in a file see 3D write or add object 2 to object 1 see 3D add before generating the torus Note that this procedure tries to generate appropriate expansions when appropri ate expansions are contained in the 2D construction But the procedure is not always successful A modification of the expansions therefore might be necessary 3D generate points___ Generate a set of matching points appropriate for
377. ollowing messages can be displayed pole_seems_to_be_OK No errors have been detected pole_not_tested___ The expansion has not been tested because it does not belong to the selected domain or because it is not a 3D pole that can be tested no_mat pts _found_ There are no matching points that would be required to define the boundary of the do main of this pole Check the domain numbers of the pole and of the matching points that should define the boundary pole_inside_dom_xx_ The pole is inside the domain This is only reasonable if this pole is used to simulate 128 a small antenna for example a dipole in the domain Otherwise you have to adjust the domain number of the pole or of the matching points defining the boundary of this domain It should be mentioned that the automatic detection of the domain number used here and in the main program for the computation of the plot files requires oriented boundaries The normal vector that is represented by a small line in each matching point is directed from the first domain into the second domain The numbers of the two do mains of a matching point are displayed in the boxes MPt dom1 and MPt dom2 when a matching point is in activated Moreover different fillings and colors are usually used to represent the front and the back side of a matching point In the standard desk file the fillings and colors are defined in such a way that the back side is dark Domain number one is on the b
378. olume ratio A technically very common example are thin wires section C 1 Also multipole functions of the previous section can be derived from a configuration of infinitesimally small electric or magnetic sources at their origins Each expansion function for a domain is by 2 9 equivalent to a distribution of electric and magnetic currents and charges on the entire boundary Because the singularities of the expansions are away from the boundary this distribution is very smooth as long as the boundary itself remains smooth The coefficients are chosen in such a way that the exact distribution is approximated as well as possible 3 4 Connections Another type of expansion function can be constructed by combining several expansions into a macro In the 3D MMP main program it is implemented as a connection which is the expansion function K f cl 3 4 k 1 The parameters cz are given mostly by a previous computation Connections may be nested i e be used again within another connection If the f in 3 4 are expansion functions for different domains the connection becomes a multi domain expansion There are several aspects under which connections can be useful e More Complex Excitation Functions More complex excitation functions can be defined as a superposition of simpler ones e Disturbed Problems An undisturbed problem often has higher symmetry than the disturbed one It is therefore easier to compute the undisturbed problem
379. om Newton s and Coulomb s 1 r laws For testing the effects of these laws you can modify the exponents 2 of Newton s and Coulomb s law in the boxes mex qex respectively When you have computed an electromagnetic field the electric and magnetic forces of this field acting on all electric particles are computed When you want to consider the interaction of particles without any external impressed field you should clear the field with clear pic f 0 after setting a low number of grid lines and levels two grid lines in each direction and one level is the minimum After having defined the particles with add part and cleared the field you should select an appropriate time interval dt and a reasonable number iter part like for pseudo particles Now you can play god and run move part for different initial values different sets of particles different laws You will recognize that this is a hard job even for only three particles Either you get almost no interaction or the interaction is much too strong and the particles move very rapidly You probably require several attempts until you get a relatively stable situation Moreover the very small mass of realistic particles like electrons can cause numeric problems because only single precision is used in the plot program For getting an idea of initial conditions you can read the
380. omain and delete domain Box 21 Real Data of Domains Type pull down input output Er real part of the relative permittivity r Ei imaginary part of the relative permittivity e Ur real part of the relative permeability ur Ui imaginary part of the relative permeability ur Sr real part of the conductivity Si imaginary part of the conductivity o To display the material properties of a domain in this box perform show domain Change the values with the first count up and second count down mouse button in the value area of this box and perform the command adjust domain Note All material properties are assumed to be complex in the 3D MMP code Although real values will be assumed in most cases there are special situations where complex values are helpful For example the hysteresis of lossy magnetic materials can be approximated by a complex permeability Box 22 Create Meta File Type special action input 150 meta meta file MMP_Exx aaa where xx is the meta file number and aaa is WMF when you work under Windows GEM when you work under DOS with the GEM interface Change the meta file number with the first count up and second count down mouse button in the value area of this box Meta file numbers should be within the range 0 99 Click the mouse button in the text area of this box for generating a meta file Box 23 Real Data of Constraints and Standard Plot Windows Type
381. omain 0 is used for ideal conductors this is appropriate for the conducting sphere whereas 1 is appropriate for the space outside To change the direction of the arc you can run 2D invert arc instead you might exchange the domain numbers and run 2D adjust arc which is more complicated You are asked invert_elements_OK_ in the information box on the top line Move the cursor in the information box and click any mouse button to answer this question in the affirmative The arc is inverted almost immediately see fig 15 3 218 10 To check your discretization run 2D show points now The representation of the arc is changed and you can see the matching points defined on the arc see fig 15 2 The little lines in the matching points point from dom1 into dom2 i e from the conductor into free space and allow a different check to decide whether the direction of the arc is correct or not Now it is reasonable to generate appropriate multipoles You could do this with the command 2D add pole after an appropriate setting of the integer and real expansion data in the boxes Exp and se1 But it is much simpler to use 2D generate pole instead As you can see in the guide there are different versions of the automatic pole generation selected with the number in the item box pole
382. omatically added by the editor For this plot window the data of the first screen window and the default data in the plot window data boxes are used You can adjust or delete the default plot window as indicated below 15 3 2 2D Construction and Elements 2D constructions allow to simplify 3D constructions very much because many 3D objects can be constructed easily from an appropriate 2D object For reasons of simplicity the 2D matching points are constructed as sets of matching points on 1D objects lines and arcs rather than separately I e one has the 2D graphic elements e 2D lines e 2D arcs e 2D multipoles and other 2D expansions Although 2D constructions are helpful they are not really necessary and the corre sponding 2D data files MMP_2DI xxx can be read only by the 3D MMP editor and by any text editor Note that the 2D data files MMP_2DI xxx only contain information on the 2D graphic elements and cannot be used as input files for the 2D MMP programs because some important information frequency symmetry numbers material properties etc is missing 15 3 3 Activating Inactivating Representations All graphic elements can either be active or inactive For reasons of safety and flexibility several regular actions affect active elements only There are several way to activate or inactivate elements Usually the second mouse button is used to activate a single inactive element or to inactivate a single active element To
383. ome very simple examples is demon strated First the procedure for using the most common 3D MMP features is discussed in detail Later on when you have some more experience only the most important steps are outlined and the advanced 3D MMP features are introduced Although the scientific value of simple examples is not very high it is strongly rec ommended to start with them for getting familiar with the code and for understanding the MMP technique Moreover the computation of small problems is not too time con suming and can be performed even on relatively small machines like XT compatibles For problems with more than 100 unknowns fast PCs and add on boards are strongly recommended but no such problems are considered in this tutorial All examples shown here can be computed on a PC 386 within a few minutes except the final one that requires a Fourier transform Users who can access supercomputers might prefer to run the 3D MMP codes on the supercomputer and to use the PC for the graphic input and output programs only The implementation of the 3D MMP main program on any machine with any FORTRAN 77 compiler is expected to be simple However in the following it is assumed that you work on a PC under Windows A sphere is the most simple body for 3D MMP The different orders and degrees of a multipole in the center of a sphere build a set of orthogonal functions on the surface of the sphere where the boundary conditions are matched Moreover th
384. omit boxes mouse stop during execution of a time consuming process the program inquires the mouse status and stops if a button is pressed The larger mStp the longer you have to wait until you can stop a process When you perform the command show window this box displays the integer data of the screen window selected in the item box To change the integer data of the screen window you can modify the values in this box with the first count up and second count down mouse button and perform the command adjust window afterwards Before you do this it is a good idea to perform show window This makes sure that you have all actual data of the window in the box Box 6 Clear Screen Type special action clear Clear screen and redraw all boxes Box 7 Integer Data of Constraints Integrals Field Points Gen eral Plots Plot Windows Standard Plots Type pull down input output Con pt Con pt M Con type Intg pt Intg ptM Intg typ F pt H_ F pt M F pt dom Win Win Win NWin Win Nhor Win Nver Win Nlev Win Ndom actual constraint point number number of points of a constraint type of the actual constraint actual integral point number number of points of an integral type of the actual integral actual field point number of a general plot number of field points of a general plot domain number of the actual general plot actual standard plot wi
385. once at the beginning of the MMP graphic programs The cursor is used for the screen only The shape of the cursor is a matter of taste But it should make the selection of any pixel on the screen easy idev device address screen only mgshoc idev Show cursor This function is used for the screen only Hiding and showing the cursor again is impor tant because the cursor might influence the drawing of lines and texts on the screen If this is not the case mgshoc and mghidc can be replaced by dummy routines idev device address screen only mghidc idev hide cursor This function is used for the screen only Hiding and showing the cursor again is impor tant because the cursor might influence the drawing of lines and texts on the screen If this is not the case mgshoc and mghidc can be replaced by dummy routines used for screen only 318 idev device address screen only mgmous idev 1but lxcr lycr Get status and position of mouse cursor This function is used for the screen only Three buttons are assumed and used in the graphic MMP codes Since the third button is only used to display hint boxes and to stop a movie two buttons are sufficient for most features Of course mouse buttons can be replaced by keys of the keyboard idev device address screen only lbut returns mouse status 1st bit 1 first button pressed 2nd bit 1 second button pressed 3rd bit 1 third button pressed lxcr returns horizontal pix
386. onding to the wire are generated automatically and generating mat pts_ is displayed Note that no matching points are generated when the maximum number of matching points would be exceeded or when the radius of the wire defined in the box Exp se1 is less than 1 0E 32 It is recommended to set ie5 2 3D add_____ points ___ Add a matching point Before this command is executed the additional integer and real data of the matching point to be constructed have to be selected in the corresponding boxes MPt and wgt If the maximum number of expansions defined in the include file MMP_E3D INC is exceeded too_many_mat points is displayed and the process aborted Otherwise you have to discretize the geometric data origin and two tangent vectors This requires three points in 3D space The first point is the origin or the location of the matching point The line from the first point to the second point defines the first tangent vector and the line from the first point to the third point defines the second tangent vector The construction starts with set_start_point____ Le you have to define the location of the matching point There are two ways of doing that 1 select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data 2 press the first mouse button within a window and release it as soon as the cursor is at the position w
387. onditions are matched on an ideal conductor even though two of them would be sufficient When surface impedance conditions are used instead you have only two conditions in each matching point Nonetheless the resulting system of equations is still overdetermined even for over equal to 1 If you like you can reduce the overdetermination by manually increasing the orders of the multipole and look what happens especially as soon as you have too many unknowns It has to be pointed out that the errors in the matching points are a far less reliable measure of the accuracy for a weak overdetermination Thus you have to be careful when reducing the overdetermination To look what happens you can use two models with a different number of matching points but with identical expansions You can compute the parameters with both models and compare them Moreover you can 231 1 Compute the parameters with the first model 2 Copy the parameters of this model on the parameter file of the second model 3 Compute the errors in the matching points of the second model with the parameters of the first one The errors computed between the matching points used for determining the parameters are similar to the errors in the matching points now used provided that the system of equations is sufficiently overdetermined For weakly overdetermined systems the errors between the matching points can be much larger and the errors computed in t
388. oordinates clear field variable cf add field components compute field components by multiplying rows with parameter vector produce rows integer function determine length of a row produce rows for matching points produce rows for field points change sign of an expansion in cup2 formulate boundary conditions for the field components in cup2 integer function isolate a figure from an integer number insert coefficients from cup2 into cup and clear cup determine weight for rows symmetrize expansion 306 conn inisym nexsym setise setisp inisz nexsz addsz File ANS F entnr adraht hadr a2d ha2d0 ha2dm a2dtem a3d ha3d0 ha3dm aquad arund aplwv aevan nullen ncon ndraht n2d hn2d0 hn2dm n2dtem n3d hn3d0 hn3dm nplwv nevan isyg isyu File ETC F messag dispz dispm zeich evaluate connection initialize loop over symmetry components logical determine next symmetry component true if there is one symmetry considerations for expansions symmetry considerations for matching points and field points initialize symmetrization of arbitrary expansion logical determine next component for symmetrizations true if there is one add expansions from cup3 to cup2 for symmetrizations prepare call of one of the expansion functions thin wire expansion C 4 field components for single thin wire segments auxiliary to adraht 2D expansion C 8 2D expansion of degree m 0 auxiliary to a2d 2D expans
389. or be tween matching points does not differ much from that in the matching points themselves provided that the system is sufficiently overdetermined 6 2 Field The total field in a field point r is N 1 fw 5 ci fir 6 4 i 1 34 For evaluation of only the scattered field f the incident field f fy 1 can be omitted A very useful feature for the production of plots within regions with several domains is the automatic detection of the domains In order to determine the domain of a field point specified by the coordinates x y z the next matching point is determined With the convention that the surface normal for a matching point on D is always pointing from D into D the domain can be determined in practically all cases For the rare circumstances where this does not work additional dummy matching points can be added in which no boundary conditions are enforced 6 3 Integrals In addition to the fields integral quantities like voltage flux power flux etc are of interest The integrals usually have to be evaluated numerically and are implemented as Riemann sums section 10 7 35 7 Symmetries 7 1 Boundary Value Problems and Symmetry The geometry of boundary value problems is often symmetric i e invariant to certain symmetry transformations in space Exploiting these symmetries pays off in a con siderable reduction of computational time and memory requirements and furthermore brings numerical
390. or drawing the shades of vectors The question invert_light_vector allows you to invert the axis and leaving the light vector unchanged invert__ wind This command inverts the direction of the second tangent vector of the window plane with the number selected in the item box If no such window is present window NOT_defined _ is displayed invert_ part Invert the velocity vector of the particle selected in the item box If the number in the item box is out of range for example equal to zero the velocities of all particles are inverted The error message NO_particles_______ indicates that no particles have yet been defined 16 5 11 adjust__ adjust__ pic f Adjust the field values in all points or in all points with the domain number selected in the item box You are first asked adjust_ALL_points_ If you answer in the negative you are asked adjust_domain_xxxx_ where xxxx indicates the domain number When you answer this question in the negative 176 as well the process is aborted with the message field _not adjusted Otherwise the field is adjusted i e the field data field vectors and domain number are replaced by the values defined in the corresponding boxes adjust_ axis_ Adjust the vector respectively axis and the light vector For graphical constructions it is helpful to use always the same plane in the first windows and to perform the constructions
391. or getting better results This technique is not considered here 17 10 Lossy Sphere in Rectangular Waveguide Model For the computation of waveguide discontinuities similar techniques as in the models 25 27 are used see 13 and 44 for more details Let us consider a rectangular waveguide with a lossy sphere in the center see fig 17 10 For reasons of simplicity we assume 249 28 that only one guided mode i e the H01 mode can propagate In a sufficient distance of the sphere the field can be approximated by H01 modes only Thus it is reasonable to subdivide the waveguide into three parts e an undisturbed rectangular waveguide with incident and reflected H01 modes e a disturbed rectangular waveguide with sphere e an undisturbed rectangular waveguide with transmitted H01 mode only The field of all modes of rectangular and circular waveguides is known analytically and is available in the 3D MMP code as special expansion Thus you can easily introduce the modes in parts 1 and 3 whereas the field in part 2 can be approximated by ordinary MMP expansions Since you get a somehow disturbed H01 mode in part 2 you can add such a mode to the MMP expansions in part 2 Moreover only the boundaries of part 2 have to be modeled because the boundary conditions on the walls of the waveguide in part 1 and 3 are fulfilled exactly by the special expansions The expansions in part 2 are matched with the special expansions in part 1 and 3 o
392. orce proportional to the velocity of the particle but in opposite direction This force does not depend on the other particles The plot program computes the gravitation as well as the electromagnetic interaction between the particles Coulomb and Lorentz forces Finally the plot program takes the electromagnetic field into account that is defined in the field points This field is considered to be generated by unknown charges that are impressed i e it is assumed that the particles have no influence on the impressed charges The field is interpolated between the field points provided that the field points are on a regular grid Nonetheless problems can occur if the grid is too rough and near boundaries between different domains and near the boundaries of the plot window When you want to study the interaction of particles without an impressed field you have to set a zero field In this case the following is very important 1 The force due to the impressed field is nonetheless computed I e for avoiding unnecessary computations you should use a very coarse grid 2 When a particle moves outside the regular grid where the field is defined it is stopped since the interpolation routine does not work anymore Thus you should define a sufficiently large grid for the field From the force acting on a particle the acceleration the new velocity and the new location after a time step dt are computed and the actual time tim is
393. order to decide whether the matching points of the first the second or 137 both objects shall be used to generate the field points of a constraint the questions use_objects_1 2___ use_object_1_only__ use_object_2_only__ are asked If all three questions are answered in the negative nothing is done and process_aborted___ is displayed Both the maximum number of constraints and the maximum number of field points per constraint are defined in the include file MMP_E3D INC Since constraints are a quite exotic time and memory consuming feature of the MMP code both numbers usually are quite small If they are exceeded one of the messages too_many_constraints too_many_points___ is displayed and the process is aborted Note that the matching points required to generate a set of field points are not deleted automatically when this command is executed If they have solely been created for generating a constraint you have to delete them 3D generate field pts Generate field points for general plots from a set of matching points Field values can also be computed on an arbitrary set of field points in 3D space instead of the usual rectangular grid The geometric data defining a field point is exactly the same as the one defining a matching point In order to simplify the code field points cannot be manipulated like matching points Instead the matching points of one or both objects can be used to generate a set of fiel
394. ot exactly intend For this reason an invisible rectangular grid with invisible horizontal and vertical grid lines i e an additional integer coordinate system is used During discretization the closest grid point is used instead of the pixel coordinates of the cursor and the corresponding coordinates are displayed Selecting an appropriate number of grid lines in horizontal and vertical direction allows to get accurately the intended coordinate values Note that the number of invisible grid lines should be smaller than the number of pixels of a window 30 up to 100 invisible grid lines are convenient in most cases 87 Projection and Hiding In the MMP graphic programs parallel projection and a simplified hiding procedure is applied The plot program can represent objects using perspective projection as well Since perspective projection is not useful during construction of objects it has not been implemented in the editor For perspective projection the point of the eye is defined simply by its height above the screen window plane If the height is zero or negative parallel projection is used Parts of an object are usually hidden behind other parts of the object or behind other objects In the graphic 3D MMP codes only those graphic elements that are not too far away from the window plane are shown Points with a distance from the screen window plane that exceeds the drawing depth are not shown This allows to make invisible parts of an o
395. otal power loss select power and activate Pe Pm and pj i e boxes 17 18 and 19 The vector potential A and the scalar potential V are not defined when you have read the field from a plot file generated with the MMP main program 185 Box 15 Question Information YES Start Box Type text output response start regular action The content of this box is overwritten during program execution It is used to display messages give instructions ask questions and to input answers in the affirmative When a question is asked in this box the program execution is paused until the question is answered either in the affirmative click this box with the first button or in the negative click this box with the second button Instead of answering you can abort the actual process by clicking the escape box on the right hand side of this box Clicking any other box or a window will have no effect When an instruction is given in this box the program execution is paused until you have performed the required action mostly the discretization of a point either in one of the windows or by defining the coordinates in the first three boxes When a message is displayed in this box and the box is activated the program execution is paused until you click a mouse button for removing the message When the message ready_for_action__ is displayed in this box the previous action is terminated and the program is ready for a new action Select the action to
396. ould be selected afterwards because the items that can be selected depend on the action The corresponding information is contained in the file MMP_P3D ACT The program tries to read this file when the item box is clicked the first time If this file is missing you get the message error_reading ACT As a consequence all items are displayed when the item box is clicked with the first or second mouse button This and the selection of the action after the selection of the item allow to select a regular action that has not been implemented If you try to start an 153 undefined regular action the message action_not_implem _ is displayed Some of the regular actions require you to perform some work e g define a point within one of the windows In such cases a command is displayed in the ques tion information box The regular action is continued when a mouse button has been pressed and released 16 3 2 Window Actions There are two types of window actions 1 actions for manipulating the size and location of screen windows and 2 actions for manipulating the graphic elements displayed in a window The former are identical with those in the editor The latter are used for in activating field points displaying the field values in a field points and for adjusting the field values in a set of field points within a rectangular area Moving a Screen Window When you want to move a screen window to another location on the screen select the
397. outines those routines in file ANS F starting with the letter a All of the expansion routines have the same call structure Parameters are the co ordinates x y z of the points in which the field components shall be computed the number of the expansion and a parameter last which returns the length of the expan sion The field components of the expansions are directly written into an array cup3 see below Both the coordinates x y z and the field components are in the system of the expansion z Ey z It is therefore quite easy to add expansions to the existing code Subroutine nullen determines the length of the expansions in order to insert zero blocks into the matrix rows In view of the many symmetries which can be considered closed form expressions for this length are tedious to obtain Instead dummy routines are called which have exactly the same structure as the expansion routines but are stripped of unnecessary computations They have the same names as the expansion routines except that they start with the letter n instead of a From the variables point of view there are three separate sets of rows cup3 cup2 and cup The expansion routines a write the coefficients into cup3 From there entsym makes the symmetry decomposition 7 3 by adding the components into cup2 After completion of an expansion the boundary conditions are applied to cup2 if necessary and the coefficients are inserted into cup with routine einscl
398. oxes of the MMP desk are required These data are contained in the desk files MMP_E3D DSK for the editor MMP_E3D and MMP_P3D DSK for the 3D plot program MMP_P3D Beside this the files containing information on the implemented actions MMP_E3D ACT and MMP_P3D ACT and hints for all boxes of the desk MMP_E3D xxx and MMP_P3D xxx where xxx is the box number should be installed All these files are searched 1 on the actual directory 2 on directory MMP of the actual drive 3 on directory C MMP Therefore it is most convenient to copy all files from the directory GRFIL of the 3D MMP distribution diskette on C MMP This is done automatically when you use INSTALL BAT for installing 3D MMP on drive C If you should have not enough space left on drive C for storing all these files you should store them on X MMP where X is a disk drive with a sufficient amount of free memory In this case you should either run all your 3D MMP jobs on the drive X or you should create the directory MMP on drive C as well and copy at least the desk files on this directory for example with the DOS command COPY 21 2 Running 3D MMP You can run the 3D MMP codes with several Windows features The most simple one is clicking the corresponding icon when the 3D MMP package has been installed properly It is important to note that Windows should run in enhanced mode Although the outfit of 3D MMP graphics is different from typical Windows applications you can st
399. p_m3d MMP_Cyy xxx connection file read only MMP_PAR xxx parameter file read write MMP_ERR xxx error file write only MMP_INT xxx integral file s write only MMP_Pyy xxx plot file s write only MMP_M3D LOG log file write only MMP_FOU FRQ frequency file read only Files for the Editor MMP_E3D The 3D MMP editor MMP_E3D uses the following data files MMP_E3D DSK desk file read only necessary to run MMP_E3D MMP_E3D ACT action file read only can be missing MMP_E3D xxx hint files read only can be missing MMP_E3D LOG log file write only currently unused MMP_Eyy WMF Windows meta file write only MMP_WIN xxx window file read write used by MMP_P3D as well MMP_3DI xxx input file read write used by MMP_M3D and MMP_P3D as well MMP_ERR xxx error file read only generated by MMP_M3D used by MMP_P3D as well MMP_2DI xxx 2D input file read write 295 Files for the Plot Program MMP_P3D The 3D MMP plot program MMP_P3D uses the following data files MMP_P3D DSK desk file read only necessary to run MMP_P3D MMP_P3D ACT action file read only can be missing MMP_P3D xxx hint files read only can be missing MMP_P3D LOG log file write only information on performed actions MMP_Pyy WMF Windows meta file write only MMP_WIN xxx window file read write used by MMP_P3D as well MMP_3DI xxx input file read only generated by MMP_E3D used by MMP_M3D as well MMP_ERR xxx error file read only generated by MMP_M3D u
400. phic workstation has been opened the desk is displayed and some default values are set If this has been done the program tries to read the hint file MMP_P3D 000 If this file can be read its contents are displayed in the center of the screen otherwise no hint box is displayed To remove the hint box you have to click one of the mouse buttons After this the hint box will disappear and the program expects that one of the mouse buttons is pressed The standard plot desk consists of one window and of 35 boxes see fig 16 1 The number of boxes is fixed defined in the file MMP_P3D DSK but you can increase the number of windows 16 2 Program Exit Most of the boxes are used to read and display data or to define actions to be performed and representations of the field The most important exception is the last box in the top line that is used to leave the program There are two alternatives that can be selected with the second mouse button in this box If the content of this box is QUIT the program is terminated without saving any data when the box is clicked with the first mouse button If the content of this box is EXIT the program saves the data of the current windows on the file MMP_WIN 000 If this file does already exist you are asked overwrite wind file Answering in the negative has the same effect as the command quit i e the program will stop without saving the window data Otherwise th
401. points are moved by 10 towards the center end of the segment if it is 2 by 20 and so on If it is 9 no matching points are generated for the corresponding segment The matching points of the thin wire expansion do not appear in the input file but are generated within the program and appended to the ordinary matching points Therefore make sure that the maximum number of matching points is not exceeded 56 For the modeling of matching points with thin wire expansions see sections 8 5 and 17 7 e Line multipole or wire multipole have been implemented by Pascal Leucht mann 42 They can be cosidered to be a generalization of the thin wires The field of thin wires is rotationally symmetric whereas the field of wire multipoles has a harmonic angular dependence Unlike thin wires wire multipoles are not seg mented in the actual implementation i e they consist of one segment only Thus the length of a wire multipole should be about a tenth of the wavelength The direction of the wire is in the direction it starts at the origin iel 111 expansion corresponding to a 3D multipole with IE1 301 ie2 not used in the actual implementation ie3 maximum order ie4 not used in the actual implementation ied 0 both currents 1 cos current only 2 sin current only ie6 0 without magnetic current 1 with magnetic current sel not used in the actual implementation se2 length of wire multipole iel 112 expansion corresponding to a 3D multipole wi
402. ponding boxes when either the element is in activated or if the corresponding 3D show action has been performed When this data is incorrect the values in the boxes have to be adjusted first For safety reasons this does not change the corresponding values of the element before the 3D adjust command has been performed I e this command essentially plays the role of the enter key Unlike the usual enter key the 3D adjust command allows to adjust the data of several elements at a time 129 3D adjust__ wire_____ Adjust the additional data of a wire expansion and of the corresponding matching points boxes MPt and wgt The value in the box se2 i e the length of the wire is not adjusted But the location of the matching points at the ends of the wires is adjusted if necessary Note that the length can be adjusted with the command 3D blow wire Either all or only the active wires can be adjusted If only a single wire has do be adjusted the 3D show command can be used first to activate the desired wire Thus if the question adjust_ALL_wires__ is answered in the negative only the active wires are adjusted 3D adjust__ points___ Adjust either the additional data boxes MPt and wgt of either all or only the active matching points If only
403. probably won der what is being displayed You can see this in the top line of the screen in the boxes between the Esc box and the EXIT box When you did not modify the contents of these boxes the boxes E x yl z are active indicating that all components of the electric field are shown When you want to see the Poynting vector field instead simply click E to inactivate it and click S to activate it Similarly you can inactivate for example the x and y boxes when you are interested in the normal component of the field only Also the three vector fields visible in the boxes E H S are most in teresting there are many other interesting fields in electromagnetics as well To obtain them click the box field1 When you do that you will see that not only the content of this box is changed but also the content of the boxes E H S This allows to select a total number of 15 different vector and scalar fields Note that when you activate more than one of the three boxes of a field set only the leftmost field is shown when it is a vector field whereas the three scalar fields are associated with the three components of a vector that can be represented For example you can activate the electric and magnetic energy density at the same time and you will get a vector
404. proportional to the error in the corresponding point An automatic scaling is used that guarantees a reasonable representation in most cases Nonetheless the scaling can be adjusted with two factors selected in the err and in the nrm box The first factor affects the filling and color of the points as well as the length of the line whereas the second factor affects the lines only If nrm is zero no lines are shown Note Since the number of reasonable fillings is relatively small the same fillings and colors are used in this representation for both the front and the back side of the matching points This is the one and only exception 3D add_____ wire Add wire expansion Select the additional integer and real data of the wire to be con structed in the corresponding boxes Exp and se1 se2 will be defined by the construction If the number of expansions a wire is a special type of an expansion exceeds the maximum number defined in the include file MMP_3DI INC too many_expansions is displayed and the process aborted If the type of the expansion selected in the box Exp IE1 is not equal to 101 it will be set to this value Unlike in the construction of other expansions only two points start and end point of the wire in 3D space are required here Thus you are asked set_start_point____ first There are two ways
405. pute the parameters with model 21 i e using all bound ary conditions in the matching points rather than the longitudinal component of the electric field only as in model 20 The computation time is much longer but the same accuracy of the results is about the same Compare the parameters of both models and you get some more information on the accuracy 17 7 3 A Refined Model Model 22 From the analysis of the errors in the previous models you see that the largest errors are always found near the end of the wire In fact the shape of the ending of the wire is not well defined To improve the model you can add some appropriate multipoles and matching points at the end of the wire Since multipole expansions work best near spherical boundaries we choose a spherical shape of the ending see fig 17 4 In order to keep the model simple we introduce only a single multipole in the center of this sphere This obviously leads to much better results When proceeding as indicated in the description of model 21 you find that the errors near the ending of the wire are considerably reduced The relative errors are still large near the XZ plane but this is not bad because the field is relatively small in this area and the absolute errors are well balanced along the wire Thus there is no need for additional multipoles near the XZ plane 17 7 4 Becoming Active Model 23 The wires in the previous models can be considered as passive antennas illuminated
406. r reading any of the previous models for example the simple model 1 with the plane wave excitation Above all a second domain inside the sphere has to be introduced After selecting the material properties in the boxes Er Ur etc perform the command 2D add domain This was not necessary in the previous models because the material 229 properties of free space are predefined as domain 1 in the editor However let us begin with a simple dielectric with relative permittivity of 4 Since domain O has been replaced by domain 2 the corresponding number has to be replaced in all matching points on the sphere 1 Activate all matching points on the sphere 2 Replace 0 by 2 in the box MPt domi 3 Run 3D adjust points What is missing is an appropriate expansion for the domain 2 Of course you can try to generate appropriate multipoles with the command 3D generate pole This is not very easy Therefore you might prefer to start with the 2D construction and generate 2D multipoles first This is considered to be reasonable in most cases but when the dielectric is a sphere or a similar body it is much easier to use a normal expansion instead Usually this even leads to better results Unlike multipoles you should use only one normal expansion and its origin should be on the symmetry planes i e in the center of the sphere in our example It is certain
407. r condition number and are at any rate numerically better due to their lower dimension An additional reduction of problem size takes place if some symmetry components bz of b are equal to zero because of a symmetry of the excitation Therefore the corresponding part of the problem has only the trivial solution cz 0 In homogeneous boundary value problems eigenvalue problems splitting the problem into symmetry adapted ones helps to separate modes and especially degenerate solutions Instead of explicitly performing the transformation T on A it is also possible to directly set up the matrices A using symmetry adapted expansion functions 7 2 Reflective Symmetries in the 3D MMP Code In the 3D MMP code one or more reflective symmetries about the coordinate planes X 0 Y 0 and Z 0 of the global coordinate system are implemented Due to 36 Ay Ax Figure 7 1 If A has the symmetry of a group G a transformation T can be found which transforms A into a block diagonal matrix A The number and the size of the blocks Ay is determined by G the orthogonality of these planes the consideration of symmetries can be made quite intuitively for one plane of symmetry at a time With respect to one symmetry plane a scalar field f can be split up into an even and an odd component f and f f ft f 7 3a ft Z IFP f O P 7 3b f 5 P IP 7 50 and denote the even and odd components P and P stand for a
408. r increasing its efficiency and accuracy For example in addition to the multipole basis functions one has thin wire expansions known from MoM codes wire and ring multipoles waveg uide modes connections etc Moreover the generalized point matching procedure the special matrix solvers the excellent graphic interfaces etc are not only interesting for GMT experts but also for designers of MoM and other codes as well as for FORTRAN programmers It is hoped that this package contains useful tools and many fruitful ideas for students teachers engineers scientists and those who develop new codes This documentation contains six parts First the theory is outlined Readers who are already familiar with the generalized multipole technique and hackers might prefer to skip this part Since the main program runs on very different machined whereas the graphic programs are designed especially for personal computers the corresponding user s guides are contained in separate parts If you intend to work with the 3D MMP graphic editor you can ignore many hints given in the user s guide of the main program because the graphic editor takes care of several difficulties and simplifies modelling considerably Otherwise you should carefully read the second part 3D electromagnetics is a demanding task Thus it is certainly useful to first exercise with 2D electromagnetics If you are already familiar with the 2D MMP package 4 you might prefer to start directl
409. r of expansions that have been defined all expansions are inactivated Otherwise activate_all_poles_ is asked 114 3D show____ domain___ Show matching points bordering a domain All matching points belong to two different domains For this reason two different domain numbers n1 and n2 have to be selected in the item box and in the additional integer data box M respectively The colors and fillings of the matching points used when this action is performed depends on the agreement of the domain numbers m1 and m2 of the matching point with the numbers n1 and n2 If neither n1 nor n2 is equal to m1 or m2 transparent mode is used filling and color number one defined in the desk file are used if either n1 or n2 is equal to m1 or m2 and filling and color number two are used if both n1 and n2 are equal to m1 or m2 Note a matching point has a front and a back side the fillings and colors of both sides can be different Precisely speaking filling and color number x is used for the front side and number x is used for the back side This distinction has not been made in the statements above for reasons of simplicity 3D show____ constrain Show points of one constraint Select the corresponding number in the item box If this number is either less than 1 or larger than the number of constraints that have been defined no_such_constraint_ is displayed Otherwise the points are shown with t
410. r representations you probably would like to have a perspective projection instead of the parallel projection used so far All you have to is to define the distance of the eye above the window plane in the box d_eye When this value is positive perspective projection is used There is a third representation of the field indicated by When you select it you will get iso lines in addition to the grid representation Usually this representation looks much better than but it is more time consuming Unlike the simple grid representation iso lines are useful when the window plane is parallel to the plane of 195 the field points The number of iso lines is selected in the box itself Above all when large and small field values are present you will like to have logarithmic iso lines instead of linear iso lines The values of neighbor iso lines in the logarithmic case are multiplied by a factor This factor should be bigger than one and can be selected in the box f log If it is equal or less than one linear iso lines are shown If your field is defined on a regular grid on several levels you can show all levels at the same time selecting the value 0 in the box level __ Probably you will not manage to find a point of view from where you can see all field points at the same time Most of the points will be hidden behind other points You can
411. r slide shows and movies or when always a slide with the extension number zzz 000 is generated Since the generation of movies is time consuming the procedure first checks the directive file MMP_DIR xxx As soon as an error is detected errorttxxx_linetyyyyy is displayed where xxx is the error number and yyyyy the number of the line of the directive file where the error has been found In most cases errors in the directives are very simple to find and correct The error checking routine does not only detect syntax errors in the directive file it does also check whether the requested data files are available or not 170 generate meta_ Generate a meta file MMP_Pxx WMF Select the file number xx in the item box If a meta file with the number xx does already exist you are asked overwrite_0K_ _ _YES If this question is answered in the negative no meta file is generated and NO_meta_file_gener is displayed Otherwise the program starts generating a meta file with the message generating meta_file The information written on a meta file is essentially what would be displayed on the screen if the regular action show would be performed For generating meta files a new workstation is opened If this fails cannot_open_workst is displayed generate part Generate and move a random set of particles The number selected in the item box is the number of articles When it is less than one or bigger than
412. rdi nates EXR tl component of the real part of the electric field in the field point local coordinates EXI tl component of the imaginary part of the electric field in the field point local coordinates HXR tl component of the real part of the magnetic field in the field point local coordinates HXI tl component of the imaginary part of the magnetic field in the field point local coordinates AXR tl component of the real part of the vector potential in the field point local coordinates AXI tl component of the imaginary part of the vector potential in the field point local coordinates Click the second mouse button in the window near a field point for obtaining the components of the field vectors in this point The values in this box except the first line are copied on the corresponding values of a field point when the field is adjusted either with the corresponding regular action or with the corresponding window action The t component in local coordinates is the component in the direction of the first tangent vector defining the plane in the field point Box 28 t2 Component of Field in Field Point Type output 189 vy EYR EYI HYR HYI AYR AYI t2 i e Yy component of the field shown in the field point local coor dinates t2 component of the real part of the electric field in the field point local coordinates t2 component of the imaginary part of the electric field in the field point local
413. re functions P x or P x section B 3 The matrix routines are in package CHOL F Most of them are modifications of LIN PACK algorithms 31 13 8 Additional Programs for Transputer Pipelines The parallel version is intended to run on a pipeline of N transputers 1 to N Several programs are needed for the various processors e The 3D MMP main program for the root transputer processor 1 e The chi program for the transputer between the root and the last transputer in the pipeline processors 2 to N 1 e The chl program for the last transputer in the pipeline processor N Programs chi and ch1 just do the updating of the distributed matrix shares and the back substitution The main programs do the communication with the neighboring processors and therefore call a lot of low level subroutines provided with the 3L compiler or the Meiko compiler respectively For clearing updating and back substitution routines in file CHLC F which contains a selection of subroutines from COMPL F and CHOL F are called 13 9 Utilities 13 9 1 MMP_PAR Parameter Labeling Program The MMP_PAR program reads a parameter file from MMP_PAR xxx and copies it to MMP_PAL xxx with labels attached to each parameter The source is in the file MMP_PAR F and in the include file MMPAR SRC MMP_PAR performs a loop over the symmetries and an analogous inner loop as e g zeile or zfp and zmp respectively Subroutine ansatz calls dummy routines m similar
414. rea of the corresponding box and click the first or second mouse button Now you can pull down the box and read all values contained in it Above all you have to modify the value of Rfrq i e the real part of the frequency in the real data box Let us start with a value of 150 MHz i e 1 500E 08 For doing this keep the mouse button pressed when the cursor is in the text area of the box and move the cursor to the line to be modified As soon as the button is released the box disappears but the line selected is displayed Move the cursor on the digit to be changed and increase or decrease the corresponding value by clicking the first or second mouse button For the moment leave all other values unchanged 2 Move the cursor in the question information box and click the first mouse button NO_such_element____ will be displayed in the top line This indicates that no 2D element has been defined yet Actually you did run the command 2D show line as you can see in the first three boxes of the top line The most convenient 2D element for generating a sphere is certainly an arc so add a 2D arc by selecting 2D add arc in the first three boxes of the top line in a similar way as you did select Rfrq before Remember that an arc is used for defining a set of matching points Therefore check the integer and real data of matching points in the boxes MPt nMat and wgt The only
415. rectangular part of the screen in a file This function is only used for generating movies and does not affect any other MMP feature idev device address screen only 1xul horizontal pixel coordinate of upper left corner lyul vertical pixel coordinate of upper left corner 319 lwid pixel width of rectangle lhgt pixel length of rectangle fname file name mgrfil idev 1lxul lyul lwid lhgt fname Restore pixels of a rectangular part of the screen from a file This function is only used for showing movies and does not affect any other MMP fea ture idev device address screen only 1xul horizontal pixel coordinate of upper left corner lyul vertical pixel coordinate of upper left corner lwid pixel width of rectangle lhgt pixel length of rectangle fname file name mgwait lhsec Wait lhsec seconds This function is used in the MMP code in order to reduce the speed of the input boxes Thus the wait time needs not to be very accurate I e this function can be replaced by a dummy routine that takes about 0 1 seconds to be performed lhsec wait time in 1 100 seconds F 3 Important Parameters and Variables in the Graphic Progams File MMP_GRF INC Important Parameters MBox maximum number of boxes MBoxT maximum number of texts and variables in all boxes MWin maximum number of windows MPull maximum number of lines of the pull boxes MPoly maximum number of elements of the arrays used to draw poly lines Important Variables
416. rections are ky mr a and ky n7 b for both E and H modes The propagation constant is y k K2 42 It is imaginary for frequencies lower than the cutoff frequency The electric modes Emn for m gt land n gt 1 are ELEM ink COS KoT Sin kyy e Y C 17a ae iyky sin KT COS Kyy e C 17b Elem k sin keg sin kyy e C 17c HET _iwe ky sin Ket COS Kyy e Y C 17d HP WE Ky COS Ki T sin Kyy e C 17e 291 emm 9 C 17f and the magnetic modes Hmn for m gt 0andn gt 1orm gt landn gt 0 Emm iwpky COS Kga sin kyy e C 18a pm WHKg S N KT COS KyY e C 18b EE y C 18c Hmm Y ki sin kya COS kyy e C 18d HY i ky COS KT SiN kyy e7 C 18e Hm k cos kga cos Kyy C 18f Symmetries are not implemented for these expansions The magnetic modes are scaled with the inverse of the wave impedance C 5 Circular Waveguide Sl y ry Figure C 2 Circular Waveguide Circular waveguide modes are solutions in polar coordinates in lossless domains o 0 e with an ideally conducting boundary at p R and therefore 2D solutions with a special transverse wave number The propagation constant is y Vk It is imaginary for frequencies lower than the cutoff frequency For the electric transverse magnetic modes Emn m gt 0 and n gt 1 amp amn Po where amn is the n th zero of Jm Kp ae nm 159 kpJm 1 5p cos my e C 19a
417. rgest errors near the plane The optimal position for the multipole is near the position that is tolerated by the checking routine One can say that the checking routine is too cautious When you play not only with the position but also with other parameters like the maximum order and degree of the multipole you can see that the situation is not so simple the optimal position of the multipole depends on other parameters as well Being careful is certainly a reasonable strategy especially for solving more complicated 3D problems 3D show errors 17 generating meta file NO meta 4 clear EXIT fac 6 000E 01 M_ 2 Domain 1 MPt M el 10 Exp dom 1 Win Winf 2 x11 6 000E 01 ix11 323 Er 1 0000E 00 wgt 1 000E 00 jsel 0 000 00 Win h 1 0E 01 x 0 000E 00 y 5 500E 01 z 0 000 00 Figure 17 1 Error distribution of a deformed sphere with two multipoles on the horizontal axis 236 17 6 Fat Dipoles 17 6 1 Ideally Conducting Fat Dipole Model 18 In the previous models non spherical models have been generated by deformation of a sphere This procedure does not allow to easily generate bodies of a well defined shape For example a fat dipole consisting of a circular cylinder with spherical ends cannot be obtained this way Keeping the features used for generating the sphere in mind you can see that the generation of a fat dipole is not much different Since thi
418. rigin completely you are asked to set its height above the plane in the next step set_height_above_pln Only a vertical movement of the cursor will affect this value The actual height is displayed in the second box of the bottom line as long as the mouse button is pressed down If you did use method 1 to discretize the origin set_end_point_data_ indicates that you are expected to give the coordinates of the end point of the first tangent vector in the same way I e select the global 3D coordinates in the three boxes of the bottom line and click one of the windows when you want to enter these data If you did use method 2 to discretize the origin set_end_point______ indicates that you are expected to discretize the end point of the first tangent vector in the same way as the origin Of course you will be asked set_height_above_pln if you apply method 2 Needless to say that you are expected now to discretize the end point of the second tangent vector similarly set_2nd_end_point__ Of course you will have to set_height_above_pln once more if you are working with method 2 If the number of plot windows is less than the maximum number defined in the include file MMP_E3D INC you are asked add_plot_window____ If you answer this question in the affirmative the plane of the plot window has to be defined For reasons of simplicity the plane of the screen window with the same number is used when such a window has already been defin
419. rizontal and vertical directions of the screen I e they must be orthogonal to each other Since it is not simple to define orthogonal vectors in 3D space graphically the 3D MMP codes automatically orthogonalize va if necessary Since an infinite plane cannot be represented on a screen the limits of the represen tation have to be defined In the MMP graphic programs the limits are defined with the real valued local plane coordinates of the lower left and upper right corners of the window These data are referred to as limits In addition the physical size and location of a window on the screen has to be defined These data are referred to as corners in the MMP graphic programs and are defined in integer valued pixel coordinates with an origin in the upper left corner of the screen Note that these coordinates are device dependent In order to get rid of the device dependence of the pixel coordinates one more integer coordinate system is used in the desk files for storing the locations of the corners of a screen window Integer values are used as well but the lower left corner of the screen has the coordinates 0 0 and the upper right corner has the coordinates 1000 1000 This guarantees that the MMP desks look similar for different screens The same coordinate system is used for storing the corners of the boxes of the MMP desk The transformation of pixel coordinates into real valued plane coordinates usually leads to numbers that you do n
420. rnatively the exponential functions e and e The relations between the bases are cosmo e gime B 22 m NIe sin mp ae e ime B 23 The choice of cos my and sin my has advantages for reflective symmetries cos my is even and sin my is odd about y 0 for all m cos m is odd about y 7 for m odd and even for m even whereas sinmy is even for m odd and odd for m even This simplifies the construction of symmetry adapted expansions Furthermore sin and cos are real valued for real arguments When calculated from Cartesian coordinates x and y they can be more easily obtained by cosy and siny 4 B 24 p p where p yx y For a given argument the values for different m can be obtained by recurrence cos my cos cos m 1 y sin ysin m 1 p B 25a sin my sin y cos m 1 y cos psin m 1 B 25b with the starting values cos 0 1 sin0 0 cosy and sin y Analogous recurrence rela tions exist for the terms p cos m and p cos my which occur in the TEM expansions C 10 285 C Expansions C 1 Thin Wire Expansion Equation 3 2 can be solved in closed form for an infinitesimally thin straight current filament with a cos kz or sin kz current where k is the wave number of the medium For a current I z Io S kz the expressions for the field components in cylindrical coordinates are o b METRO e ia a RR osi Eo Amiwe
421. rogram execution is paused until the question is answered either in the affirmative click this box with the first button or in the negative click this box with the second button Instead of answering you can abort the actual process by clicking the escape box on the right hand side of this box Clicking any other box or a window will have no effect When a message is displayed in this box and the box is activated the program execution is paused until you click a mouse button for removing the message When the message ready_for_action__ is displayed in this box the previous action is terminated and the program is ready for a new action Select the action to be performed and start regular actions by clicking this box with the first or second mouse button Box 16 Escape Box Type fixed text response Esc This box is used to escape a process instead of answering a question asked in box 15 The content of this box is fixed 148 Box 17 Real Data of Expansions Type pull down input output sel expansion parameter se2 expansion parameter ReG expansion parameter real part of propagation constant ImG expansion parameter imaginary part of propagation constant For the meaning of the expansion data see section 10 5 When an expansion is in activated with the second mouse button in a window or with the show pole command the corresponding values are displayed in this box Change the values with the first count up and se
422. ropriate file numbers In this case no file is read and file_not_read_____ is displayed Otherwise the program attempts to read the data or asks additional ques tions if necessary read pic f Read the pixel information of a picture that has previously been generated and stored with the command write pic f Since a picture file MMP_Fyy xxx is characterized with two numbers both numbers have to be selected in the item and file extension boxes If no file with the numbers selected is found on the actual directory picture_not_found__ is displayed Useful results are only obtained if the actual screen driver is identical with the screen driver used during generation of the picture It should be mentioned that the size and location of the picture that is shown is identical with the size and location of the window used when the picture was generated This can differ from the actual window position read____ wind Read the window information form the window file with the number selected in the item box If no such file exists error_reading window is displayed Otherwise reading window file indicates that everything is correct Note that the actual windows are replaced by the 164 windows defined in the window file For this reason it might be a good idea to save the actual windows first on a special window file with the command write wind Note that the window files used in the 3D MMP e
423. rtant when you want to compare different pictures with each other During computation of a picture the following information is displayed in order to indicate what is being done initializing field_ computing_aaaaaaa__ where the string aaaaaaa indicates the field that is being computed Sometimes the message constant_field_____ is displayed and no picture is drawn In most cases this indicates that the field is zero The most important reason for this message is that the scaling factor is zero which would lead to overflows Thus this can happen when you have answered the question mentioned above in the negative although the program would be able to show a picture after computing a new scaling factor The remaining error messages wrong level_number_ not_enough grd lin s can occur in grid representations only The first one indicates that the selected level number is out of range and the second one indicates that either in horizontal or in vertical direction less than two grid lines are present For more information see section 16 7 show____ movie Show a previously generated movie If no movie with the number selected in the item box is available error_opening file_ is displayed Otherwise the first sequence of the movie is displayed starting with the first picture Useful results are only obtained if the actual screen driver is identical with the screen driver used during generation of the movie The firs
424. s 159 that are defined in the 3D MMP editor and stored in the input files MMP_3DI xxx The plot program can read this information as well and show the matching points in addition to the field points if requested see fig 16 4 Moreover the error files can be read and the corresponding errors can be shown in the matching points see fig 16 5 Since the 3D MMP main program can produce general error files that contain not only the errors but also the field values in the matching points the plot program can read these data and convert the matching points into general field points This allows to show interesting fields like the current and charge densities on ideal conductors generate meta_ 9 12 computing S field No E H s field1 lx y zme wei 0 EXIT 53 sequ M 49 sc 4 000E 00 311 plane 11 color 3Darr 1 rx 11 1 0008 00 ER 1 00000E 90 vx 0 00000E 00 vz_ 0 00000E 00 an total FPt 225 27 2 85000E 00 y 1 20000E 00 z 0 00000E 00 iter part i gt p mt gt gt gt gt gt gt gt _ gt teu edu td S S E S E YA AAA 144948444 SeX lt dsbdbsese ed ve vse gs byYubsirrv seg tim 0 00000E 00 part type 1 mO 1 00000E 00 Figure 16 4 Desk of the 3D MMP plot program showing the time average of the Poynting vector for a plane wave incident on a lossy sphere In addition to
425. s you are asked the following ques tions set_vector_ex____ set_vector_ey_____ set_vector_ez_____ If you answer any of these questions in the affirmative the corresponding message 135 new_axis_is_ x_axis new_axis_is_ty_axis new_axis_is_ z_axis indicates that the axis has been set and the remaining questions are suppressed If all questions are answered in the negative the actual axis is used Although any direction of the axis can be used it should be noted that it can be very difficult to imagine the shape of the object that is generated when the axis is not within or perpendicular to the plane of the 2D construction i e the XY plane When no 3D object is present the object will become the first 3D object Otherwise it becomes object number two If object 2 does already exist it is overwritten when you answer the question overwrite_object_2_ in the affirmative Otherwise the process is aborted i e the object is not generated and the message object_NOT_generated is displayed In this case you can either store object 2 in a file see 3D write or add object 2 to object 1 see 3D add before generating the new object Note that this procedure tries to generate appropriate expansions when appropri ate expansions are contained in the 2D construction But the procedure is not always successful A modification of the expansions therefore might be necessary 3D generate pole_
426. s a b d to h and o to z complex variables start with the letter c logicals are explicitly defined Many of the variables below are arrays Parameters for Maximal Size of the Problem These parameters determine the maximum size of the problems which can be computed with the 3D MMP main program For installation see also section 20 3 2 ngebm maximum number of domains nmatm maximum number of matching points nentm maximum number of expansions nordm maximum order of an expansion nkolm maximum number of columns of A or c respectively nkolcm maximum total number of parameters of the connections nloesm maximum number of symmetry components nrekm maximum recursion depth for connections nnbedm maximum number of constraints nnbptm maximum total number of integral points for constraints nfreqm maximum number of frequencies ncam maximum number elements of R or X R in the parallel version nwindm maximum number of plot windows or field point sets nprocm maximum number of processors for parallel version Some Other Parameters iex ihz indices of the field components in various coordinates isi isy indices for surface impedance boundary conditions isk values for symmetries no symmetry isu odd symmetry isg even symmetry isb both odd and even symmetries 310 Unit Numbers for Files ifinp ifout ifpar ifscr ifplt iferr ifconn ifint iffou input file output file parameter file standard output plot file error f
427. s are not compatible with the 2D input files of the 2D MMP code 4 nEnt xexp yexp ient ig iel 6 sel se2 nEle iEle1 5 rEle1 5 number of 2D expansions poles coordinates of the origin in XY plane additional integer data additional real data number of 2D elements lines and arcs number of element number of matching points on the element domain numbers 1 and 2 identification number for boundary conditions additional real data 297 D 4 Parameter Files MMP_PAR xxx MMP_PAL xxx Unlabelled parameter files MMP_PAR xxx and labelled parameter files MMP_PAL xxx have essentially the same format nsym iprob is1 is2 is3 npar cpir cpii nent number of partial symmetries symmetries of problem number of parameters parameters c number of expansions ient ig iel 6 sel se2 cegam identification and parameters xe ye ze Xex yex zex xey yey zey origin Terp of the expansion vi V2 D 5 Connection Files MMP_Cyy xxx 3D MMP adds the expansions from the input file to the parameter fileMMP_PAR xxx This allows to use these files as connection files by simply copying them on a file MMP_Cyy xxx Consequently the format of connection files is identical with the format of parameter files see above D 6 Error File MMP_ERR xxx The standard error file created by task 2 of the main program contains the residual errors in the matchingpoints and the value of the constraints 2 nmat ip sperr fvali fval2 sperrp nnbe
428. s as desired The lens should be near the center of the window and a sufficiently large space should be around the lens because of the non absorbing boundary conditions In the next step you have to generate an appropriate grid for the FDTD algorithm When you select 100 horizontal and 100 vertical grid lines on one level you have a 2D grid with a distance of 10cm between the grid lines Run clear pic f 2 for generating a new grid and setting the domain numbers according to the matching points at the same time Before you start the FDTD algorithm with the type iter type you have to perform some simple computations for correctly setting the time step dt and the pulse duration Tmx It is reasonable to have pulse length of about ten grid lines i e 1m Since the 261 speed is c 3E8m s Tmx 3 333E 9 and dt 1 0E 10 is reasonable Note that the wavelength inside the lens is shorter than in free space Now you have to select the time dependence and polarization of the incident plane wave For having a sin wt pulse and the electric field in Y direction select iter info 20 To get the exact frequency w note that wI mx should be equal to m I e select Re_Om 9 425E8 Now you have to select the desired field representation and the number of iterations to be performed before a picture is drawn Note that about three iteratio
429. s containing the Cartesian coor dinates and click one of the windows when you want to enter these data 2 press the first mouse button within a window and release it as soon as the cursor is at the position where you want to have the projection of the point on the actual window plane In order to define the location of the point completely you are asked to set the height of the point above the plane in the next step If you did use method 1 to discretize the origin set_end_point_data_ indicates that you are expected to give the coordinates of the end point in the same way Le select the global 3D coordinates in the three boxes containing the Cartesian coordinates and click one of the windows when you want to enter these data 177 set_height_above_pln indicates that you did use method 2 to discretize the axis or vector Now you are expected to give the height of the start point above the window plane Only a vertical movement of the cursor will affect this value The actual height is displayed in the box containing the Cartesian Y coordinate as long as the mouse button is pressed down set_end_point______ indicates that the start point of the axis or vector has been discretized Now you have to discretize its end point in the same way set_height_above_pln indicates once more that you did use method 2 to discretize the axis or vector Now you are expected to give the height of the end point above the window plane The direction of t
430. s exactly one parameter To install the new expansion e Choose an expansion number ie1 which is not yet occupied e Check that the initialization routine inians in file etc f does not initialize param eters differently from what you expect Insert the call for routine auser into routine entnr in file ANS F Insert the call for routine nuser into routine nullen in file ANS F e Insert the call for routine muser into routine ansatz in file MMP_PAR F 79 Part III User s Guide of the Graphic Interface 14 Graphics Introduction 14 1 Overview The 3D MMP graphics package includes an interface for calling graphic functions of Microsoft Windows from Watcom FORTRAN libraries with a large number of 2D and 3D graphic functions the 3D MMP editor and the 3D MMP plot program running under Windows 3 in enhanced mode In addition interfaces to GEMVDI which is a part of GEM a product of Digital Research Inc for different FORTRAN compilers a Windows 3 interface for the Micro Way i860 number smasher etc are available upon request It is important that the 3D MMP graphic programs run under Windows but their outfit and handling considerably differs from the one of typical Windows applications There are two main reasons for that 1 The typical graphic elements and features of Windows are considered to be neither comfortable nor very appropriate for our needs It is expected that an experienced user is able to work faster with 3D MMP than
431. s is obtained This affects the error distribution Moreover it is important to keep in mind that the orientation of a multipole is not fixed at all The multipole in the center of the sphere must be parallel or perpendicular respectively to the symmetry planes so there are essentially three different orientations Try what happens when you change the orientation of the multipole Although you might believe that the multipole should have the same orientation as the dipole describing the incident field this is not necessary Even in this very simple model it is possible to improve the results without increasing the computation time For complicated models this is even more important Although this procedure is a dirty trick for getting fast benchmarks with a lot of work for you there are good reasons for playing with multipole orders locations and orientations as well you can get experience and you can compare different computations of a problem with very different error distributions which is helpful for validating the results 17 3 4 Optimizing the Matching Point Distribution Model 8 Since the orientation of the multipole in the center of the sphere affects the error distri bution rotate the matching points of the sphere as well For doing that you can read models 3 and 4 move object 2 matching points and expansions of model 4 as you did for generating model 5 Now you can rotate object 1 i e the matching points and expansions of m
432. s is still an object with rotational symmetry it can be generated with the command 3D generate torus after an appropriate 2D construction consisting of a line for the cylindrical part of the fat dipole and an arc for the spherical part Needless to say that you can and should take advantage of the symmetry planes in the same way as described for model 1 When you construct for example an ideally conducting fat dipole of 0 5 m total length and 0 1 m diameter you can construct first a 2D line parallel to the Y axis starting from the point X 0 05 on the X axis ending at the point X 0 05 Y 0 2 Afterwards you can add a 2D arc with center X 0 Y 0 2 start point X 0 05 Y 0 2 and end point X 0 Y 0 25 A problem occurs as soon as you generate appropriate 2D multipoles with the command 2D generate pole When you select 0 in the item box the automatic procedure generates a pole in the center of the arc and it generates a pole for the line at a point with negative X coordinate Because of the symmetry plane X 0 this pole is automatically reflected Unfortunately the reflected pole is not at a useful position and therefore is deleted I e you don t get a complete 2D MMP expansion When running 2D lt check pole you see that not the whole boundary is correlated with the multipole To get additional multipoles you can add them manually or you can adjust the type of the automatic procedure in t
433. s is used in most cases you are asked set_vector_ez_____ If you answer this question in the affirmative the message new_axis_is_ z_axis indicates that the axis of the cylinder will be parallel to the Z axis Otherwise the actual axis is used Note that the length of the axis is ignored i e the length of the cylinder is not affected at all by the length of the axis When no 3D object is present the cylinder will become the first 3D object Otherwise it becomes object number two If object 2 already exists it is overwritten when you answer the question overwrite_object_2_ in the affirmative Otherwise the process is aborted i e the cylinder is not generated and the message object_NOT_generated is displayed In this case you can either store object 2 in a file see 3D write or add object 2 to object 1 see 3D add before generating the cylinder 3D generate torus____ Generate a 3D object by rotating a 2D construction This command uses the matching points and expansions of the actual 2D construction the axis and two real values that have to be selected in the boxes ang and fac It rotates all 2D matching points and expansions around the axis with a maximum angle ang The ratio of the lengths of the tangent vectors of the matching points is defined by fac Moreover multip
434. s of XTs and ATs without coprocessors and for all others is certainly an add on board with one or several IMS T800 transputers that have about the same speed as an 80486 with his built in coprocessor Since the 3D MMP graphic programs have not yet been parallelized only one T800 is required whereas additional transputers reduce the computation time of the 3D MMP main programs see section 5 5 The auxiliaries for compiling and configuring the non graphic 3D MMP programs on a Micro Way Quadputer board with 4 T800 processors running in parallel and similar T800 boards with 3L parallel FORTRAN are included in this package The resulting code runs under DOS A graphic GEM interface for 3L parallel FORTRAN is available upon request Unfortunately the data transfer between the host and the root transputer is very slow when the alien file server delivered with 3L Parallel FORTRAN for transputer boards in PCs under MS DOS is applied Unlike the main program the graphic programs are affected considerably by this I e the transputer version of the 3D MMP graphics is relatively slow which makes it impossible to run movies with the transputer version Thus a 386 387 or 486 machine is certainly the best choice for MMP graphics For the same reasons as mentioned in the previous section transputer boards should have 4Mbytes of memory on the root transputer at least Micro Way offers a Videoputer add on board with a T800 transputer and a separate video outp
435. s or filament currents in the 2D case or many dipoles in the 3D case are used 28 29 The charge simulation method with its multiple point charges is an analogous example from numerical electrostatics The other analytical end of this road can be seen in the continuous field or source distributions on the boundaries of the domains as they occur together with spherically symmetric Green s functions in the vector Kirchhoff integrals of the Huygens principle In some cases expansions with Bessel functions Jn or jn for the radial behavior which are called normal expansions are more efficient than multiple multipoles A normal expansion can be seen as the superposition of incoming and outgoing HY and Hi or Aw and RP waves The Bessel function is regular because the singularities at the origin cancel each other out therefore the origin may be within the domain Normal expansions cannot be used multiply because they do not have a local behavior As a consequence they can only be used for nearly spherical domains Experiments with multipole and normal expansions in more complicated oblate sphe roidal coordinate systems have also been made 5 but the necessary functions are much more demanding to evaluate Usually the field in domains with geometries where such an expansion might be efficient is easy to expand with multiple spherical multipoles alone Expansions other than multipoles and normal expansions are denoted as special ex pansions mai
436. s with a domain number smaller than one is left unchanged by most algorithms The material properties of all domains have to be defined This can be done with add dom and adjust dom When the geometry is complicated you can generate an appropriate model with the 3D MMP editor read the corresponding input file in the plot program and run clear pic f 2 In this case the domain numbers in the field points will be computed from the matching point data 16 9 2 Defining and Starting an Iteration Above all you have to select the type of the iteration in the box iter type In the actual version the following algorithms are implemented e 0 Mandelbrot Computation of the famous Mandelbrot set This set is computed in the complex plane The complex plane is the xy plane Reset the field to zero 207 with clear pic f 0 for a relatively large number of grid lines in horizontal and vertical direction iterate and show the scalar potential 1 Newton Solve the equation z 1 0 with the Newton algorithms for different start points in the complex plane The complex plane is the xy plane The exponent n is defined in the box iter info Interesting pictures are obtained for 2 lt n For n lt 2 and n gt 9 an error message is displayed Reset the field to the position vector with clear pic f 1 for a relatively large number of grid lines in horizontal and
437. screen windows used in this program and plot windows that are used in the 3D MMP main program for generating standard plot files If you want to add a screen window you should have some space on the screen where you can set the window The additional real and integer data of screen windows have to be defined in the corresponding boxes Wx11 Wy11 etc and ix11 iy11 etc The pixel coordinates of the lower left and upper right corners can be given either manually in the integer data boxes or they can be discretized with the mouse The additional real and integer data of plot windows have to be defined in the boxes Wx11 Wy11 etc and Win h If the number of screen windows and the number of plot windows exceeds the max imum number defined in the include file MMP E3D INC the process is aborted and the message too_many_windows___ is displayed Otherwise if the number of screen windows is less than the maximum num ber defined in the include file MMP_E3D INC you are asked add_screen_window__ If you decide to add a screen window you are asked set_corners_manual If you answer this question in the affirmative you will have to set the lower left and the upper right corner of the window manually by pressing one of the mouse buttons when the cursor is at the desired location of the lower left corner and releasing it when the cursor is at the desired location of the upper rig
438. sed by MMP_E3D as well MMP_Pyy xxx complex plot file read write generated by MMP_M3D or MMP_P3D MMP_Tyy xxx real plot file read only generated by MMP_M3D MMP_DAT PLT complex plot file read only generated by the 2D MMP code MMP_PLF xxx complex plot file read only generated by the 2D MMP code MMP_PLT xxx real plot file read only generated by the 2D MMP code MMP_PRT xxx particle definition file read write MMP_DIR xxx directive file read only generated by the user text editor MMP_Fyy xxx picture file read write pixel information of picture MMP_Iyy xxx picture information file read write ASCII information of picture Utilities MMP_Pyy xxx complex plot file read by MMP_F3D MMP_Tyy xxx real plot file created by MMP_F3D MMP_FOU TIM fourier time value file read by MMP_F3D and MMP_FAN utilities MMP_FOU FRQ fourier frequency file read by MMP_F3D generated by MMP_FAN MMP_PAR xxx unlabelled parameter file read by MMP_PAR MMP_PAL xxx labelled parameter file written by MMP_PAR D 2 3D Input File MMP_3DI xxx The input file contains the data defining a MMP problem for the 3D MMP main program and is also used for saving objects in the 3D MMP editor The meaning of the variables is described in chapter 10 iprob nexc problem type and number of excitations msscr msfil amount of output on screen and in output file cfreq complex frequency isi is2 is3 symmetries of the problem ngeb number of domains igeb cer cur csig domain nu
439. simply connected closed domains a single origin ex pansion of infinite order with Bessel functions is sufficient to express any field In more complicated multiply connected domains with several complementary domains an ad ditional Hankel multipole expansion is required in each of the complementary domains 21 The proof for completeness of a minimal base of this kind has been given by Vekua for the 2D case in 27 for the 3D case no corresponding theorem is known to the authors The numerical realization of this single multipole approach is only feasible for do mains with a nearly spherical or cylindrical shape of the domain itself or its complemen tary domains the origins of the multipoles have to be near the centers of these spheres or cylinders The more the shapes differ from this case the slower the convergence is The key to more flexible use of multipoles is to base an expansion on multiple finite HP or HP multipoles C 16 or C 8 or C 10 respectively with different origins A few heuristic rules are sufficient to keep the basis functions sufficiently independent even for numerical purposes because each finite multipole has only a relatively local influence on the unknown field The highest orders and the number of multipoles are closely correlated The fewer orders the more poles In the MMP approach relatively few multipoles with high orders are used cf chapter 8 In other implementations of the GMT many monopole
440. sist of a window plane and some additional data The additional data of screen and plot windows are slightly different see below A window plane is defined with a 3D vector pointing at the origin of the plane and two 3D vectors tangential to the plane see below Although a plane is an infinite object usually only a rectangular part of the plane is considered In the case of a screen window this part is mapped on the screen The origin of a screen window can be anywhere on the screen or even outside whereas the origin of a plot window is always in the center of the rectangle Note that the main program computes regular field plots in the rectangle of the plot window and in additional parallel rectangles above the window plane if the number of levels is bigger than one The data of screen windows are stored in special window files MMP_WIN xxx whereas the plot window data are stored in the 3D input file MMP_3DI xxx At least one screen window is required for working with the editor but two screen windows are the default because it is convenient for 3D constructions to have two different sights of 3D objects In the plot program one has only one default screen window because one usually prefers to have a large window when electromagnetic fields are plotted Plot windows are defined in the editor The data of existent screen windows can be used for doing this Moreover plot windows can be converted to screen windows by the editor and plot program when
441. sked overwrite_part file If you answer in the negative the process is aborted with the message process_aborted____ When there is not enough memory for opening a particle file cannot_open_file__ is displayed Otherwise writing_partic file indicates that everything is correct 16 5 4 generate generate pic f This command is used for generating and displaying a field with one of the iterative procedures of the plot program Like in the command show pic f you are asked first compute_new_scaling and you usually will answer that in the affirmative Then you are asked 169 initialize field When you answer in the affirmative the field is reset to values appropriate for the actual algorithm before the iteration is started When you already have performed some iterations and would like to add some more iterations you should answer in the negative After the computation of the field it is drawn and you can obtain the same messages as mentioned in the command show pic f Note that you have not only to select the data defining the representation of the field before you start this action but also the data defining the iterative procedure i e the values in the boxes tim dt Tmx iter aaaa etc When the number ipic mov is bigger than 1 a movie with as many pictures as indicated in this box is generated automatically The movie
442. sonable when the areas of active matching points are not very large 7 Delete or shift multipoles that you consider to be inconvenient 8 Repeat the steps above with decreasing type numbers until only small areas of uncorrelated matching points are left Steps 5 and 6 can be performed automatically with a decreasing type number If a negative type number is selected the procedure starts with the absolute value of the type number and repeats the steps with decreasing type number until it is 1 3D generate constrain Generate a constraint from a set of matching points A constraint essentially consists of a type and of one or several integral points The geometric data defining an integral point are exactly the same as one defining a matching point In order to simplify the code integral points cannot be manipulated like matching points Instead the matching points of one or both objects can be used to generate a set of integral points of a constraint If such a set does already exist when the command 3D generate constrain is executed you can either add the matching points to the existing integral points or replace the existing integral points by the matching points Thus you are asked first add_to_existing_pts Answering this question in the negative will cause the question replace_exist _pts_ If this question is answered in the negative as well nothing is done and process_aborted___ is displayed In
443. sszp irek Domains cer cesr ce cur cu csig ck CZ Expansions xe ze xex ZeZ ient ig iel ie6 sel se2 cegam ies Connections cpic number of expansions in input file total number of expansions including those within connections number of columns number of columns number of matrix elements problem type option for matrix algorithm symmetries in input file current symmetry number of symmetry components of problem current symmetries which can be considered by an expansion symmetrization components of an expansion signs of components in symmetrizations signs of E components in symmetrizations signs of components in symmetrizations plane x 0 y 0 z 0 about which symmetry of expansion ise is components of field which have to be considered in a point symmetrization necessary for particular matching point or field point actual recursion depth relative permittivity complex relative permittivity e complex permittivity relative permeability ur permeability u conductivity o wave number k wave impedance Z E leo origin Terp orientation z Ey z identification number of expansion domain number integer parameters real parameters complex parameter symmetries for connections parameter vector for all connections 312 c con cuptmp Xpr zpr ikolc nkolc temporary variable for evaluation of connection temporary variable for evaluation of connect
444. st of the Windows and GEM device drivers support either 2 16 or 256 colors but 3D MMP uses 2 or 16 colors only Moreover Windows and GEM know several fill patterns but only 8 are used in the 3D MMP codes for increasing the intelligibility of the graphic representations Many color device drivers of Windows have an important drawback they do not allow to set the color palette as desired and most colors are simulated by mixing different colors When any fill pattern is used the colors are replaced by one of 16 predefined colors Since the predefined colors are neither very nice nor useful for getting nice field plots the pictures obtained with a 16 or even 256 color driver of Windows look much worse than the ones obtained under GEM with 16 colors Since color movies run considerable slower than monochrome movies 2 color device drivers are preferred for generating and watching movies Moreover the memory required for saving the pixel data behind hint and pull down boxes can be large when high resolution drivers with 256 colors are used Such drivers can cause undesired problems and reduce the performance of the program Thus it is recommended to test all available Window device drivers and select the most appropriate one for the corresponding application To change the screen driver under Windows run Windows setup by clicking the corresponding icon in the Main window of the Program Manager and select Change System Settings
445. st the additional data box F pt of the set of field points with the number selected in the item box NO_such_field points indicates that no set of field points with the selected number has been defined 3D adjust__ integrals Adjust the additional data box Intg of the integral with the number selected in the item box NO_such_integral__ indicates that no integral with the selected number has been defined 15 7 11 3D generate Generate 3D objects from a 2D construction i e its matching points and expansions The 3D generate commands have very different effects that are described below Some of them require the definition of certain data before they are executed 133 3D generate cylinder_ Generate a 3D object by a translation of a 2D construction A cylinder of length len parallel to the vector axis is generated Two real values be selected in the boxes len and fac It generates a cylinder of length len parallel to the vector The first tangent vector of the matching points becomes parallel to the tangent vector of the corresponding 2D matching point i e it has no longitudinal component The second tangent vector of the matching points is parallel to the vector The ratio of the lengths of the tangent vectors is defined by fac Since you might have forgotten to adjust the vector axis and a vector parallel to the Z axi
446. straints The error sperr is the average over the residuals as defined by 6 1 Ele El E y2 r 2 sperr pj 7 E By By Ej Eb 6 lez H uH 2 v t at aaa bib Fa for perfectly conducting boundaries by 6 2 sperr p ei 2 21 12a 7 1 3 Tk and for surface impedance boundary conditions by 6 3 sperr p Et Z HE a E ZH Tk For reduced boundary conditions only the matched conditions are averaged Along with the error in the matching point an assessment of the field s intensity near the matching points is given in analogy to the error definition by 1 1 el Bi pH fval1 6 i 7 t En Eil 4 2 2 pE mai E lee ATA 1 leE H evana 3 Gt al h retar zzy L ear c M5 65 All components regardless of the boundary conditions are taken An error in percent is defined by 2 sperr 1 11 1 ae fval1 fval2 00 a between general domains and sperrp SPETT 100 11 1b fvali on the surface of perfectly and imperfectly conducting domains Note that the percentage error can be tricky It can be larger than 100 If the percentage error is high the solution must not be completely wrong Where the field on the boundaries is small e g in shadow regions or in waveguides and cavity like problems the percentage error sperrp can be high even if the solution is quite good In the
447. subroutines themselves 13 5 3 Initializations init1 does initializations right after the start of the program e g initialize or compute constants and explicitly clear some variables and arrays After an input file has been read or when a new frequency step starts init2 is called It initializes variables which depend on values defined in the input file as amount of output frequency dependent variables etc 13 6 Parameters and Variables Practically all of the parameters and variables are defined in file comm inc and are made available to most of the routines by include statements A list is given in appendix E 77 FORTRAN INTRINSIC type definition is used whenever possible Complex variables start with the letter c though they are implemented as pairs of real numbers Integer variables start with i to n The other letters are real variables logical variables are explicitly defined 13 7 Basic Packages Double precision complex numbers are defined as pairs of real numbers This is com patible with DOUBLE PRECISION COMPLEX or COMPLEX 16 where available The basic operations are implemented as subroutines which can be found in COMPL F The cylindrical Bessel functions B z section B 1 in file CYLC F have been copied from the 2D codes 4 File SPHF F contains subroutines for computation of the spherical Bessel functions bn z section B 2 the trigonometric functions cos my and sin my section B 4 and the associated Legend
448. t i f Wa Wxil 1 0008 00 ix11 6 Br 1 0000E 00 wgt 1 000E 00 sel 0 000E 00 Con w 0 0E 00 x 0 oooz 00 Jly 0 000400 z 0 0008 00 Figure 15 1 Desk of the 3D MMP editor program showing a sphere 15 3 Graphic Elements and Constructions The graphic elements that can be shown in the windows essentially depend on the di mension of the construction 15 3 1 3D Construction and Elements In 3D MMP models one has mainly the standard elements e 3D matching points e 3D multipoles and other 3D expansions The expansions especially multipoles and the matching points are usually associated with each other Therefore in the 3D MMP editor they can be combined into an object These objects can be saved in files MMP_3DI xxx the same format as the input files to the main program and used in constructions with other objects 95 In addition to these elements three types of 3D points can play a role in the 3D MMP main programs e constraints e integrals e sets of field points used for defining general plots In order to simplify the code the corresponding points are constructed indirectly First a set of matching points has to be generated Then these matching points are used to generate a constraint integral or set of field points Finally the matching points have to be deleted if they are not used as ordinary matching points Last but not least the plot windows are 3D elements One plot window is aut
449. t of Field Points Adjust the drawing depth appropriately Points that are in a bigger distance from the window plane will not be affected in the following Now you can select a rectangle 154 within the window by pressing the first mouse button when the cursor is near a corner of the rectangle and releasing the button when the cursor is near the opposite corner of the rectangle All data of the field points that are visible within this rectangle will be adjusted i e replaced by the values defined in the corresponding boxes 16 3 3 Special Actions There is only one special action for leaving the 3D plot program see 16 2 The special actions of the 3D editor for clearing the desk and for generating a meta file are regular actions in the plot program 16 4 Graphic Representations 16 4 1 Regular and General Plots According to the two types of plot files generated by the 3D MMP main program the 3D MMP plot program has to represent either regular plots or general plots Regular plots consist of field values that are given in field points on a regular rectangular grid whereas the field points of a general plot are just anywhere in space The advantages of regular plots are the following e It is much easier to imagine the locations of points on a regular grid than the location of points anywhere in 3D space e For each field point one has some known neighbors l e there is a certain correla tion between the field points This allows
450. t of angular frequency Re_Ga real part of propagation constant in z direction Im_Ga imaginary part of propagation constant Change values with the first count up and second count down mouse button in the value area of this box Note do not change the angular frequency if there is no good reason for doing that Box 14 Field Set Type roll field1 vector field set 1 E 5 energy scalar field set 1 we Wm P power_ scalar field set 2 pe Pm Pj field2 vector field set 2 jes En X H V field3 vector field set 3 D B A Clicking the mouse button 1 increases the line number of this box and the correlated boxes 17 19 After the last line line 1 is displayed Clicking the mouse button 2 decreases the line number of this box and the correlated boxes 17 19 After the first line the last one is displayed Note When more than one of the three parts of a vector field set is activated in the boxes 17 19 only the first one is shown The three scalar fields of a set can be shown at the same time They are represented by the three components of a vector when a vector representation is used otherwise they are added p jE i is a power density rather than an energy density Thus it is not reasonable to show we Wm and p at the same time Moreover p is identical with p for real conductivities i e in most cases To display the total energy density select energy and activate both we and wm i e boxes 17 and 18 To display the t
451. t parameter stored in cpic ie5 initialized to last parameter stored in cpic Thin wire expansion C 4 with sin kl and cos kl currents on the segments The direction of the wire is in the direction it starts at the origin iel 101 ie2 number of segments ie3 weight w r of matching points at the end of a segment ie4 weight w r of matching points in the center of a segment ied number of matching points per segment ie6 matching point modeling on last segments sel radius of the wire se2 length L of the wire A simple set of matching points including dummy matching points can be generated automatically with the expansion The number of matching points per segment as well as the weight distribution can be varied The weight distribution on a segment is sinusoidal between the center and the end of the segment It is recommended to use ie5 2 i e two matching points per segment In this case the matching points will be distributed along the segments according to the fourth order approximation formula given in 40 provided that the length of the segment exceeds 0 6 times the radius of the wires In all other cases the matching points are distributed uniformly along the segments which is considered to be worse The first and second digit of the two digit number ie6 determine the distribution on the first and last segment respectively If the digit is zero the distribution is the same as on the other segment if it is 1 the matching
452. t sequence of a movie is repeated until one of the mouse buttons is pressed The first mouse button is used for stopping the movie as long as the button is pressed down When the second mouse button is pressed the sequence is terminated and the next sequence is started After the last sequence the first one is started again To exit a movie either the third or both the first and second mouse button have to be pressed The speed of a movie can be reduced by increasing the delay time in the additional real data box It should be mentioned that the size and location of the pictures that are shown is identical with the size and location of the window used when the movie was generated This can differ from the actual window position show___ axis_ Show actual axis 163 show____ wind Show the origin and the two tangent vectors of the window plane with the number xx selected in the item box show____ part Show particles and display data of the particle selected in the item box If the selected particle number is out of range it is set equal to the number of particles show____ dom _ Show data of the domain selected in the item box If the selected domain number is out of range domain_NOT_defined_ is displayed 16 5 2 read___ Read data from file The question read_file_OK______ allows you to stop reading by answering in the negative when you have forgotten to select the app
453. ted wave analytically To introduce both the incident wave and the reflected wave in the MMP code you can write an appropriate connection file with a text editor or instead generate such a connection file with a simplified model of the plate without the aperture For a plane plate this model can be very simple only one matching point is required Unfortunately a third problem is created The superposition of the incident wave and the reflected wave is useful only on one side of the plate In order to solve the second and third problem we apply a technique that is helpful in many complicated models simply subdivide a domain into two domains introducing a fictitious boundary You are free to choose the shape of the fictitious boundary so usually you will prefer a shape that can easily be modeled For example you can introduce a plane fictitious boundary in the aperture model 25 As a result you get two domains on both sides of the plate The field in the first domain consists of the incident wave the reflected wave and a wave generated by the aperture The latter can be approximated by a multipole with origin near the aperture in the second domain In the second domain you have only a wave originated by the aperture that can be modeled by a multipole with origin near the aperture in the first domain The local behavior of the multipoles guarantees that the boundary conditions far away from the aperture are satisfied even if you don t place an
454. ted number has been defined window_NOT_defined_ is displayed 3D invert__ object___ Invert the direction of the matching points and expansions of object 1 or 2 If the number selected in the item box is neither 1 nor 2 both objects are inverted 3D invert__ pole____ Invert the direction of active expansions by inverting their second tangent vectors vz 15 7 9 3D lt check Check multipoles and matching points For reasons of simplicity the 3D checking pro cedures act on multipoles and matching points that belong to one domain only The number of the domain has to be selected first in the Domain box 127 3D lt check points___ Checks the number of multipoles correlated with all matching points Upon completion all matching points are represented with fillings and colors that indicate whether 0 1 2 or more than 2 poles are correlated with them The fillings and colors are defined in the desk file MMP_E3D DSK Filling and color number 0 is used for matching points that have not been checked i e that do not belong to the selected domain Moreover all matching points that are not correlated with a multipole are activated and all other matching points inactivated This is helpful if the command 3D generate pole is to be applied afterwards As a rule the regions of matching points that are either not correlated or correlated with more than one multipole s
455. ter affects the length of the steps The predefined value 0 1 is reasonable here but in general you probably have to try several values Note that the particles immediately run outside the window if the value is too big and move very slowly if the value is too small iter part 10 means that each step you see on the screen is subdivided into ten steps for increasing the accuracy When you prefer to get lines rather then dots where the particles are set the value part rep equal to 2 As soon as you have several field lines you probably want to clean the screen before you draw additional lines This can be done with clear pic f Note that you must avoid that the field is changed with this command by answering the question set_ in the negative When you want to combine a usual field representation with field lines you have to run show pic f again Since this is time consuming you better save the pixel data of the field without field lines before you start drawing field lines with write pic f and clean up with read pic f instead of clear pic f Probably showing the entire field on all levels is too much Thus you probably want to combine a plot of the field in the lowest first level with the field lines above For doing this proceed as follows before you draw any field line 1 Set the level number 0 and run show pic f with new sc
456. th IE1 302 ie2 not used in the actual implementation ie3 minimum order ie4 maximum order ied 0 both currents 1 cos current only 2 sin current only ie6 0 without magnetic current 1 with magnetic current sel not used in the actual implementation se2 length of wire multipole iel 113 expansion like expansion 1E1 112 but TM field only ie2 not used in the actual implementation ie3 minimum order ie4 maximum order ied 0 both currents 1 cos current only 2 sin current only ie6 0 without magnetic current 1 with magnetic current sel not used in the actual implementation se2 length of wire multipole iel 114 expansion like expansion IE1 112 but TE field only ie2 not used in the actual implementation ie3 minimum order ie4 maximum order ied 0 both currents 1 cos current only 2 sin current only ie6 0 without magnetic current 1 with magnetic current sel not used in the actual implementation se2 length of wire multipole e 2D expansion C 8 with orders 0 M 57 iel ie2 ie3 sel se2 201 radial function 1 J Kp Y xp 3 1 xp 4 1 xp order M scaling radius Psca see below scaling factor Ssca see below cegam propagation constant y initialized for iprob 200 299 2D problems e 2D expansion C 8 with orders Minin Mmaz iel ie2 ie3 ie4 sel se2 202 H and E modes 203 E modes only 204 H modes only radial function 1 J xp Y xp 3 H Kp 4 H xp minimum order Min maximum order M
457. the additional real data box fac and the object number 2 in the item box Answer the questions blow___elements_0K_ set_blow_type 0__ blow_w center_point in the affirmative When you are sure that the start point of the axis is in the center of the spheres you can answer the question set_new_axis______ in the negative If you didn t modify the axis before this certainly is correct Otherwise you have to set the axis with start point in the center of the sphere The end point is irrelevant here 6 Adjust the data of all matching points of object 2 the domain number 3 must be replaced by 1 because the coating is surrounded by free space and the domain number 2 must be replaced by 3 the domain number of the coating 7 Add a multipole and a normal expansion with origin in the center of the sphere for domain 3 You can do this either manually with the command 3D add pole or with the commands 3D copy pole and 3D adjust pole This is not so easy here because the origins of all expansions are in the same point Thus clicking a pole with the second mouse button is not useful Instead the command 3D show pole has to be applied for activating the desired expansions Although processing the input file with a text editor is much easier it is recommended to use the MMP editor for getting familiar with its features Once more you don t forget that the expansion descr
458. the electric transverse magnetic case for m gt 0 are Emn bnlkr os S ESP nad r sin 0P cos COS mp C 11a Cmn bn k EST kb 1 kr 1 al n cos 9P cos 9 n m P cos Gn me C 11b Cae br kr x si EES _ kb _a kr n 0 2 mBr cos 0 _ SE mo C 11c Cc HES y C 11d E mn _ TR sin Hy iwe bn kr mP cos 9 _ cos MP C 11e e x 2 peste iwe b kr n cos VP cos 9 n m P cos 9 sin Me C 11f For m 0 the expressions simplify to HE E n n 1 bnlkr P cos Y C 12a r bn ws gs ESO kbn 1 kr n e sin VP cos D C 12b Bee 0 C 12c Hee 0 C 12d Hoon 0 C 12e HPO iwe b kr sin VP cos v C 12f 289 The magnetic transverse electric solutions for m gt 0 are pES i C bars ES 5 Z iwpbn kr mP cos 9 _ cos Mp c EF smn C Hoe _ n n ts 1 C HES kby_a kr n E H S _ kb _a kr n and for m 0 bn kr bn kr r sin 9 P cos Y ae mo n cos 0P cos 9 n m P cos 9 in Mp ELO 0 pen 6 o H HcOn n n 4 1 Tr HE0 0 n kr r En iwpby kr sin 0P cos 9 by kr r P cos Y The solutions have the following symmetries pm jj m Pr cos V0 _ e me He kbp 1 kr _ jn sin oP cos Y r C 13a C 13b iwpbn kr n cos UP cos Y n m P cos
459. the graphic data For this a device independent meta file can be generated which subsequently can be reproduced on a wide range of output devices with full resolution using a Windows application that is able to print Windows meta files The meta file comprises either the whole desk with or without all actual box values Note that it contains information of points that are hidden behind other points Above all in 3D representations with many field points or matching points meta files can be very large They are characterized by the extension WMF Windows itself does not include an output program for printing meta files Thus the procedure of printing Windows meta files cannot be outlined here Moreover it is important to note that some Windows applications are not able to read big meta files Windows allows to generate hardcopies without meta files as well Usual Windows applications have a command called cut for doing this In the 3D MMP graphic pro grams you can simply press the button Print Scrn on your keyboard during a Windows session Windows will generate a file in the clipboard with the actual pixel information of the screen You can read and print this file for example with the application paint brush Note that this allows to manipulate pictures generated with the MMP programs but it does not take advantage of the full resolution of your printer since only the pixel information is transferred to the clipboard Moreover only one pic
460. the last few chapters is azi p cs bj p Gg 1 M i 1 N 5 1 or more simply Ac b 5 2 As the expansion functions are produced using recurrence relations A naturally is com puted row by row Scaling of the columns and weighting of the rows has already been discussed in sections 3 5 and 4 5 The parameters are determined for just one right hand side as only one excitation is considered at a time The number of rows M is usually about 2 to 10 times the number of unknowns N The equations are solved by least squares i e by minimizing the 2 norm of the residual vector n 2 Ac b 2 In most cases N and M are so large that the time needed for computing the rows is considerably smaller than the time needed for solving the matrix equation Different algorithms exist for solving the linear system Each is a tradeoff between numerical qualities memory consumption computational time and the desired results The algorithms used in the 3D MMP main program are all modifications of LINPACK routines a detailed description can be found in 31 fa Se Figure 5 1 Typical shape of the rectangular system matrix A M 2 10N and the triangular matrix R or X for a problem with 3 domains 5 2 Solution with Normal Equations The classical method to solve 5 2 is to form the normal equations and solve the square system A Ac A b 5 3 29 Because A A is hermitian only the upper triangle needs to be stored
461. the matching points the expansions can be represented in the same way as in the 3D MMP editor but this feature is considered to be of minor importance The graphic representation of matching points is almost trivial Essentially the same style as in the 3D MMP editor is used i e a rectangle is drawn that indicates the tangential plane in the matching point The fill pattern and the color used for drawing these rectangles allow to add some more information like the error in the matching point 16 4 5 Projections and Hiding Even for representations of simple 3D objects the projection on the 2D screen or sheet of paper is not obvious Above all the point of observation has to be moved to an appropriate 160 Y T z T generate meta_ 11 12 computing S field NO E H S fieldl x y z M P gt O EXIT SM 1 sequ M 41 1 7 metav 8 0008 02 fill plane_ 2 color 3Darr 1 linew 1 000 00 ix _low left 19 ER 1 00000E 00 vx_ 0 00000E 00 vz_ 0 00000E 00 total FPt 225 y 4 00000 01_ z 0 00000E 00 iter part 1 tim 0 00000E 00 part type 1 m0 1 00000E 00 Figure 16 5 Desk of the 3D MMP plot program showing the time dependent Poynting vector for a plane wave incident on a lossy sphere and the errors on the sphere The window plane is rotated and the manager representation is turned on position In the actual version of the plot program either perspec
462. the maximum number of particles a random number of particles is defined First all particles are set in the origin with random mass value between 0 and 10 charge between 1 and 1 and friction constant between 0 and 1 Afterwards they are moved with a random vector The length of this vector is proportional to the value selected in the box sequ M As soon as all particles are outside the window they are reset to the origin Note that the random number generator is not excellent You can replace it by a better one in the module MMP_P3P F When there is not enough memory left for saving the space occupied by the particles on the screen ERROR_set_particle_ is displayed 16 5 5 add____ Before this command is executed the additional window data should be selected in the corresponding boxes Moreover some space should be left on the screen where to put the window If the number of screen windows and the number of plot windows exceeds the maximum number defined in the include file MMP_P3D INC the process is aborted and the message too_many_windows___ is displayed Otherwise you are asked set_corners_manual If you answer this question in the affirmative you will have to set the lower left and the upper right corner of the window manually by pressing one of the mouse buttons when the cursor is at the desired location of the lower left corner and releasing it when the cursor is at the desired locatio
463. the question adjust window plane is answered in the positive the window plane can be adjusted The construction is the same as in the 3D add window command If the question adjust_window_data_ is answered in the positive the data contained in the different boxes mentioned above is entered It is strongly recommended to use the command 3D show window before the data in the boxes is adjusted Otherwise there is a good chance that you forget to modify some of the values appropriately and get unexpected results Moreover the command 3D write window is certainly helpful for unexperienced users Needless to say no_such_window____ indicates that neither a screen nor a plot window with the number selected in the item box exists 3D adjust_ object___ Adjust the additional data of the matching points boxes MPt and wgt and expansions boxes Exp and se1 se2 etc belonging to the object with the number selected in the item box If this number is neither 1 nor 2 all matching points and expansions are adjusted 3D adjust__ pole_____ Adjust the additional data boxes Exp and sel se2 etc of either all or only the active expansions Moreover the orders of 3D multipoles can be adjusted automatically according to the r
464. the real part is used for storing the new field of the actual step In fact you can use all fields as you wish as long as you do not want that the plot program correctly derives energy densities Poynting vectors etc When you want to derive fields from the potentials you have to define the corresponding algorithm in the subroutine genField as well Below the computed goto for the different iterative algorithms you can find the algorithm for computing the electric field as the gradient of the scalar potential There is no other algorithm for deriving the field in the actual version of the code but you can see that there is already another computed goto that allows you to easily add your own algorithms The type of the algorithm for deriving the field from the potential is characterized by the variable iPot You have to define this type for every algorithm in your new subroutine NewAlg So far iPot 0 stands for do not derive any field and iPot 1 stands for derive the electric field as the gradient of the scalar potential In addition you have to say in this subroutine whether the field is time harmonic ltim false or not 1tim true Since the imaginary part is often used for storing the old field whereas the field is considered to be real rather than complex the old field has to be removed i e the imaginary part has to be cleared before another field is derived and before a picture is drawn This has done i
465. the same time When an object is shown the drawing usually starts in the first window and ends in the last one The manipulation of the location and size of screen windows on the screen is similar but simpler than the manipulation of windows in typical Windows applications For moving a window on the screen you can press down the first mouse button when the cursor points on the lower left corner and move the mouse to the desired location while you keep the button pressed For doing the same in usual Windows applications the cursor must point on the title bar of the window For changing the window size you similarly can press down the first mouse button when the cursor points on the upper right corner It is often desirable to resize a window without changing the shape ratio of horizontal and vertical side length This can be done by pressing the first mouse button when the cursor is on the right border of the window Note that the shape of the cursor is never changed whereas it is changed in typical Windows applications when it is somewhere on the border for indicating that you now can change the shape or location of the window In addition to the operations mentioned above there are many additional and more complex ways to handle windows in 3D MMP programs It has already been mentioned that a screen window consists of a window plane and some additional data The additional data are either real or integer numbers Real values are appropriate for de
466. the top line and run show pic f When you want to show field lines you probably do not want to show the field first but the command show pic f is necessary for computing the Poynting field on the grid This is done before the drawing of the field begins Thus you can abort the process by pressing down the first mouse button as soon as the program starts drawing Once more it is important that the level number is 0 before you start show pic f because otherwise only one level would be computed 3 Add some pseudo particles with the command add part after having defined the properties of the particles in the boxes near the bottom of the desk If you do not like to read manuals use the hint feature of the plot program for getting some information When you are not sure you can get an idea when you read the particle file 31 included in the package with read part 31 4 Save the particle data with write part This is reasonable because you probably want to reset the particles to the original positions after having moved them If you have saved the positions you can do this with read part 5 Select the time difference dt and iter part 10 and move the particles with move part 0 The time difference seems to be meaningless for drawing field lines but since this is done by pseudo particles this parame
467. tic components weighted with 8 11100 on ideal conductors 11000000 surface impedance boundary conditions for imperfectly conducting do mains 0 for dummy matching points see below If ir is negative the boundary conditions are initialized automatically ir 011100 if ig1 0 or ig2 0 ir 111111 otherwise Dummy matching points are matching points which are not used for determining the parameters but for detection of the domains and evaluation of the error Applications are the rare cases where the ordinary matching points are not sufficient for the automatic detection of domains or those cases where the error between the ordinary matching points is of interest e g near corners and edges Dummy matching points may be introduced by setting ir 0 or alternatively sgp 0 0 If ir 0 no evaluation of errors see section 11 2 will be done if only sgp 0 0 the errors will be computed as for ordinary matching points 10 7 Constraints Scaling Integrals Integral blocks are used for constraints section 4 4 and for evaluation of integral quan tities section 6 3 iint integer number for identification in input and output programs not significant to the MMP program inttyp type of the integral ipts number of integral points rnbgew weight constraints only The type of the integral depends on the integer parameter inttyp inttyp Integral inttyp Integral inttyp Integral 1 f Ede 2 f Hae 3 fiEx Hda 4 Daa 5 Bd 6 fix
468. tion of human beings Usually one has to compress the information contained in the electromagnetic field in order to obtain comprehensible plots In most cases it is convenient to represent only a scalar field that is derived either from the whole electromagnetic field or from a part of it The plot program allows to show all three components two or only_one components of the following well known vector fields E H D B de A and Ho Ho is the vector product Hx en Where e is the normal unit vector in the field point On an ideal conductor this is the surface current Note that the vector potential A as well as the scalar potential V is not used in the 3D MMP main program Nonetheless the plot program can represent potentials that have been computed by another program or in the plot program itself For regular plots the definition of the field components is obvious For general plots it is most reasonable to use a local Cartesian coordinate system in each field point that you can define rather than a general Cartesian coordinate system The most simple reason is that you want to know for example the normal component of the D field on an ideal conductor the charge density the normal component of the Poynting vector on a surface that indicates the energy flow through the surface and so on However the field components that can be selected and displayed in the 3D MMP plot program are components with respect to the local coor
469. tion of the field does not need much time anyway The choice of the principal domain i e the side on which the expansions and match ing points are considered is not unique In the MMP programs it generally assumed to be the intersection of the positive half spaces i e the side on which the coordinates are positive of the symmetry planes involved Having expansions on the other side of a symmetry plane can result in a change of sign of the corresponding columns and as a consequence of the parameters Having matching points on the other side of the sym metry plane can affect only the sign of the corresponding rows and therefore does not influence the solution 39 8 Modeling and Validation 8 1 General Remarks Creating good models of realistic configurations is an art that needs a great deal of ex perience and that is hard to express in words This is especially true with regard to the limits of numerical computations The maximum size of problems which can be solved by the 3D MMP code within a reasonable time makes strong simplifications indispens able in most cases However in this chapter these limitations are only of subordinate interest We assume that an appropriate idealized configuration of homogeneous linear and isotropic materials already exists What remains to be done is mainly the transfer of this structure into an MMP model with matching points and expansions As long as the boundary remains relatively smooth the actual
470. tions 20 3 2 and E 2 9 2 Program Start After preparation of the input file s start the program under Windows by double click ing the corresponding icon After this you sometimes obtain error messages issued by Windows Since these messages are not issued by the 3D MMP program you have to consult your Windows manual for more information Note that the working directory is defined as command line parameter The predefined working directory is subdirectory EX3D of the directory MMP3D i e the place where the example input files are stored If you want to work on a different directory you can click the icon of the 3D MMP editor once select Properties in the menu File of the Windows Program Manager and modify the Command Line according to your needs Instead of this you can use any of the features provided by Windows for running an application for example you can se lect Run in the menu File of the Windows Program Manager After sucessfully starting the 3D MMP main program the following messages and questions appear parallel version number of t800 processors xxx 3D MMP VERSION 3 3 49 Note aaaaa is working directory tasks O EXIT 1 compute parameter file 2 compute standard error file 3 compute integrals 4 compute standard plot p00 p49 files 5 compute general plot p50 p99 files 6 compute extended error file 9 call routine USER factorization method 1 Givens 2
471. tions that have been performed during a 3D MMP plot program session This file can be helpful when a directive file MMP_DIR XXX has to be created by the user for generating a movie 305 E Overview of the Main Source E 1 Subroutines of 3D MMP Main Program File MAIN SRC gt MAIN F mmpall lerbuf user update faktor solve datum zeit outop t8ini File MMP F mmp resall resid fehler pl1tp00 pltp50 intega norm integ nbedz nbedw intval feldfp feldk fclear fadd floes zeile lzeile zmp zip chasig rbed irbed einscl setgew entsym main routine UNIX only frame for user definable routine call specific updating functions call Cholesky factorization call back substitution return string with date determine CPU time since program start and since last call open output file determine size of matrix shares for parallel version compute parameter vectors c determine all errors of matching points and constraints compute residues in a single matching point function compute error 6 1 6 2 6 3 from residues produce regular plot file MMP_Pyy xxx yy 0 49 produce general plot file MMP_Pyy xxx yy 50 99 evaluate all integrals evaluate scaling integral and scale the parameters evaluate single integral produce row for constraint evaluate constraint compute integral addends from field components field components in a field point in field point coordinates field components in a field point in global c
472. tistically rough surfaces Applied Scientific Research B vol 8 pp 437 462 1960 M M Waldrop Congress finds bugs in software Science vol 246 Nov 1989 P Balma and W Fitler Programmer s Guide to GEM San Francisco Sybex 1986 D Prochnow The GEM Operating System Handbook Blue Ridge Summit PA TAB Books 1987 338
473. tive projection or the most simple parallel projection is applied Using several windows allows to see an object from different directions which is certainly helpful A difficulty arises from the fact that parts of an object are in most cases behind other parts of the object or behind another object When a transparent drawing mode is used select fill pattern 1 one has a huge number of lines on the screen that make it very difficult to recognize how an object really looks like For this reason hiding procedures are required In the 3D MMP graphic programs a fast incomplete hiding is implemented Hiding has another drawback very often one wants to see hidden things like objects behind or even inside another object For this reason the 3D MMP graphic programs draw only the points of an object that are within a certain distance from the window plane the so called drawing depth Of course this is important for field points as well see fig 16 6 Although regular plots are computed on rectangular grids with several levels it is convenient to show only one level at a time or a few levels with a sufficient distance between the levels in order to avoid hiding of big parts of a level by other levels 161 generate jmeta_ 12 12 computing S field no la n s si0181 x y 2 lne O EXIT ER 1 00000E 00 vy_ 0 00000E 00 vz_ 0 00000E 00 fotalf FPt 2257 x 9 500008 01 y 4 000008 01 z 0
474. tkWi and drwpic 4 set the last window before the directive enddir For example when you want to have two windows in the movie given as an example in the previous subsection define the windows add a third one containing both the first and second window and use the following directives seq 1 setphi 18 0 enddir 1 parts 20 pictures 204 incphi 18 0 setkWi 1 drwpic setkWi 2 drwpic setkWi 3 enddir end 16 8 5 Error Messages The file MMP_DIR xxx is checked in the subroutines getdir and readir These checks are not complete at all but they should detect the most important fatal errors In getdir the following errors can occur 1 directive seq start of sequence expected in the actual line 2 the number of directives exceeds the maximum number mdir mdir is defined in the include file MMP_P3D INC 3 the number of parts sets of a sequence is either 0 or it exceeds the maximum number mpart defined in the include file MMP_P3D INC the number of pictures is less than 1 the number of pictures exceeds 999 the file MMP_DIR zzz cannot be opened error reading file MMP_DIR zzz co oa A In readir the following errors are detected 11 wrong value in data of current directive 12 window number out of range 1 nWin 18 an data file MMP_Pyy MMP_Tyy MMP_ERR MMP_3DI cannot be opened 19 error reading file MMP_DIR zzz 99 unknown directive 16 8 6 Starting and Stopping a Movie To start a movie select show mo
475. to a movement of the origin within the plane but only a 2D vector is required here to define the movement Finally the position of the location of a screen window can be moved The latter can be done by pressing the first mouse button when the cursor is near the lower left corner of the window It should be noted that the graphic objects represented in a window are virtually moved in the opposite direction if either the origin or the limits of the plane are moved You can move the origin of the window plane if you answer the question move_window_plane__ in the affirmative This requires the definition of a 3D vector or axis You can either use the vector respectively axis that has previously been defined and answer the question set_new_axis______ in the negative or you can adjust the axis now and answer the question in the affirmative If you have answered the question 123 move _window_plane__ in the negative you are assumed to move the window limits and set_from to_vector_ indicates that you should press the mouse button when the cursor is at the start point and release it when the cursor is at the destination point message window NOT_defined _ indicates that the window that you are trying to move does not exist 3D move____ object___ Needless to say that the Move the object with the number selected in the item box If this number is neither 1 nor 2 both objects are moved 3D move____ pole____
476. too For example in simplified models of magnetic materials losses due to hysteresis can be taken into account with a complex permittivity To generate a lossy magnetic sphere you can essentially proceed as in model 12 17 4 5 Coated Sphere Model 15 After the exploration of a simple sphere with different material properties it is most natural to consider a coated sphere now Of course you can use different material prop erties for the sphere and the coating To check the model it is a good idea to set the material properties of the sphere equal to the material properties of the coating Then the boundary between the sphere and the coating can be considered as fictitious and the same field should result as with a simpler model without coating In more complicated applications the introduction of fictitious boundaries can be very helpful for simplifying the geometric shape of the domains which simplifies the MMP expansions as well There are different ways to generate a coated sphere with the editor Of course you can start with an appropriate 2D model consisting of two concentric arcs When you run the automatic 2D pole generation multipoles outside the sphere and outside the coating are generated Since normal expansions are much better suited for simple spheres replace 232 the outer multipoles by normal expansions in the center of the sphere Since the coating has two boundaries you should have both a multipole
477. trix R from R when a row x ax j 1 N 1 is added to the original matrix A Zeroes are introduced into x in the following fashion 5 13 Bl H H H H E H HASH H BOB A Hi BR Hi Hr Br HE Er Bi Al z z 00 0 0 Hi LH o S S o oz H H 8 H 5 l Hi y Starting with an initially empty triangular matrix the rows of A can successively be updated Finally we end up with R Note that it is not necessary to keep the entire matrix A in memory Storage is required only for R which is dense and for the rows currently being updated These rows are discarded during updating For determination of the residuals they have to be recomputed This algorithm does not fail in case of a bad condition of A Problems with more than 1500 unknowns have been solved with good results The QR factorization of a matrix A needs MN 2 times 20 FLOPS Other orthogo nalization algorithms e g those using Householder transformations are faster but need the entire matrix A and therefore considerably more memory 31 5 4 Exact Equations In chapter 4 it was shown that is useful to satisfy some of the equations exactly i e to impose constraints on the least squares problem An attractive alternative to the direct elimination of these equations is to treat them as ordinary least squares equations with a high weight A tradeoff has to be made between getti
478. ts In the 3D MMP plot program the field is scaled in such a way that the field vectors remain essentially inside the rectangle of the plane in each field point Moreover the size of the elements is limited When the limits are exceeded the elements are filled with different patterns if desired indicating the strength Users interested in the direction of small field values can increase the field scaling factor see additional real data box as desired Instead the program can display the numeric values of the vector components in any field point Scalar fields on regular grids can simply be represented with deformed grid lines cf fig 16 3 The deformation is always a shift of the grid points perpendicular to the plane of the field points This gives a good impression of propagating waves Unfortu nately grid lines cannot easily be shown for general plots because the field points are not necessarily arranged along curved or straight grid lines Nonetheless a somehow 158 similar representation can be achieved when every rectangle representing a field point is shifted perpendicular to its plane Needless to say that the shifting distance is propor tional to the value of the scalar field in the corresponding field point This leads to a field representation similar to diagrams often used by managers The manager repre sentation of dynamic fields may look strange for scientists Nonetheless it can be both helpful and impressive espe
479. ts When symmetry planes are present the matching points usually are defined on one side of the plane only The symmetric matching points on the opposite side of a symmetry plane are generated by the program when the question perform_symm oper _ is answered in the affirmative After reading the input file with the message reading MMP_3DI xxx the program will start generating the symmetric matching points and display gen _symmetric_pts_ When a large number of matching points is defined in the input file the memory re quired for saving all matching points with their symmetric counterparts might exceed the memory available In this case too_many_match _pts is displayed Similarly too_many_poles____ is displayed when too many poles are defined in the input files Note that no sym metric poles are generated because this has not been found to be convenient When an expansion is a wire expansion the corresponding matching points are generated if any Otherwise NO_mat pts_on_wires is displayed Needless to say error_reading_input indicates that an error has been found during reading i e the input file format probably is defect read error Read a 3D MMP error file MMP_ERR xxx Select the extension number xxx in the item box These data are used above all for displaying the errors in the matching points For this reason the corresponding input file that contains the matching point data must be read first Sin
480. ts of the field ft on rectangular grids Whereas the determination of the parameters is expensive in terms of both computational time and required memory the cost for computing errors and plots is usually quite small 20 3 Expansion Functions 3 1 General Remarks The expansion functions used for the MMP programs are solutions of both Maxwell and Helmholtz equations 2 6 The expressions for the expansions currently implemented in the 3D MMP main program can be found in appendix C For deductions please consult textbooks 23 24 25 In the following some basic principles underlying the choice of expansions in the MMP programs are discussed The demands on expansion functions for analytical and for numerical purposes are different An analytical expansion in the form of 1 4 is generally infinite It is important that the expansion be complete i e that the difference between approximate and exact solution disappears as N gt oo Usually eigenfunctions of the differential operator in various systems of coordinates form natural complete bases In numerical computations it is more important that the field can be modeled with as few functions as possible and the error quickly drops below a certain limit The purely analytical approach may not converge fast enough Completeness in form of convergence for N oo is secondary for numerical expansions and may even have to be sacrificed As a consequence different criteria for choosing the
481. ture can be on the clip board whereas you can generate several different meta files without leaving the 3D MMP graphic program 93 15 3D Graphic Editor 15 1 Program Start To run the 3D MMP graphic editor under Windows you can double click the corre sponding item After starting the editor you sometimes obtain error messages issued by Windows Since these messages are not issued by the 3D MMP program you have to consult your Windows manual for more information Note that the working directory is defined as command line parameter The predefined working directory is subdirectory EX3D of the directory MMP3D i e the place where the example input files are stored If you want to work on a different directory you can click the icon of the 3D MMP editor once select Properties in the menu File of the Windows Program Manager and modify the Command Line according to your needs Instead of this you can use any of the features provided by Windows for running an application for example you can select Run in the menu File of the Windows Program Manager If the graphic workstation has been opened the desk is displayed and some default values are set If this has been done the program tries to read the hint file MMP_E3D 000 If this file can be read its contents are displayed in the center of the screen otherwise no hint box is displayed To remove the hint box you have to click one of the mouse
482. tween pole and matching point will be Afterwards the pole is tested and eventually eliminated as for type number 0 For small type numbers many low order poles are generated close to the boundary For large values of over the orders of such multipoles become zero and the multipoles are deleted therefore In most cases type numbers of 4 up to 9 and an overdetermination of 1 4 is convenient Since the procedure is time consuming when a large number of matching points is active the following messages are displayed during the execution 136 start generate poles dist xx_initializing dist xx_mat pt yyyyy check_xxxxx_of_yyyyy deleting wrong_poles In most cases the following interactive procedure is useful 1 Check the matching points with 3D lt check points This will activate all uncorrelated matching points 2 Inactivate some of the active matching points manually especially when large areas of active matching points are present This can reduce the time required for the next step 3 Generate poles with pole setting type O 4 Delete or shift multipoles that you consider to be inconvenient 5 Check the matching points again with 3D lt check points 6 If there are large areas of matching points without appropriate poles left generate poles in a relatively large distance with a relatively large type number for example 9 Lower numbers are rea
483. u try to start such an undefined regular action the message action_not_implem _ is displayed Several of the regular actions require you to perform some additional work For example you have to define a point within one of the windows In such cases a mes sage is displayed in the question information box The message indicates what you are expected to do Such a user action is performed in any window during 3D constructions and in the first window only during 2D constructions 15 4 2 Window Actions There are two types of window actions 1 actions for manipulating the size and location of screen windows and 2 actions for manipulating the graphic elements displayed in a window The former are identical with those in the plot program The latter are used for in activating different graphic elements and for displaying the corresponding data Moving a Screen Window When you want to move a screen window to another location on the screen select the window number in the corresponding item box and press the first mouse button when the cursor is near the lower left corner of the window Move the cursor and release the button when the window is at the desired location Make sure that the entire window is on the screen Note that the size of the window is fixed during this action Adjusting the Size of a Screen Window When you want to adjust the physical size a screen window select the window number in the corresponding item box and press the f
484. ual coordinates w and yy Of the cursor are displayed in the first two boxes of the bottom line as long as the button is pressed Afterwards set_start_point_winl tells you to define the start point of the arc within the first window Finally set_end_point_win1_ tells you to define the end point of the arc within the first window Since the radius of the arc is already known from the definition of the start point only the angle of the end point with respect to the center is used to define the arc completely 2D add_____ window___ See 3D constructions Manually add an expansion Before its execution select the additional data belonging to the expansion in the corresponding boxes Note that the same boxes are used for 3D and 2D expansions since the latter are used to generate the former Although this is the 2D part of your construction you should keep in mind that the poles defined here finally will be 3D poles in most cases If the maximum number of expansions is exceeded the message too_many_poles____ is displayed Otherwise set_center_in win1_ tells you to define the origin of the expansion within the first window Click the first mouse button in the first window and release it at the position where you want to put 104 the origin The actual coordinates x and Yw of the cursor are displayed in the first two boxes of the bottom line as long as the button is pressed 2D add_____ domain___ Add a new
485. ual values for e and u e In order to be compatible with the error method and the projection method the equations in the matching points need to be multiplied with a weight wg which is a combination of the square root of surface s of the element associated with the matching point k and a weighting function w r we y 5gw rr 4 8 w r can be used to emphasize some regions or points more than others and to simulate exact equations If the optimum weighting factors which depend on eg y and Z are different for the domains bordering the matching point the geometric mean is used because of the good experiences which have been made with this choice The actual boundary conditions in the matching point k on D are consequently 1 wg 6 E e Ei 0 4 9a ese w E Ej 0 4 9b w El El 0 4 9c y 122 i Wk wif uj H 0 4 9d vy lhini i we Zi Z Hi Hi 0 4 9e wr ZiZ Hig Hi 0 4 91 and for perfectly conducting surfaces wre 0 4 10a 27 w Et 0 wr Z Hi 0 The surface impedance boundary conditions are Ww E Zj Hio we Eta Zj Hin 0 0 4 10b 4 10c 4 11a 4 11b Constraints are mostly added to the system of equations with a very high weight in order to simulate exact equations section 5 4 28 5 Solving the System of Equations 5 1 General Remarks The complex system of equations which has been set up in
486. uced The total error on the matching points of the wire seems to be considerably lower when equal weights are selected in the boxes Exp IE3 and Exp IE4 It is very important to note that the errors computed in the matching points do not take the unmatched boundary conditions into account Since two of three conditions are turned off in the matching points of the wire the errors may be misleading Moreover you should compare the errors with the strength of the incident wave rather than with the total field in a matching point Finally you can obtain systematic errors that are hard to detect 240 5 gt ka 5 4 generate meta_ 14 20 computing_S field_ Ino E n s fieldl x y m e gt 0 EXIT sequ JM a angle 3 000E 01 fill plane_ 2 jix low left 19 A ER 1 00000E 00 vy_ 0 00000E 00 wz 0 000908400 cotal FPt 225 k 9 50000E 01 iz 0 00000E 00 tim 0 00000E 00 m0 1 00000E 00 Figure 17 3 Desk of the 3D MMP plot program showing the time average of the Poynting vector field for a plane wave incident on a thin wire 17 7 2 A Closer Look at the Errors Model 21 When you are curious about the total errors including the unmatched conditions you can proceed as follows 1 Load model 20 and adjust the wire with the command selecting 0 matching points per segment in the box Exp IE5 3D adjust wire
487. ul with your model for obtaining not too large errors This and similar models have extensively been studied and compared with other codes in 14 and 15 17 7 Thin Dipoles 17 7 1 A Simple Thin Wire Model 20 The thinner a dipole the more multipoles are required on its axis for modeling the scattered field outside Although very low maximum degrees of the multipoles and a very 238 Tes r generate meta 13 19 comput ing E field No E H S fieldi x y z Mjp gt O EXIT sequ M 41 AAA f sc 2 000E 00 A Sa Tl depth 2 0008 02 fix low left 19 ER 1 000008 00 wx 0 00000E 00 ivy_ 0 00000E 00 EN ftotal FPt 225 g ee y 4 000008 jz 0 00000E 00 ba cir jiter part a part type 1 Figure 17 2 Desk of the 3D MMP plot program showing the electric field for a plane wave incident on a lossy fat dipole rough model are sufficient in most cases the numerical expenditure certainly becomes too large For such problems the well known thin wire approximation which is used in many codes is much more efficient than an MMP expansion Thin wires are implemented in 3D MMP as a special expansion with the identification number 101 They consist of straight wires subdivided into a given number of segments It has been found that only the longitudinal component of the electric field should be matched in the matching points on the surface of a wire Moreover
488. ules and the factor of the overdiscretization box over Thus the question adj _automatically_ is asked first Then 132 adjust ALL poles__ is asked If you did answer the first question in the negative either all expansions or only the active expansions are adjusted as soon as the second question is answered If you want to adjust the poles automatically adjust_active_poles is asked when you answer the second question in the negative If you answer this question in the negative as well the pole with the number selected in the item box is checked and adjusted The message number_out_of_range indicates that no pole with such a number has been defined It must be pointed out that no other expansions than 3D multipoles can be adjusted automatically 3D adjust__ domain___ Adjust the material properties of a domain First select the domain number in the item box and the desired complex material properties r ur and o in the corresponding real data boxes Er Ei Ur Uil Sr Si where the character i indicates the imaginary parts 3D adjust__ constrain Adjust the additional data boxes Con and Con w of the constraint with the number selected in the item box NO_such_constraint_ indicates that no constraint with the selected number has been defined 3D adjust__ field_pts Adju
489. ultipoles because they are not helpful for modeling the scattered field 248 earls 5 A Tes Ela 1 generate meta 20l 27 computing S field_ No E a S ifieldl slylz up gt __ 0 EXIT sequ M 37 Re_Om 3 000E 08 ER 1 00000E 00 vx 0 00000 00 vy_ 0 00000E 00 yz_ 0 00000E 00 total FPt 225 z 0 00000E 00 iter part E m0 1 000008 00 Figure 17 9 Desk of the 3D MMP plot program showing the time average of the Poynting vector for a plane wave incident on a plate of finite thickness with a circular aperture two spherical fictitious boundaries around the aperture Since fictitious boundaries are quite arbitrary it is certainly reasonable to try different fictitious boundaries For doing that it is most convenient to save the 2D files used for generating the 3D models Equally when working with more complicated models it can be helpful to split the whole model into several parts that are saved on separate MMP_3DI files Like for all problems with rotational symmetry ring multipoles are very helpful for circular appertures Thus you should try this type of expansion here Moreover for solving the boundary conditions far away from the aperture you should try to write a connection file MMP_C40 040 containing the incident and the reflected plane waves with the appropriate parameters Finally it should be noted that the special 3D MMP feature called constraints is useful f
490. ure File MMP_Fyy xxx e 305 D 22 Windows Meta Files MMP_Eyy WMF and MMP_Pyy WMF 305 D 23 Main Program Log File MMP_MBD LOG o 305 D 24 Editor Log File MMP_E3D LOG o o e 305 D 25 Plot Program Log File MMP_P3D LOG 305 Overview of the Main Source 306 E 1 Subroutines of 3D MMP Main Program 306 E 2 Parameters and Variables in File COMM SRC gt COMM INC 310 Overview of the Graphics Source 316 F 1 Source Files of the 3D MMP Graphics Package 316 F 2 Elementary MMP Graphic Subroutines o o 316 F 3 Important Parameters and Variables in the Graphic Progams 320 Limitations of the Compiled Version 325 Gil Main Program cit a ds A 325 G 2 Parameter Labelling Program o o 325 G3 Fourier Programs rato Muted a BP Ohne od Pe a es eg 325 G4 Graphic Editor s oo e e086 ea ee eA ee eee 325 G 5 Graphic Plot Program ee 326 Preface When the concept of the MMP Multiple Multipole Program code was borne the in tention was to develop a numerical technique with a solid theoretical background which should allow to provide some information on the influence of well known assumptions made for obtaining analytical solutions I e the code should reliably and accurately compute relatively simple models with a reduced set of assumptions First the major
491. use the required information is missing in the description of the NDP tools Because of the insufficient support of Micro Way and because of the license required for the DOS extender we do not recommend this compiler anymore The GEMVDI interface for the NDP 386 compiler is included in the 2D MMP package 4 This interface should run with NDP 486 as well provided that the PharLap tools are used Microway NDP 386 compiler versions 1 4 and 2 0 for 386 or 486 based PCs This compiler is very similar to Microway NDP 486 with PharLap tools It should be noted that older versions of the NDP 386 compilers are not able to compile the GEMVDI interface included in the 2D MMP package 4 correctly For the same reasons as indicated above we do not recommend this compiler Meiko 77 compiler version 1 0 for transputer boards under HELIOS No graphic interface is available for this compiler Moreover the connection feature of the 3D MMP main program will cause the program to hang because the compiler does not handle the return addresses of subroutines properly Several 77 compilers under UNIX on SUN workstations CONVEX mini supercomputers etc No graphic interfaces have been written for these compilers but a separate 3D MMP graphics package written in C is available for SUN workstations 270 e VAX 77 compiler under VMS This compiler did not cause problems but it is not actively supported 271 20 Installation and Compilation Before
492. ut Although Micro Way supports 3L compilers the Videoputer library does 265 not support 3L FORTRAN Moreover the price of the Videoputer board with an ad ditional monitor is considered to be too high For these reasons 3D MMP does not support Micro Way Videoputers 18 3 i860 Number Smasher The Micro Way i860 Number Smasher is the fastest of the add on boards for PCs tested by the authors The most time consuming part of large 3D MMP computations i e the computation of the parameters runs about ten times as fast as on a transputer a PC 486 with 25Mhz clock or a PC 386 with 33MHz clock To reach about the same speed on a transputer pipeline more than 20 T800 25Mhz clock are required because the pipeline is not very efficient except for very large problems The i860 even outperforms mini supercomputers like the CONVEX C220 with two vector processors Since the i860 is a very demanding chip the i860 Number Smasher does not run on PCs with a weak power supply The authors have made excellent experience with the 40Mhz 32Mbytes version of the Micro Way i860 Number Smasher in a portable Toshiba T5200 with a small additional ventilator and in a Compaq Deskpro 386 33L Meanwhile many different i860 boards are available It seems that the Micro Way i860 Number Smasher is a good choice because of the excellent Micro Way NDP Fortran compiler running on this board The data transfer between the Micro Way i860 Number Smasher and the host is r
493. ut file msfi1 2 If msfil 0 the output file is only opened if an error or warning message is issued Although some additional output on the screen is very instructive it can considerably increase the turn around time on multiuser systems and on PCs when transputer boards are used or when the codes run under Microsoft Windows 10 3 3 Frequency cfreq is the complex frequency for which the problem is computed in a single frequency run For multiple frequency runs the frequencies are read from file MMP_FOU FRQ Note that cfreq is an ordinary frequency measured in Hz whereas the frequencies defined in MMP_FOU FRQ are angular frequencies 10 3 4 Symmetries The MMP program allows reflective symmetries of the scattering object about the planes X 0 Y 0 and Z 0 which are indicated by is1 is2 and is3 respectively If a scattering object is symmetric the scattering problem splits up into an odd and an even symmetry component with respect to that plane An MMP problem is solved for each of the symmetry components and the components are recombined during the evaluation of errors and field values Depending on the symmetry of the excitation either both or only the odd or the even component can be computed isi is2 and is3 may take the following values 53 isi is2 is3 Considered Symmetries 0 no symmetries about this plane 1 symmetry about this plane only the odd symmetry component of the problem is considered E 40 E
494. utation of errors and for the automatic determination of the domain in which a field point with given coordinates is lying Dummy matching points which do not contribute to the size of A may be added for these purposes 8 3 Multipoles Multipoles or simply poles are the most flexible expansions within the MMP code Their origins have to be set outside of the domain in which the field is modeled i e in the complementary domain If several poles are used for the same domain special care has to be taken to avoid dependencies between them A multipole is characterized by its region of influence i e the region within which it is able to efficiently fulfill boundary conditions For a full multipole this region is a sphere with a radius of 1 2 to 1 4 times the distance to the nearest matching point this number also grows with the order of the pole No other pole should be within this region without the danger of numerical dependencies The matching points within the region of influence are denoted as associated matching points A matching point is usually associated to one but not to more than two poles for the same domain For flat boundaries the maximum angle under which the set of associated matching points is seen from the pole should not exceed 7 2 The problem of finding origins for the multipoles can be visualized with a simple analogy Imagine the boundary of a domain being covered by as large as possible spheres or regions of influe
495. uted If they have solely been created for generating an integral you have to delete them 15 7 12 3D read___ Read 3D files 3D read___ window___ Read window file MMP_WIN xxx Select the extension number xxx in the item box The message reading window file is displayed as long as the corresponding file is read If either the file cannot be opened or if an error occurs when the file is read error_reading_ window is displayed and the process aborted 3D read____ errors___ Read error file MMP_ERR xxx Select the extension number xxx in the item box The message reading_error_data _ is displayed as long as the corresponding file is read If the actual number of matching points differs from the number in the error file wrong _number_of pts is displayed and the process is aborted If the error file with the number selected in the item box is not found the message error_file missing is displayed The error file has to be computed by the 3D MMP main program When it is read the matching points used when the error file was computed should be identical with the matching points that are actually defined in the editor Thus the corresponding input file should be read immediately before the error file is read Otherwise the error representation might be meaningless Although errors are results of the MMP main program that are usually visualized with the MMP plot program they are helpful when a model has to be
496. value you have to think about for the moment is MPt M el that defines the number of matching points on the element you want to add The best suited value depends above all on the size of the object with respect to the wavelength Larger values 217 result in a finer discretization larger computation times and more accurate results Because the predefined value 5 might be too small let us try the value 10 Click the first mouse button when the cursor is in the question information box once more Nothing seems to happen but set_center_in_win1_ is displayed in the top line Although you can put the center of the arc anywhere in the window keep in mind that you have to rotate the arc around an axis for generating the desired 3D sphere Since the predefined axis is the Y axis put the center of the arc on the Y axis Why not use the origin i e the center of the first window As soon as you have clicked the first mouse button the cursor coordinates are displayed in the boxes of the bottom line When the cursor is in the center the values 0 000E 00 should be displayed and you can release the button A small cross indicates the location of the origin and set_start_point_win1 in the top line indicates that you have to select the start point of the arc in window 1 This point should be on the Y axis as well Since this point defines the radius r of the arc put it a the position Y r If you press the
497. vector represented by an arrow and of grid lines color plane_ color of plane in field point color z comp color of n component perpendicular to plane color T comp color of tangential components 190 color 3Dtria color of 3D vector represented by triangle color shadow color of shadow of 3D vector triangle color grid__ color of grid representation of scalar fields When negative numbers are selected the borders of the corresponding element will not be drawn The colors corresponding to the different color numbers depend on the number of colors available and on the definition of the colors in the desk file MMP_P3D DSK For monochrome drivers all color numbers bigger than 1 have a similar effect as color number 1 but some graphic systems add fill patterns that should simulate the different intensities of different colors For this reason only color numbers 1 0 1 should be used in conjunction with monochrome drivers Many screen drivers support only 16 colors and in the desk file the color representa tion of the colors with the numbers 0 up to 15 are defined Thus the numbers 15 15 are reasonable Box 31 Particle Real data Type pull down input output m0 mass qe electric charge fr friction constant x x coordinate of position global coordinates y y coordinate of position global coordinates z z coordinate of position global coordinates vx x coordinate of velocity vector global coordinates vy y coordi
498. ver for running the compiled 3D MMP version included in this package a 486 machine or a 386 machine with 387 numeric coprocessor is required A reduced version of 3D MMP for XT compatibles is available upon request It is well known that an abacus like the Weitek 1167 3167 etc can be used to increase the numeric speed of a PC 386 or 486 Some of the compilers used by the authors support Weiteks but the experience of the authors with an 1167 in an Olivetti M380 XP5 was not encouraging Fast add on boards see below are considered to be much more helpful 3D computations require not only fast processors but also enough memory The 640kbytes of memory that can be used under MS DOS is sufficient for relatively small applications only Since memory has become cheap most PCs have more than 640kbytes of memory For handling this some DOS Extender and an appropriate FORTRAN com piler is required Useful FORTRAN compilers that can handle extended memory work on 386 and 486 machines only Concerning the 3D MMP graphics 4Mbytes including 640kbytes real memory of memory have been found to be most appropriate and sufficient for modeling large problems Moreover 4Mbytes of memory is sufficient for computing medium 3D problems with the 3D MMP main program It should be mentioned that one can generate codes for machines with only 2Mbytes of memory 640kbytes real memory 1 36Mbytes extended memory but on such a machine it is difficult to compile large cod
499. verse magnetic with respect to the longitudinal axis of the problem In order to reduce computation time and avoid dependencies among the expansion functions only the E or H parts of the expansions may be used in these cases 8 8 Validation Validation of the model as an idealization of reality and validation of the computation of a particular model are two different things While the first is clearly beyond the scope of this document the 3D MMP code provides good facilities for the second The norm of the residual vector p n is a direct result of the updating algorithm and can give a first assessment of the overall error of the solution and of the error contribution of the symmetry components The error distribution a graphical representation of the errors in the matching points shows in which parts of the model the solution is good and in which it is poor It is a good basis for optimizing models Moreover the error between the original matching points can be computed with dummy matching points e g near edges corners or ends of wires However this is usually not necessary Field plots give a good impression of the qualitative correctness of the solution Es pecially animated plots are very instructive and facilitate considerably a deeper under standing of what happens Critical regions can quickly be zoomed in Convergence of the parameters of a multipole can show whether it is sufficient to model the field and whether the order o
500. vert __ invert item lt check replace arc by its complement if the item is an arc 2D only otherwise check item adjust __ adjust item generate generate item read____ read item write___ write item Select regular action to be performed when the first mouse button is clicked in one of the windows For more information see description of regular actions Box 10 Dimension for Regular Actions Type pull down 2D two dimensional construction 3D three dimensional construction 145 Select dimension of regular action to be performed when the first mouse button is clicked in one of the windows For more information see description of regular actions Box 11 Items for Regular Actions Type pull down input output points___ vect axis window ___ parts____ object___ domain___ constrain field_pts integrals errors___ 2D line set of equally spaced matching points on a line During 3D constructions the contents of this line is changed to 3D wire expansion type number 101 2D arc set of equally spaced matching points on an arc matching points vector or axis used for several constructions move rotate etc and vector representation of lines and arcs during 2D construction screen or plot window parts of 3D objects part of object 1 inside object 2 etc object containing matching points and expansions expansion domain constraint general plot set of field points integral errors on matching points contain
501. vertical movement of the cursor will affect this value The actual height is displayed in the box containing the Cartesian Y coordinate as long as the mouse button is pressed down If you did use method 1 to discretize the origin set_end_point_data_ indicates that you are expected to give the coordinates of the end point of the first tangent vector in the same way I e select the global 3D coordinates in the three boxes containing the Cartesian coordinates and click one of the windows when you want to enter these data If you did use method 2 to discretize the origin set_end_point______ indicates that you are expected to discretize the end point of the first tangent vector in the same way as the origin Of course you will be asked set_height_above_pln if you apply method 2 Needless to say that you are expected now to discretize the end point of the second tangent vector similarly set_2nd end point_ Of course you will have to set_height_above_pln once more if you are working with method 2 172 Add a new particle You are asked set_r v_manually _ When you answer in the affirmative you will have to set the origin and the velocity of the particle exactly as indicated in the command adjust axis Otherwise the data in the boxes x_ vx etc are used The error message too_many_particles_ indicates that the domain cannot be added because the maximum number of domains would be exceeded Whe
502. vie yy in the first two boxes of the top line where yy is the number of the movie and click one of the windows with the first mouse button First all pictures of the first sequence of the movie are shown Usually the sequence is repeated starting with the first picture when the last picture has been shown If the number of sets of a sequence has been negative when the movie was generated the sequence is shown in forward backward mode i e you will see the pictures 1 2 n n 1 n 2 2 1 2 rather than This procedure is repeated until the second mouse button is pressed After the last sequence of a movie the first one is started again To stop this process press the third mouse button When the first mouse button is pressed the movie is stopped until the button is released Afterwards the movie is continued The performance of movies with a large number of pictures is sometimes not very smooth due to a varying time required for accessing the different files MMP_Fxx yyy To overcome this problem the DOS command FASTOPEN should be used before the graphic output program is started 16 8 7 Slide Shows The speed of hard disks on PCs is not sufficient to show color movies when the correspond ing window contains a reasonably large number of pixels For example on a portable Toshiba T5200 with a 80386 processor with 20MHz clock and a VGA monitor one can show about 1 picture per second Although this is too slow for
503. w coordinate of the window plane Wdh_ drawing depth perpendicular to the window plane nrm scaling factor for length of normal vectors in matching points err error scaling factor wLin unit line width in thousandth of screen width When you perform the command show window this box displays the real data of the screen window selected in the item box To change the real data of the screen window you can modify the values in this box with the first count up and second count down mouse button and perform the command adjust window afterwards Before you do this it is a good idea to perform show window This makes sure that you have all actual data of the window in the box Box 5 Integer Data of Screen Windows Type pull down input output ix11 lower left corner horizontal position on the screen in pixel coordinates iyll lower left corner vertical position on the screen in pixel coordinates ixur upper right corner horizontal position on the screen in pixel coordi nates iyur upper right corner vertical position on the screen in pixel coordinates 143 horizontal resolution number of invisible grid lines vertical resolution number of invisible grid lines number of screen windows Change this value with the commands add window and delete window actual screen window number Change this value with show window boxes in meta files 1 show boxes 0
504. wards If you answer the latter in the affirmative the command blow wind is started see below Blowing field values can be helpful when very large or very small values are obtained during iterative procedures blow____ wind Blow the limits of the window with the number selected in the item box When no such window exists cannot_blow_window_ 175 is displayed and the process aborted Since you can blow the window either with the factor selected in the blow box or graphically by selecting a rectangular part of the actual window you are asked blow_with_factor____ If you answer in the affirmative the window limits are multiplied with the blowing factor Otherwise the message set_new_limits____ indicates that you have to press the first mouse button when the cursor is at the lower left corner of the area in the window that shall become the new lower left corner Release the button when you have selected an appropriate area of the window The error message square must_be_ gt _0_ indicates that you have to select a square are with positive side lengths Note that it might be difficult to undo this action and that it essentially consists of both moving and blowing with a factor smaller than 1 the window limits 16 5 10 invert invert__ axis_ Invert the direction of the vector respectively axis used in several constructions and the direction of the light vector that is used f
505. window limits or the window corners i e the physical size of a window on the screen According to that you are asked blow_window_corners and blow_window_limits_ The second question is asked if a screen or a plot window with the number selected in the item box exists whereas the first question is only asked if a screen window with the selected number exists If neither a screen or a plot window with this number exists cannot_blow_window_ is displayed and the process aborted 125 3D blow____ object___ Blow object 1 or 2 i e the matching points and expansions If the number selected in the item box is neither 1 nor 2 both objects are blown The procedure with the corresponding questions and messages is described above 3D blow____ pole_____ Blow active expansions 15 7 7 3D rotate _ Rotate 3D elements around an axis For safety reasons you are asked rotate_elements_0K_ when you try to rotate anything Answering this question in the negative will abort the process with the message process_aborted____ Set the rotation angle in degrees in the additional real data box angle The axis is used for several regular actions and can be manipulated with 3D adjust vect axis If you did forget to set the axis appropriately you get the chance to do that by answering the question set_new_axis_ _ _YES in the positive In this case a simplified 3D adjust vect axis procedure is p
506. window with the same limits and plane as the plot window is created and stored in a window file MMP_WIN xxx When this file is read in the plot program the origin is in the lower left corner as desired This method has another drawback The window is placed in the plot program at the same position on the screen where it was in the editor and this might not be appropriate However these problems are considered to be of minor importance 14 5 Mouse Use and Actions The mouse is used above all to move the cursor to the desired location on the screen One can distinct the following areas on the screen e windows e text area of boxes e value area of boxes e outside windows and boxes The meaning of the mouse buttons depends above all on the area where the cursor is and on the contents of the question information box Unlike in typical Windows applications the mouse cursor never changes its shape Before you start any action you should make sure that all necessary additional data required by the action have been properly defined and that the program is ready Le check the following 1 Make sure that the program is ready for starting a regular action i e 1 it is not performing an action started earlier 2 it is not asking a question i e there is no question mark in the question information box 3 it is not waiting for an action of the user i e there is no exclamation mark at the end of the question information box except wh
507. with typical Windows applications 2 Taking advantage of the large number of Windows graphic elements would considerably reduce the portability of 3D MMP The number of graphic functions required for 3D MMP is so small that a high portability is guaranteed This is considered to be very important for future developments However experienced Windows users should read the following rather than trying to handle 3D MMP like a typical Windows application The editor has been especially designed for generating and modifying input files re quired by the 3D MMP main program MMP_M3D Although any 3D MMP input file can entirely be generated and modified with the editor it sometimes is reasonable to modify the input files with usual text editors The 3D MMP plot program is designed for representing the plot files generated by the 3D MMP main program but it might be helpful for users of other numeric codes that are able to compute 3D electromagnetics as well Moreover it contains a large number of iterative algorithms Mandelbrot and Julia sets cellular automata like 2D and 3D life several FD and FDTD procedures moving particles for testing and for tutorial purpose Finally the interfaces and the graphics library is certainly interesting for all FOR TRAN programmers looking for nice almost device independent graphics on PCs 14 2 Introduction The 3D MMP graphic interface provides an easy way to prepare input for the 3D MMP main program and to view
508. with four digits that is defined in the box iter info Standard 2D life is characterized by the number 2333 7 3D life An extension of 2D life A cell has 26 neighbors i e four numbers with two digits each are required Since useful results are obtained for relatively small numbers only the same notation as for 2D life is used Above all try the versions 4555 and 5766 8 Julia Computation of the famous Julia set The Julia set is closely related to the Mandelbrot set It depends on a complex number that has to be defined in the boxes Re_Ga and Im_Ga The set is computed in the complex plane The complex plane is the xy plane Reset the field to the position vector with clear pic f 1 for a relatively large number of grid lines in horizontal and vertical direction iterate and show the scalar potential 208 e 9 3D FDTD 7 point operator electrodynamics without absorbing boundary con ditions The imaginary parts of the material properties are ignored in this proce dure Instead of absorbing boundary conditions simple boundary conditions are implemented here in such a way that 2D electrodynamic problems can be computed with the same algorithm The incident field is a plane wave propagating in X direc tion Sources of the field are assumed to be in field points on the left border The amplitude of the incident H field is 1 the amplitude of the incident H field is equal to t
509. xcitations the specified number usually is equal to or greater than zero It is used as extension for both input and output files If it is less than zero it will be set to zero If multiple excitations have been defined in the input file the single frequency option has to be selected because multiple excitations are incompatible with multiple frequencies In this case the output files parameters errors plots etc will be numbered from 000 to one less than the number of excitations Already existing files will be overwritten For multiple frequency computations if the specified number is equal to or greater than zero this input file is used for all frequencies but the extension for the output files loops from 0 to nome nome is specified in file MMP_FOU FRQ If the specified number is less than zero the extensions for both the input and output files loop from 0 to nfreq In this way different input files and consequently different models can be used for the different frequencies If the corresponding input file is missing the input file from the last frequency step is reused i e only one input file MMP_3DI 000 is necessary The output files will be numbered and overwritten like for multiple excitations 51 10 Input 10 1 General Remarks The main task in using the 3D MMP code is generating a reasonable input file MMP_3DI xxx For more special problems connection files MMP_Cyy xxx and frequency files MMP_FOU FRQ are also needed T
510. xes colors etc in the 3D MMP editor This file is searched first on the current directory then on the directory MMP of the current drive and finally on the directory MMP of drive C If it is missing the editor cannot be started nWin number of windows iWin1 6 x and y coordinates of lower left corner x and y coordinates of upper right corner resolution in x and y direction invisible grid lines nBox number of Boxes iBox1 5 x and y coordinates of lower left corner length of text area in characters length of variable area in characters number of lines contained in the box if negative the initial status of the box is active bright and the absolute value indicates the number of lines BoxInt BoxRea initial integer and real value of the current line BoxTxt initial text area of the current line The following line is repeated 16 times for the colors 0 15 irgb1 3 red green blue intensity of corresponding color icolr color of windows and inactive boxes 301 icole color of 2D element lines and arcs icolb color of the axis and vector icolc color for the pole check icolv color of pole dependences and active boxes icolobj 2 2 colors used for 3D objects icolpar 4 4 colors used for parts of 3D objects icoldom 2 2 colors used for domains icolb color of the axis and vector icolb color of the axis and vector icolpol color of poles expansions icolchk 4 4 icolerr 0 9 icolmat 1 1 colors for mat
511. y would like to generate a movie for illustrating how the field changes For doing this you have to write a simple directive file This might look like this seg 1 enddir 1 parts 20 pictures drwpic incfrq enddir end The most important directive is incfrq i e increase frequency Of course the fre quency is identical for all excitations in this case But incfrq essentially increases the file extension number of the plot file in the Fourier case this corresponds to an increase of the frequency Note that you have to read the first plot file MMP_P00 000 and to select the appropriate field representation before you start generate movie because the di rectives indicated above do not contain any initial directives Moreover the directive 20 pictures means that you have 20 excitations i e the files MMP_P00 000 MMP_P00 001 etc up to MMP_P00 019 In the input file included in the package only two excitations are defined 17 13 Field Lines Model 31 When you study the electromagnetic field of the models 18 and 19 you will notice that the time average of the Poynting vector behaves quite complicated although the models are very simple From the vector plots it is hard to imagine how this field really looks like The plot program includes a feature called pseudo particle that is very useful for visualizing such fields Pseudo particles are non realistic particles without mass and charge that simple follow the l
512. y active expansions 15 7 5 3D move____ Move 3D elements to a new position For safety reasons you are asked move___elements_OK_ when you try to move anything Answering this question in the negative will abort the process with the message process_aborted____ All 3D move commands are used to move the items from the original location to a destination Thus a vector that points from the original location to the destination is required This vector is used for several regular actions and can be manipulated with 3D adjust vect axis If you did forget to set the vector appropriately you get the chance to do that when you answer the question set_new_vector _YES in the positive In this case a simplified 3D adjust vect axis procedure is performed before the 3D move command is executed you have to set the start and end point of the vector respectively axis during this procedure 3D move____ wire_____ Move active wires 3D move____ points___ Move active matching points 3D move____ window___ Move a window A window is a relatively complicated thing It can be either a screen or a plot window Both window types contain a plane that can be moved like a matching point I e one can move the origin of the plane with a 3D vector Moreover the limits of the window i e the real window coordinates of the window can be moved This is equivalent
513. y installing 3D MMP according to the fifth part and to try solving the problems discussed in the tutorial i e part four This should be possible because the structures of the 3D code and of the 2D code are similar The tutorial contains some very simple examples that are not very time consuming Nonetheless it explains all important features of the code and outlines some useful tricks Finally part six contains some more detailed information that is important for those who intend to modify parts of the code The package contains the source of 3D MMP with all essential files and auxiliaries for compilation with Watcom FORTRAN the corresponding graphic interface to Microsoft Windows 3 all executables for running 3D MMP on a 486 or 386 machine with nu meric coprocessor 4Mbytes or more memory under Windows and the source necessary for running the 3D MMP kernel on a transputer pipeline in parallel In addition a graphic interface for running 3D MMP under Microsoft DOS with GEM a product of Digital Research Inc auxiliaries for running 3D MMP on the Micro Way i860 number smasher including graphic interfaces to Windows and GEM a graphic interface for T800 transputers under DOS with GEM versions for other machines and configurations etc are available We would like to thank all our colleagues who actively supported our work Last but not least we would like point out that the excellent graphic interfaces to GEM and to Microsoft Windows 3 0 h
514. y matching points there Thus you have to model only a small part of the plate around the aperture see fig 17 7 Of course you can compute apertures of different shape but to start with we try a circular aperture The main advantage of a circular aperture is that it can easily be generated with the 3D generate torus command A circular aperture in a plane plate has three perpendicular symmetry planes but as soon as a fictitious boundary is introduced at least one of these symmetries goes lost Of course the fictitious boundary is chosen in such a way that only one symmetry goes lost Despite of its simplicity and of the two symmetry planes more than 100 unknowns are required for solving this problem Since all models in this tutorial are designed for small computers that are not able to solve systems of equations with more than 100 unknowns inaccurate results are obtained In some matching points you get even more than 100 percent errors Nonetheless the results are not completely wrong see fig 17 8 and a useful technique is demonstrated It is assumed that users working with reasonable machines are able to get much more accurate results 246 r E i T generate meta_ 19 25 computing S field_ Ivo p H s field1 Txlylz uP gt o EXIT fill 3Darrow 2 lcolor 3Darr 1 ee z 9 500008 01 y 4 00000E 01 AA z 0 00000E 00 EAN crer part gt part type 1 m0
515. y or indirectly with the command 3D show parts cannot_delete_part_ indicates that you have selected either a part number less than 1 or bigger than 4 There are no more than 4 parts because each of the two objects has two parts inside and outside the other object 3D delete__ object___ Delete object If the number selected in the item box is either 1 or 2 the corresponding object is deleted Otherwise you are asked delete ALL_objects_ If this question is answered in the negative nothing is deleted and the message process_aborted____ is displayed Otherwise both objects i e all matching points and expansions are deleted 3D delete__ pole_____ Delete active expansions 3D delete__ domain___ Delete the domain with the number selected in the item box 3D delete__ constrain Delete the constraint with the number selected in the item box no_such_constraint_ indicates that the process has been aborted because the constraint to be deleted does not exist 121 3D delete__ field pts Delete the set of field points with the number selected in the item box no such field points indicates that the process has been aborted because the set of field points to be deleted does not exist 3D delete__ integrals Delete the integral with the number selected in the item box no_such_integral__ indicates that the process has
516. you get several warnings but you find a location where 3D lt check points does not show active matching points and where 3D lt check pole issues only a warning of minor importance indicating that the or ders are too high This problem can easily be eliminated with the automatic routine built in the command 3D adjust pole When you take care of the orientation of the multipole as you have done before you should get either more accurate results with the same computation time or about the same accuracy with less computation time The effect is not very large because the deformation of the body is still moderate But when you continue with more complicated bodies an MMP i e Multiple Multi Pole expansion is much better than a single multipole expansion Nonetheless it is not always easy to find an appropriate MMP expansion Note that it is not necessary that the checks men tioned above do not issue any warnings These checks indicate violations of some simple rules that might cause problems leading to inaccurate results Since the automatic pole generation routines never violate these rules they usually generate too few multipoles and you have to modify the proposed MMP expansions if necessary When you look at the error distribution obtained with the two multipoles on the X axis you find that the maximal errors are obtained near the plane i e between the two multipoles when the multipoles are i
517. you should set a sufficiently fine grid and set the field on the grid to appropriate initial values with clear pic f For the beginning 20 horizontal and 20 vertical grid lines on one level will be sufficient Before you start any FD algorithm you can reset the field to zero with clear pic f 0 This command not only sets all field and potential values to zero in all field points but it also sets the domain numbers FPt_dom iF of all points to one The predefined material properties of this domain are the properties of free space ER 1 EI 0 UR 1 UI 0 SR 0 SI 1 Note that the imaginary parts of the permittivity permeability and conductivity are unused in all of the predefined iterative procedures Since we are in electrostatics now only the real part of the permittivity ER has an effect When you previously have read in domain data with one of the input or plot files you now might have more than one domains and domain number one might not be free space You can use the commands adjust dom _ add dom _ delete dom _ etc for defining the domains Note that you do not have to define the material properties of ideal conductors electrodes since this is domain number 0 like in the 3D MMP main program In the FD procedure the potential in all points with domain number 0 is left unchanged After having defined
518. yy xxx or MMP_PLT xxx file To perform this command the files MMP_Tyy xxx MMP_Pyy 000 and MMP_3DI 000 or MMP_PLT xxx must be present iles ii file number yy if i1 gt 1 use 2D plot file if i1 lt 0 i2 time step number xxx i3 use window defined in MMP_Pyy xxx if i3 gt 0 setphi set phase wt of time harmonic fields ri phase in degrees setaxi set axis for rotations Td 6 global Cartesian coordinates of origin and tangent vector setpln set window plane r1 9 global Cartesian coordinates of origin r and tangent vectors Uj U2 198 setwin ri seteye ri setwdh ri setndh il setrep il setavr il setvec il setfil il 4 9 7 set window limits local 2D Cartesian coordinates on widow plane of lower left and upper right corners set eye distance for perspective projection distance of the eye above the window plane use a negative value for parallel projection set width drawing depth of window width only objects with distance less than r1 from window plane are shown set number of slices for hiding number of slices 0 no hiding 20 50 recommended set field representation 11 0 1 E we Pe je D turned off on i2 0 1 Wm Pm En X B turned off on i3 0 1 S field turned off on i4 1 2 3 field1 energy power current field2 i5 0 1 t1 component turned off on i6 0 1 t2 component turned off on i7 0 1 n component turned off on i8 0 1 matching point representation turned off on
519. ze arrays of the 3D MMP main program are too small for the problem specified in the input file s You have to solve a smaller problem or use a version of the program with larger arrays see sections 20 3 2 and E 2 Errors in Input Data expansion not implemented An expansion number ie1 is wrong domain number out of range The domain numbers have to be chosen in the range 1 ngebm domain with zero permittivity domain with zero permeability Warning that e or ur respectively are equal to zero for a domain 69 wrong expansion parameter ie2 The parameter ie2 of an expansion is wrong zero frequency not possible The frequency of the current problem is equal to zero Static problems have to be computed with a low but non zero frequency wrong integral type The integral type inttyp in the input file is not defined no scaling integral No scaling integral is specified in the input file even though inorm is not equal to zero Miscellaneous Errors expansion does not match symmetries excitation does not match symmetries An expansion has no symmetry adapted components and therefore completely disap pears This is fatal for an excitation cylindrical bessel function returned error message The cylindrical Bessel functions have not been computed exactly enough The reason can be an extreme argument or that the array for recurrence has not been large enough Try a version with a bigger parameter nordm see sections 20 3 2 and E 2

Hafner-Bomholt-the 3d electrodynamic wave simulator-1993-17

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