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1. This creates the files ex_y25_tl5 jpg amp ex_y25_t30 jpg The jpg is automatically added to the file name when the image file is created Here are the images Output Time Step 15 Output Time Step 30 y z direction y z direction 10 20 30 40 50 i 10 20 40 50 30 x y direction x y direction To save space on the page the colorbar was cropped from the Output Time Step 30 image Because the slice is at y 25 the horizontal axis corresponds to the x direction and the vertical axis corresponds to the z direction Sample Simulation 2 Spiral Antenna The spiral antenna simulation uses a material input file psi_spiral dat for the antenna It also uses a user defined source which requires the user to define excitation points and directions Here we will show how to determine what the excitation should be The input file contains the text 165 165 61 grid size 089 089 089 grid cell size in cm 6000 number of time steps LOOOE 11 Time step size sec 0 Number of new materials 1 Number of background layers 1 Material type of layer 1 1 Number of objects built in objects amp material files 0 Object type psi_spiral_frsp dat Material input filename 3 Orientation 31 Height 5 5 Starting point x y 157 157 Width x y 2 Number of material output files printed 3 31 direction location of material output file 1 79 direction location of material output file
2. Building Material Distributions A big advantage of FD techniques is that any grid point can contain any material which allows arbitrary material distributions to be modeled This does mean that one could build material distributions that are completely unrealistic such as a layer of air between two soil layers Itis up to the user to ensure that the simulated material distribution is accurate While FDTD makes field calculations with arbitrary material distributions routine building those distributions can be challenging This code features two techniques for building material distributions background layers and foreground objects One important point to remember when building material distributions is that FDTD treats features diagonally adjacent as being separate pieces for a feature to be treated as one continuous piece it must be connected horizontally vertically 1 e one must be able to move a chess rook along it Thus in the figures below the green feature on the left will be treated as two separate pieces whereas the red feature on the right will be treated as one continuous piece This point is particularly important when designing antennae because fields can get through metal antenna pieces that are not connected horizontally vertically even though this is not physically realistic Background Layers Input The first means of building material distributions is through background layers This feature was initially
3. the simulation will run automatically How to input is explained in the Using The Command Window section the input parameters are explained in the Input Parameters section 3 View the output files Output files are the simulation s results How to view the results is explained in the Viewing Output Files section How To Run The Code The code was developed using the software application Microsoft Developer Studio Fortran PowerStation 4 0 If further work is done using different software then instructions for running the code through the software may vary No matter what software is used the code can be run by double clicking on its executable file nufdtd exe If the code was previously ran through PowerStation then the executable file may appear in the Debug folder If changes to the code have been made since the previous time it was run then the code needs to be recompiled The code is automatically recompiled if it is executed from PowerStation To execute the code from PowerStation choose Execute nufdtd exe from the Build menu at the top of the screen or hit Ctrl F5 Using The Command Window Command Window Basics Input in the code is entered via a text based command window interface This interface asks the user a series of questions which the user types in and then hits Enter to progress to the next question Answers to previous questions cannot be changed Instead to correct earlier errors t
4. 1 i 1 j k 1 Eg 1 j k 1 F fx a i y E i 1 j K i 1 j k i j 1 K H i j 1 k k ADS i 1 j K E i j 1 k i 1 j 1 K Field Components Material Point Relationships Using the previous Yee cube images the location of a field component can be determined from its grid coordinate For example Ex 11 23 4 1s between the material points 11 23 4 and 12 23 4 Hx 11 23 4 is between the material points 11 23 4 11 23 5 11 24 4 and 11 24 5 While field components are located between multiple material points for the code s calculations each field component is linked to a single material point the grid point in the direction of the origin 1 e the grid point found by subtracting 1 2 from all of the shifted coordinates i1 j 1 i K Te i j 1 k 1 1 Fa PA y i 4 K lijo Ki 1 j 1 K Thus the code behaves as 1f the field components linked to a material point are in regions composed of that point s material This is done to avoid the memory inefficient measure of creating separate matrices of material points for each field component Overview Of How To Perform A Simulation There are several steps necessary for performing a successful simulation These are 1 Run the code This starts the simulation and opens the command window How to run the code is explained below 2 Input the simulation parameters into the command window Once the parameters have been inputted
5. 2 Source type 4 Number of excitation points 82 80 31 Excitation point coords 1 00 1 00 00 Directional exn strengths 82 79 31 Excitation point coords 2 00 1 00 00 Directional exn strengths 83 80 31 Excitation point coords 3 00 1 00 00 Directional exn strengths 83 79 31 Excitation point coords 4 00 1 00 00 Directional exn strengths 2 Pulse shape 50 0 Gaussian pulse width time steps 200 0 Gaussian peak time time steps 1500E 10 Pulse frequency 20 Number of time steps between outputs 4 field component slice series 5 1 78 Specs field component slice 4 53 31 Specs field component slice 2 53 29 Specs field component slice 6 53 15 Specs field component slice 5 Sample Simulation 2 Spiral Antenna Continued If we didn t know the coordinates of the excitation points we could figure this out from a plot of the antenna To do this first run the code and paste the input through the material output files section a MATERIAL OUTPUT FILES How many material output files to print i Number of material output Files printed Enter direction location of mat out file First number direction 1i x y z plane gt 2 y 3 2 Second number location slice coordinate 3 31 direction location of material output file Then from MatLab plot the material output file Note that the file is of the slice that the material input file which contains the antenna was placed
6. 40 60 80 100 120 140 160 x y direction The companion codes use MatLab commands to rearrange the data flipud and image axis xy to achieve this Plotting the above image without these commands gives an image with the same appearance but with a different coordinate system 10 20 30 40 50 60 20 40 60 80 100 120 140 160 The bottom image s coordinates printed without altering the data match those of the actual matrix as long as 1 j matrix coordinates vertical horizontal are used as seen in the following lines Here gold is positive and blue is negative 0 0116 gt gt 60 50 777 Index exceeds matrix dimensions gt gt E 10 80 gt 50 880 ans em Ulz ans Field Component Locations In FDTD electric and magnetic field vectors are broken up into components in the x y and z directions These field components are all defined at each grid point Thus there are a total of seven separate 3D grids Ex Ey Ez Hx Hy Hz and the material distribution The field component grids are actually 4D because they also vary with time This FDTD code does not handle time varying material distributions although such a scheme is possible with FDTD For subtle reasons not discussed here field component points are not located at the same places as each other or the material points The electric field components are shifted half of a grid cell in one direction the same direction as the field compo
7. ASEE E T File Edit Format View Help 0015305420000000 0017168280000000 0020747850000000 0022388210000000 0025175500000000 0026246890000000 0027572750000000 0027768210000000 0027109880000000 0026225710000000 0023313470000000 0021289070000000 0016154290000000 0013079480000000 0006035692 O00000 00021 258684 000000 0006293384000000 0010734820000000 0019891850000000 0024532950000000 However text editors typically use i j coordinate systems in their line column or row column designations as seen here in the bottom right corner of this screenshot from Microsoft Developer Studio Microsoft Developer Studio nufdtd3d C ey_n078_bO20 c Ioj x File Edit View Insert Build Tools Window Help x aema He 0000246298900000 0000382965000000 0055687240000000 0062152010000000 04374518000000 0003096296000000 0000303719400000 000 0427781300000 QOO65S5S05680000000 0068977360000000 05104451000000 0003813773000000 b d Ready Lao Cot 2 As text editors can be a useful means of analyzing files such as for determining where to place excitation points for antennae built from material input files understanding text editor coordinate systems can be important MatLab Coordinate Systems The MatLab companion codes produce images oriented in the same fashion Output Time Step 20 60 50 40 30 20 y z direction 10 20
8. E is for exponential Here aEb a 10 so for example 1000E 11 10 Input Parameters The code groups its input into several sections For example the previous image shows part of the Time Dimensions input section The following user manual parts describe each of these input sections in the order in which they appear in the command window 1 2 3 4 5 6 7 8 Space Dimensions Time Dimension Create New Materials Background Layers Foreground Objects Material Output Excitation Field Component Output Sections and 2 define the FDTD discretization Sections 3 4 and 5 define the material distribution Section 7 defines the electric field excitation Sections 6 and 8 define the portions of the material and field component distributions to save to the hard disk for analysis Space Dimensions Input Two sets of numbers are required to define the FD grid e grid size in each direction nx ny nz e grid cell size in each direction Ax Az Az dx dy dz or delx dely delz The grid size variables represent the number of grid points in each direction and are unitless quantities The grid cell size variables represent the size in each direction of one grid cell 1 e how far apart the grid points are and are measured in this code in centimeters Other FDTD codes may use other units of distance In FDTD the amount of computer memory RAM required to run a simulation 1s roughly proportional to the
9. Output Files Directly Material or field component output files can be viewed directly by opening them up in a text editor word processor spreadsheet or other program The material or field component points will be oriented in the scheme described in the Coordinate Systems section with the origin in the bottom left corner If the program includes a system for assigning coordinates to points in the file it may be possible to use these coordinates to determine what grid points values in the file are from However there may be several complications to this procedure First many programs place the origin in the top left corner in which case the values it gives for the y z vertical direction will be wrong Also while spreadsheets will typically place each value in a cell word processors generally count in the x y horizontal direction by column character by character meaning that column number will not correspond to grid coordinate At best the column number may be a multiple of the grid coordinate Finally line wrapping will occur if there are more points in the x y horizontal direction than can fit on one line in the text editor further complicating the relationship between grid points and points in the program in use Here is a screenshot of part of a material file viewed in Microsoft Notepad Eid _y025 dat Notepad Ioj x File Edit Format View Help bk KE PERPRBRBPERBRERBBBRBBRBEBEEEKEFR 1n n on aon LA aA A LA A a
10. To do this use the program mt_readplot m Then zoom in on the center where the excitation is supposed to go id z031 dat material distribution at z 31 82 81 oo am y z direction D 78 uf 76 5 77 775 78 785 79 795 80 805 x y direction Using the material i d number system we can tell that blue is free space and red is metal The excitation goes in the free space between the bottom and top pieces of metal Because the image shows a z direction slice we know that the horizontal axis corresponds to the x direction and the vertical axis corresponds to the y direction Because the slice is at z 31 it s clear that the excitation coordinates are 78 79 31 78 80 31 79 79 31 and 79 80 31 Also we can see that the path between the two pieces of metal is in the y direction so the excitation points should all have the directional excitation strengths are all 0 1 0 O 1 0 would also work The rest of the simulation follows from the previous Sample Simulation and will not be discussed further
11. files include fc_read m read in field components output files fc_animate m animate field component matrices mt_readplot m read in amp plot material files mx_getval m get Cartesian coordinate value of a 2D matrix Further information about these files is available in the files themselves or through MatLab s help command For example to view information about fc_read m first go to the file s directory using the cd change directory then type help fc_read Sample Simulation 1 Monopole Antenna Here we ll walk through the simulation of a simple monopole antenna from the input through visualization of the results The first thing to do is run the simulation either double click on the executable file nufdtd exe or execute it from the code development software such as Microsoft Developer Studio Fortran PowerStation The input file contains the text 50 50 90 grid size 089 089 089 grid cell size in cm 1000 number of time steps LOOOE 11 Time step size sec 0 Number of new materials 1 Number of background layers 1 Material type of layer 1 1 Number of objects built in objects amp material files 4 Object type 25 25 70 Gj k of antenna top center 1 5 3 Core radius dielectric thickness amp shield thickness 50 45 Dielectric core length shield length 2 Number of material output files printed 2 25 direction location of material output file 3 30 direction location of mat
12. grid size If the grid size is too large for a computer s RAM then the simulation will use paging file and run extremely slowly If the grid size is too large for a computer s RAM paging file then the simulation will not run The code allocates a fixed grid size in each direction and the grid size cannot be set to anything larger without changing this allocation and recompiling the code Smaller grid sizes can be run without changing this and recompiling The grid size allocation is changed by changing the grid size numbers at the top of the code s parameters file prerr EE EEE SEE eee ee eee eee ee E c FFF These parameters are case specific and need to be manually entered prerr SEE EEE EEE EE Ee ee ee Ee ee ee eee F parame t r npx DH Grid size parameter i i of soil layers parameter npexcnpts 99 Number of excitation points npexcnpts 15 arbitrary 1f a built in antenna 1 e monopole 1s used parameter npout 99 Number of output files per output time step Time Dimension Input The input for the time dimension is similar to that for the space dimensions because similar to how it handles space FDTD discretizes time in uniform intervals or time steps There are two values to input e Number of time steps to run the code nts e Time step size dt or At nts is unitless dt is measured in seconds nts dt time in seconds the code will simulate The code runs one time step at a time scanning
13. material number 5 dielectric modeled as dispersive soil for this The outer cylinder the shield is also made of metal The core and dielectric have the same height the shield s height is smaller The tops of the three cylinders are all along the same plane Immediately above this top layer is a layer of metal one grid cell thick Side View X y Top View Monopole Antenna Input To build a monopole antenna the following input is required e coordinates in grid points of antenna top center o z direction coordinate is of top metal layer e core radius dielectric thickness and shield thickness in grid points e dielectric core length and shield length in grid points coordinate M o o G 1 grid cell shield length shield thickness x y sctricfcore length ah core radius Monopole antennae objects can be used in the excitation Only one monopole antenna can be used in the excitation for any given simulation When building multiple monopole antenna objects the last one to be built is the one that can be used in the excitation If a monopole excitation is selected that last monopole antenna is automatically excited in the appropriate fashion Material Input File The material input file is a special object type that allows the user to easily define arbitrary material distributions A material input file is a text file containing a 2D grid of numbers located in the same director
14. through the spatial grid calculating electric and magnetic field values Thus the larger the number of time steps is the longer the code will take to run However the number of time steps has no effect on a simulation s memory consumption so any computer can run any number of time steps In order for an FDTD simulation to run properly input must satisfy the Courant condition eee ee ee de ee eg Ri gt Ax AV Az Here co is the speed of light in free space vacuum At is time step size Ax Ay amp Az are space step grid cell sizes Using co gives an upper bound for At or alternatively a lower bound for Ax Ay amp Az If the material distribution does not include free space then this bound is not tight It is used to guarantee that the Courant condition will not be violated no matter what the eventual material distribution is In the code Ax Ay amp Az are inputted before At so if the value for At entered does not satisfy the Courant condition the user is prompted to enter a new value for At If instead the user prefers changing Ax Ay amp Az then that command window must be closed and input entry must be restarted Create New Materials Input Our code comes with several built in material types each with a pre set number label as well as several pre set number labels reserved for user defined materials l Free Space 2 Metal PEC 4 Dielectric relative permittivity 2 3 4 THT s D
15. ut time step 78O0utput time step 77O0ut put time step Program terminated Ss any key to continue If the messages Output time step appear on separate lines instead of on the same lines as seen here that is fine The messages are simply a convenience for the user to monitor simulation progress and do not affect the simulation Sample Simulation 1 Monopole Antenna Continued This is an image of the part of the project folder after the simulation ran showing some of the field component output files the input file the two material output files and the code and project files t ez_yO25_t086 dat ez_z2030_t044 dat amp ez_2030_t100 dat lez _yO25_t089 dat ez_2030_t045 dat E input txt lez _yO25_t090 dat ez_z030_tO46 dat amp mt_y025 dat lez y025_t091 dat ez_2030_t047 dat mt_2030 dat Wlez_y025_t092 dat E ez_2030_tO48 dat nufdtd3d F Wlez_y025_t093 dat amp ez_2030_t049 dat nufdtd3d mak ez_y025_t094 dat ez_2030_t0S0 dat nufdtd3d mdp t ez yO25_t095 dat t ez z030 t051 dat E nufdktd3d_parans t This is an image of part of the file ex_z030_t040 dat which contains the x direction component of the electric field at the slice z 30 and at the 40 output time step or the 400 total time step because the simulation used 10 time steps between outputs or 4x10 seconds after the start of the simulation because the time step size was 1000E 11 seconds Bex 2030 t040 dat Notepad File Edit Format V
16. values at the excitation points are fixed to the values given by the pulse In a soft source the field values are the sum of the pulse values and the values previously calculated at the excitation points Either one may give better results in different circumstances User defined sources are generally chosen when the antenna used for the excitation is built with material input files In order for a monopole sources to function properly a monopole antenna must have already been built using the monopole antenna option in the foreground objects section If more than one monopole antenna was built the last one to be built will be the one used for the excitation If a user defined source options 1 or 2 is chosen then the following input is needed e number of excitation points For each excitation point the following input is needed e coordinates The grid location 1 j k of the excitation point e directional excitation strengths The magnitude of the excitation in each direction x y Z These define the magnitude of the x y and z components of the excitation s electric field Generally numbers in the interval 1 1 are chosen although this need not be the case Excitation Input Pulse Shape Then for all source types the following input is needed pulse sha pe The options are Harrow Width Gaussian Cosine Modulated Gaussian Harrow Width Half Gauss ian Cosine Modulated Half Gaussian For each pulse sha
17. User Manual FDTD amp Code Basics The code is a three dimensional finite difference time domain FDTD electromagnetics simulation It discretizes the Maxwell equations within a three dimensional rectangular prism of space the computational domain and a finite period of time The material distribution within the computational domain is static it is the same at all points in time Each simulation requires as input the distribution of materials within the computational domain as well as values for an electric field excitation during the time period It also requires that the electric and magnetic field values within the computational domain be zero at the beginning of the time period The code then calculates electric and magnetic field component values 1 e values of electric and magnetic fields in the x y and z directions at each point in the computational domain for each point in time As specified by the user field component values and parts of the material distribution can be printed to data files output files on the computer s hard drive The code consists of two separate Fortran files nufdtd f and nufdtd_params f The first file nufdtd f contains the main program It never needs to be modified by the user The second file nufdtd_params f contains definitions of parameters and other variables used in the main code Certain parts of it may occasionally need to be modified by the user Any time the parameters file is cha
18. ariables Cintegers only for slice 360 Specs Field component slice variables Cintegers only for slice 360 Specs Field component slice 5 variables Cintegers only for slice 6 3 3A Specs Field component slice 6 Output time step 10utput time step 20utput time step 30utput time step 4Out put time step SOutput time step b0utput time step Output time step 8O0utput time step 7 aa Output time step 410utput time step 420utput time step 43J0utput time step 440utput time step 450utput time step 460utput time step 4 7Output time step 48Output time step 470utput time step SHOutput time step S1Output time 5S20utput time step S30utput time step S40ut put t S5SOutput time step S60utput time step 5 7Out p S8Out put time step S7Output time step 64 time step 610utput time step 620utput time step 630utput time step b40utput time step 650utput time step 660utput time step b 7O0ut put time step 68O0utput time step 67Output time step HOut put time step 10utput time step f2OQutput time step fJOutput time step 40utput t foUut put time step 60utput time step rrUutp 8Output time step f Output time step SH gt step 810ut put time step BeQOut put time step SI0utput time step 840utput time step SoO0utput time step 60utput time step B Output time step S8Out put time step 87Output time step 7HOutput time step 710utput time atep T2 0utput time step 7IOUtC put time step 740ut put t lime step 750utput time step 760utput time step 7 Outp
19. developed for the code s ground penetrating radar application as to simulate stratified regions of ground Background layers are homogenous rectangular prisms that span the entire the x y plane The first input needed is e number of background layers There must be at least one layer and there cannot be more layers than there are grid points in the z direction Then for each background layer the following input is needed e layer thickness in grid cells Layers must be at least one grid cell thick and must be small enough that all remaining layers can be at least one grid cell thick o For the top background layer no thickness input is taken because its thickness is automatically set to the number of remaining grid cells in the z direction e material type A homogenous background can be created by making one layer this is equivalent to making all layers with the same material Foreground Objects Input Once the layer s have been defined the user can place any number at least zero of foreground objects in the material distribution They are called foreground objects because their material values overwrite those of the background layers Objects come in various shapes and sizes can be placed anywhere in the grid and can be of any available material Each object type is labeled in the code by a number similar to material type numbers Available object types include O Material Input File 1 Rectangular Prism cy
20. ections vertical and horizontal were intentionally made different to demonstrate that they need not be the same c shows an FD discretization of the material distribution based on this FD grid It simply fills in each rectangle with the color that is predominant within the rectangle in b d adds a material numbering scheme FD computer codes generally represent materials with number labels as seen here Coordinate Systems z is the vertical direction x and y are arbitrary horizontal directions In the code z counts upwards i e Z 1 is closer to the center of the Earth and z nz is closer to the sky For this document we will have x pointing to the right and y pointing towards the reader up down The Fortran code and the MatLab companion codes all make extensive use of 2D slices of the 3D grid For all of these standard Cartesian coordinates as opposed to 1 matrix coordinates are used Z x direction y direction y z slice x z slice A y z direction x y slice Text Editor Coordinate Systems Care must be taken to ensure consistency in coordinate systems when converting matrices between data types All Fortran matrices use the standard Cartesian coordinate systems explained below When matrices are printed to data files they are written so that they follow this convention when viewed with a text editor For example the following x direction field component slice has the coordinate system shown here Z
21. electric modeled as dispersive material relative permittivity 2 3 B Lossy Puerto Rican soil tss 20ps fT 1L 5GHz F Lossy Puerto Rican soil tss L0ps fT 1 5GHz B Lossy Bosnian soil tss 2005 T 1 5GHz G Lossy Bosnian soll tss LO00s T 1 5GHz 1O Lossy Bosnian soil tss 295 T L 5GH2 Ti water tss 50 os T LOOMHz le Bosnian soil 2 5 water tss 50ps T LOOMHz 13 Bosnian soil 5 0 water tss 50ps T LOOMHz 14 Bosnian soil 10 0 water tss 50ps T LOOMHz 15 Bosnian soil 20 0 water tss 50ps T LOOMHz l6 sandy soil 4 0 water tss 295 f 1 3GHZ l sandy soll 17 0 water tss 295 T 1 3GHz2 18 sandy soil 4 0 water tss 2005 f 1 3GHZ 19 sandy soll 17 0 water tss 2005 f 1 3GHZ Q sandy soil 17 0 water tss 6ps f 1 3GHZ 21 Tef lon 22 34 00tT onal user defined material When creating new materials the first input needed is e number of new materials Then for each material the relevant physical properties must be entered e relative permittivity e If the material is not frequency dispersive 1 e its properties do not vary as a function of the frequency of electromagnetic radiation passing through it then electric conductivity must be entered o If the material is a lossless dielectric then the conductivity should be set to 0 e Ifthe material is frequency dispersive then four special dispersion variables al bO b1 amp b2 must be entered o bO is the same as the conductivity in the non dispersive case
22. erial Output Files Input Once the material distribution has been built parts or all of it can be checked by printing material output files These files contain slices of the final material distribution appear in the same directory as the simulation For example one could print out the materials at x 19 or Z 1 The numbers in the files correspond to the material number labels at the grid points along the slice The first input needed is e number of material output files to print Then for each material output file the following input is needed e the direction and location of the slice 1 e x 23 etc The material distribution then gets printed to a text file in the same directory as the simulation The file name begins with the letters mt for material followed by an underscore followed by a letter x y or z representing the slice direction followed by a three digit number representing the slice location followed by the extension dat Thus the slice at x 23 will have the file name mt_x023 dat Excitation Input The code initializes all electric and magnetic field to zero and without any non zero field values added its calculations will produce all zero values These added values are the excitation The first input needed is e source type The options are User defined hard source User defined soft source Monopole hard source Monopole soft source In a hard source the field
23. erial output file 3 Source type 2 Pulse shape 50 0 Gaussian pulse width time steps 200 0 Gaussian peak time time steps 1500E 10 Pulse frequency 10 Number of time steps between outputs 6 field component slice series 42 25 Specs field component slice 1 52 25 Specs field component slice 2 62 25 Specs field component slice 3 43 30 Specs field component slice 4 53 30 Specs field component slice 5 63 30 Specs field component slice 6 This text can be copied and pasted directly into the command window If while pasting it in the command window closes check the parameters file to make sure that the grid size allocation npx npy npz is large enough Sample Simulation 1 Monopole Antenna Continued This is what the command window will look like just after the input has been entered E C aardvark nufdtd3d Debug 16 Number of time steps between outputs Enter number of Field component slice series t amp field component slice series Enter Field component slice variables field direction location Field Field to output 1 Hx 2 Hy 3 Hz 4 Ex 5 Ey 6 Ez direction Direction of slice 1 x3 2 40 3 2z location Location coordinate of slice Enter variables integers only gt for slice 4 2 25 E e a component slice variables lt Cintegers only for slice 25 Specs Field component slice variables Cintegers only for slice 25 t Specs Field component slice v
24. he command window must be closed the program must be re run and all of the data must be re entered from the beginning Input must also be in a certain format For example if a question asks for an integer no letters can be included in the answer If the question asks for a real number letters cannot be included in the answer except for an optional e for exponent For example 2e1 2x10 1 20 Input can be copied and pasted from a text file into the command window The paste command is found by choosing Edit after clicking on the icon in the top left corner of the command window ey Ch aardy ark proj Debug proja exe amp Restore ONE ENS LONS Size ze nx ny nz Minimize O Maximize A Close Defaults Properties Select All Scroll Find Command Window Basics Continued Alternatively if QuickEdit Mode is checked from the Properties box a paste can be performed by clicking the right mouse button Checking insert mode causes inserted text to be inserted between characters instead of overwriting them ch oroja exe Properties x Options Font Layout Colors Cursor Size Display Options f Small Medium Large Window C Full Screen Edit Options i GuickEdit Mode W Insert Mode Command History Butter Size pO Number of Buffers Discard Old Duplicates Input Files A good way to stream
25. iew Help OO0011 24444 00000 00001298484 00000 OO004 81107 100000 00004 72991000000 000014 lr r B0000 OO001L8434 s00000 000083 45 5400000 O00062 51 784200000 O0001 Fla 9so0000 0000201658800000 OO008S 4 0500000 OOO08TTO968100000 This is an image of a series of MatLab commands used to create a movie file of the series of field component output files containing the z direction component of the electric field at the slice y 25 gt gt fc fc_read ez y 25 100 gt gt mY fc_animate fc 1 100 gt gt boviecavi mv MV ez y25 avi Warning The frame height has been padded to be a multiple of four as required by Intel gt In C MATLABSp5 toolbox matlabyiotun favifile addtrame m at line 139 In C HATLAB6p5 toolbox matlab iofun moviezcavi m at line 67 Warning The frame width has been padded to be a multiple of four as required by Intel gt In C MATLAB6p5 toolbox matlab ioftun favifile addtrame m at line 145 In C MATLABGpS toolbox matlab iofun moviezcavi b at line 67 ao Sample Simulation 1 Monopole Antenna Continued This is an image of a series of MatLab commands used to print jpeg image files of the field component output files containing the x direction component of the electric field at the slice y 25 at the output time steps 15 and 30 gt gt fe fc read ex y 25 100 gt gt fig fc _ jpg ic 1l5 ex y25 tl5 gt gt fig fc _jpo tc 30 ex y25_t30
26. in which field component files are written are called output time steps Simulations then produce series of field component output files each containing the same field component slice at successive output time steps For one simulation all field component slices will be printed at all output time steps Thus the following input is needed e number of time steps between outputs e number of output files per output time step the number of field component slices to print at each output time step For each field component slice the following input is needed e field component slice variables field direction location o field field to output Uses the labels 1 Hx 2 Hy 3 Hz 4 Ex 5 Ey 6 Ez o direction direction of slice Uses the labels 1 x 2 y 3 Z o location location coordinate of slice Field output files will appear in the same directory as the simulation The file name begins with two letters representing the field component followed by an underscore followed by a letter x y or Z representing the slice direction followed by a three digit number representing the slice location followed by a second underscore followed by the letter t and a three digit number representing the output time step number followed by the extension dat Thus the Ex field component at the slice x 23 and at output time step 5 will have the file name ex_ x023 t0O05 dat Viewing Output Files Viewing
27. linder Use Tor landmines Sphere Monopole Antenna Each object type has its own set of input to be entered Rectangular Prism Input Creates a solid rectangular prism of uniform material Making a rectangular prism of width 1 1 1 is an easy way to define the material in a single grid point e Starting coordinates coordinates in grid points of the corner of the prism closest to the grid point 1 1 1 e Width in each direction in grid points e Material type width z direction x direction width starting y direction coordinate Cylinder Input Creates a solid cylinder oriented with its parallel planes oriented along the x y plane A cylinder made with the TNT material type reasonably approximates some landmines e Starting coordinates coordinates in grid points of the circle s center at it s lowest point closest to z 1 e Circle radius and vertical height in grid points e Material type width x z direction y e starting coordinate Sphere Input Creates a solid sphere e Starting coordinates coordinates in grid points of the sphere s center e Sphere radius e Material type starting coordinate radius Monopole Antenna The monopole antenna commonly used in ground penetrating radar is essentially a series of three concentric cylinders The inner cylinder the core is made of metal The middle cylinder the dielectric is made of dielectric The code uses
28. line the process of re entering the same or similar sets of input is to create and use an input file containing some or all of the input which if properly formatted can then be copied and pasted in its entirety into the command window Properly formatted input files include line breaks between lines of input and can include comments after an exclamation mark Using an exclamation mark for commenting comes from Fortran syntax For example the input file text 4000 number of time steps JLOGOE 1L Time step 51z8 sec can be inserted into a command window producing eee TIME DIMENSIONS Enter total number of time steps to run the code HHA number of time steps Enter time step size in sec vdt To statisfy Courant Condition need dt lt x 1 713992E 12 LHQHHE 11 Time step size sec The code creates an input file automatically as input is being entered by the user Thus if the user stops entering input after 5 questions then it will contain exactly those 5 lines of input This feature is particularly useful when data is initially entered manually 1 e by typing input in directly instead of copying and pasting it The input file created appears on the hard drive in the same directory as the simulation with the file name input txt Because the code automatically overwrites any pre existing files named input txt it is a good idea to avoid using this file name for other purposes Note that the
29. nA aA aA A aA A an aA A eA eA ana Ln Ln en an an an an an an an an an an an an un PI AE Ae ee Ae ana Ln on en an an an an an an an an an an an an an I eE AE ee Ee eA 1n Ln on an LA aA A LA A anA aA aA A aA A an aA A eA e n ona on on on on oA oA A on on on oA A aAa an an e eE e un ona n on aon n aon an an an aon an an an ana an an I eE Ae LALA on on LA oA A on nA A inn e e e an oa on an an an an an an an oo an ana an an I eA Ae a BPERPRPRBPBERBBRBBBRBBEBEBEER 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 The astute observer may recognize this as being from a vertical slice through a monopole antenna Viewing Output Files In MatLab Loading material or field component output files into a program that can effectively plot them offers significant advantages over viewing the files directly All data in a file can be interpreted by observing the plots colors which is generally easier and more effective than reading the underlying numbers in a direct viewing Some programs can even create animations to view all or parts of a field component slice series or some other sequence of output files Images can be saved for use in papers and other reports A collection of MatLab files designed to read and plot the code s output files has been included with the main Fortran code to help users visualize output files Use of these MatLab files is explained here and should be fairly easy even for those with limited MatLab expertise These
30. nent is oriented Thus Ex is shifted half of a grid cell in the x direction The magnetic field components are shifted half of a grid cell in two directions the directions that the field component is not oriented in Thus Hx is shifted half a grid cell in the y and z directions For both electric and magnetic fields the shifts are in the positive direction 1 e away from the origin 1 1 1 A common representation of this is the Yee cube named for Kane S Yee FDTD s main creator In this diagram the black dots represent locations of material points blue arrows represent electric field components and red arrows represent magnetic field components Field Component Coordinates The same Yee cube can be redrawn with material points and field components coordinates assuming that the cube runs from point i j k to point G 1 j 1 k 1 i j K 1 Ex it j k 1 9 i44 j k 1 a wie radinan rE a i j 1 k 1 1 EPA Adit E i 1 ap K 2 i 1 414 k 4 i j K 1t 72 1 K 72 Wa K i 1 j k i 1 JTA k i 1 j 1 K E j 1 i K Clearly the electric and magnetic field components coordinates contain non integer values However code matrices and indeed matrices in general require integer indices Thus a scheme is required to convert the non integer values to integer values We simply subtract 1 2 from all non integer matrices giving the shifted Yee cube i k Ex i j k
31. nged the main code must be recompiled built and executed Otherwise the same executable file can be used for any simulation A suite of companion MatLab codes is also included e fc_read m Reads in field component slice sequences 1 e the data files for a 2D slice of specific field component at various points in time e fc_animate m Animates a field component slice sequence already read into MatLab e fc_animate2 m Similar to fc_animate m but adjusted to work with fc_mv m e fc _mv m Reads in animates and creates avi movie files for a collection of field component slice sequences e fc_jpg Plots and prints a jpeg image file of a field component slice already read into MatLab e mt_readplot m Reads and plots a material slice e pulse_plot Plots pulses of various shapes given pulse parameters Finite Difference Discretization In all FD simulations including both FDTD and FDFD a 2D or 3D region of space is approximated as a uniformly spaced 2D or 3D grid of grid cells or grid points The grid need only be uniform within the same direction the number and spacing of grid points in different directions need not be the same For example a simple discretization of a 2D region containing four materials could be a a shows the original material distribution with each color representing some different material b shows an FD grid superimposed on a The number and spacing of the grid points in the two dir
32. pe the following input is needed e pulse width in time steps e pulse peak time in time steps For the cosine modulated pulse shapes the following input is also needed e pulse frequency in Hertz Excitation Input Pulse Shape Continued The narrow width Gaussian is a discretized version of the standard Gaussian pulse n 2 AE f n e s where n is time step number ex2 7183 p is the pulse peak time and w is the pulse width The cosine modulated Gaussian is a discretized version of the standard Gaussian multiplied by a cosine _ 7 a P 2 f n e a cos 27 f nAt where f is the pulse frequency and At is the time step size The half Gaussian pulses are equivalent to their regular Gaussian counterparts until the pulse peak time is reached At that point the narrow width half Gaussian s value is fixed to one and the cosine modulated half Gaussian s values are fixed to the values produced by the cosine term Narrow Width Gaussian Cosine Modulated Gaussian 1000 1500 2000 2500 3000 3500 a 2600 3000 3500 Narrow VVidth Half Gaussian 1 500 1000 1500 200 20 0 0 Time ps Excitation Input Points Per Wavelength In order for an FDTD to properly simulate wave propagation there must be enough spatial grid points per wavelength to accurately model the wave Using more points per wavelength increases both model resolution which is desirable and memory requirements which is undesirable Thus in general
33. the minimum number of points per wavelength that will give sufficient accuracy is sought 10 points per wavelength is a common choice Points Per Wavelength 3 Points Per Wavelength 5 1 1 0 8 0 8 06 0 6 0 4 0 4 0 2 0 2 y oO 0 D 0 2 0 2 0 4 0 4 0 6 0 6 0 8 0 8 j a 0 1 2 3 4 5 6 fan 1 2 3 4 5 6 7 Points Per Wavelength 10 Points Per Wavelength 15 sin x If a pulse shape with cosine modulation has been selected then the code calculates and displays points per wavelength after pulse frequency has been entered This display can be used to determine 1f a satisfactory number of points per wavelength are being used However the code will not make such judgments on its own the user is able to run simulations with any number of points per wavelength If a narrow width pulse shape has been selected then points per wavelength is not calculated because there is no frequency entered Field Component Output Input Electric and magnetic field values can be printed to field output files on the computer s hard drive Field output files are text files containing the field values of a particular field component Ex Ey Ez Hx Hy or Hz along a particular slice through the computational domain and at a specific time step In order to avoid clogging hard disks with excessive amounts of field component output files users can choose to write field component output files at regular intervals of time steps The time steps
34. y as the simulation The numbers must be separated by spaces The grid must be rectangular 1 e all rows and all columns must have the same size Rows need not have the same size as columns The numbers in the file must correspond to material type numbers However the code does not check this Itis up to the user to make sure that the correct numbers have been entered JE sample tut Notepad O x File Edit Format View Help The above file sample txt could be a 4x3 material file containing two rows of material number 2 metal below one row of material number 1 free space Material input files have the following specifications Filename the name of the file including its extension e g sample txt Orientation direction x y or z for the file to be placed Height the coordinate for the file to be placed in its direction of orientation Starting point the two coordinates in the non height directions of the bottom corner of where the material input file should be placed 1 e the corner closest to 1 1 1 e Width the number of points in the two non height directions to read The width cannot be larger than the number of the points in the computer file but it can be fewer If itis fewer the code will start from the beginning of the file and stop reading before reaching the end The width also cannot be so big that it will not fit in the simulation grid given the grid size and the material file starting point Mat

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