Home

FEAP Parallel Manual - Department of : Civil and Environmental

1. 0 8 99 Index Command language solution 25 Eigensolution Arnoldi Lanczos method 18 Subspace method 18 Equation structure 10 11 Graph partitioning 2 METIS 2 ParMETIS 3 GRAPh partitions During solution 29 Initial conditions 12 Linear equation solution Iterative 30 36 Mesh Input file form 7 Structure 5 Mesh command BCIN 7 9 DOMAin 7 11 EQUAtion 7 11 FORMat 7 9 GETData 7 9 LOCAI 7 9 MATRix 7 10 SENDdata 7 9 Nonlinear equation solution Tolerance 36 Output domain meshes During solution 33 Output with global node numbers 16 Parallel solution control 34 Paraview 20 Plots Graphic outputs 19 Solution command DISPlacements 26 GLISt 16 27 GNODe 16 GPLOt 19 28 GRAPh 2 4 GRAPh partitions 29 ITER 16 ITERative 30 NDATa 20 32 OUTDomains 2 4 33 PARPack 18 PETSc 14 34 PSUBspace 18 STREss 35 TOL 16 TOLerance 36 Solution process 13 PETSc activation 13 14 PETSc array output 14 Tolerances 16 60
2. Preparation of this file is described in the FEAP User Manual H 1 3 1 METIS version After the file is constructed and its validity checked a serial execution of the parallel FEAP program built in the parfeap directory may be performed Using the GRAPh solution command statement followed by an OUTDomains solution command will gen erate the needed parallel execution input files To use this option a basic form for the input file is given as FEAP Start record and title Control and mesh description data END mesh lt Initial condition data for transient problems gt BATCh GRAPh node numd METIS partitions numd nodal domains OUTDomains Creates numd partitioned meshes END batch STOP CHAPTER 1 INTRODUCTION 3 where the node on the GRAPh command is optional Options for OUTDomains are ex plained below in Sect 1 3 3 Using these commands METIS will split a problem into numd partitions by partitioning the node graph and output numd input files for a subsequent parallel solution of the problem The initial condition data is only required for transient solutions in which inital data is non zero Otherwise this data is omitted The form of the initial condition data is described in the basic User manual For efficiency of assembly it is necessary to pre allocate matrix memory requirements In PETSc there are two basic matrix formats A J and BAIJ By default FEAP stores the pre allocation information in the par
3. libraries are used to par tition each mesh for parallel solution The present parallel version of FEAP may only be used in a UNIX Linux including Mac OS X environment and includes an integrated set of modules to perform 1 Input of data describing a finite element model 2 An interface to METIS to perform a graph partitioning of the mesh nodes A stand alone module exists to also use ParMETIS to perform the graph parti tioning for very large problems 3 An interface to PETSc 6 to perform the parallel solution steps 4 Construction of solution algorithms to address a wide range of applications and 5 Graphical and numerical output of solution results CHAPTER 1 INTRODUCTION 2 1 2 Problem solution The solution of a problem using the parallel versions starts from a standard input file for a serial solution This file must contain all the data necessary to define nodal coordinate element connection boundary condition codes loading conditions and material property data That is if it were possible this file must be capable of solving the problem using the serial version However at this stage of problem solving the only solution commands included in the file are those necessary to partition the problem for the number of processors to be used in the parallel solution steps 1 3 Graph partitioning To use the parallel version of FEAP it is first necessary to construct a standard input file for the serial version of FEAP
4. 1 FORM SOLV NEXT since the TANG command has significant set up costs especially for multi grid methods Indeed for some problems more than one iteration is needed in the loop 3 2 2 GLIST GNODE Output of results with global node numbers In normal execution each partition creates its own output file e g Ofilename_0001 etc with printed data given with the local node and element numbers of the proces sor s input data file In some cases the global node numbers are known and it is desired CHAPTER 3 SOLUTION PROCESS 17 to identify which processor to which the node is associated This may be accomplished by including a GLISt command in the solution statements along with the list of global node numbers to be output The option is restricted to 3 lists each with a maximum of 100 nodes The command sequence is given by BATCh GLISt lt 1 2 3 gt END list of global node numbers 8 per record blank termination record The list will be converted by each processor into the local node numbers to be output using the command DISP LIST lt 1 2 3 gt The command may also be used with VELOcity ACCEleration and STREss see the relevant manual pages in the FEAP Users Manual It is also possible to directly output the global node number associated with individual local node numbers using the command statement DISP GNODe nstart nend ninc where nstart and nend are global node numbers This command form also may be used
5. 1 5 32 41 83 16238 127 85 1 6 APPENDIX D PARALLEL VALIDATION 45 D 1 10 Eigenmodes of Mock Turbine In this test we look at the computation of the first 5 eigen modes of the small 552960 element mock turbine model Again the mesh is composed of 8 node brick elements and the model has 1 771 488 equations A lumped mass is utilized and the algorithm tested is the ARPA symmetric option Due to the large number of inner outer iterations the timing runs are done only for 8 16 and 32 processors Scaling is thus computed relative to the 8 processor run Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 E E 4 e E E 8 916 9 3757 2744 16 507 1 1122 2876 95 32 248 3 14042 2723 93 D 2 Serial to Parallel Verification Serial to parallel code verification is reported upon below For all test run the program is run in serial mode with a direct solver and in parallel mode on 4 processors forcing inter and intra node communications Then various computation output quantities are compared between the parallel and serial runs In all cases it is observed that the outputs match to the computed accuracy D 2 1 Linear elastic block In this test a linear elastic unit block discretized into 5 x 5 x 5 8 node brick elements is clamped on one face and loaded on the opposite face with a uniform load in all coordinate directions The displacements are compared at glob
6. data for a partition END MESH DOMAin numpn numtn numteq FORMat lt AIJ BAIJ gt lt BCIN BLOCked nsbk gt Required for BAIJ LOCA1 to GLOBal node numbers GETData POlNter nget_pnt GETData VALUes nget_val SENDdata POINter nsend_pnt SENDdata VALUes nsend_val MATRix storage lt EQUAtion gt numbers If BCIN is not present END DOMAIN BATCh Optional initial conditions INITial DISPlacements END BATCH List of initial conditions INCLude solve filename STOP Figure 2 1 Input file structure for parallel solution CHAPTER 2 INPUT FILES FOR PARALLEL SOLUTION 9 problem numteq Note that the number of nodes in the partition numpn is always less or equal to the number of nodes given on the control record numnp due to the presence of the ghost nodes The sum over all partitions of the number of nodes in each partition numpn is equal to the total number of nodes in the problem numtn 2 1 2 FORMat Format of matrix equations This data set defines the format assumed for the matrix pre allocation data as well as the local to global node number data The valid options are AIJ and BAIJ ATJ is the default 2 1 3 BCIN BLOCked Boundary equations in assembly This data set is optional For matrix formats that include the degrees of freedom associated with Dirichlet boundary conditions in the matrix assembly this command will be present It takes a single numerical parameter indicating the blocking size which is always an
7. execution of the parallel version of feap may be performed using for example the command line statement mpirun n NPROC FEAPHOME8_4 parfeap feap ksp_type cg pc_type jacobi or the command line statement mpirun n NPROC FEAPHOME8_4 parfeap feap ksp_type cg pc_type prometheus for details on using other solvers as well as optional parameters for these choices see the makefile in the parfeap subdirectory The parameters setting the number of processors NPROC and the execution path FEAPHOME8_4 must be defined before issuing the command This can be done by setting shell environment variables Once parallel FEAP starts the input file should be set to Ifilename_0001 where filename is the name of the solution file to be solved Each processor reads its input file up to the END DOMAIN statement and then starts processing command language statements In a parallel solution using FEAP the same command language statements must be provided for each partition This is accomplished by the statement INCLude solve filename appearing after the END DOMAin statement where filename is the name of the input data file with the leading I and the trailing partition number removed Thus for the file named Iblock_0001 the command is given as solve block All solution commands are then placed in a file with this name and can include both BATCh and INTEractive commands For example a simple solution may be given by the commands 13 CHAPTER 3 SOLUTIO
8. form This is only needed for problems so large that they can not be partitioned with METIS CHAPTER 1 INTRODUCTION 4 FEAP Start record and title Control record COORdinates All nodal coordinate records ELEMent All element connection records remaining mesh statemnts END mesh The flat form for an input file may be created from any FEAP input file using the solution command OUTMesh This creates an input file with the same name and the extender rev If a TIE mesh manipulation command is used the output mesh will remove unused nodes and renumber the node numbers Once the flat input file exists a parallel partitioning is performed by executing the command mpirun n nump partition numd Ifile where nump is the number of processors that ParMETIS uses numd is the number of mesh partitions to create and Ifile is the name of the flat FEAP input file For an input file originally named Ifile the program creates a graph file with the name graph file The graph file contains the following information 1 The processor assignment for each node numnp 2 The pointer array for the nodal graph numnp 1 3 The adjacency lists for the nodal graph To create the partitioned mesh input files the flat input file is used again in the same directory containing the graph file in a serial execution of the parallel FEAP together with the solution commands CHAPTER 1 INTRODUCTION 5 GRAPh FILE OUTDomains See the n
9. form described above This form is given by the set of commands TANGent MASS lt LUMPed CONSistent gt PARPack lt SYMMetric gt nmodes lt maxiters gt lt eigtol gt Use of the command MASS alone also will employ a consistent mass or the mass produced by the quadrature specified 3 4 Graphics output During a solution the graphics commands may be given in a standard manner However each processor will open a graphics window and display only the parts that belong to that processor Scaling is also done processor by processor unless the PLOT RANGe command is used to set the range for the plot values 3 4 1 GPLOt command An option does exist to collect all the results together and present on a single graphics window This option also permits postscript outputs to be constructed and saved in files To collect the results together it is necessary to write the results to disk for each item to be graphically presented This is accomplished using the GPLOt command This command has the options GPLOt DISPlacement n GPLOt STREss n GPLOt PSTRess n CHAPTER 3 SOLUTION PROCESS 20 where n denotes the component of a displacement DISP nodal stress STRE or prin cipal stress PSTRE Each use of the command creates a file for each processor with the form Gproblem_domain xyyyy where problem domain is the name of the problem file for the domain x is d s or p for a displacement stress or principal stress respectively and yyyy is a u
10. is 1 0d 16 and for dtol is 1 0d 16 Appendix C Program structure C 1 Introduction This section describes the parallel infrastructure for the general purpose finite element program FEAP The current version of the parallel code modifies the serial version of FEAP to interface to the PETSc library system available from Argonne National Laboratories In addition the METIS and ParMETIS libraries are used to par tition each mesh for parallel solution The necessary modifications and additions for the parallel features are contained in the directory parfeap There are four sub directories contained in parfeap 1 packages Contains the subdirectory arpack with the files needed for the op tional ARPACK eigen solution module see Section 3 3 2 partition Contains the program and include file used to construct the nodal graph partition using ParMETIS see Section 1 3 3 unix Contains the subprogram files for UNIX based systems 39 Appendix D Parallel Validation The validation of the parallel portion of FEAP has been performed on a number of different basic problems to verify that the parallel extension of FEAP will solve such problems and that the parallel version performs properly in the sense that it scales with processor number in an acceptable manner Furthermore a series of comparison tests have been performed to verify that the parallel version of the program produces the same answers as the serial version Be
11. the diagonal nodal blocks i e the ndf x ndf nodal blocks or reduced size blocks if displacement boundary conditions are imposed as the precondi tioner This option is used if the command is given as ITERative BPCG Another option is to use a banded preconditioner where the non zero profile inside a specified half band is used This option is used if the command is given as ITERative PPCG v1 where v1 is the size of the half band to use for the preconditioner The iterative solution options currently available are not very effective for poorly con ditioned problems Poor conditioning occurs when the material model is highly non APPENDIX B SOLUTION COMMAND MANUAL 31 linear e g plasticity the model has a long thin structure like a beam or when structural elements such as frame plate or shell elements are employed For compact three dimensional bodies with linear elastic material behavior the iterative solution is often very effective Another option is to solve the equations using a direct method see the DIREct com mand language manual page Parallel solutions For the parallel version the control of the PETSc preconditioned iterative solvers is controlled by the command ITER TOL itol atol dtol where itol is the tolerance for the preconditioned equations default 1 d 08 atol is the tolerance for the original equations default 1 d 16 and dtol is a divergence protection when the equations do not converge defa
12. to the other processors The lists have identical structure to the GETData lists and are given by SENDdata POINter nparts np_1 np_2 np_nparts and SENDdata VALUes nvalue local_node_1 local_node_2 local_node_nvalue where again the local _node_i numbers are grouped so that the first np_1 are sent to processor 1 the next np_2 to processor 2 etc It is possible for a local node number to appear more than once in the SENDdata VALUes list as it could be a ghost node for more than one other partition np_i should be zero for input file Ifilename_000i 2 1 6 MATRix storage equation structure Each equation in the global matrix consists of the number of terms that are associated with the current partition and the number of terms associated with other partitions This information is provided for each equation or equation block when in BAIJ format CHAPTER 2 INPUT FILES FOR PARALLEL SOLUTION 11 by the MATRix storage data set Each record in the set is given by the global equation number followed by the number of terms associated with the current partition and then the number of terms associated with other partitions The use of this data is critical to obtain rapid assembly of the global matrices by PETSc If it is incorrect the assembly time will be very large compared to the time needed to compute the matrix coefficients or even solve the equations When the matrix format is BAIJ the data is given for each block equation Thus the fir
13. use of the command creates files with different names These results may be processed by a serial run of the problem using the mesh for the total problem To display the nodal values command NDATa is used See manual page on NDATa APPENDIX B SOLUTION COMMAND MANUAL 29 GRAPh FEAP COMMAND INPUT COMMAND MANUAL grap num_d grap node num_d grap file grap part num_d The use of the GRAPh command activates the interface to the METIS multilevel par tioner The graph partition into num_d parts is performed based on a nodal graph The nodal partition divides the total number of nodes i e numnp values into num_d nearly equal parts If the GRAPh command is given with the option file the graph data is input from the file graph filename where filename is the same as the input file without the leading I character The data contained in the graph filename is created using the stand alone partitioner program which employs the PARMETIS multilevel partitioner It is also possible to execute PARMETIS to perform the partitioning directly during a mesh input It is necessary to have a mesh which contains all the nodal coordinate and element data in the input file This is accomplished using the command set OUTMesh GRAPh PARTition num_d OUTDomains where num_d is the number of domains to create The command OUTMesh creates a file with all the nodal and element data and is destroyed after execution of the GRAPh command APPENDIX B SOLUTION CO
14. 05 7 4499E 05 1 1587E 01 1 1587E 01 3 5000E 00 1 4893E 04 1 4893E 04 1 1732E 01 1 1732E 01 3 7500E 00 1 9767E 04 1 9767E 04 4 3679E 02 4 3678E 02 4 0000E 00 1 8873E 04 1 8873E 04 2 1461E 01 2 1461E 01 4 2500E 00 5 7747E 04 5 7747E 04 2 6870E 01 2 6871E 01 4 5000E 00 1 3268E 03 1 3268E 03 3 2132E 01 3 2132E 01 4 7500E 00 1 3859E 03 1 3859E 03 1 3378E 01 1 3378E 01 5 0000E 00 2 5241E 03 2 5241E 03 6 6854E 01 6 6854E 01 53 APPENDIX D PARALLEL VALIDATION Stresses at Global Node 1 Time Serial Values Parallel Values Step J Principal von Mises J Principal von Mises 1 7 5561E 02 9 5922E 02 7 5561E 02 9 5922E 02 2 2 4364E 01 3 0328E 01 2 4364E 01 3 0328E 01 3 3 4447E 01 4 2623E 01 3 4447E 01 4 2623E 01 4 4 0833E 01 5 1265E 01 4 0833E 01 5 1265E 01 5 2 5260E 01 3 1018E 01 2 5260E 01 3 1018E 01 6 1 5934E 01 3 6208E 01 1 5934E 01 3 6208E 01 7 3 5077E 01 7 7659E 01 3 5077E 01 7 7659E 01 8 4 3971E 01 9 8767E 01 4 3971E 01 9 8767E 01 9 4 4131E 01 9 8761E 01 4 4131E 01 9 8761E 01 10 2 5587E 01 5 6437E 01 2 5587E 01 5 6437E 01 11 1 2681E 01 2 3667E 01 1 2681E 01 2 3667E 01 12 2 3099E 02 3 6287E 02 2 3099E 02 3 6286E 02 13 9 8640E 02 2 2004E 01 9 8640E 02 2 2004E 01 14 2 0000E 01 2 4597E 01 2 0000E 01 2 4597E 01 15 1 1798E 01 1 6039E 01 1 1798E 01 1 6039E 01 16 1 866
15. 07 z Disp at 0 6 1 0 1 0 Elastic Plastic Serial Plastic Parallel Displacement Time Figure D 12 Z displacement for the node located at 0 6 1 0 1 0 the structure and the time histories are followed and compared for the displacements at a particular point the first stress component in a given element and the 1st principal stress and von Mises stress at a particular node The time history is followed for 150 time steps The time integration is performed using Newmark s method As a benchmark the elastic response from the serial computation is also shown in each figure The agreement between the parallel and serial runs is seen to be perfect 98 APPENDIX D PARALLEL VALIDATION Stress 91 in element nearest 1 6 0 2 0 8 T T Elastic Plastic Serial Plastic Parallel 0 6 Time Figure D 13 11 component of the stress in the element nearest 1 6 0 2 0 8 o at 1 6 0 2 0 8 0 7 Elastic Plastic Serial Plastic Parallel 0 6 7 Stress Time Step Figure D 14 1st principal stress at the node located at 1 6 0 2 0 8 APPENDIX D PARALLEL VALIDATION Von Mises Stress at 1 6 0 2 0 8 1 4 T T Elastic Plastic Serial Plastic Parallel 0 8 Stress 0 47 0 2 SS i 0 50 100 150 Time Step Figure D 15 von Mises stress at the node located at 1 6 0 2
16. 8E 01 4 2255E 01 1 8668E 01 4 2255E 01 Abra 4 3432E 01 5 2267E 01 4 3432E 01 5 2267E 01 18 5 8732E 01 7 3503E 01 5 8732E 01 7 3503E 01 19 2 7197E 01 3 7066E 01 2 7197E 01 3 7066E 01 20 1 1706E 00 1 4434E 00 1 1706E 00 1 4434E 00 D 2 6 Nonlinear elastic block Static analysis 54 In this test a unit neo hookean block is clamped on one side and subjected to surface load on the opposite side The displacements at two random nodes are compared as well as the max equivalent shear stress von Mises over the entire mesh All values are seen to be the same between the serial and parallel computation Serial Displacements Node X Coor y coor Z COOr x disp y disp z disp 50 0 00E 00 0 00E 00 1 67E 01 0 0000E 00 0 0000E 00 0 0000E 00 100 1 67E 01 0 00E 00 3 33E 01 5 6861E 04 1 0501E 04 1 5672E 04 Serial Maximum Equivalent Shear 0 881 APPENDIX D PARALLEL VALIDATION 59 Parallel Displacements P Node x coor y coor Z COOr x disp y disp z disp 2 27 0 00E 00 0 00E 00 1 67E 01 5 8777E 17 4 9956E 18 6 3059E 17 2 54 1 67E 01 0 00E 00 3 33E 01 5 6861E 04 1 0501E 04 1 5672E 04 Note Processor 2 s nodes 27 and 54 correspond to global nodes 50 and 100 Parallel Maximum Equivalent Shear 0 881 D 2 7 Nonlinear elastic block Dy
17. E 00 Figure D 11 von Mises stresses at the end of the loading left serial right parallel drives the plate well into the plastic range The displacement history is followed for a point on the loaded edge of the plate As seen in the tables the parallel and serial runs match Also shown are the contours of the von Mises stresses at the end of the run with the plastic zone emanating from the plate hole these also match perfectly within the accuracy of the computation y Displacement Load Serial Run Parallel Run Step Node 5700 Node 1376 Part 4 0 0000E 00 0 0000E 00 0 0000E 00 1 0000E 01 1 5260E 02 1 5260E 02 2 0000E 01 3 0520E 02 3 0520E 02 3 0000E 01 4 5780E 02 4 5780E 02 4 0000E 01 6 1039E 02 6 1039E 02 5 0000E 01 7 6308E 02 7 6308E 02 6 0000E 01 9 1639E 02 9 1639E 02 7 0000E 01 1 0707E 01 1 0707E 01 8 0000E 01 1 2264E 01 1 2264E 01 9 0000E 01 1 3848E 01 1 3848E 01 1 0000E 00 1 5519E 01 1 5519E 01 Note Local node 1376 on processor 4 corresponds to global node 5700 D 2 9 Transient plastic This test involves a mixed element test with shells bricks and beams under a random dynamic load with load sufficient to cause extensive plastic yielding in the system The basic geometry consists of a cantilever shell with a brick block above it which has a an embedded beam protruding from it The loading is randomly prescribed on the top of APPENDIX D PARALLEL VALIDATION 57 x 1
18. ES Prometheus BAIJ format GMRES Block Jacobi Often gives indefinite factor GMRES ASM ILU SuperLU direct AIJ format has BLAS conflict on Mac OS X gt 10 7 5 Spooles direct AIJ format MUMPS direct AIJ format The solvers together with the necessary options for preconditioning are specified on the mpirun line For convenience it is recommended to place these in the provided Table 3 1 Linear solvers and pre conditioners tested CHAPTER 3 SOLUTION PROCESS 16 makefile and to run them with the make command Several options are pre provided in the distributed makefile 3 2 1 Tolerance for iterative equation methods The basic form of iterative solution for linear equations in PETSc is a Krylov subspace scheme These methods terminate their iterations based on assumed tolerances and can be changed as desired Termination tolerances for the solvers are given by either TOL ITER rtol atol dtol or ITER TOL rtol atol dtol where rtol is the tolerance for the preconditioned equations atol the tolerance for the original equations and dtol a value at which divergence is assumed The default values are rtol 1 d 8 atol 1d 16 and dtol 1 d 16 For many problems it is advisable to check that the actual solution is accurate when using iterative methods since termination of the iterative solution is performed based on the rtol value A check should be performed using the command sequence TANG 1 LOOP
19. FEAP A Finite Element Analysis Program Version 8 4 Parallel User Manual Robert L Taylor amp Sanjay Govindjee Department of Civil and Environmental Engineering University of California at Berkeley Berkeley California 94720 1710 USA E Mail rltGce berkeley edu or s_g berkeley edu May 2013 Contents 1 Introduction 1 TI G neral features ns esi ena et Ae a a a a AO ye he 1 T2 Problemi sol tioh E a 2 Ls Graph partitioning s sees a AA A a 2 TiL MEE version ase a a e A oes ag 3h 2 13 2 ParMETIS Parallel graph partitioning 3 1 3 3 Structure of parallel meshes 5 2 Input files for parallel solution 7 2 1 Basic structure of parallel file aserto te Wess T 2 1 1 DOMAIN Domain description ias do a 7 2 1 2 FORMat Format of matrix equations 9 2 1 3 BCIN BLOCked Boundary equations in assembly 9 2 1 4 LOCal to GLOBal node numbering 9 2 1 5 GETData and SENDdata Ghost node get and send 9 2 1 6 MATRix storage equation structure 10 2 1 7 EQUAtion number data 0 iba dw ibe oe ee ee eo es 11 2 1 8 END DOMAIN record 3 ta eee lS Be ee awe ad 11 2 159 Mitia l conditions lt a gs Ake Be A Ee ee ee Be eg 12 3 Solution process 13 3 1 Command language statements 000002 14 3 1 1 PETSc Command aaa At Ad la la he ee oe 14 3 2 Solution of linear equations 1 i hoe pd ls Peale eS ES 15 3 2 1 Tolerance
20. MMAND MANUAL 30 ITERative FEAP COMMAND INPUT COMMAND MANUAL iter icgit iter bpcg vi icgit iter ppcg v1 icgit iter tol v1 v2 v3 The ITERative command sets the mode of solution to iterative for the linear algebraic equations generated by a TANGent Currently iterative options exist only for symmetric positive definite tangent arrays consequently the use of the UTANgent command should be avoided An iterative solution requires the sparse matrix form of the tangent matrix to fit within the available memory of the computer Serial solutions In the serial version the solution of the equations is governed by the relative residual for the problem i e the ratio of the current residual to the first iteration in the current time step The tolerance for convergence may be set using the ITER TOL vi v2 option The parameter v1 controls the relative residual error given by RRO lt v1 RTR y and for implementations using PETSc the parameter v2 controls the absolute residual error given by RTR lt v2 The default for v1 is 1 0d 08 and for v2 is 1 0d 16 By default the maximum number of iterations allowed is equal to the number of equations to be solved however this may be reduced or increased by specifying a positive value of the paramter icgit The symmetric equations are solved by a preconditioned conjugate gradient method Without options the preconditioner is taken as the diagonal of the tangent matrix Options exist to use
21. N PROCESS 14 BATCh PETSc ON TOL ITER 1 d 07 1 d 08 1 d 20 TANGent 1 END INTEractive placed in the solve filename file Note that both batch and interactive modes of solution are optionally included Interactive commands need only be entered once and are sent to other processors automatically In the subsequent subsections we describe some of the special commands that control the parallel execution mode of FEAP 3 1 Command language statements Most of the standard command language statements available in the serial version of FEAP see users manual 1 may be used in the parallel version of feap New com mands are available also that are specifically related to performing a parallel solution 3 1 1 PETSc Command The PETSc command is used to activate the parallel solution process The command PETSc lt ON OFF gt may be used to turn on and off the parallel execution It is only required for single processor solutions and is optional when two or more processors are used in the so lution process When required it should always be the first solution command It is automatically included in the default solve filename generated by OUTDomains The command may also be used with the VIEW parameter to create outputs for the tangent matrix solution residual or mass matrix Thus use as PETSc VIEW MASS PETSc NOVIew will create a file named mass m that contains all the non zero values of the total mass matrix The parameter VIEW turn
22. ON 50 DISPLACEMENT 1 EIGENV 4 5 53E 02 4 94E 04 4 61E 02 4 12E 04 3 69E 02 3 30E 04 2 77E 02 2 47E 04 1 84E 02 1 65E 04 9 22E 03 8 24E 05 5 87E 12 4 72E 10 9 22E 03 8 24E 05 1 84E 02 1 65E 04 2 77E 02 2 47E 04 3 69E 02 3 30E 04 4 61E 02 4 12E 04 5 53E 02 4 94E 04 Value 4 86E 02 Hz Time 0 00E 00 Figure D 4 Comparison of Serial left to Parallel right mode shape 4 degree of freedom 1 DISPLACEMENT 2 EIGENV 5 6 98E 02 3 70E 04 5 82E 02 3 08E 04 4 65E 02 2 47E 04 3 49E 02 1 85E 04 2 33E 02 1 23E 04 1 16E 02 6 17E 05 5 23E 12 8 57E 09 1 16E 02 6 17E 05 2 33E 02 1 23E 04 3 49E 02 1 85E 04 4 65E 02 2 47E 04 5 82E 02 3 08E 04 6 98E 02 3 70E 04 Value 4 86E 02 Hz Time 0 00E 00 Figure D 5 Comparison of Serial left to Parallel right mode shape 5 degree of freedom 2 APPENDIX D PARALLEL VALIDATION ol Figure D 6 Comparison of Serial left to Parallel right mode shape 1 degree of freedom 1 Figure D 7 Comparison of Serial left to Parallel right mode shape 2 degree of freedom 2 Serial Eigenvalues rad sec Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 4 46503673E 01 4 52047021E 01 9 08496135E 01 2 32244552E 02 3 04152767E 02 Parallel Eigenvalues rad sec 4 46503674E 01 4 52047021E 01 9 08496136E 01 2 32244552E 02 3 04152767E 02 D 2 5 Transient This test involves a mixed element test with shel
23. Scaling is thus computed relative to the 8 processor run Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 E z 4 E E z 8 220 80 4434 2973 16 107 70 8425 2908 95 32 59 03 15645 2868 88 D 1 4 Box Beam Shells In this test a box beam is modeled using 40000 linear elastic 4 node shell elements 6 dof per node The beam has a 1 to 1 aspect ratio with each face modeled by 100 x 100 elements One end is fully clamped and the other is loaded with equal forces in the three coordinate directions There are 242 400 equations the block size is 6 x 6 Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 49 43 510 195 4 16 37 1619 190 159 8 12 46 1972 188 97 16 5 03 5246 181 129 32 3 28 8177 184 100 D 1 5 Linear Elastic Block 10 node Tets In this test the linear elastic unit block from the first test is re discretized using 10 node tetrahedral elements As in the 8 node brick case there are 1 073 733 equations in this problem In the table below we also provide the ratio of times for the same prob lem when solved using 8 node brick elements This indicates the difficulty in solving problems iteratively that emanate from quadratic approximations Essentially per dof tets solve in the ideal case 1 5 times slower APPENDIX D PARALLEL VALIDATION 43 Number Time se
24. ad in all coordinate directions The displacements are compared at global nodes 55 and 160 and the maximum overall principal stress is also determined from both runs All values are seen to be identical For the parallel runs the processor number containing the value is given in parenthesis and the reported node number is the local processor node number Serial Displacements Node X COOr y coor Z COOr x disp y disp z disp 55 8 33E 01 0 00E 00 1 67E 01 4 9509E 01 4 3175E 01 4 2867E 01 160 8 33E 01 1 67E 01 5 00E 01 2 1305E 01 4 2030E 01 4 1548E 01 Serial Max Principal Stress Node Stress 8 9 0048E 01 Parallel Displacements P Node x coor y coor Z COor x disp y disp z disp 3 23 8 33E 01 0 00E 00 1 67E 01 4 9509E 01 4 3175E 01 4 2867E 01 1 17 8 33E 01 1 67E 01 5 00E 01 2 1305E 01 4 2030E 01 4 1548E 01 APPENDIX D PARALLEL VALIDATION 48 Parallel Max Principal Stress P Node Stress 4 6 9 0048E 01 Note Processor 4 s local node 6 corresponds to global node 8 D 2 4 Mock Turbine Modal Analysis In this test we examine a small mock turbine model with 30528 equations where the discretization is made with 8 node brick elements We compute using the serial code subspace method the first 5 eigenvalues using a lumped mass With the parallel
25. al nodes 100 and 200 and the maximum overall principal stress is also determined from both runs All values are seen to be identical For the parallel runs the processor number containing the value is given in parenthesis and the reported node number is the local processor node number Serial Displacements Node X COOr y coor Z COOr x disp y disp z disp 100 6 00E 01 8 00E 01 4 00E 01 1 3778E 01 1 1198E 00 1 1241E 00 200 2 00E 01 6 00E 01 1 00E 00 4 1519E 01 2 3568E 01 2 6592E 01 APPENDIX D PARALLEL VALIDATION 46 Serial Max Principal Stress Node Stress 1 4 0881E 02 Parallel Displacements P Node X COOr y coor Z COOr x disp y disp z disp 4 49 6 00E 01 8 00E 01 4 00E 01 1 3778E 01 1 1198E 00 1 1241E 00 2 38 2 00E 01 6 00E 01 1 00E 00 4 1519E 01 2 3568E 01 2 6592E 01 Parallel Max Principal Stress P Node Stress 3 1 4 0881E 02 Note Processor 3 s local node 1 corresponds to global node 1 D 2 2 Box Beam In this test a linear elastic unit box beam discretized into 4 x 20 x 20 4 node shell elements is clamped on one face and loaded on the opposite face with a uniform load in all coordinate directions The displacements are compared at global nodes 500 and 1000 and the maximum overall principal bending moment is also determined from both ru
26. c Mflops Number Scaling Slow down Processors KSP Solve Solves Ideal vs Brick 2 216 8 1299 30 1 7 4 110 4 2615 30 101 1 5 8 56 62 5059 29 97 1 6 16 31 44 9370 30 90 1 5 32 17 07 17659 28 85 1 3 D 1 6 Transient In this test a short 2 to 1 aspect ratio neohookean beam is subjected to a step displacement in the axial direction The modeling employs symmetry boundary con ditions on three orthogonal planes The beam is discretized into uniform size 8 node brick elements 10 x 10 x 20 for a total of 7623 equations The dynamic vibrations of the material are followed for 40 time steps using Newmark s method The steep drop off in performance should be noted This is due to the small problems size There is too little work for each processor to be effectively utilized here Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 95 37 1079 1385 4 58 91 1687 1420 78 8 39 03 2645 1382 61 16 32 15 3138 1376 36 32 33 61 3123 1371 18 D 1 7 Mock turbine In this test we model a mock turbine fan blade with 12 fins The system is loaded using an Rw body force term which is computed consistently Overall there are 1 080 000 8 node brick elements in the mesh and 3 415 320 equations It should be noted that problem at roughly 3 5 million equations provides enough work for the processors that even at 32 processors there is no degradation
27. caam rice edu software ARPACK J Demmel J Dongarra and et al LAPACK Linear Algebra PACKage June 2010 http netlib org lapack G Karypis ParMETIS parallel graph partitioning see internet address http www users cs unm edu karypis metis parmetis 2003 R L Taylor FEAP A Finite Element Analysis Program Installation Manual University of California Berkeley http www ce berkeley edu feap Appendix A Installation The installation of the parallel version of FEAP is accomplished after first building a serial version see FEAP Installation Manual for instructions to build the serial version A 1 Installing PETSc In order to build the parallel version it is necessary to have an installed version of PETSc 4 that includes Metis and ParMetis 4 It is further important to install several of the optional pre conditioner and solver packages In the appropriate bash_xxx file it is useful but not necessary to insert lines similar to export PETSC_DIR Users rlt Software petsc 3 3 p5 export PETSC_ARCH gnu opt This saves on some typing later on The files manuals and installation instruction for PETSc may be downloaded from http www mcs anl gov petsc However in short after downloading and unpacking the source file the PETSc libraries need to be built and tested Our typical non debugging installation is performed as follows 23 APPENDIX A INSTALLATION 24 export PETSC_DIR Users rl
28. cause of the enormous variety of analyses that one can perform with FEAP it is not possible to provide parallel tests for all possible combinations of program features Nonetheless below one will find some basic validation tests that highlight the performance of the parallel version of the code on a variety of problems All validation tests were performed on a cluster of AMD Opteron 250 processors connected together via a Quadrics QsNet Il interconnect Code performance is often strongly related to the computational sub systems employed All tests reported utilized GCC v3 3 4 MPI v1 2 4 PETSc v2 3 2 p3 AMD ACML BLAS LAPACK v3 5 0 ParMetis v3 1 Prometheus v1 8 5 and ARPACK 92001 The batch scheduler assures that no other jobs are running on the same compute nodes during the runs All runs have utilized the algebraic multigrid solver Prometheus in blocked form with coordinate information Run times are as reported from PETSc summary statistics from a single run Mflops are those associated with PETSc s KSPsolve object Number of solves is the total number of Ax b solves during the KSP iterations in the total problem and Scaling of ideal is computed as Mflops np Mflops 2 x 100 40 APPENDIX D PARALLEL VALIDATION 41 D 1 Timing Tests D 1 1 Linear Elastic Block In this test a linear elastic unit block discretized into 70 x 70 x 70 8 node brick elements is clamped on one face and loaded on the opposite face with a uniform loa
29. code we compute the same eigenvalues using a parallel eigensolve implicitly restarted Arnoldi The computed frequencies and from the first 5 modes are compared and seen to be the same within the accuracy of the computation Serial Eigenvalues rad sec Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 8 10609997E 02 8 13523152E 02 8 13523152E 02 9 33393875E 02 9 33393875E 02 Parallel Eigenvalues rad sec 8 10609790E 02 8 13522933E 02 8 13522972E 02 9 33393392E 02 9 33393864E 02 The comparison of eigenvectors is a bit harder for this problem because of repeated eigenvalues The first eigenvalue is not repeated and it can easily be seen that the se rial and parallel codes have produced the same eigenmode up to an arbitrary scaling factor Eigenvalues 2 and 3 are repeated and thus the vectors computed are permis sibly drawn from a subspace and thus direct comparison is not evident The same holds for eigenvalues 4 and 5 though it can be observed that vector 4 from the serial computation does closely resemble vector 5 from the parallel computations i e they appear to be drawn from a similar region of the subspace As a test of the claim of differing eigenmodes due to selection of different eigenvectors from a subspace we also compute the first 5 modes of an asymmetric structure that does not possess repeated eigenvalues The basic geometry is that of perturbed cube The first 5 eigenva
30. d in all coordinate directions In blocked form there are 1 073 733 equations in this problem Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 129 20 1241 13 4 71 69 2171 13 87 8 35 77 4646 14 94 16 21 30 8347 14 84 32 13 19 14561 14 73 D 1 2 Nonlinear Elastic Block In this test a nonlinear neohookean unit block discretized into 50 x 50 x 50 8 node brick elements is clamped on one face and loaded on the opposite face with a uniform load in all coordinate directions In blocked form there are 397 953 equations in this problem To solve the problem to default tolerances takes 4 Newton iterations within which there are on average 12 KSP iterations Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 166 7 1142 53 4 82 66 2356 54 103 8 43 48 4642 53 102 16 27 15 7846 56 86 32 15 58 13988 52 77 D 1 3 Plasticity In this test one quarter of a plate with a hole is modeled using 364500 8 node brick elements and pulled in tension beyond yield The problem involves 10 uniform size load steps which drives the plate well into the plastic range each load step takes between 3 and 10 Newton iterations There are 1 183 728 equations Due to the large number APPENDIX D PARALLEL VALIDATION 42 of overall KSP iterations needed for this problem it has only been solved using 8 16 and 32 processors
31. e can significantly reduce the amount of storage needed to store the sparse coefficient matrix created by TANGent or UTANgent when a problem has a mix of element types and the matrix is in BAIJ format For example if a problem has a large number of solid elements with 3 degrees of freedom per node and additional frame or shell elements with 6 degrees of freedom per node specifying bsize 3 can save considerable memory Further the setting of the block size can improve the rate of convergence of iterative and direct solvers The use of the unity flag in OUTDomains AIJ 1 forces the inclusion of all even pre scribed degrees of freedom in the matrix assembly for AIJ format This permits the use of blocking for AIJ format matrices something that is in general not possible if prescribed degrees of freedom are not assembled This is the default behavior for BAIJ format matrices APPENDIX B SOLUTION COMMAND MANUAL 34 PETSc FEAP COMMAND INPUT COMMAND MANUAL pets pets on pets off pets view pets noview The use of the PETSc command activates on or deactivates off parallel solution op tions respectively To turn on parallel computing the command may be given in the simple form PETSc When more than one partition is created i e the number of solution processors is 2 or more the PETSc option is on by default The command must be the first command of the command language program when only 1 processor is used The option PETSc VIEW wil
32. e parallel executable for FEAP is built from the parfeap subdirectory using the command make install If the ARPAck libraries have been built one should edit the makefile to ensure that they are linked by uncommenting the appropriate lines Appendix B Solution Command Manual Pages FEAP has a few options that are used only to solve parallel problems The commands are additions to the command language approach in which users write each step using available commands The following pages summarize the commands currently added to the parallel version of FEAP 25 APPENDIX B SOLUTION COMMAND MANUAL 26 DISPlacements FEAP COMMAND INPUT COMMAND MANUAL disp gnod lt n1 n2 n3 gt Other options of this command are described in the FEAP User Manual The com mand DISPlacement may be used to print the current values of the solution generalized displacement vector associated with the global node numbers of the original mesh The command is given as disp gnod ni n2 n3 prints out the current solution vector for global nodes n1 to n2 at increments of n3 default increment 1 If n2 is not specified only the value of node n1 is output If both n1 and n2 are not specified only the first node solution is reported APPENDIX B SOLUTION COMMAND MANUAL 27 GLISt FEAP COMMAND INPUT COMMAND MANUAL glist n1 lt values gt The command GLISt is used to specify lists of global node numbers for output of nodal values It is possible to specify up to
33. early time steps in the solution Convergence will be assumed if either the normal convergence criteria or the one relative to the specified maximum energy is satisfied The TOL command also permits setting the maximum energy value used for conver gence The command is issued as TOL EMAXimum vi where v1 is the value of the maximum energy quantity Note that the TIME command sets the maximum energy to zero thus the value of EMAXimum must be reset after each time step using for example a set of commands LOOP time n TIME TOL EMAX 5 e 3 LOOP newton m TANG 1 NEXT etc NEXT to force convergence check against a specified maximum energy The above two forms for setting the convergence are nearly equivalent however the ENERgy tolerance form can be set once whereas the EMAXimum form must be reset after each time command The command TOL ITERation itol atol dtol is used to control the solution accuracy when an iterative solution process is used to solve the equations Kdu R In this case the parameter tol sets the relative error for the solution accuracy i e when RTR lt itol RTR A The parameter atol is only used when solutions are performed using the KSP schemes in a PETSc implementation to control the absolute residual error RTR lt atol APPENDIX B SOLUTION COMMAND MANUAL 38 The dtol parameter is used to terminate the solution when divergence occurs The default for itol is 1 0d 08 that for atol
34. ext section for a discussion of possible options for OUTDomains It is usually also possible to also create the graph file in parallel without separately running partition from the command line by using the command set OUTMesh GRAPh PARTition numd OUTDomains where numd is the number of domains to create For this to work the program mpirun must be in your path Here the parameter nump is equal to numd The use of the command OUTMesh is required to ensure that a flat input file is available and after execution it is destroyed 1 3 3 Structure of parallel meshes It is assumed that numd represents the number of processors to be used in the parallel solution Each partition is assigned numpn nodes The number can differ slightly among the various partitions but is approximately the total number of nodes in the problem divided by numd In the current release no weights are assigned to the node or the node graph edges to reflect possible differences in solution or communication effort Each partitioned input file also contains ghost nodes for effecting the evaluation of element residuals The sum of the nodes in a partition numpn and its ghost nodes defines the total number of nodes in each partitioned data file i e the total number of nodes numnp in each mesh partition In the parallel solution the global equations are numbered sequentially from 1 to the total number of equations in the problem numteq The nodes in partition 1 are ass
35. for iterative equation methods 16 3 2 2 GLIST amp GNODE Output of results with global node numbers 16 3 3 Eigenproblem solution for modal problems 17 3 3 1 Subspace method solutions crol 18 3 3 2 Arnoldi Lanczos method solutions 18 3A Graphies Output AE 19 34 1 GPEOt command amp aws ei a e iaa 19 3 4 2 NDATa command e so e lit a toa d ee Foy bs G ee Bs ea ii 20 AA Paa EN e a aea edn a eek O 20 CONTENTS ii A Installation 23 A 1 Installing PETSe is a ena a aos chal e ems e e eta a 23 A 2 Installing parallel FEAP Sd te and oh Se OG ebm ba e de 24 B Solution Command Manual 25 C Program structure 39 A A O 39 D Parallel Validation 40 Dd Eiming Tests anny a A E A ee 41 Dell Linear Plastic Block 2 2040 ta A A a 41 D 1 2 Nonlinear Elastic Block o oo aaa a 41 D134 Plasticity tz a ee Bats E a aas 41 D 1 4 Box Beam Shells 42 D 1 5 Linear Elastic Block 10 node Tets 42 D 1 6 Transient riese aui Ae ioa ie e E a a a eS e a TE E 43 D 1 7 Mock turbine oaaae 43 D 1 8 Mock turbine Small 44 D 1 9 Mock turbine Tets o 44 D 1 10 Eigenmodes of Mock Turbine 45 D 2 Serial to Parallel Verification 2 0 a a a a 45 D 2 1 Linear elastic block ooa 45 D22 BoxsBean ei a li a e ade 46 D 2 3 Linear Elastic Block Tets 47 D 2 4 Mock Turb
36. h 8 added vectors and 20 iterations are needed to converge to an acceptable error it is necessary to perform 360 solutions of the linear equations Thus for large problems the method will be very time consuming 3 3 2 Arnoldi Lanczos method solutions In order to reduce the computational effort for eigenproblems the Arnoldi Lanczos methods implemented in the ARPACK module available from Rice University has been modified to work with the parallel version of FEAP Two modes of the ARPACK solution methods are included in the program 1 Mode 1 Solves the problem reformed as MKM G WA where M This form is most efficient when the mass matrix is diagonal lumped and thus in the current release of parallel FEAP is implemented only for diagonal lumped mass forms This mode form is specified by the solution command set CHAPTER 3 SOLUTION PROCESS 19 TANGent MASS LUMPed PARPack LUMPed nmodes lt maxiters gt lt eigtol gt where nmodes is the number of desired modes Optionally maxiters is the number of iterations to perform default is 300 and eigtol the solution tolerance on eigenvalues default is the maximum of 1 d 12 and the values set by the command TOL 2 Mode 3 Solves the general linear eigenproblem directly and requires solution of the linear problem Kx y for each iteration Fewer iterations are normally required than in the subspace method however the method is generally far less efficient than the Mode 1
37. hod for Solid and Structural Mechanics Elsevier Oxford 6 edition 2005 O C Zienkiewicz R L Taylor and P Nithiarasu The Finite Element Method for Fluid Dynamics Elsevier Oxford 6 edition 2005 S Balay K Buschelman W D Gropp D Kaushik M G Knepley L C McInnes B F Smith and H Zhang PETSc Web page 2001 http www mcs anl gov petsc S Balay K Buschelman V Eijkhout W D Gropp D Kaushik M G Knepley L C McInnes B F Smith and H Zhang PETSc users manual Technical Report ANL 95 11 Revision 2 1 5 Argonne National Laboratory 2004 G Karypis METIS Family of multilevel partitioning algorithms http www users ce umn edu karypis metis G Karypis ParMETIS parallel graph partitioning see internet address http www users cs unm edu karypis metis parmetis 2003 S Balay W D Gropp L C McInnes and B F Smith Efficient management of parallelism in object oriented numerical software libraries In E Arge A M Bruaset and H P Langtangen editors Modern Software Tools in Scientific Com puting pages 163 202 Birkhauser Press 1997 M Adams PROMETHEUS Parallel multigrid solver library for unstructured finite element problems http www columbia edu ma2325 21 BIBLIOGRAPHY 22 11 12 13 14 15 MATLAB www mathworks com 2011 R Lehoucq K Maschhoff D Sorensen and C Yang ARPACK Arnoldi lanczos package for eigensolutions http www
38. ine Modal Analysis 48 D 2 5 Transient leo 2 ec aa ld A ea A a 51 D 2 6 Nonlinear elastic block Static analysis 54 D 2 7 Nonlinear elastic block Dynamic analysis 55 D287 Plastic plate a they nek ira a de la les a id a eh 55 D29 Transient plastic 2 3 2c 2 6 ae ty do Pe da 56 List of Figures 1 1 Structure of stiffness matrix in partitioned equations 6 2 1 Input file structure for parallel solution 8 D 1 Comparison of Serial left to Parallel right mode shape 1 degree of freedork Ir aur Angrep Bn A eS Bones Gate a pe thawed A ted ap Chuck 49 D 2 Comparison of Serial left to Parallel right mode shape 2 degree of freedom Ze Ys t ama Gee de he BE ae ak Se net Se dt hE hee n Sig 49 D 3 Comparison of Serial left to Parallel right mode shape 3 degree of freedom OE pra A hac see Bad ety ends a Se eh Sa dors ape at Be et 49 D 4 Comparison of Serial left to Parallel right mode shape 4 degree of a AA os fe Meas a ia ds T Gee sh Gy E ouit 50 D 5 Comparison of Serial left to Parallel right mode shape 5 degree of PCCD A ae Hn ak Gey eRe Siete oh ae Se U Gh ee Ae E iah 50 D 6 Comparison of Serial left to Parallel right mode shape 1 degree of PVCU OME A E A A Awe Bee ee gfe 51 D 7 Comparison of Serial left to Parallel right mode shape 2 degree of freedom Zire ad ds si a pur a Tea eed ae 51 D 8 Comparison of Serial left to Parallel right
39. integer factor of ndf 2 1 4 LOCal to GLOBal node numbering Each record in this set defines three values 1 a local node number in the partition 2 the global node associated with the local number and 3 the global equation block number associated with the local node The first numpn records in the set are the nodes associated with the current partition the remaining records with the ghost nodes 2 1 5 GETData and SENDdata Ghost node get and send The current partition retrieves GETData the solution values for its ghost nodes from other partitions The data is divided into two parts 1 A POINTER part which defines the number of values to obtain from each partition and 2 The VALUes list of local node numbers needing values The pointer data is given as GETData POINter nparts np_1 np_2 np_nparts CHAPTER 2 INPUT FILES FOR PARALLEL SOLUTION 10 where np_i defines the number of values to get from partition 1 note the number should always be a zero for the current partition The nodal values list is given as GETData VALUes nvalue local_node_1 local_node_2 local_node_nvalue The local_node_i numbers are grouped so that the first np_1 are obtained from pro cessor 1 the next np_2 from processor 2 etc The local node 1 is the number of a local ghost node to be obtained from another processor and may appear only once in the list of GETData VALUes A corresponding pair of lists is given for the data to be sent SENDdata
40. ion of linear equations 3 Convergence of the subspace eigenpair solution which is measured in terms of the change in subsequent eigenvalues computed The basic command TOL tol without any arguments sets the parameter tol used in the solution of non linear problems where the command sequence LOOP 30 TANG 1 NEXT is given In this case the loop is terminated either when the number of iterations reaches 30 or whatever number is given in this position or when the energy error is less than tol The energy error is given by E du R lt tol du R Eo in which R is the residual of the equatons and du is the solution increment The default value of tol for the solution of nonlinear problems is 1 0d 16 The TOL command also permits setting a value for the energy below which convergence is assumed to occur The command is issued as TOL ENERgy v1 where v1 is the value of the converged energy i e it is equivalent to the tolerance times the maximum energy value Normally FEAP performs nonlinear iterations until the value of the energy is less than the TOLerance value times the value of the energy from the first iteration APPENDIX B SOLUTION COMMAND MANUAL 37 as shown above However for some transient problems the value of the initial energy is approaching zero e g for highly damped solutions which are converging to some steady state limit In this case it is useful to specify the energy for convergence relative to
41. ioning algorithm on the total problem for example that given by say the mesh file Ifilename FEAP produces numd files for the partitions and these serve as input for the parallel solution Each new input file is named Ifilename_0001 etc up to the number of partitions specified i e numd partitions The first part of each file contains a standard FEAP input file for the nodes and elements belonging to the partition This is followed by a set of commands that begin with DOMAin and end with END DOMAin All of the data contained between the DOMAin and END DOMAin is produced automatically by FEAP when using OUTDomains The file structure for a parallel solution is shown in Figure 2 1 and is provided only to describe how the necessary data is given to each partition No changes are allowed to be made to these statements 2 1 Basic structure of parallel file Each part of the data following the END MESH statement performs a specific task in the parallel solution It is important that the data not be altered in any way as this can adversely affect the solution process Below we describe the role each data set plays during the solution 2 1 1 DOMAIN Domain description The DOMAIN data defines the number of nodes belonging to this partition numpn the number of total nodes in the problem numtn and the number of total equations in the CHAPTER 2 INPUT FILES FOR PARALLEL SOLUTION FEAP Start record and title Control and mesh description
42. l result in the creation of debug files containing important parallel matrices and vectors The output is in MATLAB sparse format This option should only be used for very small problems to check that a formulation produces correct results i e there is another set of terms to which a comparison is to be made The option is turned off using the statement PETSc NOVIew The default is NOVIew APPENDIX B SOLUTION COMMAND MANUAL 30 STREss FEAP COMMAND INPUT COMMAND MANUAL stre gnod lt n1 n2 n3 gt Other options for this command are given in the FEAP User Manual The STREss command is used to output nodal stress results at global node numbers n1 to n2 at increments of n2 default 1 The command specified as stre gnode n1 n2 n3 prints out the stresses for global nodes n1 to n2 at increments of n3 default increment 1 If n2 is not specified only the value of node n1 is output If both nl and n2 are not specified only the first node solution is reported APPENDIX B SOLUTION COMMAND MANUAL 36 TOLerance FEAP COMMAND INPUT COMMAND MANUAL tol vl tol ener vl tol emax vl tol iter v1 v2 v3 The TOL command is used to specify the solution tolerance values to be used at various stages in the analysis Uses include 1 Convergence of nonlinear problems in terms of the norm of energy in the current iterate the inner dot product of the displacement increment and the solution residual vectors 2 Convergence of iterative solut
43. llel right mode shape 4 degree of freedom 1 DISPLACEMENT 2 3 11E 01 2 54E 01 1 98E 01 1 42E 01 8 53E 02 2 89E 02 2 75E 02 8 38E 02 1 40E 01 1 97E 01 2 53E 01 3 09E 01 3 66E 01 Value 2 78E 00 Hz Figure D 10 Comparison of Serial left to Parallel right mode shape 5 degree of freedom 2 __EIGENV 5 1 07E 00 9 01E 01 7 37E 01 5 78E 01 4 08E 01 2 44E 01 8 00E 02 8 43E 02 2 49E 01 4 13E 01 5 77E 01 7 41E 01 9 06E 01 Time 0 00E 00 APPENDIX D PARALLEL VALIDATION z Displacement at 0 6 1 1 Ore M Element 1 Time Serial Value Parallel Value Serial Value Parallel Value 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 2 5000E 01 2 5181E 04 2 5181E 04 3 9640E 02 3 9640E 02 5 0000E 01 6 0174E 04 6 0174E 04 1 3681E 01 1 3681E 01 7 5000E 01 8 3328E 04 8 3328E 04 1 9837E 01 1 9837E 01 1 0000E 00 1 1250E 03 1 1250E 03 2 2532E 01 2 2532E 01 1 2500E 00 4 2010E 04 4 2010E 04 1 5061E 01 1 5061E 01 1 5000E 00 7 1610E 04 7 1610E 04 1 5312E 01 1 5312E 01 1 7500E 00 1 3485E 03 1 3485E 03 3 7978E 01 3 7978E 01 2 0000E 00 2 2463E 03 2 2463E 03 4 2376E 01 4 2376E 01 2 2500E 00 1 8943E 03 1 8943E 03 4 4457E 01 4 4457E 01 2 5000E 00 9 1891E 04 9 1891E 04 2 9013E 01 2 9013E 01 2 7500E 00 6 8862E 04 6 8862E 04 1 4539E 02 1 4539E 02 3 0000E 00 3 8305E 05 3 8306E 05 1 1134E 03 1 1139E 03 3 2500E 00 7 4499E
44. ls bricks and beams under a random dynamic load The basic geometry consists of a cantilever shell with a brick block above it which has an embedded beam protruding from it The loading is randomly prescribed on the top of the structure and the time histories are followed and compared for the displacements at a particular point the first stress component in a given element and the Ist principal stress and von Mises stress at a particular node The time history is followed for 20 time steps The time integration is performed using Newmark s method Agreement is seen to be perfect to the accuracy of the computations APPENDIX D PARALLEL VALIDATION 52 __EIGENV 3 1 71E 00 1 42E 00 1 13E 00 8 43E 01 5 54E 01 2 65E 01 2 42E 02 3 13E 01 6 02E 01 8 91E 01 1 18E 00 1 47E 00 1 76E 00 Time 0 00E 00 DISPLACEMENT 3 1 00E 00 8 36E 01 6 71E 01 5 07E 01 3 43E 01 1 78E 01 1 38E 02 1518 01 3 15E 01 4 79E 01 6 44E 01 8 08E 01 9 72E 01 Value 1 52E 00 Hz Figure D 8 Comparison of Serial left to Parallel right mode shape 3 degree of freedom 3 DISPLACEMENT 1 _EIGENV 4 _ 0 00E 00 5 18E 09 8 33E 02 1 34E 01 1 67E 01 2 69E 01 2 50E 01 4 03E 01 3 33E 01 5 38E 01 4 17E 01 6 72E 01 5 00E 01 8 06E 01 5 83E 01 9 41E 01 6 67E 01 1 08E 00 7 50E 01 1 21E 00 8 33E 01 1 34E 00 9 17E 01 1 48E 00 1 00E 00 1 61E 00 Value 2 43E 00 Hz Time 0 00E 00 Figure D 9 Comparison of Serial left to Para
45. lues and modes are compared and show proper agreement to within the accuracy of the computations for both the eigenvalues and the eigenmodes APPENDIX D PARALLEL VALIDATION 49 DISPLACEMENT 1 EIGENV 1 7 23E 02 3 45E 04 6 02E 02 2 88E 04 4 82E 02 2 30E 04 3 61E 02 1 73E 04 2 41E 02 1 15E 04 1 20E 02 5 75E 05 8 68E 14 9 00E 12 1 20E 02 5 75E 05 2 41E 02 1 15E 04 3 61E 02 1 73E 04 4 82E 02 2 30E 04 6 02E 02 2 88E 04 7 23E 02 3 45E 04 Value 4 53E 02 Hz Time 0 00E 00 Figure D 1 Comparison of Serial left to Parallel right mode shape 1 degree of freedom 1 DISPLACEMENT 2 EIGENV 2 7 07E 02 3 04E 04 5 89E 02 2 54E 04 4 72E 02 2 03E 04 3 54E 02 1 52E 04 2 36E 02 1 01E 04 1 18E 02 5 07E 05 4 54E 05 6 36E 08 1 17E 02 5 08E 05 2 35E 02 1 02E 04 3 53E 02 1 52E 04 4 71E 02 2 03E 04 5 88E 02 2 54E 04 7 08E 02 3 04E 04 Value 4 54E 02 Hz Time 0 00E 00 Figure D 2 Comparison of Serial left to Parallel right mode shape 2 degree of freedom 2 DISPLACEMENT 3 EIGENV 3 1 00E 00 6 77E 03 8 33E 01 5 64E 03 6 67E 01 4 51E 03 5 00E 01 3 38E 03 3 33E 01 2 26E 03 1 67E 01 1 13E 03 3 91E 10 4 33E 08 1 67E 01 1 13E 03 3 33E 01 2 26E 03 5 00E 01 3 39E 03 6 67E 01 4 518 03 8 33E 01 5 64E 03 1 00E 00 6 77E 03 Value 4 54E 02 Hz Time 0 00E 00 Figure D 3 Comparison of Serial left to Parallel right mode shape 3 degree of freedom 3 APPENDIX D PARALLEL VALIDATI
46. mode shape 3 degree of fredon gt e BA dae Gh eB ages oe e a dls a 52 D 9 Comparison of Serial left to Parallel right mode shape 4 degree of feedom I runie A e AE A A E he P BR a 52 D 10 Comparison of Serial left to Parallel right mode shape 5 degree of freedom Ds maa li A AAA 52 D 11 von Mises stresses at the end of the loading left serial right parallel 56 D 12 Z displacement for the node located at 0 6 1 0 1 0 57 D 13 11 component of the stress in the element nearest 1 6 0 2 0 8 58 D 14 1st principal stress at the node located at 1 6 0 2 0 8 58 D 15 von Mises stress at the node located at 1 6 0 2 0 8 59 iii Chapter 1 INTRODUCTION 1 1 General features This manual describes features for the parallel version of the general purpose Finite Element Analysis Program FEAP It is assumed that the reader of this manual is familiar with the use of the serial version of FEAP as described in the basic user manual It is also assumed that the reader of this manual is familiar with the finite element method as describe in standard reference books on the subject e g The Finite Element Method 6th edition by O C Zienkiewicz R L Taylor et al 2 3 4 The current version of the parallel code modifies the serial version of FEAP to in terface to the PETSc library system version 3 3 available from Argonne National Laboratories Y In addition the METIS and ParMETIS
47. namic analysis In this test a non linear neo hookean block is subjected to a step displacement at one end while the other is end is clamped The time history of the displacement at the center of the block is followed The time integration is performed using Newmark s method Agreement is seen to be perfect to the accuracy of the computation x Displacement Serial Run Parallel Run Time Node 172 Node 25 Processor 3 0 0000E 00 0 0000E 00 0 0000E 00 1 0000E 02 6 6173E 07 6 6173E 07 2 0000E 02 1 1588E 05 1 1588E 05 3 0000E 02 4 8502E 05 4 8502E 05 4 0000E 02 4 8177E 05 4 8177E 05 5 0000E 02 2 6189E 04 2 6189E 04 6 0000E 02 7 8251E 04 7 8251E 04 7 0000E 02 1 0785E 03 1 0785E 03 8 0000E 02 9 7015E 04 9 7015E 04 9 0000E 02 7 7567E 04 7 7567E 04 1 0000E 01 8 2252E 04 8 2252E 04 Note Local node 25 of processor 3 corresponds to global node 172 D 2 8 Plastic plate In this test a small version of the quarter plastic plate from the timing runs is used with 4500 8 node brick elements The problem involves 10 uniform size load steps which APPENDIX D PARALLEL VALIDATION 56 Mises Stress PSTRESS 6 5 53E 01 8 82E 01 1 218 02 5 53E 01 8 82E 01 1 21E 02 1 54E 02 1 87E 02 2 20E 02 2 53E 02 2 86E 02 3 18E 02 3 51E 02 3 84E 02 4 17E 02 4 50E 02 1 54E 02 1 87E 02 2 20E 02 2 53E 02 2 86E 02 3 18E 02 3 51E 02 3 84E 02 4 17E 02 4 50E 02 Time 1 00E 00 Time 1 00
48. nique plot number it will be between 0001 and 9999 3 4 2 NDATa command Once the GPLOt files have been created they may be plotted using a serial execution of the parallel FEAP program i e using the original pre partioning step file Ifilename The command may be given in INTEractive mode only as one of the options Plot gt NDATa DISP1 n Plot gt NDATa STREss n Plot gt NDATa PSTRess n where n is the value of yyyy used to write the file WARNING Plots by FEAP use substantial memory and thus this option may not work for very large problems One should minimize the number of commands used during input of the problem description i e remove input commands in the mesh that create new memory 3 4 3 Paraview An alternate scheme for plotting parallel solutions can be achieved by use of the Par aview system This is a convenient open source tool that can be used with FEAP This integration is provided as a user macro extension to the program and can be downloaded from http www ce berkeley edu sanjay FEAP feap html See http www paraview org Bibliography 1 R L Taylor FEAP A Finite Element Analysis Program User Manual Univer sity of California Berkeley http www ce berkeley edu feap O C Zienkiewicz R L Taylor and J Z Zhu The Finite Element Method Its Basis and Fundamentals Elsevier Oxford 6 edition 2005 O C Zienkiewicz and R L Taylor The Finite Element Met
49. ns All values are seen to be identical For the parallel runs the processor number containing the value is given in parenthesis and the reported node number is the local processor node number Serial Displacements Rotations Node X coor y coor Z COOr x disp y disp z disp x rot y rot Z rot 500 8 00E 01 1 00E 01 1 00E 00 3 6632E 03 3 2924E 03 2 3266E 03 4 4272E 02 7 3033E 04 2 1595E 02 1000 1 00E 00 3 00E 01 2 00E 01 2 2972E 02 1 5303E 03 1 6876E 02 4 8140E 02 2 8224E 02 1 3278E 01 Serial Max Principal Bending Moment Node Stress 1 1 7091E 01 APPENDIX D PARALLEL VALIDATION 47 Parallel Displacements Rotations P Node x coor y coor Z COOr x disp y disp z disp x rot y rot Z rot 1 29 8 00E 01 1 00E 01 1 00E 00 3 6632E 03 3 2924E 03 2 3266E 03 4 4272E 02 7 3033E 04 2 1595E 02 2 280 1 00E 00 3 00E 01 2 00E 01 2 2972E 02 1 5303E 03 1 6876E 02 4 8140E 02 2 8224E 02 1 3278E 01 Parallel Max Principal Bending Moment P Node Stress 4 1 1 7091E 01 Note Processor 4 s local node 1 corresponds to global node 1 D 2 3 Linear Elastic Block Tets In this test a linear elastic unit block discretized into 162 10 node tetrahedral elements is clamped on one face and loaded on the opposite face with a uniform lo
50. ociated with the first set of equations the nodes in partition 2 the second set etc For each partition the stiffness and or the mass matrix is also partitioned and each partition matrix has two parts a a diagonal block for all the nodes in the partition i e numpn nodes and b off diagonal blocks associated with the ghost nodes as shown in Figure 1 1 In solving a set of linear equations Kdu R associated with an implicit solution step the solution vector du and the residual R are also split according to each partition The residual for each partition contains only 2Use of this command set requires the path to the location of the partition program to be set in the pstart F file located in the parfeap directory CHAPTER 1 INTRODUCTION 6 the terms associated with the equations of the partition The solution vector however has both the terms associated with the partition as well as those associated with the equations of its ghost nodes In this way it is only necessary to exchange values for the displacement quantities associated with the respective ghost nodes after each solution iteration This optimizes the communication costs In the next chapter we describe how the input data files for each partition are organized Processor 1 29 Processor 2 Figure 1 1 Structure of stiffness matrix in partitioned equations Chapter 2 Input files for parallel solution After using the METIS or the ParMETIS partit
51. of performance The scaling is perfect APPENDIX D PARALLEL VALIDATION Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 854 3 806 116 4 362 4 1931 112 120 8 172 9 4085 110 127 16 88 99 8232 115 128 32 46 68 16159 112 125 D 1 8 Mock turbine Small 44 In this test we model again a mock turbine fan blade with 12 fins The system is loaded using an Rw body force term which is computed consistently Overall however there are only 552960 8 node brick elements in the mesh and 1 771 488 equations Number Time sec Mflops Number Scaling Processors KSP Solve Solves Ideal 2 347 40 1097 125 4 199 50 1878 132 86 8 91 63 4064 122 93 16 47 68 8024 126 91 32 26 32 15400 119 88 D 1 9 Mock turbine Tets In this test we model again a mock turbine fan blade with 12 fins The system is loaded using an Rw body force term which is computed consistently This time however we utilize 10 node tetrahedral elements with a model that has 1 771 488 equations This computation can be directly compared to the small mock turbine benchmark The slow down is given in the last column of the table below Number Time sec Mflops Number Scaling Slow Down Processors KSP Solve Solves Ideal vs Brick 2 507 7 1193 126 1 5 4 304 2 1934 1 29 81 1 5 8 131 0 4675 131 98 1 4 16 70 01 8860 134 93
52. s on output arrays and this remains in effect for all CHAPTER 3 SOLUTION PROCESS 15 commands until the command is given with the NOVIew parameter The file is created in a format that may be directly used by MATLAB This command should only be used with small problems to verify the correctness of results as large files will result otherwise 3 2 Solution of linear equations The parallel version of FEAP can use most all of the SLES linear solvers available in PETSc as well as the parallel multigrid solvers Prometheus and GAMG This also includes most of the direct solvers that can optionally be built with PETSc The actual type of linear solver used is specified on the mpirun line and several useful examples are contained in the makefile located in the parfeap directory see Sect 3 above Once the solution is initiated the solution of linear equations is performed whenever a TANG 1 or SOLVe command is given The types of solvers and the associated pre conditioners tested to date are described in Table 3 1 This is only a small sampling of the many options available in PETSc Solver Preconditioner Matrix format Notes CG Jacobi AIJ and BAIJ formats CG Prometheus BAIJ format CG Hypre with Boomerang AIJ format CG ML Trilinos AIJ format CG GAMG Successor to Prometheus AIJ with BCIN format MINRES Jacobi AIJ and BAIJ formats MINRES Prometheus BAIJ format GMRES Jacobi AIJ and BAIJ formats GMR
53. st nsbk equations are associated with block 1 the second with block 2 etc The total number of equations numteq for this form is numtn x nsbk Here each record of the MATRix storage data is given by the global block number the number of blocks associated with the current partition and the number of blocks associated with other partitions When the optional BCIN command is present every node has ndf equations independent of any boundary conditions If a degree of freedom DOF is of displacement type we assemble a unit value on the diagonal and all off diagonal entries are zero That is the equations for any DOF a that are fixed will be assembled as 1 du Ra du where du denotes a specified valued for the solution In some cases this can improve the efficiency of the solver and for some solvers it is required e g the Prometheus multi grid pre conditioner and GAMG the geometric algebraic multi grid pre conditioner 2 1 7 EQUAtion number data This data set is not present when the boundary equations are assembled BCIN How ever when the equations are in A J format and BCIN has not been set then it is necessary to fully describe the equation numbering associated with each node in the partition This is provided by the EQUAtion number data set The set consists of numnp records which contain the local node number followed by the global equation number for every degree of freedom associated with the node If a degree of freedom is res
54. t Software petsc 3 3 p5 export PETSC_ARCH gnu opt cd PETSC_DIR configure download spooles parmetis superlu_dist prometheus mpich ml hypre metis mumps scalapack blacs with debugging 0 Once the configuration is completed the PETSc library is compiled using make PETSC_DIR Users rlt Software petsc 3 3 p5 PETSC_ARCH gnu opt all and tested using make PETSC_DIR Users rlt Software petsc 3 3 p5 PETSC_ARCH gnu opt test This will create a PETSc system that includes Metis ParMetis Spooles SuperLU MUMPS Prometheus ML Trilinos Hypre as well as an MPI environment ScaLapack and BLACS are needed by MUMPS Of these only Metis and ParMetis are required assuming you already have an MPI environment Leave off the with debugging 0 flag if you want to build a debugging version In general it is best to build both a debugging and non debugging version The above instructions assume use of a bash shell For other operating systems or shells see the PETSc documentation at 6 Not all the listed packages are needed but these tend to be useful for a wide variety of problem classes A 2 Installing parallel FEAP Optionally one can include the ARPAck modules in the build To do so first build the archive archivelib a in the directory packages arpack archive using the command make install Then build the archive parpacklib a in the directory parfeap packages arpack using the command make install With the PETSc libraries available th
55. three different lists where the list number corresponds to n1 default 1 The list of nodes to be output is input with up to 8 values per record The input terminates when less than 8 values are specified or a blank record is encountered No more than 100 items may be placed in any one list List outputs are then obtained by specifying the command name list ni where name may be DISPlacement VELOcity ACCEleration or STREss and n1 is the desired list number Example BATCh GLISt 1 END 1 5 8 20 BATCh DISP LIST 1 END The global list of nodes is processed to determine the processor and the associated local node number Each processor then outputs its active values if any and gives both the local node number in the partition as well as the global node number APPENDIX B SOLUTION COMMAND MANUAL 28 GPLOt FEAP COMMAND INPUT COMMAND MANUAL gplo disp n gplo velo n gplo acce n gplo stre n Use of plot commands during execution of the parallel version of FEAP create the same number of graphic windows as processors used to solve the problem Each window contains only the part of the problem contained on that processor The use of the GPLOt command is used to save files containing the results for all nodal dispacements velocities accelerations or stresses in the total problem The only action occuring after the use of this command is the creation of a file containing the current results for the quantity specified Repeated
56. titioned input files in the AIJ format when using OUTDomains This format is compatible with most of PETSc s solver op tions However if one wishes to use a solver that requires or benefits from the BAIJ blocked format then one can issue the command OUTDomains BAIJ The block size can optionally be controlled by OUTDomains BAIJ lt nsbk gt The block size nsbk can be any integer factor of ndf and defaults to ndf if not specified Note that in the BAIJ format degrees of freedom with Dirichlet boundary are included in the matrix assembly Issuing OUTDomains AIJ forces A J format In this format it is also possible to include the degrees of freedom with Dirichlet boundary conditions in the matrix assembly as is required for certain PETSc solvers This is done by setting the boundary equation flag to unity OUTDomains AIJ 1 lt nsbk gt In this format one can optionally provide PETSc with a hint to the equation block size nsbk As with BA1J this value defaults to ndf if not specified 1 3 2 ParMETIS Parallel graph partitioning A stand alone parallel graph partitioner also exists The parallel partitioner partition located in the FEAPHOME8_4 parfeap partition subdirectory uses ParMETIS to perform the construction of the nodal split To use this program it is necessary to have a FEAP input file that contains all the nodal coordinate and all the element connection records That is there must be a file with the
57. trained i e of displacement or Dirichlet type the equation is not active and a zero appears This form results in fewer unknown values but may not be used with any equation solution requiring all equations to be present in particular Prometheus and GAMG 2 18 END DOMAIN record The parallel domain data is terminated by the END DOMAIN record It is followed by the solution commands CHAPTER 2 INPUT FILES FOR PARALLEL SOLUTION 12 2 1 9 Initial conditions Following the domain data the list of any initial conditions applied to a transient problem will appear The initial conditions must be fully specified in the original input data file Initial conditions for displacements will appear as shown in Fig 2 1 However if rate type conditions are applied the data will appear as BATCh Initial rate conditions TRANsient type c1 c2 c3 INITial RATE END BATCH List of rate conditions where type is one of the standard feap transient solution algorithms and c1 c2 c3 are the values of the transient solution parameters For example if the Newmark method is used then type will be output as NEWMark and c1 c2 will be the values of the 6 y Newmark parameters The final parameter c3 is not used by Newark but appears as unity If both initial displacements and intial rates are specified then both BATCh END pairs of data will appear in the domain input file Chapter 3 Solution process Once the parallel input mesh files are created an
58. ult 1 d 16 APPENDIX B SOLUTION COMMAND MANUAL 32 NDATa FEAP COMMAND INPUT COMMAND MANUAL ndat disp n ndat velo n ndat acce n ndat stre n This command is used in a serial execution of parallel FEAP using the mesh for the total problem It is necessary for files to be created during a parallel execution using the GPLOt command See manual page on GPLOt The command is given by NDATa DISPlacement num where the parameter num is the number corresponding to the order the DISPlacement are created Thus the command sequence NDATa DISPlacement 2 NDATa STREss 2 would display the results for the second files created for the displacements and stresses Note this command is Plot level command APPENDIX B SOLUTION COMMAND MANUAL 33 OUTDomains FEAP COMMAND INPUT COMMAND MANUAL outd lt aij gt outd aij 1 lt bsize gt outd baij lt bsize gt The use of the OUTDomains command may only be used after the GRAPh command partitions the mesh into num_d parts see GRAPh command language page for details Using the command OUTDomains AIJ or OUTDomains BAIJ creates num_d input files for a subsequent parallel solution in which the matrix format will be created in AIJ or BAIJ format respectively AIJ is the default The parameter bsize defines the block size and must be an integer divisor of ndf That is if ndf 6 then bsize may be 1 2 3 or 6 By default each block in the equations has a size ndf The setting of the block siz
59. with VELOcity ACCEleration and STREss 3 3 Eigenproblem solution for modal problems The computation of the natural modes and frequencies of free vibration of an undamped linear structural problem requires the solution of the general linear eigenproblem K MOA In the above K and M are the stiffness and mass matrices respectively and and A are the normal modes and frequencies squared Normally the constraint 6 M I is used to scale the eigenvectors In this case one also obtains the relation KS A CHAPTER 3 SOLUTION PROCESS 18 3 3 1 Subspace method solutions The subspace algorithm contained in FEAP has been extended to solve the above problem in a parallel mode The use of the subspace algorithm requires a linear solution of the equations Kx y for each vector in the subspace and for each subspace iteration The parallel subspace solution is performed using the command set TANGent MASS lt LUMPed CONSistent gt PSUBspace lt print gt nmodes lt nadded gt where nmodes is the desired number of modes nadded is the number of extra vectors used to accelerate the convergence default is maximum of nmodes and 8 and print produces a print of the subspace projections of K and M The accuracy of the com puted eigenvalues is the maximum of 1 d 12 and the value set by the TOL solution command The method may be used with either a lumped or a consistend mass matrix If it is desired to extract 10 eigenvectors wit

FEAP Parallel Manual - Department of : Civil and Environmental

Contents

Download Pdf Manuals

Related Search

Related Contents