Date: 2022-03-31T04:47:20+00:00

Actual source code: ex18.c

      1: static char help[] = "Demonstrates the use of the COO interface to PETSc matrices for finite element computations\n\n";

      3: /*
      4:      The COO interface for PETSc matrices provides a convenient way to provide finite element element stiffness matrices to PETSc matrix that should work
      5:    well on both CPUs and GPUs. It is an alternative to using MatSetValues()

      7:      This example is intended for people who are NOT using DMPLEX or libCEED or any other higher-level infrastructure for finite elements;
      8:    it is only to demonstrate the concepts in a simple way for those people who are interested and for those people who are using PETSc for
      9:    linear algebra solvers but are managing their own finite element process.

     11:      Please do NOT use this example as a starting point to writing your own finite element code from scratch!

     13:      Each element in this example has three vertices; hence the the usage below needs to be adjusted for elements of a different number of vertices.
     14: */

     16: #include <petscmat.h>
     17: #include "ex18.h"

     19: static PetscErrorCode CreateFEStruct(FEStruct *fe)
     20: {
     22:   fe->Nv = 5;
     23:   fe->Ne = 3;
     24:   PetscMalloc1(3*fe->Ne,&fe->vertices);
     25:   /* the three vertices associated with each element in order of element */
     26:   fe->vertices[0 + 0] = 0;
     27:   fe->vertices[0 + 1] = 1;
     28:   fe->vertices[0 + 2] = 2;
     29:   fe->vertices[3 + 0] = 2;
     30:   fe->vertices[3 + 1] = 1;
     31:   fe->vertices[3 + 2] = 3;
     32:   fe->vertices[6 + 0] = 2;
     33:   fe->vertices[6 + 1] = 4;
     34:   fe->vertices[6 + 2] = 3;
     35:   fe->n  = 5;
     36:   return 0;
     37: }

     39: static PetscErrorCode DestroyFEStruct(FEStruct *fe)
     40: {
     42:   PetscFree(fe->vertices);
     43:   PetscFree(fe->coo);
     44:   return 0;
     45: }

     47: static PetscErrorCode CreateMatrix(FEStruct *fe,Mat *A)
     48: {
     49:   PetscInt *oor,*ooc,cnt = 0;

     52:   MatCreate(PETSC_COMM_WORLD,A);
     53:   MatSetSizes(*A,fe->n,fe->n,PETSC_DECIDE,PETSC_DECIDE);
     54:   MatSetFromOptions(*A);

     56:   /* determine for each entry in each element stiffness matrix the global row and colum */
     57:   /* since the element is triangular with piecewise linear basis functions there are three degrees of freedom per element, one for each vertex */
     58:   PetscMalloc2(3*3*fe->Ne,&oor,3*3*fe->Ne,&ooc);
     59:   for (PetscInt e=0; e<fe->Ne; e++) {
     60:     for (PetscInt vi=0; vi<3; vi++) {
     61:       for (PetscInt vj=0; vj<3; vj++) {
     62:         oor[cnt]   = fe->vertices[3*e+vi];
     63:         ooc[cnt++] = fe->vertices[3*e+vj];
     64:       }
     65:     }
     66:   }
     67:   MatSetPreallocationCOO(*A,3*3*fe->Ne,oor,ooc);
     68:   PetscFree2(oor,ooc);

     70:   /* determine the offset into the COO value array the offset of each element stiffness; there are 9 = 3*3 entries for each element stiffness */
     71:   /* for lists of elements with different numbers of degrees of freedom assocated with each element the offsets will not be uniform */
     72:   PetscMalloc1(fe->Ne,&fe->coo);
     73:   fe->coo[0] = 0;
     74:   for (PetscInt e=1; e<fe->Ne; e++) {
     75:     fe->coo[e] = fe->coo[e-1] + 3*3;
     76:   }
     77:   return 0;
     78: }

     80: static PetscErrorCode FillMatrixCPU(FEStruct *fe,Mat A)
     81: {
     82:   PetscScalar s[9];

     85:   /* simulation of traditional PETSc CPU based finite assembly process */
     86:   for (PetscInt e=0; e<fe->Ne; e++) {
     87:     for (PetscInt vi=0; vi<3; vi++) {
     88:       for (PetscInt vj=0; vj<3; vj++) {
     89:         s[3*vi+vj] = vi+2*vj;
     90:       }
     91:     }
     92:     MatSetValues(A,3,fe->vertices + 3*e,3, fe->vertices + 3*e,s,ADD_VALUES);
     93:   }
     94:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     95:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     96:   return 0;
     97: }

     99: /*
    100:    Shows an example of tracking element offsets explicitly, which allows for
    101:    mixed-topology meshes and combining both volume and surface parts into the weak form.
    102: */
    103: static PetscErrorCode FillMatrixCPUCOO(FEStruct *fe,Mat A)
    104: {
    105:   PetscScalar *v,*s;

    108:   /* simulation of CPU based finite assembly process with COO */
    109:   PetscMalloc1(3*3*fe->Ne,&v);
    110:   for (PetscInt e=0; e<fe->Ne; e++) {
    111:     s = v + fe->coo[e]; /* point to location in COO of current element stiffness */
    112:     for (PetscInt vi=0; vi<3; vi++) {
    113:       for (PetscInt vj=0; vj<3; vj++) {
    114:         s[3*vi+vj] = vi+2*vj;
    115:       }
    116:     }
    117:   }
    118:   MatSetValuesCOO(A,v,ADD_VALUES);
    119:   PetscFree(v);
    120:   return 0;
    121: }

    123: /*
    124:   Uses a multi-dimensional indexing technique that works for homogeneous meshes
    125:   such as single-topology with volume integral only.
    126: */
    127: static PetscErrorCode FillMatrixCPUCOO3d(FEStruct *fe,Mat A)
    128: {
    129:   PetscScalar (*s)[3][3];

    132:   /* simulation of CPU based finite assembly process with COO */
    133:   PetscMalloc1(fe->Ne,&s);
    134:   for (PetscInt e=0; e<fe->Ne; e++) {
    135:     for (PetscInt vi=0; vi<3; vi++) {
    136:       for (PetscInt vj=0; vj<3; vj++) {
    137:         s[e][vi][vj] = vi+2*vj;
    138:       }
    139:     }
    140:   }
    141:   MatSetValuesCOO(A,(PetscScalar*)s,INSERT_VALUES);
    142:   PetscFree(s);
    143:   return 0;
    144: }

    146: int main(int argc, char **args)
    147: {
    148:   Mat             A;
    149:   FEStruct        fe;
    150:   PetscMPIInt     size;
    151:   PetscBool       is_kokkos,is_cuda;

    153:   PetscInitialize(&argc,&args,(char*)0,help);
    154:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    157:   CreateFEStruct(&fe);
    158:   CreateMatrix(&fe,&A);

    160:   FillMatrixCPU(&fe,A);
    161:   MatView(A,PETSC_VIEWER_STDOUT_WORLD);

    163:   MatZeroEntries(A);
    164:   FillMatrixCPUCOO(&fe,A);
    165:   MatView(A,PETSC_VIEWER_STDOUT_WORLD);

    167:   MatZeroEntries(A);
    168:   FillMatrixCPUCOO3d(&fe,A);
    169:   MatView(A,PETSC_VIEWER_STDOUT_WORLD);

    171:   MatZeroEntries(A);
    172:   PetscObjectBaseTypeCompare((PetscObject)A,MATSEQAIJKOKKOS,&is_kokkos);
    173:   PetscObjectBaseTypeCompare((PetscObject)A,MATSEQAIJCUSPARSE,&is_cuda);
    174:  #if defined(PETSC_HAVE_KOKKOS)
    175:   if (is_kokkos) FillMatrixKokkosCOO(&fe,A);
    176:  #endif
    177:  #if defined(PETSC_HAVE_CUDA)
    178:   if (is_cuda) FillMatrixCUDACOO(&fe,A);
    179:  #endif
    180:   MatView(A,PETSC_VIEWER_STDOUT_WORLD);

    182:   MatDestroy(&A);
    183:   DestroyFEStruct(&fe);
    184:   PetscFinalize();
    185:   return 0;
    186: }

    188: /*TEST
    189:   build:
    190:     requires: cuda kokkos_kernels
    191:     depends: ex18cu.cu ex18kok.kokkos.cxx

    193:   testset:
    194:     filter: grep -v "type"
    195:     output_file: output/ex18_1.out

    197:     test:
    198:       suffix: kok
    199:       requires: kokkos_kernels
    200:       args: -mat_type aijkokkos

    202:     test:
    203:       suffix: cuda
    204:       requires: cuda
    205:       args: -mat_type aijcusparse

    207: TEST*/