Date: 2026-07-30T21:14:20+00:00

Actual source code: ex3.c

      1: static char help[] = "Illustration of MatIS using a 1D Laplacian assembly\n\n";

      3: /*
      4:   MatIS means that the matrix is not assembled. The easiest way to think of this (for me) is that processes do not have
      5:   to hold full matrix rows. One process can hold part of row i, and another processes can hold another part. However, there
      6:   are still the same number of global rows. The local size here is not the size of the local IS block, which we call the
      7:   overlap size, since that is a property only of MatIS. It is the size of the local piece of the vector you multiply in
      8:   MatMult(). This allows PETSc to understand the parallel layout of the Vec, and how it matches the Mat. If you only know
      9:   the overlap size when assembling, it is best to use PETSC_DECIDE for the local size in the creation routine, so that PETSc
     10:   automatically partitions the unknowns.

     12:   Each P_1 element matrix for a cell will be

     14:     /  1 -1 \
     15:     \ -1  1 /

     17:   so that the assembled matrix has a tridiagonal [-1, 2, -1] pattern. We will use 1 cell per process for illustration,
     18:   and allow PETSc to decide the ownership.
     19: */

     21: #include <petscmat.h>

     23: int main(int argc, char **argv)
     24: {
     25:   MPI_Comm               comm;
     26:   Mat                    A;
     27:   Vec                    x, y;
     28:   ISLocalToGlobalMapping map;
     29:   PetscScalar            elemMat[4] = {1.0, -1.0, -1.0, 1.0};
     30:   PetscReal              error;
     31:   PetscInt               overlapSize = 2, globalIdx[2];
     32:   PetscMPIInt            rank, size;

     34:   PetscFunctionBeginUser;
     35:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     36:   comm = PETSC_COMM_WORLD;
     37:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
     38:   PetscCallMPI(MPI_Comm_size(comm, &size));
     39:   /* Create local-to-global map */
     40:   globalIdx[0] = rank;
     41:   globalIdx[1] = rank + 1;
     42:   PetscCall(ISLocalToGlobalMappingCreate(comm, 1, overlapSize, globalIdx, PETSC_COPY_VALUES, &map));
     43:   /* Create matrix */
     44:   PetscCall(MatCreateIS(comm, 1, PETSC_DECIDE, PETSC_DECIDE, size + 1, size + 1, map, map, &A));
     45:   PetscCall(PetscObjectSetName((PetscObject)A, "A"));
     46:   PetscCall(ISLocalToGlobalMappingDestroy(&map));
     47:   PetscCall(MatISSetPreallocation(A, overlapSize, NULL, overlapSize, NULL));
     48:   PetscCall(MatSetValues(A, 2, globalIdx, 2, globalIdx, elemMat, ADD_VALUES));
     49:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
     50:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
     51:   /* Check that the constant vector is in the nullspace */
     52:   PetscCall(MatCreateVecs(A, &x, &y));
     53:   PetscCall(VecSet(x, 1.0));
     54:   PetscCall(PetscObjectSetName((PetscObject)x, "x"));
     55:   PetscCall(VecViewFromOptions(x, NULL, "-x_view"));
     56:   PetscCall(MatMult(A, x, y));
     57:   PetscCall(PetscObjectSetName((PetscObject)y, "y"));
     58:   PetscCall(VecViewFromOptions(y, NULL, "-y_view"));
     59:   PetscCall(VecNorm(y, NORM_2, &error));
     60:   PetscCheck(error <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Invalid output, x should be in the nullspace of A");
     61:   /* Check that an interior unit vector gets mapped to something of 1-norm 4 */
     62:   if (size > 1) {
     63:     PetscCall(VecSet(x, 0.0));
     64:     PetscCall(VecSetValue(x, 1, 1.0, INSERT_VALUES));
     65:     PetscCall(VecAssemblyBegin(x));
     66:     PetscCall(VecAssemblyEnd(x));
     67:     PetscCall(MatMult(A, x, y));
     68:     PetscCall(VecNorm(y, NORM_1, &error));
     69:     PetscCheck(PetscAbsReal(error - 4) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Invalid output for matrix multiply");
     70:   }
     71:   /* Cleanup */
     72:   PetscCall(MatDestroy(&A));
     73:   PetscCall(VecDestroy(&x));
     74:   PetscCall(VecDestroy(&y));
     75:   PetscCall(PetscFinalize());
     76:   return 0;
     77: }

     79: /*TEST

     81:   test:
     82:     suffix: 0
     83:     requires:
     84:     args:
     85:     output_file: output/empty.out

     87:   test:
     88:     suffix: 1
     89:     nsize: 3
     90:     args:
     91:     output_file: output/empty.out

     93:   test:
     94:     suffix: 2
     95:     nsize: 7
     96:     args:
     97:     output_file: output/empty.out

     99: TEST*/