[petsc-users] Some issues about DMDA and MatSetValuesStencil

[wangxq2020 at mail.ustc.edu.cn]

Hello!
I am a beginner about petsc，and I'm studing the DMDA recently. I hava a exercise code below, i run it with 4 processes， why is the size of A matrix is 15×15? The user manual said A is the Jobian matix, is there any detailed material that explain the process？ Another question is the setting values for A. I don't understand why a loop using the grid distribution information of each process can assign a value to A. The MatStencil mentioned in the user manual is a Data structure (C struct) for storing information about a single row or column of a matrix, why MatStencil contains i and j at the same time, and the row only needs i. Very much looking forward to reply，thanks.


  DM grid;
  ierr = DMDACreate2d            // IN:
    ( comm,                      // collective on this communicator
      DM_BOUNDARY_NONE,DM_BOUNDARY_NONE, // no periodicity and such
      DMDA_STENCIL_STAR,         // no cross connections
      4,4,                 // global size 100x100; can be changed with options
      PETSC_DECIDE,PETSC_DECIDE, // processors in each direction
      1,                         // degree of freedom per node
      1,                         // stencil width
      NULL,NULL,                 // arrays of local sizes in each direction
      &grid                      // OUT: resulting object
      ); CHKERRQ(ierr);
  ierr = DMSetUp(grid); CHKERRQ(ierr);


  Mat A;
  ierr = DMCreateMatrix(grid,&A); CHKERRQ(ierr);
  DMDALocalInfo  info;
  ierr = DMDAGetLocalInfo(grid,&info);CHKERRQ(ierr);
  for (int j=info.ys; j<info.ys+info.ym; j++) {
    for (int i=info.xs; i<info.xs+info.xm; i++) {
      MatStencil  row = {0},col[5] = {{0}};
      PetscScalar v[5];
      PetscInt    ncols = 0;
      row.j        = j; row.i = i;
      printf("procno: %d;j:%d; i:%d\n",procno,j,i);
      /**** local connection: diagonal element ****/
      col[ncols].j = j; col[ncols].i = i; v[ncols++] = 4.;
      printf("procno: %d, j:%d. col[%d].j = %d, col[%d].i = %d, v[%d]=4\n",procno,j,ncols-1,j,ncols-1,i,ncols);
      /* boundaries: top row */
      if (i>0)         {
        col[ncols].j = j;   col[ncols].i = i-1; v[ncols++] = -1.;
        printf("procno: %d, j:%d. col[%d].j = %d, col[%d].i = %d, v[%d]=4\n",procno,j,ncols-1,j,ncols-1,i-1,ncols);
        }
      if (j>0){
        col[ncols].j = j-1; col[ncols].i = i;   v[ncols++] = -1.;
        printf("procno: %d, j:%d. col[%d].j = %d, col[%d].i = %d, v[%d]=4\n",procno,j,ncols-1,j-1,ncols-1,i,ncols);
        }
      if (j<info.my-1) {
        col[ncols].j = j+1; col[ncols].i = i;   v[ncols++] = -1.;
        printf("procno: %d, j:%d. col[%d].j = %d, col[%d].i = %d, v[%d]=-1\n",procno,j,ncols-1,j+1,ncols-1,i+1,ncols);
        }


      /* boundary: bottom row */
      if (i<info.mx-1) {
        col[ncols].j = j;   col[ncols].i = i+1; v[ncols++] = -1.;
        printf("procno: %d, j:%d. col[%d].j = %d, col[%d].i = %d, v[%d]=-1\n",procno,j,ncols-1,j,ncols-1,i+1,ncols);
        }
      ierr = MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);CHKERRQ(ierr);
    }
  }
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