[petsc-users] Some issues about DMDA and MatSetValuesStencil

[Matthew Knepley]

On Wed, Aug 3, 2022 at 9:17 AM wangxq2020--- via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> 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?
>

Are you sure it is not 16x16? The grid has 4 vertices in both the x- and
y-directions, so 16 vertices. You have 1 dof per vertex. This means that a
function
over this grid has 16 variables, so vectors have length 16. The Jacobian
relates the (linearized) change in the residual for a change in each
variables,
so it is a matrix of size 16 x 16.

  Thanks,

      Matt


> 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);
>     }
>   }
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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