学习poisson.c

 static char help[] = "A structured-grid Poisson problem with DMDA+KSP.\n\n";

 #include <petsc.h>

 extern PetscErrorCode formMatrix(DM, Mat);
 extern PetscErrorCode formExact(DM, Vec);
 extern PetscErrorCode formRHS(DM, Vec);

 //STARTMAIN
 int main(int argc,char **args) {
   PetscErrorCode ierr;
   DM            da;
   Mat           A;
   Vec           b,u,uexact;
   KSP           ksp;
   double        errnorm;
   DMDALocalInfo info;

   PetscInitialize(&argc,&args,(char*),help);

   // default size (9 x 9) can be changed using -da_refine X or
   //     -da_grid_x M -da_grid_y N
   ierr = DMDACreate2d(PETSC_COMM_WORLD,
       DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR,
       ,,PETSC_DECIDE,PETSC_DECIDE,,,NULL,NULL,&da); CHKERRQ(ierr);

   // create linear system matrix A
   ierr = DMSetFromOptions(da); CHKERRQ(ierr);
   ierr = DMSetUp(da); CHKERRQ(ierr);
   ierr = DMCreateMatrix(da,&A); CHKERRQ(ierr);
   ierr = MatSetFromOptions(A); CHKERRQ(ierr);

   // create right-hand-side (RHS) b, approx solution u, exact solution uexact
   ierr = DMCreateGlobalVector(da,&b); CHKERRQ(ierr);
   ierr = VecDuplicate(b,&u); CHKERRQ(ierr);
   ierr = VecDuplicate(b,&uexact); CHKERRQ(ierr);

   // fill vectors and assemble linear system
   ierr = formExact(da,uexact); CHKERRQ(ierr);
   ierr = formRHS(da,b); CHKERRQ(ierr);
   ierr = formMatrix(da,A); CHKERRQ(ierr);

   // create and solve the linear system
   ierr = KSPCreate(PETSC_COMM_WORLD,&ksp); CHKERRQ(ierr);
   ierr = KSPSetOperators(ksp,A,A); CHKERRQ(ierr);
   ierr = KSPSetFromOptions(ksp); CHKERRQ(ierr);
   ierr = KSPSolve(ksp,b,u); CHKERRQ(ierr);

   // report on grid and numerical error
   ierr = VecAXPY(u,-1.0,uexact); CHKERRQ(ierr);    // u <- u + (-1.0) uxact
   ierr = VecNorm(u,NORM_INFINITY,&errnorm); CHKERRQ(ierr);
   ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
   ierr = PetscPrintf(PETSC_COMM_WORLD,
              "on %d x %d grid:  error |u-uexact|_inf = %g\n",
              info.mx,info.my,errnorm); CHKERRQ(ierr);

   VecDestroy(&u);  VecDestroy(&uexact);  VecDestroy(&b);
   MatDestroy(&A);  KSPDestroy(&ksp);  DMDestroy(&da);
   return PetscFinalize();
 }
 //ENDMAIN

 //STARTMATRIX
 PetscErrorCode formMatrix(DM da, Mat A) {
   PetscErrorCode ierr;
   DMDALocalInfo info;
   MatStencil    row, col[];
   double        hx, hy, v[];
   int           i, j, ncols;

   ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
   hx = 1.0/(info.mx-);  hy = 1.0/(info.my-);
   for (j = info.ys; j < info.ys+info.ym; j++) {
     for (i = info.xs; i < info.xs+info.xm; i++) {
       row.j = j;           // row of A corresponding to (x_i,y_j)
       row.i = i;
       col[].j = j;        // in this diagonal entry
       col[].i = i;
       ncols = ;
       if (i== || i==info.mx- || j== || j==info.my-) {
         v[] = 1.0;  // if on boundary, just insert diagonal entry
       } else {
         v[] = *(hy/hx + hx/hy); // ... everywhere else we build a row
         // if neighbor is NOT a known boundary value then we put an entry
         if (i- > ) {
           col[ncols].j = j;    col[ncols].i = i-;  v[ncols++] = -hy/hx;  }
         if (i+ < info.mx-) {
           col[ncols].j = j;    col[ncols].i = i+;  v[ncols++] = -hy/hx;  }
         if (j- > ) {
           col[ncols].j = j-;  col[ncols].i = i;    v[ncols++] = -hx/hy;  }
         if (j+ < info.my-) {
           col[ncols].j = j+;  col[ncols].i = i;    v[ncols++] = -hx/hy;  }
       }
       ierr = MatSetValuesStencil(A,,&row,ncols,col,v,INSERT_VALUES); CHKERRQ(ierr);
     }
   }
   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
   return ;
 }
 //ENDMATRIX

 //STARTEXACT
 PetscErrorCode formExact(DM da, Vec uexact) {
   PetscErrorCode ierr;
   DMDALocalInfo info;
   int           i, j;
   double        hx, hy, x, y, **auexact;

   ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
   hx = 1.0/(info.mx-);  hy = 1.0/(info.my-);
   ierr = DMDAVecGetArray(da, uexact, &auexact);CHKERRQ(ierr);
   for (j = info.ys; j < info.ys+info.ym; j++) {
     y = j * hy;
     for (i = info.xs; i < info.xs+info.xm; i++) {
       x = i * hx;
       auexact[j][i] = x*x * (1.0 - x*x) * y*y * (y*y - 1.0);
     }
   }
   ierr = DMDAVecRestoreArray(da, uexact, &auexact);CHKERRQ(ierr);
   return ;
 }

 PetscErrorCode formRHS(DM da, Vec b) {
   PetscErrorCode ierr;
   int           i, j;
   double        hx, hy, x, y, f, **ab;
   DMDALocalInfo info;

   ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
   hx = 1.0/(info.mx-);  hy = 1.0/(info.my-);
   ierr = DMDAVecGetArray(da, b, &ab);CHKERRQ(ierr);
   for (j=info.ys; j<info.ys+info.ym; j++) {
     y = j * hy;
     for (i=info.xs; i<info.xs+info.xm; i++) {
       x = i * hx;
       if (i== || i==info.mx- || j== || j==info.my-) {
         ab[j][i] = 0.0;                    // on bdry the eqn is 1*u = 0
       } else {  // if not bdry; note  f = - (u_xx + u_yy)  where u is exact
         f = 2.0 * ( (1.0 - 6.0*x*x) * y*y * (1.0 - y*y)
                     + (1.0 - 6.0*y*y) * x*x * (1.0 - x*x) );
         ab[j][i] = hx * hy * f;
       }
     }
   }
   ierr = DMDAVecRestoreArray(da, b, &ab); CHKERRQ(ierr);
   return ;
 }
 //ENDEXACT