Actual source code: ex66.c

      1: /*   DMDA/KSP solving a system of linear equations.
      2:      Poisson equation in 2D:

      4:      div(grad p) = f,  0 < x,y < 1
      5:      with
      6:        forcing function f = -cos(m*pi*x)*cos(n*pi*y),
      7:        Periodic boundary conditions
      8:          p(x=0) = p(x=1)
      9:        Neuman boundary conditions
     10:          dp/dy = 0 for y = 0, y = 1.

     12:        This example uses the DM_BOUNDARY_MIRROR to implement the Neumann boundary conditions, see the manual pages for DMBoundaryType

     14:        Compare to ex50.c
     15: */

     17: static char help[] = "Solves 2D Poisson equation,\n\
     18:                       using mirrored boundaries to implement Neumann boundary conditions,\n\
     19:                       using multigrid.\n\n";

     21: #include <petscdm.h>
     22: #include <petscdmda.h>
     23: #include <petscksp.h>
     24: #include <petscsys.h>
     25: #include <petscvec.h>

     27: extern PetscErrorCode ComputeJacobian(KSP,Mat,Mat,void*);
     28: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

     30: typedef struct {
     31:   PetscScalar uu, tt;
     32: } UserContext;

     34: int main(int argc,char **argv)
     35: {
     36:   KSP            ksp;
     37:   DM             da;
     38:   UserContext    user;

     40:   PetscInitialize(&argc,&argv,(char*)0,help);
     41:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     42:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, DM_BOUNDARY_MIRROR,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     43:   DMSetFromOptions(da);
     44:   DMSetUp(da);
     45:   KSPSetDM(ksp,(DM)da);
     46:   DMSetApplicationContext(da,&user);

     48:   user.uu     = 1.0;
     49:   user.tt     = 1.0;

     51:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
     52:   KSPSetComputeOperators(ksp,ComputeJacobian,&user);
     53:   KSPSetFromOptions(ksp);
     54:   KSPSolve(ksp,NULL,NULL);

     56:   DMDestroy(&da);
     57:   KSPDestroy(&ksp);
     58:   PetscFinalize();
     59:   return 0;
     60: }

     62: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
     63: {
     64:   UserContext    *user = (UserContext*)ctx;
     65:   PetscInt       i,j,M,N,xm,ym,xs,ys;
     66:   PetscScalar    Hx,Hy,pi,uu,tt;
     67:   PetscScalar    **array;
     68:   DM             da;
     69:   MatNullSpace   nullspace;

     72:   KSPGetDM(ksp,&da);
     73:   DMDAGetInfo(da, 0, &M, &N, 0,0,0,0,0,0,0,0,0,0);
     74:   uu   = user->uu; tt = user->tt;
     75:   pi   = 4*PetscAtanReal(1.0);
     76:   Hx   = 1.0/(PetscReal)(M);
     77:   Hy   = 1.0/(PetscReal)(N);

     79:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0); /* Fine grid */
     80:   DMDAVecGetArray(da, b, &array);
     81:   for (j=ys; j<ys+ym; j++) {
     82:     for (i=xs; i<xs+xm; i++) {
     83:       array[j][i] = -PetscCosScalar(uu*pi*((PetscReal)i+0.5)*Hx)*PetscCosScalar(tt*pi*((PetscReal)j+0.5)*Hy)*Hx*Hy;
     84:     }
     85:   }
     86:   DMDAVecRestoreArray(da, b, &array);
     87:   VecAssemblyBegin(b);
     88:   VecAssemblyEnd(b);

     90:   /* force right hand side to be consistent for singular matrix */
     91:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
     92:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
     93:   MatNullSpaceRemove(nullspace,b);
     94:   MatNullSpaceDestroy(&nullspace);
     95:   return 0;
     96: }

     98: PetscErrorCode ComputeJacobian(KSP ksp,Mat J, Mat jac,void *ctx)
     99: {
    100:   PetscInt       i, j, M, N, xm, ym, xs, ys;
    101:   PetscScalar    v[5], Hx, Hy, HydHx, HxdHy;
    102:   MatStencil     row, col[5];
    103:   DM             da;
    104:   MatNullSpace   nullspace;

    107:   KSPGetDM(ksp,&da);
    108:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,0,0,0,0,0,0);
    109:   Hx    = 1.0 / (PetscReal)(M);
    110:   Hy    = 1.0 / (PetscReal)(N);
    111:   HxdHy = Hx/Hy;
    112:   HydHx = Hy/Hx;
    113:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
    114:   for (j=ys; j<ys+ym; j++) {
    115:     for (i=xs; i<xs+xm; i++) {
    116:       row.i = i; row.j = j;
    117:       v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
    118:       v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
    119:       v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
    120:       v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
    121:       v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
    122:       MatSetValuesStencil(jac,1,&row,5,col,v,ADD_VALUES);
    123:     }
    124:   }
    125:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    126:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

    128:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    129:   MatSetNullSpace(J,nullspace);
    130:   MatNullSpaceDestroy(&nullspace);
    131:   return 0;
    132: }

    134: /*TEST

    136:    build:
    137:       requires: !complex !single

    139:    test:
    140:       args: -pc_type mg -pc_mg_type full -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type svd -ksp_view

    142:    test:
    143:       suffix: 2
    144:       nsize: 4
    145:       args: -pc_type mg -pc_mg_type full -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type redundant -mg_coarse_redundant_pc_type svd -ksp_view

    147: TEST*/