Date: 2022-08-02T03:14:47+00:00

Actual source code: ex50.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:        Neuman boundary conditions
      8:         dp/dx = 0 for x = 0, x = 1.
      9:         dp/dy = 0 for y = 0, y = 1.

     11:      Contributed by Michael Boghosian <boghmic@iit.edu>, 2008,
     12:          based on petsc/src/ksp/ksp/tutorials/ex29.c and ex32.c

     14:      Compare to ex66.c

     16:      Example of Usage:
     17:           ./ex50 -da_grid_x 3 -da_grid_y 3 -pc_type mg -da_refine 3 -ksp_monitor -ksp_view -dm_view draw -draw_pause -1
     18:           ./ex50 -da_grid_x 100 -da_grid_y 100 -pc_type mg  -pc_mg_levels 1 -mg_levels_0_pc_type ilu -mg_levels_0_pc_factor_levels 1 -ksp_monitor -ksp_view
     19:           ./ex50 -da_grid_x 100 -da_grid_y 100 -pc_type mg -pc_mg_levels 1 -mg_levels_0_pc_type lu -mg_levels_0_pc_factor_shift_type NONZERO -ksp_monitor
     20:           mpiexec -n 4 ./ex50 -da_grid_x 3 -da_grid_y 3 -pc_type mg -da_refine 10 -ksp_monitor -ksp_view -log_view
     21: */

     23: static char help[] = "Solves 2D Poisson equation using multigrid.\n\n";

     25: #include <petscdm.h>
     26: #include <petscdmda.h>
     27: #include <petscksp.h>
     28: #include <petscsys.h>
     29: #include <petscvec.h>

     31: extern PetscErrorCode ComputeJacobian(KSP,Mat,Mat,void*);
     32: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

     34: typedef struct {
     35:   PetscScalar uu, tt;
     36: } UserContext;

     38: int main(int argc,char **argv)
     39: {
     40:   KSP            ksp;
     41:   DM             da;
     42:   UserContext    user;

     44:   PetscInitialize(&argc,&argv,(char*)0,help);
     45:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     46:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     47:   DMSetFromOptions(da);
     48:   DMSetUp(da);
     49:   KSPSetDM(ksp,(DM)da);
     50:   DMSetApplicationContext(da,&user);

     52:   user.uu     = 1.0;
     53:   user.tt     = 1.0;

     55:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
     56:   KSPSetComputeOperators(ksp,ComputeJacobian,&user);
     57:   KSPSetFromOptions(ksp);
     58:   KSPSolve(ksp,NULL,NULL);

     60:   DMDestroy(&da);
     61:   KSPDestroy(&ksp);
     62:   PetscFinalize();
     63:   return 0;
     64: }

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

     76:   KSPGetDM(ksp,&da);
     77:   DMDAGetInfo(da, 0, &M, &N, 0,0,0,0,0,0,0,0,0,0);
     78:   uu   = user->uu; tt = user->tt;
     79:   pi   = 4*atan(1.0);
     80:   Hx   = 1.0/(PetscReal)(M);
     81:   Hy   = 1.0/(PetscReal)(N);

     83:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0); /* Fine grid */
     84:   DMDAVecGetArray(da, b, &array);
     85:   for (j=ys; j<ys+ym; j++) {
     86:     for (i=xs; i<xs+xm; i++) {
     87:       array[j][i] = -PetscCosScalar(uu*pi*((PetscReal)i+0.5)*Hx)*PetscCosScalar(tt*pi*((PetscReal)j+0.5)*Hy)*Hx*Hy;
     88:     }
     89:   }
     90:   DMDAVecRestoreArray(da, b, &array);
     91:   VecAssemblyBegin(b);
     92:   VecAssemblyEnd(b);

     94:   /* force right hand side to be consistent for singular matrix */
     95:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
     96:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
     97:   MatNullSpaceRemove(nullspace,b);
     98:   MatNullSpaceDestroy(&nullspace);
     99:   return 0;
    100: }

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

    111:   KSPGetDM(ksp,&da);
    112:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,0,0,0,0,0,0);
    113:   Hx    = 1.0 / (PetscReal)(M);
    114:   Hy    = 1.0 / (PetscReal)(N);
    115:   HxdHy = Hx/Hy;
    116:   HydHx = Hy/Hx;
    117:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
    118:   for (j=ys; j<ys+ym; j++) {
    119:     for (i=xs; i<xs+xm; i++) {
    120:       row.i = i; row.j = j;

    122:       if (i==0 || j==0 || i==M-1 || j==N-1) {
    123:         num=0; numi=0; numj=0;
    124:         if (j!=0) {
    125:           v[num] = -HxdHy;              col[num].i = i;   col[num].j = j-1;
    126:           num++; numj++;
    127:         }
    128:         if (i!=0) {
    129:           v[num] = -HydHx;              col[num].i = i-1; col[num].j = j;
    130:           num++; numi++;
    131:         }
    132:         if (i!=M-1) {
    133:           v[num] = -HydHx;              col[num].i = i+1; col[num].j = j;
    134:           num++; numi++;
    135:         }
    136:         if (j!=N-1) {
    137:           v[num] = -HxdHy;              col[num].i = i;   col[num].j = j+1;
    138:           num++; numj++;
    139:         }
    140:         v[num] = ((PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx); col[num].i = i;   col[num].j = j;
    141:         num++;
    142:         MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
    143:       } else {
    144:         v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
    145:         v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
    146:         v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
    147:         v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
    148:         v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
    149:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
    150:       }
    151:     }
    152:   }
    153:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    154:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

    156:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    157:   MatSetNullSpace(J,nullspace);
    158:   MatNullSpaceDestroy(&nullspace);
    159:   return 0;
    160: }

    162: /*TEST

    164:    build:
    165:       requires: !complex !single

    167:    test:
    168:       args: -pc_type mg -pc_mg_type full -ksp_type cg -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type svd -ksp_view

    170:    test:
    171:       suffix: 2
    172:       nsize: 4
    173:       args: -pc_type mg -pc_mg_type full -ksp_type cg -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type redundant -mg_coarse_redundant_pc_type svd -ksp_view

    175:    test:
    176:       suffix: 3
    177:       nsize: 2
    178:       args: -pc_type mg -pc_mg_type full -ksp_monitor_short -da_refine 5 -mg_coarse_ksp_type cg -mg_coarse_ksp_converged_reason -mg_coarse_ksp_rtol 1e-2 -mg_coarse_ksp_max_it 5 -mg_coarse_pc_type none -pc_mg_levels 2 -ksp_type pipefgmres -ksp_pipefgmres_shift 1.5

    180:    test:
    181:       suffix: tut_1
    182:       nsize: 1
    183:       args: -da_grid_x 4 -da_grid_y 4 -mat_view

    185:    test:
    186:       suffix: tut_2
    187:       requires: superlu_dist parmetis
    188:       nsize: 4
    189:       args: -da_grid_x 120 -da_grid_y 120 -pc_type lu -pc_factor_mat_solver_type superlu_dist -ksp_monitor -ksp_view

    191:    test:
    192:       suffix: tut_3
    193:       nsize: 4
    194:       args: -da_grid_x 1025 -da_grid_y 1025 -pc_type mg -pc_mg_levels 9 -ksp_monitor

    196: TEST*/