Date: 2022-03-04T17:39:13+00:00

Actual source code: ex45.c

      2: /*
      3: Laplacian in 3D. Modeled by the partial differential equation

      5:    - Laplacian u = 1,0 < x,y,z < 1,

      7: with boundary conditions

      9:    u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.

     11:    This uses multigrid to solve the linear system

     13:    See src/snes/tutorials/ex50.c

     15:    Can also be run with -pc_type exotic -ksp_type fgmres

     17: */

     19: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";

     21: #include <petscksp.h>
     22: #include <petscdm.h>
     23: #include <petscdmda.h>

     25: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
     26: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
     27: extern PetscErrorCode ComputeInitialGuess(KSP,Vec,void*);

     29: int main(int argc,char **argv)
     30: {
     32:   KSP            ksp;
     33:   PetscReal      norm;
     34:   DM             da;
     35:   Vec            x,b,r;
     36:   Mat            A;

     38:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

     40:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     41:   DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,7,7,7,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);
     42:   DMSetFromOptions(da);
     43:   DMSetUp(da);
     44:   KSPSetDM(ksp,da);
     45:   KSPSetComputeInitialGuess(ksp,ComputeInitialGuess,NULL);
     46:   KSPSetComputeRHS(ksp,ComputeRHS,NULL);
     47:   KSPSetComputeOperators(ksp,ComputeMatrix,NULL);
     48:   DMDestroy(&da);

     50:   KSPSetFromOptions(ksp);
     51:   KSPSolve(ksp,NULL,NULL);
     52:   KSPGetSolution(ksp,&x);
     53:   KSPGetRhs(ksp,&b);
     54:   VecDuplicate(b,&r);
     55:   KSPGetOperators(ksp,&A,NULL);

     57:   MatMult(A,x,r);
     58:   VecAXPY(r,-1.0,b);
     59:   VecNorm(r,NORM_2,&norm);
     60:   PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)norm);

     62:   VecDestroy(&r);
     63:   KSPDestroy(&ksp);
     64:   PetscFinalize();
     65:   return ierr;
     66: }

     68: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
     69: {
     71:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
     72:   DM             dm;
     73:   PetscScalar    Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
     74:   PetscScalar    ***barray;

     77:   KSPGetDM(ksp,&dm);
     78:   DMDAGetInfo(dm,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
     79:   Hx      = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
     80:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
     81:   DMDAGetCorners(dm,&xs,&ys,&zs,&xm,&ym,&zm);
     82:   DMDAVecGetArray(dm,b,&barray);

     84:   for (k=zs; k<zs+zm; k++) {
     85:     for (j=ys; j<ys+ym; j++) {
     86:       for (i=xs; i<xs+xm; i++) {
     87:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
     88:           barray[k][j][i] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
     89:         } else {
     90:           barray[k][j][i] = Hx*Hy*Hz;
     91:         }
     92:       }
     93:     }
     94:   }
     95:   DMDAVecRestoreArray(dm,b,&barray);
     96:   return(0);
     97: }

     99: PetscErrorCode ComputeInitialGuess(KSP ksp,Vec b,void *ctx)
    100: {

    104:   VecSet(b,0);
    105:   return(0);
    106: }

    108: PetscErrorCode ComputeMatrix(KSP ksp,Mat jac,Mat B,void *ctx)
    109: {
    110:   DM             da;
    112:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
    113:   PetscScalar    v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
    114:   MatStencil     row,col[7];

    117:   KSPGetDM(ksp,&da);
    118:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
    119:   Hx      = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
    120:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
    121:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

    123:   for (k=zs; k<zs+zm; k++) {
    124:     for (j=ys; j<ys+ym; j++) {
    125:       for (i=xs; i<xs+xm; i++) {
    126:         row.i = i; row.j = j; row.k = k;
    127:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
    128:           v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
    129:           MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);
    130:         } else {
    131:           v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
    132:           v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
    133:           v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
    134:           v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
    135:           v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
    136:           v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
    137:           v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
    138:           MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);
    139:         }
    140:       }
    141:     }
    142:   }
    143:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    144:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    145:   return(0);
    146: }

    148: /*TEST

    150:    test:
    151:       nsize: 4
    152:       args: -pc_type exotic -ksp_monitor_short -ksp_type fgmres -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type bjacobi
    153:       output_file: output/ex45_1.out

    155:    test:
    156:       suffix: 2
    157:       nsize: 4
    158:       args: -ksp_monitor_short -da_grid_x 21 -da_grid_y 21 -da_grid_z 21 -pc_type mg -pc_mg_levels 3 -mg_levels_ksp_type richardson -mg_levels_ksp_max_it 1 -mg_levels_pc_type bjacobi

    160:    test:
    161:       suffix: telescope
    162:       nsize: 4
    163:       args: -ksp_type fgmres -ksp_monitor_short -pc_type mg -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -pc_mg_levels 2 -da_grid_x 65 -da_grid_y 65 -da_grid_z 65 -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_ignore_kspcomputeoperators -mg_coarse_pc_telescope_reduction_factor 4 -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_galerkin pmat -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_levels_ksp_type richardson -mg_coarse_telescope_mg_levels_pc_type jacobi -mg_levels_ksp_type richardson -mg_coarse_telescope_mg_levels_ksp_type richardson -ksp_rtol 1.0e-4

    165:    test:
    166:       suffix: telescope_2
    167:       nsize: 4
    168:       args: -ksp_type fgmres -ksp_monitor_short -pc_type mg -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -pc_mg_levels 2 -da_grid_x 65 -da_grid_y 65 -da_grid_z 65 -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_reduction_factor 2 -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_galerkin pmat -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_levels_ksp_type richardson -mg_coarse_telescope_mg_levels_pc_type jacobi -mg_levels_ksp_type richardson -mg_coarse_telescope_mg_levels_ksp_type richardson -ksp_rtol 1.0e-4

    170: TEST*/