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*/
```