Actual source code: ex45.c
1: /*
2: Laplacian in 3D. Modeled by the partial differential equation
4: - Laplacian u = 1,0 < x,y,z < 1,
6: with boundary conditions
8: u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
10: This uses multigrid to solve the linear system
12: See src/snes/tutorials/ex50.c
14: Can also be run with -pc_type exotic -ksp_type fgmres
16: */
18: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";
20: #include <petscksp.h>
21: #include <petscdm.h>
22: #include <petscdmda.h>
24: extern PetscErrorCode ComputeMatrix(KSP, Mat, Mat, void *);
25: extern PetscErrorCode ComputeRHS(KSP, Vec, void *);
26: extern PetscErrorCode ComputeInitialGuess(KSP, Vec, void *);
28: int main(int argc, char **argv)
29: {
30: KSP ksp;
31: PetscReal norm;
32: DM da;
33: Vec x, b, r;
34: Mat A;
36: PetscFunctionBeginUser;
37: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
39: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
40: PetscCall(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));
41: PetscCall(DMSetFromOptions(da));
42: PetscCall(DMSetUp(da));
43: PetscCall(KSPSetDM(ksp, da));
44: PetscCall(KSPSetComputeInitialGuess(ksp, ComputeInitialGuess, NULL));
45: PetscCall(KSPSetComputeRHS(ksp, ComputeRHS, NULL));
46: PetscCall(KSPSetComputeOperators(ksp, ComputeMatrix, NULL));
47: PetscCall(DMDestroy(&da));
49: PetscCall(KSPSetFromOptions(ksp));
50: PetscCall(KSPSolve(ksp, NULL, NULL));
51: PetscCall(KSPGetSolution(ksp, &x));
52: PetscCall(KSPGetRhs(ksp, &b));
53: PetscCall(VecDuplicate(b, &r));
54: PetscCall(KSPGetOperators(ksp, &A, NULL));
56: PetscCall(MatMult(A, x, r));
57: PetscCall(VecAXPY(r, -1.0, b));
58: PetscCall(VecNorm(r, NORM_2, &norm));
59: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Residual norm %g\n", (double)norm));
61: PetscCall(VecDestroy(&r));
62: PetscCall(KSPDestroy(&ksp));
63: PetscCall(PetscFinalize());
64: return 0;
65: }
67: PetscErrorCode ComputeRHS(KSP ksp, Vec b, void *ctx)
68: {
69: PetscInt i, j, k, mx, my, mz, xm, ym, zm, xs, ys, zs;
70: DM dm;
71: PetscScalar Hx, Hy, Hz, HxHydHz, HyHzdHx, HxHzdHy;
72: PetscScalar ***barray;
74: PetscFunctionBeginUser;
75: PetscCall(KSPGetDM(ksp, &dm));
76: PetscCall(DMDAGetInfo(dm, 0, &mx, &my, &mz, 0, 0, 0, 0, 0, 0, 0, 0, 0));
77: Hx = 1.0 / (PetscReal)(mx - 1);
78: Hy = 1.0 / (PetscReal)(my - 1);
79: Hz = 1.0 / (PetscReal)(mz - 1);
80: HxHydHz = Hx * Hy / Hz;
81: HxHzdHy = Hx * Hz / Hy;
82: HyHzdHx = Hy * Hz / Hx;
83: PetscCall(DMDAGetCorners(dm, &xs, &ys, &zs, &xm, &ym, &zm));
84: PetscCall(DMDAVecGetArray(dm, b, &barray));
86: for (k = zs; k < zs + zm; k++) {
87: for (j = ys; j < ys + ym; j++) {
88: for (i = xs; i < xs + xm; i++) {
89: if (i == 0 || j == 0 || k == 0 || i == mx - 1 || j == my - 1 || k == mz - 1) {
90: barray[k][j][i] = 2.0 * (HxHydHz + HxHzdHy + HyHzdHx);
91: } else {
92: barray[k][j][i] = Hx * Hy * Hz;
93: }
94: }
95: }
96: }
97: PetscCall(DMDAVecRestoreArray(dm, b, &barray));
98: PetscFunctionReturn(PETSC_SUCCESS);
99: }
101: PetscErrorCode ComputeInitialGuess(KSP ksp, Vec b, void *ctx)
102: {
103: PetscFunctionBeginUser;
104: PetscCall(VecSet(b, 0));
105: PetscFunctionReturn(PETSC_SUCCESS);
106: }
108: PetscErrorCode ComputeMatrix(KSP ksp, Mat jac, Mat B, void *ctx)
109: {
110: DM da;
111: PetscInt i, j, k, mx, my, mz, xm, ym, zm, xs, ys, zs;
112: PetscScalar v[7], Hx, Hy, Hz, HxHydHz, HyHzdHx, HxHzdHy;
113: MatStencil row, col[7];
115: PetscFunctionBeginUser;
116: PetscCall(KSPGetDM(ksp, &da));
117: PetscCall(DMDAGetInfo(da, 0, &mx, &my, &mz, 0, 0, 0, 0, 0, 0, 0, 0, 0));
118: Hx = 1.0 / (PetscReal)(mx - 1);
119: Hy = 1.0 / (PetscReal)(my - 1);
120: Hz = 1.0 / (PetscReal)(mz - 1);
121: HxHydHz = Hx * Hy / Hz;
122: HxHzdHy = Hx * Hz / Hy;
123: HyHzdHx = Hy * Hz / Hx;
124: PetscCall(DMDAGetCorners(da, &xs, &ys, &zs, &xm, &ym, &zm));
126: for (k = zs; k < zs + zm; k++) {
127: for (j = ys; j < ys + ym; j++) {
128: for (i = xs; i < xs + xm; i++) {
129: row.i = i;
130: row.j = j;
131: row.k = k;
132: if (i == 0 || j == 0 || k == 0 || i == mx - 1 || j == my - 1 || k == mz - 1) {
133: v[0] = 2.0 * (HxHydHz + HxHzdHy + HyHzdHx);
134: PetscCall(MatSetValuesStencil(B, 1, &row, 1, &row, v, INSERT_VALUES));
135: } else {
136: v[0] = -HxHydHz;
137: col[0].i = i;
138: col[0].j = j;
139: col[0].k = k - 1;
140: v[1] = -HxHzdHy;
141: col[1].i = i;
142: col[1].j = j - 1;
143: col[1].k = k;
144: v[2] = -HyHzdHx;
145: col[2].i = i - 1;
146: col[2].j = j;
147: col[2].k = k;
148: v[3] = 2.0 * (HxHydHz + HxHzdHy + HyHzdHx);
149: col[3].i = row.i;
150: col[3].j = row.j;
151: col[3].k = row.k;
152: v[4] = -HyHzdHx;
153: col[4].i = i + 1;
154: col[4].j = j;
155: col[4].k = k;
156: v[5] = -HxHzdHy;
157: col[5].i = i;
158: col[5].j = j + 1;
159: col[5].k = k;
160: v[6] = -HxHydHz;
161: col[6].i = i;
162: col[6].j = j;
163: col[6].k = k + 1;
164: PetscCall(MatSetValuesStencil(B, 1, &row, 7, col, v, INSERT_VALUES));
165: }
166: }
167: }
168: }
169: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
170: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
171: PetscFunctionReturn(PETSC_SUCCESS);
172: }
174: /*TEST
176: test:
177: nsize: 4
178: 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
179: output_file: output/ex45_1.out
181: test:
182: suffix: 2
183: nsize: 4
184: 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
186: test:
187: suffix: telescope
188: nsize: 4
189: 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
191: test:
192: suffix: telescope_2
193: nsize: 4
194: 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
196: TEST*/