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: {
31: KSP ksp;
32: PetscReal norm;
33: DM da;
34: Vec x, b, r;
35: Mat A;
37: PetscFunctionBeginUser;
38: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
40: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
41: 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));
42: PetscCall(DMSetFromOptions(da));
43: PetscCall(DMSetUp(da));
44: PetscCall(KSPSetDM(ksp, da));
45: PetscCall(KSPSetComputeInitialGuess(ksp, ComputeInitialGuess, NULL));
46: PetscCall(KSPSetComputeRHS(ksp, ComputeRHS, NULL));
47: PetscCall(KSPSetComputeOperators(ksp, ComputeMatrix, NULL));
48: PetscCall(DMDestroy(&da));
50: PetscCall(KSPSetFromOptions(ksp));
51: PetscCall(KSPSolve(ksp, NULL, NULL));
52: PetscCall(KSPGetSolution(ksp, &x));
53: PetscCall(KSPGetRhs(ksp, &b));
54: PetscCall(VecDuplicate(b, &r));
55: PetscCall(KSPGetOperators(ksp, &A, NULL));
57: PetscCall(MatMult(A, x, r));
58: PetscCall(VecAXPY(r, -1.0, b));
59: PetscCall(VecNorm(r, NORM_2, &norm));
60: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Residual norm %g\n", (double)norm));
62: PetscCall(VecDestroy(&r));
63: PetscCall(KSPDestroy(&ksp));
64: PetscCall(PetscFinalize());
65: return 0;
66: }
68: PetscErrorCode ComputeRHS(KSP ksp, Vec b, void *ctx)
69: {
70: PetscInt i, j, k, mx, my, mz, xm, ym, zm, xs, ys, zs;
71: DM dm;
72: PetscScalar Hx, Hy, Hz, HxHydHz, HyHzdHx, HxHzdHy;
73: PetscScalar ***barray;
75: PetscFunctionBeginUser;
76: PetscCall(KSPGetDM(ksp, &dm));
77: PetscCall(DMDAGetInfo(dm, 0, &mx, &my, &mz, 0, 0, 0, 0, 0, 0, 0, 0, 0));
78: Hx = 1.0 / (PetscReal)(mx - 1);
79: Hy = 1.0 / (PetscReal)(my - 1);
80: Hz = 1.0 / (PetscReal)(mz - 1);
81: HxHydHz = Hx * Hy / Hz;
82: HxHzdHy = Hx * Hz / Hy;
83: HyHzdHx = Hy * Hz / Hx;
84: PetscCall(DMDAGetCorners(dm, &xs, &ys, &zs, &xm, &ym, &zm));
85: PetscCall(DMDAVecGetArray(dm, b, &barray));
87: for (k = zs; k < zs + zm; k++) {
88: for (j = ys; j < ys + ym; j++) {
89: for (i = xs; i < xs + xm; i++) {
90: if (i == 0 || j == 0 || k == 0 || i == mx - 1 || j == my - 1 || k == mz - 1) {
91: barray[k][j][i] = 2.0 * (HxHydHz + HxHzdHy + HyHzdHx);
92: } else {
93: barray[k][j][i] = Hx * Hy * Hz;
94: }
95: }
96: }
97: }
98: PetscCall(DMDAVecRestoreArray(dm, b, &barray));
99: PetscFunctionReturn(PETSC_SUCCESS);
100: }
102: PetscErrorCode ComputeInitialGuess(KSP ksp, Vec b, void *ctx)
103: {
104: PetscFunctionBeginUser;
105: PetscCall(VecSet(b, 0));
106: PetscFunctionReturn(PETSC_SUCCESS);
107: }
109: PetscErrorCode ComputeMatrix(KSP ksp, Mat jac, Mat B, void *ctx)
110: {
111: 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];
116: PetscFunctionBeginUser;
117: PetscCall(KSPGetDM(ksp, &da));
118: PetscCall(DMDAGetInfo(da, 0, &mx, &my, &mz, 0, 0, 0, 0, 0, 0, 0, 0, 0));
119: Hx = 1.0 / (PetscReal)(mx - 1);
120: Hy = 1.0 / (PetscReal)(my - 1);
121: Hz = 1.0 / (PetscReal)(mz - 1);
122: HxHydHz = Hx * Hy / Hz;
123: HxHzdHy = Hx * Hz / Hy;
124: HyHzdHx = Hy * Hz / Hx;
125: PetscCall(DMDAGetCorners(da, &xs, &ys, &zs, &xm, &ym, &zm));
127: for (k = zs; k < zs + zm; k++) {
128: for (j = ys; j < ys + ym; j++) {
129: for (i = xs; i < xs + xm; i++) {
130: row.i = i;
131: row.j = j;
132: row.k = k;
133: if (i == 0 || j == 0 || k == 0 || i == mx - 1 || j == my - 1 || k == mz - 1) {
134: v[0] = 2.0 * (HxHydHz + HxHzdHy + HyHzdHx);
135: PetscCall(MatSetValuesStencil(B, 1, &row, 1, &row, v, INSERT_VALUES));
136: } else {
137: v[0] = -HxHydHz;
138: col[0].i = i;
139: col[0].j = j;
140: col[0].k = k - 1;
141: v[1] = -HxHzdHy;
142: col[1].i = i;
143: col[1].j = j - 1;
144: col[1].k = k;
145: v[2] = -HyHzdHx;
146: col[2].i = i - 1;
147: col[2].j = j;
148: col[2].k = k;
149: v[3] = 2.0 * (HxHydHz + HxHzdHy + HyHzdHx);
150: col[3].i = row.i;
151: col[3].j = row.j;
152: col[3].k = row.k;
153: v[4] = -HyHzdHx;
154: col[4].i = i + 1;
155: col[4].j = j;
156: col[4].k = k;
157: v[5] = -HxHzdHy;
158: col[5].i = i;
159: col[5].j = j + 1;
160: col[5].k = k;
161: v[6] = -HxHydHz;
162: col[6].i = i;
163: col[6].j = j;
164: col[6].k = k + 1;
165: PetscCall(MatSetValuesStencil(B, 1, &row, 7, col, v, INSERT_VALUES));
166: }
167: }
168: }
169: }
170: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
171: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
172: PetscFunctionReturn(PETSC_SUCCESS);
173: }
175: /*TEST
177: test:
178: nsize: 4
179: 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
180: output_file: output/ex45_1.out
182: test:
183: suffix: 2
184: nsize: 4
185: 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
187: test:
188: suffix: telescope
189: nsize: 4
190: 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
192: test:
193: suffix: telescope_2
194: nsize: 4
195: 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
197: TEST*/