Actual source code: ex29.c
1: /*
2: Added at the request of Marc Garbey.
4: Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation
6: -div \rho grad u = f, 0 < x,y < 1,
8: with forcing function
10: f = e^{-x^2/\nu} e^{-y^2/\nu}
12: with Dirichlet boundary conditions
14: u = f(x,y) for x = 0, x = 1, y = 0, y = 1
16: or pure Neumman boundary conditions
18: This uses multigrid to solve the linear system
19: */
21: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";
23: #include <petscdm.h>
24: #include <petscdmda.h>
25: #include <petscksp.h>
27: extern PetscErrorCode ComputeMatrix(KSP, Mat, Mat, void *);
28: extern PetscErrorCode ComputeRHS(KSP, Vec, void *);
30: typedef enum {
31: DIRICHLET,
32: NEUMANN
33: } BCType;
35: typedef struct {
36: PetscReal rho;
37: PetscReal nu;
38: BCType bcType;
39: } UserContext;
41: int main(int argc, char **argv)
42: {
43: KSP ksp;
44: DM da;
45: UserContext user;
46: const char *bcTypes[2] = {"dirichlet", "neumann"};
47: PetscInt bc;
48: Vec b, x;
49: PetscBool testsolver = PETSC_FALSE;
51: PetscFunctionBeginUser;
52: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
53: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
54: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 3, 3, PETSC_DECIDE, PETSC_DECIDE, 1, 1, 0, 0, &da));
55: PetscCall(DMSetFromOptions(da));
56: PetscCall(DMSetUp(da));
57: PetscCall(DMDASetUniformCoordinates(da, 0, 1, 0, 1, 0, 0));
58: PetscCall(DMDASetFieldName(da, 0, "Pressure"));
60: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");
61: user.rho = 1.0;
62: PetscCall(PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL));
63: user.nu = 0.1;
64: PetscCall(PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL));
65: bc = (PetscInt)DIRICHLET;
66: PetscCall(PetscOptionsEList("-bc_type", "Type of boundary condition", "ex29.c", bcTypes, 2, bcTypes[0], &bc, NULL));
67: user.bcType = (BCType)bc;
68: PetscCall(PetscOptionsBool("-testsolver", "Run solver multiple times, useful for performance studies of solver", "ex29.c", testsolver, &testsolver, NULL));
69: PetscOptionsEnd();
71: PetscCall(KSPSetComputeRHS(ksp, ComputeRHS, &user));
72: PetscCall(KSPSetComputeOperators(ksp, ComputeMatrix, &user));
73: PetscCall(KSPSetDM(ksp, da));
74: PetscCall(KSPSetFromOptions(ksp));
75: PetscCall(KSPSetUp(ksp));
76: PetscCall(KSPSolve(ksp, NULL, NULL));
78: if (testsolver) {
79: PetscCall(KSPGetSolution(ksp, &x));
80: PetscCall(KSPGetRhs(ksp, &b));
81: PetscCall(KSPSetDMActive(ksp, PETSC_FALSE));
82: PetscCall(KSPSolve(ksp, b, x));
83: {
84: PetscLogStage stage;
85: PetscInt i, n = 20;
87: PetscCall(PetscLogStageRegister("Solve only", &stage));
88: PetscCall(PetscLogStagePush(stage));
89: for (i = 0; i < n; i++) PetscCall(KSPSolve(ksp, b, x));
90: PetscCall(PetscLogStagePop());
91: }
92: }
94: PetscCall(DMDestroy(&da));
95: PetscCall(KSPDestroy(&ksp));
96: PetscCall(PetscFinalize());
97: return 0;
98: }
100: PetscErrorCode ComputeRHS(KSP ksp, Vec b, void *ctx)
101: {
102: UserContext *user = (UserContext *)ctx;
103: PetscInt i, j, mx, my, xm, ym, xs, ys;
104: PetscScalar Hx, Hy;
105: PetscScalar **array;
106: DM da;
108: PetscFunctionBeginUser;
109: PetscCall(KSPGetDM(ksp, &da));
110: PetscCall(DMDAGetInfo(da, 0, &mx, &my, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
111: Hx = 1.0 / (PetscReal)(mx - 1);
112: Hy = 1.0 / (PetscReal)(my - 1);
113: PetscCall(DMDAGetCorners(da, &xs, &ys, 0, &xm, &ym, 0));
114: PetscCall(DMDAVecGetArray(da, b, &array));
115: for (j = ys; j < ys + ym; j++) {
116: for (i = xs; i < xs + xm; i++) array[j][i] = PetscExpScalar(-((PetscReal)i * Hx) * ((PetscReal)i * Hx) / user->nu) * PetscExpScalar(-((PetscReal)j * Hy) * ((PetscReal)j * Hy) / user->nu) * Hx * Hy;
117: }
118: PetscCall(DMDAVecRestoreArray(da, b, &array));
119: PetscCall(VecAssemblyBegin(b));
120: PetscCall(VecAssemblyEnd(b));
122: /* force right-hand side to be consistent for singular matrix */
123: /* note this is really a hack, normally the model would provide you with a consistent right handside */
124: if (user->bcType == NEUMANN) {
125: MatNullSpace nullspace;
127: PetscCall(MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, 0, &nullspace));
128: PetscCall(MatNullSpaceRemove(nullspace, b));
129: PetscCall(MatNullSpaceDestroy(&nullspace));
130: }
131: PetscFunctionReturn(PETSC_SUCCESS);
132: }
134: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
135: {
136: PetscFunctionBeginUser;
137: if ((i > mx / 3.0) && (i < 2.0 * mx / 3.0) && (j > my / 3.0) && (j < 2.0 * my / 3.0)) {
138: *rho = centerRho;
139: } else {
140: *rho = 1.0;
141: }
142: PetscFunctionReturn(PETSC_SUCCESS);
143: }
145: PetscErrorCode ComputeMatrix(KSP ksp, Mat J, Mat jac, void *ctx)
146: {
147: UserContext *user = (UserContext *)ctx;
148: PetscReal centerRho;
149: PetscInt i, j, mx, my, xm, ym, xs, ys;
150: PetscScalar v[5];
151: PetscReal Hx, Hy, HydHx, HxdHy, rho;
152: MatStencil row, col[5];
153: DM da;
154: PetscBool check_matis = PETSC_FALSE;
156: PetscFunctionBeginUser;
157: PetscCall(KSPGetDM(ksp, &da));
158: centerRho = user->rho;
159: PetscCall(DMDAGetInfo(da, 0, &mx, &my, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
160: Hx = 1.0 / (PetscReal)(mx - 1);
161: Hy = 1.0 / (PetscReal)(my - 1);
162: HxdHy = Hx / Hy;
163: HydHx = Hy / Hx;
164: PetscCall(DMDAGetCorners(da, &xs, &ys, 0, &xm, &ym, 0));
165: for (j = ys; j < ys + ym; j++) {
166: for (i = xs; i < xs + xm; i++) {
167: row.i = i;
168: row.j = j;
169: PetscCall(ComputeRho(i, j, mx, my, centerRho, &rho));
170: if (i == 0 || j == 0 || i == mx - 1 || j == my - 1) {
171: if (user->bcType == DIRICHLET) {
172: v[0] = 2.0 * rho * (HxdHy + HydHx);
173: PetscCall(MatSetValuesStencil(jac, 1, &row, 1, &row, v, INSERT_VALUES));
174: } else if (user->bcType == NEUMANN) {
175: PetscInt numx = 0, numy = 0, num = 0;
176: if (j != 0) {
177: v[num] = -rho * HxdHy;
178: col[num].i = i;
179: col[num].j = j - 1;
180: numy++;
181: num++;
182: }
183: if (i != 0) {
184: v[num] = -rho * HydHx;
185: col[num].i = i - 1;
186: col[num].j = j;
187: numx++;
188: num++;
189: }
190: if (i != mx - 1) {
191: v[num] = -rho * HydHx;
192: col[num].i = i + 1;
193: col[num].j = j;
194: numx++;
195: num++;
196: }
197: if (j != my - 1) {
198: v[num] = -rho * HxdHy;
199: col[num].i = i;
200: col[num].j = j + 1;
201: numy++;
202: num++;
203: }
204: v[num] = numx * rho * HydHx + numy * rho * HxdHy;
205: col[num].i = i;
206: col[num].j = j;
207: num++;
208: PetscCall(MatSetValuesStencil(jac, 1, &row, num, col, v, INSERT_VALUES));
209: }
210: } else {
211: v[0] = -rho * HxdHy;
212: col[0].i = i;
213: col[0].j = j - 1;
214: v[1] = -rho * HydHx;
215: col[1].i = i - 1;
216: col[1].j = j;
217: v[2] = 2.0 * rho * (HxdHy + HydHx);
218: col[2].i = i;
219: col[2].j = j;
220: v[3] = -rho * HydHx;
221: col[3].i = i + 1;
222: col[3].j = j;
223: v[4] = -rho * HxdHy;
224: col[4].i = i;
225: col[4].j = j + 1;
226: PetscCall(MatSetValuesStencil(jac, 1, &row, 5, col, v, INSERT_VALUES));
227: }
228: }
229: }
230: PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
231: PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
232: PetscCall(MatViewFromOptions(jac, NULL, "-view_mat"));
233: PetscCall(PetscOptionsGetBool(NULL, NULL, "-check_matis", &check_matis, NULL));
234: if (check_matis) {
235: void (*f)(void);
236: Mat J2;
237: MatType jtype;
238: PetscReal nrm;
240: PetscCall(MatGetType(jac, &jtype));
241: PetscCall(MatConvert(jac, MATIS, MAT_INITIAL_MATRIX, &J2));
242: PetscCall(MatViewFromOptions(J2, NULL, "-view_conv"));
243: PetscCall(MatConvert(J2, jtype, MAT_INPLACE_MATRIX, &J2));
244: PetscCall(MatGetOperation(jac, MATOP_VIEW, &f));
245: PetscCall(MatSetOperation(J2, MATOP_VIEW, f));
246: PetscCall(MatSetDM(J2, da));
247: PetscCall(MatViewFromOptions(J2, NULL, "-view_conv_assembled"));
248: PetscCall(MatAXPY(J2, -1., jac, DIFFERENT_NONZERO_PATTERN));
249: PetscCall(MatNorm(J2, NORM_FROBENIUS, &nrm));
250: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error MATIS %g\n", (double)nrm));
251: PetscCall(MatViewFromOptions(J2, NULL, "-view_conv_err"));
252: PetscCall(MatDestroy(&J2));
253: }
254: if (user->bcType == NEUMANN) {
255: MatNullSpace nullspace;
257: PetscCall(MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, 0, &nullspace));
258: PetscCall(MatSetNullSpace(J, nullspace));
259: PetscCall(MatNullSpaceDestroy(&nullspace));
260: }
261: PetscFunctionReturn(PETSC_SUCCESS);
262: }
264: /*TEST
266: test:
267: args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -ksp_rtol 1.e-3
269: test:
270: suffix: 2
271: args: -bc_type neumann -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -mg_coarse_pc_factor_shift_type nonzero
272: requires: !single
274: test:
275: suffix: telescope
276: nsize: 4
277: args: -ksp_monitor_short -da_grid_x 257 -da_grid_y 257 -pc_type mg -pc_mg_galerkin pmat -pc_mg_levels 4 -ksp_type richardson -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_ignore_kspcomputeoperators -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 chebyshev -mg_coarse_telescope_mg_levels_pc_type jacobi -mg_coarse_pc_telescope_reduction_factor 4
279: test:
280: suffix: 3
281: args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_pc_type jacobi
283: test:
284: suffix: 4
285: args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_ksp_max_it 3 -mg_levels_ksp_max_it 4
287: testset:
288: suffix: aniso
289: args: -da_grid_x 10 -da_grid_y 2 -da_refine 2 -pc_type mg -ksp_monitor_short -mg_levels_ksp_max_it 6 -mg_levels_pc_type jacobi
290: test:
291: suffix: first
292: args: -mg_levels_ksp_chebyshev_kind first
293: test:
294: suffix: fourth
295: args: -mg_levels_ksp_chebyshev_kind fourth
296: test:
297: suffix: opt_fourth
298: args: -mg_levels_ksp_chebyshev_kind opt_fourth
300: test:
301: suffix: 5
302: nsize: 2
303: requires: hypre !complex
304: args: -pc_type mg -da_refine 2 -ksp_monitor -matptap_via hypre -pc_mg_galerkin both
306: test:
307: suffix: 6
308: args: -pc_type svd -pc_svd_monitor ::all
310: TEST*/