Actual source code: ex29.c
1: static char help[] = "Tests ML interface. Modified from ~src/ksp/ksp/tests/ex19.c \n\
2: -mx <xg>, where <xg> = number of grid points in the x-direction\n\
3: -my <yg>, where <yg> = number of grid points in the y-direction\n\
4: -Nx <npx>, where <npx> = number of processors in the x-direction\n\
5: -Ny <npy>, where <npy> = number of processors in the y-direction\n\n";
7: /*
8: This problem is modeled by
9: the partial differential equation
11: -Laplacian u = g, 0 < x,y < 1,
13: with boundary conditions
15: u = 0 for x = 0, x = 1, y = 0, y = 1.
17: A finite difference approximation with the usual 5-point stencil
18: is used to discretize the boundary value problem to obtain a nonlinear
19: system of equations.
21: Usage: ./ex29 -ksp_type gmres -ksp_monitor
22: -pc_mg_type <multiplicative> (one of) additive multiplicative full kascade
23: -mg_coarse_ksp_max_it 10 -mg_levels_3_ksp_max_it 10 -mg_levels_2_ksp_max_it 10
24: -mg_levels_1_ksp_max_it 10 -mg_fine_ksp_max_it 10
25: */
27: #include <petscksp.h>
28: #include <petscdm.h>
29: #include <petscdmda.h>
31: /* User-defined application contexts */
32: typedef struct {
33: PetscInt mx, my; /* number grid points in x and y direction */
34: Vec localX, localF; /* local vectors with ghost region */
35: DM da;
36: Vec x, b, r; /* global vectors */
37: Mat J; /* Jacobian on grid */
38: Mat A, P, R;
39: KSP ksp;
40: } GridCtx;
41: extern PetscErrorCode FormJacobian_Grid(GridCtx *, Mat *);
43: int main(int argc, char **argv)
44: {
45: PetscInt its, n, Nx = PETSC_DECIDE, Ny = PETSC_DECIDE, nlocal, i;
46: PetscMPIInt size;
47: PC pc;
48: PetscInt mx, my;
49: Mat A;
50: GridCtx fine_ctx;
51: KSP ksp;
52: PetscBool flg;
54: PetscFunctionBeginUser;
55: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
56: /* set up discretization matrix for fine grid */
57: /* ML requires input of fine-grid matrix. It determines nlevels. */
58: fine_ctx.mx = 9;
59: fine_ctx.my = 9;
60: PetscCall(PetscOptionsGetInt(NULL, NULL, "-mx", &mx, &flg));
61: if (flg) fine_ctx.mx = mx;
62: PetscCall(PetscOptionsGetInt(NULL, NULL, "-my", &my, &flg));
63: if (flg) fine_ctx.my = my;
64: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Fine grid size %" PetscInt_FMT " by %" PetscInt_FMT "\n", fine_ctx.mx, fine_ctx.my));
65: n = fine_ctx.mx * fine_ctx.my;
67: MPI_Comm_size(PETSC_COMM_WORLD, &size);
68: PetscCall(PetscOptionsGetInt(NULL, NULL, "-Nx", &Nx, NULL));
69: PetscCall(PetscOptionsGetInt(NULL, NULL, "-Ny", &Ny, NULL));
71: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, fine_ctx.mx, fine_ctx.my, Nx, Ny, 1, 1, NULL, NULL, &fine_ctx.da));
72: PetscCall(DMSetFromOptions(fine_ctx.da));
73: PetscCall(DMSetUp(fine_ctx.da));
74: PetscCall(DMCreateGlobalVector(fine_ctx.da, &fine_ctx.x));
75: PetscCall(VecDuplicate(fine_ctx.x, &fine_ctx.b));
76: PetscCall(VecGetLocalSize(fine_ctx.x, &nlocal));
77: PetscCall(DMCreateLocalVector(fine_ctx.da, &fine_ctx.localX));
78: PetscCall(VecDuplicate(fine_ctx.localX, &fine_ctx.localF));
79: PetscCall(MatCreateFromOptions(PETSC_COMM_WORLD, NULL, 1, nlocal, nlocal, n, n, &A));
80: PetscCall(FormJacobian_Grid(&fine_ctx, &A));
82: /* create linear solver */
83: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
84: PetscCall(KSPGetPC(ksp, &pc));
85: PetscCall(PCSetType(pc, PCML));
87: /* set options, then solve system */
88: PetscCall(KSPSetFromOptions(ksp)); /* calls PCSetFromOptions_MG/ML */
90: for (i = 0; i < 3; i++) {
91: if (i < 2) {
92: /* set values for rhs vector */
93: PetscCall(VecSet(fine_ctx.b, i + 1.0));
94: /* modify A */
95: PetscCall(MatShift(A, 1.0));
96: PetscCall(MatScale(A, 2.0));
97: PetscCall(KSPSetOperators(ksp, A, A));
98: } else { /* test SAME_NONZERO_PATTERN */
99: PetscCall(KSPSetOperators(ksp, A, A));
100: }
101: PetscCall(KSPSolve(ksp, fine_ctx.b, fine_ctx.x));
102: PetscCall(KSPGetIterationNumber(ksp, &its));
103: if (its > 6) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: Number of iterations = %" PetscInt_FMT " greater than expected\n", its));
104: }
106: /* free data structures */
107: PetscCall(VecDestroy(&fine_ctx.x));
108: PetscCall(VecDestroy(&fine_ctx.b));
109: PetscCall(DMDestroy(&fine_ctx.da));
110: PetscCall(VecDestroy(&fine_ctx.localX));
111: PetscCall(VecDestroy(&fine_ctx.localF));
112: PetscCall(MatDestroy(&A));
113: PetscCall(KSPDestroy(&ksp));
114: PetscCall(PetscFinalize());
115: return 0;
116: }
118: PetscErrorCode FormJacobian_Grid(GridCtx *grid, Mat *J)
119: {
120: Mat jac = *J;
121: PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym, col[5];
122: PetscInt grow;
123: const PetscInt *ltog;
124: PetscScalar two = 2.0, one = 1.0, v[5], hx, hy, hxdhy, hydhx, value;
125: ISLocalToGlobalMapping ltogm;
127: mx = grid->mx;
128: my = grid->my;
129: hx = one / (PetscReal)(mx - 1);
130: hy = one / (PetscReal)(my - 1);
131: hxdhy = hx / hy;
132: hydhx = hy / hx;
134: /* Get ghost points */
135: PetscCall(DMDAGetCorners(grid->da, &xs, &ys, 0, &xm, &ym, 0));
136: PetscCall(DMDAGetGhostCorners(grid->da, &Xs, &Ys, 0, &Xm, &Ym, 0));
137: PetscCall(DMGetLocalToGlobalMapping(grid->da, <ogm));
138: PetscCall(ISLocalToGlobalMappingGetIndices(ltogm, <og));
140: /* Evaluate Jacobian of function */
141: for (j = ys; j < ys + ym; j++) {
142: row = (j - Ys) * Xm + xs - Xs - 1;
143: for (i = xs; i < xs + xm; i++) {
144: row++;
145: grow = ltog[row];
146: if (i > 0 && i < mx - 1 && j > 0 && j < my - 1) {
147: v[0] = -hxdhy;
148: col[0] = ltog[row - Xm];
149: v[1] = -hydhx;
150: col[1] = ltog[row - 1];
151: v[2] = two * (hydhx + hxdhy);
152: col[2] = grow;
153: v[3] = -hydhx;
154: col[3] = ltog[row + 1];
155: v[4] = -hxdhy;
156: col[4] = ltog[row + Xm];
157: PetscCall(MatSetValues(jac, 1, &grow, 5, col, v, INSERT_VALUES));
158: } else if ((i > 0 && i < mx - 1) || (j > 0 && j < my - 1)) {
159: value = .5 * two * (hydhx + hxdhy);
160: PetscCall(MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES));
161: } else {
162: value = .25 * two * (hydhx + hxdhy);
163: PetscCall(MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES));
164: }
165: }
166: }
167: PetscCall(ISLocalToGlobalMappingRestoreIndices(ltogm, <og));
168: PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
169: PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
170: return PETSC_SUCCESS;
171: }
173: /*TEST
175: test:
176: output_file: output/ex29.out
177: args: -mat_no_inode
178: requires: ml
180: test:
181: suffix: 2
182: nsize: 3
183: requires: ml
185: TEST*/