Actual source code: ex29.c
2: static char help[] = "Tests ML interface. Modified from ~src/ksp/ksp/tests/ex19.c \n\
3: -mx <xg>, where <xg> = number of grid points in the x-direction\n\
4: -my <yg>, where <yg> = number of grid points in the y-direction\n\
5: -Nx <npx>, where <npx> = number of processors in the x-direction\n\
6: -Ny <npy>, where <npy> = number of processors in the y-direction\n\n";
8: /*
9: This problem is modeled by
10: the partial differential equation
12: -Laplacian u = g, 0 < x,y < 1,
14: with boundary conditions
16: u = 0 for x = 0, x = 1, y = 0, y = 1.
18: A finite difference approximation with the usual 5-point stencil
19: is used to discretize the boundary value problem to obtain a nonlinear
20: system of equations.
22: Usage: ./ex29 -ksp_type gmres -ksp_monitor
23: -pc_mg_type <multiplicative> (one of) additive multiplicative full kascade
24: -mg_coarse_ksp_max_it 10 -mg_levels_3_ksp_max_it 10 -mg_levels_2_ksp_max_it 10
25: -mg_levels_1_ksp_max_it 10 -mg_fine_ksp_max_it 10
26: */
28: #include <petscksp.h>
29: #include <petscdm.h>
30: #include <petscdmda.h>
32: /* User-defined application contexts */
33: typedef struct {
34: PetscInt mx, my; /* number grid points in x and y direction */
35: Vec localX, localF; /* local vectors with ghost region */
36: DM da;
37: Vec x, b, r; /* global vectors */
38: Mat J; /* Jacobian on grid */
39: Mat A, P, R;
40: KSP ksp;
41: } GridCtx;
42: extern int FormJacobian_Grid(GridCtx *, Mat *);
44: int main(int argc, char **argv)
45: {
46: PetscInt its, n, Nx = PETSC_DECIDE, Ny = PETSC_DECIDE, nlocal, i;
47: PetscMPIInt size;
48: PC pc;
49: PetscInt mx, my;
50: Mat A;
51: GridCtx fine_ctx;
52: KSP ksp;
53: PetscBool flg;
56: PetscInitialize(&argc, &argv, NULL, help);
57: /* set up discretization matrix for fine grid */
58: /* ML requires input of fine-grid matrix. It determines nlevels. */
59: fine_ctx.mx = 9;
60: fine_ctx.my = 9;
61: PetscOptionsGetInt(NULL, NULL, "-mx", &mx, &flg);
62: if (flg) fine_ctx.mx = mx;
63: PetscOptionsGetInt(NULL, NULL, "-my", &my, &flg);
64: if (flg) fine_ctx.my = my;
65: PetscPrintf(PETSC_COMM_WORLD, "Fine grid size %" PetscInt_FMT " by %" PetscInt_FMT "\n", fine_ctx.mx, fine_ctx.my);
66: n = fine_ctx.mx * fine_ctx.my;
68: MPI_Comm_size(PETSC_COMM_WORLD, &size);
69: PetscOptionsGetInt(NULL, NULL, "-Nx", &Nx, NULL);
70: PetscOptionsGetInt(NULL, NULL, "-Ny", &Ny, NULL);
72: 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);
73: DMSetFromOptions(fine_ctx.da);
74: DMSetUp(fine_ctx.da);
75: DMCreateGlobalVector(fine_ctx.da, &fine_ctx.x);
76: VecDuplicate(fine_ctx.x, &fine_ctx.b);
77: VecGetLocalSize(fine_ctx.x, &nlocal);
78: DMCreateLocalVector(fine_ctx.da, &fine_ctx.localX);
79: VecDuplicate(fine_ctx.localX, &fine_ctx.localF);
80: MatCreateAIJ(PETSC_COMM_WORLD, nlocal, nlocal, n, n, 5, NULL, 3, NULL, &A);
81: FormJacobian_Grid(&fine_ctx, &A);
83: /* create linear solver */
84: KSPCreate(PETSC_COMM_WORLD, &ksp);
85: KSPGetPC(ksp, &pc);
86: PCSetType(pc, PCML);
88: /* set options, then solve system */
89: KSPSetFromOptions(ksp); /* calls PCSetFromOptions_MG/ML */
91: for (i = 0; i < 3; i++) {
92: if (i < 2) {
93: /* set values for rhs vector */
94: VecSet(fine_ctx.b, i + 1.0);
95: /* modify A */
96: MatShift(A, 1.0);
97: MatScale(A, 2.0);
98: KSPSetOperators(ksp, A, A);
99: } else { /* test SAME_NONZERO_PATTERN */
100: KSPSetOperators(ksp, A, A);
101: }
102: KSPSolve(ksp, fine_ctx.b, fine_ctx.x);
103: KSPGetIterationNumber(ksp, &its);
104: if (its > 6) PetscPrintf(PETSC_COMM_WORLD, "Warning: Number of iterations = %" PetscInt_FMT " greater than expected\n", its);
105: }
107: /* free data structures */
108: VecDestroy(&fine_ctx.x);
109: VecDestroy(&fine_ctx.b);
110: DMDestroy(&fine_ctx.da);
111: VecDestroy(&fine_ctx.localX);
112: VecDestroy(&fine_ctx.localF);
113: MatDestroy(&A);
114: KSPDestroy(&ksp);
115: PetscFinalize();
116: return 0;
117: }
119: int FormJacobian_Grid(GridCtx *grid, Mat *J)
120: {
121: Mat jac = *J;
122: PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym, col[5];
123: PetscInt grow;
124: const PetscInt *ltog;
125: PetscScalar two = 2.0, one = 1.0, v[5], hx, hy, hxdhy, hydhx, value;
126: ISLocalToGlobalMapping ltogm;
128: mx = grid->mx;
129: my = grid->my;
130: hx = one / (PetscReal)(mx - 1);
131: hy = one / (PetscReal)(my - 1);
132: hxdhy = hx / hy;
133: hydhx = hy / hx;
135: /* Get ghost points */
136: DMDAGetCorners(grid->da, &xs, &ys, 0, &xm, &ym, 0);
137: DMDAGetGhostCorners(grid->da, &Xs, &Ys, 0, &Xm, &Ym, 0);
138: DMGetLocalToGlobalMapping(grid->da, <ogm);
139: ISLocalToGlobalMappingGetIndices(ltogm, <og);
141: /* Evaluate Jacobian of function */
142: for (j = ys; j < ys + ym; j++) {
143: row = (j - Ys) * Xm + xs - Xs - 1;
144: for (i = xs; i < xs + xm; i++) {
145: row++;
146: grow = ltog[row];
147: if (i > 0 && i < mx - 1 && j > 0 && j < my - 1) {
148: v[0] = -hxdhy;
149: col[0] = ltog[row - Xm];
150: v[1] = -hydhx;
151: col[1] = ltog[row - 1];
152: v[2] = two * (hydhx + hxdhy);
153: col[2] = grow;
154: v[3] = -hydhx;
155: col[3] = ltog[row + 1];
156: v[4] = -hxdhy;
157: col[4] = ltog[row + Xm];
158: MatSetValues(jac, 1, &grow, 5, col, v, INSERT_VALUES);
159: } else if ((i > 0 && i < mx - 1) || (j > 0 && j < my - 1)) {
160: value = .5 * two * (hydhx + hxdhy);
161: MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES);
162: } else {
163: value = .25 * two * (hydhx + hxdhy);
164: MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES);
165: }
166: }
167: }
168: ISLocalToGlobalMappingRestoreIndices(ltogm, <og);
169: MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY);
170: MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY);
171: return 0;
172: }
174: /*TEST
176: test:
177: output_file: output/ex29.out
178: args: -mat_no_inode
179: requires: ml
181: test:
182: suffix: 2
183: nsize: 3
184: requires: ml
186: TEST*/