Actual source code: ex19.c
2: static char help[] = "Solvers Laplacian with multigrid, bad way.\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.
21: */
23: #include <petscksp.h>
24: #include <petscdm.h>
25: #include <petscdmda.h>
27: /* User-defined application contexts */
29: typedef struct {
30: PetscInt mx, my; /* number grid points in x and y direction */
31: Vec localX, localF; /* local vectors with ghost region */
32: DM da;
33: Vec x, b, r; /* global vectors */
34: Mat J; /* Jacobian on grid */
35: } GridCtx;
37: typedef struct {
38: GridCtx fine;
39: GridCtx coarse;
40: KSP ksp_coarse;
41: PetscInt ratio;
42: Mat Ii; /* interpolation from coarse to fine */
43: } AppCtx;
45: #define COARSE_LEVEL 0
46: #define FINE_LEVEL 1
48: extern PetscErrorCode FormJacobian_Grid(AppCtx *, GridCtx *, Mat *);
50: /*
51: Mm_ratio - ration of grid lines between fine and coarse grids.
52: */
53: int main(int argc, char **argv)
54: {
55: AppCtx user;
56: PetscInt its, N, n, Nx = PETSC_DECIDE, Ny = PETSC_DECIDE, nlocal, Nlocal;
57: PetscMPIInt size;
58: KSP ksp, ksp_fine;
59: PC pc;
60: PetscScalar one = 1.0;
62: PetscFunctionBeginUser;
63: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
64: user.ratio = 2;
65: user.coarse.mx = 5;
66: user.coarse.my = 5;
68: PetscCall(PetscOptionsGetInt(NULL, NULL, "-Mx", &user.coarse.mx, NULL));
69: PetscCall(PetscOptionsGetInt(NULL, NULL, "-My", &user.coarse.my, NULL));
70: PetscCall(PetscOptionsGetInt(NULL, NULL, "-ratio", &user.ratio, NULL));
72: user.fine.mx = user.ratio * (user.coarse.mx - 1) + 1;
73: user.fine.my = user.ratio * (user.coarse.my - 1) + 1;
75: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Coarse grid size %" PetscInt_FMT " by %" PetscInt_FMT "\n", user.coarse.mx, user.coarse.my));
76: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Fine grid size %" PetscInt_FMT " by %" PetscInt_FMT "\n", user.fine.mx, user.fine.my));
78: n = user.fine.mx * user.fine.my;
79: N = user.coarse.mx * user.coarse.my;
81: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
82: PetscCall(PetscOptionsGetInt(NULL, NULL, "-Nx", &Nx, NULL));
83: PetscCall(PetscOptionsGetInt(NULL, NULL, "-Ny", &Ny, NULL));
85: /* Set up distributed array for fine grid */
86: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, user.fine.mx, user.fine.my, Nx, Ny, 1, 1, NULL, NULL, &user.fine.da));
87: PetscCall(DMSetFromOptions(user.fine.da));
88: PetscCall(DMSetUp(user.fine.da));
89: PetscCall(DMCreateGlobalVector(user.fine.da, &user.fine.x));
90: PetscCall(VecDuplicate(user.fine.x, &user.fine.r));
91: PetscCall(VecDuplicate(user.fine.x, &user.fine.b));
92: PetscCall(VecGetLocalSize(user.fine.x, &nlocal));
93: PetscCall(DMCreateLocalVector(user.fine.da, &user.fine.localX));
94: PetscCall(VecDuplicate(user.fine.localX, &user.fine.localF));
95: PetscCall(MatCreateAIJ(PETSC_COMM_WORLD, nlocal, nlocal, n, n, 5, NULL, 3, NULL, &user.fine.J));
97: /* Set up distributed array for coarse grid */
98: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, user.coarse.mx, user.coarse.my, Nx, Ny, 1, 1, NULL, NULL, &user.coarse.da));
99: PetscCall(DMSetFromOptions(user.coarse.da));
100: PetscCall(DMSetUp(user.coarse.da));
101: PetscCall(DMCreateGlobalVector(user.coarse.da, &user.coarse.x));
102: PetscCall(VecDuplicate(user.coarse.x, &user.coarse.b));
103: PetscCall(VecGetLocalSize(user.coarse.x, &Nlocal));
104: PetscCall(DMCreateLocalVector(user.coarse.da, &user.coarse.localX));
105: PetscCall(VecDuplicate(user.coarse.localX, &user.coarse.localF));
106: PetscCall(MatCreateAIJ(PETSC_COMM_WORLD, Nlocal, Nlocal, N, N, 5, NULL, 3, NULL, &user.coarse.J));
108: /* Create linear solver */
109: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
111: /* set two level additive Schwarz preconditioner */
112: PetscCall(KSPGetPC(ksp, &pc));
113: PetscCall(PCSetType(pc, PCMG));
114: PetscCall(PCMGSetLevels(pc, 2, NULL));
115: PetscCall(PCMGSetType(pc, PC_MG_ADDITIVE));
117: PetscCall(FormJacobian_Grid(&user, &user.coarse, &user.coarse.J));
118: PetscCall(FormJacobian_Grid(&user, &user.fine, &user.fine.J));
120: /* Create coarse level */
121: PetscCall(PCMGGetCoarseSolve(pc, &user.ksp_coarse));
122: PetscCall(KSPSetOptionsPrefix(user.ksp_coarse, "coarse_"));
123: PetscCall(KSPSetFromOptions(user.ksp_coarse));
124: PetscCall(KSPSetOperators(user.ksp_coarse, user.coarse.J, user.coarse.J));
125: PetscCall(PCMGSetX(pc, COARSE_LEVEL, user.coarse.x));
126: PetscCall(PCMGSetRhs(pc, COARSE_LEVEL, user.coarse.b));
128: /* Create fine level */
129: PetscCall(PCMGGetSmoother(pc, FINE_LEVEL, &ksp_fine));
130: PetscCall(KSPSetOptionsPrefix(ksp_fine, "fine_"));
131: PetscCall(KSPSetFromOptions(ksp_fine));
132: PetscCall(KSPSetOperators(ksp_fine, user.fine.J, user.fine.J));
133: PetscCall(PCMGSetR(pc, FINE_LEVEL, user.fine.r));
135: /* Create interpolation between the levels */
136: PetscCall(DMCreateInterpolation(user.coarse.da, user.fine.da, &user.Ii, NULL));
137: PetscCall(PCMGSetInterpolation(pc, FINE_LEVEL, user.Ii));
138: PetscCall(PCMGSetRestriction(pc, FINE_LEVEL, user.Ii));
140: PetscCall(KSPSetOperators(ksp, user.fine.J, user.fine.J));
142: PetscCall(VecSet(user.fine.b, one));
144: /* Set options, then solve nonlinear system */
145: PetscCall(KSPSetFromOptions(ksp));
147: PetscCall(KSPSolve(ksp, user.fine.b, user.fine.x));
148: PetscCall(KSPGetIterationNumber(ksp, &its));
149: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Number of iterations = %" PetscInt_FMT "\n", its));
151: /* Free data structures */
152: PetscCall(MatDestroy(&user.fine.J));
153: PetscCall(VecDestroy(&user.fine.x));
154: PetscCall(VecDestroy(&user.fine.r));
155: PetscCall(VecDestroy(&user.fine.b));
156: PetscCall(DMDestroy(&user.fine.da));
157: PetscCall(VecDestroy(&user.fine.localX));
158: PetscCall(VecDestroy(&user.fine.localF));
160: PetscCall(MatDestroy(&user.coarse.J));
161: PetscCall(VecDestroy(&user.coarse.x));
162: PetscCall(VecDestroy(&user.coarse.b));
163: PetscCall(DMDestroy(&user.coarse.da));
164: PetscCall(VecDestroy(&user.coarse.localX));
165: PetscCall(VecDestroy(&user.coarse.localF));
167: PetscCall(KSPDestroy(&ksp));
168: PetscCall(MatDestroy(&user.Ii));
169: PetscCall(PetscFinalize());
170: return 0;
171: }
173: PetscErrorCode FormJacobian_Grid(AppCtx *user, GridCtx *grid, Mat *J)
174: {
175: Mat jac = *J;
176: PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym, col[5];
177: PetscInt grow;
178: const PetscInt *ltog;
179: PetscScalar two = 2.0, one = 1.0, v[5], hx, hy, hxdhy, hydhx, value;
180: ISLocalToGlobalMapping ltogm;
182: mx = grid->mx;
183: my = grid->my;
184: hx = one / (PetscReal)(mx - 1);
185: hy = one / (PetscReal)(my - 1);
186: hxdhy = hx / hy;
187: hydhx = hy / hx;
189: /* Get ghost points */
190: PetscCall(DMDAGetCorners(grid->da, &xs, &ys, 0, &xm, &ym, 0));
191: PetscCall(DMDAGetGhostCorners(grid->da, &Xs, &Ys, 0, &Xm, &Ym, 0));
192: PetscCall(DMGetLocalToGlobalMapping(grid->da, <ogm));
193: PetscCall(ISLocalToGlobalMappingGetIndices(ltogm, <og));
195: /* Evaluate Jacobian of function */
196: for (j = ys; j < ys + ym; j++) {
197: row = (j - Ys) * Xm + xs - Xs - 1;
198: for (i = xs; i < xs + xm; i++) {
199: row++;
200: grow = ltog[row];
201: if (i > 0 && i < mx - 1 && j > 0 && j < my - 1) {
202: v[0] = -hxdhy;
203: col[0] = ltog[row - Xm];
204: v[1] = -hydhx;
205: col[1] = ltog[row - 1];
206: v[2] = two * (hydhx + hxdhy);
207: col[2] = grow;
208: v[3] = -hydhx;
209: col[3] = ltog[row + 1];
210: v[4] = -hxdhy;
211: col[4] = ltog[row + Xm];
212: PetscCall(MatSetValues(jac, 1, &grow, 5, col, v, INSERT_VALUES));
213: } else if ((i > 0 && i < mx - 1) || (j > 0 && j < my - 1)) {
214: value = .5 * two * (hydhx + hxdhy);
215: PetscCall(MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES));
216: } else {
217: value = .25 * two * (hydhx + hxdhy);
218: PetscCall(MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES));
219: }
220: }
221: }
222: PetscCall(ISLocalToGlobalMappingRestoreIndices(ltogm, <og));
223: PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
224: PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
226: return PETSC_SUCCESS;
227: }
229: /*TEST
231: test:
232: args: -ksp_gmres_cgs_refinement_type refine_always -pc_type jacobi -ksp_monitor_short -ksp_type gmres
234: test:
235: suffix: 2
236: nsize: 3
237: args: -ksp_monitor_short
239: TEST*/