1 static char help[] = "Solvers Laplacian with multigrid, bad way.\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";
6
7 /*
8 This problem is modeled by
9 the partial differential equation
10
11 -Laplacian u = g, 0 < x,y < 1,
12
13 with boundary conditions
14
15 u = 0 for x = 0, x = 1, y = 0, y = 1.
16
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.
20 */
21
22 #include <petscksp.h>
23 #include <petscdm.h>
24 #include <petscdmda.h>
25
26 /* User-defined application contexts */
27
28 typedef struct {
29 PetscInt mx, my; /* number grid points in x and y direction */
30 Vec localX, localF; /* local vectors with ghost region */
31 DM da;
32 Vec x, b, r; /* global vectors */
33 Mat J; /* Jacobian on grid */
34 } GridCtx;
35
36 typedef struct {
37 GridCtx fine;
38 GridCtx coarse;
39 KSP ksp_coarse;
40 PetscInt ratio;
41 Mat Ii; /* interpolation from coarse to fine */
42 } AppCtx;
43
44 #define COARSE_LEVEL 0
45 #define FINE_LEVEL 1
46
47 extern PetscErrorCode FormJacobian_Grid(AppCtx *, GridCtx *, Mat *);
48
49 /*
50 Mm_ratio - ration of grid lines between fine and coarse grids.
51 */
main(int argc,char ** argv)52 int main(int argc, char **argv)
53 {
54 AppCtx user;
55 PetscInt its, N, n, Nx = PETSC_DECIDE, Ny = PETSC_DECIDE, nlocal, Nlocal;
56 PetscMPIInt size;
57 KSP ksp, ksp_fine;
58 PC pc;
59 PetscScalar one = 1.0;
60
61 PetscFunctionBeginUser;
62 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
63 user.ratio = 2;
64 user.coarse.mx = 5;
65 user.coarse.my = 5;
66
67 PetscCall(PetscOptionsGetInt(NULL, NULL, "-Mx", &user.coarse.mx, NULL));
68 PetscCall(PetscOptionsGetInt(NULL, NULL, "-My", &user.coarse.my, NULL));
69 PetscCall(PetscOptionsGetInt(NULL, NULL, "-ratio", &user.ratio, NULL));
70
71 user.fine.mx = user.ratio * (user.coarse.mx - 1) + 1;
72 user.fine.my = user.ratio * (user.coarse.my - 1) + 1;
73
74 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Coarse grid size %" PetscInt_FMT " by %" PetscInt_FMT "\n", user.coarse.mx, user.coarse.my));
75 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Fine grid size %" PetscInt_FMT " by %" PetscInt_FMT "\n", user.fine.mx, user.fine.my));
76
77 n = user.fine.mx * user.fine.my;
78 N = user.coarse.mx * user.coarse.my;
79
80 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
81 PetscCall(PetscOptionsGetInt(NULL, NULL, "-Nx", &Nx, NULL));
82 PetscCall(PetscOptionsGetInt(NULL, NULL, "-Ny", &Ny, NULL));
83
84 /* Set up distributed array for fine grid */
85 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));
86 PetscCall(DMSetFromOptions(user.fine.da));
87 PetscCall(DMSetUp(user.fine.da));
88 PetscCall(DMCreateGlobalVector(user.fine.da, &user.fine.x));
89 PetscCall(VecDuplicate(user.fine.x, &user.fine.r));
90 PetscCall(VecDuplicate(user.fine.x, &user.fine.b));
91 PetscCall(VecGetLocalSize(user.fine.x, &nlocal));
92 PetscCall(DMCreateLocalVector(user.fine.da, &user.fine.localX));
93 PetscCall(VecDuplicate(user.fine.localX, &user.fine.localF));
94 PetscCall(MatCreateFromOptions(PETSC_COMM_WORLD, NULL, 1, nlocal, nlocal, n, n, &user.fine.J));
95
96 /* Set up distributed array for coarse grid */
97 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));
98 PetscCall(DMSetFromOptions(user.coarse.da));
99 PetscCall(DMSetUp(user.coarse.da));
100 PetscCall(DMCreateGlobalVector(user.coarse.da, &user.coarse.x));
101 PetscCall(VecDuplicate(user.coarse.x, &user.coarse.b));
102 PetscCall(VecGetLocalSize(user.coarse.x, &Nlocal));
103 PetscCall(DMCreateLocalVector(user.coarse.da, &user.coarse.localX));
104 PetscCall(VecDuplicate(user.coarse.localX, &user.coarse.localF));
105 PetscCall(MatCreateFromOptions(PETSC_COMM_WORLD, NULL, 1, Nlocal, Nlocal, N, N, &user.coarse.J));
106
107 /* Create linear solver */
108 PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
109
110 /* set two level additive Schwarz preconditioner */
111 PetscCall(KSPGetPC(ksp, &pc));
112 PetscCall(PCSetType(pc, PCMG));
113 PetscCall(PCMGSetLevels(pc, 2, NULL));
114 PetscCall(PCMGSetType(pc, PC_MG_ADDITIVE));
115
116 PetscCall(FormJacobian_Grid(&user, &user.coarse, &user.coarse.J));
117 PetscCall(FormJacobian_Grid(&user, &user.fine, &user.fine.J));
118
119 /* Create coarse level */
120 PetscCall(PCMGGetCoarseSolve(pc, &user.ksp_coarse));
121 PetscCall(KSPSetOptionsPrefix(user.ksp_coarse, "coarse_"));
122 PetscCall(KSPSetFromOptions(user.ksp_coarse));
123 PetscCall(KSPSetOperators(user.ksp_coarse, user.coarse.J, user.coarse.J));
124 PetscCall(PCMGSetX(pc, COARSE_LEVEL, user.coarse.x));
125 PetscCall(PCMGSetRhs(pc, COARSE_LEVEL, user.coarse.b));
126
127 /* Create fine level */
128 PetscCall(PCMGGetSmoother(pc, FINE_LEVEL, &ksp_fine));
129 PetscCall(KSPSetOptionsPrefix(ksp_fine, "fine_"));
130 PetscCall(KSPSetFromOptions(ksp_fine));
131 PetscCall(KSPSetOperators(ksp_fine, user.fine.J, user.fine.J));
132 PetscCall(PCMGSetR(pc, FINE_LEVEL, user.fine.r));
133
134 /* Create interpolation between the levels */
135 PetscCall(DMCreateInterpolation(user.coarse.da, user.fine.da, &user.Ii, NULL));
136 PetscCall(PCMGSetInterpolation(pc, FINE_LEVEL, user.Ii));
137 PetscCall(PCMGSetRestriction(pc, FINE_LEVEL, user.Ii));
138
139 PetscCall(KSPSetOperators(ksp, user.fine.J, user.fine.J));
140
141 PetscCall(VecSet(user.fine.b, one));
142
143 /* Set options, then solve nonlinear system */
144 PetscCall(KSPSetFromOptions(ksp));
145
146 PetscCall(KSPSolve(ksp, user.fine.b, user.fine.x));
147 PetscCall(KSPGetIterationNumber(ksp, &its));
148 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Number of iterations = %" PetscInt_FMT "\n", its));
149
150 /* Free data structures */
151 PetscCall(MatDestroy(&user.fine.J));
152 PetscCall(VecDestroy(&user.fine.x));
153 PetscCall(VecDestroy(&user.fine.r));
154 PetscCall(VecDestroy(&user.fine.b));
155 PetscCall(DMDestroy(&user.fine.da));
156 PetscCall(VecDestroy(&user.fine.localX));
157 PetscCall(VecDestroy(&user.fine.localF));
158
159 PetscCall(MatDestroy(&user.coarse.J));
160 PetscCall(VecDestroy(&user.coarse.x));
161 PetscCall(VecDestroy(&user.coarse.b));
162 PetscCall(DMDestroy(&user.coarse.da));
163 PetscCall(VecDestroy(&user.coarse.localX));
164 PetscCall(VecDestroy(&user.coarse.localF));
165
166 PetscCall(KSPDestroy(&ksp));
167 PetscCall(MatDestroy(&user.Ii));
168 PetscCall(PetscFinalize());
169 return 0;
170 }
171
FormJacobian_Grid(AppCtx * user,GridCtx * grid,Mat * J)172 PetscErrorCode FormJacobian_Grid(AppCtx *user, GridCtx *grid, Mat *J)
173 {
174 Mat jac = *J;
175 PetscInt i, j, row, mx, my, xs, ys, xm, ym, Xs, Ys, Xm, Ym, col[5];
176 PetscInt grow;
177 const PetscInt *ltog;
178 PetscScalar two = 2.0, one = 1.0, v[5], hx, hy, hxdhy, hydhx, value;
179 ISLocalToGlobalMapping ltogm;
180
181 mx = grid->mx;
182 my = grid->my;
183 hx = one / (PetscReal)(mx - 1);
184 hy = one / (PetscReal)(my - 1);
185 hxdhy = hx / hy;
186 hydhx = hy / hx;
187
188 /* Get ghost points */
189 PetscCall(DMDAGetCorners(grid->da, &xs, &ys, 0, &xm, &ym, 0));
190 PetscCall(DMDAGetGhostCorners(grid->da, &Xs, &Ys, 0, &Xm, &Ym, 0));
191 PetscCall(DMGetLocalToGlobalMapping(grid->da, <ogm));
192 PetscCall(ISLocalToGlobalMappingGetIndices(ltogm, <og));
193
194 /* Evaluate Jacobian of function */
195 for (j = ys; j < ys + ym; j++) {
196 row = (j - Ys) * Xm + xs - Xs - 1;
197 for (i = xs; i < xs + xm; i++) {
198 row++;
199 grow = ltog[row];
200 if (i > 0 && i < mx - 1 && j > 0 && j < my - 1) {
201 v[0] = -hxdhy;
202 col[0] = ltog[row - Xm];
203 v[1] = -hydhx;
204 col[1] = ltog[row - 1];
205 v[2] = two * (hydhx + hxdhy);
206 col[2] = grow;
207 v[3] = -hydhx;
208 col[3] = ltog[row + 1];
209 v[4] = -hxdhy;
210 col[4] = ltog[row + Xm];
211 PetscCall(MatSetValues(jac, 1, &grow, 5, col, v, INSERT_VALUES));
212 } else if ((i > 0 && i < mx - 1) || (j > 0 && j < my - 1)) {
213 value = .5 * two * (hydhx + hxdhy);
214 PetscCall(MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES));
215 } else {
216 value = .25 * two * (hydhx + hxdhy);
217 PetscCall(MatSetValues(jac, 1, &grow, 1, &grow, &value, INSERT_VALUES));
218 }
219 }
220 }
221 PetscCall(ISLocalToGlobalMappingRestoreIndices(ltogm, <og));
222 PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
223 PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
224
225 return PETSC_SUCCESS;
226 }
227
228 /*TEST
229
230 test:
231 args: -ksp_gmres_cgs_refinement_type refine_always -pc_type jacobi -ksp_monitor_short -ksp_type gmres
232
233 test:
234 suffix: 2
235 nsize: 3
236 args: -ksp_monitor_short
237
238 TEST*/
239