Actual source code: ex19.c

  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";

  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.
 20: */

 22: #include <petscksp.h>
 23: #include <petscdm.h>
 24: #include <petscdmda.h>

 26: /* User-defined application contexts */

 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;

 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;

 44: #define COARSE_LEVEL 0
 45: #define FINE_LEVEL   1

 47: extern PetscErrorCode FormJacobian_Grid(AppCtx *, GridCtx *, Mat *);

 49: /*
 50:       Mm_ratio - ration of grid lines between fine and coarse grids.
 51: */
 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;

 61:   PetscFunctionBeginUser;
 62:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
 63:   user.ratio     = 2;
 64:   user.coarse.mx = 5;
 65:   user.coarse.my = 5;

 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));

 71:   user.fine.mx = user.ratio * (user.coarse.mx - 1) + 1;
 72:   user.fine.my = user.ratio * (user.coarse.my - 1) + 1;

 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));

 77:   n = user.fine.mx * user.fine.my;
 78:   N = user.coarse.mx * user.coarse.my;

 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));

 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));

 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));

107:   /* Create linear solver */
108:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));

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));

116:   PetscCall(FormJacobian_Grid(&user, &user.coarse, &user.coarse.J));
117:   PetscCall(FormJacobian_Grid(&user, &user.fine, &user.fine.J));

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));

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));

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));

139:   PetscCall(KSPSetOperators(ksp, user.fine.J, user.fine.J));

141:   PetscCall(VecSet(user.fine.b, one));

143:   /* Set options, then solve nonlinear system */
144:   PetscCall(KSPSetFromOptions(ksp));

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));

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));

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));

166:   PetscCall(KSPDestroy(&ksp));
167:   PetscCall(MatDestroy(&user.Ii));
168:   PetscCall(PetscFinalize());
169:   return 0;
170: }

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;

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;

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, &ltogm));
192:   PetscCall(ISLocalToGlobalMappingGetIndices(ltogm, &ltog));

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, &ltog));
222:   PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
223:   PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));

225:   return PETSC_SUCCESS;
226: }

228: /*TEST

230:     test:
231:       args: -ksp_gmres_cgs_refinement_type refine_always -pc_type jacobi -ksp_monitor_short -ksp_type gmres

233:     test:
234:       suffix: 2
235:       nsize: 3
236:       args: -ksp_monitor_short

238: TEST*/