1: static char help[] = "Reduced formulation of the mother problem of PDE-constrained optimisation.\n";

 37:  #include <petsc.h>
 38:  #include <petscfe.h>
 39:  #include <petscviewerhdf5.h>

 41: typedef struct {
 42:   DM  dm;
 43:   Mat mass;
 44:   Vec data;
 45:   Vec state;
 46:   Vec tmp1;
 47:   Vec tmp2;
 48:   Vec adjoint;
 49:   Mat laplace;
 50:   KSP ksp_laplace;
 51:   PetscInt  num_bc_dofs;
 52:   PetscInt* bc_indices;
 53:   PetscScalar* bc_values;
 54:   PetscBool use_riesz;
 55: } AppCtx;

 57: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
 58: {
 59:   DM             distributedMesh = NULL;
 61:   const PetscInt dim = 2;
 62:   char filename[2048];
 63:   PetscBool flg;

 66:   PetscOptionsBegin(comm, "", "Poisson mother problem options", "DMPLEX");
 67:   filename[0] = '\0';
 68:   user->use_riesz = PETSC_TRUE;

 70:   PetscOptionsBool("-use_riesz", "Use the Riesz map to achieve mesh independence", "ex2.c", user->use_riesz, &user->use_riesz, NULL);
 71:   PetscOptionsString("-f", "filename to read", "ex2.c", filename, filename, sizeof(filename), &flg);
 72:   PetscOptionsEnd();

 74:   if (!flg) {
 75:     DMPlexCreateBoxMesh(comm, dim, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);
 76:   } else {
 77: #if defined(PETSC_HAVE_HDF5)
 78:     const PetscInt vertices_per_cell = 3;
 79:     PetscViewer    viewer;
 80:     Vec            coordinates;
 81:     Vec            topology;
 82:     PetscInt       numCells;
 83:     PetscInt       numVertices;
 84:     PetscScalar*   coords;
 85:     PetscScalar*   topo_f;
 86:     PetscInt*      cells;
 87:     PetscInt       j;
 88:     DMLabel        label;

 90:     /* Read in FEniCS HDF5 output */
 91:     PetscViewerHDF5Open(comm, filename, FILE_MODE_READ, &viewer);

 93:     /* create Vecs to read in the data from H5 */
 94:     VecCreate(comm, &coordinates);
 95:     PetscObjectSetName((PetscObject)coordinates, "coordinates");
 96:     VecSetBlockSize(coordinates, dim);
 97:     VecCreate(comm, &topology);
 98:     PetscObjectSetName((PetscObject)topology, "topology");
 99:     VecSetBlockSize(topology, vertices_per_cell);

101:     /* navigate to the right group */
102:     PetscViewerHDF5PushGroup(viewer, "/Mesh/mesh");

104:     /* Read the Vecs */
105:     VecLoad(coordinates, viewer);
106:     VecLoad(topology, viewer);

108:     /* do some ugly calculations */
109:     VecGetSize(topology, &numCells);
110:     numCells = numCells / vertices_per_cell;
111:     VecGetSize(coordinates, &numVertices);
112:     numVertices = numVertices / dim;

114:     VecGetArray(coordinates, &coords);
115:     VecGetArray(topology, &topo_f);
116:     /* and now we have to convert the double representation to integers to pass over, argh */
117:     PetscMalloc1(numCells*vertices_per_cell, &cells);
118:     for (j = 0; j < numCells*vertices_per_cell; j++) {
119:       cells[j] = (PetscInt) topo_f[j];
120:     }

122:     /* Now create the DM */
123:     DMPlexCreateFromCellList(comm, dim, numCells, numVertices, vertices_per_cell, PETSC_TRUE, cells, dim, coords, dm);
124:     /* Check for flipped first cell */
125:     {
126:       PetscReal v0[3], J[9], invJ[9], detJ;

128:       DMPlexComputeCellGeometryFEM(*dm, 0, NULL, v0, J, invJ, &detJ);
129:       if (detJ < 0) {
130:         DMPlexReverseCell(*dm, 0);
131:         DMPlexComputeCellGeometryFEM(*dm, 0, NULL, v0, J, invJ, &detJ);
132:         if (detJ < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Something is wrong");
133:       }
134:     }
135:     DMPlexOrient(*dm);
136:     DMCreateLabel(*dm, "marker");
137:     DMGetLabel(*dm, "marker", &label);
138:     DMPlexMarkBoundaryFaces(*dm, 1, label);
139:     DMPlexLabelComplete(*dm, label);

141:     PetscViewerDestroy(&viewer);
142:     VecRestoreArray(coordinates, &coords);
143:     VecRestoreArray(topology, &topo_f);
144:     PetscFree(cells);
145:     VecDestroy(&coordinates);
146:     VecDestroy(&topology);
147: #else
148:     SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Reconfigure PETSc with --download-hdf5");
149: #endif
150:   }

152:   PetscObjectSetName((PetscObject) *dm, "Mesh");
153:   DMPlexDistribute(*dm, 0, NULL, &distributedMesh);
154:   if (distributedMesh) {
155:     DMDestroy(dm);
156:     *dm  = distributedMesh;
157:   }

159:   DMSetFromOptions(*dm);
160:   DMViewFromOptions(*dm, NULL, "-dm_view");
161:   return(0);
162: }

164: void mass_kernel(PetscInt dim, PetscInt Nf, PetscInt NfAux,
165:            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
166:            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
167:            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
168: {
169:   g0[0] = 1.0;
170: }

172: void laplace_kernel(PetscInt dim, PetscInt Nf, PetscInt NfAux,
173:            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
174:            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
175:            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
176: {
177:   PetscInt d;
178:   for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0;
179: }

181: /* data we seek to match */
182: PetscErrorCode data_kernel(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *y, void *ctx)
183: {
184:   *y = 1.0/(2*PETSC_PI*PETSC_PI) * PetscSinReal(PETSC_PI*x[0]) * PetscSinReal(PETSC_PI*x[1]);
185:   /* the associated control is sin(pi*x[0])*sin(pi*x[1]) */
186:   return 0;
187: }
188: PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
189: {
190:   *u = 0.0;
191:   return 0;
192: }

194: PetscErrorCode CreateCtx(DM dm, AppCtx* user)
195: {

198:   DM             dm_mass;
199:   DM             dm_laplace;
200:   PetscDS        prob_mass;
201:   PetscDS        prob_laplace;
202:   PetscFE        fe;
203:   DMLabel        label;
204:   PetscSection   section;
205:   PetscInt       n, k, p, d;
206:   PetscInt       dof, off;
207:   IS             is;
208:   const PetscInt* points;
209:   const PetscInt dim = 2;
210:   const PetscInt id  = 1;
211:   PetscErrorCode (**wtf)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);


215:   /* make the data we seek to match */
216:   PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, 1, PETSC_TRUE, NULL, 4, &fe);

218:   DMSetField(dm, 0, NULL, (PetscObject) fe);
219:   DMCreateDS(dm);
220:   DMCreateGlobalVector(dm, &user->data);

222:   /* ugh, this is hideous */
223:   /* y_d = interpolate(Expression("sin(x[0]) + .."), V) */
224:   PetscMalloc(1 * sizeof(void (*)(const PetscReal[], PetscScalar *, void *)), &wtf);
225:   wtf[0] = data_kernel;
226:   DMProjectFunction(dm, 0.0, wtf, NULL, INSERT_VALUES, user->data);
227:   PetscFree(wtf);

229:   /* assemble(inner(u, v)*dx), almost */
230:   DMClone(dm, &dm_mass);
231:   DMCopyDisc(dm, dm_mass);
232:   DMSetNumFields(dm_mass, 1);
233:   DMPlexCopyCoordinates(dm, dm_mass); /* why do I have to do this separately? */
234:   DMGetDS(dm_mass, &prob_mass);
235:   PetscDSSetJacobian(prob_mass, 0, 0, mass_kernel, NULL, NULL, NULL);
236:   PetscDSSetDiscretization(prob_mass, 0, (PetscObject) fe);
237:   DMCreateMatrix(dm_mass, &user->mass);
238:   DMPlexSNESComputeJacobianFEM(dm_mass, user->data, user->mass, user->mass, NULL);
239:   MatSetOption(user->mass, MAT_SYMMETRIC, PETSC_TRUE);
240:   DMDestroy(&dm_mass);

242:   /* inner(grad(u), grad(v))*dx with homogeneous Dirichlet boundary conditions */
243:   DMClone(dm, &dm_laplace);
244:   DMCopyDisc(dm, dm_laplace);
245:   DMSetNumFields(dm_laplace, 1);
246:   DMPlexCopyCoordinates(dm, dm_laplace);
247:   DMGetDS(dm_laplace, &prob_laplace);
248:   PetscDSSetJacobian(prob_laplace, 0, 0, NULL, NULL, NULL, laplace_kernel);
249:   PetscDSSetDiscretization(prob_laplace, 0, (PetscObject) fe);
250:   DMCreateMatrix(dm_laplace, &user->laplace);
251:   DMPlexSNESComputeJacobianFEM(dm_laplace, user->data, user->laplace, user->laplace, NULL);

253:   /* Code from Matt to get the indices associated with the boundary dofs */
254:   PetscDSAddBoundary(prob_laplace, DM_BC_ESSENTIAL, "wall", "marker", 0, 0, NULL, (void (*)(void)) zero, 1, &id, NULL);
255:   DMGetLocalSection(dm_laplace, &section);
256:   DMGetLabel(dm_laplace, "marker", &label);
257:   DMLabelGetStratumSize(label, 1, &n);
258:   DMLabelGetStratumIS(label, 1, &is);
259:   ISGetIndices(is, &points);
260:   user->num_bc_dofs = 0;
261:   for (p = 0; p < n; ++p) {
262:     PetscSectionGetDof(section, points[p], &dof);
263:     user->num_bc_dofs += dof;
264:   }
265:   PetscMalloc1(user->num_bc_dofs, &user->bc_indices);
266:   for (p = 0, k = 0; p < n; ++p) {
267:     PetscSectionGetDof(section, points[p], &dof);
268:     PetscSectionGetOffset(section, points[p], &off);
269:     for (d = 0; d < dof; ++d) user->bc_indices[k++] = off+d;
270:   }
271:   ISRestoreIndices(is, &points);
272:   ISDestroy(&is);
273:   DMDestroy(&dm_laplace);

275:   /* This is how I handle boundary conditions. I can't figure out how to get
276:      plex to play with the way I want to impose the BCs. This loses symmetry,
277:      but not in a disastrous way. If someone can improve it, please do! */
278:   MatZeroRows(user->laplace, user->num_bc_dofs, user->bc_indices, 1.0, NULL, NULL);
279:   PetscCalloc1(user->num_bc_dofs, &user->bc_values);

281:   /* also create the KSP for solving the Laplace system */
282:   KSPCreate(PETSC_COMM_WORLD, &user->ksp_laplace);
283:   KSPSetOperators(user->ksp_laplace, user->laplace, user->laplace);
284:   KSPSetOptionsPrefix(user->ksp_laplace, "laplace_");
285:   KSPSetFromOptions(user->ksp_laplace);

287:   /* A bit of setting up the user context */
288:   user->dm = dm;
289:   VecDuplicate(user->data, &user->state);
290:   VecDuplicate(user->data, &user->adjoint);
291:   VecDuplicate(user->data, &user->tmp1);
292:   VecDuplicate(user->data, &user->tmp2);

294:   PetscFEDestroy(&fe);

296:   return(0);
297: }

299: PetscErrorCode DestroyCtx(AppCtx* user)
300: {


305:   MatDestroy(&user->mass);
306:   MatDestroy(&user->laplace);
307:   KSPDestroy(&user->ksp_laplace);
308:   VecDestroy(&user->data);
309:   VecDestroy(&user->state);
310:   VecDestroy(&user->adjoint);
311:   VecDestroy(&user->tmp1);
312:   VecDestroy(&user->tmp2);
313:   PetscFree(user->bc_indices);
314:   PetscFree(user->bc_values);

316:   return(0);
317: }

319: PetscErrorCode ReducedFunctionGradient(Tao tao, Vec u, PetscReal* func, Vec g, void* userv)
320: {
322:   AppCtx* user = (AppCtx*) userv;
323:   const PetscReal alpha = 1.0e-6; /* regularisation parameter */
324:   PetscReal inner;


328:   MatMult(user->mass, u, user->tmp1);
329:   VecDot(u, user->tmp1, &inner);               /* regularisation contribution to */
330:   *func = alpha * 0.5 * inner;                                      /* the functional                 */

332:   VecSet(g, 0.0);
333:   VecAXPY(g, alpha, user->tmp1);               /* regularisation contribution to the gradient */

335:   /* Now compute the forward state. */
336:   VecSetValues(user->tmp1, user->num_bc_dofs, user->bc_indices, user->bc_values, INSERT_VALUES);
337:   VecAssemblyBegin(user->tmp1);
338:   VecAssemblyEnd(user->tmp1);
339:   KSPSolve(user->ksp_laplace, user->tmp1, user->state); /* forward solve */

341:   /* Now compute the adjoint state also. */
342:   VecCopy(user->state, user->tmp1);
343:   VecAXPY(user->tmp1, -1.0, user->data);
344:   MatMult(user->mass, user->tmp1, user->tmp2);
345:   VecDot(user->tmp1, user->tmp2, &inner);      /* misfit contribution to */
346:   *func += 0.5 * inner;                                             /* the functional         */

348:   VecSetValues(user->tmp2, user->num_bc_dofs, user->bc_indices, user->bc_values, INSERT_VALUES);
349:   VecAssemblyBegin(user->tmp2);
350:   VecAssemblyEnd(user->tmp2);
351:   KSPSolve(user->ksp_laplace, user->tmp2, user->adjoint); /* adjoint solve */

353:   /* And bring it home with the gradient. */
354:   MatMult(user->mass, user->adjoint, user->tmp1);
355:   VecAXPY(g, 1.0, user->tmp1);                 /* adjoint contribution to the gradient */

357:   return(0);
358: }

360: int main(int argc, char **argv)
361: {
362:   DM             dm;
363:   Tao            tao;
364:   Vec            u, lb, ub;
365:   AppCtx         user;

368:   PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
369:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
370:   CreateCtx(dm, &user);

372:   DMCreateGlobalVector(dm, &u);
373:   VecSet(u, 0.0);
374:   VecDuplicate(u, &lb);
375:   VecDuplicate(u, &ub);
376:   VecSet(lb, 0.0); /* satisfied at the minimum anyway */
377:   VecSet(ub, 0.8); /* a nontrivial upper bound */

379:   TaoCreate(PETSC_COMM_WORLD, &tao);
380:   TaoSetInitialVector(tao, u);
381:   TaoSetObjectiveAndGradientRoutine(tao, ReducedFunctionGradient, &user);
382:   TaoSetVariableBounds(tao, lb, ub);
383:   TaoSetType(tao, TAOBLMVM);
384:   TaoSetFromOptions(tao);

386:   if (user.use_riesz) {
387:     TaoLMVMSetH0(tao, user.mass);       /* crucial for mesh independence */
388:     TaoSetGradientNorm(tao, user.mass);
389:   }

391:   TaoSolve(tao);

393:   DMViewFromOptions(dm, NULL, "-dm_view");
394:   VecViewFromOptions(u, NULL, "-sol_view");

396:   TaoDestroy(&tao);
397:   DMDestroy(&dm);
398:   VecDestroy(&u);
399:   VecDestroy(&lb);
400:   VecDestroy(&ub);
401:   DestroyCtx(&user);
402:   PetscFinalize();
403:   return ierr;
404: }

406: /*TEST

408:     build:
409:       requires: !complex !single

411:     test:
412:       requires: hdf5 double datafilespath !define(PETSC_USE_64BIT_INDICES) hypre
413:       args: -laplace_ksp_type cg -laplace_pc_type hypre -laplace_ksp_monitor_true_residual -laplace_ksp_max_it 4 -mat_lmvm_ksp_type cg -mat_lmvm_pc_type gamg -tao_monitor -petscspace_degree 1 -tao_converged_reason -tao_gatol 1.0e-9 -dm_view hdf5:solution.h5 -sol_view hdf5:solution.h5::append -use_riesz 1 -f $DATAFILESPATH/meshes/mesh-1.h5
414:       filter: sed -e "s/-nan/nan/g"

416:     test:
417:       suffix: guess_pod
418:       requires: double triangle
419:       args: -laplace_ksp_type cg -laplace_pc_type gamg  -laplace_pc_gamg_esteig_ksp_type cg -laplace_ksp_converged_reason -mat_lmvm_ksp_type cg -mat_lmvm_pc_type gamg -tao_monitor -petscspace_degree 1 -tao_converged_reason -dm_refine 3 -laplace_ksp_guess_type pod -tao_gatol 1e-6 -mat_lmvm_pc_gamg_esteig_ksp_type cg
420:       filter: sed -e "s/-nan/nan/g"

422: TEST*/