Actual source code: ex36.c

  1: static char help[] = "First example in homogenization book\n\n";

  3: #include <petscsnes.h>
  4: #include <petscdmplex.h>
  5: #include <petscds.h>
  6: #include <petscconvest.h>
  7: #include <petscbag.h>

  9: /*
 10:   To control the refinement use -dm_plex_box_faces <n> or -dm_refine <k>, or both

 12:   To see the exact and computed solutions

 14:     -compare_view draw -draw_size 500,500 -draw_pause -1

 16:   To see the delay in convergence of the discretization use

 18:     -snes_convergence_estimate -convest_num_refine 7 -convest_monitor

 20:   and to see the proper rate use

 22:     -dm_refine 5 -snes_convergence_estimate -convest_num_refine 2 -convest_monitor
 23: */

 25: typedef enum {
 26:   MOD_CONSTANT,
 27:   MOD_OSCILLATORY,
 28:   MOD_TANH,
 29:   NUM_MOD_TYPES
 30: } ModType;
 31: const char *modTypes[NUM_MOD_TYPES + 1] = {"constant", "oscillatory", "tanh", "unknown"};

 33: /* Constants */
 34: enum {
 35:   EPSILON,
 36:   NUM_CONSTANTS
 37: };

 39: typedef struct {
 40:   PetscReal epsilon; /* Wavelength of fine scale oscillation */
 41: } Parameter;

 43: typedef struct {
 44:   PetscBag bag;     /* Holds problem parameters */
 45:   ModType  modType; /* Model type */
 46: } AppCtx;

 48: static PetscErrorCode trig_homogeneous_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
 49: {
 50:   PetscInt d;
 51:   *u = 1.0;
 52:   for (d = 0; d < dim; ++d) *u *= PetscSinReal(2.0 * PETSC_PI * x[d]);
 53:   return PETSC_SUCCESS;
 54: }

 56: static PetscErrorCode oscillatory_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
 57: {
 58:   Parameter      *param = (Parameter *)ctx;
 59:   const PetscReal eps   = param->epsilon;

 61:   u[0] = x[0] - x[0] * x[0] + (eps / (2. * PETSC_PI)) * (0.5 - x[0]) * PetscSinReal(2. * PETSC_PI * x[0] / eps) + PetscSqr(eps / (2. * PETSC_PI)) * (1. - PetscCosReal(2. * PETSC_PI * x[0] / eps));
 62:   return PETSC_SUCCESS;
 63: }

 65: static void f0_trig_homogeneous_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 66: {
 67:   PetscInt d;
 68:   for (d = 0; d < dim; ++d) {
 69:     PetscScalar v = 1.;
 70:     for (PetscInt e = 0; e < dim; e++) {
 71:       if (e == d) {
 72:         v *= -4.0 * PetscSqr(PETSC_PI) * PetscSinReal(2.0 * PETSC_PI * x[d]);
 73:       } else {
 74:         v *= PetscSinReal(2.0 * PETSC_PI * x[d]);
 75:       }
 76:     }
 77:     f0[0] += v;
 78:   }
 79: }

 81: static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 82: {
 83:   PetscInt d;
 84:   for (d = 0; d < dim; ++d) f1[d] = u_x[d];
 85: }

 87: static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
 88: {
 89:   PetscInt d;
 90:   for (d = 0; d < dim; ++d) g3[d * dim + d] = 1.0;
 91: }

 93: static void f0_oscillatory_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 94: {
 95:   f0[0] = -1.;
 96: }

 98: static void f1_oscillatory_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 99: {
100:   const PetscReal eps = PetscRealPart(constants[EPSILON]);

102:   f1[0] = u_x[0] / (2. + PetscCosReal(2. * PETSC_PI * x[0] / eps));
103: }

105: static void g3_oscillatory_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
106: {
107:   const PetscReal eps = PetscRealPart(constants[EPSILON]);

109:   g3[0] = 1. / (2. + PetscCosReal(2. * PETSC_PI * x[0] / eps));
110: }

112: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
113: {
114:   PetscInt mod;

116:   PetscFunctionBeginUser;
117:   options->modType = MOD_CONSTANT;
118:   PetscOptionsBegin(comm, "", "Homogenization Problem Options", "DMPLEX");
119:   mod = options->modType;
120:   PetscCall(PetscOptionsEList("-mod_type", "The model type", "ex36.c", modTypes, NUM_MOD_TYPES, modTypes[options->modType], &mod, NULL));
121:   options->modType = (ModType)mod;
122:   PetscOptionsEnd();
123:   PetscFunctionReturn(PETSC_SUCCESS);
124: }

126: static PetscErrorCode SetupParameters(MPI_Comm comm, AppCtx *user)
127: {
128:   PetscBag   bag;
129:   Parameter *p;

131:   PetscFunctionBeginUser;
132:   PetscCall(PetscBagCreate(comm, sizeof(Parameter), &user->bag));
133:   PetscCall(PetscBagGetData(user->bag, (void **)&p));
134:   PetscCall(PetscBagSetName(user->bag, "par", "Homogenization parameters"));
135:   bag = user->bag;
136:   PetscCall(PetscBagRegisterReal(bag, &p->epsilon, 1.0, "epsilon", "Wavelength of fine scale oscillation"));
137:   PetscFunctionReturn(PETSC_SUCCESS);
138: }

140: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
141: {
142:   PetscFunctionBeginUser;
143:   PetscCall(DMCreate(comm, dm));
144:   PetscCall(DMSetType(*dm, DMPLEX));
145:   PetscCall(DMSetFromOptions(*dm));
146:   PetscCall(DMSetApplicationContext(*dm, user));
147:   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
148:   PetscFunctionReturn(PETSC_SUCCESS);
149: }

151: static PetscErrorCode SetupPrimalProblem(DM dm, AppCtx *user)
152: {
153:   PetscDS             ds;
154:   DMLabel             label;
155:   PetscSimplePointFn *ex;
156:   const PetscInt      id = 1;
157:   void               *ctx;

159:   PetscFunctionBeginUser;
160:   PetscCall(DMGetDS(dm, &ds));
161:   PetscCall(PetscBagGetData(user->bag, (void **)&ctx));
162:   switch (user->modType) {
163:   case MOD_CONSTANT:
164:     PetscCall(PetscDSSetResidual(ds, 0, f0_trig_homogeneous_u, f1_u));
165:     PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu));
166:     PetscCall(DMGetLabel(dm, "marker", &label));
167:     ex = trig_homogeneous_u;
168:     PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void))ex, NULL, ctx, NULL));
169:     break;
170:   case MOD_OSCILLATORY:
171:     PetscCall(PetscDSSetResidual(ds, 0, f0_oscillatory_u, f1_oscillatory_u));
172:     PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_oscillatory_uu));
173:     PetscCall(DMGetLabel(dm, "marker", &label));
174:     ex = oscillatory_u;
175:     PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void))ex, NULL, ctx, NULL));
176:     break;
177:   default:
178:     SETERRQ(PetscObjectComm((PetscObject)ds), PETSC_ERR_ARG_WRONG, "Unsupported model type: %s (%d)", modTypes[PetscMin(user->modType, NUM_MOD_TYPES)], user->modType);
179:   }
180:   PetscCall(PetscDSSetExactSolution(ds, 0, ex, ctx));
181:   /* Setup constants */
182:   {
183:     Parameter  *param;
184:     PetscScalar constants[NUM_CONSTANTS];

186:     PetscCall(PetscBagGetData(user->bag, (void **)&param));

188:     constants[EPSILON] = param->epsilon;
189:     PetscCall(PetscDSSetConstants(ds, NUM_CONSTANTS, constants));
190:   }
191:   PetscFunctionReturn(PETSC_SUCCESS);
192: }

194: static PetscErrorCode SetupDiscretization(DM dm, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *user)
195: {
196:   DM        cdm = dm;
197:   PetscFE   fe;
198:   PetscBool simplex;
199:   PetscInt  dim;
200:   char      prefix[PETSC_MAX_PATH_LEN];

202:   PetscFunctionBeginUser;
203:   PetscCall(DMGetDimension(dm, &dim));
204:   PetscCall(DMPlexIsSimplex(dm, &simplex));
205:   /* Create finite element */
206:   PetscCall(PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name));
207:   PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, name ? prefix : NULL, -1, &fe));
208:   PetscCall(PetscObjectSetName((PetscObject)fe, name));
209:   /* Set discretization and boundary conditions for each mesh */
210:   PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe));
211:   PetscCall(DMCreateDS(dm));
212:   PetscCall((*setup)(dm, user));
213:   while (cdm) {
214:     PetscCall(DMCopyDisc(dm, cdm));
215:     PetscCall(DMGetCoarseDM(cdm, &cdm));
216:   }
217:   PetscCall(PetscFEDestroy(&fe));
218:   PetscFunctionReturn(PETSC_SUCCESS);
219: }

221: static PetscErrorCode CompareView(Vec u)
222: {
223:   DM                dm;
224:   Vec               v[2], lv[2], exact;
225:   PetscOptions      options;
226:   PetscViewer       viewer;
227:   PetscViewerFormat format;
228:   PetscBool         flg;
229:   PetscInt          i;
230:   const char       *name, *prefix;

232:   PetscFunctionBeginUser;
233:   PetscCall(VecGetDM(u, &dm));
234:   PetscCall(PetscObjectGetOptions((PetscObject)dm, &options));
235:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)dm, &prefix));
236:   PetscCall(PetscOptionsGetViewer(PetscObjectComm((PetscObject)dm), options, prefix, "-compare_view", &viewer, &format, &flg));
237:   if (flg) {
238:     PetscCall(DMGetGlobalVector(dm, &exact));
239:     PetscCall(DMComputeExactSolution(dm, 0.0, exact, NULL));
240:     v[0] = u;
241:     v[1] = exact;
242:     for (i = 0; i < 2; ++i) {
243:       PetscCall(DMGetLocalVector(dm, &lv[i]));
244:       PetscCall(PetscObjectGetName((PetscObject)v[i], &name));
245:       PetscCall(PetscObjectSetName((PetscObject)lv[i], name));
246:       PetscCall(DMGlobalToLocalBegin(dm, v[i], INSERT_VALUES, lv[i]));
247:       PetscCall(DMGlobalToLocalEnd(dm, v[i], INSERT_VALUES, lv[i]));
248:       PetscCall(DMPlexInsertBoundaryValues(dm, PETSC_TRUE, lv[i], 0., NULL, NULL, NULL));
249:     }
250:     PetscCall(DMPlexVecView1D(dm, 2, lv, viewer));
251:     for (i = 0; i < 2; ++i) PetscCall(DMRestoreLocalVector(dm, &lv[i]));
252:     PetscCall(DMRestoreGlobalVector(dm, &exact));
253:     PetscCall(PetscOptionsRestoreViewer(&viewer));
254:   }
255:   PetscFunctionReturn(PETSC_SUCCESS);
256: }

258: typedef struct {
259:   Mat Mcoarse;   /* Mass matrix on the coarse space */
260:   Mat Mfine;     /* Mass matrix on the fine space */
261:   Mat Ifine;     /* Interpolator from coarse to fine */
262:   Vec Iscale;    /* Scaling vector for restriction */
263:   KSP kspCoarse; /* Solver for the coarse mass matrix */
264:   Vec tmpfine;   /* Temporary vector in the fine space */
265:   Vec tmpcoarse; /* Temporary vector in the coarse space */
266: } ProjStruct;

268: static PetscErrorCode DestroyCoarseProjection(Mat Pi)
269: {
270:   ProjStruct *ctx;

272:   PetscFunctionBegin;
273:   PetscCall(MatShellGetContext(Pi, (void **)&ctx));
274:   PetscCall(MatDestroy(&ctx->Mcoarse));
275:   PetscCall(MatDestroy(&ctx->Mfine));
276:   PetscCall(MatDestroy(&ctx->Ifine));
277:   PetscCall(VecDestroy(&ctx->Iscale));
278:   PetscCall(KSPDestroy(&ctx->kspCoarse));
279:   PetscCall(VecDestroy(&ctx->tmpcoarse));
280:   PetscCall(VecDestroy(&ctx->tmpfine));
281:   PetscCall(PetscFree(ctx));
282:   PetscCall(MatShellSetContext(Pi, NULL));
283:   PetscFunctionReturn(PETSC_SUCCESS);
284: }

286: static PetscErrorCode CoarseProjection(Mat Pi, Vec x, Vec y)
287: {
288:   ProjStruct *ctx;

290:   PetscFunctionBegin;
291:   PetscCall(MatShellGetContext(Pi, (void **)&ctx));
292:   PetscCall(MatMult(ctx->Mfine, x, ctx->tmpfine));
293:   PetscCall(PetscObjectSetName((PetscObject)ctx->tmpfine, "Fine DG RHS"));
294:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)ctx->tmpfine, "fine_dg_"));
295:   PetscCall(VecViewFromOptions(ctx->tmpfine, NULL, "-rhs_view"));
296:   PetscCall(MatMultTranspose(ctx->Ifine, ctx->tmpfine, ctx->tmpcoarse));
297:   PetscCall(PetscObjectSetName((PetscObject)ctx->tmpcoarse, "Coarse DG RHS"));
298:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)ctx->tmpcoarse, "coarse_dg_"));
299:   PetscCall(VecViewFromOptions(ctx->tmpcoarse, NULL, "-rhs_view"));
300:   PetscCall(VecPointwiseMult(ctx->tmpcoarse, ctx->Iscale, ctx->tmpcoarse));
301:   PetscCall(VecViewFromOptions(ctx->tmpcoarse, NULL, "-rhs_view"));
302:   PetscCall(KSPSolve(ctx->kspCoarse, ctx->tmpcoarse, y));
303:   PetscFunctionReturn(PETSC_SUCCESS);
304: }

306: static PetscErrorCode CreateCoarseProjection(DM dmc, DM dmf, Mat *Pi)
307: {
308:   ProjStruct *ctx;
309:   PetscInt    m, n, M, N;

311:   PetscFunctionBegin;
312:   PetscCall(PetscMalloc1(1, &ctx));
313:   PetscCall(DMCreateGlobalVector(dmc, &ctx->tmpcoarse));
314:   PetscCall(DMCreateGlobalVector(dmf, &ctx->tmpfine));
315:   PetscCall(VecGetLocalSize(ctx->tmpcoarse, &m));
316:   PetscCall(VecGetSize(ctx->tmpcoarse, &M));
317:   PetscCall(VecGetLocalSize(ctx->tmpfine, &n));
318:   PetscCall(VecGetSize(ctx->tmpfine, &N));
319:   PetscCall(DMCreateMassMatrix(dmc, dmc, &ctx->Mcoarse));
320:   PetscCall(DMCreateMassMatrix(dmf, dmf, &ctx->Mfine));
321:   PetscCall(DMCreateInterpolation(dmc, dmf, &ctx->Ifine, &ctx->Iscale));
322:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)dmc), &ctx->kspCoarse));
323:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)ctx->kspCoarse, "coarse_"));
324:   PetscCall(KSPSetOperators(ctx->kspCoarse, ctx->Mcoarse, ctx->Mcoarse));
325:   PetscCall(KSPSetFromOptions(ctx->kspCoarse));
326:   PetscCall(MatCreateShell(PetscObjectComm((PetscObject)dmc), m, n, M, N, ctx, Pi));
327:   PetscCall(MatShellSetOperation(*Pi, MATOP_DESTROY, (void (*)(void))DestroyCoarseProjection));
328:   PetscCall(MatShellSetOperation(*Pi, MATOP_MULT, (void (*)(void))CoarseProjection));
329:   PetscFunctionReturn(PETSC_SUCCESS);
330: }

332: typedef struct {
333:   Mat Ifdg; /* Embed the fine space into the DG version */
334:   Mat Pi;   /* The L_2 stable projection to the DG coarse space */
335:   Vec tmpc; /* A temporary vector in the DG coarse space */
336:   Vec tmpf; /* A temporary vector in the DG fine space */
337: } QuasiInterp;

339: static PetscErrorCode DestroyQuasiInterpolator(Mat P)
340: {
341:   QuasiInterp *ctx;

343:   PetscFunctionBegin;
344:   PetscCall(MatShellGetContext(P, (void **)&ctx));
345:   PetscCall(MatDestroy(&ctx->Ifdg));
346:   PetscCall(MatDestroy(&ctx->Pi));
347:   PetscCall(VecDestroy(&ctx->tmpc));
348:   PetscCall(VecDestroy(&ctx->tmpf));
349:   PetscCall(PetscFree(ctx));
350:   PetscCall(MatShellSetContext(P, NULL));
351:   PetscFunctionReturn(PETSC_SUCCESS);
352: }

354: static PetscErrorCode QuasiInterpolate(Mat P, Vec x, Vec y)
355: {
356:   QuasiInterp *ctx;
357:   DM           dmcdg, dmc;
358:   Vec          ly;

360:   PetscFunctionBegin;
361:   PetscCall(MatShellGetContext(P, (void **)&ctx));
362:   PetscCall(MatMult(ctx->Ifdg, x, ctx->tmpf));

364:   PetscCall(PetscObjectSetName((PetscObject)ctx->tmpf, "Fine DG Potential"));
365:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)ctx->tmpf, "fine_dg_"));
366:   PetscCall(VecViewFromOptions(ctx->tmpf, NULL, "-vec_view"));
367:   PetscCall(MatMult(ctx->Pi, x, ctx->tmpc));

369:   PetscCall(PetscObjectSetName((PetscObject)ctx->tmpc, "Coarse DG Potential"));
370:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)ctx->tmpc, "coarse_dg_"));
371:   PetscCall(VecViewFromOptions(ctx->tmpc, NULL, "-vec_view"));
372:   PetscCall(VecGetDM(ctx->tmpc, &dmcdg));

374:   PetscCall(VecGetDM(y, &dmc));
375:   PetscCall(DMGetLocalVector(dmc, &ly));
376:   PetscCall(DMPlexComputeClementInterpolant(dmcdg, ctx->tmpc, ly));
377:   PetscCall(DMLocalToGlobalBegin(dmc, ly, INSERT_VALUES, y));
378:   PetscCall(DMLocalToGlobalEnd(dmc, ly, INSERT_VALUES, y));
379:   PetscCall(DMRestoreLocalVector(dmc, &ly));
380:   PetscFunctionReturn(PETSC_SUCCESS);
381: }

383: static PetscErrorCode CreateQuasiInterpolator(DM dmc, DM dmf, Mat *P)
384: {
385:   QuasiInterp   *ctx;
386:   DM             dmcdg, dmfdg;
387:   PetscFE        fe;
388:   Vec            x, y;
389:   DMPolytopeType ct;
390:   PetscInt       dim, cStart, m, n, M, N;

392:   PetscFunctionBegin;
393:   PetscCall(PetscCalloc1(1, &ctx));
394:   PetscCall(DMGetGlobalVector(dmc, &x));
395:   PetscCall(DMGetGlobalVector(dmf, &y));
396:   PetscCall(VecGetLocalSize(x, &m));
397:   PetscCall(VecGetSize(x, &M));
398:   PetscCall(VecGetLocalSize(y, &n));
399:   PetscCall(VecGetSize(y, &N));
400:   PetscCall(DMRestoreGlobalVector(dmc, &x));
401:   PetscCall(DMRestoreGlobalVector(dmf, &y));

403:   PetscCall(DMClone(dmf, &dmfdg));
404:   PetscCall(DMGetDimension(dmfdg, &dim));
405:   PetscCall(DMPlexGetHeightStratum(dmfdg, 0, &cStart, NULL));
406:   PetscCall(DMPlexGetCellType(dmfdg, cStart, &ct));
407:   PetscCall(PetscFECreateByCell(PETSC_COMM_SELF, dim, 1, ct, "fine_dg_", PETSC_DETERMINE, &fe));
408:   PetscCall(DMSetField(dmfdg, 0, NULL, (PetscObject)fe));
409:   PetscCall(PetscFEDestroy(&fe));
410:   PetscCall(DMCreateDS(dmfdg));
411:   PetscCall(DMCreateInterpolation(dmf, dmfdg, &ctx->Ifdg, NULL));
412:   PetscCall(DMCreateGlobalVector(dmfdg, &ctx->tmpf));
413:   PetscCall(DMDestroy(&dmfdg));

415:   PetscCall(DMClone(dmc, &dmcdg));
416:   PetscCall(DMGetDimension(dmcdg, &dim));
417:   PetscCall(DMPlexGetHeightStratum(dmcdg, 0, &cStart, NULL));
418:   PetscCall(DMPlexGetCellType(dmcdg, cStart, &ct));
419:   PetscCall(PetscFECreateByCell(PETSC_COMM_SELF, dim, 1, ct, "coarse_dg_", PETSC_DETERMINE, &fe));
420:   PetscCall(DMSetField(dmcdg, 0, NULL, (PetscObject)fe));
421:   PetscCall(PetscFEDestroy(&fe));
422:   PetscCall(DMCreateDS(dmcdg));

424:   PetscCall(CreateCoarseProjection(dmcdg, dmf, &ctx->Pi));
425:   PetscCall(DMCreateGlobalVector(dmcdg, &ctx->tmpc));
426:   PetscCall(DMDestroy(&dmcdg));

428:   PetscCall(MatCreateShell(PetscObjectComm((PetscObject)dmc), m, n, M, N, ctx, P));
429:   PetscCall(MatShellSetOperation(*P, MATOP_DESTROY, (void (*)(void))DestroyQuasiInterpolator));
430:   PetscCall(MatShellSetOperation(*P, MATOP_MULT, (void (*)(void))QuasiInterpolate));
431:   PetscFunctionReturn(PETSC_SUCCESS);
432: }

434: static PetscErrorCode CoarseTest(DM dm, Vec u, AppCtx *user)
435: {
436:   DM  dmc;
437:   Mat P; /* The quasi-interpolator to the coarse space */
438:   Vec uc;

440:   PetscFunctionBegin;
441:   if (user->modType == MOD_CONSTANT) PetscFunctionReturn(PETSC_SUCCESS);
442:   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), &dmc));
443:   PetscCall(DMSetType(dmc, DMPLEX));
444:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dmc, "coarse_"));
445:   PetscCall(DMSetApplicationContext(dmc, user));
446:   PetscCall(DMSetFromOptions(dmc));
447:   PetscCall(DMViewFromOptions(dmc, NULL, "-dm_view"));

449:   PetscCall(SetupDiscretization(dmc, "potential", SetupPrimalProblem, user));
450:   PetscCall(DMCreateGlobalVector(dmc, &uc));
451:   PetscCall(PetscObjectSetName((PetscObject)uc, "potential"));
452:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)uc, "coarse_"));

454:   PetscCall(CreateQuasiInterpolator(dmc, dm, &P));
455: #if 1
456:   PetscCall(MatMult(P, u, uc));
457: #else
458:   {
459:     Mat In;
460:     Vec sc;

462:     PetscCall(DMCreateInterpolation(dmc, dm, &In, &sc));
463:     PetscCall(MatMultTranspose(In, u, uc));
464:     PetscCall(VecPointwiseMult(uc, sc, uc));
465:     PetscCall(MatDestroy(&In));
466:     PetscCall(VecDestroy(&sc));
467:   }
468: #endif
469:   PetscCall(CompareView(uc));

471:   PetscCall(MatDestroy(&P));
472:   PetscCall(VecDestroy(&uc));
473:   PetscCall(DMDestroy(&dmc));
474:   PetscFunctionReturn(PETSC_SUCCESS);
475: }

477: int main(int argc, char **argv)
478: {
479:   DM     dm;   /* Problem specification */
480:   SNES   snes; /* Nonlinear solver */
481:   Vec    u;    /* Solutions */
482:   AppCtx user; /* User-defined work context */

484:   PetscFunctionBeginUser;
485:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
486:   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
487:   PetscCall(SetupParameters(PETSC_COMM_WORLD, &user));
488:   /* Primal system */
489:   PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
490:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
491:   PetscCall(SNESSetDM(snes, dm));
492:   PetscCall(SetupDiscretization(dm, "potential", SetupPrimalProblem, &user));
493:   PetscCall(DMCreateGlobalVector(dm, &u));
494:   PetscCall(VecSet(u, 0.0));
495:   PetscCall(PetscObjectSetName((PetscObject)u, "potential"));
496:   PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &user));
497:   PetscCall(SNESSetFromOptions(snes));
498:   PetscCall(DMSNESCheckFromOptions(snes, u));
499:   PetscCall(SNESSolve(snes, NULL, u));
500:   PetscCall(SNESGetSolution(snes, &u));
501:   PetscCall(VecViewFromOptions(u, NULL, "-potential_view"));
502:   PetscCall(CompareView(u));
503:   /* Looking at a coarse problem */
504:   PetscCall(CoarseTest(dm, u, &user));
505:   /* Cleanup */
506:   PetscCall(VecDestroy(&u));
507:   PetscCall(SNESDestroy(&snes));
508:   PetscCall(DMDestroy(&dm));
509:   PetscCall(PetscBagDestroy(&user.bag));
510:   PetscCall(PetscFinalize());
511:   return 0;
512: }

514: /*TEST

516:   test:
517:     suffix: 1d_p1_constant
518:     args: -dm_plex_dim 1 -dm_plex_box_faces 4 -potential_petscspace_degree 1 -dmsnes_check

520:   test:
521:     suffix: 1d_p1_constant_conv
522:     args: -dm_plex_dim 1 -dm_plex_box_faces 4 -potential_petscspace_degree 1 \
523:           -snes_convergence_estimate -convest_num_refine 2

525:   test:
526:     suffix: 1d_p1_oscillatory
527:     args: -mod_type oscillatory -epsilon 0.03125 \
528:           -dm_plex_dim 1 -dm_plex_box_faces 4 -potential_petscspace_degree 1 -dm_refine 2 -dmsnes_check \
529:           -coarse_dm_plex_dim 1 -coarse_dm_plex_box_faces 4 -coarse_dm_plex_hash_location \
530:           -fine_dg_petscspace_degree 1 -fine_dg_petscdualspace_lagrange_continuity 0 \
531:           -coarse_dg_petscspace_degree 1 -coarse_dg_petscdualspace_lagrange_continuity 0

533: TEST*/