Actual source code: convest.c

  1: #include "petscsys.h"
  2: #include <petscconvest.h>
  3: #include <petscdmplex.h>
  4: #include <petscds.h>

  6: #include <petsc/private/petscconvestimpl.h>

  8: static PetscErrorCode zero_private(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, PetscCtx ctx)
  9: {
 10:   PetscInt c;
 11:   for (c = 0; c < Nc; ++c) u[c] = 0.0;
 12:   return PETSC_SUCCESS;
 13: }

 15: /*@
 16:   PetscConvEstDestroy - Destroys a PETSc convergence estimator `PetscConvEst` object

 18:   Collective

 20:   Input Parameter:
 21: . ce - The `PetscConvEst` object

 23:   Level: beginner

 25: .seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
 26: @*/
 27: PetscErrorCode PetscConvEstDestroy(PetscConvEst *ce)
 28: {
 29:   PetscFunctionBegin;
 30:   if (!*ce) PetscFunctionReturn(PETSC_SUCCESS);
 32:   if (--((PetscObject)*ce)->refct > 0) {
 33:     *ce = NULL;
 34:     PetscFunctionReturn(PETSC_SUCCESS);
 35:   }
 36:   PetscCall(PetscFree3((*ce)->initGuess, (*ce)->exactSol, (*ce)->ctxs));
 37:   PetscCall(PetscFree2((*ce)->dofs, (*ce)->errors));
 38:   PetscCall(PetscHeaderDestroy(ce));
 39:   PetscFunctionReturn(PETSC_SUCCESS);
 40: }

 42: /*@
 43:   PetscConvEstSetFromOptions - Sets a convergence estimator `PetscConvEst` object based on values in the options database

 45:   Collective

 47:   Input Parameter:
 48: . ce - The `PetscConvEst` object

 50:   Level: beginner

 52: .seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
 53: @*/
 54: PetscErrorCode PetscConvEstSetFromOptions(PetscConvEst ce)
 55: {
 56:   PetscFunctionBegin;
 57:   PetscOptionsBegin(PetscObjectComm((PetscObject)ce), "", "Convergence Estimator Options", "PetscConvEst");
 58:   PetscCall(PetscOptionsInt("-convest_num_refine", "The number of refinements for the convergence check", "PetscConvEst", ce->Nr, &ce->Nr, NULL));
 59:   PetscCall(PetscOptionsReal("-convest_refine_factor", "The increase in resolution in each dimension", "PetscConvEst", ce->r, &ce->r, NULL));
 60:   PetscCall(PetscOptionsBool("-convest_monitor", "Monitor the error for each convergence check", "PetscConvEst", ce->monitor, &ce->monitor, NULL));
 61:   PetscCall(PetscOptionsBool("-convest_no_refine", "Debugging flag to run on the same mesh each time", "PetscConvEst", ce->noRefine, &ce->noRefine, NULL));
 62:   PetscOptionsEnd();
 63:   PetscFunctionReturn(PETSC_SUCCESS);
 64: }

 66: /*@
 67:   PetscConvEstView - Views a `PetscConvEst` object

 69:   Collective

 71:   Input Parameters:
 72: + ce     - The `PetscConvEst` object
 73: - viewer - The `PetscViewer`

 75:   Level: beginner

 77: .seealso: `PetscConvEst`, `PetscViewer`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
 78: @*/
 79: PetscErrorCode PetscConvEstView(PetscConvEst ce, PetscViewer viewer)
 80: {
 81:   PetscFunctionBegin;
 82:   PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)ce, viewer));
 83:   PetscCall(PetscViewerASCIIPrintf(viewer, "ConvEst with %" PetscInt_FMT " levels\n", ce->Nr + 1));
 84:   PetscFunctionReturn(PETSC_SUCCESS);
 85: }

 87: /*@
 88:   PetscConvEstGetSolver - Gets the solver used to produce discrete solutions

 90:   Not Collective

 92:   Input Parameter:
 93: . ce - The `PetscConvEst` object

 95:   Output Parameter:
 96: . solver - The solver

 98:   Level: intermediate

100: .seealso: `PetscConvEst`, `PetscConvEstSetSolver()`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
101: @*/
102: PetscErrorCode PetscConvEstGetSolver(PetscConvEst ce, PetscObject *solver)
103: {
104:   PetscFunctionBegin;
106:   PetscAssertPointer(solver, 2);
107:   *solver = ce->solver;
108:   PetscFunctionReturn(PETSC_SUCCESS);
109: }

111: /*@
112:   PetscConvEstSetSolver - Sets the solver used to produce discrete solutions

114:   Not Collective

116:   Input Parameters:
117: + ce     - The `PetscConvEst` object
118: - solver - The solver, must be a `KSP`, `SNES`, or `TS` object with an attached `DM`/`DS`, that can compute an exact solution

120:   Level: intermediate

122: .seealso: `PetscConvEst`, `PetscConvEstGetSNES()`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
123: @*/
124: PetscErrorCode PetscConvEstSetSolver(PetscConvEst ce, PetscObject solver)
125: {
126:   PetscFunctionBegin;
129:   ce->solver = solver;
130:   PetscUseTypeMethod(ce, setsolver, solver);
131:   PetscFunctionReturn(PETSC_SUCCESS);
132: }

134: /*@
135:   PetscConvEstSetUp - After the solver is specified, create data structures needed for estimating convergence

137:   Collective

139:   Input Parameter:
140: . ce - The `PetscConvEst` object

142:   Level: beginner

144: .seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`
145: @*/
146: PetscErrorCode PetscConvEstSetUp(PetscConvEst ce)
147: {
148:   PetscInt Nf, f, Nds, s;

150:   PetscFunctionBegin;
151:   PetscCall(DMGetNumFields(ce->idm, &Nf));
152:   ce->Nf = PetscMax(Nf, 1);
153:   PetscCall(PetscMalloc2((ce->Nr + 1) * ce->Nf, &ce->dofs, (ce->Nr + 1) * ce->Nf, &ce->errors));
154:   PetscCall(PetscCalloc3(ce->Nf, &ce->initGuess, ce->Nf, &ce->exactSol, ce->Nf, &ce->ctxs));
155:   for (f = 0; f < Nf; ++f) ce->initGuess[f] = zero_private;
156:   PetscCall(DMGetNumDS(ce->idm, &Nds));
157:   for (s = 0; s < Nds; ++s) {
158:     PetscDS         ds;
159:     DMLabel         label;
160:     IS              fieldIS;
161:     const PetscInt *fields;
162:     PetscInt        dsNf;

164:     PetscCall(DMGetRegionNumDS(ce->idm, s, &label, &fieldIS, &ds, NULL));
165:     PetscCall(PetscDSGetNumFields(ds, &dsNf));
166:     if (fieldIS) PetscCall(ISGetIndices(fieldIS, &fields));
167:     for (f = 0; f < dsNf; ++f) {
168:       const PetscInt field = fields[f];
169:       PetscCall(PetscDSGetExactSolution(ds, field, &ce->exactSol[field], &ce->ctxs[field]));
170:     }
171:     if (fieldIS) PetscCall(ISRestoreIndices(fieldIS, &fields));
172:   }
173:   for (f = 0; f < Nf; ++f) PetscCheck(ce->exactSol[f], PetscObjectComm((PetscObject)ce), PETSC_ERR_ARG_WRONG, "DS must contain exact solution functions in order to estimate convergence, missing for field %" PetscInt_FMT, f);
174:   PetscFunctionReturn(PETSC_SUCCESS);
175: }

177: /*@
178:   PetscConvEstComputeInitialGuess - Fill `u` with the initial guess to use on refinement level `r` of a convergence-estimation run

180:   Collective

182:   Input Parameters:
183: + ce - the `PetscConvEst` object
184: . r  - the refinement level
185: - dm - the `DM` on which `u` is defined (may be `NULL`)

187:   Output Parameter:
188: . u - the initial-guess vector

190:   Level: developer

192: .seealso: `PetscConvEst`, `PetscConvEstComputeError()`, `PetscConvEstGetConvRate()`
193: @*/
194: PetscErrorCode PetscConvEstComputeInitialGuess(PetscConvEst ce, PetscInt r, DM dm, Vec u)
195: {
196:   PetscFunctionBegin;
200:   PetscUseTypeMethod(ce, initguess, r, dm, u);
201:   PetscFunctionReturn(PETSC_SUCCESS);
202: }

204: /*@
205:   PetscConvEstComputeError - Compute per-field discretization errors of `u` on refinement level `r`

207:   Collective

209:   Input Parameters:
210: + ce - the `PetscConvEst` object
211: . r  - the refinement level
212: . dm - the `DM` on which `u` is defined (may be `NULL`)
213: - u  - the computed solution

215:   Output Parameter:
216: . errors - array of length `Nf` (number of fields in the DS) filled with the error in each field

218:   Level: developer

220: .seealso: `PetscConvEst`, `PetscConvEstComputeInitialGuess()`, `PetscConvEstGetConvRate()`
221: @*/
222: PetscErrorCode PetscConvEstComputeError(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
223: {
224:   PetscFunctionBegin;
228:   PetscAssertPointer(errors, 5);
229:   PetscUseTypeMethod(ce, computeerror, r, dm, u, errors);
230:   PetscFunctionReturn(PETSC_SUCCESS);
231: }

233: /*@
234:   PetscConvEstMonitorDefault - Monitors the convergence estimation loop

236:   Collective

238:   Input Parameters:
239: + ce - The `PetscConvEst` object
240: - r  - The refinement level

242:   Options Database Key:
243: . -convest_monitor - Activate the monitor

245:   Level: intermediate

247: .seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`, `SNESSolve()`, `TSSolve()`
248: @*/
249: PetscErrorCode PetscConvEstMonitorDefault(PetscConvEst ce, PetscInt r)
250: {
251:   MPI_Comm comm;
252:   PetscInt f;

254:   PetscFunctionBegin;
255:   if (ce->monitor) {
256:     PetscInt  *dofs   = &ce->dofs[r * ce->Nf];
257:     PetscReal *errors = &ce->errors[r * ce->Nf];

259:     PetscCall(PetscObjectGetComm((PetscObject)ce, &comm));
260:     PetscCall(PetscPrintf(comm, "N: "));
261:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "["));
262:     for (f = 0; f < ce->Nf; ++f) {
263:       if (f > 0) PetscCall(PetscPrintf(comm, ", "));
264:       PetscCall(PetscPrintf(comm, "%7" PetscInt_FMT, dofs[f]));
265:     }
266:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "]"));
267:     PetscCall(PetscPrintf(comm, "  "));
268:     PetscCall(PetscPrintf(comm, "L_2 Error: "));
269:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "["));
270:     for (f = 0; f < ce->Nf; ++f) {
271:       if (f > 0) PetscCall(PetscPrintf(comm, ", "));
272:       if (errors[f] < 1.0e-11) PetscCall(PetscPrintf(comm, "< 1e-11"));
273:       else PetscCall(PetscPrintf(comm, "%g", (double)errors[f]));
274:     }
275:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "]"));
276:     PetscCall(PetscPrintf(comm, "\n"));
277:   }
278:   PetscFunctionReturn(PETSC_SUCCESS);
279: }

281: static PetscErrorCode PetscConvEstSetSNES_Private(PetscConvEst ce, PetscObject solver)
282: {
283:   PetscClassId id;

285:   PetscFunctionBegin;
286:   PetscCall(PetscObjectGetClassId(ce->solver, &id));
287:   PetscCheck(id == SNES_CLASSID, PetscObjectComm((PetscObject)ce), PETSC_ERR_ARG_WRONG, "Solver was not a SNES");
288:   PetscCall(SNESGetDM((SNES)ce->solver, &ce->idm));
289:   PetscFunctionReturn(PETSC_SUCCESS);
290: }

292: static PetscErrorCode PetscConvEstInitGuessSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u)
293: {
294:   PetscFunctionBegin;
295:   PetscCall(DMProjectFunction(dm, 0.0, ce->initGuess, ce->ctxs, INSERT_VALUES, u));
296:   PetscFunctionReturn(PETSC_SUCCESS);
297: }

299: static PetscErrorCode PetscConvEstComputeErrorSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
300: {
301:   const char *prefix;
302:   PetscBool   errorView = PETSC_FALSE;

304:   PetscFunctionBegin;
305:   PetscCall(DMComputeL2FieldDiff(dm, 0.0, ce->exactSol, ce->ctxs, u, errors));
306:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ce, &prefix));
307:   PetscCall(PetscOptionsHasName(NULL, prefix, "-convest_error_view", &errorView));
308:   if (errorView) {
309:     DM                   dmError;
310:     PetscFE              feError, fe;
311:     PetscQuadrature      quad;
312:     Vec                  e;
313:     PetscDS              ds;
314:     PetscSimplePointFn **funcs;
315:     void               **ctxs;
316:     PetscInt             dim, Nf;

318:     PetscCall(DMGetDimension(dm, &dim));
319:     PetscCall(DMGetDS(dm, &ds));
320:     PetscCall(PetscDSGetNumFields(ds, &Nf));
321:     PetscCall(PetscMalloc2(Nf, &funcs, Nf, &ctxs));
322:     for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscDSGetExactSolution(ds, f, &funcs[f], &ctxs[f]));
323:     PetscCall(DMClone(dm, &dmError));
324:     PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, 0, PETSC_DETERMINE, &feError));
325:     PetscCall(DMGetField(dm, 0, NULL, (PetscObject *)&fe));
326:     PetscCall(PetscFEGetQuadrature(fe, &quad));
327:     PetscCall(PetscFESetQuadrature(feError, quad));
328:     PetscCall(DMSetField(dmError, 0, NULL, (PetscObject)feError));
329:     PetscCall(PetscFEDestroy(&feError));
330:     PetscCall(DMCreateDS(dmError));
331:     PetscCall(DMGetGlobalVector(dmError, &e));
332:     PetscCall(PetscObjectSetName((PetscObject)e, "Error"));
333:     PetscCall(DMPlexComputeL2DiffVec(dm, 0., funcs, ctxs, u, e));
334:     PetscCall(VecViewFromOptions(e, NULL, "-convest_error_view"));
335:     PetscCall(DMRestoreGlobalVector(dmError, &e));
336:     PetscCall(DMDestroy(&dmError));
337:     PetscCall(PetscFree2(funcs, ctxs));
338:   }
339:   PetscFunctionReturn(PETSC_SUCCESS);
340: }

342: static PetscErrorCode PetscConvEstSetJacobianNullSpace_Private(PetscConvEst ce, SNES snes)
343: {
344:   DM       dm;
345:   PetscInt f;

347:   PetscFunctionBegin;
348:   PetscCall(SNESGetDM(snes, &dm));
349:   for (f = 0; f < ce->Nf; ++f) {
350:     PetscErrorCode (*nspconstr)(DM, PetscInt, PetscInt, MatNullSpace *);

352:     PetscCall(DMGetNullSpaceConstructor(dm, f, &nspconstr));
353:     if (nspconstr) {
354:       MatNullSpace nullsp;
355:       Mat          J;

357:       PetscCall((*nspconstr)(dm, f, f, &nullsp));
358:       PetscCall(SNESSetUp(snes));
359:       PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL));
360:       PetscCall(MatSetNullSpace(J, nullsp));
361:       PetscCall(MatNullSpaceDestroy(&nullsp));
362:       break;
363:     }
364:   }
365:   PetscFunctionReturn(PETSC_SUCCESS);
366: }

368: static PetscErrorCode PetscConvEstGetConvRateSNES_Private(PetscConvEst ce, PetscReal alpha[])
369: {
370:   SNES        snes = (SNES)ce->solver;
371:   DM         *dm;
372:   PetscObject disc;
373:   PetscReal  *x, *y, slope, intercept;
374:   PetscInt    Nr = ce->Nr, r, f, dim, oldlevel, oldnlev;
375:   void       *ctx;

377:   PetscFunctionBegin;
378:   PetscCheck(ce->r == 2.0, PetscObjectComm((PetscObject)ce), PETSC_ERR_SUP, "Only refinement factor 2 is currently supported (not %g)", (double)ce->r);
379:   PetscCall(DMGetDimension(ce->idm, &dim));
380:   PetscCall(DMGetApplicationContext(ce->idm, &ctx));
381:   PetscCall(DMPlexSetRefinementUniform(ce->idm, PETSC_TRUE));
382:   PetscCall(DMGetRefineLevel(ce->idm, &oldlevel));
383:   PetscCall(PetscMalloc1(Nr + 1, &dm));
384:   /* Loop over meshes */
385:   dm[0] = ce->idm;
386:   for (r = 0; r <= Nr; ++r) {
387:     Vec           u;
388:     PetscLogStage stage;
389:     char          stageName[PETSC_MAX_PATH_LEN];
390:     const char   *dmname, *uname;

392:     PetscCall(PetscSNPrintf(stageName, PETSC_MAX_PATH_LEN - 1, "ConvEst Refinement Level %" PetscInt_FMT, r));
393:     PetscCall(PetscLogStageGetId(stageName, &stage));
394:     if (stage < 0) PetscCall(PetscLogStageRegister(stageName, &stage));
395:     PetscCall(PetscLogStagePush(stage));
396:     if (r > 0) {
397:       if (!ce->noRefine) {
398:         PetscCall(DMRefine(dm[r - 1], MPI_COMM_NULL, &dm[r]));
399:         PetscCall(DMSetCoarseDM(dm[r], dm[r - 1]));
400:       } else {
401:         DM cdm, rcdm;

403:         PetscCall(DMClone(dm[r - 1], &dm[r]));
404:         PetscCall(DMCopyDisc(dm[r - 1], dm[r]));
405:         PetscCall(DMGetCoordinateDM(dm[r - 1], &cdm));
406:         PetscCall(DMGetCoordinateDM(dm[r], &rcdm));
407:         PetscCall(DMCopyDisc(cdm, rcdm));
408:       }
409:       PetscCall(DMCopyTransform(ce->idm, dm[r]));
410:       PetscCall(PetscObjectGetName((PetscObject)dm[r - 1], &dmname));
411:       PetscCall(PetscObjectSetName((PetscObject)dm[r], dmname));
412:       for (f = 0; f < ce->Nf; ++f) {
413:         PetscErrorCode (*nspconstr)(DM, PetscInt, PetscInt, MatNullSpace *);

415:         PetscCall(DMGetNullSpaceConstructor(dm[r - 1], f, &nspconstr));
416:         PetscCall(DMSetNullSpaceConstructor(dm[r], f, nspconstr));
417:       }
418:     }
419:     PetscCall(DMViewFromOptions(dm[r], NULL, "-conv_dm_view"));
420:     /* Create solution */
421:     PetscCall(DMCreateGlobalVector(dm[r], &u));
422:     PetscCall(DMGetField(dm[r], 0, NULL, &disc));
423:     PetscCall(PetscObjectGetName(disc, &uname));
424:     PetscCall(PetscObjectSetName((PetscObject)u, uname));
425:     /* Setup solver */
426:     PetscCall(SNESReset(snes));
427:     PetscCall(SNESSetDM(snes, dm[r]));
428:     PetscCall(DMPlexSetSNESLocalFEM(dm[r], PETSC_FALSE, ctx));
429:     PetscCall(DMPlexSetSNESVariableBounds(dm[r], snes));
430:     PetscCall(SNESSetFromOptions(snes));
431:     /* Set nullspace for Jacobian */
432:     PetscCall(PetscConvEstSetJacobianNullSpace_Private(ce, snes));
433:     /* Create initial guess */
434:     PetscCall(PetscConvEstComputeInitialGuess(ce, r, dm[r], u));
435:     PetscCall(SNESSolve(snes, NULL, u));
436:     PetscCall(PetscLogEventBegin(ce->event, ce, 0, 0, 0));
437:     PetscCall(PetscConvEstComputeError(ce, r, dm[r], u, &ce->errors[r * ce->Nf]));
438:     PetscCall(PetscLogEventEnd(ce->event, ce, 0, 0, 0));
439:     for (f = 0; f < ce->Nf; ++f) {
440:       PetscSection s, fs;
441:       PetscInt     lsize;

443:       /* Could use DMGetOutputDM() to add in Dirichlet dofs */
444:       PetscCall(DMGetLocalSection(dm[r], &s));
445:       PetscCall(PetscSectionGetField(s, f, &fs));
446:       PetscCall(PetscSectionGetConstrainedStorageSize(fs, &lsize));
447:       PetscCallMPI(MPIU_Allreduce(&lsize, &ce->dofs[r * ce->Nf + f], 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)snes)));
448:       PetscCall(PetscLogEventSetDof(ce->event, f, ce->dofs[r * ce->Nf + f]));
449:       PetscCall(PetscLogEventSetError(ce->event, f, ce->errors[r * ce->Nf + f]));
450:     }
451:     /* Monitor */
452:     PetscCall(PetscConvEstMonitorDefault(ce, r));
453:     if (!r) {
454:       /* PCReset() does not wipe out the level structure */
455:       KSP ksp;
456:       PC  pc;

458:       PetscCall(SNESGetKSP(snes, &ksp));
459:       PetscCall(KSPGetPC(ksp, &pc));
460:       PetscCall(PCMGGetLevels(pc, &oldnlev));
461:     }
462:     /* Cleanup */
463:     PetscCall(VecDestroy(&u));
464:     PetscCall(PetscLogStagePop());
465:   }
466:   for (r = 1; r <= Nr; ++r) PetscCall(DMDestroy(&dm[r]));
467:   /* Fit convergence rate */
468:   PetscCall(PetscMalloc2(Nr + 1, &x, Nr + 1, &y));
469:   for (f = 0; f < ce->Nf; ++f) {
470:     for (r = 0; r <= Nr; ++r) {
471:       x[r] = PetscLog10Real(ce->dofs[r * ce->Nf + f]);
472:       y[r] = PetscLog10Real(ce->errors[r * ce->Nf + f]);
473:     }
474:     PetscCall(PetscLinearRegression(Nr + 1, x, y, &slope, &intercept));
475:     /* Since h^{-dim} = N, lg err = s lg N + b = -s dim lg h + b */
476:     alpha[f] = -slope * dim;
477:   }
478:   PetscCall(PetscFree2(x, y));
479:   PetscCall(PetscFree(dm));
480:   /* Restore solver */
481:   PetscCall(SNESReset(snes));
482:   {
483:     /* PCReset() does not wipe out the level structure */
484:     KSP ksp;
485:     PC  pc;

487:     PetscCall(SNESGetKSP(snes, &ksp));
488:     PetscCall(KSPGetPC(ksp, &pc));
489:     PetscCall(PCMGSetLevels(pc, oldnlev, NULL));
490:     PetscCall(DMSetRefineLevel(ce->idm, oldlevel)); /* The damn DMCoarsen() calls in PCMG can reset this */
491:   }
492:   PetscCall(SNESSetDM(snes, ce->idm));
493:   PetscCall(DMPlexSetSNESLocalFEM(ce->idm, PETSC_FALSE, ctx));
494:   PetscCall(DMPlexSetSNESVariableBounds(ce->idm, snes));
495:   PetscCall(SNESSetFromOptions(snes));
496:   PetscCall(PetscConvEstSetJacobianNullSpace_Private(ce, snes));
497:   PetscFunctionReturn(PETSC_SUCCESS);
498: }

500: /*@
501:   PetscConvEstGetConvRate - Returns an estimate of the convergence rate for the discretization

503:   Not Collective

505:   Input Parameter:
506: . ce - The `PetscConvEst` object

508:   Output Parameter:
509: . alpha - The convergence rate for each field

511:   Options Database Keys:
512: + -snes_convergence_estimate - Execute convergence estimation inside `SNESSolve()` and print out the rate
513: - -ts_convergence_estimate   - Execute convergence estimation inside `TSSolve()` and print out the rate

515:   Level: intermediate

517:   Notes:
518:   The convergence rate alpha is defined by

520:   $$
521:   || u_\Delta - u_{exact} || < C \Delta^\alpha
522:   $$

524:   where $u_{\Delta} $ is the discrete solution, and $\Delta$ is a measure of the discretization size. We usually use $h$ for the
525:   spatial resolution and $\Delta t $ for the temporal resolution.

527:   We solve a series of problems using increasing resolution (refined meshes or decreased timesteps), calculate an error
528:   based upon the exact solution in the `PetscDS`, and then fit the result to our model above using linear regression.

530: .seealso: `PetscConvEstSetSolver()`, `PetscConvEstCreate()`, `SNESSolve()`, `TSSolve()`
531: @*/
532: PetscErrorCode PetscConvEstGetConvRate(PetscConvEst ce, PetscReal alpha[])
533: {
534:   PetscInt f;

536:   PetscFunctionBegin;
537:   if (ce->event < 0) PetscCall(PetscLogEventRegister("ConvEst Error", PETSC_OBJECT_CLASSID, &ce->event));
538:   for (f = 0; f < ce->Nf; ++f) alpha[f] = 0.0;
539:   PetscUseTypeMethod(ce, getconvrate, alpha);
540:   PetscFunctionReturn(PETSC_SUCCESS);
541: }

543: /*@
544:   PetscConvEstRateView - Displays the convergence rate obtained from `PetscConvEstGetConvRate()` using a `PetscViewer`

546:   Collective

548:   Input Parameters:
549: + ce     - iterative context obtained from `SNESCreate()`
550: . alpha  - the convergence rate for each field
551: - viewer - the viewer to display the reason

553:   Options Database Key:
554: . -snes_convergence_estimate - print the convergence rate

556:   Level: developer

558: .seealso: `PetscConvEst`, `PetscConvEstGetConvRate()`
559: @*/
560: PetscErrorCode PetscConvEstRateView(PetscConvEst ce, const PetscReal alpha[], PetscViewer viewer)
561: {
562:   PetscBool isAscii;

564:   PetscFunctionBegin;
565:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isAscii));
566:   if (isAscii) {
567:     PetscInt Nf = ce->Nf, f;

569:     PetscCall(PetscViewerASCIIAddTab(viewer, ((PetscObject)ce)->tablevel));
570:     PetscCall(PetscViewerASCIIPrintf(viewer, "L_2 convergence rate: "));
571:     if (Nf > 1) PetscCall(PetscViewerASCIIPrintf(viewer, "["));
572:     for (f = 0; f < Nf; ++f) {
573:       if (f > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
574:       PetscCall(PetscViewerASCIIPrintf(viewer, "%#.2g", (double)alpha[f]));
575:     }
576:     if (Nf > 1) PetscCall(PetscViewerASCIIPrintf(viewer, "]"));
577:     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
578:     PetscCall(PetscViewerASCIISubtractTab(viewer, ((PetscObject)ce)->tablevel));
579:   }
580:   PetscFunctionReturn(PETSC_SUCCESS);
581: }

583: /*@
584:   PetscConvEstCreate - Create a `PetscConvEst` object. This is used to study the convergence rate of approximations on grids to a continuum solution

586:   Collective

588:   Input Parameter:
589: . comm - The communicator for the `PetscConvEst` object

591:   Output Parameter:
592: . ce - The `PetscConvEst` object

594:   Level: beginner

596: .seealso: `PetscConvEst`, `PetscConvEstDestroy()`, `PetscConvEstGetConvRate()`, `DMAdaptorCreate()`, `DMAdaptor`
597: @*/
598: PetscErrorCode PetscConvEstCreate(MPI_Comm comm, PetscConvEst *ce)
599: {
600:   PetscFunctionBegin;
601:   PetscAssertPointer(ce, 2);
602:   PetscCall(PetscSysInitializePackage());
603:   PetscCall(PetscHeaderCreate(*ce, PETSC_OBJECT_CLASSID, "PetscConvEst", "ConvergenceEstimator", "SNES", comm, PetscConvEstDestroy, PetscConvEstView));
604:   (*ce)->monitor           = PETSC_FALSE;
605:   (*ce)->r                 = 2.0;
606:   (*ce)->Nr                = 4;
607:   (*ce)->event             = -1;
608:   (*ce)->ops->setsolver    = PetscConvEstSetSNES_Private;
609:   (*ce)->ops->initguess    = PetscConvEstInitGuessSNES_Private;
610:   (*ce)->ops->computeerror = PetscConvEstComputeErrorSNES_Private;
611:   (*ce)->ops->getconvrate  = PetscConvEstGetConvRateSNES_Private;
612:   PetscFunctionReturn(PETSC_SUCCESS);
613: }