Actual source code: convest.c

petsc-master 2020-01-26
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  1:  #include <petscconvest.h>
  2:  #include <petscdmplex.h>
  3:  #include <petscds.h>

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

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

 14: /*@
 15:   PetscConvEstDestroy - Destroys a PetscConvEst object

 17:   Collective on PetscConvEst

 19:   Input Parameter:
 20: . ce - The PetscConvEst object

 22:   Level: beginner

 24: .seealso: PetscConvEstCreate(), PetscConvEstGetConvRate()
 25: @*/
 26: PetscErrorCode PetscConvEstDestroy(PetscConvEst *ce)
 27: {

 31:   if (!*ce) return(0);
 33:   if (--((PetscObject)(*ce))->refct > 0) {
 34:     *ce = NULL;
 35:     return(0);
 36:   }
 37:   PetscFree3((*ce)->initGuess, (*ce)->exactSol, (*ce)->ctxs);
 38:   PetscFree((*ce)->errors);
 39:   PetscHeaderDestroy(ce);
 40:   return(0);
 41: }

 43: /*@
 44:   PetscConvEstSetFromOptions - Sets a PetscConvEst object from options

 46:   Collective on PetscConvEst

 48:   Input Parameters:
 49: . ce - The PetscConvEst object

 51:   Level: beginner

 53: .seealso: PetscConvEstCreate(), PetscConvEstGetConvRate()
 54: @*/
 55: PetscErrorCode PetscConvEstSetFromOptions(PetscConvEst ce)
 56: {

 60:   PetscOptionsBegin(PetscObjectComm((PetscObject) ce), "", "Convergence Estimator Options", "PetscConvEst");
 61:   PetscOptionsInt("-convest_num_refine", "The number of refinements for the convergence check", "PetscConvEst", ce->Nr, &ce->Nr, NULL);
 62:   PetscOptionsReal("-convest_refine_factor", "The increase in resolution in each dimension", "PetscConvEst", ce->r, &ce->r, NULL);
 63:   PetscOptionsBool("-convest_monitor", "Monitor the error for each convergence check", "PetscConvEst", ce->monitor, &ce->monitor, NULL);
 64:   PetscOptionsEnd();
 65:   return(0);
 66: }

 68: /*@
 69:   PetscConvEstView - Views a PetscConvEst object

 71:   Collective on PetscConvEst

 73:   Input Parameters:
 74: + ce     - The PetscConvEst object
 75: - viewer - The PetscViewer object

 77:   Level: beginner

 79: .seealso: PetscConvEstCreate(), PetscConvEstGetConvRate()
 80: @*/
 81: PetscErrorCode PetscConvEstView(PetscConvEst ce, PetscViewer viewer)
 82: {

 86:   PetscObjectPrintClassNamePrefixType((PetscObject) ce, viewer);
 87:   PetscViewerASCIIPrintf(viewer, "ConvEst with %D levels\n", ce->Nr+1);
 88:   return(0);
 89: }

 91: /*@
 92:   PetscConvEstGetSolver - Gets the solver used to produce discrete solutions

 94:   Not collective

 96:   Input Parameter:
 97: . ce     - The PetscConvEst object

 99:   Output Parameter:
100: . solver - The solver

102:   Level: intermediate

104: .seealso: PetscConvEstSetSolver(), PetscConvEstCreate(), PetscConvEstGetConvRate()
105: @*/
106: PetscErrorCode PetscConvEstGetSolver(PetscConvEst ce, PetscObject *solver)
107: {
111:   *solver = ce->solver;
112:   return(0);
113: }

115: /*@
116:   PetscConvEstSetSolver - Sets the solver used to produce discrete solutions

118:   Not collective

120:   Input Parameters:
121: + ce     - The PetscConvEst object
122: - solver - The solver

124:   Level: intermediate

126:   Note: The solver MUST have an attached DM/DS, so that we know the exact solution

128: .seealso: PetscConvEstGetSNES(), PetscConvEstCreate(), PetscConvEstGetConvRate()
129: @*/
130: PetscErrorCode PetscConvEstSetSolver(PetscConvEst ce, PetscObject solver)
131: {

137:   ce->solver = solver;
138:   (*ce->ops->setsolver)(ce, solver);
139:   return(0);
140: }

142: /*@
143:   PetscConvEstSetUp - After the solver is specified, we create structures for estimating convergence

145:   Collective on PetscConvEst

147:   Input Parameters:
148: . ce - The PetscConvEst object

150:   Level: beginner

152: .seealso: PetscConvEstCreate(), PetscConvEstGetConvRate()
153: @*/
154: PetscErrorCode PetscConvEstSetUp(PetscConvEst ce)
155: {
156:   PetscDS        ds;
157:   PetscInt       Nf, f;

161:   DMGetDS(ce->idm, &ds);
162:   PetscDSGetNumFields(ds, &Nf);
163:   ce->Nf = PetscMax(Nf, 1);
164:   PetscMalloc1((ce->Nr+1)*ce->Nf, &ce->errors);
165:   PetscMalloc3(ce->Nf, &ce->initGuess, ce->Nf, &ce->exactSol, ce->Nf, &ce->ctxs);
166:   for (f = 0; f < Nf; ++f) ce->initGuess[f] = zero_private;
167:   for (f = 0; f < Nf; ++f) {
168:     PetscDSGetExactSolution(ds, f, &ce->exactSol[f], &ce->ctxs[f]);
169:     if (!ce->exactSol[f]) SETERRQ1(PetscObjectComm((PetscObject) ce), PETSC_ERR_ARG_WRONG, "DS must contain exact solution functions in order to estimate convergence, missing for field %D", f);
170:   }
171:   return(0);
172: }

174: PetscErrorCode PetscConvEstComputeInitialGuess(PetscConvEst ce, PetscInt r, DM dm, Vec u)
175: {

182:   (*ce->ops->initguess)(ce, r, dm, u);
183:   return(0);
184: }

186: PetscErrorCode PetscConvEstComputeError(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
187: {

195:   (*ce->ops->computeerror)(ce, r, dm, u, errors);
196:   return(0);
197: }

199: static PetscErrorCode PetscConvEstMonitor_Private(PetscConvEst ce, PetscInt r)
200: {
201:   MPI_Comm       comm;
202:   PetscInt       f;

206:   if (ce->monitor) {
207:     PetscReal *errors = &ce->errors[r*ce->Nf];

209:     PetscObjectGetComm((PetscObject) ce, &comm);
210:     PetscPrintf(comm, "L_2 Error: ");
211:     if (ce->Nf > 1) {PetscPrintf(comm, "[");}
212:     for (f = 0; f < ce->Nf; ++f) {
213:       if (f > 0) {PetscPrintf(comm, ", ");}
214:       if (errors[f] < 1.0e-11) {PetscPrintf(comm, "< 1e-11");}
215:       else                     {PetscPrintf(comm, "%g", (double) errors[f]);}
216:     }
217:     if (ce->Nf > 1) {PetscPrintf(comm, "]");}
218:     PetscPrintf(comm, "\n");
219:   }
220:   return(0);
221: }

223: static PetscErrorCode PetscConvEstSetSNES_Private(PetscConvEst ce, PetscObject solver)
224: {
225:   PetscClassId   id;

229:   PetscObjectGetClassId(ce->solver, &id);
230:   if (id != SNES_CLASSID) SETERRQ(PetscObjectComm((PetscObject) ce), PETSC_ERR_ARG_WRONG, "Solver was not a SNES");
231:   SNESGetDM((SNES) ce->solver, &ce->idm);
232:   return(0);
233: }

235: static PetscErrorCode PetscConvEstInitGuessSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u)
236: {

240:   DMProjectFunction(dm, 0.0, ce->initGuess, ce->ctxs, INSERT_VALUES, u);
241:   return(0);
242: }

244: static PetscErrorCode PetscConvEstComputeErrorSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
245: {

249:   DMComputeL2FieldDiff(dm, 0.0, ce->exactSol, ce->ctxs, u, errors);
250:   return(0);
251: }

253: static PetscErrorCode PetscConvEstGetConvRateSNES_Private(PetscConvEst ce, PetscReal alpha[])
254: {
255:   SNES           snes = (SNES) ce->solver;
256:   DM            *dm;
257:   PetscObject    disc;
258:   PetscReal     *x, *y, slope, intercept;
259:   PetscInt      *dof, Nr = ce->Nr, r, f, dim, oldlevel, oldnlev;
260:   void          *ctx;

264:   if (ce->r != 2.0) SETERRQ1(PetscObjectComm((PetscObject) ce), PETSC_ERR_SUP, "Only refinement factor 2 is currently supported (not %g)", (double) ce->r);
265:   DMGetDimension(ce->idm, &dim);
266:   DMGetApplicationContext(ce->idm, &ctx);
267:   DMPlexSetRefinementUniform(ce->idm, PETSC_TRUE);
268:   DMGetRefineLevel(ce->idm, &oldlevel);
269:   PetscMalloc2((Nr+1), &dm, (Nr+1)*ce->Nf, &dof);
270:   /* Loop over meshes */
271:   dm[0] = ce->idm;
272:   for (r = 0; r <= Nr; ++r) {
273:     Vec           u;
274:     PetscLogStage stage;
275:     char          stageName[PETSC_MAX_PATH_LEN];
276:     const char   *dmname, *uname;

278:     PetscSNPrintf(stageName, PETSC_MAX_PATH_LEN-1, "ConvEst Refinement Level %D", r);
279:     PetscLogStageRegister(stageName, &stage);
280:     PetscLogStagePush(stage);
281:     if (r > 0) {
282:       DMRefine(dm[r-1], MPI_COMM_NULL, &dm[r]);
283:       DMSetCoarseDM(dm[r], dm[r-1]);
284:       DMCopyDisc(ce->idm, dm[r]);
285:       DMCopyTransform(ce->idm, dm[r]);
286:       PetscObjectGetName((PetscObject) dm[r-1], &dmname);
287:       PetscObjectSetName((PetscObject) dm[r], dmname);
288:       for (f = 0; f <= ce->Nf; ++f) {
289:         PetscErrorCode (*nspconstr)(DM, PetscInt, MatNullSpace *);

291:         DMGetNullSpaceConstructor(dm[r-1], f, &nspconstr);
292:         DMSetNullSpaceConstructor(dm[r],   f,  nspconstr);
293:       }
294:     }
295:     DMViewFromOptions(dm[r], NULL, "-conv_dm_view");
296:     /* Create solution */
297:     DMCreateGlobalVector(dm[r], &u);
298:     DMGetField(dm[r], 0, NULL, &disc);
299:     PetscObjectGetName(disc, &uname);
300:     PetscObjectSetName((PetscObject) u, uname);
301:     /* Setup solver */
302:     SNESReset(snes);
303:     SNESSetDM(snes, dm[r]);
304:     DMPlexSetSNESLocalFEM(dm[r], ctx, ctx, ctx);
305:     SNESSetFromOptions(snes);
306:     /* Create initial guess */
307:     PetscConvEstComputeInitialGuess(ce, r, dm[r], u);
308:     SNESSolve(snes, NULL, u);
309:     PetscLogEventBegin(ce->event, ce, 0, 0, 0);
310:     PetscConvEstComputeError(ce, r, dm[r], u, &ce->errors[r*ce->Nf]);
311:     PetscLogEventEnd(ce->event, ce, 0, 0, 0);
312:     for (f = 0; f < ce->Nf; ++f) {
313:       PetscSection s, fs;
314:       PetscInt     lsize;

316:       /* Could use DMGetOutputDM() to add in Dirichlet dofs */
317:       DMGetLocalSection(dm[r], &s);
318:       PetscSectionGetField(s, f, &fs);
319:       PetscSectionGetConstrainedStorageSize(fs, &lsize);
320:       MPI_Allreduce(&lsize, &dof[r*ce->Nf+f], 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject) snes));
321:       PetscLogEventSetDof(ce->event, f, dof[r*ce->Nf+f]);
322:       PetscLogEventSetError(ce->event, f, ce->errors[r*ce->Nf+f]);
323:     }
324:     /* Monitor */
325:     PetscConvEstMonitor_Private(ce, r);
326:     if (!r) {
327:       /* PCReset() does not wipe out the level structure */
328:       KSP ksp;
329:       PC  pc;

331:       SNESGetKSP(snes, &ksp);
332:       KSPGetPC(ksp, &pc);
333:       PCMGGetLevels(pc, &oldnlev);
334:     }
335:     /* Cleanup */
336:     VecDestroy(&u);
337:     PetscLogStagePop();
338:   }
339:   for (r = 1; r <= Nr; ++r) {
340:     DMDestroy(&dm[r]);
341:   }
342:   /* Fit convergence rate */
343:   PetscMalloc2(Nr+1, &x, Nr+1, &y);
344:   for (f = 0; f < ce->Nf; ++f) {
345:     for (r = 0; r <= Nr; ++r) {
346:       x[r] = PetscLog10Real(dof[r*ce->Nf+f]);
347:       y[r] = PetscLog10Real(ce->errors[r*ce->Nf+f]);
348:     }
349:     PetscLinearRegression(Nr+1, x, y, &slope, &intercept);
350:     /* Since h^{-dim} = N, lg err = s lg N + b = -s dim lg h + b */
351:     alpha[f] = -slope * dim;
352:   }
353:   PetscFree2(x, y);
354:   PetscFree2(dm, dof);
355:   /* Restore solver */
356:   SNESReset(snes);
357:   {
358:     /* PCReset() does not wipe out the level structure */
359:     KSP ksp;
360:     PC  pc;

362:     SNESGetKSP(snes, &ksp);
363:     KSPGetPC(ksp, &pc);
364:     PCMGSetLevels(pc, oldnlev, NULL);
365:     DMSetRefineLevel(ce->idm, oldlevel); /* The damn DMCoarsen() calls in PCMG can reset this */
366:   }
367:   SNESSetDM(snes, ce->idm);
368:   DMPlexSetSNESLocalFEM(ce->idm, ctx, ctx, ctx);
369:   SNESSetFromOptions(snes);
370:   return(0);
371: }

373: /*@
374:   PetscConvEstGetConvRate - Returns an estimate of the convergence rate for the discretization

376:   Not collective

378:   Input Parameter:
379: . ce   - The PetscConvEst object

381:   Output Parameter:
382: . alpha - The convergence rate for each field

384:   Note: The convergence rate alpha is defined by
385: $ || u_\Delta - u_exact || < C \Delta^alpha
386: where u_\Delta is the discrete solution, and Delta is a measure of the discretization size. We usually use h for the
387: spatial resolution and \Delta t for the temporal resolution.

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

392:   Options database keys:
393: + -snes_convergence_estimate : Execute convergence estimation inside SNESSolve() and print out the rate
394: - -ts_convergence_estimate : Execute convergence estimation inside TSSolve() and print out the rate

396:   Level: intermediate

398: .seealso: PetscConvEstSetSolver(), PetscConvEstCreate(), PetscConvEstGetConvRate(), SNESSolve(), TSSolve()
399: @*/
400: PetscErrorCode PetscConvEstGetConvRate(PetscConvEst ce, PetscReal alpha[])
401: {
402:   PetscInt       f;

406:   if (ce->event < 0) {PetscLogEventRegister("ConvEst Error", PETSC_OBJECT_CLASSID, &ce->event);}
407:   for (f = 0; f < ce->Nf; ++f) alpha[f] = 0.0;
408:   (*ce->ops->getconvrate)(ce, alpha);
409:   return(0);
410: }

412: /*@
413:   PetscConvEstRateView - Displays the convergence rate to a viewer

415:    Collective on SNES

417:    Parameter:
418: +  snes - iterative context obtained from SNESCreate()
419: .  alpha - the convergence rate for each field
420: -  viewer - the viewer to display the reason

422:    Options Database Keys:
423: .  -snes_convergence_estimate - print the convergence rate

425:    Level: developer

427: .seealso: PetscConvEstGetRate()
428: @*/
429: PetscErrorCode PetscConvEstRateView(PetscConvEst ce, const PetscReal alpha[], PetscViewer viewer)
430: {
431:   PetscBool      isAscii;

435:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isAscii);
436:   if (isAscii) {
437:     PetscInt Nf = ce->Nf, f;

439:     PetscViewerASCIIAddTab(viewer, ((PetscObject) ce)->tablevel);
440:     PetscViewerASCIIPrintf(viewer, "L_2 convergence rate: ");
441:     if (Nf > 1) {PetscViewerASCIIPrintf(viewer, "[");}
442:     for (f = 0; f < Nf; ++f) {
443:       if (f > 0) {PetscViewerASCIIPrintf(viewer, ", ");}
444:       PetscViewerASCIIPrintf(viewer, "%#.2g", (double) alpha[f]);
445:     }
446:     if (Nf > 1) {PetscViewerASCIIPrintf(viewer, "]");}
447:     PetscViewerASCIIPrintf(viewer, "\n");
448:     PetscViewerASCIISubtractTab(viewer, ((PetscObject) ce)->tablevel);
449:   }
450:   return(0);
451: }

453: /*@
454:   PetscConvEstCreate - Create a PetscConvEst object

456:   Collective

458:   Input Parameter:
459: . comm - The communicator for the PetscConvEst object

461:   Output Parameter:
462: . ce   - The PetscConvEst object

464:   Level: beginner

466: .seealso: PetscConvEstDestroy(), PetscConvEstGetConvRate()
467: @*/
468: PetscErrorCode PetscConvEstCreate(MPI_Comm comm, PetscConvEst *ce)
469: {

474:   PetscSysInitializePackage();
475:   PetscHeaderCreate(*ce, PETSC_OBJECT_CLASSID, "PetscConvEst", "ConvergenceEstimator", "SNES", comm, PetscConvEstDestroy, PetscConvEstView);
476:   (*ce)->monitor = PETSC_FALSE;
477:   (*ce)->r       = 2.0;
478:   (*ce)->Nr      = 4;
479:   (*ce)->event   = -1;
480:   (*ce)->ops->setsolver    = PetscConvEstSetSNES_Private;
481:   (*ce)->ops->initguess    = PetscConvEstInitGuessSNES_Private;
482:   (*ce)->ops->computeerror = PetscConvEstComputeErrorSNES_Private;
483:   (*ce)->ops->getconvrate  = PetscConvEstGetConvRateSNES_Private;
484:   return(0);
485: }