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: PetscErrorCode PetscConvEstComputeInitialGuess(PetscConvEst ce, PetscInt r, DM dm, Vec u)
    178: {
    179:   PetscFunctionBegin;
    183:   PetscUseTypeMethod(ce, initguess, r, dm, u);
    184:   PetscFunctionReturn(PETSC_SUCCESS);
    185: }

    187: PetscErrorCode PetscConvEstComputeError(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
    188: {
    189:   PetscFunctionBegin;
    193:   PetscAssertPointer(errors, 5);
    194:   PetscUseTypeMethod(ce, computeerror, r, dm, u, errors);
    195:   PetscFunctionReturn(PETSC_SUCCESS);
    196: }

    198: /*@
    199:   PetscConvEstMonitorDefault - Monitors the convergence estimation loop

    201:   Collective

    203:   Input Parameters:
    204: + ce - The `PetscConvEst` object
    205: - r  - The refinement level

    207:   Options Database Key:
    208: . -convest_monitor - Activate the monitor

    210:   Level: intermediate

    212: .seealso: `PetscConvEst`, `PetscConvEstCreate()`, `PetscConvEstGetConvRate()`, `SNESSolve()`, `TSSolve()`
    213: @*/
    214: PetscErrorCode PetscConvEstMonitorDefault(PetscConvEst ce, PetscInt r)
    215: {
    216:   MPI_Comm comm;
    217:   PetscInt f;

    219:   PetscFunctionBegin;
    220:   if (ce->monitor) {
    221:     PetscInt  *dofs   = &ce->dofs[r * ce->Nf];
    222:     PetscReal *errors = &ce->errors[r * ce->Nf];

    224:     PetscCall(PetscObjectGetComm((PetscObject)ce, &comm));
    225:     PetscCall(PetscPrintf(comm, "N: "));
    226:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "["));
    227:     for (f = 0; f < ce->Nf; ++f) {
    228:       if (f > 0) PetscCall(PetscPrintf(comm, ", "));
    229:       PetscCall(PetscPrintf(comm, "%7" PetscInt_FMT, dofs[f]));
    230:     }
    231:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "]"));
    232:     PetscCall(PetscPrintf(comm, "  "));
    233:     PetscCall(PetscPrintf(comm, "L_2 Error: "));
    234:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "["));
    235:     for (f = 0; f < ce->Nf; ++f) {
    236:       if (f > 0) PetscCall(PetscPrintf(comm, ", "));
    237:       if (errors[f] < 1.0e-11) PetscCall(PetscPrintf(comm, "< 1e-11"));
    238:       else PetscCall(PetscPrintf(comm, "%g", (double)errors[f]));
    239:     }
    240:     if (ce->Nf > 1) PetscCall(PetscPrintf(comm, "]"));
    241:     PetscCall(PetscPrintf(comm, "\n"));
    242:   }
    243:   PetscFunctionReturn(PETSC_SUCCESS);
    244: }

    246: static PetscErrorCode PetscConvEstSetSNES_Private(PetscConvEst ce, PetscObject solver)
    247: {
    248:   PetscClassId id;

    250:   PetscFunctionBegin;
    251:   PetscCall(PetscObjectGetClassId(ce->solver, &id));
    252:   PetscCheck(id == SNES_CLASSID, PetscObjectComm((PetscObject)ce), PETSC_ERR_ARG_WRONG, "Solver was not a SNES");
    253:   PetscCall(SNESGetDM((SNES)ce->solver, &ce->idm));
    254:   PetscFunctionReturn(PETSC_SUCCESS);
    255: }

    257: static PetscErrorCode PetscConvEstInitGuessSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u)
    258: {
    259:   PetscFunctionBegin;
    260:   PetscCall(DMProjectFunction(dm, 0.0, ce->initGuess, ce->ctxs, INSERT_VALUES, u));
    261:   PetscFunctionReturn(PETSC_SUCCESS);
    262: }

    264: static PetscErrorCode PetscConvEstComputeErrorSNES_Private(PetscConvEst ce, PetscInt r, DM dm, Vec u, PetscReal errors[])
    265: {
    266:   const char *prefix;
    267:   PetscBool   errorView = PETSC_FALSE;

    269:   PetscFunctionBegin;
    270:   PetscCall(DMComputeL2FieldDiff(dm, 0.0, ce->exactSol, ce->ctxs, u, errors));
    271:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ce, &prefix));
    272:   PetscCall(PetscOptionsHasName(NULL, prefix, "-convest_error_view", &errorView));
    273:   if (errorView) {
    274:     DM                   dmError;
    275:     PetscFE              feError, fe;
    276:     PetscQuadrature      quad;
    277:     Vec                  e;
    278:     PetscDS              ds;
    279:     PetscSimplePointFn **funcs;
    280:     void               **ctxs;
    281:     PetscInt             dim, Nf;

    283:     PetscCall(DMGetDimension(dm, &dim));
    284:     PetscCall(DMGetDS(dm, &ds));
    285:     PetscCall(PetscDSGetNumFields(ds, &Nf));
    286:     PetscCall(PetscMalloc2(Nf, &funcs, Nf, &ctxs));
    287:     for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscDSGetExactSolution(ds, f, &funcs[f], &ctxs[f]));
    288:     PetscCall(DMClone(dm, &dmError));
    289:     PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, 1, PETSC_FALSE, 0, PETSC_DETERMINE, &feError));
    290:     PetscCall(DMGetField(dm, 0, NULL, (PetscObject *)&fe));
    291:     PetscCall(PetscFEGetQuadrature(fe, &quad));
    292:     PetscCall(PetscFESetQuadrature(feError, quad));
    293:     PetscCall(DMSetField(dmError, 0, NULL, (PetscObject)feError));
    294:     PetscCall(PetscFEDestroy(&feError));
    295:     PetscCall(DMCreateDS(dmError));
    296:     PetscCall(DMGetGlobalVector(dmError, &e));
    297:     PetscCall(PetscObjectSetName((PetscObject)e, "Error"));
    298:     PetscCall(DMPlexComputeL2DiffVec(dm, 0., funcs, ctxs, u, e));
    299:     PetscCall(VecViewFromOptions(e, NULL, "-convest_error_view"));
    300:     PetscCall(DMRestoreGlobalVector(dmError, &e));
    301:     PetscCall(DMDestroy(&dmError));
    302:     PetscCall(PetscFree2(funcs, ctxs));
    303:   }
    304:   PetscFunctionReturn(PETSC_SUCCESS);
    305: }

    307: static PetscErrorCode PetscConvEstSetJacobianNullSpace_Private(PetscConvEst ce, SNES snes)
    308: {
    309:   DM       dm;
    310:   PetscInt f;

    312:   PetscFunctionBegin;
    313:   PetscCall(SNESGetDM(snes, &dm));
    314:   for (f = 0; f < ce->Nf; ++f) {
    315:     PetscErrorCode (*nspconstr)(DM, PetscInt, PetscInt, MatNullSpace *);

    317:     PetscCall(DMGetNullSpaceConstructor(dm, f, &nspconstr));
    318:     if (nspconstr) {
    319:       MatNullSpace nullsp;
    320:       Mat          J;

    322:       PetscCall((*nspconstr)(dm, f, f, &nullsp));
    323:       PetscCall(SNESSetUp(snes));
    324:       PetscCall(SNESGetJacobian(snes, &J, NULL, NULL, NULL));
    325:       PetscCall(MatSetNullSpace(J, nullsp));
    326:       PetscCall(MatNullSpaceDestroy(&nullsp));
    327:       break;
    328:     }
    329:   }
    330:   PetscFunctionReturn(PETSC_SUCCESS);
    331: }

    333: static PetscErrorCode PetscConvEstGetConvRateSNES_Private(PetscConvEst ce, PetscReal alpha[])
    334: {
    335:   SNES        snes = (SNES)ce->solver;
    336:   DM         *dm;
    337:   PetscObject disc;
    338:   PetscReal  *x, *y, slope, intercept;
    339:   PetscInt    Nr = ce->Nr, r, f, dim, oldlevel, oldnlev;
    340:   void       *ctx;

    342:   PetscFunctionBegin;
    343:   PetscCheck(ce->r == 2.0, PetscObjectComm((PetscObject)ce), PETSC_ERR_SUP, "Only refinement factor 2 is currently supported (not %g)", (double)ce->r);
    344:   PetscCall(DMGetDimension(ce->idm, &dim));
    345:   PetscCall(DMGetApplicationContext(ce->idm, &ctx));
    346:   PetscCall(DMPlexSetRefinementUniform(ce->idm, PETSC_TRUE));
    347:   PetscCall(DMGetRefineLevel(ce->idm, &oldlevel));
    348:   PetscCall(PetscMalloc1(Nr + 1, &dm));
    349:   /* Loop over meshes */
    350:   dm[0] = ce->idm;
    351:   for (r = 0; r <= Nr; ++r) {
    352:     Vec           u;
    353:     PetscLogStage stage;
    354:     char          stageName[PETSC_MAX_PATH_LEN];
    355:     const char   *dmname, *uname;

    357:     PetscCall(PetscSNPrintf(stageName, PETSC_MAX_PATH_LEN - 1, "ConvEst Refinement Level %" PetscInt_FMT, r));
    358:     PetscCall(PetscLogStageGetId(stageName, &stage));
    359:     if (stage < 0) PetscCall(PetscLogStageRegister(stageName, &stage));
    360:     PetscCall(PetscLogStagePush(stage));
    361:     if (r > 0) {
    362:       if (!ce->noRefine) {
    363:         PetscCall(DMRefine(dm[r - 1], MPI_COMM_NULL, &dm[r]));
    364:         PetscCall(DMSetCoarseDM(dm[r], dm[r - 1]));
    365:       } else {
    366:         DM cdm, rcdm;

    368:         PetscCall(DMClone(dm[r - 1], &dm[r]));
    369:         PetscCall(DMCopyDisc(dm[r - 1], dm[r]));
    370:         PetscCall(DMGetCoordinateDM(dm[r - 1], &cdm));
    371:         PetscCall(DMGetCoordinateDM(dm[r], &rcdm));
    372:         PetscCall(DMCopyDisc(cdm, rcdm));
    373:       }
    374:       PetscCall(DMCopyTransform(ce->idm, dm[r]));
    375:       PetscCall(PetscObjectGetName((PetscObject)dm[r - 1], &dmname));
    376:       PetscCall(PetscObjectSetName((PetscObject)dm[r], dmname));
    377:       for (f = 0; f < ce->Nf; ++f) {
    378:         PetscErrorCode (*nspconstr)(DM, PetscInt, PetscInt, MatNullSpace *);

    380:         PetscCall(DMGetNullSpaceConstructor(dm[r - 1], f, &nspconstr));
    381:         PetscCall(DMSetNullSpaceConstructor(dm[r], f, nspconstr));
    382:       }
    383:     }
    384:     PetscCall(DMViewFromOptions(dm[r], NULL, "-conv_dm_view"));
    385:     /* Create solution */
    386:     PetscCall(DMCreateGlobalVector(dm[r], &u));
    387:     PetscCall(DMGetField(dm[r], 0, NULL, &disc));
    388:     PetscCall(PetscObjectGetName(disc, &uname));
    389:     PetscCall(PetscObjectSetName((PetscObject)u, uname));
    390:     /* Setup solver */
    391:     PetscCall(SNESReset(snes));
    392:     PetscCall(SNESSetDM(snes, dm[r]));
    393:     PetscCall(DMPlexSetSNESLocalFEM(dm[r], PETSC_FALSE, ctx));
    394:     PetscCall(DMPlexSetSNESVariableBounds(dm[r], snes));
    395:     PetscCall(SNESSetFromOptions(snes));
    396:     /* Set nullspace for Jacobian */
    397:     PetscCall(PetscConvEstSetJacobianNullSpace_Private(ce, snes));
    398:     /* Create initial guess */
    399:     PetscCall(PetscConvEstComputeInitialGuess(ce, r, dm[r], u));
    400:     PetscCall(SNESSolve(snes, NULL, u));
    401:     PetscCall(PetscLogEventBegin(ce->event, ce, 0, 0, 0));
    402:     PetscCall(PetscConvEstComputeError(ce, r, dm[r], u, &ce->errors[r * ce->Nf]));
    403:     PetscCall(PetscLogEventEnd(ce->event, ce, 0, 0, 0));
    404:     for (f = 0; f < ce->Nf; ++f) {
    405:       PetscSection s, fs;
    406:       PetscInt     lsize;

    408:       /* Could use DMGetOutputDM() to add in Dirichlet dofs */
    409:       PetscCall(DMGetLocalSection(dm[r], &s));
    410:       PetscCall(PetscSectionGetField(s, f, &fs));
    411:       PetscCall(PetscSectionGetConstrainedStorageSize(fs, &lsize));
    412:       PetscCallMPI(MPIU_Allreduce(&lsize, &ce->dofs[r * ce->Nf + f], 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)snes)));
    413:       PetscCall(PetscLogEventSetDof(ce->event, f, ce->dofs[r * ce->Nf + f]));
    414:       PetscCall(PetscLogEventSetError(ce->event, f, ce->errors[r * ce->Nf + f]));
    415:     }
    416:     /* Monitor */
    417:     PetscCall(PetscConvEstMonitorDefault(ce, r));
    418:     if (!r) {
    419:       /* PCReset() does not wipe out the level structure */
    420:       KSP ksp;
    421:       PC  pc;

    423:       PetscCall(SNESGetKSP(snes, &ksp));
    424:       PetscCall(KSPGetPC(ksp, &pc));
    425:       PetscCall(PCMGGetLevels(pc, &oldnlev));
    426:     }
    427:     /* Cleanup */
    428:     PetscCall(VecDestroy(&u));
    429:     PetscCall(PetscLogStagePop());
    430:   }
    431:   for (r = 1; r <= Nr; ++r) PetscCall(DMDestroy(&dm[r]));
    432:   /* Fit convergence rate */
    433:   PetscCall(PetscMalloc2(Nr + 1, &x, Nr + 1, &y));
    434:   for (f = 0; f < ce->Nf; ++f) {
    435:     for (r = 0; r <= Nr; ++r) {
    436:       x[r] = PetscLog10Real(ce->dofs[r * ce->Nf + f]);
    437:       y[r] = PetscLog10Real(ce->errors[r * ce->Nf + f]);
    438:     }
    439:     PetscCall(PetscLinearRegression(Nr + 1, x, y, &slope, &intercept));
    440:     /* Since h^{-dim} = N, lg err = s lg N + b = -s dim lg h + b */
    441:     alpha[f] = -slope * dim;
    442:   }
    443:   PetscCall(PetscFree2(x, y));
    444:   PetscCall(PetscFree(dm));
    445:   /* Restore solver */
    446:   PetscCall(SNESReset(snes));
    447:   {
    448:     /* PCReset() does not wipe out the level structure */
    449:     KSP ksp;
    450:     PC  pc;

    452:     PetscCall(SNESGetKSP(snes, &ksp));
    453:     PetscCall(KSPGetPC(ksp, &pc));
    454:     PetscCall(PCMGSetLevels(pc, oldnlev, NULL));
    455:     PetscCall(DMSetRefineLevel(ce->idm, oldlevel)); /* The damn DMCoarsen() calls in PCMG can reset this */
    456:   }
    457:   PetscCall(SNESSetDM(snes, ce->idm));
    458:   PetscCall(DMPlexSetSNESLocalFEM(ce->idm, PETSC_FALSE, ctx));
    459:   PetscCall(DMPlexSetSNESVariableBounds(ce->idm, snes));
    460:   PetscCall(SNESSetFromOptions(snes));
    461:   PetscCall(PetscConvEstSetJacobianNullSpace_Private(ce, snes));
    462:   PetscFunctionReturn(PETSC_SUCCESS);
    463: }

    465: /*@
    466:   PetscConvEstGetConvRate - Returns an estimate of the convergence rate for the discretization

    468:   Not Collective

    470:   Input Parameter:
    471: . ce - The `PetscConvEst` object

    473:   Output Parameter:
    474: . alpha - The convergence rate for each field

    476:   Options Database Keys:
    477: + -snes_convergence_estimate - Execute convergence estimation inside `SNESSolve()` and print out the rate
    478: - -ts_convergence_estimate   - Execute convergence estimation inside `TSSolve()` and print out the rate

    480:   Level: intermediate

    482:   Notes:
    483:   The convergence rate alpha is defined by

    485:   $$
    486:   || u_\Delta - u_{exact} || < C \Delta^\alpha
    487:   $$

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

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

    495: .seealso: `PetscConvEstSetSolver()`, `PetscConvEstCreate()`, `SNESSolve()`, `TSSolve()`
    496: @*/
    497: PetscErrorCode PetscConvEstGetConvRate(PetscConvEst ce, PetscReal alpha[])
    498: {
    499:   PetscInt f;

    501:   PetscFunctionBegin;
    502:   if (ce->event < 0) PetscCall(PetscLogEventRegister("ConvEst Error", PETSC_OBJECT_CLASSID, &ce->event));
    503:   for (f = 0; f < ce->Nf; ++f) alpha[f] = 0.0;
    504:   PetscUseTypeMethod(ce, getconvrate, alpha);
    505:   PetscFunctionReturn(PETSC_SUCCESS);
    506: }

    508: /*@
    509:   PetscConvEstRateView - Displays the convergence rate obtained from `PetscConvEstGetConvRate()` using a `PetscViewer`

    511:   Collective

    513:   Input Parameters:
    514: + ce     - iterative context obtained from `SNESCreate()`
    515: . alpha  - the convergence rate for each field
    516: - viewer - the viewer to display the reason

    518:   Options Database Key:
    519: . -snes_convergence_estimate - print the convergence rate

    521:   Level: developer

    523: .seealso: `PetscConvEst`, `PetscConvEstGetConvRate()`
    524: @*/
    525: PetscErrorCode PetscConvEstRateView(PetscConvEst ce, const PetscReal alpha[], PetscViewer viewer)
    526: {
    527:   PetscBool isAscii;

    529:   PetscFunctionBegin;
    530:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isAscii));
    531:   if (isAscii) {
    532:     PetscInt Nf = ce->Nf, f;

    534:     PetscCall(PetscViewerASCIIAddTab(viewer, ((PetscObject)ce)->tablevel));
    535:     PetscCall(PetscViewerASCIIPrintf(viewer, "L_2 convergence rate: "));
    536:     if (Nf > 1) PetscCall(PetscViewerASCIIPrintf(viewer, "["));
    537:     for (f = 0; f < Nf; ++f) {
    538:       if (f > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
    539:       PetscCall(PetscViewerASCIIPrintf(viewer, "%#.2g", (double)alpha[f]));
    540:     }
    541:     if (Nf > 1) PetscCall(PetscViewerASCIIPrintf(viewer, "]"));
    542:     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
    543:     PetscCall(PetscViewerASCIISubtractTab(viewer, ((PetscObject)ce)->tablevel));
    544:   }
    545:   PetscFunctionReturn(PETSC_SUCCESS);
    546: }

    548: /*@
    549:   PetscConvEstCreate - Create a `PetscConvEst` object. This is used to study the convergence rate of approximations on grids to a continuum solution

    551:   Collective

    553:   Input Parameter:
    554: . comm - The communicator for the `PetscConvEst` object

    556:   Output Parameter:
    557: . ce - The `PetscConvEst` object

    559:   Level: beginner

    561: .seealso: `PetscConvEst`, `PetscConvEstDestroy()`, `PetscConvEstGetConvRate()`, `DMAdaptorCreate()`, `DMAdaptor`
    562: @*/
    563: PetscErrorCode PetscConvEstCreate(MPI_Comm comm, PetscConvEst *ce)
    564: {
    565:   PetscFunctionBegin;
    566:   PetscAssertPointer(ce, 2);
    567:   PetscCall(PetscSysInitializePackage());
    568:   PetscCall(PetscHeaderCreate(*ce, PETSC_OBJECT_CLASSID, "PetscConvEst", "ConvergenceEstimator", "SNES", comm, PetscConvEstDestroy, PetscConvEstView));
    569:   (*ce)->monitor           = PETSC_FALSE;
    570:   (*ce)->r                 = 2.0;
    571:   (*ce)->Nr                = 4;
    572:   (*ce)->event             = -1;
    573:   (*ce)->ops->setsolver    = PetscConvEstSetSNES_Private;
    574:   (*ce)->ops->initguess    = PetscConvEstInitGuessSNES_Private;
    575:   (*ce)->ops->computeerror = PetscConvEstComputeErrorSNES_Private;
    576:   (*ce)->ops->getconvrate  = PetscConvEstGetConvRateSNES_Private;
    577:   PetscFunctionReturn(PETSC_SUCCESS);
    578: }