Actual source code: dmplexts.c

      1: #include <petsc/private/dmpleximpl.h>
      2: #include <petsc/private/tsimpl.h>
      3: #include <petsc/private/snesimpl.h>
      4: #include <petscds.h>
      5: #include <petscfv.h>

      7: static PetscErrorCode DMTSConvertPlex(DM dm, DM *plex, PetscBool copy)
      8: {
      9:   PetscBool isPlex;

     11:   PetscFunctionBegin;
     12:   PetscCall(PetscObjectTypeCompare((PetscObject)dm, DMPLEX, &isPlex));
     13:   if (isPlex) {
     14:     *plex = dm;
     15:     PetscCall(PetscObjectReference((PetscObject)dm));
     16:   } else {
     17:     PetscCall(PetscObjectQuery((PetscObject)dm, "dm_plex", (PetscObject *)plex));
     18:     if (!*plex) {
     19:       PetscCall(DMConvert(dm, DMPLEX, plex));
     20:       PetscCall(PetscObjectCompose((PetscObject)dm, "dm_plex", (PetscObject)*plex));
     21:     } else {
     22:       PetscCall(PetscObjectReference((PetscObject)*plex));
     23:     }
     24:     if (copy) {
     25:       PetscCall(DMCopyDMTS(dm, *plex));
     26:       PetscCall(DMCopyDMSNES(dm, *plex));
     27:       PetscCall(DMCopyAuxiliaryVec(dm, *plex));
     28:     }
     29:   }
     30:   PetscFunctionReturn(PETSC_SUCCESS);
     31: }

     33: PetscErrorCode DMPlexTSComputeRHSFunctionFVMCEED(DM dm, PetscReal time, Vec locX, Vec F, void *user)
     34: {
     35: #ifdef PETSC_HAVE_LIBCEED
     36:   PetscFV    fv;
     37:   Vec        locF;
     38:   Ceed       ceed;
     39:   DMCeed     sd = dm->dmceed;
     40:   CeedVector clocX, clocF;
     41: #endif

     43: #ifdef PETSC_HAVE_LIBCEED
     44:   PetscFunctionBegin;
     45:   PetscCall(DMGetCeed(dm, &ceed));
     46:   PetscCheck(sd, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "This DM has no CEED data. Call DMCeedCreate() before computing the residual.");
     47:   if (time == 0.) PetscCall(DMCeedComputeGeometry(dm, sd));
     48:   PetscCall(DMGetField(dm, 0, NULL, (PetscObject *)&fv));
     49:   PetscCall(DMPlexInsertBoundaryValuesFVM(dm, fv, locX, time, NULL));
     50:   PetscCall(DMGetLocalVector(dm, &locF));
     51:   PetscCall(VecZeroEntries(locF));
     52:   PetscCall(VecGetCeedVectorRead(locX, ceed, &clocX));
     53:   PetscCall(VecGetCeedVector(locF, ceed, &clocF));
     54:   PetscCallCEED(CeedOperatorApplyAdd(sd->op, clocX, clocF, CEED_REQUEST_IMMEDIATE));
     55:   PetscCall(VecRestoreCeedVectorRead(locX, &clocX));
     56:   PetscCall(VecRestoreCeedVector(locF, &clocF));
     57:   PetscCall(DMLocalToGlobalBegin(dm, locF, ADD_VALUES, F));
     58:   PetscCall(DMLocalToGlobalEnd(dm, locF, ADD_VALUES, F));
     59:   PetscCall(DMRestoreLocalVector(dm, &locF));
     60:   PetscCall(VecViewFromOptions(F, NULL, "-fv_rhs_view"));
     61:   PetscFunctionReturn(PETSC_SUCCESS);
     62: #else
     63:   SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "This requires libCEED. Reconfigure using --download-libceed");
     64: #endif
     65: }

     67: /*@
     68:   DMPlexTSComputeRHSFunctionFVM - Form the forcing `F` from the local input `locX` using pointwise functions specified by the user

     70:   Input Parameters:
     71: + dm   - The mesh
     72: . time - The time
     73: . locX - Local solution
     74: - user - The user context

     76:   Output Parameter:
     77: . F - Global output vector

     79:   Level: developer

     81: .seealso: [](ch_ts), `DMPLEX`, `TS`, `DMPlexComputeJacobianActionFEM()`
     82: @*/
     83: PetscErrorCode DMPlexTSComputeRHSFunctionFVM(DM dm, PetscReal time, Vec locX, Vec F, void *user)
     84: {
     85:   Vec          locF;
     86:   IS           cellIS;
     87:   DM           plex;
     88:   PetscInt     depth;
     89:   PetscFormKey key = {NULL, 0, 0, 0};

     91:   PetscFunctionBegin;
     92:   PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
     93:   PetscCall(DMPlexGetDepth(plex, &depth));
     94:   PetscCall(DMGetStratumIS(plex, "dim", depth, &cellIS));
     95:   if (!cellIS) PetscCall(DMGetStratumIS(plex, "depth", depth, &cellIS));
     96:   PetscCall(DMGetLocalVector(plex, &locF));
     97:   PetscCall(VecZeroEntries(locF));
     98:   PetscCall(DMPlexComputeResidual_Internal(plex, key, cellIS, time, locX, NULL, time, locF, user));
     99:   PetscCall(DMLocalToGlobalBegin(plex, locF, ADD_VALUES, F));
    100:   PetscCall(DMLocalToGlobalEnd(plex, locF, ADD_VALUES, F));
    101:   PetscCall(DMRestoreLocalVector(plex, &locF));
    102:   PetscCall(ISDestroy(&cellIS));
    103:   PetscCall(DMDestroy(&plex));
    104:   PetscCall(VecViewFromOptions(F, NULL, "-fv_rhs_view"));
    105:   PetscFunctionReturn(PETSC_SUCCESS);
    106: }

    108: /*@
    109:   DMPlexTSComputeBoundary - Insert the essential boundary values into the local input `locX` and/or its time derivative `locX_t` using pointwise functions specified by the user

    111:   Input Parameters:
    112: + dm     - The mesh
    113: . time   - The time
    114: . locX   - Local solution
    115: . locX_t - Local solution time derivative, or `NULL`
    116: - user   - The user context

    118:   Level: developer

    120: .seealso: [](ch_ts), `DMPLEX`, `TS`, `DMPlexComputeJacobianActionFEM()`
    121: @*/
    122: PetscErrorCode DMPlexTSComputeBoundary(DM dm, PetscReal time, Vec locX, Vec locX_t, void *user)
    123: {
    124:   DM       plex;
    125:   Vec      faceGeometryFVM = NULL;
    126:   PetscInt Nf, f;

    128:   PetscFunctionBegin;
    129:   PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
    130:   PetscCall(DMGetNumFields(plex, &Nf));
    131:   if (!locX_t) {
    132:     /* This is the RHS part */
    133:     for (f = 0; f < Nf; f++) {
    134:       PetscObject  obj;
    135:       PetscClassId id;

    137:       PetscCall(DMGetField(plex, f, NULL, &obj));
    138:       PetscCall(PetscObjectGetClassId(obj, &id));
    139:       if (id == PETSCFV_CLASSID) {
    140:         PetscCall(DMPlexGetGeometryFVM(plex, &faceGeometryFVM, NULL, NULL));
    141:         break;
    142:       }
    143:     }
    144:   }
    145:   PetscCall(DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, time, faceGeometryFVM, NULL, NULL));
    146:   PetscCall(DMPlexInsertTimeDerivativeBoundaryValues(plex, PETSC_TRUE, locX_t, time, faceGeometryFVM, NULL, NULL));
    147:   PetscCall(DMDestroy(&plex));
    148:   PetscFunctionReturn(PETSC_SUCCESS);
    149: }

    151: /*@
    152:   DMPlexTSComputeIFunctionFEM - Form the local residual `locF` from the local input `locX` using pointwise functions specified by the user

    154:   Input Parameters:
    155: + dm     - The mesh
    156: . time   - The time
    157: . locX   - Local solution
    158: . locX_t - Local solution time derivative, or `NULL`
    159: - user   - The user context

    161:   Output Parameter:
    162: . locF - Local output vector

    164:   Level: developer

    166: .seealso: [](ch_ts), `DMPLEX`, `TS`, `DMPlexTSComputeRHSFunctionFEM()`
    167: @*/
    168: PetscErrorCode DMPlexTSComputeIFunctionFEM(DM dm, PetscReal time, Vec locX, Vec locX_t, Vec locF, void *user)
    169: {
    170:   DM       plex;
    171:   IS       allcellIS;
    172:   PetscInt Nds, s;

    174:   PetscFunctionBegin;
    175:   PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
    176:   PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS));
    177:   PetscCall(DMGetNumDS(dm, &Nds));
    178:   for (s = 0; s < Nds; ++s) {
    179:     PetscDS      ds;
    180:     IS           cellIS;
    181:     PetscFormKey key;

    183:     PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds, NULL));
    184:     key.value = 0;
    185:     key.field = 0;
    186:     key.part  = 0;
    187:     if (!key.label) {
    188:       PetscCall(PetscObjectReference((PetscObject)allcellIS));
    189:       cellIS = allcellIS;
    190:     } else {
    191:       IS pointIS;

    193:       key.value = 1;
    194:       PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS));
    195:       PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS));
    196:       PetscCall(ISDestroy(&pointIS));
    197:     }
    198:     PetscCall(DMPlexComputeResidual_Internal(plex, key, cellIS, time, locX, locX_t, time, locF, user));
    199:     PetscCall(ISDestroy(&cellIS));
    200:   }
    201:   PetscCall(ISDestroy(&allcellIS));
    202:   PetscCall(DMDestroy(&plex));
    203:   PetscFunctionReturn(PETSC_SUCCESS);
    204: }

    206: /*@
    207:   DMPlexTSComputeIJacobianFEM - Form the Jacobian `Jac` from the local input `locX` using pointwise functions specified by the user

    209:   Input Parameters:
    210: + dm       - The mesh
    211: . time     - The time
    212: . locX     - Local solution
    213: . locX_t   - Local solution time derivative, or `NULL`
    214: . X_tShift - The multiplicative parameter for dF/du_t
    215: - user     - The user context

    217:   Output Parameters:
    218: + Jac  - the Jacobian
    219: - JacP - an additional approximation for the Jacobian to be used to compute the preconditioner (often is `Jac`)

    221:   Level: developer

    223: .seealso: [](ch_ts), `TS`, `DM`, `DMPlexTSComputeIFunctionFEM()`, `DMPlexTSComputeRHSFunctionFEM()`
    224: @*/
    225: PetscErrorCode DMPlexTSComputeIJacobianFEM(DM dm, PetscReal time, Vec locX, Vec locX_t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
    226: {
    227:   DM        plex;
    228:   IS        allcellIS;
    229:   PetscBool hasJac, hasPrec;
    230:   PetscInt  Nds, s;

    232:   PetscFunctionBegin;
    233:   PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
    234:   PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS));
    235:   PetscCall(DMGetNumDS(dm, &Nds));
    236:   for (s = 0; s < Nds; ++s) {
    237:     PetscDS      ds;
    238:     IS           cellIS;
    239:     PetscFormKey key;

    241:     PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds, NULL));
    242:     key.value = 0;
    243:     key.field = 0;
    244:     key.part  = 0;
    245:     if (!key.label) {
    246:       PetscCall(PetscObjectReference((PetscObject)allcellIS));
    247:       cellIS = allcellIS;
    248:     } else {
    249:       IS pointIS;

    251:       key.value = 1;
    252:       PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS));
    253:       PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS));
    254:       PetscCall(ISDestroy(&pointIS));
    255:     }
    256:     if (!s) {
    257:       PetscCall(PetscDSHasJacobian(ds, &hasJac));
    258:       PetscCall(PetscDSHasJacobianPreconditioner(ds, &hasPrec));
    259:       if (hasJac && hasPrec) PetscCall(MatZeroEntries(Jac));
    260:       PetscCall(MatZeroEntries(JacP));
    261:     }
    262:     PetscCall(DMPlexComputeJacobian_Internal(plex, key, cellIS, time, X_tShift, locX, locX_t, Jac, JacP, user));
    263:     PetscCall(ISDestroy(&cellIS));
    264:   }
    265:   PetscCall(ISDestroy(&allcellIS));
    266:   PetscCall(DMDestroy(&plex));
    267:   PetscFunctionReturn(PETSC_SUCCESS);
    268: }

    270: /*@
    271:   DMPlexTSComputeRHSFunctionFEM - Form the local residual `locG` from the local input `locX` using pointwise functions specified by the user

    273:   Input Parameters:
    274: + dm   - The mesh
    275: . time - The time
    276: . locX - Local solution
    277: - user - The user context

    279:   Output Parameter:
    280: . locG - Local output vector

    282:   Level: developer

    284: .seealso: [](ch_ts), `TS`, `DM`, `DMPlexTSComputeIFunctionFEM()`, `DMPlexTSComputeIJacobianFEM()`
    285: @*/
    286: PetscErrorCode DMPlexTSComputeRHSFunctionFEM(DM dm, PetscReal time, Vec locX, Vec locG, void *user)
    287: {
    288:   DM       plex;
    289:   IS       allcellIS;
    290:   PetscInt Nds, s;

    292:   PetscFunctionBegin;
    293:   PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
    294:   PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS));
    295:   PetscCall(DMGetNumDS(dm, &Nds));
    296:   for (s = 0; s < Nds; ++s) {
    297:     PetscDS      ds;
    298:     IS           cellIS;
    299:     PetscFormKey key;

    301:     PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds, NULL));
    302:     key.value = 0;
    303:     key.field = 0;
    304:     key.part  = 100;
    305:     if (!key.label) {
    306:       PetscCall(PetscObjectReference((PetscObject)allcellIS));
    307:       cellIS = allcellIS;
    308:     } else {
    309:       IS pointIS;

    311:       key.value = 1;
    312:       PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS));
    313:       PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS));
    314:       PetscCall(ISDestroy(&pointIS));
    315:     }
    316:     PetscCall(DMPlexComputeResidual_Internal(plex, key, cellIS, time, locX, NULL, time, locG, user));
    317:     PetscCall(ISDestroy(&cellIS));
    318:   }
    319:   PetscCall(ISDestroy(&allcellIS));
    320:   PetscCall(DMDestroy(&plex));
    321:   PetscFunctionReturn(PETSC_SUCCESS);
    322: }

    324: /*@
    325:   DMTSCheckResidual - Check the residual of the exact solution

    327:   Input Parameters:
    328: + ts  - the `TS` object
    329: . dm  - the `DM`
    330: . t   - the time
    331: . u   - a `DM` vector
    332: . u_t - a `DM` vector
    333: - tol - A tolerance for the check, or -1 to print the results instead

    335:   Output Parameter:
    336: . residual - The residual norm of the exact solution, or `NULL`

    338:   Level: developer

    340: .seealso: [](ch_ts), `DM`, `DMTSCheckFromOptions()`, `DMTSCheckJacobian()`, `DNSNESCheckFromOptions()`, `DMSNESCheckDiscretization()`, `DMSNESCheckJacobian()`
    341: @*/
    342: PetscErrorCode DMTSCheckResidual(TS ts, DM dm, PetscReal t, Vec u, Vec u_t, PetscReal tol, PetscReal *residual)
    343: {
    344:   MPI_Comm  comm;
    345:   Vec       r;
    346:   PetscReal res;

    348:   PetscFunctionBegin;
    352:   if (residual) PetscAssertPointer(residual, 7);
    353:   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
    354:   PetscCall(DMComputeExactSolution(dm, t, u, u_t));
    355:   PetscCall(VecDuplicate(u, &r));
    356:   PetscCall(TSComputeIFunction(ts, t, u, u_t, r, PETSC_FALSE));
    357:   PetscCall(VecNorm(r, NORM_2, &res));
    358:   if (tol >= 0.0) {
    359:     PetscCheck(res <= tol, comm, PETSC_ERR_ARG_WRONG, "L_2 Residual %g exceeds tolerance %g", (double)res, (double)tol);
    360:   } else if (residual) {
    361:     *residual = res;
    362:   } else {
    363:     PetscCall(PetscPrintf(comm, "L_2 Residual: %g\n", (double)res));
    364:     PetscCall(VecFilter(r, 1.0e-10));
    365:     PetscCall(PetscObjectCompose((PetscObject)r, "__Vec_bc_zero__", (PetscObject)dm));
    366:     PetscCall(PetscObjectSetName((PetscObject)r, "Initial Residual"));
    367:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)r, "res_"));
    368:     PetscCall(VecViewFromOptions(r, NULL, "-vec_view"));
    369:     PetscCall(PetscObjectCompose((PetscObject)r, "__Vec_bc_zero__", NULL));
    370:   }
    371:   PetscCall(VecDestroy(&r));
    372:   PetscFunctionReturn(PETSC_SUCCESS);
    373: }

    375: /*@
    376:   DMTSCheckJacobian - Check the Jacobian of the exact solution against the residual using the Taylor Test

    378:   Input Parameters:
    379: + ts  - the `TS` object
    380: . dm  - the `DM`
    381: . t   - the time
    382: . u   - a `DM` vector
    383: . u_t - a `DM` vector
    384: - tol - A tolerance for the check, or -1 to print the results instead

    386:   Output Parameters:
    387: + isLinear - Flag indicaing that the function looks linear, or `NULL`
    388: - convRate - The rate of convergence of the linear model, or `NULL`

    390:   Level: developer

    392: .seealso: [](ch_ts), `DNTSCheckFromOptions()`, `DMTSCheckResidual()`, `DNSNESCheckFromOptions()`, `DMSNESCheckDiscretization()`, `DMSNESCheckResidual()`
    393: @*/
    394: PetscErrorCode DMTSCheckJacobian(TS ts, DM dm, PetscReal t, Vec u, Vec u_t, PetscReal tol, PetscBool *isLinear, PetscReal *convRate)
    395: {
    396:   MPI_Comm     comm;
    397:   PetscDS      ds;
    398:   Mat          J, M;
    399:   MatNullSpace nullspace;
    400:   PetscReal    dt, shift, slope, intercept;
    401:   PetscBool    hasJac, hasPrec, isLin = PETSC_FALSE;

    403:   PetscFunctionBegin;
    407:   if (isLinear) PetscAssertPointer(isLinear, 7);
    408:   if (convRate) PetscAssertPointer(convRate, 8);
    409:   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
    410:   PetscCall(DMComputeExactSolution(dm, t, u, u_t));
    411:   /* Create and view matrices */
    412:   PetscCall(TSGetTimeStep(ts, &dt));
    413:   shift = 1.0 / dt;
    414:   PetscCall(DMCreateMatrix(dm, &J));
    415:   PetscCall(DMGetDS(dm, &ds));
    416:   PetscCall(PetscDSHasJacobian(ds, &hasJac));
    417:   PetscCall(PetscDSHasJacobianPreconditioner(ds, &hasPrec));
    418:   if (hasJac && hasPrec) {
    419:     PetscCall(DMCreateMatrix(dm, &M));
    420:     PetscCall(TSComputeIJacobian(ts, t, u, u_t, shift, J, M, PETSC_FALSE));
    421:     PetscCall(PetscObjectSetName((PetscObject)M, "Preconditioning Matrix"));
    422:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "jacpre_"));
    423:     PetscCall(MatViewFromOptions(M, NULL, "-mat_view"));
    424:     PetscCall(MatDestroy(&M));
    425:   } else {
    426:     PetscCall(TSComputeIJacobian(ts, t, u, u_t, shift, J, J, PETSC_FALSE));
    427:   }
    428:   PetscCall(PetscObjectSetName((PetscObject)J, "Jacobian"));
    429:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)J, "jac_"));
    430:   PetscCall(MatViewFromOptions(J, NULL, "-mat_view"));
    431:   /* Check nullspace */
    432:   PetscCall(MatGetNullSpace(J, &nullspace));
    433:   if (nullspace) {
    434:     PetscBool isNull;
    435:     PetscCall(MatNullSpaceTest(nullspace, J, &isNull));
    436:     PetscCheck(isNull, comm, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
    437:   }
    438:   /* Taylor test */
    439:   {
    440:     PetscRandom rand;
    441:     Vec         du, uhat, uhat_t, r, rhat, df;
    442:     PetscReal   h;
    443:     PetscReal  *es, *hs, *errors;
    444:     PetscReal   hMax = 1.0, hMin = 1e-6, hMult = 0.1;
    445:     PetscInt    Nv, v;

    447:     /* Choose a perturbation direction */
    448:     PetscCall(PetscRandomCreate(comm, &rand));
    449:     PetscCall(VecDuplicate(u, &du));
    450:     PetscCall(VecSetRandom(du, rand));
    451:     PetscCall(PetscRandomDestroy(&rand));
    452:     PetscCall(VecDuplicate(u, &df));
    453:     PetscCall(MatMult(J, du, df));
    454:     /* Evaluate residual at u, F(u), save in vector r */
    455:     PetscCall(VecDuplicate(u, &r));
    456:     PetscCall(TSComputeIFunction(ts, t, u, u_t, r, PETSC_FALSE));
    457:     /* Look at the convergence of our Taylor approximation as we approach u */
    458:     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv);
    459:     PetscCall(PetscCalloc3(Nv, &es, Nv, &hs, Nv, &errors));
    460:     PetscCall(VecDuplicate(u, &uhat));
    461:     PetscCall(VecDuplicate(u, &uhat_t));
    462:     PetscCall(VecDuplicate(u, &rhat));
    463:     for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv) {
    464:       PetscCall(VecWAXPY(uhat, h, du, u));
    465:       PetscCall(VecWAXPY(uhat_t, h * shift, du, u_t));
    466:       /* F(\hat u, \hat u_t) \approx F(u, u_t) + J(u, u_t) (uhat - u) + J_t(u, u_t) (uhat_t - u_t) = F(u) + h * J(u) du + h * shift * J_t(u) du = F(u) + h F' du */
    467:       PetscCall(TSComputeIFunction(ts, t, uhat, uhat_t, rhat, PETSC_FALSE));
    468:       PetscCall(VecAXPBYPCZ(rhat, -1.0, -h, 1.0, r, df));
    469:       PetscCall(VecNorm(rhat, NORM_2, &errors[Nv]));

    471:       es[Nv] = PetscLog10Real(errors[Nv]);
    472:       hs[Nv] = PetscLog10Real(h);
    473:     }
    474:     PetscCall(VecDestroy(&uhat));
    475:     PetscCall(VecDestroy(&uhat_t));
    476:     PetscCall(VecDestroy(&rhat));
    477:     PetscCall(VecDestroy(&df));
    478:     PetscCall(VecDestroy(&r));
    479:     PetscCall(VecDestroy(&du));
    480:     for (v = 0; v < Nv; ++v) {
    481:       if ((tol >= 0) && (errors[v] > tol)) break;
    482:       else if (errors[v] > PETSC_SMALL) break;
    483:     }
    484:     if (v == Nv) isLin = PETSC_TRUE;
    485:     PetscCall(PetscLinearRegression(Nv, hs, es, &slope, &intercept));
    486:     PetscCall(PetscFree3(es, hs, errors));
    487:     /* Slope should be about 2 */
    488:     if (tol >= 0) {
    489:       PetscCheck(isLin || PetscAbsReal(2 - slope) <= tol, comm, PETSC_ERR_ARG_WRONG, "Taylor approximation convergence rate should be 2, not %0.2f", (double)slope);
    490:     } else if (isLinear || convRate) {
    491:       if (isLinear) *isLinear = isLin;
    492:       if (convRate) *convRate = slope;
    493:     } else {
    494:       if (!isLin) PetscCall(PetscPrintf(comm, "Taylor approximation converging at order %3.2f\n", (double)slope));
    495:       else PetscCall(PetscPrintf(comm, "Function appears to be linear\n"));
    496:     }
    497:   }
    498:   PetscCall(MatDestroy(&J));
    499:   PetscFunctionReturn(PETSC_SUCCESS);
    500: }

    502: /*@C
    503:   DMTSCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information based on
    504:   values in the options database

    506:   Input Parameters:
    507: + ts - the `TS` object
    508: - u  - representative `TS` vector

    510:   Level: developer

    512:   Note:
    513:   The user must call `PetscDSSetExactSolution()` beforehand

    515:   Developer Notes:
    516:   What is the purpose of `u`, does it need to already have a solution or some other value in it?

    518: .seealso: `DMTS`
    519: @*/
    520: PetscErrorCode DMTSCheckFromOptions(TS ts, Vec u)
    521: {
    522:   DM        dm;
    523:   SNES      snes;
    524:   Vec       sol, u_t;
    525:   PetscReal t;
    526:   PetscBool check;

    528:   PetscFunctionBegin;
    529:   PetscCall(PetscOptionsHasName(((PetscObject)ts)->options, ((PetscObject)ts)->prefix, "-dmts_check", &check));
    530:   if (!check) PetscFunctionReturn(PETSC_SUCCESS);
    531:   PetscCall(VecDuplicate(u, &sol));
    532:   PetscCall(VecCopy(u, sol));
    533:   PetscCall(TSSetSolution(ts, u));
    534:   PetscCall(TSGetDM(ts, &dm));
    535:   PetscCall(TSSetUp(ts));
    536:   PetscCall(TSGetSNES(ts, &snes));
    537:   PetscCall(SNESSetSolution(snes, u));

    539:   PetscCall(TSGetTime(ts, &t));
    540:   PetscCall(DMSNESCheckDiscretization(snes, dm, t, sol, -1.0, NULL));
    541:   PetscCall(DMGetGlobalVector(dm, &u_t));
    542:   PetscCall(DMTSCheckResidual(ts, dm, t, sol, u_t, -1.0, NULL));
    543:   PetscCall(DMTSCheckJacobian(ts, dm, t, sol, u_t, -1.0, NULL, NULL));
    544:   PetscCall(DMRestoreGlobalVector(dm, &u_t));

    546:   PetscCall(VecDestroy(&sol));
    547:   PetscFunctionReturn(PETSC_SUCCESS);
    548: }