Actual source code: fe.c

  1: /* Basis Jet Tabulation

  3: We would like to tabulate the nodal basis functions and derivatives at a set of points, usually quadrature points. We
  4: follow here the derviation in http://www.math.ttu.edu/~kirby/papers/fiat-toms-2004.pdf. The nodal basis $\psi_i$ can
  5: be expressed in terms of a prime basis $\phi_i$ which can be stably evaluated. In PETSc, we will use the Legendre basis
  6: as a prime basis.

  8:   \psi_i = \sum_k \alpha_{ki} \phi_k

 10: Our nodal basis is defined in terms of the dual basis $n_j$

 12:   n_j \cdot \psi_i = \delta_{ji}

 14: and we may act on the first equation to obtain

 16:   n_j \cdot \psi_i = \sum_k \alpha_{ki} n_j \cdot \phi_k
 17:        \delta_{ji} = \sum_k \alpha_{ki} V_{jk}
 18:                  I = V \alpha

 20: so the coefficients of the nodal basis in the prime basis are

 22:    \alpha = V^{-1}

 24: We will define the dual basis vectors $n_j$ using a quadrature rule.

 26: Right now, we will just use the polynomial spaces P^k. I know some elements use the space of symmetric polynomials
 27: (I think Nedelec), but we will neglect this for now. Constraints in the space, e.g. Arnold-Winther elements, can
 28: be implemented exactly as in FIAT using functionals $L_j$.

 30: I will have to count the degrees correctly for the Legendre product when we are on simplices.

 32: We will have three objects:
 33:  - Space, P: this just need point evaluation I think
 34:  - Dual Space, P'+K: This looks like a set of functionals that can act on members of P, each n is defined by a Q
 35:  - FEM: This keeps {P, P', Q}
 36: */
 37: #include <petsc/private/petscfeimpl.h>
 38: #include <petscdmplex.h>

 40: PetscBool  FEcite       = PETSC_FALSE;
 41: const char FECitation[] = "@article{kirby2004,\n"
 42:                           "  title   = {Algorithm 839: FIAT, a New Paradigm for Computing Finite Element Basis Functions},\n"
 43:                           "  journal = {ACM Transactions on Mathematical Software},\n"
 44:                           "  author  = {Robert C. Kirby},\n"
 45:                           "  volume  = {30},\n"
 46:                           "  number  = {4},\n"
 47:                           "  pages   = {502--516},\n"
 48:                           "  doi     = {10.1145/1039813.1039820},\n"
 49:                           "  year    = {2004}\n}\n";

 51: PetscClassId PETSCFE_CLASSID = 0;

 53: PetscLogEvent PETSCFE_SetUp;

 55: PetscFunctionList PetscFEList              = NULL;
 56: PetscBool         PetscFERegisterAllCalled = PETSC_FALSE;

 58: /*@C
 59:   PetscFERegister - Adds a new `PetscFEType`

 61:   Not Collective, No Fortran Support

 63:   Input Parameters:
 64: + sname    - The name of a new user-defined creation routine
 65: - function - The creation routine

 67:   Example Usage:
 68: .vb
 69:     PetscFERegister("my_fe", MyPetscFECreate);
 70: .ve

 72:   Then, your PetscFE type can be chosen with the procedural interface via
 73: .vb
 74:     PetscFECreate(MPI_Comm, PetscFE *);
 75:     PetscFESetType(PetscFE, "my_fe");
 76: .ve
 77:   or at runtime via the option
 78: .vb
 79:     -petscfe_type my_fe
 80: .ve

 82:   Level: advanced

 84:   Note:
 85:   `PetscFERegister()` may be called multiple times to add several user-defined `PetscFE`s

 87: .seealso: `PetscFE`, `PetscFEType`, `PetscFERegisterAll()`, `PetscFERegisterDestroy()`
 88: @*/
 89: PetscErrorCode PetscFERegister(const char sname[], PetscErrorCode (*function)(PetscFE))
 90: {
 91:   PetscFunctionBegin;
 92:   PetscCall(PetscFunctionListAdd(&PetscFEList, sname, function));
 93:   PetscFunctionReturn(PETSC_SUCCESS);
 94: }

 96: /*@
 97:   PetscFESetType - Builds a particular `PetscFE`

 99:   Collective

101:   Input Parameters:
102: + fem  - The `PetscFE` object
103: - name - The kind of FEM space

105:   Options Database Key:
106: . -petscfe_type type - Sets the `PetscFE` type; use -help for a list of available types

108:   Level: intermediate

110: .seealso: `PetscFEType`, `PetscFE`, `PetscFEGetType()`, `PetscFECreate()`
111: @*/
112: PetscErrorCode PetscFESetType(PetscFE fem, PetscFEType name)
113: {
114:   PetscErrorCode (*r)(PetscFE);
115:   PetscBool match;

117:   PetscFunctionBegin;
119:   PetscCall(PetscObjectTypeCompare((PetscObject)fem, name, &match));
120:   if (match) PetscFunctionReturn(PETSC_SUCCESS);

122:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());
123:   PetscCall(PetscFunctionListFind(PetscFEList, name, &r));
124:   PetscCheck(r, PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscFE type: %s", name);

126:   PetscTryTypeMethod(fem, destroy);
127:   fem->ops->destroy = NULL;

129:   PetscCall((*r)(fem));
130:   PetscCall(PetscObjectChangeTypeName((PetscObject)fem, name));
131:   PetscFunctionReturn(PETSC_SUCCESS);
132: }

134: /*@
135:   PetscFEGetType - Gets the `PetscFEType` (as a string) from the `PetscFE` object.

137:   Not Collective

139:   Input Parameter:
140: . fem - The `PetscFE`

142:   Output Parameter:
143: . name - The `PetscFEType` name

145:   Level: intermediate

147: .seealso: `PetscFEType`, `PetscFE`, `PetscFESetType()`, `PetscFECreate()`
148: @*/
149: PetscErrorCode PetscFEGetType(PetscFE fem, PetscFEType *name)
150: {
151:   PetscFunctionBegin;
153:   PetscAssertPointer(name, 2);
154:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());
155:   *name = ((PetscObject)fem)->type_name;
156:   PetscFunctionReturn(PETSC_SUCCESS);
157: }

159: /*@
160:   PetscFEViewFromOptions - View from a `PetscFE` based on values in the options database

162:   Collective

164:   Input Parameters:
165: + A    - the `PetscFE` object
166: . obj  - Optional object that provides the options prefix, pass `NULL` to use the options prefix of `A`
167: - name - command line option name

169:   Level: intermediate

171: .seealso: `PetscFE`, `PetscFEView()`, `PetscObjectViewFromOptions()`, `PetscFECreate()`
172: @*/
173: PetscErrorCode PetscFEViewFromOptions(PetscFE A, PeOp PetscObject obj, const char name[])
174: {
175:   PetscFunctionBegin;
177:   PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
178:   PetscFunctionReturn(PETSC_SUCCESS);
179: }

181: /*@
182:   PetscFEView - Views a `PetscFE`

184:   Collective

186:   Input Parameters:
187: + fem    - the `PetscFE` object to view
188: - viewer - the viewer

190:   Level: beginner

192: .seealso: `PetscFE`, `PetscViewer`, `PetscFEDestroy()`, `PetscFEViewFromOptions()`
193: @*/
194: PetscErrorCode PetscFEView(PetscFE fem, PetscViewer viewer)
195: {
196:   PetscBool isascii;

198:   PetscFunctionBegin;
201:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)fem), &viewer));
202:   PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)fem, viewer));
203:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
204:   PetscTryTypeMethod(fem, view, viewer);
205:   PetscFunctionReturn(PETSC_SUCCESS);
206: }

208: /*@
209:   PetscFESetFromOptions - sets parameters in a `PetscFE` from the options database

211:   Collective

213:   Input Parameter:
214: . fem - the `PetscFE` object to set options for

216:   Options Database Keys:
217: + -petscfe_num_blocks  - the number of cell blocks to integrate concurrently
218: - -petscfe_num_batches - the number of cell batches to integrate serially

220:   Level: intermediate

222: .seealso: `PetscFE`, `PetscFEView()`
223: @*/
224: PetscErrorCode PetscFESetFromOptions(PetscFE fem)
225: {
226:   const char *defaultType;
227:   char        name[256];
228:   PetscBool   flg;

230:   PetscFunctionBegin;
232:   if (!((PetscObject)fem)->type_name) defaultType = PETSCFEBASIC;
233:   else defaultType = ((PetscObject)fem)->type_name;
234:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());

236:   PetscObjectOptionsBegin((PetscObject)fem);
237:   PetscCall(PetscOptionsFList("-petscfe_type", "Finite element space", "PetscFESetType", PetscFEList, defaultType, name, 256, &flg));
238:   if (flg) PetscCall(PetscFESetType(fem, name));
239:   else if (!((PetscObject)fem)->type_name) PetscCall(PetscFESetType(fem, defaultType));
240:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_blocks", "The number of cell blocks to integrate concurrently", "PetscSpaceSetTileSizes", fem->numBlocks, &fem->numBlocks, NULL, 1));
241:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_batches", "The number of cell batches to integrate serially", "PetscSpaceSetTileSizes", fem->numBatches, &fem->numBatches, NULL, 1));
242:   PetscTryTypeMethod(fem, setfromoptions, PetscOptionsObject);
243:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
244:   PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)fem, PetscOptionsObject));
245:   PetscOptionsEnd();
246:   PetscCall(PetscFEViewFromOptions(fem, NULL, "-petscfe_view"));
247:   PetscFunctionReturn(PETSC_SUCCESS);
248: }

250: /*@
251:   PetscFESetUp - Construct data structures for the `PetscFE` after the `PetscFEType` has been set

253:   Collective

255:   Input Parameter:
256: . fem - the `PetscFE` object to setup

258:   Level: intermediate

260: .seealso: `PetscFE`, `PetscFEView()`, `PetscFEDestroy()`
261: @*/
262: PetscErrorCode PetscFESetUp(PetscFE fem)
263: {
264:   PetscFunctionBegin;
266:   if (fem->setupcalled) PetscFunctionReturn(PETSC_SUCCESS);
267:   PetscCall(PetscLogEventBegin(PETSCFE_SetUp, fem, 0, 0, 0));
268:   fem->setupcalled = PETSC_TRUE;
269:   PetscTryTypeMethod(fem, setup);
270:   PetscCall(PetscLogEventEnd(PETSCFE_SetUp, fem, 0, 0, 0));
271:   PetscFunctionReturn(PETSC_SUCCESS);
272: }

274: /*@
275:   PetscFEDestroy - Destroys a `PetscFE` object

277:   Collective

279:   Input Parameter:
280: . fem - the `PetscFE` object to destroy

282:   Level: beginner

284: .seealso: `PetscFE`, `PetscFEView()`
285: @*/
286: PetscErrorCode PetscFEDestroy(PetscFE *fem)
287: {
288:   PetscFunctionBegin;
289:   if (!*fem) PetscFunctionReturn(PETSC_SUCCESS);

292:   if (--((PetscObject)*fem)->refct > 0) {
293:     *fem = NULL;
294:     PetscFunctionReturn(PETSC_SUCCESS);
295:   }
296:   ((PetscObject)*fem)->refct = 0;

298:   if ((*fem)->subspaces) {
299:     PetscInt dim, d;

301:     PetscCall(PetscDualSpaceGetDimension((*fem)->dualSpace, &dim));
302:     for (d = 0; d < dim; ++d) PetscCall(PetscFEDestroy(&(*fem)->subspaces[d]));
303:   }
304:   PetscCall(PetscFree((*fem)->subspaces));
305:   PetscCall(PetscFree((*fem)->invV));
306:   PetscCall(PetscTabulationDestroy(&(*fem)->T));
307:   PetscCall(PetscTabulationDestroy(&(*fem)->Tf));
308:   PetscCall(PetscTabulationDestroy(&(*fem)->Tc));
309:   PetscCall(PetscSpaceDestroy(&(*fem)->basisSpace));
310:   PetscCall(PetscDualSpaceDestroy(&(*fem)->dualSpace));
311:   PetscCall(PetscQuadratureDestroy(&(*fem)->quadrature));
312:   PetscCall(PetscQuadratureDestroy(&(*fem)->faceQuadrature));
313: #ifdef PETSC_HAVE_LIBCEED
314:   PetscCallCEED(CeedBasisDestroy(&(*fem)->ceedBasis));
315:   PetscCallCEED(CeedDestroy(&(*fem)->ceed));
316: #endif

318:   PetscTryTypeMethod(*fem, destroy);
319:   PetscCall(PetscHeaderDestroy(fem));
320:   PetscFunctionReturn(PETSC_SUCCESS);
321: }

323: /*@
324:   PetscFECreate - Creates an empty `PetscFE` object. The type can then be set with `PetscFESetType()`.

326:   Collective

328:   Input Parameter:
329: . comm - The communicator for the `PetscFE` object

331:   Output Parameter:
332: . fem - The `PetscFE` object

334:   Level: beginner

336: .seealso: `PetscFE`, `PetscFEType`, `PetscFESetType()`, `PetscFECreateDefault()`, `PETSCFEGALERKIN`
337: @*/
338: PetscErrorCode PetscFECreate(MPI_Comm comm, PetscFE *fem)
339: {
340:   PetscFE f;

342:   PetscFunctionBegin;
343:   PetscAssertPointer(fem, 2);
344:   PetscCall(PetscCitationsRegister(FECitation, &FEcite));
345:   PetscCall(PetscFEInitializePackage());

347:   PetscCall(PetscHeaderCreate(f, PETSCFE_CLASSID, "PetscFE", "Finite Element", "PetscFE", comm, PetscFEDestroy, PetscFEView));

349:   f->basisSpace    = NULL;
350:   f->dualSpace     = NULL;
351:   f->numComponents = 1;
352:   f->subspaces     = NULL;
353:   f->invV          = NULL;
354:   f->T             = NULL;
355:   f->Tf            = NULL;
356:   f->Tc            = NULL;
357:   PetscCall(PetscArrayzero(&f->quadrature, 1));
358:   PetscCall(PetscArrayzero(&f->faceQuadrature, 1));
359:   f->blockSize  = 0;
360:   f->numBlocks  = 1;
361:   f->batchSize  = 0;
362:   f->numBatches = 1;

364:   *fem = f;
365:   PetscFunctionReturn(PETSC_SUCCESS);
366: }

368: /*@
369:   PetscFEGetSpatialDimension - Returns the spatial dimension of the element

371:   Not Collective

373:   Input Parameter:
374: . fem - The `PetscFE` object

376:   Output Parameter:
377: . dim - The spatial dimension

379:   Level: intermediate

381: .seealso: `PetscFE`, `PetscFECreate()`
382: @*/
383: PetscErrorCode PetscFEGetSpatialDimension(PetscFE fem, PetscInt *dim)
384: {
385:   DM dm;

387:   PetscFunctionBegin;
389:   PetscAssertPointer(dim, 2);
390:   PetscCall(PetscDualSpaceGetDM(fem->dualSpace, &dm));
391:   PetscCall(DMGetDimension(dm, dim));
392:   PetscFunctionReturn(PETSC_SUCCESS);
393: }

395: /*@
396:   PetscFESetNumComponents - Sets the number of field components in the element

398:   Not Collective

400:   Input Parameters:
401: + fem  - The `PetscFE` object
402: - comp - The number of field components

404:   Level: intermediate

406: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`, `PetscFEGetNumComponents()`
407: @*/
408: PetscErrorCode PetscFESetNumComponents(PetscFE fem, PetscInt comp)
409: {
410:   PetscFunctionBegin;
412:   fem->numComponents = comp;
413:   PetscFunctionReturn(PETSC_SUCCESS);
414: }

416: /*@
417:   PetscFEGetNumComponents - Returns the number of components in the element

419:   Not Collective

421:   Input Parameter:
422: . fem - The `PetscFE` object

424:   Output Parameter:
425: . comp - The number of field components

427:   Level: intermediate

429: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`
430: @*/
431: PetscErrorCode PetscFEGetNumComponents(PetscFE fem, PetscInt *comp)
432: {
433:   PetscFunctionBegin;
435:   PetscAssertPointer(comp, 2);
436:   *comp = fem->numComponents;
437:   PetscFunctionReturn(PETSC_SUCCESS);
438: }

440: /*@
441:   PetscFESetTileSizes - Sets the tile sizes for evaluation

443:   Not Collective

445:   Input Parameters:
446: + fem        - The `PetscFE` object
447: . blockSize  - The number of elements in a block
448: . numBlocks  - The number of blocks in a batch
449: . batchSize  - The number of elements in a batch
450: - numBatches - The number of batches in a chunk

452:   Level: intermediate

454: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetTileSizes()`
455: @*/
456: PetscErrorCode PetscFESetTileSizes(PetscFE fem, PetscInt blockSize, PetscInt numBlocks, PetscInt batchSize, PetscInt numBatches)
457: {
458:   PetscFunctionBegin;
460:   fem->blockSize  = blockSize;
461:   fem->numBlocks  = numBlocks;
462:   fem->batchSize  = batchSize;
463:   fem->numBatches = numBatches;
464:   PetscFunctionReturn(PETSC_SUCCESS);
465: }

467: /*@
468:   PetscFEGetTileSizes - Returns the tile sizes for evaluation

470:   Not Collective

472:   Input Parameter:
473: . fem - The `PetscFE` object

475:   Output Parameters:
476: + blockSize  - The number of elements in a block, pass `NULL` if not needed
477: . numBlocks  - The number of blocks in a batch, pass `NULL` if not needed
478: . batchSize  - The number of elements in a batch, pass `NULL` if not needed
479: - numBatches - The number of batches in a chunk, pass `NULL` if not needed

481:   Level: intermediate

483: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFESetTileSizes()`
484: @*/
485: PetscErrorCode PetscFEGetTileSizes(PetscFE fem, PeOp PetscInt *blockSize, PeOp PetscInt *numBlocks, PeOp PetscInt *batchSize, PeOp PetscInt *numBatches)
486: {
487:   PetscFunctionBegin;
489:   if (blockSize) PetscAssertPointer(blockSize, 2);
490:   if (numBlocks) PetscAssertPointer(numBlocks, 3);
491:   if (batchSize) PetscAssertPointer(batchSize, 4);
492:   if (numBatches) PetscAssertPointer(numBatches, 5);
493:   if (blockSize) *blockSize = fem->blockSize;
494:   if (numBlocks) *numBlocks = fem->numBlocks;
495:   if (batchSize) *batchSize = fem->batchSize;
496:   if (numBatches) *numBatches = fem->numBatches;
497:   PetscFunctionReturn(PETSC_SUCCESS);
498: }

500: /*@
501:   PetscFEGetBasisSpace - Returns the `PetscSpace` used for the approximation of the solution for the `PetscFE`

503:   Not Collective

505:   Input Parameter:
506: . fem - The `PetscFE` object

508:   Output Parameter:
509: . sp - The `PetscSpace` object

511:   Level: intermediate

513: .seealso: `PetscFE`, `PetscSpace`, `PetscFECreate()`
514: @*/
515: PetscErrorCode PetscFEGetBasisSpace(PetscFE fem, PetscSpace *sp)
516: {
517:   PetscFunctionBegin;
519:   PetscAssertPointer(sp, 2);
520:   *sp = fem->basisSpace;
521:   PetscFunctionReturn(PETSC_SUCCESS);
522: }

524: /*@
525:   PetscFESetBasisSpace - Sets the `PetscSpace` used for the approximation of the solution

527:   Not Collective

529:   Input Parameters:
530: + fem - The `PetscFE` object
531: - sp  - The `PetscSpace` object

533:   Level: intermediate

535:   Developer Notes:
536:   There is `PetscFESetBasisSpace()` but the `PetscFESetDualSpace()`, likely the Basis is unneeded in the function name

538: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetDualSpace()`
539: @*/
540: PetscErrorCode PetscFESetBasisSpace(PetscFE fem, PetscSpace sp)
541: {
542:   PetscFunctionBegin;
545:   PetscCall(PetscSpaceDestroy(&fem->basisSpace));
546:   fem->basisSpace = sp;
547:   PetscCall(PetscObjectReference((PetscObject)fem->basisSpace));
548:   PetscFunctionReturn(PETSC_SUCCESS);
549: }

551: /*@
552:   PetscFEGetDualSpace - Returns the `PetscDualSpace` used to define the inner product for a `PetscFE`

554:   Not Collective

556:   Input Parameter:
557: . fem - The `PetscFE` object

559:   Output Parameter:
560: . sp - The `PetscDualSpace` object

562:   Level: intermediate

564: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
565: @*/
566: PetscErrorCode PetscFEGetDualSpace(PetscFE fem, PetscDualSpace *sp)
567: {
568:   PetscFunctionBegin;
570:   PetscAssertPointer(sp, 2);
571:   *sp = fem->dualSpace;
572:   PetscFunctionReturn(PETSC_SUCCESS);
573: }

575: /*@
576:   PetscFESetDualSpace - Sets the `PetscDualSpace` used to define the inner product

578:   Not Collective

580:   Input Parameters:
581: + fem - The `PetscFE` object
582: - sp  - The `PetscDualSpace` object

584:   Level: intermediate

586: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetBasisSpace()`
587: @*/
588: PetscErrorCode PetscFESetDualSpace(PetscFE fem, PetscDualSpace sp)
589: {
590:   PetscFunctionBegin;
593:   PetscCall(PetscDualSpaceDestroy(&fem->dualSpace));
594:   fem->dualSpace = sp;
595:   PetscCall(PetscObjectReference((PetscObject)fem->dualSpace));
596:   PetscFunctionReturn(PETSC_SUCCESS);
597: }

599: /*@
600:   PetscFEGetQuadrature - Returns the `PetscQuadrature` used to calculate inner products

602:   Not Collective

604:   Input Parameter:
605: . fem - The `PetscFE` object

607:   Output Parameter:
608: . q - The `PetscQuadrature` object

610:   Level: intermediate

612: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`
613: @*/
614: PetscErrorCode PetscFEGetQuadrature(PetscFE fem, PetscQuadrature *q)
615: {
616:   PetscFunctionBegin;
618:   PetscAssertPointer(q, 2);
619:   *q = fem->quadrature;
620:   PetscFunctionReturn(PETSC_SUCCESS);
621: }

623: /*@
624:   PetscFESetQuadrature - Sets the `PetscQuadrature` used to calculate inner products

626:   Not Collective

628:   Input Parameters:
629: + fem - The `PetscFE` object
630: - q   - The `PetscQuadrature` object

632:   Level: intermediate

634: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFEGetFaceQuadrature()`
635: @*/
636: PetscErrorCode PetscFESetQuadrature(PetscFE fem, PetscQuadrature q)
637: {
638:   PetscInt Nc, qNc;

640:   PetscFunctionBegin;
642:   if (q == fem->quadrature) PetscFunctionReturn(PETSC_SUCCESS);
643:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
644:   PetscCall(PetscQuadratureGetNumComponents(q, &qNc));
645:   PetscCheck(!(qNc != 1) || !(Nc != qNc), PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_SIZ, "FE components %" PetscInt_FMT " != Quadrature components %" PetscInt_FMT " and non-scalar quadrature", Nc, qNc);
646:   PetscCall(PetscTabulationDestroy(&fem->T));
647:   PetscCall(PetscTabulationDestroy(&fem->Tc));
648:   PetscCall(PetscObjectReference((PetscObject)q));
649:   PetscCall(PetscQuadratureDestroy(&fem->quadrature));
650:   fem->quadrature = q;
651:   PetscFunctionReturn(PETSC_SUCCESS);
652: }

654: /*@
655:   PetscFEGetFaceQuadrature - Returns the `PetscQuadrature` used to calculate inner products on faces

657:   Not Collective

659:   Input Parameter:
660: . fem - The `PetscFE` object

662:   Output Parameter:
663: . q - The `PetscQuadrature` object

665:   Level: intermediate

667:   Developer Notes:
668:   There is a special face quadrature but not edge, likely this API would benefit from a refactorization

670: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
671: @*/
672: PetscErrorCode PetscFEGetFaceQuadrature(PetscFE fem, PetscQuadrature *q)
673: {
674:   PetscFunctionBegin;
676:   PetscAssertPointer(q, 2);
677:   *q = fem->faceQuadrature;
678:   PetscFunctionReturn(PETSC_SUCCESS);
679: }

681: /*@
682:   PetscFESetFaceQuadrature - Sets the `PetscQuadrature` used to calculate inner products on faces

684:   Not Collective

686:   Input Parameters:
687: + fem - The `PetscFE` object
688: - q   - The `PetscQuadrature` object

690:   Level: intermediate

692: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`
693: @*/
694: PetscErrorCode PetscFESetFaceQuadrature(PetscFE fem, PetscQuadrature q)
695: {
696:   PetscInt Nc, qNc;

698:   PetscFunctionBegin;
700:   if (q == fem->faceQuadrature) PetscFunctionReturn(PETSC_SUCCESS);
701:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
702:   PetscCall(PetscQuadratureGetNumComponents(q, &qNc));
703:   PetscCheck(!(qNc != 1) || !(Nc != qNc), PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_SIZ, "FE components %" PetscInt_FMT " != Quadrature components %" PetscInt_FMT " and non-scalar quadrature", Nc, qNc);
704:   PetscCall(PetscTabulationDestroy(&fem->Tf));
705:   PetscCall(PetscObjectReference((PetscObject)q));
706:   PetscCall(PetscQuadratureDestroy(&fem->faceQuadrature));
707:   fem->faceQuadrature = q;
708:   PetscFunctionReturn(PETSC_SUCCESS);
709: }

711: /*@
712:   PetscFECopyQuadrature - Copy both volumetric and surface quadrature to a new `PetscFE`

714:   Not Collective

716:   Input Parameters:
717: + sfe - The `PetscFE` source for the quadratures
718: - tfe - The `PetscFE` target for the quadratures

720:   Level: intermediate

722: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
723: @*/
724: PetscErrorCode PetscFECopyQuadrature(PetscFE sfe, PetscFE tfe)
725: {
726:   PetscQuadrature q;

728:   PetscFunctionBegin;
731:   PetscCall(PetscFEGetQuadrature(sfe, &q));
732:   PetscCall(PetscFESetQuadrature(tfe, q));
733:   PetscCall(PetscFEGetFaceQuadrature(sfe, &q));
734:   PetscCall(PetscFESetFaceQuadrature(tfe, q));
735:   PetscFunctionReturn(PETSC_SUCCESS);
736: }

738: /*@C
739:   PetscFEGetNumDof - Returns the number of dofs (dual basis vectors) associated to mesh points on the reference cell of a given dimension

741:   Not Collective

743:   Input Parameter:
744: . fem - The `PetscFE` object

746:   Output Parameter:
747: . numDof - Array of length `dim` with the number of dofs in each dimension

749:   Level: intermediate

751: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
752: @*/
753: PetscErrorCode PetscFEGetNumDof(PetscFE fem, const PetscInt *numDof[])
754: {
755:   PetscFunctionBegin;
757:   PetscAssertPointer(numDof, 2);
758:   PetscCall(PetscDualSpaceGetNumDof(fem->dualSpace, numDof));
759:   PetscFunctionReturn(PETSC_SUCCESS);
760: }

762: /*@C
763:   PetscFEGetCellTabulation - Returns the tabulation of the basis functions at the quadrature points on the reference cell

765:   Not Collective

767:   Input Parameters:
768: + fem - The `PetscFE` object
769: - k   - The highest derivative we need to tabulate, very often 1

771:   Output Parameter:
772: . T - The basis function values and derivatives at quadrature points

774:   Level: intermediate

776:   Note:
777: .vb
778:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
779:   T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
780:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e
781: .ve

783: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
784: @*/
785: PetscErrorCode PetscFEGetCellTabulation(PetscFE fem, PetscInt k, PetscTabulation *T)
786: {
787:   PetscInt         npoints;
788:   const PetscReal *points;

790:   PetscFunctionBegin;
792:   PetscAssertPointer(T, 3);
793:   PetscCall(PetscQuadratureGetData(fem->quadrature, NULL, NULL, &npoints, &points, NULL));
794:   if (!fem->T) PetscCall(PetscFECreateTabulation(fem, 1, npoints, points, k, &fem->T));
795:   PetscCheck(!fem->T || k <= fem->T->K || (!fem->T->cdim && !fem->T->K), PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_OUTOFRANGE, "Requested %" PetscInt_FMT " derivatives, but only tabulated %" PetscInt_FMT, k, fem->T->K);
796:   *T = fem->T;
797:   PetscFunctionReturn(PETSC_SUCCESS);
798: }

800: PetscErrorCode PetscFEExpandFaceQuadrature(PetscFE fe, PetscQuadrature fq, PetscQuadrature *efq)
801: {
802:   DM               dm;
803:   PetscDualSpace   sp;
804:   const PetscInt  *faces;
805:   const PetscReal *points, *weights;
806:   DMPolytopeType   ct;
807:   PetscReal       *facePoints, *faceWeights;
808:   PetscInt         dim, cStart, Nf, Nc, Np, order;

810:   PetscFunctionBegin;
811:   PetscCall(PetscFEGetDualSpace(fe, &sp));
812:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
813:   PetscCall(DMGetDimension(dm, &dim));
814:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
815:   PetscCall(DMPlexGetConeSize(dm, cStart, &Nf));
816:   PetscCall(DMPlexGetCone(dm, cStart, &faces));
817:   PetscCall(PetscQuadratureGetData(fq, NULL, &Nc, &Np, &points, &weights));
818:   PetscCall(PetscMalloc1(Nf * Np * dim, &facePoints));
819:   PetscCall(PetscMalloc1(Nf * Np * Nc, &faceWeights));
820:   for (PetscInt f = 0; f < Nf; ++f) {
821:     const PetscReal xi0[3] = {-1., -1., -1.};
822:     PetscReal       v0[3], J[9], detJ;

824:     PetscCall(DMPlexComputeCellGeometryFEM(dm, faces[f], NULL, v0, J, NULL, &detJ));
825:     for (PetscInt q = 0; q < Np; ++q) {
826:       CoordinatesRefToReal(dim, dim - 1, xi0, v0, J, &points[q * (dim - 1)], &facePoints[(f * Np + q) * dim]);
827:       for (PetscInt c = 0; c < Nc; ++c) faceWeights[(f * Np + q) * Nc + c] = weights[q * Nc + c];
828:     }
829:   }
830:   PetscCall(PetscQuadratureCreate(PetscObjectComm((PetscObject)fq), efq));
831:   PetscCall(PetscQuadratureGetCellType(fq, &ct));
832:   PetscCall(PetscQuadratureSetCellType(*efq, ct));
833:   PetscCall(PetscQuadratureGetOrder(fq, &order));
834:   PetscCall(PetscQuadratureSetOrder(*efq, order));
835:   PetscCall(PetscQuadratureSetData(*efq, dim, Nc, Nf * Np, facePoints, faceWeights));
836:   PetscFunctionReturn(PETSC_SUCCESS);
837: }

839: /*@C
840:   PetscFEGetFaceTabulation - Returns the tabulation of the basis functions at the face quadrature points for each face of the reference cell

842:   Not Collective

844:   Input Parameters:
845: + fem - The `PetscFE` object
846: - k   - The highest derivative we need to tabulate, very often 1

848:   Output Parameter:
849: . Tf - The basis function values and derivatives at face quadrature points

851:   Level: intermediate

853:   Note:
854: .vb
855:   T->T[0] = Bf[((f*Nq + q)*pdim + i)*Nc + c] is the value at point f,q for basis function i and component c
856:   T->T[1] = Df[(((f*Nq + q)*pdim + i)*Nc + c)*dim + d] is the derivative value at point f,q for basis function i, component c, in direction d
857:   T->T[2] = Hf[((((f*Nq + q)*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point f,q for basis function i, component c, in directions d and e
858: .ve

860: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
861: @*/
862: PetscErrorCode PetscFEGetFaceTabulation(PetscFE fem, PetscInt k, PetscTabulation *Tf)
863: {
864:   PetscFunctionBegin;
866:   PetscAssertPointer(Tf, 3);
867:   if (!fem->Tf) {
868:     PetscQuadrature fq;

870:     PetscCall(PetscFEGetFaceQuadrature(fem, &fq));
871:     if (fq) {
872:       PetscQuadrature  efq;
873:       const PetscReal *facePoints;
874:       PetscInt         Np, eNp;

876:       PetscCall(PetscFEExpandFaceQuadrature(fem, fq, &efq));
877:       PetscCall(PetscQuadratureGetData(fq, NULL, NULL, &Np, NULL, NULL));
878:       PetscCall(PetscQuadratureGetData(efq, NULL, NULL, &eNp, &facePoints, NULL));
879:       if (PetscDefined(USE_DEBUG)) {
880:         PetscDualSpace sp;
881:         DM             dm;
882:         PetscInt       cStart, Nf;

884:         PetscCall(PetscFEGetDualSpace(fem, &sp));
885:         PetscCall(PetscDualSpaceGetDM(sp, &dm));
886:         PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
887:         PetscCall(DMPlexGetConeSize(dm, cStart, &Nf));
888:         PetscCheck(Nf == eNp / Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of faces %" PetscInt_FMT " != %" PetscInt_FMT " number of quadrature replicas", Nf, eNp / Np);
889:       }
890:       PetscCall(PetscFECreateTabulation(fem, eNp / Np, Np, facePoints, k, &fem->Tf));
891:       PetscCall(PetscQuadratureDestroy(&efq));
892:     }
893:   }
894:   PetscCheck(!fem->Tf || k <= fem->Tf->K, PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_OUTOFRANGE, "Requested %" PetscInt_FMT " derivatives, but only tabulated %" PetscInt_FMT, k, fem->Tf->K);
895:   *Tf = fem->Tf;
896:   PetscFunctionReturn(PETSC_SUCCESS);
897: }

899: /*@C
900:   PetscFEGetFaceCentroidTabulation - Returns the tabulation of the basis functions at the face centroid points

902:   Not Collective

904:   Input Parameter:
905: . fem - The `PetscFE` object

907:   Output Parameter:
908: . Tc - The basis function values at face centroid points

910:   Level: intermediate

912:   Note:
913: .vb
914:   T->T[0] = Bf[(f*pdim + i)*Nc + c] is the value at point f for basis function i and component c
915: .ve

917: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetFaceTabulation()`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
918: @*/
919: PetscErrorCode PetscFEGetFaceCentroidTabulation(PetscFE fem, PetscTabulation *Tc)
920: {
921:   PetscFunctionBegin;
923:   PetscAssertPointer(Tc, 2);
924:   if (!fem->Tc) {
925:     PetscDualSpace  sp;
926:     DM              dm;
927:     const PetscInt *cone;
928:     PetscReal      *centroids;
929:     PetscInt        dim, numFaces, f;

931:     PetscCall(PetscFEGetDualSpace(fem, &sp));
932:     PetscCall(PetscDualSpaceGetDM(sp, &dm));
933:     PetscCall(DMGetDimension(dm, &dim));
934:     PetscCall(DMPlexGetConeSize(dm, 0, &numFaces));
935:     PetscCall(DMPlexGetCone(dm, 0, &cone));
936:     PetscCall(PetscMalloc1(numFaces * dim, &centroids));
937:     for (f = 0; f < numFaces; ++f) PetscCall(DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, &centroids[f * dim], NULL));
938:     PetscCall(PetscFECreateTabulation(fem, 1, numFaces, centroids, 0, &fem->Tc));
939:     PetscCall(PetscFree(centroids));
940:   }
941:   *Tc = fem->Tc;
942:   PetscFunctionReturn(PETSC_SUCCESS);
943: }

945: /*@C
946:   PetscFECreateTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided.

948:   Not Collective

950:   Input Parameters:
951: + fem     - The `PetscFE` object
952: . nrepl   - The number of replicas
953: . npoints - The number of tabulation points in a replica
954: . points  - The tabulation point coordinates
955: - K       - The number of derivatives calculated

957:   Output Parameter:
958: . T - The basis function values and derivatives at tabulation points

960:   Level: intermediate

962:   Note:
963: .vb
964:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
965:   T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
966:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis
967:   T->function i, component c, in directions d and e
968: .ve

970: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`
971: @*/
972: PetscErrorCode PetscFECreateTabulation(PetscFE fem, PetscInt nrepl, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation *T)
973: {
974:   DM             dm;
975:   PetscDualSpace Q;
976:   PetscInt       Nb;   /* Dimension of FE space P */
977:   PetscInt       Nc;   /* Field components */
978:   PetscInt       cdim; /* Reference coordinate dimension */
979:   PetscInt       k;

981:   PetscFunctionBegin;
982:   if (!npoints || !fem->dualSpace || K < 0) {
983:     *T = NULL;
984:     PetscFunctionReturn(PETSC_SUCCESS);
985:   }
987:   PetscAssertPointer(points, 4);
988:   PetscAssertPointer(T, 6);
989:   PetscCall(PetscFEGetDualSpace(fem, &Q));
990:   PetscCall(PetscDualSpaceGetDM(Q, &dm));
991:   PetscCall(DMGetDimension(dm, &cdim));
992:   PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
993:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
994:   PetscCall(PetscMalloc1(1, T));
995:   (*T)->K    = !cdim ? 0 : K;
996:   (*T)->Nr   = nrepl;
997:   (*T)->Np   = npoints;
998:   (*T)->Nb   = Nb;
999:   (*T)->Nc   = Nc;
1000:   (*T)->cdim = cdim;
1001:   PetscCall(PetscMalloc1((*T)->K + 1, &(*T)->T));
1002:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscCalloc1(nrepl * npoints * Nb * Nc * PetscPowInt(cdim, k), &(*T)->T[k]));
1003:   PetscUseTypeMethod(fem, computetabulation, nrepl * npoints, points, K, *T);
1004:   PetscFunctionReturn(PETSC_SUCCESS);
1005: }

1007: /*@C
1008:   PetscFEComputeTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided.

1010:   Not Collective

1012:   Input Parameters:
1013: + fem     - The `PetscFE` object
1014: . npoints - The number of tabulation points
1015: . points  - The tabulation point coordinates
1016: . K       - The number of derivatives calculated
1017: - T       - An existing tabulation object with enough allocated space

1019:   Output Parameter:
1020: . T - The basis function values and derivatives at tabulation points

1022:   Level: intermediate

1024:   Note:
1025: .vb
1026:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
1027:   T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
1028:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e
1029: .ve

1031: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`
1032: @*/
1033: PetscErrorCode PetscFEComputeTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation T)
1034: {
1035:   PetscFunctionBeginHot;
1036:   if (!npoints || !fem->dualSpace || K < 0) PetscFunctionReturn(PETSC_SUCCESS);
1038:   PetscAssertPointer(points, 3);
1039:   PetscAssertPointer(T, 5);
1040:   if (PetscDefined(USE_DEBUG)) {
1041:     DM             dm;
1042:     PetscDualSpace Q;
1043:     PetscInt       Nb;   /* Dimension of FE space P */
1044:     PetscInt       Nc;   /* Field components */
1045:     PetscInt       cdim; /* Reference coordinate dimension */

1047:     PetscCall(PetscFEGetDualSpace(fem, &Q));
1048:     PetscCall(PetscDualSpaceGetDM(Q, &dm));
1049:     PetscCall(DMGetDimension(dm, &cdim));
1050:     PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
1051:     PetscCall(PetscFEGetNumComponents(fem, &Nc));
1052:     PetscCheck(T->K == (!cdim ? 0 : K), PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation K %" PetscInt_FMT " must match requested K %" PetscInt_FMT, T->K, !cdim ? 0 : K);
1053:     PetscCheck(T->Nb == Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nb %" PetscInt_FMT " must match requested Nb %" PetscInt_FMT, T->Nb, Nb);
1054:     PetscCheck(T->Nc == Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nc %" PetscInt_FMT " must match requested Nc %" PetscInt_FMT, T->Nc, Nc);
1055:     PetscCheck(T->cdim == cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation cdim %" PetscInt_FMT " must match requested cdim %" PetscInt_FMT, T->cdim, cdim);
1056:   }
1057:   T->Nr = 1;
1058:   T->Np = npoints;
1059:   PetscUseTypeMethod(fem, computetabulation, npoints, points, K, T);
1060:   PetscFunctionReturn(PETSC_SUCCESS);
1061: }

1063: /*@
1064:   PetscTabulationDestroy - Frees memory from the associated tabulation.

1066:   Not Collective

1068:   Input Parameter:
1069: . T - The tabulation

1071:   Level: intermediate

1073: .seealso: `PetscTabulation`, `PetscFECreateTabulation()`, `PetscFEGetCellTabulation()`
1074: @*/
1075: PetscErrorCode PetscTabulationDestroy(PetscTabulation *T)
1076: {
1077:   PetscInt k;

1079:   PetscFunctionBegin;
1080:   PetscAssertPointer(T, 1);
1081:   if (!T || !*T) PetscFunctionReturn(PETSC_SUCCESS);
1082:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscFree((*T)->T[k]));
1083:   PetscCall(PetscFree((*T)->T));
1084:   PetscCall(PetscFree(*T));
1085:   *T = NULL;
1086:   PetscFunctionReturn(PETSC_SUCCESS);
1087: }

1089: static PetscErrorCode PetscFECreatePointTraceDefault_Internal(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
1090: {
1091:   PetscSpace      bsp, bsubsp;
1092:   PetscDualSpace  dsp, dsubsp;
1093:   PetscInt        dim, depth, numComp, i, j, coneSize, order;
1094:   DM              dm;
1095:   DMLabel         label;
1096:   PetscReal      *xi, *v, *J, detJ;
1097:   const char     *name;
1098:   PetscQuadrature origin, fullQuad, subQuad;

1100:   PetscFunctionBegin;
1101:   PetscCall(PetscFEGetBasisSpace(fe, &bsp));
1102:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
1103:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
1104:   PetscCall(DMGetDimension(dm, &dim));
1105:   PetscCall(DMPlexGetDepthLabel(dm, &label));
1106:   PetscCall(DMLabelGetValue(label, refPoint, &depth));
1107:   PetscCall(PetscCalloc1(depth, &xi));
1108:   PetscCall(PetscMalloc1(dim, &v));
1109:   PetscCall(PetscMalloc1(dim * dim, &J));
1110:   for (i = 0; i < depth; i++) xi[i] = 0.;
1111:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &origin));
1112:   PetscCall(PetscQuadratureSetData(origin, depth, 0, 1, xi, NULL));
1113:   PetscCall(DMPlexComputeCellGeometryFEM(dm, refPoint, origin, v, J, NULL, &detJ));
1114:   /* CellGeometryFEM computes the expanded Jacobian, we want the true jacobian */
1115:   for (i = 1; i < dim; i++) {
1116:     for (j = 0; j < depth; j++) J[i * depth + j] = J[i * dim + j];
1117:   }
1118:   PetscCall(PetscQuadratureDestroy(&origin));
1119:   PetscCall(PetscDualSpaceGetPointSubspace(dsp, refPoint, &dsubsp));
1120:   PetscCall(PetscSpaceCreateSubspace(bsp, dsubsp, v, J, NULL, NULL, PETSC_OWN_POINTER, &bsubsp));
1121:   PetscCall(PetscSpaceSetUp(bsubsp));
1122:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), trFE));
1123:   PetscCall(PetscFESetType(*trFE, PETSCFEBASIC));
1124:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
1125:   PetscCall(PetscFESetNumComponents(*trFE, numComp));
1126:   PetscCall(PetscFESetBasisSpace(*trFE, bsubsp));
1127:   PetscCall(PetscFESetDualSpace(*trFE, dsubsp));
1128:   PetscCall(PetscObjectGetName((PetscObject)fe, &name));
1129:   if (name) PetscCall(PetscFESetName(*trFE, name));
1130:   PetscCall(PetscFEGetQuadrature(fe, &fullQuad));
1131:   PetscCall(PetscQuadratureGetOrder(fullQuad, &order));
1132:   PetscCall(DMPlexGetConeSize(dm, refPoint, &coneSize));
1133:   if (coneSize == 2 * depth) PetscCall(PetscDTGaussTensorQuadrature(depth, 1, (order + 2) / 2, -1., 1., &subQuad));
1134:   else PetscCall(PetscDTSimplexQuadrature(depth, order, PETSCDTSIMPLEXQUAD_DEFAULT, &subQuad));
1135:   PetscCall(PetscFESetQuadrature(*trFE, subQuad));
1136:   PetscCall(PetscFESetUp(*trFE));
1137:   PetscCall(PetscQuadratureDestroy(&subQuad));
1138:   PetscCall(PetscSpaceDestroy(&bsubsp));
1139:   PetscFunctionReturn(PETSC_SUCCESS);
1140: }

1142: PETSC_EXTERN PetscErrorCode PetscFECreatePointTrace(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
1143: {
1144:   PetscFunctionBegin;
1146:   PetscAssertPointer(trFE, 3);
1147:   if (fe->ops->createpointtrace) PetscUseTypeMethod(fe, createpointtrace, refPoint, trFE);
1148:   else PetscCall(PetscFECreatePointTraceDefault_Internal(fe, refPoint, trFE));
1149:   PetscFunctionReturn(PETSC_SUCCESS);
1150: }

1152: PetscErrorCode PetscFECreateHeightTrace(PetscFE fe, PetscInt height, PetscFE *trFE)
1153: {
1154:   PetscInt       hStart, hEnd;
1155:   PetscDualSpace dsp;
1156:   DM             dm;

1158:   PetscFunctionBegin;
1160:   PetscAssertPointer(trFE, 3);
1161:   *trFE = NULL;
1162:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
1163:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
1164:   PetscCall(DMPlexGetHeightStratum(dm, height, &hStart, &hEnd));
1165:   if (hEnd <= hStart) PetscFunctionReturn(PETSC_SUCCESS);
1166:   PetscCall(PetscFECreatePointTrace(fe, hStart, trFE));
1167:   PetscFunctionReturn(PETSC_SUCCESS);
1168: }

1170: /*@
1171:   PetscFEGetDimension - Get the dimension of the finite element space on a cell

1173:   Not Collective

1175:   Input Parameter:
1176: . fem - The `PetscFE`

1178:   Output Parameter:
1179: . dim - The dimension

1181:   Level: intermediate

1183: .seealso: `PetscFE`, `PetscFECreate()`, `PetscSpaceGetDimension()`, `PetscDualSpaceGetDimension()`
1184: @*/
1185: PetscErrorCode PetscFEGetDimension(PetscFE fem, PetscInt *dim)
1186: {
1187:   PetscFunctionBegin;
1189:   PetscAssertPointer(dim, 2);
1190:   PetscTryTypeMethod(fem, getdimension, dim);
1191:   PetscFunctionReturn(PETSC_SUCCESS);
1192: }

1194: /*@
1195:   PetscFEPushforward - Map the reference element function to real space

1197:   Input Parameters:
1198: + fe     - The `PetscFE`
1199: . fegeom - The cell geometry
1200: . Nv     - The number of function values
1201: - vals   - The function values

1203:   Output Parameter:
1204: . vals - The transformed function values

1206:   Level: advanced

1208:   Notes:
1209:   This just forwards the call onto `PetscDualSpacePushforward()`.

1211:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

1213: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscDualSpacePushforward()`
1214: @*/
1215: PetscErrorCode PetscFEPushforward(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
1216: {
1217:   PetscFunctionBeginHot;
1218:   PetscCall(PetscDualSpacePushforward(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
1219:   PetscFunctionReturn(PETSC_SUCCESS);
1220: }

1222: /*@
1223:   PetscFEPushforwardGradient - Map the reference element function gradient to real space

1225:   Input Parameters:
1226: + fe     - The `PetscFE`
1227: . fegeom - The cell geometry
1228: . Nv     - The number of function gradient values
1229: - vals   - The function gradient values

1231:   Output Parameter:
1232: . vals - The transformed function gradient values

1234:   Level: advanced

1236:   Notes:
1237:   This just forwards the call onto `PetscDualSpacePushforwardGradient()`.

1239:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

1241: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardGradient()`, `PetscDualSpacePushforward()`
1242: @*/
1243: PetscErrorCode PetscFEPushforwardGradient(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
1244: {
1245:   PetscFunctionBeginHot;
1246:   PetscCall(PetscDualSpacePushforwardGradient(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
1247:   PetscFunctionReturn(PETSC_SUCCESS);
1248: }

1250: /*@
1251:   PetscFEPushforwardHessian - Map the reference element function Hessian to real space

1253:   Input Parameters:
1254: + fe     - The `PetscFE`
1255: . fegeom - The cell geometry
1256: . Nv     - The number of function Hessian values
1257: - vals   - The function Hessian values

1259:   Output Parameter:
1260: . vals - The transformed function Hessian values

1262:   Level: advanced

1264:   Notes:
1265:   This just forwards the call onto `PetscDualSpacePushforwardHessian()`.

1267:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

1269:   Developer Notes:
1270:   It is unclear why all these one line convenience routines are desirable

1272: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardHessian()`, `PetscDualSpacePushforward()`
1273: @*/
1274: PetscErrorCode PetscFEPushforwardHessian(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
1275: {
1276:   PetscFunctionBeginHot;
1277:   PetscCall(PetscDualSpacePushforwardHessian(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
1278:   PetscFunctionReturn(PETSC_SUCCESS);
1279: }

1281: /*
1282: Purpose: Compute element vector for chunk of elements

1284: Input:
1285:   Sizes:
1286:      Ne:  number of elements
1287:      Nf:  number of fields
1288:      PetscFE
1289:        dim: spatial dimension
1290:        Nb:  number of basis functions
1291:        Nc:  number of field components
1292:        PetscQuadrature
1293:          Nq:  number of quadrature points

1295:   Geometry:
1296:      PetscFEGeom[Ne] possibly *Nq
1297:        PetscReal v0s[dim]
1298:        PetscReal n[dim]
1299:        PetscReal jacobians[dim*dim]
1300:        PetscReal jacobianInverses[dim*dim]
1301:        PetscReal jacobianDeterminants
1302:   FEM:
1303:      PetscFE
1304:        PetscQuadrature
1305:          PetscReal   quadPoints[Nq*dim]
1306:          PetscReal   quadWeights[Nq]
1307:        PetscReal   basis[Nq*Nb*Nc]
1308:        PetscReal   basisDer[Nq*Nb*Nc*dim]
1309:      PetscScalar coefficients[Ne*Nb*Nc]
1310:      PetscScalar elemVec[Ne*Nb*Nc]

1312:   Problem:
1313:      PetscInt f: the active field
1314:      f0, f1

1316:   Work Space:
1317:      PetscFE
1318:        PetscScalar f0[Nq*dim];
1319:        PetscScalar f1[Nq*dim*dim];
1320:        PetscScalar u[Nc];
1321:        PetscScalar gradU[Nc*dim];
1322:        PetscReal   x[dim];
1323:        PetscScalar realSpaceDer[dim];

1325: Purpose: Compute element vector for N_cb batches of elements

1327: Input:
1328:   Sizes:
1329:      N_cb: Number of serial cell batches

1331:   Geometry:
1332:      PetscReal v0s[Ne*dim]
1333:      PetscReal jacobians[Ne*dim*dim]        possibly *Nq
1334:      PetscReal jacobianInverses[Ne*dim*dim] possibly *Nq
1335:      PetscReal jacobianDeterminants[Ne]     possibly *Nq
1336:   FEM:
1337:      static PetscReal   quadPoints[Nq*dim]
1338:      static PetscReal   quadWeights[Nq]
1339:      static PetscReal   basis[Nq*Nb*Nc]
1340:      static PetscReal   basisDer[Nq*Nb*Nc*dim]
1341:      PetscScalar coefficients[Ne*Nb*Nc]
1342:      PetscScalar elemVec[Ne*Nb*Nc]

1344: ex62.c:
1345:   PetscErrorCode PetscFEIntegrateResidualBatch(PetscInt Ne, PetscInt numFields, PetscInt field, PetscQuadrature quad[], const PetscScalar coefficients[],
1346:                                                const PetscReal v0s[], const PetscReal jacobians[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[],
1347:                                                void (*f0_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]),
1348:                                                void (*f1_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]), PetscScalar elemVec[])

1350: ex52.c:
1351:   PetscErrorCode IntegrateLaplacianBatchCPU(PetscInt Ne, PetscInt Nb, const PetscScalar coefficients[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscInt Nq, const PetscReal quadPoints[], const PetscReal quadWeights[], const PetscReal basisTabulation[], const PetscReal basisDerTabulation[], PetscScalar elemVec[], AppCtx *user)
1352:   PetscErrorCode IntegrateElasticityBatchCPU(PetscInt Ne, PetscInt Nb, PetscInt Ncomp, const PetscScalar coefficients[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscInt Nq, const PetscReal quadPoints[], const PetscReal quadWeights[], const PetscReal basisTabulation[], const PetscReal basisDerTabulation[], PetscScalar elemVec[], AppCtx *user)

1354: ex52_integrateElement.cu
1355: __global__ void integrateElementQuadrature(int N_cb, realType *coefficients, realType *jacobianInverses, realType *jacobianDeterminants, realType *elemVec)

1357: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt Nbl, const PetscScalar coefficients[],
1358:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
1359:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

1361: ex52_integrateElementOpenCL.c:
1362: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt N_bl, const PetscScalar coefficients[],
1363:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
1364:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

1366: __kernel void integrateElementQuadrature(int N_cb, __global float *coefficients, __global float *jacobianInverses, __global float *jacobianDeterminants, __global float *elemVec)
1367: */

1369: /*@
1370:   PetscFEIntegrate - Produce the integral for the given field for a chunk of elements by quadrature integration

1372:   Not Collective

1374:   Input Parameters:
1375: + prob            - The `PetscDS` specifying the discretizations and continuum functions
1376: . field           - The field being integrated
1377: . Ne              - The number of elements in the chunk
1378: . cgeom           - The cell geometry for each cell in the chunk
1379: . coefficients    - The array of FEM basis coefficients for the elements
1380: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1381: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

1383:   Output Parameter:
1384: . integral - the integral for this field

1386:   Level: intermediate

1388:   Developer Notes:
1389:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

1391: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrateBd()`
1392: @*/
1393: PetscErrorCode PetscFEIntegrate(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[])
1394: {
1395:   PetscFE fe;

1397:   PetscFunctionBegin;
1399:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
1400:   if (fe->ops->integrate) PetscCall((*fe->ops->integrate)(prob, field, Ne, cgeom, coefficients, probAux, coefficientsAux, integral));
1401:   PetscFunctionReturn(PETSC_SUCCESS);
1402: }

1404: /*@C
1405:   PetscFEIntegrateBd - Produce the integral for the given field for a chunk of elements by quadrature integration

1407:   Not Collective

1409:   Input Parameters:
1410: + prob            - The `PetscDS` specifying the discretizations and continuum functions
1411: . field           - The field being integrated
1412: . obj_func        - The function to be integrated
1413: . Ne              - The number of elements in the chunk
1414: . geom            - The face geometry for each face in the chunk
1415: . coefficients    - The array of FEM basis coefficients for the elements
1416: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1417: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

1419:   Output Parameter:
1420: . integral - the integral for this field

1422:   Level: intermediate

1424:   Developer Notes:
1425:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

1427: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrate()`
1428: @*/
1429: PetscErrorCode PetscFEIntegrateBd(PetscDS prob, PetscInt field, void (*obj_func)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), PetscInt Ne, PetscFEGeom *geom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[])
1430: {
1431:   PetscFE fe;

1433:   PetscFunctionBegin;
1435:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
1436:   if (fe->ops->integratebd) PetscCall((*fe->ops->integratebd)(prob, field, obj_func, Ne, geom, coefficients, probAux, coefficientsAux, integral));
1437:   PetscFunctionReturn(PETSC_SUCCESS);
1438: }

1440: /*@
1441:   PetscFEIntegrateResidual - Produce the element residual vector for a chunk of elements by quadrature integration

1443:   Not Collective

1445:   Input Parameters:
1446: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1447: . key             - The (label+value, field) being integrated
1448: . Ne              - The number of elements in the chunk
1449: . cgeom           - The cell geometry for each cell in the chunk
1450: . coefficients    - The array of FEM basis coefficients for the elements
1451: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1452: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1453: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1454: - t               - The time

1456:   Output Parameter:
1457: . elemVec - the element residual vectors from each element

1459:   Level: intermediate

1461:   Note:
1462: .vb
1463:   Loop over batch of elements (e):
1464:     Loop over quadrature points (q):
1465:       Make u_q and gradU_q (loops over fields,Nb,Ncomp) and x_q
1466:       Call f_0 and f_1
1467:     Loop over element vector entries (f,fc --> i):
1468:       elemVec[i] += \psi^{fc}_f(q) f0_{fc}(u, \nabla u) + \nabla\psi^{fc}_f(q) \cdot f1_{fc,df}(u, \nabla u)
1469: .ve

1471: .seealso: `PetscFEIntegrateBdResidual()`
1472: @*/
1473: PetscErrorCode PetscFEIntegrateResidual(PetscDS ds, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
1474: {
1475:   PetscFE fe;

1477:   PetscFunctionBeginHot;
1479:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
1480:   if (fe->ops->integrateresidual) PetscCall((*fe->ops->integrateresidual)(ds, key, Ne, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
1481:   PetscFunctionReturn(PETSC_SUCCESS);
1482: }

1484: /*@
1485:   PetscFEIntegrateBdResidual - Produce the element residual vector for a chunk of elements by quadrature integration over a boundary

1487:   Not Collective

1489:   Input Parameters:
1490: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1491: . wf              - The PetscWeakForm object holding the pointwise functions
1492: . key             - The (label+value, field) being integrated
1493: . Ne              - The number of elements in the chunk
1494: . fgeom           - The face geometry for each cell in the chunk
1495: . coefficients    - The array of FEM basis coefficients for the elements
1496: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1497: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1498: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1499: - t               - The time

1501:   Output Parameter:
1502: . elemVec - the element residual vectors from each element

1504:   Level: intermediate

1506: .seealso: `PetscFEIntegrateResidual()`
1507: @*/
1508: PetscErrorCode PetscFEIntegrateBdResidual(PetscDS ds, PetscWeakForm wf, PetscFormKey key, PetscInt Ne, PetscFEGeom *fgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
1509: {
1510:   PetscFE fe;

1512:   PetscFunctionBegin;
1514:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
1515:   if (fe->ops->integratebdresidual) PetscCall((*fe->ops->integratebdresidual)(ds, wf, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
1516:   PetscFunctionReturn(PETSC_SUCCESS);
1517: }

1519: /*@
1520:   PetscFEIntegrateHybridResidual - Produce the element residual vector for a chunk of hybrid element faces by quadrature integration

1522:   Not Collective

1524:   Input Parameters:
1525: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1526: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for input
1527: . key             - The (label+value, field) being integrated
1528: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
1529: . Ne              - The number of elements in the chunk
1530: . fgeom           - The face geometry for each cell in the chunk
1531: . cgeom           - The cell geometry for each neighbor cell in the chunk
1532: . coefficients    - The array of FEM basis coefficients for the elements
1533: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1534: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1535: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1536: - t               - The time

1538:   Output Parameter:
1539: . elemVec - the element residual vectors from each element

1541:   Level: developer

1543: .seealso: `PetscFEIntegrateResidual()`
1544: @*/
1545: PetscErrorCode PetscFEIntegrateHybridResidual(PetscDS ds, PetscDS dsIn, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
1546: {
1547:   PetscFE fe;

1549:   PetscFunctionBegin;
1552:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
1553:   if (fe->ops->integratehybridresidual) PetscCall((*fe->ops->integratehybridresidual)(ds, dsIn, key, s, Ne, fgeom, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
1554:   PetscFunctionReturn(PETSC_SUCCESS);
1555: }

1557: /*@
1558:   PetscFEIntegrateJacobian - Produce the element Jacobian for a chunk of elements by quadrature integration

1560:   Not Collective

1562:   Input Parameters:
1563: + rds             - The `PetscDS` specifying the row discretizations and continuum functions
1564: . cds             - The `PetscDS` specifying the column discretizations
1565: . jtype           - The type of matrix pointwise functions that should be used
1566: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
1567: . Ne              - The number of elements in the chunk
1568: . cgeom           - The cell geometry for each cell in the chunk
1569: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
1570: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1571: . dsAux           - The `PetscDS` specifying the auxiliary discretizations
1572: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1573: . t               - The time
1574: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

1576:   Output Parameter:
1577: . elemMat - the element matrices for the Jacobian from each element

1579:   Level: intermediate

1581:   Note:
1582: .vb
1583:   Loop over batch of elements (e):
1584:     Loop over element matrix entries (f,fc,g,gc --> i,j):
1585:       Loop over quadrature points (q):
1586:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
1587:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1588:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1589:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1590:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1591: .ve

1593: .seealso: `PetscFEIntegrateResidual()`
1594: @*/
1595: PetscErrorCode PetscFEIntegrateJacobian(PetscDS rds, PetscDS cds, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS dsAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
1596: {
1597:   PetscFE  fe;
1598:   PetscInt Nf;

1600:   PetscFunctionBegin;
1603:   PetscCall(PetscDSGetNumFields(rds, &Nf));
1604:   PetscCall(PetscDSGetDiscretization(rds, key.field / Nf, (PetscObject *)&fe));
1605:   if (fe->ops->integratejacobian) PetscCall((*fe->ops->integratejacobian)(rds, cds, jtype, key, Ne, cgeom, coefficients, coefficients_t, dsAux, coefficientsAux, t, u_tshift, elemMat));
1606:   PetscFunctionReturn(PETSC_SUCCESS);
1607: }

1609: /*@
1610:   PetscFEIntegrateBdJacobian - Produce the boundary element Jacobian for a chunk of elements by quadrature integration

1612:   Not Collective

1614:   Input Parameters:
1615: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1616: . wf              - The PetscWeakForm holding the pointwise functions
1617: . jtype           - The type of matrix pointwise functions that should be used
1618: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
1619: . Ne              - The number of elements in the chunk
1620: . fgeom           - The face geometry for each cell in the chunk
1621: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
1622: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1623: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1624: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1625: . t               - The time
1626: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

1628:   Output Parameter:
1629: . elemMat - the element matrices for the Jacobian from each element

1631:   Level: intermediate

1633:   Note:
1634: .vb
1635:   Loop over batch of elements (e):
1636:     Loop over element matrix entries (f,fc,g,gc --> i,j):
1637:       Loop over quadrature points (q):
1638:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
1639:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1640:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1641:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1642:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1643: .ve

1645: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
1646: @*/
1647: PetscErrorCode PetscFEIntegrateBdJacobian(PetscDS ds, PetscWeakForm wf, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *fgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
1648: {
1649:   PetscFE  fe;
1650:   PetscInt Nf;

1652:   PetscFunctionBegin;
1654:   PetscCall(PetscDSGetNumFields(ds, &Nf));
1655:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
1656:   if (fe->ops->integratebdjacobian) PetscCall((*fe->ops->integratebdjacobian)(ds, wf, jtype, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
1657:   PetscFunctionReturn(PETSC_SUCCESS);
1658: }

1660: /*@
1661:   PetscFEIntegrateHybridJacobian - Produce the boundary element Jacobian for a chunk of hybrid elements by quadrature integration

1663:   Not Collective

1665:   Input Parameters:
1666: + ds              - The `PetscDS` specifying the discretizations and continuum functions for the output
1667: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for the input
1668: . jtype           - The type of matrix pointwise functions that should be used
1669: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
1670: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
1671: . Ne              - The number of elements in the chunk
1672: . fgeom           - The face geometry for each cell in the chunk
1673: . cgeom           - The cell geometry for each neighbor cell in the chunk
1674: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
1675: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1676: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1677: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1678: . t               - The time
1679: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

1681:   Output Parameter:
1682: . elemMat - the element matrices for the Jacobian from each element

1684:   Level: developer

1686:   Note:
1687: .vb
1688:   Loop over batch of elements (e):
1689:     Loop over element matrix entries (f,fc,g,gc --> i,j):
1690:       Loop over quadrature points (q):
1691:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
1692:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1693:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1694:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1695:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1696: .ve

1698: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
1699: @*/
1700: PetscErrorCode PetscFEIntegrateHybridJacobian(PetscDS ds, PetscDS dsIn, PetscFEJacobianType jtype, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
1701: {
1702:   PetscFE  fe;
1703:   PetscInt Nf;

1705:   PetscFunctionBegin;
1707:   PetscCall(PetscDSGetNumFields(ds, &Nf));
1708:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
1709:   if (fe->ops->integratehybridjacobian) PetscCall((*fe->ops->integratehybridjacobian)(ds, dsIn, jtype, key, s, Ne, fgeom, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
1710:   PetscFunctionReturn(PETSC_SUCCESS);
1711: }

1713: /*@
1714:   PetscFEGetHeightSubspace - Get the subspace of this space for a mesh point of a given height

1716:   Input Parameters:
1717: + fe     - The finite element space
1718: - height - The height of the `DMPLEX` point

1720:   Output Parameter:
1721: . subfe - The subspace of this `PetscFE` space

1723:   Level: advanced

1725:   Note:
1726:   For example, if we want the subspace of this space for a face, we would choose height = 1.

1728: .seealso: `PetscFECreateDefault()`
1729: @*/
1730: PetscErrorCode PetscFEGetHeightSubspace(PetscFE fe, PetscInt height, PetscFE *subfe)
1731: {
1732:   PetscSpace      P, subP;
1733:   PetscDualSpace  Q, subQ;
1734:   PetscQuadrature subq;
1735:   PetscInt        dim, Nc;

1737:   PetscFunctionBegin;
1739:   PetscAssertPointer(subfe, 3);
1740:   if (height == 0) {
1741:     *subfe = fe;
1742:     PetscFunctionReturn(PETSC_SUCCESS);
1743:   }
1744:   PetscCall(PetscFEGetBasisSpace(fe, &P));
1745:   PetscCall(PetscFEGetDualSpace(fe, &Q));
1746:   PetscCall(PetscFEGetNumComponents(fe, &Nc));
1747:   PetscCall(PetscFEGetFaceQuadrature(fe, &subq));
1748:   PetscCall(PetscDualSpaceGetDimension(Q, &dim));
1749:   PetscCheck(height <= dim && height >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Asked for space at height %" PetscInt_FMT " for dimension %" PetscInt_FMT " space", height, dim);
1750:   if (!fe->subspaces) PetscCall(PetscCalloc1(dim, &fe->subspaces));
1751:   if (height <= dim) {
1752:     if (!fe->subspaces[height - 1]) {
1753:       PetscFE     sub = NULL;
1754:       const char *name;

1756:       PetscCall(PetscSpaceGetHeightSubspace(P, height, &subP));
1757:       PetscCall(PetscDualSpaceGetHeightSubspace(Q, height, &subQ));
1758:       if (subQ) {
1759:         PetscCall(PetscObjectReference((PetscObject)subP));
1760:         PetscCall(PetscObjectReference((PetscObject)subQ));
1761:         PetscCall(PetscObjectReference((PetscObject)subq));
1762:         PetscCall(PetscFECreateFromSpaces(subP, subQ, subq, NULL, &sub));
1763:       }
1764:       if (sub) {
1765:         PetscCall(PetscObjectGetName((PetscObject)fe, &name));
1766:         if (name) PetscCall(PetscFESetName(sub, name));
1767:       }
1768:       fe->subspaces[height - 1] = sub;
1769:     }
1770:     *subfe = fe->subspaces[height - 1];
1771:   } else {
1772:     *subfe = NULL;
1773:   }
1774:   PetscFunctionReturn(PETSC_SUCCESS);
1775: }

1777: /*@
1778:   PetscFERefine - Create a "refined" `PetscFE` object that refines the reference cell into
1779:   smaller copies.

1781:   Collective

1783:   Input Parameter:
1784: . fe - The initial `PetscFE`

1786:   Output Parameter:
1787: . feRef - The refined `PetscFE`

1789:   Level: advanced

1791:   Notes:
1792:   This is typically used to generate a preconditioner for a higher order method from a lower order method on a
1793:   refined mesh having the same number of dofs (but more sparsity). It is also used to create an
1794:   interpolation between regularly refined meshes.

1796: .seealso: `PetscFEType`, `PetscFECreate()`, `PetscFESetType()`
1797: @*/
1798: PetscErrorCode PetscFERefine(PetscFE fe, PetscFE *feRef)
1799: {
1800:   PetscSpace       P, Pref;
1801:   PetscDualSpace   Q, Qref;
1802:   DM               K, Kref;
1803:   PetscQuadrature  q, qref;
1804:   const PetscReal *v0, *jac;
1805:   PetscInt         numComp, numSubelements;
1806:   PetscInt         cStart, cEnd, c;
1807:   PetscDualSpace  *cellSpaces;

1809:   PetscFunctionBegin;
1810:   PetscCall(PetscFEGetBasisSpace(fe, &P));
1811:   PetscCall(PetscFEGetDualSpace(fe, &Q));
1812:   PetscCall(PetscFEGetQuadrature(fe, &q));
1813:   PetscCall(PetscDualSpaceGetDM(Q, &K));
1814:   /* Create space */
1815:   PetscCall(PetscObjectReference((PetscObject)P));
1816:   Pref = P;
1817:   /* Create dual space */
1818:   PetscCall(PetscDualSpaceDuplicate(Q, &Qref));
1819:   PetscCall(PetscDualSpaceSetType(Qref, PETSCDUALSPACEREFINED));
1820:   PetscCall(DMRefine(K, PetscObjectComm((PetscObject)fe), &Kref));
1821:   PetscCall(DMGetCoordinatesLocalSetUp(Kref));
1822:   PetscCall(PetscDualSpaceSetDM(Qref, Kref));
1823:   PetscCall(DMPlexGetHeightStratum(Kref, 0, &cStart, &cEnd));
1824:   PetscCall(PetscMalloc1(cEnd - cStart, &cellSpaces));
1825:   /* TODO: fix for non-uniform refinement */
1826:   for (c = 0; c < cEnd - cStart; c++) cellSpaces[c] = Q;
1827:   PetscCall(PetscDualSpaceRefinedSetCellSpaces(Qref, cellSpaces));
1828:   PetscCall(PetscFree(cellSpaces));
1829:   PetscCall(DMDestroy(&Kref));
1830:   PetscCall(PetscDualSpaceSetUp(Qref));
1831:   /* Create element */
1832:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), feRef));
1833:   PetscCall(PetscFESetType(*feRef, PETSCFECOMPOSITE));
1834:   PetscCall(PetscFESetBasisSpace(*feRef, Pref));
1835:   PetscCall(PetscFESetDualSpace(*feRef, Qref));
1836:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
1837:   PetscCall(PetscFESetNumComponents(*feRef, numComp));
1838:   PetscCall(PetscFESetUp(*feRef));
1839:   PetscCall(PetscSpaceDestroy(&Pref));
1840:   PetscCall(PetscDualSpaceDestroy(&Qref));
1841:   /* Create quadrature */
1842:   PetscCall(PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL));
1843:   PetscCall(PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref));
1844:   PetscCall(PetscFESetQuadrature(*feRef, qref));
1845:   PetscCall(PetscQuadratureDestroy(&qref));
1846:   PetscFunctionReturn(PETSC_SUCCESS);
1847: }

1849: static PetscErrorCode PetscFESetDefaultName_Private(PetscFE fe)
1850: {
1851:   PetscSpace     P;
1852:   PetscDualSpace Q;
1853:   DM             K;
1854:   DMPolytopeType ct;
1855:   PetscInt       degree;
1856:   char           name[64];

1858:   PetscFunctionBegin;
1859:   PetscCall(PetscFEGetBasisSpace(fe, &P));
1860:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
1861:   PetscCall(PetscFEGetDualSpace(fe, &Q));
1862:   PetscCall(PetscDualSpaceGetDM(Q, &K));
1863:   PetscCall(DMPlexGetCellType(K, 0, &ct));
1864:   switch (ct) {
1865:   case DM_POLYTOPE_SEGMENT:
1866:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1867:   case DM_POLYTOPE_QUADRILATERAL:
1868:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1869:   case DM_POLYTOPE_HEXAHEDRON:
1870:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1871:     PetscCall(PetscSNPrintf(name, sizeof(name), "Q%" PetscInt_FMT, degree));
1872:     break;
1873:   case DM_POLYTOPE_TRIANGLE:
1874:   case DM_POLYTOPE_TETRAHEDRON:
1875:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT, degree));
1876:     break;
1877:   case DM_POLYTOPE_TRI_PRISM:
1878:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1879:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT "xQ%" PetscInt_FMT, degree, degree));
1880:     break;
1881:   default:
1882:     PetscCall(PetscSNPrintf(name, sizeof(name), "FE"));
1883:   }
1884:   PetscCall(PetscFESetName(fe, name));
1885:   PetscFunctionReturn(PETSC_SUCCESS);
1886: }

1888: /*@
1889:   PetscFECreateFromSpaces - Create a `PetscFE` from the basis and dual spaces

1891:   Collective

1893:   Input Parameters:
1894: + P  - The basis space
1895: . Q  - The dual space
1896: . q  - The cell quadrature
1897: - fq - The face quadrature

1899:   Output Parameter:
1900: . fem - The `PetscFE` object

1902:   Level: beginner

1904:   Note:
1905:   The `PetscFE` takes ownership of these spaces by calling destroy on each. They should not be used after this call, and for borrowed references from `PetscFEGetSpace()` and the like, the caller must use `PetscObjectReference` before this call.

1907: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`,
1908:           `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
1909: @*/
1910: PetscErrorCode PetscFECreateFromSpaces(PetscSpace P, PetscDualSpace Q, PetscQuadrature q, PetscQuadrature fq, PetscFE *fem)
1911: {
1912:   PetscInt    Nc;
1913:   PetscInt    p_Ns = -1, p_Nc = -1, q_Ns = -1, q_Nc = -1;
1914:   PetscBool   p_is_uniform_sum = PETSC_FALSE, p_interleave_basis = PETSC_FALSE, p_interleave_components = PETSC_FALSE;
1915:   PetscBool   q_is_uniform_sum = PETSC_FALSE, q_interleave_basis = PETSC_FALSE, q_interleave_components = PETSC_FALSE;
1916:   const char *prefix;

1918:   PetscFunctionBegin;
1919:   PetscCall(PetscObjectTypeCompare((PetscObject)P, PETSCSPACESUM, &p_is_uniform_sum));
1920:   if (p_is_uniform_sum) {
1921:     PetscSpace subsp_0 = NULL;
1922:     PetscCall(PetscSpaceSumGetNumSubspaces(P, &p_Ns));
1923:     PetscCall(PetscSpaceGetNumComponents(P, &p_Nc));
1924:     PetscCall(PetscSpaceSumGetConcatenate(P, &p_is_uniform_sum));
1925:     PetscCall(PetscSpaceSumGetInterleave(P, &p_interleave_basis, &p_interleave_components));
1926:     for (PetscInt s = 0; s < p_Ns; s++) {
1927:       PetscSpace subsp;

1929:       PetscCall(PetscSpaceSumGetSubspace(P, s, &subsp));
1930:       if (!s) {
1931:         subsp_0 = subsp;
1932:       } else if (subsp != subsp_0) {
1933:         p_is_uniform_sum = PETSC_FALSE;
1934:       }
1935:     }
1936:   }
1937:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &q_is_uniform_sum));
1938:   if (q_is_uniform_sum) {
1939:     PetscDualSpace subsp_0 = NULL;
1940:     PetscCall(PetscDualSpaceSumGetNumSubspaces(Q, &q_Ns));
1941:     PetscCall(PetscDualSpaceGetNumComponents(Q, &q_Nc));
1942:     PetscCall(PetscDualSpaceSumGetConcatenate(Q, &q_is_uniform_sum));
1943:     PetscCall(PetscDualSpaceSumGetInterleave(Q, &q_interleave_basis, &q_interleave_components));
1944:     for (PetscInt s = 0; s < q_Ns; s++) {
1945:       PetscDualSpace subsp;

1947:       PetscCall(PetscDualSpaceSumGetSubspace(Q, s, &subsp));
1948:       if (!s) {
1949:         subsp_0 = subsp;
1950:       } else if (subsp != subsp_0) {
1951:         q_is_uniform_sum = PETSC_FALSE;
1952:       }
1953:     }
1954:   }
1955:   if (p_is_uniform_sum && q_is_uniform_sum && (p_interleave_basis == q_interleave_basis) && (p_interleave_components == q_interleave_components) && (p_Ns == q_Ns) && (p_Nc == q_Nc)) {
1956:     PetscSpace     scalar_space;
1957:     PetscDualSpace scalar_dspace;
1958:     PetscFE        scalar_fe;

1960:     PetscCall(PetscSpaceSumGetSubspace(P, 0, &scalar_space));
1961:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &scalar_dspace));
1962:     PetscCall(PetscObjectReference((PetscObject)scalar_space));
1963:     PetscCall(PetscObjectReference((PetscObject)scalar_dspace));
1964:     PetscCall(PetscObjectReference((PetscObject)q));
1965:     PetscCall(PetscObjectReference((PetscObject)fq));
1966:     PetscCall(PetscFECreateFromSpaces(scalar_space, scalar_dspace, q, fq, &scalar_fe));
1967:     PetscCall(PetscFECreateVector(scalar_fe, p_Ns, p_interleave_basis, p_interleave_components, fem));
1968:     PetscCall(PetscFEDestroy(&scalar_fe));
1969:   } else {
1970:     PetscCall(PetscFECreate(PetscObjectComm((PetscObject)P), fem));
1971:     PetscCall(PetscFESetType(*fem, PETSCFEBASIC));
1972:   }
1973:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
1974:   PetscCall(PetscFESetNumComponents(*fem, Nc));
1975:   PetscCall(PetscFESetBasisSpace(*fem, P));
1976:   PetscCall(PetscFESetDualSpace(*fem, Q));
1977:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)P, &prefix));
1978:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*fem, prefix));
1979:   PetscCall(PetscFESetUp(*fem));
1980:   PetscCall(PetscSpaceDestroy(&P));
1981:   PetscCall(PetscDualSpaceDestroy(&Q));
1982:   PetscCall(PetscFESetQuadrature(*fem, q));
1983:   PetscCall(PetscFESetFaceQuadrature(*fem, fq));
1984:   PetscCall(PetscQuadratureDestroy(&q));
1985:   PetscCall(PetscQuadratureDestroy(&fq));
1986:   PetscCall(PetscFESetDefaultName_Private(*fem));
1987:   PetscFunctionReturn(PETSC_SUCCESS);
1988: }

1990: static PetscErrorCode PetscFECreate_Internal(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt degree, PetscInt qorder, PetscBool setFromOptions, PetscFE *fem)
1991: {
1992:   DM              K;
1993:   PetscSpace      P;
1994:   PetscDualSpace  Q;
1995:   PetscQuadrature q, fq;
1996:   PetscBool       tensor;

1998:   PetscFunctionBegin;
1999:   if (prefix) PetscAssertPointer(prefix, 5);
2000:   PetscAssertPointer(fem, 9);
2001:   switch (ct) {
2002:   case DM_POLYTOPE_SEGMENT:
2003:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2004:   case DM_POLYTOPE_QUADRILATERAL:
2005:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2006:   case DM_POLYTOPE_HEXAHEDRON:
2007:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2008:     tensor = PETSC_TRUE;
2009:     break;
2010:   default:
2011:     tensor = PETSC_FALSE;
2012:   }
2013:   /* Create space */
2014:   PetscCall(PetscSpaceCreate(comm, &P));
2015:   PetscCall(PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL));
2016:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)P, prefix));
2017:   PetscCall(PetscSpacePolynomialSetTensor(P, tensor));
2018:   PetscCall(PetscSpaceSetNumComponents(P, Nc));
2019:   PetscCall(PetscSpaceSetNumVariables(P, dim));
2020:   if (degree >= 0) {
2021:     PetscCall(PetscSpaceSetDegree(P, degree, PETSC_DETERMINE));
2022:     if (ct == DM_POLYTOPE_TRI_PRISM || ct == DM_POLYTOPE_TRI_PRISM_TENSOR) {
2023:       PetscSpace Pend, Pside;

2025:       PetscCall(PetscSpaceSetNumComponents(P, 1));
2026:       PetscCall(PetscSpaceCreate(comm, &Pend));
2027:       PetscCall(PetscSpaceSetType(Pend, PETSCSPACEPOLYNOMIAL));
2028:       PetscCall(PetscSpacePolynomialSetTensor(Pend, PETSC_FALSE));
2029:       PetscCall(PetscSpaceSetNumComponents(Pend, 1));
2030:       PetscCall(PetscSpaceSetNumVariables(Pend, dim - 1));
2031:       PetscCall(PetscSpaceSetDegree(Pend, degree, PETSC_DETERMINE));
2032:       PetscCall(PetscSpaceCreate(comm, &Pside));
2033:       PetscCall(PetscSpaceSetType(Pside, PETSCSPACEPOLYNOMIAL));
2034:       PetscCall(PetscSpacePolynomialSetTensor(Pside, PETSC_FALSE));
2035:       PetscCall(PetscSpaceSetNumComponents(Pside, 1));
2036:       PetscCall(PetscSpaceSetNumVariables(Pside, 1));
2037:       PetscCall(PetscSpaceSetDegree(Pside, degree, PETSC_DETERMINE));
2038:       PetscCall(PetscSpaceSetType(P, PETSCSPACETENSOR));
2039:       PetscCall(PetscSpaceTensorSetNumSubspaces(P, 2));
2040:       PetscCall(PetscSpaceTensorSetSubspace(P, 0, Pend));
2041:       PetscCall(PetscSpaceTensorSetSubspace(P, 1, Pside));
2042:       PetscCall(PetscSpaceDestroy(&Pend));
2043:       PetscCall(PetscSpaceDestroy(&Pside));

2045:       if (Nc > 1) {
2046:         PetscSpace scalar_P = P;

2048:         PetscCall(PetscSpaceCreate(comm, &P));
2049:         PetscCall(PetscSpaceSetNumVariables(P, dim));
2050:         PetscCall(PetscSpaceSetNumComponents(P, Nc));
2051:         PetscCall(PetscSpaceSetType(P, PETSCSPACESUM));
2052:         PetscCall(PetscSpaceSumSetNumSubspaces(P, Nc));
2053:         PetscCall(PetscSpaceSumSetConcatenate(P, PETSC_TRUE));
2054:         PetscCall(PetscSpaceSumSetInterleave(P, PETSC_TRUE, PETSC_FALSE));
2055:         for (PetscInt i = 0; i < Nc; i++) PetscCall(PetscSpaceSumSetSubspace(P, i, scalar_P));
2056:         PetscCall(PetscSpaceDestroy(&scalar_P));
2057:       }
2058:     }
2059:   }
2060:   if (setFromOptions) PetscCall(PetscSpaceSetFromOptions(P));
2061:   PetscCall(PetscSpaceSetUp(P));
2062:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
2063:   PetscCall(PetscSpacePolynomialGetTensor(P, &tensor));
2064:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
2065:   /* Create dual space */
2066:   PetscCall(PetscDualSpaceCreate(comm, &Q));
2067:   PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
2068:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)Q, prefix));
2069:   PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
2070:   PetscCall(PetscDualSpaceSetDM(Q, K));
2071:   PetscCall(DMDestroy(&K));
2072:   PetscCall(PetscDualSpaceSetNumComponents(Q, Nc));
2073:   PetscCall(PetscDualSpaceSetOrder(Q, degree));
2074:   PetscCall(PetscDualSpaceLagrangeSetTensor(Q, (tensor || (ct == DM_POLYTOPE_TRI_PRISM)) ? PETSC_TRUE : PETSC_FALSE));
2075:   if (setFromOptions) PetscCall(PetscDualSpaceSetFromOptions(Q));
2076:   PetscCall(PetscDualSpaceSetUp(Q));
2077:   /* Create quadrature */
2078:   PetscDTSimplexQuadratureType qtype = PETSCDTSIMPLEXQUAD_DEFAULT;

2080:   qorder = qorder >= 0 ? qorder : degree;
2081:   if (setFromOptions) {
2082:     PetscObjectOptionsBegin((PetscObject)P);
2083:     PetscCall(PetscOptionsBoundedInt("-petscfe_default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "PetscFECreateDefault", qorder, &qorder, NULL, 0));
2084:     PetscCall(PetscOptionsEnum("-petscfe_default_quadrature_type", "Simplex quadrature type", "PetscDTSimplexQuadratureType", PetscDTSimplexQuadratureTypes, (PetscEnum)qtype, (PetscEnum *)&qtype, NULL));
2085:     PetscOptionsEnd();
2086:   }
2087:   PetscCall(PetscDTCreateQuadratureByCell(ct, qorder, qtype, &q, &fq));
2088:   /* Create finite element */
2089:   PetscCall(PetscFECreateFromSpaces(P, Q, q, fq, fem));
2090:   if (setFromOptions) PetscCall(PetscFESetFromOptions(*fem));
2091:   PetscFunctionReturn(PETSC_SUCCESS);
2092: }

2094: /*@
2095:   PetscFECreateDefault - Create a `PetscFE` for basic FEM computation

2097:   Collective

2099:   Input Parameters:
2100: + comm      - The MPI comm
2101: . dim       - The spatial dimension
2102: . Nc        - The number of components
2103: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
2104: . prefix    - The options prefix, or `NULL`
2105: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2107:   Output Parameter:
2108: . fem - The `PetscFE` object

2110:   Level: beginner

2112:   Note:
2113:   Each subobject is SetFromOption() during creation, so that the object may be customized from the command line, using the prefix specified above. See the links below for the particular options available.

2115: .seealso: `PetscFECreateLagrange()`, `PetscFECreateByCell()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2116: @*/
2117: PetscErrorCode PetscFECreateDefault(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, const char prefix[], PetscInt qorder, PetscFE *fem)
2118: {
2119:   PetscFunctionBegin;
2120:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
2121:   PetscFunctionReturn(PETSC_SUCCESS);
2122: }

2124: /*@
2125:   PetscFECreateByCell - Create a `PetscFE` for basic FEM computation

2127:   Collective

2129:   Input Parameters:
2130: + comm   - The MPI comm
2131: . dim    - The spatial dimension
2132: . Nc     - The number of components
2133: . ct     - The celltype of the reference cell
2134: . prefix - The options prefix, or `NULL`
2135: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2137:   Output Parameter:
2138: . fem - The `PetscFE` object

2140:   Level: beginner

2142:   Note:
2143:   Each subobject is SetFromOption() during creation, so that the object may be customized from the command line, using the prefix specified above. See the links below for the particular options available.

2145: .seealso: `PetscFECreateDefault()`, `PetscFECreateLagrange()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2146: @*/
2147: PetscErrorCode PetscFECreateByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt qorder, PetscFE *fem)
2148: {
2149:   PetscFunctionBegin;
2150:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
2151:   PetscFunctionReturn(PETSC_SUCCESS);
2152: }

2154: /*@
2155:   PetscFECreateLagrange - Create a `PetscFE` for the basic Lagrange space of degree k

2157:   Collective

2159:   Input Parameters:
2160: + comm      - The MPI comm
2161: . dim       - The spatial dimension
2162: . Nc        - The number of components
2163: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
2164: . k         - The degree k of the space
2165: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2167:   Output Parameter:
2168: . fem - The `PetscFE` object

2170:   Level: beginner

2172:   Note:
2173:   For simplices, this element is the space of maximum polynomial degree k, otherwise it is a tensor product of 1D polynomials, each with maximal degree k.

2175: .seealso: `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2176: @*/
2177: PetscErrorCode PetscFECreateLagrange(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, PetscInt k, PetscInt qorder, PetscFE *fem)
2178: {
2179:   PetscFunctionBegin;
2180:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), NULL, k, qorder, PETSC_FALSE, fem));
2181:   PetscFunctionReturn(PETSC_SUCCESS);
2182: }

2184: /*@
2185:   PetscFECreateLagrangeByCell - Create a `PetscFE` for the basic Lagrange space of degree k

2187:   Collective

2189:   Input Parameters:
2190: + comm   - The MPI comm
2191: . dim    - The spatial dimension
2192: . Nc     - The number of components
2193: . ct     - The celltype of the reference cell
2194: . k      - The degree k of the space
2195: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2197:   Output Parameter:
2198: . fem - The `PetscFE` object

2200:   Level: beginner

2202:   Note:
2203:   For simplices, this element is the space of maximum polynomial degree k, otherwise it is a tensor product of 1D polynomials, each with maximal degree k.

2205: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2206: @*/
2207: PetscErrorCode PetscFECreateLagrangeByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, PetscInt k, PetscInt qorder, PetscFE *fem)
2208: {
2209:   PetscFunctionBegin;
2210:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, NULL, k, qorder, PETSC_FALSE, fem));
2211:   PetscFunctionReturn(PETSC_SUCCESS);
2212: }

2214: /*@
2215:   PetscFELimitDegree - Copy a `PetscFE` but limit the degree to be in the given range

2217:   Collective

2219:   Input Parameters:
2220: + fe        - The `PetscFE`
2221: . minDegree - The minimum degree, or `PETSC_DETERMINE` for no limit
2222: - maxDegree - The maximum degree, or `PETSC_DETERMINE` for no limit

2224:   Output Parameter:
2225: . newfe - The `PetscFE` object

2227:   Level: advanced

2229:   Note:
2230:   This currently only works for Lagrange elements.

2232: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2233: @*/
2234: PetscErrorCode PetscFELimitDegree(PetscFE fe, PetscInt minDegree, PetscInt maxDegree, PetscFE *newfe)
2235: {
2236:   PetscDualSpace Q;
2237:   PetscBool      islag, issum;
2238:   PetscInt       oldk = 0, k;

2240:   PetscFunctionBegin;
2241:   PetscCall(PetscFEGetDualSpace(fe, &Q));
2242:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &islag));
2243:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &issum));
2244:   if (islag) {
2245:     PetscCall(PetscDualSpaceGetOrder(Q, &oldk));
2246:   } else if (issum) {
2247:     PetscDualSpace subQ;

2249:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &subQ));
2250:     PetscCall(PetscDualSpaceGetOrder(subQ, &oldk));
2251:   } else {
2252:     PetscCall(PetscObjectReference((PetscObject)fe));
2253:     *newfe = fe;
2254:     PetscFunctionReturn(PETSC_SUCCESS);
2255:   }
2256:   k = oldk;
2257:   if (minDegree >= 0) k = PetscMax(k, minDegree);
2258:   if (maxDegree >= 0) k = PetscMin(k, maxDegree);
2259:   if (k != oldk) {
2260:     DM              K;
2261:     PetscSpace      P;
2262:     PetscQuadrature q;
2263:     DMPolytopeType  ct;
2264:     PetscInt        dim, Nc;

2266:     PetscCall(PetscFEGetBasisSpace(fe, &P));
2267:     PetscCall(PetscSpaceGetNumVariables(P, &dim));
2268:     PetscCall(PetscSpaceGetNumComponents(P, &Nc));
2269:     PetscCall(PetscDualSpaceGetDM(Q, &K));
2270:     PetscCall(DMPlexGetCellType(K, 0, &ct));
2271:     PetscCall(PetscFECreateLagrangeByCell(PetscObjectComm((PetscObject)fe), dim, Nc, ct, k, PETSC_DETERMINE, newfe));
2272:     PetscCall(PetscFEGetQuadrature(fe, &q));
2273:     PetscCall(PetscFESetQuadrature(*newfe, q));
2274:   } else {
2275:     PetscCall(PetscObjectReference((PetscObject)fe));
2276:     *newfe = fe;
2277:   }
2278:   PetscFunctionReturn(PETSC_SUCCESS);
2279: }

2281: /*@
2282:   PetscFECreateBrokenElement - Create a discontinuous version of the input `PetscFE`

2284:   Collective

2286:   Input Parameters:
2287: . cgfe - The continuous `PetscFE` object

2289:   Output Parameter:
2290: . dgfe - The discontinuous `PetscFE` object

2292:   Level: advanced

2294:   Note:
2295:   This only works for Lagrange elements.

2297: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`, `PetscFECreateLagrange()`, `PetscFECreateLagrangeByCell()`, `PetscDualSpaceLagrangeSetContinuity()`
2298: @*/
2299: PetscErrorCode PetscFECreateBrokenElement(PetscFE cgfe, PetscFE *dgfe)
2300: {
2301:   PetscSpace      P;
2302:   PetscDualSpace  Q, dgQ;
2303:   PetscQuadrature q, fq;
2304:   PetscBool       is_lagrange, is_sum;

2306:   PetscFunctionBegin;
2307:   PetscCall(PetscFEGetBasisSpace(cgfe, &P));
2308:   PetscCall(PetscObjectReference((PetscObject)P));
2309:   PetscCall(PetscFEGetDualSpace(cgfe, &Q));
2310:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &is_lagrange));
2311:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &is_sum));
2312:   PetscCheck(is_lagrange || is_sum, PETSC_COMM_SELF, PETSC_ERR_SUP, "Can only create broken elements of Lagrange elements");
2313:   PetscCall(PetscDualSpaceDuplicate(Q, &dgQ));
2314:   PetscCall(PetscDualSpaceLagrangeSetContinuity(dgQ, PETSC_FALSE));
2315:   PetscCall(PetscDualSpaceSetUp(dgQ));
2316:   PetscCall(PetscFEGetQuadrature(cgfe, &q));
2317:   PetscCall(PetscObjectReference((PetscObject)q));
2318:   PetscCall(PetscFEGetFaceQuadrature(cgfe, &fq));
2319:   PetscCall(PetscObjectReference((PetscObject)fq));
2320:   PetscCall(PetscFECreateFromSpaces(P, dgQ, q, fq, dgfe));
2321:   PetscFunctionReturn(PETSC_SUCCESS);
2322: }

2324: /*@
2325:   PetscFESetName - Names the `PetscFE` and its subobjects

2327:   Not Collective

2329:   Input Parameters:
2330: + fe   - The `PetscFE`
2331: - name - The name

2333:   Level: intermediate

2335: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2336: @*/
2337: PetscErrorCode PetscFESetName(PetscFE fe, const char name[])
2338: {
2339:   PetscSpace     P;
2340:   PetscDualSpace Q;

2342:   PetscFunctionBegin;
2343:   PetscCall(PetscFEGetBasisSpace(fe, &P));
2344:   PetscCall(PetscFEGetDualSpace(fe, &Q));
2345:   PetscCall(PetscObjectSetName((PetscObject)fe, name));
2346:   PetscCall(PetscObjectSetName((PetscObject)P, name));
2347:   PetscCall(PetscObjectSetName((PetscObject)Q, name));
2348:   PetscFunctionReturn(PETSC_SUCCESS);
2349: }

2351: PetscErrorCode PetscFEEvaluateFieldJets_Internal(PetscDS ds, PetscInt Nf, PetscInt r, PetscInt q, PetscTabulation T[], PetscFEGeom *fegeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscScalar u[], PetscScalar u_x[], PetscScalar u_t[])
2352: {
2353:   PetscInt dOffset = 0, fOffset = 0, f, g;

2355:   for (f = 0; f < Nf; ++f) {
2356:     PetscCheck(r < T[f]->Nr, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Replica number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", r, T[f]->Nr);
2357:     PetscCheck(q < T[f]->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Point number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", q, T[f]->Np);
2358:     PetscFE          fe;
2359:     const PetscInt   k       = ds->jetDegree[f];
2360:     const PetscInt   cdim    = T[f]->cdim;
2361:     const PetscInt   dE      = fegeom->dimEmbed;
2362:     const PetscInt   Nq      = T[f]->Np;
2363:     const PetscInt   Nbf     = T[f]->Nb;
2364:     const PetscInt   Ncf     = T[f]->Nc;
2365:     const PetscReal *Bq      = &T[f]->T[0][(r * Nq + q) * Nbf * Ncf];
2366:     const PetscReal *Dq      = &T[f]->T[1][(r * Nq + q) * Nbf * Ncf * cdim];
2367:     const PetscReal *Hq      = k > 1 ? &T[f]->T[2][(r * Nq + q) * Nbf * Ncf * cdim * cdim] : NULL;
2368:     PetscInt         hOffset = 0, b, c, d;

2370:     PetscCall(PetscDSGetDiscretization(ds, f, (PetscObject *)&fe));
2371:     for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
2372:     for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
2373:     for (b = 0; b < Nbf; ++b) {
2374:       for (c = 0; c < Ncf; ++c) {
2375:         const PetscInt cidx = b * Ncf + c;

2377:         u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
2378:         for (d = 0; d < cdim; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * cdim + d] * coefficients[dOffset + b];
2379:       }
2380:     }
2381:     if (k > 1) {
2382:       for (g = 0; g < Nf; ++g) hOffset += T[g]->Nc * dE;
2383:       for (d = 0; d < dE * dE * Ncf; ++d) u_x[hOffset + fOffset * dE * dE + d] = 0.0;
2384:       for (b = 0; b < Nbf; ++b) {
2385:         for (c = 0; c < Ncf; ++c) {
2386:           const PetscInt cidx = b * Ncf + c;

2388:           for (d = 0; d < cdim * cdim; ++d) u_x[hOffset + (fOffset + c) * dE * dE + d] += Hq[cidx * cdim * cdim + d] * coefficients[dOffset + b];
2389:         }
2390:       }
2391:       PetscCall(PetscFEPushforwardHessian(fe, fegeom, 1, &u_x[hOffset + fOffset * dE * dE]));
2392:     }
2393:     PetscCall(PetscFEPushforward(fe, fegeom, 1, &u[fOffset]));
2394:     PetscCall(PetscFEPushforwardGradient(fe, fegeom, 1, &u_x[fOffset * dE]));
2395:     if (u_t) {
2396:       for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
2397:       for (b = 0; b < Nbf; ++b) {
2398:         for (c = 0; c < Ncf; ++c) {
2399:           const PetscInt cidx = b * Ncf + c;

2401:           u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
2402:         }
2403:       }
2404:       PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
2405:     }
2406:     fOffset += Ncf;
2407:     dOffset += Nbf;
2408:   }
2409:   return PETSC_SUCCESS;
2410: }

2412: PetscErrorCode PetscFEEvaluateFieldJets_Hybrid_Internal(PetscDS ds, PetscInt Nf, PetscInt rc, PetscInt qc, PetscTabulation Tab[], const PetscInt rf[], const PetscInt qf[], PetscTabulation Tabf[], PetscFEGeom *fegeom, PetscFEGeom *fegeomNbr, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscScalar u[], PetscScalar u_x[], PetscScalar u_t[])
2413: {
2414:   PetscInt dOffset = 0, fOffset = 0, f;

2416:   /* f is the field number in the DS */
2417:   for (f = 0; f < Nf; ++f) {
2418:     PetscBool isCohesive;
2419:     PetscInt  Ns, s;

2421:     if (!Tab[f]) continue;
2422:     PetscCall(PetscDSGetCohesive(ds, f, &isCohesive));
2423:     Ns = isCohesive ? 1 : 2;
2424:     {
2425:       PetscTabulation T   = isCohesive ? Tab[f] : Tabf[f];
2426:       PetscFE         fe  = (PetscFE)ds->disc[f];
2427:       const PetscInt  dEt = T->cdim;
2428:       const PetscInt  dE  = fegeom->dimEmbed;
2429:       const PetscInt  Nq  = T->Np;
2430:       const PetscInt  Nbf = T->Nb;
2431:       const PetscInt  Ncf = T->Nc;

2433:       for (s = 0; s < Ns; ++s) {
2434:         const PetscInt   r  = isCohesive ? rc : rf[s];
2435:         const PetscInt   q  = isCohesive ? qc : qf[s];
2436:         const PetscReal *Bq = &T->T[0][(r * Nq + q) * Nbf * Ncf];
2437:         const PetscReal *Dq = &T->T[1][(r * Nq + q) * Nbf * Ncf * dEt];
2438:         PetscInt         b, c, d;

2440:         PetscCheck(r < T->Nr, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " Side %" PetscInt_FMT " Replica number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", f, s, r, T->Nr);
2441:         PetscCheck(q < T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " Side %" PetscInt_FMT " Point number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", f, s, q, T->Np);
2442:         for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
2443:         for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
2444:         for (b = 0; b < Nbf; ++b) {
2445:           for (c = 0; c < Ncf; ++c) {
2446:             const PetscInt cidx = b * Ncf + c;

2448:             u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
2449:             for (d = 0; d < dEt; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * dEt + d] * coefficients[dOffset + b];
2450:           }
2451:         }
2452:         PetscCall(PetscFEPushforward(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u[fOffset]));
2453:         PetscCall(PetscFEPushforwardGradient(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u_x[fOffset * dE]));
2454:         if (u_t) {
2455:           for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
2456:           for (b = 0; b < Nbf; ++b) {
2457:             for (c = 0; c < Ncf; ++c) {
2458:               const PetscInt cidx = b * Ncf + c;

2460:               u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
2461:             }
2462:           }
2463:           PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
2464:         }
2465:         fOffset += Ncf;
2466:         dOffset += Nbf;
2467:       }
2468:     }
2469:   }
2470:   return PETSC_SUCCESS;
2471: }

2473: PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS prob, PetscInt field, PetscInt faceLoc, const PetscScalar coefficients[], PetscScalar u[])
2474: {
2475:   PetscFE         fe;
2476:   PetscTabulation Tc;
2477:   PetscInt        b, c;

2479:   if (!prob) return PETSC_SUCCESS;
2480:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
2481:   PetscCall(PetscFEGetFaceCentroidTabulation(fe, &Tc));
2482:   {
2483:     const PetscReal *faceBasis = Tc->T[0];
2484:     const PetscInt   Nb        = Tc->Nb;
2485:     const PetscInt   Nc        = Tc->Nc;

2487:     for (c = 0; c < Nc; ++c) u[c] = 0.0;
2488:     for (b = 0; b < Nb; ++b) {
2489:       for (c = 0; c < Nc; ++c) u[c] += coefficients[b] * faceBasis[(faceLoc * Nb + b) * Nc + c];
2490:     }
2491:   }
2492:   return PETSC_SUCCESS;
2493: }

2495: PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscInt e, PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
2496: {
2497:   PetscFEGeom      pgeom;
2498:   const PetscInt   dEt      = T->cdim;
2499:   const PetscInt   dE       = fegeom->dimEmbed;
2500:   const PetscInt   Nq       = T->Np;
2501:   const PetscInt   Nb       = T->Nb;
2502:   const PetscInt   Nc       = T->Nc;
2503:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
2504:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dEt];
2505:   PetscInt         q, b, c, d;

2507:   for (q = 0; q < Nq; ++q) {
2508:     for (b = 0; b < Nb; ++b) {
2509:       for (c = 0; c < Nc; ++c) {
2510:         const PetscInt bcidx = b * Nc + c;

2512:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
2513:         for (d = 0; d < dEt; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dEt + bcidx * dEt + d];
2514:         for (d = dEt; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = 0.0;
2515:       }
2516:     }
2517:     PetscCall(PetscFEGeomGetCellPoint(fegeom, e, q, &pgeom));
2518:     PetscCall(PetscFEPushforward(fe, &pgeom, Nb, tmpBasis));
2519:     PetscCall(PetscFEPushforwardGradient(fe, &pgeom, Nb, tmpBasisDer));
2520:     for (b = 0; b < Nb; ++b) {
2521:       for (c = 0; c < Nc; ++c) {
2522:         const PetscInt bcidx = b * Nc + c;
2523:         const PetscInt qcidx = q * Nc + c;

2525:         elemVec[b] += tmpBasis[bcidx] * f0[qcidx];
2526:         for (d = 0; d < dE; ++d) elemVec[b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
2527:       }
2528:     }
2529:   }
2530:   return PETSC_SUCCESS;
2531: }

2533: PetscErrorCode PetscFEUpdateElementVec_Hybrid_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscInt side, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
2534: {
2535:   const PetscInt   dE       = T->cdim;
2536:   const PetscInt   Nq       = T->Np;
2537:   const PetscInt   Nb       = T->Nb;
2538:   const PetscInt   Nc       = T->Nc;
2539:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
2540:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dE];

2542:   for (PetscInt q = 0; q < Nq; ++q) {
2543:     for (PetscInt b = 0; b < Nb; ++b) {
2544:       for (PetscInt c = 0; c < Nc; ++c) {
2545:         const PetscInt bcidx = b * Nc + c;

2547:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
2548:         for (PetscInt d = 0; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dE + bcidx * dE + d];
2549:       }
2550:     }
2551:     PetscCall(PetscFEPushforward(fe, fegeom, Nb, tmpBasis));
2552:     // TODO This is currently broken since we do not pull the geometry down to the lower dimension
2553:     // PetscCall(PetscFEPushforwardGradient(fe, fegeom, Nb, tmpBasisDer));
2554:     if (side == 2) {
2555:       // Integrating over whole cohesive cell, so insert for both sides
2556:       for (PetscInt s = 0; s < 2; ++s) {
2557:         for (PetscInt b = 0; b < Nb; ++b) {
2558:           for (PetscInt c = 0; c < Nc; ++c) {
2559:             const PetscInt bcidx = b * Nc + c;
2560:             const PetscInt qcidx = (q * 2 + s) * Nc + c;

2562:             elemVec[Nb * s + b] += tmpBasis[bcidx] * f0[qcidx];
2563:             for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * s + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
2564:           }
2565:         }
2566:       }
2567:     } else {
2568:       // Integrating over endcaps of cohesive cell, so insert for correct side
2569:       for (PetscInt b = 0; b < Nb; ++b) {
2570:         for (PetscInt c = 0; c < Nc; ++c) {
2571:           const PetscInt bcidx = b * Nc + c;
2572:           const PetscInt qcidx = q * Nc + c;

2574:           elemVec[Nb * side + b] += tmpBasis[bcidx] * f0[qcidx];
2575:           for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * side + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
2576:         }
2577:       }
2578:     }
2579:   }
2580:   return PETSC_SUCCESS;
2581: }

2583: #define petsc_elemmat_kernel_g1(_NbI, _NcI, _NbJ, _NcJ, _dE) \
2584:   do { \
2585:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
2586:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
2587:         const PetscScalar *G = g1 + (fc * (_NcJ) + gc) * _dE; \
2588:         for (PetscInt f = 0; f < (_NbI); ++f) { \
2589:           const PetscScalar tBIv = tmpBasisI[f * (_NcI) + fc]; \
2590:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
2591:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
2592:             PetscScalar        s    = 0.0; \
2593:             for (PetscInt df = 0; df < _dE; ++df) s += G[df] * tBDJ[df]; \
2594:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBIv; \
2595:           } \
2596:         } \
2597:       } \
2598:     } \
2599:   } while (0)

2601: #define petsc_elemmat_kernel_g2(_NbI, _NcI, _NbJ, _NcJ, _dE) \
2602:   do { \
2603:     for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
2604:       for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
2605:         const PetscScalar *G = g2 + (fc * (_NcJ) + gc) * _dE; \
2606:         for (PetscInt g = 0; g < (_NbJ); ++g) { \
2607:           const PetscScalar tBJv = tmpBasisJ[g * (_NcJ) + gc]; \
2608:           for (PetscInt f = 0; f < (_NbI); ++f) { \
2609:             const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
2610:             PetscScalar        s    = 0.0; \
2611:             for (PetscInt df = 0; df < _dE; ++df) s += tBDI[df] * G[df]; \
2612:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBJv; \
2613:           } \
2614:         } \
2615:       } \
2616:     } \
2617:   } while (0)

2619: #define petsc_elemmat_kernel_g3(_NbI, _NcI, _NbJ, _NcJ, _dE) \
2620:   do { \
2621:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
2622:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
2623:         const PetscScalar *G = g3 + (fc * (_NcJ) + gc) * (_dE) * (_dE); \
2624:         for (PetscInt f = 0; f < (_NbI); ++f) { \
2625:           const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
2626:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
2627:             PetscScalar        s    = 0.0; \
2628:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
2629:             for (PetscInt df = 0; df < (_dE); ++df) { \
2630:               for (PetscInt dg = 0; dg < (_dE); ++dg) s += tBDI[df] * G[df * (_dE) + dg] * tBDJ[dg]; \
2631:             } \
2632:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s; \
2633:           } \
2634:         } \
2635:       } \
2636:     } \
2637:   } while (0)

2639: PetscErrorCode PetscFEUpdateElementMat_Internal(PetscFE feI, PetscFE feJ, PetscInt r, PetscInt q, PetscTabulation TI, PetscScalar tmpBasisI[], PetscScalar tmpBasisDerI[], PetscTabulation TJ, PetscScalar tmpBasisJ[], PetscScalar tmpBasisDerJ[], PetscFEGeom *fegeom, const PetscScalar g0[], const PetscScalar g1[], const PetscScalar g2[], const PetscScalar g3[], PetscInt totDim, PetscInt offsetI, PetscInt offsetJ, PetscScalar elemMat[])
2640: {
2641:   const PetscInt   cdim      = TI->cdim;
2642:   const PetscInt   dE        = fegeom->dimEmbed;
2643:   const PetscInt   NqI       = TI->Np;
2644:   const PetscInt   NbI       = TI->Nb;
2645:   const PetscInt   NcI       = TI->Nc;
2646:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
2647:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * cdim];
2648:   const PetscInt   NqJ       = TJ->Np;
2649:   const PetscInt   NbJ       = TJ->Nb;
2650:   const PetscInt   NcJ       = TJ->Nc;
2651:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
2652:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * cdim];

2654:   for (PetscInt f = 0; f < NbI; ++f) {
2655:     for (PetscInt fc = 0; fc < NcI; ++fc) {
2656:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2658:       tmpBasisI[fidx] = basisI[fidx];
2659:       for (PetscInt df = 0; df < cdim; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * cdim + df];
2660:     }
2661:   }
2662:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
2663:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
2664:   if (feI != feJ) {
2665:     for (PetscInt g = 0; g < NbJ; ++g) {
2666:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
2667:         const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2669:         tmpBasisJ[gidx] = basisJ[gidx];
2670:         for (PetscInt dg = 0; dg < cdim; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * cdim + dg];
2671:       }
2672:     }
2673:     PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
2674:     PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
2675:   } else {
2676:     tmpBasisJ    = tmpBasisI;
2677:     tmpBasisDerJ = tmpBasisDerI;
2678:   }
2679:   if (PetscUnlikely(g0)) {
2680:     for (PetscInt f = 0; f < NbI; ++f) {
2681:       const PetscInt i = offsetI + f; /* Element matrix row */

2683:       for (PetscInt fc = 0; fc < NcI; ++fc) {
2684:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

2686:         for (PetscInt g = 0; g < NbJ; ++g) {
2687:           const PetscInt j    = offsetJ + g; /* Element matrix column */
2688:           const PetscInt fOff = i * totDim + j;

2690:           for (PetscInt gc = 0; gc < NcJ; ++gc) elemMat[fOff] += bI * g0[fc * NcJ + gc] * tmpBasisJ[g * NcJ + gc];
2691:         }
2692:       }
2693:     }
2694:   }
2695:   if (PetscUnlikely(g1)) {
2696: #if 1
2697:     if (dE == 2) {
2698:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 2);
2699:     } else if (dE == 3) {
2700:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 3);
2701:     } else {
2702:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, dE);
2703:     }
2704: #else
2705:     for (PetscInt f = 0; f < NbI; ++f) {
2706:       const PetscInt i = offsetI + f; /* Element matrix row */

2708:       for (PetscInt fc = 0; fc < NcI; ++fc) {
2709:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

2711:         for (PetscInt g = 0; g < NbJ; ++g) {
2712:           const PetscInt j    = offsetJ + g; /* Element matrix column */
2713:           const PetscInt fOff = i * totDim + j;

2715:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
2716:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2718:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += bI * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
2719:           }
2720:         }
2721:       }
2722:     }
2723: #endif
2724:   }
2725:   if (PetscUnlikely(g2)) {
2726: #if 1
2727:     if (dE == 2) {
2728:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 2);
2729:     } else if (dE == 3) {
2730:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 3);
2731:     } else {
2732:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, dE);
2733:     }
2734: #else
2735:     for (PetscInt g = 0; g < NbJ; ++g) {
2736:       const PetscInt j = offsetJ + g; /* Element matrix column */

2738:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
2739:         const PetscScalar bJ = tmpBasisJ[g * NcJ + gc]; /* Trial function basis value */

2741:         for (PetscInt f = 0; f < NbI; ++f) {
2742:           const PetscInt i    = offsetI + f; /* Element matrix row */
2743:           const PetscInt fOff = i * totDim + j;

2745:           for (PetscInt fc = 0; fc < NcI; ++fc) {
2746:             const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2748:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * bJ;
2749:           }
2750:         }
2751:       }
2752:     }
2753: #endif
2754:   }
2755:   if (PetscUnlikely(g3)) {
2756: #if 1
2757:     if (dE == 2) {
2758:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 2);
2759:     } else if (dE == 3) {
2760:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 3);
2761:     } else {
2762:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, dE);
2763:     }
2764: #else
2765:     for (PetscInt f = 0; f < NbI; ++f) {
2766:       const PetscInt i = offsetI + f; /* Element matrix row */

2768:       for (PetscInt fc = 0; fc < NcI; ++fc) {
2769:         const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2771:         for (PetscInt g = 0; g < NbJ; ++g) {
2772:           const PetscInt j    = offsetJ + g; /* Element matrix column */
2773:           const PetscInt fOff = i * totDim + j;

2775:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
2776:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2778:             for (PetscInt df = 0; df < dE; ++df) {
2779:               for (PetscInt dg = 0; dg < dE; ++dg) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g3[((fc * NcJ + gc) * dE + df) * dE + dg] * tmpBasisDerJ[gidx * dE + dg];
2780:             }
2781:           }
2782:         }
2783:       }
2784:     }
2785: #endif
2786:   }
2787:   return PETSC_SUCCESS;
2788: }

2790: #undef petsc_elemmat_kernel_g1
2791: #undef petsc_elemmat_kernel_g2
2792: #undef petsc_elemmat_kernel_g3

2794: PetscErrorCode PetscFEUpdateElementMat_Hybrid_Internal(PetscFE feI, PetscBool isHybridI, PetscFE feJ, PetscBool isHybridJ, PetscInt r, PetscInt s, PetscInt t, PetscInt q, PetscTabulation TI, PetscScalar tmpBasisI[], PetscScalar tmpBasisDerI[], PetscTabulation TJ, PetscScalar tmpBasisJ[], PetscScalar tmpBasisDerJ[], PetscFEGeom *fegeom, const PetscScalar g0[], const PetscScalar g1[], const PetscScalar g2[], const PetscScalar g3[], PetscInt eOffset, PetscInt totDim, PetscInt offsetI, PetscInt offsetJ, PetscScalar elemMat[])
2795: {
2796:   const PetscInt   dE        = TI->cdim;
2797:   const PetscInt   NqI       = TI->Np;
2798:   const PetscInt   NbI       = TI->Nb;
2799:   const PetscInt   NcI       = TI->Nc;
2800:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
2801:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * dE];
2802:   const PetscInt   NqJ       = TJ->Np;
2803:   const PetscInt   NbJ       = TJ->Nb;
2804:   const PetscInt   NcJ       = TJ->Nc;
2805:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
2806:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * dE];
2807:   const PetscInt   so        = isHybridI ? 0 : s;
2808:   const PetscInt   to        = isHybridJ ? 0 : t;
2809:   PetscInt         f, fc, g, gc, df, dg;

2811:   for (f = 0; f < NbI; ++f) {
2812:     for (fc = 0; fc < NcI; ++fc) {
2813:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2815:       tmpBasisI[fidx] = basisI[fidx];
2816:       for (df = 0; df < dE; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * dE + df];
2817:     }
2818:   }
2819:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
2820:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
2821:   for (g = 0; g < NbJ; ++g) {
2822:     for (gc = 0; gc < NcJ; ++gc) {
2823:       const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2825:       tmpBasisJ[gidx] = basisJ[gidx];
2826:       for (dg = 0; dg < dE; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * dE + dg];
2827:     }
2828:   }
2829:   PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
2830:   // TODO This is currently broken since we do not pull the geometry down to the lower dimension
2831:   // PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
2832:   for (f = 0; f < NbI; ++f) {
2833:     for (fc = 0; fc < NcI; ++fc) {
2834:       const PetscInt fidx = f * NcI + fc;           /* Test function basis index */
2835:       const PetscInt i    = offsetI + NbI * so + f; /* Element matrix row */
2836:       for (g = 0; g < NbJ; ++g) {
2837:         for (gc = 0; gc < NcJ; ++gc) {
2838:           const PetscInt gidx = g * NcJ + gc;           /* Trial function basis index */
2839:           const PetscInt j    = offsetJ + NbJ * to + g; /* Element matrix column */
2840:           const PetscInt fOff = eOffset + i * totDim + j;

2842:           elemMat[fOff] += tmpBasisI[fidx] * g0[fc * NcJ + gc] * tmpBasisJ[gidx];
2843:           for (df = 0; df < dE; ++df) {
2844:             elemMat[fOff] += tmpBasisI[fidx] * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
2845:             elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * tmpBasisJ[gidx];
2846:             for (dg = 0; dg < dE; ++dg) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g3[((fc * NcJ + gc) * dE + df) * dE + dg] * tmpBasisDerJ[gidx * dE + dg];
2847:           }
2848:         }
2849:       }
2850:     }
2851:   }
2852:   return PETSC_SUCCESS;
2853: }

2855: PetscErrorCode PetscFECreateCellGeometry(PetscFE fe, PetscQuadrature quad, PetscFEGeom *cgeom)
2856: {
2857:   PetscDualSpace  dsp;
2858:   DM              dm;
2859:   PetscQuadrature quadDef;
2860:   PetscInt        dim, cdim, Nq;

2862:   PetscFunctionBegin;
2863:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
2864:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
2865:   PetscCall(DMGetDimension(dm, &dim));
2866:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2867:   PetscCall(PetscFEGetQuadrature(fe, &quadDef));
2868:   quad = quad ? quad : quadDef;
2869:   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
2870:   PetscCall(PetscMalloc1(Nq * cdim, &cgeom->v));
2871:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->J));
2872:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->invJ));
2873:   PetscCall(PetscMalloc1(Nq, &cgeom->detJ));
2874:   cgeom->dim       = dim;
2875:   cgeom->dimEmbed  = cdim;
2876:   cgeom->numCells  = 1;
2877:   cgeom->numPoints = Nq;
2878:   PetscCall(DMPlexComputeCellGeometryFEM(dm, 0, quad, cgeom->v, cgeom->J, cgeom->invJ, cgeom->detJ));
2879:   PetscFunctionReturn(PETSC_SUCCESS);
2880: }

2882: PetscErrorCode PetscFEDestroyCellGeometry(PetscFE fe, PetscFEGeom *cgeom)
2883: {
2884:   PetscFunctionBegin;
2885:   PetscCall(PetscFree(cgeom->v));
2886:   PetscCall(PetscFree(cgeom->J));
2887:   PetscCall(PetscFree(cgeom->invJ));
2888:   PetscCall(PetscFree(cgeom->detJ));
2889:   PetscFunctionReturn(PETSC_SUCCESS);
2890: }

2892: #if 0
2893: PetscErrorCode PetscFEUpdateElementMat_Internal_SparseIndices(PetscTabulation TI, PetscTabulation TJ, PetscInt dimEmbed, const PetscInt g0[], const PetscInt g1[], const PetscInt g2[], const PetscInt g3[], PetscInt totDim, PetscInt offsetI, PetscInt offsetJ, PetscInt *n_g0, PetscInt **g0_idxs_out, PetscInt *n_g1, PetscInt **g1_idxs_out, PetscInt *n_g2, PetscInt **g2_idxs_out, PetscInt *n_g3, PetscInt **g3_idxs_out)
2894: {
2895:   const PetscInt dE      = dimEmbed;
2896:   const PetscInt NbI     = TI->Nb;
2897:   const PetscInt NcI     = TI->Nc;
2898:   const PetscInt NbJ     = TJ->Nb;
2899:   const PetscInt NcJ     = TJ->Nc;
2900:   PetscBool      has_g0  = g0 ? PETSC_TRUE : PETSC_FALSE;
2901:   PetscBool      has_g1  = g1 ? PETSC_TRUE : PETSC_FALSE;
2902:   PetscBool      has_g2  = g2 ? PETSC_TRUE : PETSC_FALSE;
2903:   PetscBool      has_g3  = g3 ? PETSC_TRUE : PETSC_FALSE;
2904:   PetscInt      *g0_idxs = NULL, *g1_idxs = NULL, *g2_idxs = NULL, *g3_idxs = NULL;
2905:   PetscInt       g0_i, g1_i, g2_i, g3_i;

2907:   PetscFunctionBegin;
2908:   g0_i = g1_i = g2_i = g3_i = 0;
2909:   if (has_g0)
2910:     for (PetscInt i = 0; i < NcI * NcJ; i++)
2911:       if (g0[i]) g0_i += NbI * NbJ;
2912:   if (has_g1)
2913:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
2914:       if (g1[i]) g1_i += NbI * NbJ;
2915:   if (has_g2)
2916:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
2917:       if (g2[i]) g2_i += NbI * NbJ;
2918:   if (has_g3)
2919:     for (PetscInt i = 0; i < NcI * NcJ * dE * dE; i++)
2920:       if (g3[i]) g3_i += NbI * NbJ;
2921:   if (g0_i == NbI * NbJ * NcI * NcJ) g0_i = 0;
2922:   if (g1_i == NbI * NbJ * NcI * NcJ * dE) g1_i = 0;
2923:   if (g2_i == NbI * NbJ * NcI * NcJ * dE) g2_i = 0;
2924:   if (g3_i == NbI * NbJ * NcI * NcJ * dE * dE) g3_i = 0;
2925:   has_g0 = g0_i ? PETSC_TRUE : PETSC_FALSE;
2926:   has_g1 = g1_i ? PETSC_TRUE : PETSC_FALSE;
2927:   has_g2 = g2_i ? PETSC_TRUE : PETSC_FALSE;
2928:   has_g3 = g3_i ? PETSC_TRUE : PETSC_FALSE;
2929:   if (has_g0) PetscCall(PetscMalloc1(4 * g0_i, &g0_idxs));
2930:   if (has_g1) PetscCall(PetscMalloc1(4 * g1_i, &g1_idxs));
2931:   if (has_g2) PetscCall(PetscMalloc1(4 * g2_i, &g2_idxs));
2932:   if (has_g3) PetscCall(PetscMalloc1(4 * g3_i, &g3_idxs));
2933:   g0_i = g1_i = g2_i = g3_i = 0;

2935:   for (PetscInt f = 0; f < NbI; ++f) {
2936:     const PetscInt i = offsetI + f; /* Element matrix row */
2937:     for (PetscInt fc = 0; fc < NcI; ++fc) {
2938:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2940:       for (PetscInt g = 0; g < NbJ; ++g) {
2941:         const PetscInt j    = offsetJ + g; /* Element matrix column */
2942:         const PetscInt fOff = i * totDim + j;
2943:         for (PetscInt gc = 0; gc < NcJ; ++gc) {
2944:           const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2946:           if (has_g0) {
2947:             if (g0[fc * NcJ + gc]) {
2948:               g0_idxs[4 * g0_i + 0] = fidx;
2949:               g0_idxs[4 * g0_i + 1] = fc * NcJ + gc;
2950:               g0_idxs[4 * g0_i + 2] = gidx;
2951:               g0_idxs[4 * g0_i + 3] = fOff;
2952:               g0_i++;
2953:             }
2954:           }

2956:           for (PetscInt df = 0; df < dE; ++df) {
2957:             if (has_g1) {
2958:               if (g1[(fc * NcJ + gc) * dE + df]) {
2959:                 g1_idxs[4 * g1_i + 0] = fidx;
2960:                 g1_idxs[4 * g1_i + 1] = (fc * NcJ + gc) * dE + df;
2961:                 g1_idxs[4 * g1_i + 2] = gidx * dE + df;
2962:                 g1_idxs[4 * g1_i + 3] = fOff;
2963:                 g1_i++;
2964:               }
2965:             }
2966:             if (has_g2) {
2967:               if (g2[(fc * NcJ + gc) * dE + df]) {
2968:                 g2_idxs[4 * g2_i + 0] = fidx * dE + df;
2969:                 g2_idxs[4 * g2_i + 1] = (fc * NcJ + gc) * dE + df;
2970:                 g2_idxs[4 * g2_i + 2] = gidx;
2971:                 g2_idxs[4 * g2_i + 3] = fOff;
2972:                 g2_i++;
2973:               }
2974:             }
2975:             if (has_g3) {
2976:               for (PetscInt dg = 0; dg < dE; ++dg) {
2977:                 if (g3[((fc * NcJ + gc) * dE + df) * dE + dg]) {
2978:                   g3_idxs[4 * g3_i + 0] = fidx * dE + df;
2979:                   g3_idxs[4 * g3_i + 1] = ((fc * NcJ + gc) * dE + df) * dE + dg;
2980:                   g3_idxs[4 * g3_i + 2] = gidx * dE + dg;
2981:                   g3_idxs[4 * g3_i + 3] = fOff;
2982:                   g3_i++;
2983:                 }
2984:               }
2985:             }
2986:           }
2987:         }
2988:       }
2989:     }
2990:   }
2991:   *n_g0 = g0_i;
2992:   *n_g1 = g1_i;
2993:   *n_g2 = g2_i;
2994:   *n_g3 = g3_i;

2996:   *g0_idxs_out = g0_idxs;
2997:   *g1_idxs_out = g1_idxs;
2998:   *g2_idxs_out = g2_idxs;
2999:   *g3_idxs_out = g3_idxs;
3000:   PetscFunctionReturn(PETSC_SUCCESS);
3001: }

3003: //example HOW TO USE
3004:       for (PetscInt i = 0; i < g0_sparse_n; i++) {
3005:         PetscInt bM = g0_sparse_idxs[4 * i + 0];
3006:         PetscInt bN = g0_sparse_idxs[4 * i + 1];
3007:         PetscInt bK = g0_sparse_idxs[4 * i + 2];
3008:         PetscInt bO = g0_sparse_idxs[4 * i + 3];
3009:         elemMat[bO] += tmpBasisI[bM] * g0[bN] * tmpBasisJ[bK];
3010:       }
3011: #endif