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 (basic|opencl|composite|vector) - Sets the `PetscFEType`

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 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:   Options Database Key:
170: . -name [viewertype][:...] - option name and values. See `PetscObjectViewFromOptions()` for the possible arguments

172:   Level: intermediate

174: .seealso: `PetscFE`, `PetscFEView()`, `PetscObjectViewFromOptions()`, `PetscFECreate()`
175: @*/
176: PetscErrorCode PetscFEViewFromOptions(PetscFE A, PeOp PetscObject obj, const char name[])
177: {
178:   PetscFunctionBegin;
180:   PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
181:   PetscFunctionReturn(PETSC_SUCCESS);
182: }

184: /*@
185:   PetscFEView - Views a `PetscFE`

187:   Collective

189:   Input Parameters:
190: + fem    - the `PetscFE` object to view
191: - viewer - the viewer

193:   Level: beginner

195: .seealso: `PetscFE`, `PetscViewer`, `PetscFEDestroy()`, `PetscFEViewFromOptions()`
196: @*/
197: PetscErrorCode PetscFEView(PetscFE fem, PetscViewer viewer)
198: {
199:   PetscBool isascii;

201:   PetscFunctionBegin;
204:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)fem), &viewer));
205:   PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)fem, viewer));
206:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
207:   PetscTryTypeMethod(fem, view, viewer);
208:   PetscFunctionReturn(PETSC_SUCCESS);
209: }

211: /*@
212:   PetscFESetFromOptions - sets parameters in a `PetscFE` from the options database

214:   Collective

216:   Input Parameter:
217: . fem - the `PetscFE` object to set options for

219:   Options Database Keys:
220: + -petscfe_num_blocks  nblocks  - the number of cell blocks to integrate concurrently
221: - -petscfe_num_batches nbatches - the number of cell batches to integrate serially

223:   Level: intermediate

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

233:   PetscFunctionBegin;
235:   if (!((PetscObject)fem)->type_name) defaultType = PETSCFEBASIC;
236:   else defaultType = ((PetscObject)fem)->type_name;
237:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());

239:   PetscObjectOptionsBegin((PetscObject)fem);
240:   PetscCall(PetscOptionsFList("-petscfe_type", "Finite element space", "PetscFESetType", PetscFEList, defaultType, name, 256, &flg));
241:   if (flg) PetscCall(PetscFESetType(fem, name));
242:   else if (!((PetscObject)fem)->type_name) PetscCall(PetscFESetType(fem, defaultType));
243:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_blocks", "The number of cell blocks to integrate concurrently", "PetscSpaceSetTileSizes", fem->numBlocks, &fem->numBlocks, NULL, 1));
244:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_batches", "The number of cell batches to integrate serially", "PetscSpaceSetTileSizes", fem->numBatches, &fem->numBatches, NULL, 1));
245:   PetscTryTypeMethod(fem, setfromoptions, PetscOptionsObject);
246:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
247:   PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)fem, PetscOptionsObject));
248:   PetscOptionsEnd();
249:   PetscCall(PetscFEViewFromOptions(fem, NULL, "-petscfe_view"));
250:   PetscFunctionReturn(PETSC_SUCCESS);
251: }

253: /*@
254:   PetscFESetUp - Construct data structures for the `PetscFE` after the `PetscFEType` has been set

256:   Collective

258:   Input Parameter:
259: . fem - the `PetscFE` object to setup

261:   Level: intermediate

263: .seealso: `PetscFE`, `PetscFEView()`, `PetscFEDestroy()`
264: @*/
265: PetscErrorCode PetscFESetUp(PetscFE fem)
266: {
267:   PetscFunctionBegin;
269:   if (fem->setupcalled) PetscFunctionReturn(PETSC_SUCCESS);
270:   PetscCall(PetscLogEventBegin(PETSCFE_SetUp, fem, 0, 0, 0));
271:   fem->setupcalled = PETSC_TRUE;
272:   PetscTryTypeMethod(fem, setup);
273:   PetscCall(PetscLogEventEnd(PETSCFE_SetUp, fem, 0, 0, 0));
274:   PetscFunctionReturn(PETSC_SUCCESS);
275: }

277: /*@
278:   PetscFEDestroy - Destroys a `PetscFE` object

280:   Collective

282:   Input Parameter:
283: . fem - the `PetscFE` object to destroy

285:   Level: beginner

287: .seealso: `PetscFE`, `PetscFEView()`
288: @*/
289: PetscErrorCode PetscFEDestroy(PetscFE *fem)
290: {
291:   PetscFunctionBegin;
292:   if (!*fem) PetscFunctionReturn(PETSC_SUCCESS);

295:   if (--((PetscObject)*fem)->refct > 0) {
296:     *fem = NULL;
297:     PetscFunctionReturn(PETSC_SUCCESS);
298:   }
299:   ((PetscObject)*fem)->refct = 0;

301:   if ((*fem)->subspaces) {
302:     PetscInt dim, d;

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

321:   PetscTryTypeMethod(*fem, destroy);
322:   PetscCall(PetscHeaderDestroy(fem));
323:   PetscFunctionReturn(PETSC_SUCCESS);
324: }

326: /*@
327:   PetscFECreate - Creates an empty `PetscFE` object. The type can then be set with `PetscFESetType()`.

329:   Collective

331:   Input Parameter:
332: . comm - The communicator for the `PetscFE` object

334:   Output Parameter:
335: . fem - The `PetscFE` object

337:   Level: beginner

339: .seealso: `PetscFE`, `PetscFEType`, `PetscFESetType()`, `PetscFECreateDefault()`, `PETSCFEGALERKIN`
340: @*/
341: PetscErrorCode PetscFECreate(MPI_Comm comm, PetscFE *fem)
342: {
343:   PetscFE f;

345:   PetscFunctionBegin;
346:   PetscAssertPointer(fem, 2);
347:   PetscCall(PetscCitationsRegister(FECitation, &FEcite));
348:   PetscCall(PetscFEInitializePackage());

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

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

367:   *fem = f;
368:   PetscFunctionReturn(PETSC_SUCCESS);
369: }

371: /*@
372:   PetscFEGetSpatialDimension - Returns the spatial dimension of the element

374:   Not Collective

376:   Input Parameter:
377: . fem - The `PetscFE` object

379:   Output Parameter:
380: . dim - The spatial dimension

382:   Level: intermediate

384: .seealso: `PetscFE`, `PetscFECreate()`
385: @*/
386: PetscErrorCode PetscFEGetSpatialDimension(PetscFE fem, PetscInt *dim)
387: {
388:   DM dm;

390:   PetscFunctionBegin;
392:   PetscAssertPointer(dim, 2);
393:   PetscCall(PetscDualSpaceGetDM(fem->dualSpace, &dm));
394:   PetscCall(DMGetDimension(dm, dim));
395:   PetscFunctionReturn(PETSC_SUCCESS);
396: }

398: /*@
399:   PetscFESetNumComponents - Sets the number of field components in the element

401:   Not Collective

403:   Input Parameters:
404: + fem  - The `PetscFE` object
405: - comp - The number of field components

407:   Level: intermediate

409: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`, `PetscFEGetNumComponents()`
410: @*/
411: PetscErrorCode PetscFESetNumComponents(PetscFE fem, PetscInt comp)
412: {
413:   PetscFunctionBegin;
415:   fem->numComponents = comp;
416:   PetscFunctionReturn(PETSC_SUCCESS);
417: }

419: /*@
420:   PetscFEGetNumComponents - Returns the number of components in the element

422:   Not Collective

424:   Input Parameter:
425: . fem - The `PetscFE` object

427:   Output Parameter:
428: . comp - The number of field components

430:   Level: intermediate

432: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`
433: @*/
434: PetscErrorCode PetscFEGetNumComponents(PetscFE fem, PetscInt *comp)
435: {
436:   PetscFunctionBegin;
438:   PetscAssertPointer(comp, 2);
439:   *comp = fem->numComponents;
440:   PetscFunctionReturn(PETSC_SUCCESS);
441: }

443: /*@
444:   PetscFESetTileSizes - Sets the tile sizes for evaluation

446:   Not Collective

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

455:   Level: intermediate

457: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetTileSizes()`
458: @*/
459: PetscErrorCode PetscFESetTileSizes(PetscFE fem, PetscInt blockSize, PetscInt numBlocks, PetscInt batchSize, PetscInt numBatches)
460: {
461:   PetscFunctionBegin;
463:   fem->blockSize  = blockSize;
464:   fem->numBlocks  = numBlocks;
465:   fem->batchSize  = batchSize;
466:   fem->numBatches = numBatches;
467:   PetscFunctionReturn(PETSC_SUCCESS);
468: }

470: /*@
471:   PetscFEGetTileSizes - Returns the tile sizes for evaluation

473:   Not Collective

475:   Input Parameter:
476: . fem - The `PetscFE` object

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

484:   Level: intermediate

486: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFESetTileSizes()`
487: @*/
488: PetscErrorCode PetscFEGetTileSizes(PetscFE fem, PeOp PetscInt *blockSize, PeOp PetscInt *numBlocks, PeOp PetscInt *batchSize, PeOp PetscInt *numBatches)
489: {
490:   PetscFunctionBegin;
492:   if (blockSize) PetscAssertPointer(blockSize, 2);
493:   if (numBlocks) PetscAssertPointer(numBlocks, 3);
494:   if (batchSize) PetscAssertPointer(batchSize, 4);
495:   if (numBatches) PetscAssertPointer(numBatches, 5);
496:   if (blockSize) *blockSize = fem->blockSize;
497:   if (numBlocks) *numBlocks = fem->numBlocks;
498:   if (batchSize) *batchSize = fem->batchSize;
499:   if (numBatches) *numBatches = fem->numBatches;
500:   PetscFunctionReturn(PETSC_SUCCESS);
501: }

503: /*@
504:   PetscFEGetBasisSpace - Returns the `PetscSpace` used for the approximation of the solution for the `PetscFE`

506:   Not Collective

508:   Input Parameter:
509: . fem - The `PetscFE` object

511:   Output Parameter:
512: . sp - The `PetscSpace` object

514:   Level: intermediate

516: .seealso: `PetscFE`, `PetscSpace`, `PetscFECreate()`
517: @*/
518: PetscErrorCode PetscFEGetBasisSpace(PetscFE fem, PetscSpace *sp)
519: {
520:   PetscFunctionBegin;
522:   PetscAssertPointer(sp, 2);
523:   *sp = fem->basisSpace;
524:   PetscFunctionReturn(PETSC_SUCCESS);
525: }

527: /*@
528:   PetscFESetBasisSpace - Sets the `PetscSpace` used for the approximation of the solution

530:   Not Collective

532:   Input Parameters:
533: + fem - The `PetscFE` object
534: - sp  - The `PetscSpace` object

536:   Level: intermediate

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 Hessian 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: /*@
801:   PetscFEExpandFaceQuadrature - Expand a face quadrature into a cell quadrature by mapping the face
802:   quadrature points and weights through each face of the cell reference geometry.

804:   Not Collective

806:   Input Parameters:
807: + fe - the `PetscFE` object whose cell geometry defines the faces
808: - fq - the face quadrature to expand

810:   Output Parameter:
811: . efq - the expanded quadrature covering all faces of the cell

813:   Level: developer

815: .seealso: `PetscFE`, `PetscQuadrature`, `PetscFECreateFaceQuadrature()`, `PetscFEGetQuadrature()`
816: @*/
817: PetscErrorCode PetscFEExpandFaceQuadrature(PetscFE fe, PetscQuadrature fq, PetscQuadrature *efq)
818: {
819:   DM               dm;
820:   PetscDualSpace   sp;
821:   const PetscInt  *faces;
822:   const PetscReal *points, *weights;
823:   DMPolytopeType   ct;
824:   PetscReal       *facePoints, *faceWeights;
825:   PetscInt         dim, cStart, Nf, Nc, Np, order;

827:   PetscFunctionBegin;
828:   PetscCall(PetscFEGetDualSpace(fe, &sp));
829:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
830:   PetscCall(DMGetDimension(dm, &dim));
831:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
832:   PetscCall(DMPlexGetConeSize(dm, cStart, &Nf));
833:   PetscCall(DMPlexGetCone(dm, cStart, &faces));
834:   PetscCall(PetscQuadratureGetData(fq, NULL, &Nc, &Np, &points, &weights));
835:   PetscCall(PetscMalloc1(Nf * Np * dim, &facePoints));
836:   PetscCall(PetscMalloc1(Nf * Np * Nc, &faceWeights));
837:   for (PetscInt f = 0; f < Nf; ++f) {
838:     const PetscReal xi0[3] = {-1., -1., -1.};
839:     PetscReal       v0[3], J[9], detJ;

841:     PetscCall(DMPlexComputeCellGeometryFEM(dm, faces[f], NULL, v0, J, NULL, &detJ));
842:     for (PetscInt q = 0; q < Np; ++q) {
843:       CoordinatesRefToReal(dim, dim - 1, xi0, v0, J, &points[q * (dim - 1)], &facePoints[(f * Np + q) * dim]);
844:       for (PetscInt c = 0; c < Nc; ++c) faceWeights[(f * Np + q) * Nc + c] = weights[q * Nc + c];
845:     }
846:   }
847:   PetscCall(PetscQuadratureCreate(PetscObjectComm((PetscObject)fq), efq));
848:   PetscCall(PetscQuadratureGetCellType(fq, &ct));
849:   PetscCall(PetscQuadratureSetCellType(*efq, ct));
850:   PetscCall(PetscQuadratureGetOrder(fq, &order));
851:   PetscCall(PetscQuadratureSetOrder(*efq, order));
852:   PetscCall(PetscQuadratureSetData(*efq, dim, Nc, Nf * Np, facePoints, faceWeights));
853:   PetscFunctionReturn(PETSC_SUCCESS);
854: }

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

859:   Not Collective

861:   Input Parameters:
862: + fem - The `PetscFE` object
863: - k   - The highest derivative we need to tabulate, very often 1

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

868:   Level: intermediate

870:   Note:
871: .vb
872:   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
873:   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
874:   T->T[2] = Hf[((((f*Nq + q)*pdim + i)*Nc + c)*dim + d)*dim + e] is the Hessian value at point f,q for basis function i, component c, in directions d and e
875: .ve

877: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
878: @*/
879: PetscErrorCode PetscFEGetFaceTabulation(PetscFE fem, PetscInt k, PetscTabulation *Tf)
880: {
881:   PetscFunctionBegin;
883:   PetscAssertPointer(Tf, 3);
884:   if (!fem->Tf) {
885:     PetscQuadrature fq;

887:     PetscCall(PetscFEGetFaceQuadrature(fem, &fq));
888:     if (fq) {
889:       PetscQuadrature  efq;
890:       const PetscReal *facePoints;
891:       PetscInt         Np, eNp;

893:       PetscCall(PetscFEExpandFaceQuadrature(fem, fq, &efq));
894:       PetscCall(PetscQuadratureGetData(fq, NULL, NULL, &Np, NULL, NULL));
895:       PetscCall(PetscQuadratureGetData(efq, NULL, NULL, &eNp, &facePoints, NULL));
896:       if (PetscDefined(USE_DEBUG)) {
897:         PetscDualSpace sp;
898:         DM             dm;
899:         PetscInt       cStart, Nf;

901:         PetscCall(PetscFEGetDualSpace(fem, &sp));
902:         PetscCall(PetscDualSpaceGetDM(sp, &dm));
903:         PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
904:         PetscCall(DMPlexGetConeSize(dm, cStart, &Nf));
905:         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);
906:       }
907:       PetscCall(PetscFECreateTabulation(fem, eNp / Np, Np, facePoints, k, &fem->Tf));
908:       PetscCall(PetscQuadratureDestroy(&efq));
909:     }
910:   }
911:   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);
912:   *Tf = fem->Tf;
913:   PetscFunctionReturn(PETSC_SUCCESS);
914: }

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

919:   Not Collective

921:   Input Parameter:
922: . fem - The `PetscFE` object

924:   Output Parameter:
925: . Tc - The basis function values at face centroid points

927:   Level: intermediate

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

934: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetFaceTabulation()`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
935: @*/
936: PetscErrorCode PetscFEGetFaceCentroidTabulation(PetscFE fem, PetscTabulation *Tc)
937: {
938:   PetscFunctionBegin;
940:   PetscAssertPointer(Tc, 2);
941:   if (!fem->Tc) {
942:     PetscDualSpace  sp;
943:     DM              dm;
944:     const PetscInt *cone;
945:     PetscReal      *centroids;
946:     PetscInt        dim, numFaces, f;

948:     PetscCall(PetscFEGetDualSpace(fem, &sp));
949:     PetscCall(PetscDualSpaceGetDM(sp, &dm));
950:     PetscCall(DMGetDimension(dm, &dim));
951:     PetscCall(DMPlexGetConeSize(dm, 0, &numFaces));
952:     PetscCall(DMPlexGetCone(dm, 0, &cone));
953:     PetscCall(PetscMalloc1(numFaces * dim, &centroids));
954:     for (f = 0; f < numFaces; ++f) PetscCall(DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, &centroids[f * dim], NULL));
955:     PetscCall(PetscFECreateTabulation(fem, 1, numFaces, centroids, 0, &fem->Tc));
956:     PetscCall(PetscFree(centroids));
957:   }
958:   *Tc = fem->Tc;
959:   PetscFunctionReturn(PETSC_SUCCESS);
960: }

962: /*@C
963:   PetscFECreateTabulation - Creates a `PetscTabulation` object to hold the basis functions, and perhaps derivatives, at the points provided.

965:   Not Collective

967:   Input Parameters:
968: + fem     - The `PetscFE` object
969: . nrepl   - The number of replicas
970: . npoints - The number of tabulation points in a replica
971: . points  - The tabulation point coordinates
972: - K       - The number of derivatives calculated

974:   Output Parameter:
975: . T - The `PetscTabulation` to hold the basis function values and derivatives at tabulation points

977:   Level: intermediate

979: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`, `PetscFEComputeTabulation()`
980: @*/
981: PetscErrorCode PetscFECreateTabulation(PetscFE fem, PetscInt nrepl, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation *T)
982: {
983:   DM             dm;
984:   PetscDualSpace Q;
985:   PetscInt       Nb;   /* Dimension of FE space P */
986:   PetscInt       Nc;   /* Field components */
987:   PetscInt       cdim; /* Reference coordinate dimension */
988:   PetscInt       k;

990:   PetscFunctionBegin;
991:   if (!npoints || !fem->dualSpace || K < 0) {
992:     *T = NULL;
993:     PetscFunctionReturn(PETSC_SUCCESS);
994:   }
996:   PetscAssertPointer(points, 4);
997:   PetscAssertPointer(T, 6);
998:   PetscCall(PetscFEGetDualSpace(fem, &Q));
999:   PetscCall(PetscDualSpaceGetDM(Q, &dm));
1000:   PetscCall(DMGetDimension(dm, &cdim));
1001:   PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
1002:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
1003:   PetscCall(PetscMalloc1(1, T));
1004:   (*T)->K    = !cdim ? 0 : K;
1005:   (*T)->Nr   = nrepl;
1006:   (*T)->Np   = npoints;
1007:   (*T)->Nb   = Nb;
1008:   (*T)->Nc   = Nc;
1009:   (*T)->cdim = cdim;
1010:   PetscCall(PetscMalloc1((*T)->K + 1, &(*T)->T));
1011:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscCalloc1(nrepl * npoints * Nb * Nc * PetscPowInt(cdim, k), &(*T)->T[k]));
1012:   PetscUseTypeMethod(fem, computetabulation, nrepl * npoints, points, K, *T);
1013:   PetscFunctionReturn(PETSC_SUCCESS);
1014: }

1016: /*@C
1017:   PetscFEComputeTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided.

1019:   Not Collective

1021:   Input Parameters:
1022: + fem     - The `PetscFE` object
1023: . npoints - The number of tabulation points
1024: . points  - The tabulation point coordinates
1025: . K       - The number of derivatives calculated
1026: - T       - An existing tabulation object with enough allocated space, created with `PetscFECreateTabulation()`

1028:   Output Parameter:
1029: . T - The basis function values and derivatives at tabulation points

1031:   Level: intermediate

1033:   Note:
1034: .vb
1035:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
1036:   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
1037:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the Hessian value at point p for basis function i, component c, in directions d and e
1038: .ve

1040: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`, `PetscFECreateTabulation()`
1041: @*/
1042: PetscErrorCode PetscFEComputeTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation T)
1043: {
1044:   PetscFunctionBeginHot;
1045:   if (!npoints || !fem->dualSpace || K < 0) PetscFunctionReturn(PETSC_SUCCESS);
1047:   PetscAssertPointer(points, 3);
1048:   PetscAssertPointer(T, 5);
1049:   if (PetscDefined(USE_DEBUG)) {
1050:     DM             dm;
1051:     PetscDualSpace Q;
1052:     PetscInt       Nb;   /* Dimension of FE space P */
1053:     PetscInt       Nc;   /* Field components */
1054:     PetscInt       cdim; /* Reference coordinate dimension */

1056:     PetscCall(PetscFEGetDualSpace(fem, &Q));
1057:     PetscCall(PetscDualSpaceGetDM(Q, &dm));
1058:     PetscCall(DMGetDimension(dm, &cdim));
1059:     PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
1060:     PetscCall(PetscFEGetNumComponents(fem, &Nc));
1061:     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);
1062:     PetscCheck(T->Nb == Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nb %" PetscInt_FMT " must match requested Nb %" PetscInt_FMT, T->Nb, Nb);
1063:     PetscCheck(T->Nc == Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nc %" PetscInt_FMT " must match requested Nc %" PetscInt_FMT, T->Nc, Nc);
1064:     PetscCheck(T->cdim == cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation cdim %" PetscInt_FMT " must match requested cdim %" PetscInt_FMT, T->cdim, cdim);
1065:   }
1066:   T->Nr = 1;
1067:   T->Np = npoints;
1068:   PetscUseTypeMethod(fem, computetabulation, npoints, points, K, T);
1069:   PetscFunctionReturn(PETSC_SUCCESS);
1070: }

1072: /*@
1073:   PetscTabulationDestroy - Frees memory from the associated tabulation.

1075:   Not Collective

1077:   Input Parameter:
1078: . T - The tabulation

1080:   Level: intermediate

1082: .seealso: `PetscTabulation`, `PetscFECreateTabulation()`, `PetscFEGetCellTabulation()`
1083: @*/
1084: PetscErrorCode PetscTabulationDestroy(PetscTabulation *T)
1085: {
1086:   PetscInt k;

1088:   PetscFunctionBegin;
1089:   PetscAssertPointer(T, 1);
1090:   if (!T || !*T) PetscFunctionReturn(PETSC_SUCCESS);
1091:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscFree((*T)->T[k]));
1092:   PetscCall(PetscFree((*T)->T));
1093:   PetscCall(PetscFree(*T));
1094:   *T = NULL;
1095:   PetscFunctionReturn(PETSC_SUCCESS);
1096: }

1098: static PetscErrorCode PetscFECreatePointTraceDefault_Internal(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
1099: {
1100:   PetscSpace      bsp, bsubsp;
1101:   PetscDualSpace  dsp, dsubsp;
1102:   PetscInt        dim, depth, numComp, i, j, coneSize, order;
1103:   DM              dm;
1104:   DMLabel         label;
1105:   PetscReal      *xi, *v, *J, detJ;
1106:   const char     *name;
1107:   PetscQuadrature origin, fullQuad, subQuad;

1109:   PetscFunctionBegin;
1110:   PetscCall(PetscFEGetBasisSpace(fe, &bsp));
1111:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
1112:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
1113:   PetscCall(DMGetDimension(dm, &dim));
1114:   PetscCall(DMPlexGetDepthLabel(dm, &label));
1115:   PetscCall(DMLabelGetValue(label, refPoint, &depth));
1116:   PetscCall(PetscCalloc1(depth, &xi));
1117:   PetscCall(PetscMalloc1(dim, &v));
1118:   PetscCall(PetscMalloc1(dim * dim, &J));
1119:   for (i = 0; i < depth; i++) xi[i] = 0.;
1120:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &origin));
1121:   PetscCall(PetscQuadratureSetData(origin, depth, 0, 1, xi, NULL));
1122:   PetscCall(DMPlexComputeCellGeometryFEM(dm, refPoint, origin, v, J, NULL, &detJ));
1123:   /* CellGeometryFEM computes the expanded Jacobian, we want the true jacobian */
1124:   for (i = 1; i < dim; i++) {
1125:     for (j = 0; j < depth; j++) J[i * depth + j] = J[i * dim + j];
1126:   }
1127:   PetscCall(PetscQuadratureDestroy(&origin));
1128:   PetscCall(PetscDualSpaceGetPointSubspace(dsp, refPoint, &dsubsp));
1129:   PetscCall(PetscSpaceCreateSubspace(bsp, dsubsp, v, J, NULL, NULL, PETSC_OWN_POINTER, &bsubsp));
1130:   PetscCall(PetscSpaceSetUp(bsubsp));
1131:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), trFE));
1132:   PetscCall(PetscFESetType(*trFE, PETSCFEBASIC));
1133:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
1134:   PetscCall(PetscFESetNumComponents(*trFE, numComp));
1135:   PetscCall(PetscFESetBasisSpace(*trFE, bsubsp));
1136:   PetscCall(PetscFESetDualSpace(*trFE, dsubsp));
1137:   PetscCall(PetscObjectGetName((PetscObject)fe, &name));
1138:   if (name) PetscCall(PetscFESetName(*trFE, name));
1139:   PetscCall(PetscFEGetQuadrature(fe, &fullQuad));
1140:   PetscCall(PetscQuadratureGetOrder(fullQuad, &order));
1141:   PetscCall(DMPlexGetConeSize(dm, refPoint, &coneSize));
1142:   if (coneSize == 2 * depth) PetscCall(PetscDTGaussTensorQuadrature(depth, 1, (order + 2) / 2, -1., 1., &subQuad));
1143:   else PetscCall(PetscDTSimplexQuadrature(depth, order, PETSCDTSIMPLEXQUAD_DEFAULT, &subQuad));
1144:   PetscCall(PetscFESetQuadrature(*trFE, subQuad));
1145:   PetscCall(PetscFESetUp(*trFE));
1146:   PetscCall(PetscQuadratureDestroy(&subQuad));
1147:   PetscCall(PetscSpaceDestroy(&bsubsp));
1148:   PetscFunctionReturn(PETSC_SUCCESS);
1149: }

1151: PETSC_EXTERN PetscErrorCode PetscFECreatePointTrace(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
1152: {
1153:   PetscFunctionBegin;
1155:   PetscAssertPointer(trFE, 3);
1156:   if (fe->ops->createpointtrace) PetscUseTypeMethod(fe, createpointtrace, refPoint, trFE);
1157:   else PetscCall(PetscFECreatePointTraceDefault_Internal(fe, refPoint, trFE));
1158:   PetscFunctionReturn(PETSC_SUCCESS);
1159: }

1161: /*@
1162:   PetscFECreateHeightTrace - Create the trace `PetscFE` for the first mesh point of the given height stratum.

1164:   Not Collective

1166:   Input Parameters:
1167: + fe     - the `PetscFE` object
1168: - height - the height of the stratum whose first point is used to construct the trace element

1170:   Output Parameter:
1171: . trFE - the trace `PetscFE`, or `NULL` if the requested height stratum is empty

1173:   Level: developer

1175: .seealso: `PetscFE`, `PetscFECreatePointTrace()`, `PetscFEGetHeightSubspace()`, `DMPlexGetHeightStratum()`
1176: @*/
1177: PetscErrorCode PetscFECreateHeightTrace(PetscFE fe, PetscInt height, PetscFE *trFE)
1178: {
1179:   PetscInt       hStart, hEnd;
1180:   PetscDualSpace dsp;
1181:   DM             dm;

1183:   PetscFunctionBegin;
1185:   PetscAssertPointer(trFE, 3);
1186:   *trFE = NULL;
1187:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
1188:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
1189:   PetscCall(DMPlexGetHeightStratum(dm, height, &hStart, &hEnd));
1190:   if (hEnd <= hStart) PetscFunctionReturn(PETSC_SUCCESS);
1191:   PetscCall(PetscFECreatePointTrace(fe, hStart, trFE));
1192:   PetscFunctionReturn(PETSC_SUCCESS);
1193: }

1195: /*@
1196:   PetscFEGetDimension - Get the dimension of the finite element space on a cell

1198:   Not Collective

1200:   Input Parameter:
1201: . fem - The `PetscFE`

1203:   Output Parameter:
1204: . dim - The dimension

1206:   Level: intermediate

1208: .seealso: `PetscFE`, `PetscFECreate()`, `PetscSpaceGetDimension()`, `PetscDualSpaceGetDimension()`
1209: @*/
1210: PetscErrorCode PetscFEGetDimension(PetscFE fem, PetscInt *dim)
1211: {
1212:   PetscFunctionBegin;
1214:   PetscAssertPointer(dim, 2);
1215:   PetscTryTypeMethod(fem, getdimension, dim);
1216:   PetscFunctionReturn(PETSC_SUCCESS);
1217: }

1219: /*@
1220:   PetscFEPushforward - Map the reference element function to real space

1222:   Input Parameters:
1223: + fe     - The `PetscFE`
1224: . fegeom - The cell geometry
1225: . Nv     - The number of function values
1226: - vals   - The function values

1228:   Output Parameter:
1229: . vals - The transformed function values

1231:   Level: advanced

1233:   Notes:
1234:   This just forwards the call onto `PetscDualSpacePushforward()`.

1236:   It only handles transformations when the embedding dimension of the geometry in `fegeom` is the same as the reference dimension.

1238: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscDualSpacePushforward()`
1239: @*/
1240: PetscErrorCode PetscFEPushforward(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
1241: {
1242:   PetscFunctionBeginHot;
1243:   PetscCall(PetscDualSpacePushforward(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
1244:   PetscFunctionReturn(PETSC_SUCCESS);
1245: }

1247: /*@
1248:   PetscFEPushforwardGradient - Map the reference element function gradient to real space

1250:   Input Parameters:
1251: + fe     - The `PetscFE`
1252: . fegeom - The cell geometry
1253: . Nv     - The number of function gradient values
1254: - vals   - The function gradient values

1256:   Output Parameter:
1257: . vals - The transformed function gradient values

1259:   Level: advanced

1261:   Notes:
1262:   This just forwards the call onto `PetscDualSpacePushforwardGradient()`.

1264:   It only handles transformations when the embedding dimension of the geometry in `fegeom` is the same as the reference dimension.

1266: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardGradient()`, `PetscDualSpacePushforward()`
1267: @*/
1268: PetscErrorCode PetscFEPushforwardGradient(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
1269: {
1270:   PetscFunctionBeginHot;
1271:   PetscCall(PetscDualSpacePushforwardGradient(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
1272:   PetscFunctionReturn(PETSC_SUCCESS);
1273: }

1275: /*@
1276:   PetscFEPushforwardHessian - Map the reference element function Hessian to real space

1278:   Input Parameters:
1279: + fe     - The `PetscFE`
1280: . fegeom - The cell geometry
1281: . Nv     - The number of function Hessian values
1282: - vals   - The function Hessian values

1284:   Output Parameter:
1285: . vals - The transformed function Hessian values

1287:   Level: advanced

1289:   Notes:
1290:   This just forwards the call onto `PetscDualSpacePushforwardHessian()`.

1292:   It only handles transformations when the embedding dimension of the geometry in `fegeom` is the same as the reference dimension.

1294:   Developer Note:
1295:   It is unclear why all these one line convenience routines are desirable

1297: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardHessian()`, `PetscDualSpacePushforward()`
1298: @*/
1299: PetscErrorCode PetscFEPushforwardHessian(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
1300: {
1301:   PetscFunctionBeginHot;
1302:   PetscCall(PetscDualSpacePushforwardHessian(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
1303:   PetscFunctionReturn(PETSC_SUCCESS);
1304: }

1306: /*
1307: Purpose: Compute element vector for chunk of elements

1309: Input:
1310:   Sizes:
1311:      Ne:  number of elements
1312:      Nf:  number of fields
1313:      PetscFE
1314:        dim: spatial dimension
1315:        Nb:  number of basis functions
1316:        Nc:  number of field components
1317:        PetscQuadrature
1318:          Nq:  number of quadrature points

1320:   Geometry:
1321:      PetscFEGeom[Ne] possibly *Nq
1322:        PetscReal v0s[dim]
1323:        PetscReal n[dim]
1324:        PetscReal jacobians[dim*dim]
1325:        PetscReal jacobianInverses[dim*dim]
1326:        PetscReal jacobianDeterminants
1327:   FEM:
1328:      PetscFE
1329:        PetscQuadrature
1330:          PetscReal   quadPoints[Nq*dim]
1331:          PetscReal   quadWeights[Nq]
1332:        PetscReal   basis[Nq*Nb*Nc]
1333:        PetscReal   basisDer[Nq*Nb*Nc*dim]
1334:      PetscScalar coefficients[Ne*Nb*Nc]
1335:      PetscScalar elemVec[Ne*Nb*Nc]

1337:   Problem:
1338:      PetscInt f: the active field
1339:      f0, f1

1341:   Work Space:
1342:      PetscFE
1343:        PetscScalar f0[Nq*dim];
1344:        PetscScalar f1[Nq*dim*dim];
1345:        PetscScalar u[Nc];
1346:        PetscScalar gradU[Nc*dim];
1347:        PetscReal   x[dim];
1348:        PetscScalar realSpaceDer[dim];

1350: Purpose: Compute element vector for N_cb batches of elements

1352: Input:
1353:   Sizes:
1354:      N_cb: Number of serial cell batches

1356:   Geometry:
1357:      PetscReal v0s[Ne*dim]
1358:      PetscReal jacobians[Ne*dim*dim]        possibly *Nq
1359:      PetscReal jacobianInverses[Ne*dim*dim] possibly *Nq
1360:      PetscReal jacobianDeterminants[Ne]     possibly *Nq
1361:   FEM:
1362:      static PetscReal   quadPoints[Nq*dim]
1363:      static PetscReal   quadWeights[Nq]
1364:      static PetscReal   basis[Nq*Nb*Nc]
1365:      static PetscReal   basisDer[Nq*Nb*Nc*dim]
1366:      PetscScalar coefficients[Ne*Nb*Nc]
1367:      PetscScalar elemVec[Ne*Nb*Nc]

1369: ex62.c:
1370:   PetscErrorCode PetscFEIntegrateResidualBatch(PetscInt Ne, PetscInt numFields, PetscInt field, PetscQuadrature quad[], const PetscScalar coefficients[],
1371:                                                const PetscReal v0s[], const PetscReal jacobians[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[],
1372:                                                void (*f0_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]),
1373:                                                void (*f1_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]), PetscScalar elemVec[])

1375: ex52.c:
1376:   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)
1377:   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)

1379: ex52_integrateElement.cu
1380: __global__ void integrateElementQuadrature(int N_cb, realType *coefficients, realType *jacobianInverses, realType *jacobianDeterminants, realType *elemVec)

1382: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt Nbl, const PetscScalar coefficients[],
1383:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
1384:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

1386: ex52_integrateElementOpenCL.c:
1387: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt N_bl, const PetscScalar coefficients[],
1388:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
1389:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

1391: __kernel void integrateElementQuadrature(int N_cb, __global float *coefficients, __global float *jacobianInverses, __global float *jacobianDeterminants, __global float *elemVec)
1392: */

1394: /*@
1395:   PetscFEIntegrate - Produce the integral for the given field for a chunk of elements by quadrature integration

1397:   Not Collective

1399:   Input Parameters:
1400: + prob            - The `PetscDS` specifying the discretizations and continuum functions
1401: . field           - The field being integrated
1402: . Ne              - The number of elements in the chunk
1403: . cgeom           - The cell geometry for each cell in the chunk
1404: . coefficients    - The array of FEM basis coefficients for the elements
1405: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1406: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

1408:   Output Parameter:
1409: . integral - the integral for this field

1411:   Level: intermediate

1413: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrateBd()`
1414: @*/
1415: PetscErrorCode PetscFEIntegrate(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[])
1416: {
1417:   PetscFE fe;

1419:   PetscFunctionBegin;
1421:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
1422:   if (fe->ops->integrate) PetscCall((*fe->ops->integrate)(prob, field, Ne, cgeom, coefficients, probAux, coefficientsAux, integral));
1423:   PetscFunctionReturn(PETSC_SUCCESS);
1424: }

1426: /*@C
1427:   PetscFEIntegrateBd - Produce the integral for the given field for a chunk of elements by quadrature integration

1429:   Not Collective

1431:   Input Parameters:
1432: + prob            - The `PetscDS` specifying the discretizations and continuum functions
1433: . field           - The field being integrated
1434: . obj_func        - The function to be integrated
1435: . Ne              - The number of elements in the chunk
1436: . geom            - The face geometry for each face in the chunk
1437: . coefficients    - The array of FEM basis coefficients for the elements
1438: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1439: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

1441:   Output Parameter:
1442: . integral - the integral for this field

1444:   Level: intermediate

1446: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrate()`
1447: @*/
1448: 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[])
1449: {
1450:   PetscFE fe;

1452:   PetscFunctionBegin;
1454:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
1455:   if (fe->ops->integratebd) PetscCall((*fe->ops->integratebd)(prob, field, obj_func, Ne, geom, coefficients, probAux, coefficientsAux, integral));
1456:   PetscFunctionReturn(PETSC_SUCCESS);
1457: }

1459: /*@
1460:   PetscFEIntegrateResidual - Produce the element residual vector for a chunk of elements by quadrature integration

1462:   Not Collective

1464:   Input Parameters:
1465: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1466: . key             - The (label+value, field) being integrated
1467: . Ne              - The number of elements in the chunk
1468: . cgeom           - The cell geometry for each cell in the chunk
1469: . coefficients    - The array of FEM basis coefficients for the elements
1470: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1471: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1472: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1473: - t               - The time

1475:   Output Parameter:
1476: . elemVec - the element residual vectors from each element

1478:   Level: intermediate

1480:   Note:
1481: .vb
1482:   Loop over batch of elements (e):
1483:     Loop over quadrature points (q):
1484:       Make u_q and gradU_q (loops over fields,Nb,Ncomp) and x_q
1485:       Call f_0 and f_1
1486:     Loop over element vector entries (f,fc --> i):
1487:       elemVec[i] += \psi^{fc}_f(q) f0_{fc}(u, \nabla u) + \nabla\psi^{fc}_f(q) \cdot f1_{fc,df}(u, \nabla u)
1488: .ve

1490: .seealso: `PetscFEIntegrateBdResidual()`
1491: @*/
1492: 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[])
1493: {
1494:   PetscFE fe;

1496:   PetscFunctionBeginHot;
1498:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
1499:   if (fe->ops->integrateresidual) PetscCall((*fe->ops->integrateresidual)(ds, key, Ne, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
1500:   PetscFunctionReturn(PETSC_SUCCESS);
1501: }

1503: /*@
1504:   PetscFEIntegrateBdResidual - Produce the element residual vector for a chunk of elements by quadrature integration over a boundary

1506:   Not Collective

1508:   Input Parameters:
1509: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1510: . wf              - The PetscWeakForm object holding the pointwise functions
1511: . key             - The (label+value, field) being integrated
1512: . Ne              - The number of elements in the chunk
1513: . fgeom           - The face geometry for each cell in the chunk
1514: . coefficients    - The array of FEM basis coefficients for the elements
1515: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1516: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1517: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1518: - t               - The time

1520:   Output Parameter:
1521: . elemVec - the element residual vectors from each element

1523:   Level: intermediate

1525: .seealso: `PetscFEIntegrateResidual()`
1526: @*/
1527: 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[])
1528: {
1529:   PetscFE fe;

1531:   PetscFunctionBegin;
1533:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
1534:   if (fe->ops->integratebdresidual) PetscCall((*fe->ops->integratebdresidual)(ds, wf, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
1535:   PetscFunctionReturn(PETSC_SUCCESS);
1536: }

1538: /*@
1539:   PetscFEIntegrateHybridResidual - Produce the element residual vector for a chunk of hybrid element faces by quadrature integration

1541:   Not Collective

1543:   Input Parameters:
1544: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1545: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for input
1546: . key             - The (label+value, field) being integrated
1547: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
1548: . Ne              - The number of elements in the chunk
1549: . fgeom           - The face geometry for each cell in the chunk
1550: . cgeom           - The cell geometry for each neighbor cell in the chunk
1551: . coefficients    - The array of FEM basis coefficients for the elements
1552: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1553: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1554: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1555: - t               - The time

1557:   Output Parameter:
1558: . elemVec - the element residual vectors from each element

1560:   Level: developer

1562: .seealso: `PetscFEIntegrateResidual()`
1563: @*/
1564: 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[])
1565: {
1566:   PetscFE fe;

1568:   PetscFunctionBegin;
1571:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
1572:   if (fe->ops->integratehybridresidual) PetscCall((*fe->ops->integratehybridresidual)(ds, dsIn, key, s, Ne, fgeom, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
1573:   PetscFunctionReturn(PETSC_SUCCESS);
1574: }

1576: /*@
1577:   PetscFEIntegrateJacobian - Produce the element Jacobian for a chunk of elements by quadrature integration

1579:   Not Collective

1581:   Input Parameters:
1582: + rds             - The `PetscDS` specifying the row discretizations and continuum functions
1583: . cds             - The `PetscDS` specifying the column discretizations
1584: . jtype           - The type of matrix pointwise functions that should be used
1585: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
1586: . Ne              - The number of elements in the chunk
1587: . cgeom           - The cell geometry for each cell in the chunk
1588: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
1589: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1590: . dsAux           - The `PetscDS` specifying the auxiliary discretizations
1591: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1592: . t               - The time
1593: - u_tshift        - A multiplier for the $dF/du_t$ term (as opposed to the $dF/du$ term)

1595:   Output Parameter:
1596: . elemMat - the element matrices for the Jacobian from each element

1598:   Level: intermediate

1600:   Note:
1601: .vb
1602:   Loop over batch of elements (e):
1603:     Loop over element matrix entries (f,fc,g,gc --> i,j):
1604:       Loop over quadrature points (q):
1605:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
1606:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1607:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1608:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1609:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1610: .ve

1612: .seealso: `PetscFEIntegrateResidual()`
1613: @*/
1614: 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[])
1615: {
1616:   PetscFE  fe;
1617:   PetscInt Nf;

1619:   PetscFunctionBegin;
1622:   PetscCall(PetscDSGetNumFields(rds, &Nf));
1623:   PetscCall(PetscDSGetDiscretization(rds, key.field / Nf, (PetscObject *)&fe));
1624:   if (fe->ops->integratejacobian) PetscCall((*fe->ops->integratejacobian)(rds, cds, jtype, key, Ne, cgeom, coefficients, coefficients_t, dsAux, coefficientsAux, t, u_tshift, elemMat));
1625:   PetscFunctionReturn(PETSC_SUCCESS);
1626: }

1628: /*@
1629:   PetscFEIntegrateBdJacobian - Produce the boundary element Jacobian for a chunk of elements by quadrature integration

1631:   Not Collective

1633:   Input Parameters:
1634: + ds              - The `PetscDS` specifying the discretizations and continuum functions
1635: . wf              - The PetscWeakForm holding the pointwise functions
1636: . jtype           - The type of matrix pointwise functions that should be used
1637: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
1638: . Ne              - The number of elements in the chunk
1639: . fgeom           - The face geometry for each cell in the chunk
1640: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
1641: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1642: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1643: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1644: . t               - The time
1645: - u_tshift        - A multiplier for the $dF/du_t$ term (as opposed to the $dF/du$ term)

1647:   Output Parameter:
1648: . elemMat - the element matrices for the Jacobian from each element

1650:   Level: intermediate

1652:   Note:
1653: .vb
1654:   Loop over batch of elements (e):
1655:     Loop over element matrix entries (f,fc,g,gc --> i,j):
1656:       Loop over quadrature points (q):
1657:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
1658:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1659:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1660:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1661:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1662: .ve

1664: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
1665: @*/
1666: 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[])
1667: {
1668:   PetscFE  fe;
1669:   PetscInt Nf;

1671:   PetscFunctionBegin;
1673:   PetscCall(PetscDSGetNumFields(ds, &Nf));
1674:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
1675:   if (fe->ops->integratebdjacobian) PetscCall((*fe->ops->integratebdjacobian)(ds, wf, jtype, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
1676:   PetscFunctionReturn(PETSC_SUCCESS);
1677: }

1679: /*@
1680:   PetscFEIntegrateHybridJacobian - Produce the boundary element Jacobian for a chunk of hybrid elements by quadrature integration

1682:   Not Collective

1684:   Input Parameters:
1685: + ds              - The `PetscDS` specifying the discretizations and continuum functions for the output
1686: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for the input
1687: . jtype           - The type of matrix pointwise functions that should be used
1688: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
1689: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
1690: . Ne              - The number of elements in the chunk
1691: . fgeom           - The face geometry for each cell in the chunk
1692: . cgeom           - The cell geometry for each neighbor cell in the chunk
1693: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
1694: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
1695: . probAux         - The `PetscDS` specifying the auxiliary discretizations
1696: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
1697: . t               - The time
1698: - u_tshift        - A multiplier for the $dF/du_t$ term (as opposed to the $dF/du$ term)

1700:   Output Parameter:
1701: . elemMat - the element matrices for the Jacobian from each element

1703:   Level: developer

1705:   Note:
1706: .vb
1707:   Loop over batch of elements (e):
1708:     Loop over element matrix entries (f,fc,g,gc --> i,j):
1709:       Loop over quadrature points (q):
1710:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
1711:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1712:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1713:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1714:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1715: .ve

1717: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
1718: @*/
1719: 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[])
1720: {
1721:   PetscFE  fe;
1722:   PetscInt Nf;

1724:   PetscFunctionBegin;
1726:   PetscCall(PetscDSGetNumFields(ds, &Nf));
1727:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
1728:   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));
1729:   PetscFunctionReturn(PETSC_SUCCESS);
1730: }

1732: /*@
1733:   PetscFEGetHeightSubspace - Get the subspace of this space for a mesh point of a given height

1735:   Input Parameters:
1736: + fe     - The finite element space
1737: - height - The height of the `DMPLEX` point

1739:   Output Parameter:
1740: . subfe - The subspace of this `PetscFE` space

1742:   Level: advanced

1744:   Note:
1745:   For example, if we want the subspace of this space for a face, we would choose height = 1.

1747: .seealso: `PetscFECreateDefault()`
1748: @*/
1749: PetscErrorCode PetscFEGetHeightSubspace(PetscFE fe, PetscInt height, PetscFE *subfe)
1750: {
1751:   PetscSpace      P, subP;
1752:   PetscDualSpace  Q, subQ;
1753:   PetscQuadrature subq;
1754:   PetscInt        dim, Nc;

1756:   PetscFunctionBegin;
1758:   PetscAssertPointer(subfe, 3);
1759:   if (height == 0) {
1760:     *subfe = fe;
1761:     PetscFunctionReturn(PETSC_SUCCESS);
1762:   }
1763:   PetscCall(PetscFEGetBasisSpace(fe, &P));
1764:   PetscCall(PetscFEGetDualSpace(fe, &Q));
1765:   PetscCall(PetscFEGetNumComponents(fe, &Nc));
1766:   PetscCall(PetscFEGetFaceQuadrature(fe, &subq));
1767:   PetscCall(PetscDualSpaceGetDimension(Q, &dim));
1768:   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);
1769:   if (!fe->subspaces) PetscCall(PetscCalloc1(dim, &fe->subspaces));
1770:   if (height <= dim) {
1771:     if (!fe->subspaces[height - 1]) {
1772:       PetscFE     sub = NULL;
1773:       const char *name;

1775:       PetscCall(PetscSpaceGetHeightSubspace(P, height, &subP));
1776:       PetscCall(PetscDualSpaceGetHeightSubspace(Q, height, &subQ));
1777:       if (subQ) {
1778:         PetscCall(PetscObjectReference((PetscObject)subP));
1779:         PetscCall(PetscObjectReference((PetscObject)subQ));
1780:         PetscCall(PetscObjectReference((PetscObject)subq));
1781:         PetscCall(PetscFECreateFromSpaces(subP, subQ, subq, NULL, &sub));
1782:       }
1783:       if (sub) {
1784:         PetscCall(PetscObjectGetName((PetscObject)fe, &name));
1785:         if (name) PetscCall(PetscFESetName(sub, name));
1786:       }
1787:       fe->subspaces[height - 1] = sub;
1788:     }
1789:     *subfe = fe->subspaces[height - 1];
1790:   } else {
1791:     *subfe = NULL;
1792:   }
1793:   PetscFunctionReturn(PETSC_SUCCESS);
1794: }

1796: /*@
1797:   PetscFERefine - Create a "refined" `PetscFE` object that refines the reference cell into
1798:   smaller copies.

1800:   Collective

1802:   Input Parameter:
1803: . fe - The initial `PetscFE`

1805:   Output Parameter:
1806: . feRef - The refined `PetscFE`

1808:   Level: advanced

1810:   Notes:
1811:   This is typically used to generate a preconditioner for a higher order method from a lower order method on a
1812:   refined mesh having the same number of dofs (but more sparsity). It is also used to create an
1813:   interpolation between regularly refined meshes.

1815: .seealso: `PetscFEType`, `PetscFECreate()`, `PetscFESetType()`
1816: @*/
1817: PetscErrorCode PetscFERefine(PetscFE fe, PetscFE *feRef)
1818: {
1819:   PetscSpace       P, Pref;
1820:   PetscDualSpace   Q, Qref;
1821:   DM               K, Kref;
1822:   PetscQuadrature  q, qref;
1823:   const PetscReal *v0, *jac;
1824:   PetscInt         numComp, numSubelements;
1825:   PetscInt         cStart, cEnd, c;
1826:   PetscDualSpace  *cellSpaces;

1828:   PetscFunctionBegin;
1829:   PetscCall(PetscFEGetBasisSpace(fe, &P));
1830:   PetscCall(PetscFEGetDualSpace(fe, &Q));
1831:   PetscCall(PetscFEGetQuadrature(fe, &q));
1832:   PetscCall(PetscDualSpaceGetDM(Q, &K));
1833:   /* Create space */
1834:   PetscCall(PetscObjectReference((PetscObject)P));
1835:   Pref = P;
1836:   /* Create dual space */
1837:   PetscCall(PetscDualSpaceDuplicate(Q, &Qref));
1838:   PetscCall(PetscDualSpaceSetType(Qref, PETSCDUALSPACEREFINED));
1839:   PetscCall(DMRefine(K, PetscObjectComm((PetscObject)fe), &Kref));
1840:   PetscCall(DMGetCoordinatesLocalSetUp(Kref));
1841:   PetscCall(PetscDualSpaceSetDM(Qref, Kref));
1842:   PetscCall(DMPlexGetHeightStratum(Kref, 0, &cStart, &cEnd));
1843:   PetscCall(PetscMalloc1(cEnd - cStart, &cellSpaces));
1844:   /* TODO: fix for non-uniform refinement */
1845:   for (c = 0; c < cEnd - cStart; c++) cellSpaces[c] = Q;
1846:   PetscCall(PetscDualSpaceRefinedSetCellSpaces(Qref, cellSpaces));
1847:   PetscCall(PetscFree(cellSpaces));
1848:   PetscCall(DMDestroy(&Kref));
1849:   PetscCall(PetscDualSpaceSetUp(Qref));
1850:   /* Create element */
1851:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), feRef));
1852:   PetscCall(PetscFESetType(*feRef, PETSCFECOMPOSITE));
1853:   PetscCall(PetscFESetBasisSpace(*feRef, Pref));
1854:   PetscCall(PetscFESetDualSpace(*feRef, Qref));
1855:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
1856:   PetscCall(PetscFESetNumComponents(*feRef, numComp));
1857:   PetscCall(PetscFESetUp(*feRef));
1858:   PetscCall(PetscSpaceDestroy(&Pref));
1859:   PetscCall(PetscDualSpaceDestroy(&Qref));
1860:   /* Create quadrature */
1861:   PetscCall(PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL));
1862:   PetscCall(PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref));
1863:   PetscCall(PetscFESetQuadrature(*feRef, qref));
1864:   PetscCall(PetscQuadratureDestroy(&qref));
1865:   PetscFunctionReturn(PETSC_SUCCESS);
1866: }

1868: static PetscErrorCode PetscFESetDefaultName_Private(PetscFE fe)
1869: {
1870:   PetscSpace     P;
1871:   PetscDualSpace Q;
1872:   DM             K;
1873:   DMPolytopeType ct;
1874:   PetscInt       degree;
1875:   char           name[64];

1877:   PetscFunctionBegin;
1878:   PetscCall(PetscFEGetBasisSpace(fe, &P));
1879:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
1880:   PetscCall(PetscFEGetDualSpace(fe, &Q));
1881:   PetscCall(PetscDualSpaceGetDM(Q, &K));
1882:   PetscCall(DMPlexGetCellType(K, 0, &ct));
1883:   switch (ct) {
1884:   case DM_POLYTOPE_SEGMENT:
1885:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1886:   case DM_POLYTOPE_QUADRILATERAL:
1887:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1888:   case DM_POLYTOPE_HEXAHEDRON:
1889:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1890:     PetscCall(PetscSNPrintf(name, sizeof(name), "Q%" PetscInt_FMT, degree));
1891:     break;
1892:   case DM_POLYTOPE_TRIANGLE:
1893:   case DM_POLYTOPE_TETRAHEDRON:
1894:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT, degree));
1895:     break;
1896:   case DM_POLYTOPE_TRI_PRISM:
1897:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1898:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT "xQ%" PetscInt_FMT, degree, degree));
1899:     break;
1900:   default:
1901:     PetscCall(PetscSNPrintf(name, sizeof(name), "FE"));
1902:   }
1903:   PetscCall(PetscFESetName(fe, name));
1904:   PetscFunctionReturn(PETSC_SUCCESS);
1905: }

1907: /*@
1908:   PetscFECreateFromSpaces - Create a `PetscFE` from the basis and dual spaces

1910:   Collective

1912:   Input Parameters:
1913: + P  - The basis space
1914: . Q  - The dual space
1915: . q  - The cell quadrature
1916: - fq - The face quadrature

1918:   Output Parameter:
1919: . fem - The `PetscFE` object

1921:   Level: beginner

1923:   Note:
1924:   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,
1925:   the caller must use `PetscObjectReference()` before this call.

1927: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`,
1928:           `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
1929: @*/
1930: PetscErrorCode PetscFECreateFromSpaces(PetscSpace P, PetscDualSpace Q, PetscQuadrature q, PetscQuadrature fq, PetscFE *fem)
1931: {
1932:   PetscInt    Nc;
1933:   PetscInt    p_Ns = -1, p_Nc = -1, q_Ns = -1, q_Nc = -1;
1934:   PetscBool   p_is_uniform_sum = PETSC_FALSE, p_interleave_basis = PETSC_FALSE, p_interleave_components = PETSC_FALSE;
1935:   PetscBool   q_is_uniform_sum = PETSC_FALSE, q_interleave_basis = PETSC_FALSE, q_interleave_components = PETSC_FALSE;
1936:   const char *prefix;

1938:   PetscFunctionBegin;
1939:   PetscCall(PetscObjectTypeCompare((PetscObject)P, PETSCSPACESUM, &p_is_uniform_sum));
1940:   if (p_is_uniform_sum) {
1941:     PetscSpace subsp_0 = NULL;
1942:     PetscCall(PetscSpaceSumGetNumSubspaces(P, &p_Ns));
1943:     PetscCall(PetscSpaceGetNumComponents(P, &p_Nc));
1944:     PetscCall(PetscSpaceSumGetConcatenate(P, &p_is_uniform_sum));
1945:     PetscCall(PetscSpaceSumGetInterleave(P, &p_interleave_basis, &p_interleave_components));
1946:     for (PetscInt s = 0; s < p_Ns; s++) {
1947:       PetscSpace subsp;

1949:       PetscCall(PetscSpaceSumGetSubspace(P, s, &subsp));
1950:       if (!s) {
1951:         subsp_0 = subsp;
1952:       } else if (subsp != subsp_0) {
1953:         p_is_uniform_sum = PETSC_FALSE;
1954:       }
1955:     }
1956:   }
1957:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &q_is_uniform_sum));
1958:   if (q_is_uniform_sum) {
1959:     PetscDualSpace subsp_0 = NULL;
1960:     PetscCall(PetscDualSpaceSumGetNumSubspaces(Q, &q_Ns));
1961:     PetscCall(PetscDualSpaceGetNumComponents(Q, &q_Nc));
1962:     PetscCall(PetscDualSpaceSumGetConcatenate(Q, &q_is_uniform_sum));
1963:     PetscCall(PetscDualSpaceSumGetInterleave(Q, &q_interleave_basis, &q_interleave_components));
1964:     for (PetscInt s = 0; s < q_Ns; s++) {
1965:       PetscDualSpace subsp;

1967:       PetscCall(PetscDualSpaceSumGetSubspace(Q, s, &subsp));
1968:       if (!s) {
1969:         subsp_0 = subsp;
1970:       } else if (subsp != subsp_0) {
1971:         q_is_uniform_sum = PETSC_FALSE;
1972:       }
1973:     }
1974:   }
1975:   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)) {
1976:     PetscSpace     scalar_space;
1977:     PetscDualSpace scalar_dspace;
1978:     PetscFE        scalar_fe;

1980:     PetscCall(PetscSpaceSumGetSubspace(P, 0, &scalar_space));
1981:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &scalar_dspace));
1982:     PetscCall(PetscObjectReference((PetscObject)scalar_space));
1983:     PetscCall(PetscObjectReference((PetscObject)scalar_dspace));
1984:     PetscCall(PetscObjectReference((PetscObject)q));
1985:     PetscCall(PetscObjectReference((PetscObject)fq));
1986:     PetscCall(PetscFECreateFromSpaces(scalar_space, scalar_dspace, q, fq, &scalar_fe));
1987:     PetscCall(PetscFECreateVector(scalar_fe, p_Ns, p_interleave_basis, p_interleave_components, fem));
1988:     PetscCall(PetscFEDestroy(&scalar_fe));
1989:   } else {
1990:     PetscCall(PetscFECreate(PetscObjectComm((PetscObject)P), fem));
1991:     PetscCall(PetscFESetType(*fem, PETSCFEBASIC));
1992:   }
1993:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
1994:   PetscCall(PetscFESetNumComponents(*fem, Nc));
1995:   PetscCall(PetscFESetBasisSpace(*fem, P));
1996:   PetscCall(PetscFESetDualSpace(*fem, Q));
1997:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)P, &prefix));
1998:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*fem, prefix));
1999:   PetscCall(PetscFESetUp(*fem));
2000:   PetscCall(PetscSpaceDestroy(&P));
2001:   PetscCall(PetscDualSpaceDestroy(&Q));
2002:   PetscCall(PetscFESetQuadrature(*fem, q));
2003:   PetscCall(PetscFESetFaceQuadrature(*fem, fq));
2004:   PetscCall(PetscQuadratureDestroy(&q));
2005:   PetscCall(PetscQuadratureDestroy(&fq));
2006:   PetscCall(PetscFESetDefaultName_Private(*fem));
2007:   PetscFunctionReturn(PETSC_SUCCESS);
2008: }

2010: static PetscErrorCode PetscFECreate_Internal(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt degree, PetscInt qorder, PetscBool setFromOptions, PetscFE *fem)
2011: {
2012:   DM                           K;
2013:   PetscSpace                   P;
2014:   PetscDualSpace               Q;
2015:   PetscQuadrature              q, fq;
2016:   PetscBool                    tensor;
2017:   PetscDTSimplexQuadratureType qtype = PETSCDTSIMPLEXQUAD_DEFAULT;

2019:   PetscFunctionBegin;
2020:   if (prefix) PetscAssertPointer(prefix, 5);
2021:   PetscAssertPointer(fem, 9);
2022:   switch (ct) {
2023:   case DM_POLYTOPE_SEGMENT:
2024:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2025:   case DM_POLYTOPE_QUADRILATERAL:
2026:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2027:   case DM_POLYTOPE_HEXAHEDRON:
2028:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2029:     tensor = PETSC_TRUE;
2030:     break;
2031:   default:
2032:     tensor = PETSC_FALSE;
2033:   }
2034:   /* Create space */
2035:   PetscCall(PetscSpaceCreate(comm, &P));
2036:   PetscCall(PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL));
2037:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)P, prefix));
2038:   PetscCall(PetscSpacePolynomialSetTensor(P, tensor));
2039:   PetscCall(PetscSpaceSetNumComponents(P, Nc));
2040:   PetscCall(PetscSpaceSetNumVariables(P, dim));
2041:   if (degree >= 0) {
2042:     PetscCall(PetscSpaceSetDegree(P, degree, PETSC_DETERMINE));
2043:     if (ct == DM_POLYTOPE_TRI_PRISM || ct == DM_POLYTOPE_TRI_PRISM_TENSOR) {
2044:       PetscSpace Pend, Pside;

2046:       PetscCall(PetscSpaceSetNumComponents(P, 1));
2047:       PetscCall(PetscSpaceCreate(comm, &Pend));
2048:       PetscCall(PetscSpaceSetType(Pend, PETSCSPACEPOLYNOMIAL));
2049:       PetscCall(PetscSpacePolynomialSetTensor(Pend, PETSC_FALSE));
2050:       PetscCall(PetscSpaceSetNumComponents(Pend, 1));
2051:       PetscCall(PetscSpaceSetNumVariables(Pend, dim - 1));
2052:       PetscCall(PetscSpaceSetDegree(Pend, degree, PETSC_DETERMINE));
2053:       PetscCall(PetscSpaceCreate(comm, &Pside));
2054:       PetscCall(PetscSpaceSetType(Pside, PETSCSPACEPOLYNOMIAL));
2055:       PetscCall(PetscSpacePolynomialSetTensor(Pside, PETSC_FALSE));
2056:       PetscCall(PetscSpaceSetNumComponents(Pside, 1));
2057:       PetscCall(PetscSpaceSetNumVariables(Pside, 1));
2058:       PetscCall(PetscSpaceSetDegree(Pside, degree, PETSC_DETERMINE));
2059:       PetscCall(PetscSpaceSetType(P, PETSCSPACETENSOR));
2060:       PetscCall(PetscSpaceTensorSetNumSubspaces(P, 2));
2061:       PetscCall(PetscSpaceTensorSetSubspace(P, 0, Pend));
2062:       PetscCall(PetscSpaceTensorSetSubspace(P, 1, Pside));
2063:       PetscCall(PetscSpaceDestroy(&Pend));
2064:       PetscCall(PetscSpaceDestroy(&Pside));

2066:       if (Nc > 1) {
2067:         PetscSpace scalar_P = P;

2069:         PetscCall(PetscSpaceCreate(comm, &P));
2070:         PetscCall(PetscSpaceSetNumVariables(P, dim));
2071:         PetscCall(PetscSpaceSetNumComponents(P, Nc));
2072:         PetscCall(PetscSpaceSetType(P, PETSCSPACESUM));
2073:         PetscCall(PetscSpaceSumSetNumSubspaces(P, Nc));
2074:         PetscCall(PetscSpaceSumSetConcatenate(P, PETSC_TRUE));
2075:         PetscCall(PetscSpaceSumSetInterleave(P, PETSC_TRUE, PETSC_FALSE));
2076:         for (PetscInt i = 0; i < Nc; i++) PetscCall(PetscSpaceSumSetSubspace(P, i, scalar_P));
2077:         PetscCall(PetscSpaceDestroy(&scalar_P));
2078:       }
2079:     }
2080:   }
2081:   if (setFromOptions) PetscCall(PetscSpaceSetFromOptions(P));
2082:   PetscCall(PetscSpaceSetUp(P));
2083:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
2084:   PetscCall(PetscSpacePolynomialGetTensor(P, &tensor));
2085:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
2086:   /* Create dual space */
2087:   PetscCall(PetscDualSpaceCreate(comm, &Q));
2088:   PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
2089:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)Q, prefix));
2090:   PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
2091:   PetscCall(PetscDualSpaceSetDM(Q, K));
2092:   PetscCall(DMDestroy(&K));
2093:   PetscCall(PetscDualSpaceSetNumComponents(Q, Nc));
2094:   PetscCall(PetscDualSpaceSetOrder(Q, degree));
2095:   PetscCall(PetscDualSpaceLagrangeSetTensor(Q, (tensor || (ct == DM_POLYTOPE_TRI_PRISM)) ? PETSC_TRUE : PETSC_FALSE));
2096:   if (setFromOptions) PetscCall(PetscDualSpaceSetFromOptions(Q));
2097:   PetscCall(PetscDualSpaceSetUp(Q));

2099:   qorder = qorder >= 0 ? qorder : degree;
2100:   if (setFromOptions) {
2101:     PetscObjectOptionsBegin((PetscObject)P);
2102:     PetscCall(PetscOptionsBoundedInt("-petscfe_default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "PetscFECreateDefault", qorder, &qorder, NULL, 0));
2103:     PetscCall(PetscOptionsEnum("-petscfe_default_quadrature_type", "Simplex quadrature type", "PetscDTSimplexQuadratureType", PetscDTSimplexQuadratureTypes, (PetscEnum)qtype, (PetscEnum *)&qtype, NULL));
2104:     PetscOptionsEnd();
2105:   }
2106:   PetscCall(PetscDTCreateQuadratureByCell(ct, qorder, qtype, &q, &fq));
2107:   /* Create finite element */
2108:   PetscCall(PetscFECreateFromSpaces(P, Q, q, fq, fem));
2109:   if (setFromOptions) PetscCall(PetscFESetFromOptions(*fem));
2110:   PetscFunctionReturn(PETSC_SUCCESS);
2111: }

2113: /*@
2114:   PetscFECreateDefault - Create a `PetscFE` for basic FEM computation

2116:   Collective

2118:   Input Parameters:
2119: + comm      - The MPI comm
2120: . dim       - The spatial dimension
2121: . Nc        - The number of components
2122: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
2123: . prefix    - The options prefix, or `NULL`
2124: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2126:   Output Parameter:
2127: . fem - The `PetscFE` object

2129:   Level: beginner

2131:   Notes:
2132:   Preferred usage is `PetscFECreateByCell()`

2134:   Each subobject is SetFromOption() during creation, so that the object may be customized from the command line, using the prefix specified above.
2135:   See the links below for the particular options available.

2137: .seealso: `PetscFE`, `PetscFECreateLagrange()`, `PetscFECreateByCell()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`,
2138:           `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2139: @*/
2140: PetscErrorCode PetscFECreateDefault(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, const char prefix[], PetscInt qorder, PetscFE *fem)
2141: {
2142:   PetscFunctionBegin;
2143:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
2144:   PetscFunctionReturn(PETSC_SUCCESS);
2145: }

2147: /*@
2148:   PetscFECreateByCell - Create a `PetscFE` for basic FEM computation

2150:   Collective

2152:   Input Parameters:
2153: + comm   - The MPI comm
2154: . dim    - The spatial dimension
2155: . Nc     - The number of components
2156: . ct     - The celltype of the reference cell
2157: . prefix - The options prefix, or `NULL`
2158: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2160:   Output Parameter:
2161: . fem - The `PetscFE` object

2163:   Level: beginner

2165:   Note:
2166:   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.

2168:   Developer Notes:
2169:   This should be called `PetscFECreateDefaultByCell()` since it is the extension/replacement for `PetscFECreateDefault()`

2171:   Since this generalizes/replaces `PetscFECreateDefault()` for different `DMPolytopeType` its name should be `PetscFECreateDefaultByPolytopeType()`

2173: .seealso: `PetscFE`, `PetscFECreateDefault()`, `PetscFECreateLagrange()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`,
2174:           `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`, `DMPolytopeType`
2175: @*/
2176: PetscErrorCode PetscFECreateByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt qorder, PetscFE *fem)
2177: {
2178:   PetscFunctionBegin;
2179:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
2180:   PetscFunctionReturn(PETSC_SUCCESS);
2181: }

2183: /*@
2184:   PetscFECreateLagrange - Create a `PetscFE` for the basic Lagrange space of degree `k`

2186:   Collective

2188:   Input Parameters:
2189: + comm      - The MPI comm
2190: . dim       - The spatial dimension
2191: . Nc        - The number of components
2192: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
2193: . k         - The degree of the space
2194: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2196:   Output Parameter:
2197: . fem - The `PetscFE` object

2199:   Level: beginner

2201:   Notes:
2202:   Preferred usage is `PetscFECreateLagrangeByCell()`

2204:   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`.

2206: .seealso: `PetscFE`, `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2207: @*/
2208: PetscErrorCode PetscFECreateLagrange(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, PetscInt k, PetscInt qorder, PetscFE *fem)
2209: {
2210:   PetscFunctionBegin;
2211:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), NULL, k, qorder, PETSC_FALSE, fem));
2212:   PetscFunctionReturn(PETSC_SUCCESS);
2213: }

2215: /*@
2216:   PetscFECreateLagrangeByCell - Create a `PetscFE` for the basic Lagrange space of degree `k`

2218:   Collective

2220:   Input Parameters:
2221: + comm   - The MPI comm
2222: . dim    - The spatial dimension
2223: . Nc     - The number of components
2224: . ct     - The celltype of the reference cell
2225: . k      - The degree of the space
2226: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

2228:   Output Parameter:
2229: . fem - The `PetscFE` object

2231:   Level: beginner

2233:   Note:
2234:   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`.

2236:   Developer Note:
2237:   Since this generalizes/replaces `PetscFECreateLagrange()` for different `DMPolytopeType` its name should be `PetscFECreateLagrangeByPolytopeType()`

2239: .seealso: `PetscFE`, `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`,
2240:           `DMPolytopeType`
2241: @*/
2242: PetscErrorCode PetscFECreateLagrangeByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, PetscInt k, PetscInt qorder, PetscFE *fem)
2243: {
2244:   PetscFunctionBegin;
2245:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, NULL, k, qorder, PETSC_FALSE, fem));
2246:   PetscFunctionReturn(PETSC_SUCCESS);
2247: }

2249: /*@
2250:   PetscFELimitDegree - Copy a `PetscFE` but limit the degree to be in the given range

2252:   Collective

2254:   Input Parameters:
2255: + fe        - The `PetscFE`
2256: . minDegree - The minimum degree, or `PETSC_DETERMINE` for no limit
2257: - maxDegree - The maximum degree, or `PETSC_DETERMINE` for no limit

2259:   Output Parameter:
2260: . newfe - The `PetscFE` object

2262:   Level: advanced

2264:   Note:
2265:   This currently only works for Lagrange elements.

2267: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2268: @*/
2269: PetscErrorCode PetscFELimitDegree(PetscFE fe, PetscInt minDegree, PetscInt maxDegree, PetscFE *newfe)
2270: {
2271:   PetscDualSpace Q;
2272:   PetscBool      islag, issum;
2273:   PetscInt       oldk = 0, k;

2275:   PetscFunctionBegin;
2276:   PetscCall(PetscFEGetDualSpace(fe, &Q));
2277:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &islag));
2278:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &issum));
2279:   if (islag) {
2280:     PetscCall(PetscDualSpaceGetOrder(Q, &oldk));
2281:   } else if (issum) {
2282:     PetscDualSpace subQ;

2284:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &subQ));
2285:     PetscCall(PetscDualSpaceGetOrder(subQ, &oldk));
2286:   } else {
2287:     PetscCall(PetscObjectReference((PetscObject)fe));
2288:     *newfe = fe;
2289:     PetscFunctionReturn(PETSC_SUCCESS);
2290:   }
2291:   k = oldk;
2292:   if (minDegree >= 0) k = PetscMax(k, minDegree);
2293:   if (maxDegree >= 0) k = PetscMin(k, maxDegree);
2294:   if (k != oldk) {
2295:     DM              K;
2296:     PetscSpace      P;
2297:     PetscQuadrature q;
2298:     DMPolytopeType  ct;
2299:     PetscInt        dim, Nc;

2301:     PetscCall(PetscFEGetBasisSpace(fe, &P));
2302:     PetscCall(PetscSpaceGetNumVariables(P, &dim));
2303:     PetscCall(PetscSpaceGetNumComponents(P, &Nc));
2304:     PetscCall(PetscDualSpaceGetDM(Q, &K));
2305:     PetscCall(DMPlexGetCellType(K, 0, &ct));
2306:     PetscCall(PetscFECreateLagrangeByCell(PetscObjectComm((PetscObject)fe), dim, Nc, ct, k, PETSC_DETERMINE, newfe));
2307:     PetscCall(PetscFEGetQuadrature(fe, &q));
2308:     PetscCall(PetscFESetQuadrature(*newfe, q));
2309:   } else {
2310:     PetscCall(PetscObjectReference((PetscObject)fe));
2311:     *newfe = fe;
2312:   }
2313:   PetscFunctionReturn(PETSC_SUCCESS);
2314: }

2316: /*@
2317:   PetscFECreateBrokenElement - Create a discontinuous version of the input `PetscFE`

2319:   Collective

2321:   Input Parameters:
2322: . cgfe - The continuous `PetscFE` object

2324:   Output Parameter:
2325: . dgfe - The discontinuous `PetscFE` object

2327:   Level: advanced

2329:   Note:
2330:   This only works for Lagrange elements.

2332: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`, `PetscFECreateLagrange()`, `PetscFECreateLagrangeByCell()`, `PetscDualSpaceLagrangeSetContinuity()`
2333: @*/
2334: PetscErrorCode PetscFECreateBrokenElement(PetscFE cgfe, PetscFE *dgfe)
2335: {
2336:   PetscSpace      P;
2337:   PetscDualSpace  Q, dgQ;
2338:   PetscQuadrature q, fq;
2339:   PetscBool       is_lagrange, is_sum;

2341:   PetscFunctionBegin;
2342:   PetscCall(PetscFEGetBasisSpace(cgfe, &P));
2343:   PetscCall(PetscObjectReference((PetscObject)P));
2344:   PetscCall(PetscFEGetDualSpace(cgfe, &Q));
2345:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &is_lagrange));
2346:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &is_sum));
2347:   PetscCheck(is_lagrange || is_sum, PETSC_COMM_SELF, PETSC_ERR_SUP, "Can only create broken elements of Lagrange elements");
2348:   PetscCall(PetscDualSpaceDuplicate(Q, &dgQ));
2349:   PetscCall(PetscDualSpaceLagrangeSetContinuity(dgQ, PETSC_FALSE));
2350:   PetscCall(PetscDualSpaceSetUp(dgQ));
2351:   PetscCall(PetscFEGetQuadrature(cgfe, &q));
2352:   PetscCall(PetscObjectReference((PetscObject)q));
2353:   PetscCall(PetscFEGetFaceQuadrature(cgfe, &fq));
2354:   PetscCall(PetscObjectReference((PetscObject)fq));
2355:   PetscCall(PetscFECreateFromSpaces(P, dgQ, q, fq, dgfe));
2356:   PetscFunctionReturn(PETSC_SUCCESS);
2357: }

2359: /*@
2360:   PetscFESetName - Names the `PetscFE` and its subobjects

2362:   Not Collective

2364:   Input Parameters:
2365: + fe   - The `PetscFE`
2366: - name - The name

2368:   Level: intermediate

2370: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
2371: @*/
2372: PetscErrorCode PetscFESetName(PetscFE fe, const char name[])
2373: {
2374:   PetscSpace     P;
2375:   PetscDualSpace Q;

2377:   PetscFunctionBegin;
2378:   PetscCall(PetscFEGetBasisSpace(fe, &P));
2379:   PetscCall(PetscFEGetDualSpace(fe, &Q));
2380:   PetscCall(PetscObjectSetName((PetscObject)fe, name));
2381:   PetscCall(PetscObjectSetName((PetscObject)P, name));
2382:   PetscCall(PetscObjectSetName((PetscObject)Q, name));
2383:   PetscFunctionReturn(PETSC_SUCCESS);
2384: }

2386: 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[])
2387: {
2388:   PetscInt dOffset = 0, fOffset = 0, f, g;

2390:   for (f = 0; f < Nf; ++f) {
2391:     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);
2392:     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);
2393:     PetscFE          fe;
2394:     const PetscInt   k       = ds->jetDegree[f];
2395:     const PetscInt   cdim    = T[f]->cdim;
2396:     const PetscInt   dE      = fegeom->dimEmbed;
2397:     const PetscInt   Nq      = T[f]->Np;
2398:     const PetscInt   Nbf     = T[f]->Nb;
2399:     const PetscInt   Ncf     = T[f]->Nc;
2400:     const PetscReal *Bq      = &T[f]->T[0][(r * Nq + q) * Nbf * Ncf];
2401:     const PetscReal *Dq      = &T[f]->T[1][(r * Nq + q) * Nbf * Ncf * cdim];
2402:     const PetscReal *Hq      = k > 1 ? &T[f]->T[2][(r * Nq + q) * Nbf * Ncf * cdim * cdim] : NULL;
2403:     PetscInt         hOffset = 0, b, c, d;

2405:     PetscCall(PetscDSGetDiscretization(ds, f, (PetscObject *)&fe));
2406:     for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
2407:     for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
2408:     for (b = 0; b < Nbf; ++b) {
2409:       for (c = 0; c < Ncf; ++c) {
2410:         const PetscInt cidx = b * Ncf + c;

2412:         u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
2413:         for (d = 0; d < cdim; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * cdim + d] * coefficients[dOffset + b];
2414:       }
2415:     }
2416:     if (k > 1) {
2417:       for (g = 0; g < Nf; ++g) hOffset += T[g]->Nc * dE;
2418:       for (d = 0; d < dE * dE * Ncf; ++d) u_x[hOffset + fOffset * dE * dE + d] = 0.0;
2419:       for (b = 0; b < Nbf; ++b) {
2420:         for (c = 0; c < Ncf; ++c) {
2421:           const PetscInt cidx = b * Ncf + c;

2423:           for (d = 0; d < cdim * cdim; ++d) u_x[hOffset + (fOffset + c) * dE * dE + d] += Hq[cidx * cdim * cdim + d] * coefficients[dOffset + b];
2424:         }
2425:       }
2426:       PetscCall(PetscFEPushforwardHessian(fe, fegeom, 1, &u_x[hOffset + fOffset * dE * dE]));
2427:     }
2428:     PetscCall(PetscFEPushforward(fe, fegeom, 1, &u[fOffset]));
2429:     PetscCall(PetscFEPushforwardGradient(fe, fegeom, 1, &u_x[fOffset * dE]));
2430:     if (u_t) {
2431:       for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
2432:       for (b = 0; b < Nbf; ++b) {
2433:         for (c = 0; c < Ncf; ++c) {
2434:           const PetscInt cidx = b * Ncf + c;

2436:           u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
2437:         }
2438:       }
2439:       PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
2440:     }
2441:     fOffset += Ncf;
2442:     dOffset += Nbf;
2443:   }
2444:   return PETSC_SUCCESS;
2445: }

2447: 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[])
2448: {
2449:   PetscInt dOffset = 0, fOffset = 0, f;

2451:   /* f is the field number in the DS */
2452:   for (f = 0; f < Nf; ++f) {
2453:     PetscBool isCohesive;
2454:     PetscInt  Ns, s;

2456:     if (!Tab[f]) continue;
2457:     PetscCall(PetscDSGetCohesive(ds, f, &isCohesive));
2458:     Ns = isCohesive ? 1 : 2;
2459:     {
2460:       PetscTabulation T   = isCohesive ? Tab[f] : Tabf[f];
2461:       PetscFE         fe  = (PetscFE)ds->disc[f];
2462:       const PetscInt  dEt = T->cdim;
2463:       const PetscInt  dE  = fegeom->dimEmbed;
2464:       const PetscInt  Nq  = T->Np;
2465:       const PetscInt  Nbf = T->Nb;
2466:       const PetscInt  Ncf = T->Nc;

2468:       for (s = 0; s < Ns; ++s) {
2469:         const PetscInt   r  = isCohesive ? rc : rf[s];
2470:         const PetscInt   q  = isCohesive ? qc : qf[s];
2471:         const PetscReal *Bq = &T->T[0][(r * Nq + q) * Nbf * Ncf];
2472:         const PetscReal *Dq = &T->T[1][(r * Nq + q) * Nbf * Ncf * dEt];
2473:         PetscInt         b, c, d;

2475:         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);
2476:         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);
2477:         for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
2478:         for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
2479:         for (b = 0; b < Nbf; ++b) {
2480:           for (c = 0; c < Ncf; ++c) {
2481:             const PetscInt cidx = b * Ncf + c;

2483:             u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
2484:             for (d = 0; d < dEt; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * dEt + d] * coefficients[dOffset + b];
2485:           }
2486:         }
2487:         PetscCall(PetscFEPushforward(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u[fOffset]));
2488:         PetscCall(PetscFEPushforwardGradient(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u_x[fOffset * dE]));
2489:         if (u_t) {
2490:           for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
2491:           for (b = 0; b < Nbf; ++b) {
2492:             for (c = 0; c < Ncf; ++c) {
2493:               const PetscInt cidx = b * Ncf + c;

2495:               u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
2496:             }
2497:           }
2498:           PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
2499:         }
2500:         fOffset += Ncf;
2501:         dOffset += Nbf;
2502:       }
2503:     }
2504:   }
2505:   return PETSC_SUCCESS;
2506: }

2508: PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS prob, PetscInt field, PetscInt faceLoc, const PetscScalar coefficients[], PetscScalar u[])
2509: {
2510:   PetscFE         fe;
2511:   PetscTabulation Tc;
2512:   PetscInt        b, c;

2514:   if (!prob) return PETSC_SUCCESS;
2515:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
2516:   PetscCall(PetscFEGetFaceCentroidTabulation(fe, &Tc));
2517:   {
2518:     const PetscReal *faceBasis = Tc->T[0];
2519:     const PetscInt   Nb        = Tc->Nb;
2520:     const PetscInt   Nc        = Tc->Nc;

2522:     for (c = 0; c < Nc; ++c) u[c] = 0.0;
2523:     for (b = 0; b < Nb; ++b) {
2524:       for (c = 0; c < Nc; ++c) u[c] += coefficients[b] * faceBasis[(faceLoc * Nb + b) * Nc + c];
2525:     }
2526:   }
2527:   return PETSC_SUCCESS;
2528: }

2530: PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscInt e, PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
2531: {
2532:   PetscFEGeom      pgeom;
2533:   const PetscInt   dEt      = T->cdim;
2534:   const PetscInt   dE       = fegeom->dimEmbed;
2535:   const PetscInt   Nq       = T->Np;
2536:   const PetscInt   Nb       = T->Nb;
2537:   const PetscInt   Nc       = T->Nc;
2538:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
2539:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dEt];
2540:   PetscInt         q, b, c, d;

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

2547:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
2548:         for (d = 0; d < dEt; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dEt + bcidx * dEt + d];
2549:         for (d = dEt; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = 0.0;
2550:       }
2551:     }
2552:     PetscCall(PetscFEGeomGetCellPoint(fegeom, e, q, &pgeom));
2553:     PetscCall(PetscFEPushforward(fe, &pgeom, Nb, tmpBasis));
2554:     PetscCall(PetscFEPushforwardGradient(fe, &pgeom, Nb, tmpBasisDer));
2555:     for (b = 0; b < Nb; ++b) {
2556:       for (c = 0; c < Nc; ++c) {
2557:         const PetscInt bcidx = b * Nc + c;
2558:         const PetscInt qcidx = q * Nc + c;

2560:         elemVec[b] += tmpBasis[bcidx] * f0[qcidx];
2561:         for (d = 0; d < dE; ++d) elemVec[b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
2562:       }
2563:     }
2564:   }
2565:   return PETSC_SUCCESS;
2566: }

2568: PetscErrorCode PetscFEUpdateElementVec_Hybrid_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscInt side, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
2569: {
2570:   const PetscInt   dE       = T->cdim;
2571:   const PetscInt   Nq       = T->Np;
2572:   const PetscInt   Nb       = T->Nb;
2573:   const PetscInt   Nc       = T->Nc;
2574:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
2575:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dE];

2577:   for (PetscInt q = 0; q < Nq; ++q) {
2578:     for (PetscInt b = 0; b < Nb; ++b) {
2579:       for (PetscInt c = 0; c < Nc; ++c) {
2580:         const PetscInt bcidx = b * Nc + c;

2582:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
2583:         for (PetscInt d = 0; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dE + bcidx * dE + d];
2584:       }
2585:     }
2586:     PetscCall(PetscFEPushforward(fe, fegeom, Nb, tmpBasis));
2587:     // TODO This is currently broken since we do not pull the geometry down to the lower dimension
2588:     // PetscCall(PetscFEPushforwardGradient(fe, fegeom, Nb, tmpBasisDer));
2589:     if (side == 2) {
2590:       // Integrating over whole cohesive cell, so insert for both sides
2591:       for (PetscInt s = 0; s < 2; ++s) {
2592:         for (PetscInt b = 0; b < Nb; ++b) {
2593:           for (PetscInt c = 0; c < Nc; ++c) {
2594:             const PetscInt bcidx = b * Nc + c;
2595:             const PetscInt qcidx = (q * 2 + s) * Nc + c;

2597:             elemVec[Nb * s + b] += tmpBasis[bcidx] * f0[qcidx];
2598:             for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * s + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
2599:           }
2600:         }
2601:       }
2602:     } else {
2603:       // Integrating over endcaps of cohesive cell, so insert for correct side
2604:       for (PetscInt b = 0; b < Nb; ++b) {
2605:         for (PetscInt c = 0; c < Nc; ++c) {
2606:           const PetscInt bcidx = b * Nc + c;
2607:           const PetscInt qcidx = q * Nc + c;

2609:           elemVec[Nb * side + b] += tmpBasis[bcidx] * f0[qcidx];
2610:           for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * side + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
2611:         }
2612:       }
2613:     }
2614:   }
2615:   return PETSC_SUCCESS;
2616: }

2618: #define petsc_elemmat_kernel_g1(_NbI, _NcI, _NbJ, _NcJ, _dE) \
2619:   do { \
2620:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
2621:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
2622:         const PetscScalar *G = g1 + (fc * (_NcJ) + gc) * _dE; \
2623:         for (PetscInt f = 0; f < (_NbI); ++f) { \
2624:           const PetscScalar tBIv = tmpBasisI[f * (_NcI) + fc]; \
2625:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
2626:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
2627:             PetscScalar        s    = 0.0; \
2628:             for (PetscInt df = 0; df < _dE; ++df) s += G[df] * tBDJ[df]; \
2629:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBIv; \
2630:           } \
2631:         } \
2632:       } \
2633:     } \
2634:   } while (0)

2636: #define petsc_elemmat_kernel_g2(_NbI, _NcI, _NbJ, _NcJ, _dE) \
2637:   do { \
2638:     for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
2639:       for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
2640:         const PetscScalar *G = g2 + (fc * (_NcJ) + gc) * _dE; \
2641:         for (PetscInt g = 0; g < (_NbJ); ++g) { \
2642:           const PetscScalar tBJv = tmpBasisJ[g * (_NcJ) + gc]; \
2643:           for (PetscInt f = 0; f < (_NbI); ++f) { \
2644:             const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
2645:             PetscScalar        s    = 0.0; \
2646:             for (PetscInt df = 0; df < _dE; ++df) s += tBDI[df] * G[df]; \
2647:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBJv; \
2648:           } \
2649:         } \
2650:       } \
2651:     } \
2652:   } while (0)

2654: #define petsc_elemmat_kernel_g3(_NbI, _NcI, _NbJ, _NcJ, _dE) \
2655:   do { \
2656:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
2657:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
2658:         const PetscScalar *G = g3 + (fc * (_NcJ) + gc) * (_dE) * (_dE); \
2659:         for (PetscInt f = 0; f < (_NbI); ++f) { \
2660:           const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
2661:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
2662:             PetscScalar        s    = 0.0; \
2663:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
2664:             for (PetscInt df = 0; df < (_dE); ++df) { \
2665:               for (PetscInt dg = 0; dg < (_dE); ++dg) s += tBDI[df] * G[df * (_dE) + dg] * tBDJ[dg]; \
2666:             } \
2667:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s; \
2668:           } \
2669:         } \
2670:       } \
2671:     } \
2672:   } while (0)

2674: 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[])
2675: {
2676:   const PetscInt   cdim      = TI->cdim;
2677:   const PetscInt   dE        = fegeom->dimEmbed;
2678:   const PetscInt   NqI       = TI->Np;
2679:   const PetscInt   NbI       = TI->Nb;
2680:   const PetscInt   NcI       = TI->Nc;
2681:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
2682:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * cdim];
2683:   const PetscInt   NqJ       = TJ->Np;
2684:   const PetscInt   NbJ       = TJ->Nb;
2685:   const PetscInt   NcJ       = TJ->Nc;
2686:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
2687:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * cdim];

2689:   for (PetscInt f = 0; f < NbI; ++f) {
2690:     for (PetscInt fc = 0; fc < NcI; ++fc) {
2691:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2693:       tmpBasisI[fidx] = basisI[fidx];
2694:       for (PetscInt df = 0; df < cdim; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * cdim + df];
2695:     }
2696:   }
2697:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
2698:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
2699:   if (feI != feJ) {
2700:     for (PetscInt g = 0; g < NbJ; ++g) {
2701:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
2702:         const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2704:         tmpBasisJ[gidx] = basisJ[gidx];
2705:         for (PetscInt dg = 0; dg < cdim; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * cdim + dg];
2706:       }
2707:     }
2708:     PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
2709:     PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
2710:   } else {
2711:     tmpBasisJ    = tmpBasisI;
2712:     tmpBasisDerJ = tmpBasisDerI;
2713:   }
2714:   if (PetscUnlikely(g0)) {
2715:     for (PetscInt f = 0; f < NbI; ++f) {
2716:       const PetscInt i = offsetI + f; /* Element matrix row */

2718:       for (PetscInt fc = 0; fc < NcI; ++fc) {
2719:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

2721:         for (PetscInt g = 0; g < NbJ; ++g) {
2722:           const PetscInt j    = offsetJ + g; /* Element matrix column */
2723:           const PetscInt fOff = i * totDim + j;

2725:           for (PetscInt gc = 0; gc < NcJ; ++gc) elemMat[fOff] += bI * g0[fc * NcJ + gc] * tmpBasisJ[g * NcJ + gc];
2726:         }
2727:       }
2728:     }
2729:   }
2730:   if (PetscUnlikely(g1)) {
2731: #if 1
2732:     if (dE == 2) {
2733:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 2);
2734:     } else if (dE == 3) {
2735:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 3);
2736:     } else {
2737:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, dE);
2738:     }
2739: #else
2740:     for (PetscInt f = 0; f < NbI; ++f) {
2741:       const PetscInt i = offsetI + f; /* Element matrix row */

2743:       for (PetscInt fc = 0; fc < NcI; ++fc) {
2744:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

2746:         for (PetscInt g = 0; g < NbJ; ++g) {
2747:           const PetscInt j    = offsetJ + g; /* Element matrix column */
2748:           const PetscInt fOff = i * totDim + j;

2750:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
2751:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2753:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += bI * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
2754:           }
2755:         }
2756:       }
2757:     }
2758: #endif
2759:   }
2760:   if (PetscUnlikely(g2)) {
2761: #if 1
2762:     if (dE == 2) {
2763:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 2);
2764:     } else if (dE == 3) {
2765:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 3);
2766:     } else {
2767:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, dE);
2768:     }
2769: #else
2770:     for (PetscInt g = 0; g < NbJ; ++g) {
2771:       const PetscInt j = offsetJ + g; /* Element matrix column */

2773:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
2774:         const PetscScalar bJ = tmpBasisJ[g * NcJ + gc]; /* Trial function basis value */

2776:         for (PetscInt f = 0; f < NbI; ++f) {
2777:           const PetscInt i    = offsetI + f; /* Element matrix row */
2778:           const PetscInt fOff = i * totDim + j;

2780:           for (PetscInt fc = 0; fc < NcI; ++fc) {
2781:             const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2783:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * bJ;
2784:           }
2785:         }
2786:       }
2787:     }
2788: #endif
2789:   }
2790:   if (PetscUnlikely(g3)) {
2791: #if 1
2792:     if (dE == 2) {
2793:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 2);
2794:     } else if (dE == 3) {
2795:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 3);
2796:     } else {
2797:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, dE);
2798:     }
2799: #else
2800:     for (PetscInt f = 0; f < NbI; ++f) {
2801:       const PetscInt i = offsetI + f; /* Element matrix row */

2803:       for (PetscInt fc = 0; fc < NcI; ++fc) {
2804:         const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2806:         for (PetscInt g = 0; g < NbJ; ++g) {
2807:           const PetscInt j    = offsetJ + g; /* Element matrix column */
2808:           const PetscInt fOff = i * totDim + j;

2810:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
2811:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2813:             for (PetscInt df = 0; df < dE; ++df) {
2814:               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];
2815:             }
2816:           }
2817:         }
2818:       }
2819:     }
2820: #endif
2821:   }
2822:   return PETSC_SUCCESS;
2823: }

2825: #undef petsc_elemmat_kernel_g1
2826: #undef petsc_elemmat_kernel_g2
2827: #undef petsc_elemmat_kernel_g3

2829: 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[])
2830: {
2831:   const PetscInt   dE        = TI->cdim;
2832:   const PetscInt   NqI       = TI->Np;
2833:   const PetscInt   NbI       = TI->Nb;
2834:   const PetscInt   NcI       = TI->Nc;
2835:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
2836:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * dE];
2837:   const PetscInt   NqJ       = TJ->Np;
2838:   const PetscInt   NbJ       = TJ->Nb;
2839:   const PetscInt   NcJ       = TJ->Nc;
2840:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
2841:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * dE];
2842:   const PetscInt   so        = isHybridI ? 0 : s;
2843:   const PetscInt   to        = isHybridJ ? 0 : t;
2844:   PetscInt         f, fc, g, gc, df, dg;

2846:   for (f = 0; f < NbI; ++f) {
2847:     for (fc = 0; fc < NcI; ++fc) {
2848:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

2850:       tmpBasisI[fidx] = basisI[fidx];
2851:       for (df = 0; df < dE; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * dE + df];
2852:     }
2853:   }
2854:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
2855:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
2856:   for (g = 0; g < NbJ; ++g) {
2857:     for (gc = 0; gc < NcJ; ++gc) {
2858:       const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

2860:       tmpBasisJ[gidx] = basisJ[gidx];
2861:       for (dg = 0; dg < dE; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * dE + dg];
2862:     }
2863:   }
2864:   PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
2865:   // TODO This is currently broken since we do not pull the geometry down to the lower dimension
2866:   // PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
2867:   for (f = 0; f < NbI; ++f) {
2868:     for (fc = 0; fc < NcI; ++fc) {
2869:       const PetscInt fidx = f * NcI + fc;           /* Test function basis index */
2870:       const PetscInt i    = offsetI + NbI * so + f; /* Element matrix row */
2871:       for (g = 0; g < NbJ; ++g) {
2872:         for (gc = 0; gc < NcJ; ++gc) {
2873:           const PetscInt gidx = g * NcJ + gc;           /* Trial function basis index */
2874:           const PetscInt j    = offsetJ + NbJ * to + g; /* Element matrix column */
2875:           const PetscInt fOff = eOffset + i * totDim + j;

2877:           elemMat[fOff] += tmpBasisI[fidx] * g0[fc * NcJ + gc] * tmpBasisJ[gidx];
2878:           for (df = 0; df < dE; ++df) {
2879:             elemMat[fOff] += tmpBasisI[fidx] * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
2880:             elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * tmpBasisJ[gidx];
2881:             for (dg = 0; dg < dE; ++dg) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g3[((fc * NcJ + gc) * dE + df) * dE + dg] * tmpBasisDerJ[gidx * dE + dg];
2882:           }
2883:         }
2884:       }
2885:     }
2886:   }
2887:   return PETSC_SUCCESS;
2888: }

2890: /*@
2891:   PetscFECreateCellGeometry - Populates the arrays in a `PetscFEGeom` for a single reference cell of a `PetscFE`.

2893:   Not Collective

2895:   Input Parameters:
2896: + fe   - the `PetscFE` whose dual-space `DM` provides the reference cell
2897: - quad - the quadrature at which to evaluate the geometry, or `NULL` to use the `PetscFE`'s own quadrature

2899:   Output Parameter:
2900: . cgeom - the `PetscFEGeom` populated with reference-cell coordinates, Jacobians, inverse Jacobians, and their determinants

2902:   Level: developer

2904:   Notes:
2905:   This does not create `cgeom`, it allocates the arrays within one

2907:   Free the storage with `PetscFEDestroyCellGeometry()`.

2909: .seealso: `PetscFE`, `PetscFEGeom`, `PetscFEDestroyCellGeometry()`, `PetscFEGetQuadrature()`, `DMPlexComputeCellGeometryFEM()`
2910: @*/
2911: PetscErrorCode PetscFECreateCellGeometry(PetscFE fe, PetscQuadrature quad, PetscFEGeom *cgeom)
2912: {
2913:   PetscDualSpace  dsp;
2914:   DM              dm;
2915:   PetscQuadrature quadDef;
2916:   PetscInt        dim, cdim, Nq;

2918:   PetscFunctionBegin;
2919:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
2920:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
2921:   PetscCall(DMGetDimension(dm, &dim));
2922:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2923:   PetscCall(PetscFEGetQuadrature(fe, &quadDef));
2924:   quad = quad ? quad : quadDef;
2925:   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
2926:   PetscCall(PetscMalloc1(Nq * cdim, &cgeom->v));
2927:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->J));
2928:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->invJ));
2929:   PetscCall(PetscMalloc1(Nq, &cgeom->detJ));
2930:   cgeom->dim       = dim;
2931:   cgeom->dimEmbed  = cdim;
2932:   cgeom->numCells  = 1;
2933:   cgeom->numPoints = Nq;
2934:   PetscCall(DMPlexComputeCellGeometryFEM(dm, 0, quad, cgeom->v, cgeom->J, cgeom->invJ, cgeom->detJ));
2935:   PetscFunctionReturn(PETSC_SUCCESS);
2936: }

2938: /*@
2939:   PetscFEDestroyCellGeometry - Free the arrays inside a `PetscFEGeom` allocated by `PetscFECreateCellGeometry()`.

2941:   Not Collective

2943:   Input Parameters:
2944: + fe    - the `PetscFE` (unused, kept for API symmetry with `PetscFECreateCellGeometry()`)
2945: - cgeom - the `PetscFEGeom` whose owned arrays should be freed

2947:   Level: developer

2949: .seealso: `PetscFE`, `PetscFEGeom`, `PetscFECreateCellGeometry()`
2950: @*/
2951: PetscErrorCode PetscFEDestroyCellGeometry(PetscFE fe, PetscFEGeom *cgeom)
2952: {
2953:   PetscFunctionBegin;
2954:   PetscCall(PetscFree(cgeom->v));
2955:   PetscCall(PetscFree(cgeom->J));
2956:   PetscCall(PetscFree(cgeom->invJ));
2957:   PetscCall(PetscFree(cgeom->detJ));
2958:   PetscFunctionReturn(PETSC_SUCCESS);
2959: }

2961: #if 0
2962: 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)
2963: {
2964:   const PetscInt dE      = dimEmbed;
2965:   const PetscInt NbI     = TI->Nb;
2966:   const PetscInt NcI     = TI->Nc;
2967:   const PetscInt NbJ     = TJ->Nb;
2968:   const PetscInt NcJ     = TJ->Nc;
2969:   PetscBool      has_g0  = g0 ? PETSC_TRUE : PETSC_FALSE;
2970:   PetscBool      has_g1  = g1 ? PETSC_TRUE : PETSC_FALSE;
2971:   PetscBool      has_g2  = g2 ? PETSC_TRUE : PETSC_FALSE;
2972:   PetscBool      has_g3  = g3 ? PETSC_TRUE : PETSC_FALSE;
2973:   PetscInt      *g0_idxs = NULL, *g1_idxs = NULL, *g2_idxs = NULL, *g3_idxs = NULL;
2974:   PetscInt       g0_i, g1_i, g2_i, g3_i;

2976:   PetscFunctionBegin;
2977:   g0_i = g1_i = g2_i = g3_i = 0;
2978:   if (has_g0)
2979:     for (PetscInt i = 0; i < NcI * NcJ; i++)
2980:       if (g0[i]) g0_i += NbI * NbJ;
2981:   if (has_g1)
2982:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
2983:       if (g1[i]) g1_i += NbI * NbJ;
2984:   if (has_g2)
2985:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
2986:       if (g2[i]) g2_i += NbI * NbJ;
2987:   if (has_g3)
2988:     for (PetscInt i = 0; i < NcI * NcJ * dE * dE; i++)
2989:       if (g3[i]) g3_i += NbI * NbJ;
2990:   if (g0_i == NbI * NbJ * NcI * NcJ) g0_i = 0;
2991:   if (g1_i == NbI * NbJ * NcI * NcJ * dE) g1_i = 0;
2992:   if (g2_i == NbI * NbJ * NcI * NcJ * dE) g2_i = 0;
2993:   if (g3_i == NbI * NbJ * NcI * NcJ * dE * dE) g3_i = 0;
2994:   has_g0 = g0_i ? PETSC_TRUE : PETSC_FALSE;
2995:   has_g1 = g1_i ? PETSC_TRUE : PETSC_FALSE;
2996:   has_g2 = g2_i ? PETSC_TRUE : PETSC_FALSE;
2997:   has_g3 = g3_i ? PETSC_TRUE : PETSC_FALSE;
2998:   if (has_g0) PetscCall(PetscMalloc1(4 * g0_i, &g0_idxs));
2999:   if (has_g1) PetscCall(PetscMalloc1(4 * g1_i, &g1_idxs));
3000:   if (has_g2) PetscCall(PetscMalloc1(4 * g2_i, &g2_idxs));
3001:   if (has_g3) PetscCall(PetscMalloc1(4 * g3_i, &g3_idxs));
3002:   g0_i = g1_i = g2_i = g3_i = 0;

3004:   for (PetscInt f = 0; f < NbI; ++f) {
3005:     const PetscInt i = offsetI + f; /* Element matrix row */
3006:     for (PetscInt fc = 0; fc < NcI; ++fc) {
3007:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

3009:       for (PetscInt g = 0; g < NbJ; ++g) {
3010:         const PetscInt j    = offsetJ + g; /* Element matrix column */
3011:         const PetscInt fOff = i * totDim + j;
3012:         for (PetscInt gc = 0; gc < NcJ; ++gc) {
3013:           const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

3015:           if (has_g0) {
3016:             if (g0[fc * NcJ + gc]) {
3017:               g0_idxs[4 * g0_i + 0] = fidx;
3018:               g0_idxs[4 * g0_i + 1] = fc * NcJ + gc;
3019:               g0_idxs[4 * g0_i + 2] = gidx;
3020:               g0_idxs[4 * g0_i + 3] = fOff;
3021:               g0_i++;
3022:             }
3023:           }

3025:           for (PetscInt df = 0; df < dE; ++df) {
3026:             if (has_g1) {
3027:               if (g1[(fc * NcJ + gc) * dE + df]) {
3028:                 g1_idxs[4 * g1_i + 0] = fidx;
3029:                 g1_idxs[4 * g1_i + 1] = (fc * NcJ + gc) * dE + df;
3030:                 g1_idxs[4 * g1_i + 2] = gidx * dE + df;
3031:                 g1_idxs[4 * g1_i + 3] = fOff;
3032:                 g1_i++;
3033:               }
3034:             }
3035:             if (has_g2) {
3036:               if (g2[(fc * NcJ + gc) * dE + df]) {
3037:                 g2_idxs[4 * g2_i + 0] = fidx * dE + df;
3038:                 g2_idxs[4 * g2_i + 1] = (fc * NcJ + gc) * dE + df;
3039:                 g2_idxs[4 * g2_i + 2] = gidx;
3040:                 g2_idxs[4 * g2_i + 3] = fOff;
3041:                 g2_i++;
3042:               }
3043:             }
3044:             if (has_g3) {
3045:               for (PetscInt dg = 0; dg < dE; ++dg) {
3046:                 if (g3[((fc * NcJ + gc) * dE + df) * dE + dg]) {
3047:                   g3_idxs[4 * g3_i + 0] = fidx * dE + df;
3048:                   g3_idxs[4 * g3_i + 1] = ((fc * NcJ + gc) * dE + df) * dE + dg;
3049:                   g3_idxs[4 * g3_i + 2] = gidx * dE + dg;
3050:                   g3_idxs[4 * g3_i + 3] = fOff;
3051:                   g3_i++;
3052:                 }
3053:               }
3054:             }
3055:           }
3056:         }
3057:       }
3058:     }
3059:   }
3060:   *n_g0 = g0_i;
3061:   *n_g1 = g1_i;
3062:   *n_g2 = g2_i;
3063:   *n_g3 = g3_i;

3065:   *g0_idxs_out = g0_idxs;
3066:   *g1_idxs_out = g1_idxs;
3067:   *g2_idxs_out = g2_idxs;
3068:   *g3_idxs_out = g3_idxs;
3069:   PetscFunctionReturn(PETSC_SUCCESS);
3070: }

3072: //example HOW TO USE
3073:       for (PetscInt i = 0; i < g0_sparse_n; i++) {
3074:         PetscInt bM = g0_sparse_idxs[4 * i + 0];
3075:         PetscInt bN = g0_sparse_idxs[4 * i + 1];
3076:         PetscInt bK = g0_sparse_idxs[4 * i + 2];
3077:         PetscInt bO = g0_sparse_idxs[4 * i + 3];
3078:         elemMat[bO] += tmpBasisI[bM] * g0[bN] * tmpBasisJ[bK];
3079:       }
3080: #endif