Actual source code: fe.c

petsc-master 2020-04-04
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  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: PetscFunctionList PetscFEList              = NULL;
54: PetscBool         PetscFERegisterAllCalled = PETSC_FALSE;

56: /*@C
57:   PetscFERegister - Adds a new PetscFE implementation

59:   Not Collective

61:   Input Parameters:
62: + name        - The name of a new user-defined creation routine
63: - create_func - The creation routine itself

65:   Notes:
66:   PetscFERegister() may be called multiple times to add several user-defined PetscFEs

68:   Sample usage:
69: .vb
70:     PetscFERegister("my_fe", MyPetscFECreate);
71: .ve

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

85: .seealso: PetscFERegisterAll(), PetscFERegisterDestroy()

87: @*/
88: PetscErrorCode PetscFERegister(const char sname[], PetscErrorCode (*function)(PetscFE))
89: {

94:   return(0);
95: }

97: /*@C
98:   PetscFESetType - Builds a particular PetscFE

100:   Collective on fem

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

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

109:   Level: intermediate

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

121:   PetscObjectTypeCompare((PetscObject) fem, name, &match);
122:   if (match) return(0);

124:   if (!PetscFERegisterAllCalled) {PetscFERegisterAll();}
125:   PetscFunctionListFind(PetscFEList, name, &r);
126:   if (!r) SETERRQ1(PetscObjectComm((PetscObject) fem), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscFE type: %s", name);

128:   if (fem->ops->destroy) {
129:     (*fem->ops->destroy)(fem);
130:     fem->ops->destroy = NULL;
131:   }
132:   (*r)(fem);
133:   PetscObjectChangeTypeName((PetscObject) fem, name);
134:   return(0);
135: }

137: /*@C
138:   PetscFEGetType - Gets the PetscFE type name (as a string) from the object.

140:   Not Collective

142:   Input Parameter:
143: . fem  - The PetscFE

145:   Output Parameter:
146: . name - The PetscFE type name

148:   Level: intermediate

150: .seealso: PetscFESetType(), PetscFECreate()
151: @*/
152: PetscErrorCode PetscFEGetType(PetscFE fem, PetscFEType *name)
153: {

159:   if (!PetscFERegisterAllCalled) {
160:     PetscFERegisterAll();
161:   }
162:   *name = ((PetscObject) fem)->type_name;
163:   return(0);
164: }

166: /*@C
167:    PetscFEViewFromOptions - View from Options

169:    Collective on PetscFE

171:    Input Parameters:
172: +  A - the PetscFE object
173: .  obj - Optional object
174: -  name - command line option

176:    Level: intermediate
177: .seealso:  PetscFE(), PetscFEView(), PetscObjectViewFromOptions(), PetscFECreate()
178: @*/
179: PetscErrorCode  PetscFEViewFromOptions(PetscFE A,PetscObject obj,const char name[])
180: {

185:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
186:   return(0);
187: }

189: /*@C
190:   PetscFEView - Views a PetscFE

192:   Collective on fem

194:   Input Parameter:
195: + fem - the PetscFE object to view
196: - viewer   - the viewer

198:   Level: beginner

200: .seealso PetscFEDestroy()
201: @*/
202: PetscErrorCode PetscFEView(PetscFE fem, PetscViewer viewer)
203: {
204:   PetscBool      iascii;

210:   if (!viewer) {PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) fem), &viewer);}
211:   PetscObjectPrintClassNamePrefixType((PetscObject)fem, viewer);
212:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
213:   if (fem->ops->view) {(*fem->ops->view)(fem, viewer);}
214:   return(0);
215: }

217: /*@
218:   PetscFESetFromOptions - sets parameters in a PetscFE from the options database

220:   Collective on fem

222:   Input Parameter:
223: . fem - the PetscFE object to set options for

225:   Options Database:
226: + -petscfe_num_blocks  - the number of cell blocks to integrate concurrently
227: - -petscfe_num_batches - the number of cell batches to integrate serially

229:   Level: intermediate

231: .seealso PetscFEView()
232: @*/
233: PetscErrorCode PetscFESetFromOptions(PetscFE fem)
234: {
235:   const char    *defaultType;
236:   char           name[256];
237:   PetscBool      flg;

242:   if (!((PetscObject) fem)->type_name) {
243:     defaultType = PETSCFEBASIC;
244:   } else {
245:     defaultType = ((PetscObject) fem)->type_name;
246:   }
247:   if (!PetscFERegisterAllCalled) {PetscFERegisterAll();}

249:   PetscObjectOptionsBegin((PetscObject) fem);
250:   PetscOptionsFList("-petscfe_type", "Finite element space", "PetscFESetType", PetscFEList, defaultType, name, 256, &flg);
251:   if (flg) {
252:     PetscFESetType(fem, name);
253:   } else if (!((PetscObject) fem)->type_name) {
254:     PetscFESetType(fem, defaultType);
255:   }
256:   PetscOptionsBoundedInt("-petscfe_num_blocks", "The number of cell blocks to integrate concurrently", "PetscSpaceSetTileSizes", fem->numBlocks, &fem->numBlocks, NULL,1);
257:   PetscOptionsBoundedInt("-petscfe_num_batches", "The number of cell batches to integrate serially", "PetscSpaceSetTileSizes", fem->numBatches, &fem->numBatches, NULL,1);
258:   if (fem->ops->setfromoptions) {
259:     (*fem->ops->setfromoptions)(PetscOptionsObject,fem);
260:   }
262:   PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject) fem);
263:   PetscOptionsEnd();
264:   PetscFEViewFromOptions(fem, NULL, "-petscfe_view");
265:   return(0);
266: }

268: /*@C
269:   PetscFESetUp - Construct data structures for the PetscFE

271:   Collective on fem

273:   Input Parameter:
274: . fem - the PetscFE object to setup

276:   Level: intermediate

278: .seealso PetscFEView(), PetscFEDestroy()
279: @*/
280: PetscErrorCode PetscFESetUp(PetscFE fem)
281: {

286:   if (fem->setupcalled) return(0);
287:   fem->setupcalled = PETSC_TRUE;
288:   if (fem->ops->setup) {(*fem->ops->setup)(fem);}
289:   return(0);
290: }

292: /*@
293:   PetscFEDestroy - Destroys a PetscFE object

295:   Collective on fem

297:   Input Parameter:
298: . fem - the PetscFE object to destroy

300:   Level: beginner

302: .seealso PetscFEView()
303: @*/
304: PetscErrorCode PetscFEDestroy(PetscFE *fem)
305: {

309:   if (!*fem) return(0);

312:   if (--((PetscObject)(*fem))->refct > 0) {*fem = 0; return(0);}
313:   ((PetscObject) (*fem))->refct = 0;

315:   if ((*fem)->subspaces) {
316:     PetscInt dim, d;

318:     PetscDualSpaceGetDimension((*fem)->dualSpace, &dim);
319:     for (d = 0; d < dim; ++d) {PetscFEDestroy(&(*fem)->subspaces[d]);}
320:   }
321:   PetscFree((*fem)->subspaces);
322:   PetscFree((*fem)->invV);
323:   PetscTabulationDestroy(&(*fem)->T);
324:   PetscTabulationDestroy(&(*fem)->Tf);
325:   PetscTabulationDestroy(&(*fem)->Tc);
326:   PetscSpaceDestroy(&(*fem)->basisSpace);
327:   PetscDualSpaceDestroy(&(*fem)->dualSpace);

331:   if ((*fem)->ops->destroy) {(*(*fem)->ops->destroy)(*fem);}
333:   return(0);
334: }

336: /*@
337:   PetscFECreate - Creates an empty PetscFE object. The type can then be set with PetscFESetType().

339:   Collective

341:   Input Parameter:
342: . comm - The communicator for the PetscFE object

344:   Output Parameter:
345: . fem - The PetscFE object

347:   Level: beginner

349: .seealso: PetscFESetType(), PETSCFEGALERKIN
350: @*/
351: PetscErrorCode PetscFECreate(MPI_Comm comm, PetscFE *fem)
352: {
353:   PetscFE        f;

358:   PetscCitationsRegister(FECitation,&FEcite);
359:   *fem = NULL;
360:   PetscFEInitializePackage();

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

364:   f->basisSpace    = NULL;
365:   f->dualSpace     = NULL;
366:   f->numComponents = 1;
367:   f->subspaces     = NULL;
368:   f->invV          = NULL;
369:   f->T             = NULL;
370:   f->Tf            = NULL;
371:   f->Tc            = NULL;
374:   f->blockSize     = 0;
375:   f->numBlocks     = 1;
376:   f->batchSize     = 0;
377:   f->numBatches    = 1;

379:   *fem = f;
380:   return(0);
381: }

383: /*@
384:   PetscFEGetSpatialDimension - Returns the spatial dimension of the element

386:   Not collective

388:   Input Parameter:
389: . fem - The PetscFE object

391:   Output Parameter:
392: . dim - The spatial dimension

394:   Level: intermediate

396: .seealso: PetscFECreate()
397: @*/
398: PetscErrorCode PetscFEGetSpatialDimension(PetscFE fem, PetscInt *dim)
399: {
400:   DM             dm;

406:   PetscDualSpaceGetDM(fem->dualSpace, &dm);
407:   DMGetDimension(dm, dim);
408:   return(0);
409: }

411: /*@
412:   PetscFESetNumComponents - Sets the number of components in the element

414:   Not collective

416:   Input Parameters:
417: + fem - The PetscFE object
418: - comp - The number of field components

420:   Level: intermediate

422: .seealso: PetscFECreate()
423: @*/
424: PetscErrorCode PetscFESetNumComponents(PetscFE fem, PetscInt comp)
425: {
428:   fem->numComponents = comp;
429:   return(0);
430: }

432: /*@
433:   PetscFEGetNumComponents - Returns the number of components in the element

435:   Not collective

437:   Input Parameter:
438: . fem - The PetscFE object

440:   Output Parameter:
441: . comp - The number of field components

443:   Level: intermediate

445: .seealso: PetscFECreate()
446: @*/
447: PetscErrorCode PetscFEGetNumComponents(PetscFE fem, PetscInt *comp)
448: {
452:   *comp = fem->numComponents;
453:   return(0);
454: }

456: /*@
457:   PetscFESetTileSizes - Sets the tile sizes for evaluation

459:   Not collective

461:   Input Parameters:
462: + fem - The PetscFE object
463: . blockSize - The number of elements in a block
464: . numBlocks - The number of blocks in a batch
465: . batchSize - The number of elements in a batch
466: - numBatches - The number of batches in a chunk

468:   Level: intermediate

470: .seealso: PetscFECreate()
471: @*/
472: PetscErrorCode PetscFESetTileSizes(PetscFE fem, PetscInt blockSize, PetscInt numBlocks, PetscInt batchSize, PetscInt numBatches)
473: {
476:   fem->blockSize  = blockSize;
477:   fem->numBlocks  = numBlocks;
478:   fem->batchSize  = batchSize;
479:   fem->numBatches = numBatches;
480:   return(0);
481: }

483: /*@
484:   PetscFEGetTileSizes - Returns the tile sizes for evaluation

486:   Not collective

488:   Input Parameter:
489: . fem - The PetscFE object

491:   Output Parameters:
492: + blockSize - The number of elements in a block
493: . numBlocks - The number of blocks in a batch
494: . batchSize - The number of elements in a batch
495: - numBatches - The number of batches in a chunk

497:   Level: intermediate

499: .seealso: PetscFECreate()
500: @*/
501: PetscErrorCode PetscFEGetTileSizes(PetscFE fem, PetscInt *blockSize, PetscInt *numBlocks, PetscInt *batchSize, PetscInt *numBatches)
502: {
509:   if (blockSize)  *blockSize  = fem->blockSize;
510:   if (numBlocks)  *numBlocks  = fem->numBlocks;
511:   if (batchSize)  *batchSize  = fem->batchSize;
512:   if (numBatches) *numBatches = fem->numBatches;
513:   return(0);
514: }

516: /*@
517:   PetscFEGetBasisSpace - Returns the PetscSpace used for approximation of the solution

519:   Not collective

521:   Input Parameter:
522: . fem - The PetscFE object

524:   Output Parameter:
525: . sp - The PetscSpace object

527:   Level: intermediate

529: .seealso: PetscFECreate()
530: @*/
531: PetscErrorCode PetscFEGetBasisSpace(PetscFE fem, PetscSpace *sp)
532: {
536:   *sp = fem->basisSpace;
537:   return(0);
538: }

540: /*@
541:   PetscFESetBasisSpace - Sets the PetscSpace used for approximation of the solution

543:   Not collective

545:   Input Parameters:
546: + fem - The PetscFE object
547: - sp - The PetscSpace object

549:   Level: intermediate

551: .seealso: PetscFECreate()
552: @*/
553: PetscErrorCode PetscFESetBasisSpace(PetscFE fem, PetscSpace sp)
554: {

560:   PetscSpaceDestroy(&fem->basisSpace);
561:   fem->basisSpace = sp;
562:   PetscObjectReference((PetscObject) fem->basisSpace);
563:   return(0);
564: }

566: /*@
567:   PetscFEGetDualSpace - Returns the PetscDualSpace used to define the inner product

569:   Not collective

571:   Input Parameter:
572: . fem - The PetscFE object

574:   Output Parameter:
575: . sp - The PetscDualSpace object

577:   Level: intermediate

579: .seealso: PetscFECreate()
580: @*/
581: PetscErrorCode PetscFEGetDualSpace(PetscFE fem, PetscDualSpace *sp)
582: {
586:   *sp = fem->dualSpace;
587:   return(0);
588: }

590: /*@
591:   PetscFESetDualSpace - Sets the PetscDualSpace used to define the inner product

593:   Not collective

595:   Input Parameters:
596: + fem - The PetscFE object
597: - sp - The PetscDualSpace object

599:   Level: intermediate

601: .seealso: PetscFECreate()
602: @*/
603: PetscErrorCode PetscFESetDualSpace(PetscFE fem, PetscDualSpace sp)
604: {

610:   PetscDualSpaceDestroy(&fem->dualSpace);
611:   fem->dualSpace = sp;
612:   PetscObjectReference((PetscObject) fem->dualSpace);
613:   return(0);
614: }

616: /*@

619:   Not collective

621:   Input Parameter:
622: . fem - The PetscFE object

624:   Output Parameter:
625: . q - The PetscQuadrature object

627:   Level: intermediate

629: .seealso: PetscFECreate()
630: @*/
632: {
637:   return(0);
638: }

640: /*@

643:   Not collective

645:   Input Parameters:
646: + fem - The PetscFE object
647: - q - The PetscQuadrature object

649:   Level: intermediate

651: .seealso: PetscFECreate()
652: @*/
654: {
655:   PetscInt       Nc, qNc;

660:   PetscFEGetNumComponents(fem, &Nc);
662:   if ((qNc != 1) && (Nc != qNc)) SETERRQ2(PetscObjectComm((PetscObject) fem), PETSC_ERR_ARG_SIZ, "FE components %D != Quadrature components %D and non-scalar quadrature", Nc, qNc);
663:   PetscTabulationDestroy(&fem->T);
664:   PetscTabulationDestroy(&fem->Tc);
667:   PetscObjectReference((PetscObject) q);
668:   return(0);
669: }

671: /*@
672:   PetscFEGetFaceQuadrature - Returns the PetscQuadrature used to calculate inner products on faces

674:   Not collective

676:   Input Parameter:
677: . fem - The PetscFE object

679:   Output Parameter:
680: . q - The PetscQuadrature object

682:   Level: intermediate

684: .seealso: PetscFECreate()
685: @*/
687: {
692:   return(0);
693: }

695: /*@
696:   PetscFESetFaceQuadrature - Sets the PetscQuadrature used to calculate inner products on faces

698:   Not collective

700:   Input Parameters:
701: + fem - The PetscFE object
702: - q - The PetscQuadrature object

704:   Level: intermediate

706: .seealso: PetscFECreate()
707: @*/
709: {
710:   PetscInt       Nc, qNc;

715:   PetscFEGetNumComponents(fem, &Nc);
717:   if ((qNc != 1) && (Nc != qNc)) SETERRQ2(PetscObjectComm((PetscObject) fem), PETSC_ERR_ARG_SIZ, "FE components %D != Quadrature components %D and non-scalar quadrature", Nc, qNc);
718:   PetscTabulationDestroy(&fem->Tf);
721:   PetscObjectReference((PetscObject) q);
722:   return(0);
723: }

725: /*@

728:   Not collective

730:   Input Parameters:
731: + sfe - The PetscFE source for the quadratures
732: - tfe - The PetscFE target for the quadratures

734:   Level: intermediate

737: @*/
738: PetscErrorCode PetscFECopyQuadrature(PetscFE sfe, PetscFE tfe)
739: {
741:   PetscErrorCode  ierr;

750:   return(0);
751: }

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

756:   Not collective

758:   Input Parameter:
759: . fem - The PetscFE object

761:   Output Parameter:
762: . numDof - Array with the number of dofs per dimension

764:   Level: intermediate

766: .seealso: PetscFECreate()
767: @*/
768: PetscErrorCode PetscFEGetNumDof(PetscFE fem, const PetscInt **numDof)
769: {

775:   PetscDualSpaceGetNumDof(fem->dualSpace, numDof);
776:   return(0);
777: }

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

782:   Not collective

784:   Input Parameter:
785: . fem - The PetscFE object

787:   Output Parameter:
788: . T - The basis function values and derivatives at quadrature points

790:   Note:
791: $T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c 792:$ 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
793: $T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e 795: Level: intermediate 797: .seealso: PetscFECreateTabulation(), PetscTabulationDestroy() 798: @*/ 799: PetscErrorCode PetscFEGetCellTabulation(PetscFE fem, PetscTabulation *T) 800: { 801: PetscInt npoints; 802: const PetscReal *points; 803: PetscErrorCode ierr; 808: PetscQuadratureGetData(fem->quadrature, NULL, NULL, &npoints, &points, NULL); 809: if (!fem->T) {PetscFECreateTabulation(fem, 1, npoints, points, 1, &fem->T);} 810: *T = fem->T; 811: return(0); 812: } 814: /*@C 815: PetscFEGetFaceTabulation - Returns the tabulation of the basis functions at the face quadrature points for each face of the reference cell 817: Not collective 819: Input Parameter: 820: . fem - The PetscFE object 822: Output Parameters: 823: . Tf - The basis function values and derviatives at face quadrature points 825: Note: 826:$ 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
827: $T->T[1] = Df[(((f*Nq + q)*pdim + i)*Nc + c)*dim + d] is the derivative value at point f,q for basis function i, component c, in direction d 828:$ T->T[2] = Hf[((((f*Nq + q)*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point f,q for basis function i, component c, in directions d and e

830:   Level: intermediate

832: .seealso: PetscFEGetCellTabulation(), PetscFECreateTabulation(), PetscTabulationDestroy()
833: @*/
834: PetscErrorCode PetscFEGetFaceTabulation(PetscFE fem, PetscTabulation *Tf)
835: {
836:   PetscErrorCode   ierr;

841:   if (!fem->Tf) {
842:     const PetscReal  xi0[3] = {-1., -1., -1.};
843:     PetscReal        v0[3], J[9], detJ;
845:     PetscDualSpace   sp;
846:     DM               dm;
847:     const PetscInt  *faces;
848:     PetscInt         dim, numFaces, f, npoints, q;
849:     const PetscReal *points;
850:     PetscReal       *facePoints;

852:     PetscFEGetDualSpace(fem, &sp);
853:     PetscDualSpaceGetDM(sp, &dm);
854:     DMGetDimension(dm, &dim);
855:     DMPlexGetConeSize(dm, 0, &numFaces);
856:     DMPlexGetCone(dm, 0, &faces);
858:     if (fq) {
859:       PetscQuadratureGetData(fq, NULL, NULL, &npoints, &points, NULL);
860:       PetscMalloc1(numFaces*npoints*dim, &facePoints);
861:       for (f = 0; f < numFaces; ++f) {
862:         DMPlexComputeCellGeometryFEM(dm, faces[f], NULL, v0, J, NULL, &detJ);
863:         for (q = 0; q < npoints; ++q) CoordinatesRefToReal(dim, dim-1, xi0, v0, J, &points[q*(dim-1)], &facePoints[(f*npoints+q)*dim]);
864:       }
865:       PetscFECreateTabulation(fem, numFaces, npoints, facePoints, 1, &fem->Tf);
866:       PetscFree(facePoints);
867:     }
868:   }
869:   *Tf = fem->Tf;
870:   return(0);
871: }

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

876:   Not collective

878:   Input Parameter:
879: . fem - The PetscFE object

881:   Output Parameters:
882: . Tc - The basis function values at face centroid points

884:   Note:
885: $T->T[0] = Bf[(f*pdim + i)*Nc + c] is the value at point f for basis function i and component c 887: Level: intermediate 889: .seealso: PetscFEGetFaceTabulation(), PetscFEGetCellTabulation(), PetscFECreateTabulation(), PetscTabulationDestroy() 890: @*/ 891: PetscErrorCode PetscFEGetFaceCentroidTabulation(PetscFE fem, PetscTabulation *Tc) 892: { 893: PetscErrorCode ierr; 898: if (!fem->Tc) { 899: PetscDualSpace sp; 900: DM dm; 901: const PetscInt *cone; 902: PetscReal *centroids; 903: PetscInt dim, numFaces, f; 905: PetscFEGetDualSpace(fem, &sp); 906: PetscDualSpaceGetDM(sp, &dm); 907: DMGetDimension(dm, &dim); 908: DMPlexGetConeSize(dm, 0, &numFaces); 909: DMPlexGetCone(dm, 0, &cone); 910: PetscMalloc1(numFaces*dim, &centroids); 911: for (f = 0; f < numFaces; ++f) {DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, &centroids[f*dim], NULL);} 912: PetscFECreateTabulation(fem, 1, numFaces, centroids, 0, &fem->Tc); 913: PetscFree(centroids); 914: } 915: *Tc = fem->Tc; 916: return(0); 917: } 919: /*@C 920: PetscFECreateTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided. 922: Not collective 924: Input Parameters: 925: + fem - The PetscFE object 926: . nrepl - The number of replicas 927: . npoints - The number of tabulation points in a replica 928: . points - The tabulation point coordinates 929: - K - The number of derivatives calculated 931: Output Parameter: 932: . T - The basis function values and derivatives at tabulation points 934: Note: 935:$ T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
936: $T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d 937:$ T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e

939:   Level: intermediate

941: .seealso: PetscFEGetCellTabulation(), PetscTabulationDestroy()
942: @*/
943: PetscErrorCode PetscFECreateTabulation(PetscFE fem, PetscInt nrepl, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation *T)
944: {
945:   DM               dm;
946:   PetscDualSpace   Q;
947:   PetscInt         Nb;   /* Dimension of FE space P */
948:   PetscInt         Nc;   /* Field components */
949:   PetscInt         cdim; /* Reference coordinate dimension */
950:   PetscInt         k;
951:   PetscErrorCode   ierr;

954:   if (!npoints || !fem->dualSpace || K < 0) {
955:     *T = NULL;
956:     return(0);
957:   }
961:   PetscFEGetDualSpace(fem, &Q);
962:   PetscDualSpaceGetDM(Q, &dm);
963:   DMGetDimension(dm, &cdim);
964:   PetscDualSpaceGetDimension(Q, &Nb);
965:   PetscFEGetNumComponents(fem, &Nc);
966:   PetscMalloc1(1, T);
967:   (*T)->K    = !cdim ? 0 : K;
968:   (*T)->Nr   = nrepl;
969:   (*T)->Np   = npoints;
970:   (*T)->Nb   = Nb;
971:   (*T)->Nc   = Nc;
972:   (*T)->cdim = cdim;
973:   PetscMalloc1((*T)->K+1, &(*T)->T);
974:   for (k = 0; k <= (*T)->K; ++k) {
975:     PetscMalloc1(nrepl*npoints*Nb*Nc*PetscPowInt(cdim, k), &(*T)->T[k]);
976:   }
977:   (*fem->ops->createtabulation)(fem, nrepl*npoints, points, K, *T);
978:   return(0);
979: }

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

984:   Not collective

986:   Input Parameters:
987: + fem     - The PetscFE object
988: . npoints - The number of tabulation points
989: . points  - The tabulation point coordinates
990: . K       - The number of derivatives calculated
991: - T       - An existing tabulation object with enough allocated space

993:   Output Parameter:
994: . T - The basis function values and derivatives at tabulation points

996:   Note:
997: $T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c 998:$ 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
999: $T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e 1001: Level: intermediate 1003: .seealso: PetscFEGetCellTabulation(), PetscTabulationDestroy() 1004: @*/ 1005: PetscErrorCode PetscFEComputeTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation T) 1006: { 1010: if (!npoints || !fem->dualSpace || K < 0) return(0); 1014: #ifdef PETSC_USE_DEBUG 1015: { 1016: DM dm; 1017: PetscDualSpace Q; 1018: PetscInt Nb; /* Dimension of FE space P */ 1019: PetscInt Nc; /* Field components */ 1020: PetscInt cdim; /* Reference coordinate dimension */ 1022: PetscFEGetDualSpace(fem, &Q); 1023: PetscDualSpaceGetDM(Q, &dm); 1024: DMGetDimension(dm, &cdim); 1025: PetscDualSpaceGetDimension(Q, &Nb); 1026: PetscFEGetNumComponents(fem, &Nc); 1027: if (T->K != (!cdim ? 0 : K)) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation K %D must match requested K %D", T->K, !cdim ? 0 : K); 1028: if (T->Nb != Nb) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nb %D must match requested Nb %D", T->Nb, Nb); 1029: if (T->Nc != Nc) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nc %D must match requested Nc %D", T->Nc, Nc); 1030: if (T->cdim != cdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation cdim %D must match requested cdim %D", T->cdim, cdim); 1031: } 1032: #endif 1033: T->Nr = 1; 1034: T->Np = npoints; 1035: (*fem->ops->createtabulation)(fem, npoints, points, K, T); 1036: return(0); 1037: } 1039: /*@C 1040: PetscTabulationDestroy - Frees memory from the associated tabulation. 1042: Not collective 1044: Input Parameter: 1045: . T - The tabulation 1047: Level: intermediate 1049: .seealso: PetscFECreateTabulation(), PetscFEGetCellTabulation() 1050: @*/ 1051: PetscErrorCode PetscTabulationDestroy(PetscTabulation *T) 1052: { 1053: PetscInt k; 1058: if (!T || !(*T)) return(0); 1059: for (k = 0; k <= (*T)->K; ++k) {PetscFree((*T)->T[k]);} 1060: PetscFree((*T)->T); 1061: PetscFree(*T); 1062: *T = NULL; 1063: return(0); 1064: } 1066: PETSC_EXTERN PetscErrorCode PetscFECreatePointTrace(PetscFE fe, PetscInt refPoint, PetscFE *trFE) 1067: { 1068: PetscSpace bsp, bsubsp; 1069: PetscDualSpace dsp, dsubsp; 1070: PetscInt dim, depth, numComp, i, j, coneSize, order; 1071: PetscFEType type; 1072: DM dm; 1073: DMLabel label; 1074: PetscReal *xi, *v, *J, detJ; 1075: const char *name; 1076: PetscQuadrature origin, fullQuad, subQuad; 1082: PetscFEGetBasisSpace(fe,&bsp); 1083: PetscFEGetDualSpace(fe,&dsp); 1084: PetscDualSpaceGetDM(dsp,&dm); 1085: DMGetDimension(dm,&dim); 1086: DMPlexGetDepthLabel(dm,&label); 1087: DMLabelGetValue(label,refPoint,&depth); 1088: PetscCalloc1(depth,&xi); 1089: PetscMalloc1(dim,&v); 1090: PetscMalloc1(dim*dim,&J); 1091: for (i = 0; i < depth; i++) xi[i] = 0.; 1092: PetscQuadratureCreate(PETSC_COMM_SELF,&origin); 1093: PetscQuadratureSetData(origin,depth,0,1,xi,NULL); 1094: DMPlexComputeCellGeometryFEM(dm,refPoint,origin,v,J,NULL,&detJ); 1095: /* CellGeometryFEM computes the expanded Jacobian, we want the true jacobian */ 1096: for (i = 1; i < dim; i++) { 1097: for (j = 0; j < depth; j++) { 1098: J[i * depth + j] = J[i * dim + j]; 1099: } 1100: } 1101: PetscQuadratureDestroy(&origin); 1102: PetscDualSpaceGetPointSubspace(dsp,refPoint,&dsubsp); 1103: PetscSpaceCreateSubspace(bsp,dsubsp,v,J,NULL,NULL,PETSC_OWN_POINTER,&bsubsp); 1104: PetscSpaceSetUp(bsubsp); 1105: PetscFECreate(PetscObjectComm((PetscObject)fe),trFE); 1106: PetscFEGetType(fe,&type); 1107: PetscFESetType(*trFE,type); 1108: PetscFEGetNumComponents(fe,&numComp); 1109: PetscFESetNumComponents(*trFE,numComp); 1110: PetscFESetBasisSpace(*trFE,bsubsp); 1111: PetscFESetDualSpace(*trFE,dsubsp); 1112: PetscObjectGetName((PetscObject) fe, &name); 1113: if (name) {PetscFESetName(*trFE, name);} 1114: PetscFEGetQuadrature(fe,&fullQuad); 1115: PetscQuadratureGetOrder(fullQuad,&order); 1116: DMPlexGetConeSize(dm,refPoint,&coneSize); 1117: if (coneSize == 2 * depth) { 1118: PetscDTGaussTensorQuadrature(depth,1,(order + 1)/2,-1.,1.,&subQuad); 1119: } else { 1120: PetscDTStroudConicalQuadrature(depth,1,(order + 1)/2,-1.,1.,&subQuad); 1121: } 1122: PetscFESetQuadrature(*trFE,subQuad); 1123: PetscFESetUp(*trFE); 1124: PetscQuadratureDestroy(&subQuad); 1125: PetscSpaceDestroy(&bsubsp); 1126: return(0); 1127: } 1129: PetscErrorCode PetscFECreateHeightTrace(PetscFE fe, PetscInt height, PetscFE *trFE) 1130: { 1131: PetscInt hStart, hEnd; 1132: PetscDualSpace dsp; 1133: DM dm; 1139: *trFE = NULL; 1140: PetscFEGetDualSpace(fe,&dsp); 1141: PetscDualSpaceGetDM(dsp,&dm); 1142: DMPlexGetHeightStratum(dm,height,&hStart,&hEnd); 1143: if (hEnd <= hStart) return(0); 1144: PetscFECreatePointTrace(fe,hStart,trFE); 1145: return(0); 1146: } 1149: /*@ 1150: PetscFEGetDimension - Get the dimension of the finite element space on a cell 1152: Not collective 1154: Input Parameter: 1155: . fe - The PetscFE 1157: Output Parameter: 1158: . dim - The dimension 1160: Level: intermediate 1162: .seealso: PetscFECreate(), PetscSpaceGetDimension(), PetscDualSpaceGetDimension() 1163: @*/ 1164: PetscErrorCode PetscFEGetDimension(PetscFE fem, PetscInt *dim) 1165: { 1171: if (fem->ops->getdimension) {(*fem->ops->getdimension)(fem, dim);} 1172: return(0); 1173: } 1175: /*@C 1176: PetscFEPushforward - Map the reference element function to real space 1178: Input Parameters: 1179: + fe - The PetscFE 1180: . fegeom - The cell geometry 1181: . Nv - The number of function values 1182: - vals - The function values 1184: Output Parameter: 1185: . vals - The transformed function values 1187: Level: advanced 1189: Note: This just forwards the call onto PetscDualSpacePushforward(). 1191: Note: This only handles tranformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension. 1193: .seealso: PetscDualSpacePushforward() 1194: @*/ 1195: PetscErrorCode PetscFEPushforward(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[]) 1196: { 1200: PetscDualSpacePushforward(fe->dualSpace, fegeom, Nv, fe->numComponents, vals); 1201: return(0); 1202: } 1204: /*@C 1205: PetscFEPushforwardGradient - Map the reference element function gradient to real space 1207: Input Parameters: 1208: + fe - The PetscFE 1209: . fegeom - The cell geometry 1210: . Nv - The number of function gradient values 1211: - vals - The function gradient values 1213: Output Parameter: 1214: . vals - The transformed function gradient values 1216: Level: advanced 1218: Note: This just forwards the call onto PetscDualSpacePushforwardGradient(). 1220: Note: This only handles tranformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension. 1222: .seealso: PetscFEPushforward(), PetscDualSpacePushforwardGradient(), PetscDualSpacePushforward() 1223: @*/ 1224: PetscErrorCode PetscFEPushforwardGradient(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[]) 1225: { 1229: PetscDualSpacePushforwardGradient(fe->dualSpace, fegeom, Nv, fe->numComponents, vals); 1230: return(0); 1231: } 1233: /* 1234: Purpose: Compute element vector for chunk of elements 1236: Input: 1237: Sizes: 1238: Ne: number of elements 1239: Nf: number of fields 1240: PetscFE 1241: dim: spatial dimension 1242: Nb: number of basis functions 1243: Nc: number of field components 1244: PetscQuadrature 1245: Nq: number of quadrature points 1247: Geometry: 1248: PetscFEGeom[Ne] possibly *Nq 1249: PetscReal v0s[dim] 1250: PetscReal n[dim] 1251: PetscReal jacobians[dim*dim] 1252: PetscReal jacobianInverses[dim*dim] 1253: PetscReal jacobianDeterminants 1254: FEM: 1255: PetscFE 1256: PetscQuadrature 1257: PetscReal quadPoints[Nq*dim] 1258: PetscReal quadWeights[Nq] 1259: PetscReal basis[Nq*Nb*Nc] 1260: PetscReal basisDer[Nq*Nb*Nc*dim] 1261: PetscScalar coefficients[Ne*Nb*Nc] 1262: PetscScalar elemVec[Ne*Nb*Nc] 1264: Problem: 1265: PetscInt f: the active field 1266: f0, f1 1268: Work Space: 1269: PetscFE 1270: PetscScalar f0[Nq*dim]; 1271: PetscScalar f1[Nq*dim*dim]; 1272: PetscScalar u[Nc]; 1273: PetscScalar gradU[Nc*dim]; 1274: PetscReal x[dim]; 1275: PetscScalar realSpaceDer[dim]; 1277: Purpose: Compute element vector for N_cb batches of elements 1279: Input: 1280: Sizes: 1281: N_cb: Number of serial cell batches 1283: Geometry: 1284: PetscReal v0s[Ne*dim] 1285: PetscReal jacobians[Ne*dim*dim] possibly *Nq 1286: PetscReal jacobianInverses[Ne*dim*dim] possibly *Nq 1287: PetscReal jacobianDeterminants[Ne] possibly *Nq 1288: FEM: 1289: static PetscReal quadPoints[Nq*dim] 1290: static PetscReal quadWeights[Nq] 1291: static PetscReal basis[Nq*Nb*Nc] 1292: static PetscReal basisDer[Nq*Nb*Nc*dim] 1293: PetscScalar coefficients[Ne*Nb*Nc] 1294: PetscScalar elemVec[Ne*Nb*Nc] 1296: ex62.c: 1297: PetscErrorCode PetscFEIntegrateResidualBatch(PetscInt Ne, PetscInt numFields, PetscInt field, PetscQuadrature quad[], const PetscScalar coefficients[], 1298: const PetscReal v0s[], const PetscReal jacobians[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], 1299: void (*f0_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]), 1300: void (*f1_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]), PetscScalar elemVec[]) 1302: ex52.c: 1303: 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) 1304: 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) 1306: ex52_integrateElement.cu 1307: __global__ void integrateElementQuadrature(int N_cb, realType *coefficients, realType *jacobianInverses, realType *jacobianDeterminants, realType *elemVec) 1309: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt Nbl, const PetscScalar coefficients[], 1310: const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[], 1311: PetscLogEvent event, PetscInt debug, PetscInt pde_op) 1313: ex52_integrateElementOpenCL.c: 1314: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt N_bl, const PetscScalar coefficients[], 1315: const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[], 1316: PetscLogEvent event, PetscInt debug, PetscInt pde_op) 1318: __kernel void integrateElementQuadrature(int N_cb, __global float *coefficients, __global float *jacobianInverses, __global float *jacobianDeterminants, __global float *elemVec) 1319: */ 1321: /*@C 1322: PetscFEIntegrate - Produce the integral for the given field for a chunk of elements by quadrature integration 1324: Not collective 1326: Input Parameters: 1327: + fem - The PetscFE object for the field being integrated 1328: . prob - The PetscDS specifying the discretizations and continuum functions 1329: . field - The field being integrated 1330: . Ne - The number of elements in the chunk 1331: . cgeom - The cell geometry for each cell in the chunk 1332: . coefficients - The array of FEM basis coefficients for the elements 1333: . probAux - The PetscDS specifying the auxiliary discretizations 1334: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements 1336: Output Parameter: 1337: . integral - the integral for this field 1339: Level: intermediate 1341: .seealso: PetscFEIntegrateResidual() 1342: @*/ 1343: PetscErrorCode PetscFEIntegrate(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *cgeom, 1344: const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[]) 1345: { 1346: PetscFE fe; 1351: PetscDSGetDiscretization(prob, field, (PetscObject *) &fe); 1352: if (fe->ops->integrate) {(*fe->ops->integrate)(prob, field, Ne, cgeom, coefficients, probAux, coefficientsAux, integral);} 1353: return(0); 1354: } 1356: /*@C 1357: PetscFEIntegrateBd - Produce the integral for the given field for a chunk of elements by quadrature integration 1359: Not collective 1361: Input Parameters: 1362: + fem - The PetscFE object for the field being integrated 1363: . prob - The PetscDS specifying the discretizations and continuum functions 1364: . field - The field being integrated 1365: . obj_func - The function to be integrated 1366: . Ne - The number of elements in the chunk 1367: . fgeom - The face geometry for each face in the chunk 1368: . coefficients - The array of FEM basis coefficients for the elements 1369: . probAux - The PetscDS specifying the auxiliary discretizations 1370: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements 1372: Output Parameter: 1373: . integral - the integral for this field 1375: Level: intermediate 1377: .seealso: PetscFEIntegrateResidual() 1378: @*/ 1379: PetscErrorCode PetscFEIntegrateBd(PetscDS prob, PetscInt field, 1380: void (*obj_func)(PetscInt, PetscInt, PetscInt, 1381: const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], 1382: const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], 1383: PetscReal, const PetscReal[], const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), 1384: PetscInt Ne, PetscFEGeom *geom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[]) 1385: { 1386: PetscFE fe; 1391: PetscDSGetDiscretization(prob, field, (PetscObject *) &fe); 1392: if (fe->ops->integratebd) {(*fe->ops->integratebd)(prob, field, obj_func, Ne, geom, coefficients, probAux, coefficientsAux, integral);} 1393: return(0); 1394: } 1396: /*@C 1397: PetscFEIntegrateResidual - Produce the element residual vector for a chunk of elements by quadrature integration 1399: Not collective 1401: Input Parameters: 1402: + fem - The PetscFE object for the field being integrated 1403: . prob - The PetscDS specifying the discretizations and continuum functions 1404: . field - The field being integrated 1405: . Ne - The number of elements in the chunk 1406: . cgeom - The cell geometry for each cell in the chunk 1407: . coefficients - The array of FEM basis coefficients for the elements 1408: . coefficients_t - The array of FEM basis time derivative coefficients for the elements 1409: . probAux - The PetscDS specifying the auxiliary discretizations 1410: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements 1411: - t - The time 1413: Output Parameter: 1414: . elemVec - the element residual vectors from each element 1416: Note: 1417:$ Loop over batch of elements (e):
1418: $Loop over quadrature points (q): 1419:$     Make u_q and gradU_q (loops over fields,Nb,Ncomp) and x_q
1420: $Call f_0 and f_1 1421:$   Loop over element vector entries (f,fc --> i):
1422: $elemVec[i] += \psi^{fc}_f(q) f0_{fc}(u, \nabla u) + \nabla\psi^{fc}_f(q) \cdot f1_{fc,df}(u, \nabla u) 1424: Level: intermediate 1426: .seealso: PetscFEIntegrateResidual() 1427: @*/ 1428: PetscErrorCode PetscFEIntegrateResidual(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *cgeom, 1429: const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[]) 1430: { 1431: PetscFE fe; 1436: PetscDSGetDiscretization(prob, field, (PetscObject *) &fe); 1437: if (fe->ops->integrateresidual) {(*fe->ops->integrateresidual)(prob, field, Ne, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec);} 1438: return(0); 1439: } 1441: /*@C 1442: PetscFEIntegrateBdResidual - Produce the element residual vector for a chunk of elements by quadrature integration over a boundary 1444: Not collective 1446: Input Parameters: 1447: + fem - The PetscFE object for the field being integrated 1448: . prob - The PetscDS specifying the discretizations and continuum functions 1449: . field - The field being integrated 1450: . Ne - The number of elements in the chunk 1451: . fgeom - The face geometry for each cell in the chunk 1452: . coefficients - The array of FEM basis coefficients for the elements 1453: . coefficients_t - The array of FEM basis time derivative coefficients for the elements 1454: . probAux - The PetscDS specifying the auxiliary discretizations 1455: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements 1456: - t - The time 1458: Output Parameter: 1459: . elemVec - the element residual vectors from each element 1461: Level: intermediate 1463: .seealso: PetscFEIntegrateResidual() 1464: @*/ 1465: PetscErrorCode PetscFEIntegrateBdResidual(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *fgeom, 1466: const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[]) 1467: { 1468: PetscFE fe; 1473: PetscDSGetDiscretization(prob, field, (PetscObject *) &fe); 1474: if (fe->ops->integratebdresidual) {(*fe->ops->integratebdresidual)(prob, field, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec);} 1475: return(0); 1476: } 1478: /*@C 1479: PetscFEIntegrateJacobian - Produce the element Jacobian for a chunk of elements by quadrature integration 1481: Not collective 1483: Input Parameters: 1484: + fem - The PetscFE object for the field being integrated 1485: . prob - The PetscDS specifying the discretizations and continuum functions 1486: . jtype - The type of matrix pointwise functions that should be used 1487: . fieldI - The test field being integrated 1488: . fieldJ - The basis field being integrated 1489: . Ne - The number of elements in the chunk 1490: . cgeom - The cell geometry for each cell in the chunk 1491: . coefficients - The array of FEM basis coefficients for the elements for the Jacobian evaluation point 1492: . coefficients_t - The array of FEM basis time derivative coefficients for the elements 1493: . probAux - The PetscDS specifying the auxiliary discretizations 1494: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements 1495: . t - The time 1496: - u_tShift - A multiplier for the dF/du_t term (as opposed to the dF/du term) 1498: Output Parameter: 1499: . elemMat - the element matrices for the Jacobian from each element 1501: Note: 1502:$ Loop over batch of elements (e):
1503: $Loop over element matrix entries (f,fc,g,gc --> i,j): 1504:$     Loop over quadrature points (q):
1505: $Make u_q and gradU_q (loops over fields,Nb,Ncomp) 1506:$         elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1507: $+ \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q) 1508:$                      + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1509: $+ \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q) 1510: Level: intermediate 1512: .seealso: PetscFEIntegrateResidual() 1513: @*/ 1514: PetscErrorCode PetscFEIntegrateJacobian(PetscDS prob, PetscFEJacobianType jtype, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFEGeom *cgeom, 1515: const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[]) 1516: { 1517: PetscFE fe; 1522: PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe); 1523: if (fe->ops->integratejacobian) {(*fe->ops->integratejacobian)(prob, jtype, fieldI, fieldJ, Ne, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat);} 1524: return(0); 1525: } 1527: /*@C 1528: PetscFEIntegrateBdJacobian - Produce the boundary element Jacobian for a chunk of elements by quadrature integration 1530: Not collective 1532: Input Parameters: 1533: + prob - The PetscDS specifying the discretizations and continuum functions 1534: . fieldI - The test field being integrated 1535: . fieldJ - The basis field being integrated 1536: . Ne - The number of elements in the chunk 1537: . fgeom - The face geometry for each cell in the chunk 1538: . coefficients - The array of FEM basis coefficients for the elements for the Jacobian evaluation point 1539: . coefficients_t - The array of FEM basis time derivative coefficients for the elements 1540: . probAux - The PetscDS specifying the auxiliary discretizations 1541: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements 1542: . t - The time 1543: - u_tShift - A multiplier for the dF/du_t term (as opposed to the dF/du term) 1545: Output Parameter: 1546: . elemMat - the element matrices for the Jacobian from each element 1548: Note: 1549:$ Loop over batch of elements (e):
1550: $Loop over element matrix entries (f,fc,g,gc --> i,j): 1551:$     Loop over quadrature points (q):
1552: $Make u_q and gradU_q (loops over fields,Nb,Ncomp) 1553:$         elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
1554: $+ \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q) 1555:$                      + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
1556: \$                      + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
1557:   Level: intermediate

1559: .seealso: PetscFEIntegrateJacobian(), PetscFEIntegrateResidual()
1560: @*/
1561: PetscErrorCode PetscFEIntegrateBdJacobian(PetscDS prob, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFEGeom *fgeom,
1562:                                           const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
1563: {
1564:   PetscFE        fe;

1569:   PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);
1570:   if (fe->ops->integratebdjacobian) {(*fe->ops->integratebdjacobian)(prob, fieldI, fieldJ, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat);}
1571:   return(0);
1572: }

1574: /*@
1575:   PetscFEGetHeightSubspace - Get the subspace of this space for a mesh point of a given height

1577:   Input Parameters:
1578: + fe     - The finite element space
1579: - height - The height of the Plex point

1581:   Output Parameter:
1582: . subfe  - The subspace of this FE space

1584:   Note: For example, if we want the subspace of this space for a face, we would choose height = 1.

1588: .seealso: PetscFECreateDefault()
1589: @*/
1590: PetscErrorCode PetscFEGetHeightSubspace(PetscFE fe, PetscInt height, PetscFE *subfe)
1591: {
1592:   PetscSpace      P, subP;
1593:   PetscDualSpace  Q, subQ;
1595:   PetscFEType     fetype;
1596:   PetscInt        dim, Nc;
1597:   PetscErrorCode  ierr;

1602:   if (height == 0) {
1603:     *subfe = fe;
1604:     return(0);
1605:   }
1606:   PetscFEGetBasisSpace(fe, &P);
1607:   PetscFEGetDualSpace(fe, &Q);
1608:   PetscFEGetNumComponents(fe, &Nc);
1610:   PetscDualSpaceGetDimension(Q, &dim);
1611:   if (height > dim || height < 0) {SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Asked for space at height %D for dimension %D space", height, dim);}
1612:   if (!fe->subspaces) {PetscCalloc1(dim, &fe->subspaces);}
1613:   if (height <= dim) {
1614:     if (!fe->subspaces[height-1]) {
1615:       PetscFE     sub;
1616:       const char *name;

1618:       PetscSpaceGetHeightSubspace(P, height, &subP);
1619:       PetscDualSpaceGetHeightSubspace(Q, height, &subQ);
1620:       PetscFECreate(PetscObjectComm((PetscObject) fe), &sub);
1621:       PetscObjectGetName((PetscObject) fe,  &name);
1622:       PetscObjectSetName((PetscObject) sub,  name);
1623:       PetscFEGetType(fe, &fetype);
1624:       PetscFESetType(sub, fetype);
1625:       PetscFESetBasisSpace(sub, subP);
1626:       PetscFESetDualSpace(sub, subQ);
1627:       PetscFESetNumComponents(sub, Nc);
1628:       PetscFESetUp(sub);
1630:       fe->subspaces[height-1] = sub;
1631:     }
1632:     *subfe = fe->subspaces[height-1];
1633:   } else {
1634:     *subfe = NULL;
1635:   }
1636:   return(0);
1637: }

1639: /*@
1640:   PetscFERefine - Create a "refined" PetscFE object that refines the reference cell into smaller copies. This is typically used
1641:   to precondition a higher order method with a lower order method on a refined mesh having the same number of dofs (but more
1642:   sparsity). It is also used to create an interpolation between regularly refined meshes.

1644:   Collective on fem

1646:   Input Parameter:
1647: . fe - The initial PetscFE

1649:   Output Parameter:
1650: . feRef - The refined PetscFE

1654: .seealso: PetscFEType, PetscFECreate(), PetscFESetType()
1655: @*/
1656: PetscErrorCode PetscFERefine(PetscFE fe, PetscFE *feRef)
1657: {
1658:   PetscSpace       P, Pref;
1659:   PetscDualSpace   Q, Qref;
1660:   DM               K, Kref;
1662:   const PetscReal *v0, *jac;
1663:   PetscInt         numComp, numSubelements;
1664:   PetscInt         cStart, cEnd, c;
1665:   PetscDualSpace  *cellSpaces;
1666:   PetscErrorCode   ierr;

1669:   PetscFEGetBasisSpace(fe, &P);
1670:   PetscFEGetDualSpace(fe, &Q);
1672:   PetscDualSpaceGetDM(Q, &K);
1673:   /* Create space */
1674:   PetscObjectReference((PetscObject) P);
1675:   Pref = P;
1676:   /* Create dual space */
1677:   PetscDualSpaceDuplicate(Q, &Qref);
1678:   PetscDualSpaceSetType(Qref, PETSCDUALSPACEREFINED);
1679:   DMRefine(K, PetscObjectComm((PetscObject) fe), &Kref);
1680:   PetscDualSpaceSetDM(Qref, Kref);
1681:   DMPlexGetHeightStratum(Kref, 0, &cStart, &cEnd);
1682:   PetscMalloc1(cEnd - cStart, &cellSpaces);
1683:   /* TODO: fix for non-uniform refinement */
1684:   for (c = 0; c < cEnd - cStart; c++) cellSpaces[c] = Q;
1685:   PetscDualSpaceRefinedSetCellSpaces(Qref, cellSpaces);
1686:   PetscFree(cellSpaces);
1687:   DMDestroy(&Kref);
1688:   PetscDualSpaceSetUp(Qref);
1689:   /* Create element */
1690:   PetscFECreate(PetscObjectComm((PetscObject) fe), feRef);
1691:   PetscFESetType(*feRef, PETSCFECOMPOSITE);
1692:   PetscFESetBasisSpace(*feRef, Pref);
1693:   PetscFESetDualSpace(*feRef, Qref);
1694:   PetscFEGetNumComponents(fe,    &numComp);
1695:   PetscFESetNumComponents(*feRef, numComp);
1696:   PetscFESetUp(*feRef);
1697:   PetscSpaceDestroy(&Pref);
1698:   PetscDualSpaceDestroy(&Qref);
1700:   PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL);
1701:   PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref);
1704:   return(0);
1705: }

1707: /*@C
1708:   PetscFECreateDefault - Create a PetscFE for basic FEM computation

1710:   Collective

1712:   Input Parameters:
1713: + comm      - The MPI comm
1714: . dim       - The spatial dimension
1715: . Nc        - The number of components
1716: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
1717: . prefix    - The options prefix, or NULL
1718: - qorder    - The quadrature order or PETSC_DETERMINE to use PetscSpace polynomial degree

1720:   Output Parameter:
1721: . fem - The PetscFE object

1723:   Note:
1724:   Each object is SetFromOption() during creation, so that the object may be customized from the command line.

1726:   Level: beginner

1728: .seealso: PetscFECreate(), PetscSpaceCreate(), PetscDualSpaceCreate()
1729: @*/
1730: PetscErrorCode PetscFECreateDefault(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, const char prefix[], PetscInt qorder, PetscFE *fem)
1731: {
1733:   DM              K;
1734:   PetscSpace      P;
1735:   PetscDualSpace  Q;
1737:   PetscBool       tensor = isSimplex ? PETSC_FALSE : PETSC_TRUE;
1738:   PetscErrorCode  ierr;

1741:   /* Create space */
1742:   PetscSpaceCreate(comm, &P);
1743:   PetscObjectSetOptionsPrefix((PetscObject) P, prefix);
1744:   PetscSpacePolynomialSetTensor(P, tensor);
1745:   PetscSpaceSetNumComponents(P, Nc);
1746:   PetscSpaceSetNumVariables(P, dim);
1747:   PetscSpaceSetFromOptions(P);
1748:   PetscSpaceSetUp(P);
1749:   PetscSpaceGetDegree(P, &order, NULL);
1750:   PetscSpacePolynomialGetTensor(P, &tensor);
1751:   /* Create dual space */
1752:   PetscDualSpaceCreate(comm, &Q);
1753:   PetscDualSpaceSetType(Q,PETSCDUALSPACELAGRANGE);
1754:   PetscObjectSetOptionsPrefix((PetscObject) Q, prefix);
1755:   PetscDualSpaceCreateReferenceCell(Q, dim, isSimplex, &K);
1756:   PetscDualSpaceSetDM(Q, K);
1757:   DMDestroy(&K);
1758:   PetscDualSpaceSetNumComponents(Q, Nc);
1759:   PetscDualSpaceSetOrder(Q, order);
1760:   PetscDualSpaceLagrangeSetTensor(Q, tensor);
1761:   PetscDualSpaceSetFromOptions(Q);
1762:   PetscDualSpaceSetUp(Q);
1763:   /* Create element */
1764:   PetscFECreate(comm, fem);
1765:   PetscObjectSetOptionsPrefix((PetscObject) *fem, prefix);
1766:   PetscFESetBasisSpace(*fem, P);
1767:   PetscFESetDualSpace(*fem, Q);
1768:   PetscFESetNumComponents(*fem, Nc);
1769:   PetscFESetFromOptions(*fem);
1770:   PetscFESetUp(*fem);
1771:   PetscSpaceDestroy(&P);
1772:   PetscDualSpaceDestroy(&Q);
1773:   /* Create quadrature (with specified order if given) */
1774:   qorder = qorder >= 0 ? qorder : order;
1775:   PetscObjectOptionsBegin((PetscObject)*fem);
1777:   PetscOptionsEnd();
1778:   quadPointsPerEdge = PetscMax(qorder + 1,1);
1779:   if (isSimplex) {
1782:   } else {
1785:   }
1790:   return(0);
1791: }

1793: /*@
1794:   PetscFECreateLagrange - Create a PetscFE for the basic Lagrange space of degree k

1796:   Collective

1798:   Input Parameters:
1799: + comm      - The MPI comm
1800: . dim       - The spatial dimension
1801: . Nc        - The number of components
1802: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
1803: . k         - The degree k of the space
1804: - qorder    - The quadrature order or PETSC_DETERMINE to use PetscSpace polynomial degree

1806:   Output Parameter:
1807: . fem       - The PetscFE object

1809:   Level: beginner

1811:   Notes:
1812:   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.

1814: .seealso: PetscFECreate(), PetscSpaceCreate(), PetscDualSpaceCreate()
1815: @*/
1816: PetscErrorCode PetscFECreateLagrange(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, PetscInt k, PetscInt qorder, PetscFE *fem)
1817: {
1819:   DM              K;
1820:   PetscSpace      P;
1821:   PetscDualSpace  Q;
1823:   PetscBool       tensor = isSimplex ? PETSC_FALSE : PETSC_TRUE;
1824:   char            name[64];
1825:   PetscErrorCode  ierr;

1828:   /* Create space */
1829:   PetscSpaceCreate(comm, &P);
1830:   PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL);
1831:   PetscSpacePolynomialSetTensor(P, tensor);
1832:   PetscSpaceSetNumComponents(P, Nc);
1833:   PetscSpaceSetNumVariables(P, dim);
1834:   PetscSpaceSetDegree(P, k, PETSC_DETERMINE);
1835:   PetscSpaceSetUp(P);
1836:   /* Create dual space */
1837:   PetscDualSpaceCreate(comm, &Q);
1838:   PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE);
1839:   PetscDualSpaceCreateReferenceCell(Q, dim, isSimplex, &K);
1840:   PetscDualSpaceSetDM(Q, K);
1841:   DMDestroy(&K);
1842:   PetscDualSpaceSetNumComponents(Q, Nc);
1843:   PetscDualSpaceSetOrder(Q, k);
1844:   PetscDualSpaceLagrangeSetTensor(Q, tensor);
1845:   PetscDualSpaceSetUp(Q);
1846:   /* Create element */
1847:   PetscFECreate(comm, fem);
1848:   PetscSNPrintf(name, 64, "P%d", (int) k);
1849:   PetscObjectSetName((PetscObject) *fem, name);
1850:   PetscFESetType(*fem, PETSCFEBASIC);
1851:   PetscFESetBasisSpace(*fem, P);
1852:   PetscFESetDualSpace(*fem, Q);
1853:   PetscFESetNumComponents(*fem, Nc);
1854:   PetscFESetUp(*fem);
1855:   PetscSpaceDestroy(&P);
1856:   PetscDualSpaceDestroy(&Q);
1857:   /* Create quadrature (with specified order if given) */
1858:   qorder = qorder >= 0 ? qorder : k;
1859:   quadPointsPerEdge = PetscMax(qorder + 1,1);
1860:   if (isSimplex) {
1863:   } else {
1866:   }
1871:   return(0);
1872: }

1874: /*@C
1875:   PetscFESetName - Names the FE and its subobjects

1877:   Not collective

1879:   Input Parameters:
1880: + fe   - The PetscFE
1881: - name - The name

1883:   Level: intermediate

1885: .seealso: PetscFECreate(), PetscSpaceCreate(), PetscDualSpaceCreate()
1886: @*/
1887: PetscErrorCode PetscFESetName(PetscFE fe, const char name[])
1888: {
1889:   PetscSpace     P;
1890:   PetscDualSpace Q;

1894:   PetscFEGetBasisSpace(fe, &P);
1895:   PetscFEGetDualSpace(fe, &Q);
1896:   PetscObjectSetName((PetscObject) fe, name);
1897:   PetscObjectSetName((PetscObject) P,  name);
1898:   PetscObjectSetName((PetscObject) Q,  name);
1899:   return(0);
1900: }

1902: 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[])
1903: {
1904:   PetscInt       dOffset = 0, fOffset = 0, f;

1907:   for (f = 0; f < Nf; ++f) {
1908:     PetscFE          fe;
1909:     const PetscInt   cdim = T[f]->cdim;
1910:     const PetscInt   Nq   = T[f]->Np;
1911:     const PetscInt   Nbf  = T[f]->Nb;
1912:     const PetscInt   Ncf  = T[f]->Nc;
1913:     const PetscReal *Bq   = &T[f]->T[0][(r*Nq+q)*Nbf*Ncf];
1914:     const PetscReal *Dq   = &T[f]->T[1][(r*Nq+q)*Nbf*Ncf*cdim];
1915:     PetscInt         b, c, d;

1917:     PetscDSGetDiscretization(ds, f, (PetscObject *) &fe);
1918:     for (c = 0; c < Ncf; ++c) u[fOffset+c] = 0.0;
1919:     for (d = 0; d < cdim*Ncf; ++d) u_x[fOffset*cdim+d] = 0.0;
1920:     for (b = 0; b < Nbf; ++b) {
1921:       for (c = 0; c < Ncf; ++c) {
1922:         const PetscInt cidx = b*Ncf+c;

1924:         u[fOffset+c] += Bq[cidx]*coefficients[dOffset+b];
1925:         for (d = 0; d < cdim; ++d) u_x[(fOffset+c)*cdim+d] += Dq[cidx*cdim+d]*coefficients[dOffset+b];
1926:       }
1927:     }
1928:     PetscFEPushforward(fe, fegeom, 1, &u[fOffset]);
1930:     if (u_t) {
1931:       for (c = 0; c < Ncf; ++c) u_t[fOffset+c] = 0.0;
1932:       for (b = 0; b < Nbf; ++b) {
1933:         for (c = 0; c < Ncf; ++c) {
1934:           const PetscInt cidx = b*Ncf+c;

1936:           u_t[fOffset+c] += Bq[cidx]*coefficients_t[dOffset+b];
1937:         }
1938:       }
1939:       PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]);
1940:     }
1941:     fOffset += Ncf;
1942:     dOffset += Nbf;
1943:   }
1944:   return 0;
1945: }

1947: PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS prob, PetscInt field, PetscInt faceLoc, const PetscScalar coefficients[], PetscScalar u[])
1948: {
1949:   PetscFE         fe;
1950:   PetscTabulation Tc;
1951:   PetscInt        b, c;
1952:   PetscErrorCode  ierr;

1954:   if (!prob) return 0;
1955:   PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);
1956:   PetscFEGetFaceCentroidTabulation(fe, &Tc);
1957:   {
1958:     const PetscReal *faceBasis = Tc->T[0];
1959:     const PetscInt   Nb        = Tc->Nb;
1960:     const PetscInt   Nc        = Tc->Nc;

1962:     for (c = 0; c < Nc; ++c) {u[c] = 0.0;}
1963:     for (b = 0; b < Nb; ++b) {
1964:       for (c = 0; c < Nc; ++c) {
1965:         const PetscInt cidx = b*Nc+c;

1967:         u[c] += coefficients[cidx]*faceBasis[faceLoc*Nb*Nc+cidx];
1968:       }
1969:     }
1970:   }
1971:   return 0;
1972: }

1974: PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
1975: {
1976:   const PetscInt   dim      = T->cdim;
1977:   const PetscInt   Nq       = T->Np;
1978:   const PetscInt   Nb       = T->Nb;
1979:   const PetscInt   Nc       = T->Nc;
1980:   const PetscReal *basis    = &T->T[0][r*Nq*Nb*Nc];
1981:   const PetscReal *basisDer = &T->T[1][r*Nq*Nb*Nc*dim];
1982:   PetscInt         q, b, c, d;
1983:   PetscErrorCode   ierr;

1985:   for (b = 0; b < Nb; ++b) elemVec[b] = 0.0;
1986:   for (q = 0; q < Nq; ++q) {
1987:     for (b = 0; b < Nb; ++b) {
1988:       for (c = 0; c < Nc; ++c) {
1989:         const PetscInt bcidx = b*Nc+c;

1991:         tmpBasis[bcidx] = basis[q*Nb*Nc+bcidx];
1992:         for (d = 0; d < dim; ++d) tmpBasisDer[bcidx*dim+d] = basisDer[q*Nb*Nc*dim+bcidx*dim+d];
1993:       }
1994:     }
1995:     PetscFEPushforward(fe, fegeom, Nb, tmpBasis);
1997:     for (b = 0; b < Nb; ++b) {
1998:       for (c = 0; c < Nc; ++c) {
1999:         const PetscInt bcidx = b*Nc+c;
2000:         const PetscInt qcidx = q*Nc+c;

2002:         elemVec[b] += tmpBasis[bcidx]*f0[qcidx];
2003:         for (d = 0; d < dim; ++d) elemVec[b] += tmpBasisDer[bcidx*dim+d]*f1[qcidx*dim+d];
2004:       }
2005:     }
2006:   }
2007:   return(0);
2008: }

2010: 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 eOffset, PetscInt totDim, PetscInt offsetI, PetscInt offsetJ, PetscScalar elemMat[])
2011: {
2012:   const PetscInt   dim       = TI->cdim;
2013:   const PetscInt   NqI       = TI->Np;
2014:   const PetscInt   NbI       = TI->Nb;
2015:   const PetscInt   NcI       = TI->Nc;
2016:   const PetscReal *basisI    = &TI->T[0][(r*NqI+q)*NbI*NcI];
2017:   const PetscReal *basisDerI = &TI->T[1][(r*NqI+q)*NbI*NcI*dim];
2018:   const PetscInt   NqJ       = TJ->Np;
2019:   const PetscInt   NbJ       = TJ->Nb;
2020:   const PetscInt   NcJ       = TJ->Nc;
2021:   const PetscReal *basisJ    = &TJ->T[0][(r*NqJ+q)*NbJ*NcJ];
2022:   const PetscReal *basisDerJ = &TJ->T[1][(r*NqJ+q)*NbJ*NcJ*dim];
2023:   PetscInt         f, fc, g, gc, df, dg;
2024:   PetscErrorCode   ierr;

2026:   for (f = 0; f < NbI; ++f) {
2027:     for (fc = 0; fc < NcI; ++fc) {
2028:       const PetscInt fidx = f*NcI+fc; /* Test function basis index */

2030:       tmpBasisI[fidx] = basisI[fidx];
2031:       for (df = 0; df < dim; ++df) tmpBasisDerI[fidx*dim+df] = basisDerI[fidx*dim+df];
2032:     }
2033:   }
2034:   PetscFEPushforward(feI, fegeom, NbI, tmpBasisI);
2036:   for (g = 0; g < NbJ; ++g) {
2037:     for (gc = 0; gc < NcJ; ++gc) {
2038:       const PetscInt gidx = g*NcJ+gc; /* Trial function basis index */

2040:       tmpBasisJ[gidx] = basisJ[gidx];
2041:       for (dg = 0; dg < dim; ++dg) tmpBasisDerJ[gidx*dim+dg] = basisDerJ[gidx*dim+dg];
2042:     }
2043:   }
2044:   PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ);
2046:   for (f = 0; f < NbI; ++f) {
2047:     for (fc = 0; fc < NcI; ++fc) {
2048:       const PetscInt fidx = f*NcI+fc; /* Test function basis index */
2049:       const PetscInt i    = offsetI+f; /* Element matrix row */
2050:       for (g = 0; g < NbJ; ++g) {
2051:         for (gc = 0; gc < NcJ; ++gc) {
2052:           const PetscInt gidx = g*NcJ+gc; /* Trial function basis index */
2053:           const PetscInt j    = offsetJ+g; /* Element matrix column */
2054:           const PetscInt fOff = eOffset+i*totDim+j;

2056:           elemMat[fOff] += tmpBasisI[fidx]*g0[fc*NcJ+gc]*tmpBasisJ[gidx];
2057:           for (df = 0; df < dim; ++df) {
2058:             elemMat[fOff] += tmpBasisI[fidx]*g1[(fc*NcJ+gc)*dim+df]*tmpBasisDerJ[gidx*dim+df];
2059:             elemMat[fOff] += tmpBasisDerI[fidx*dim+df]*g2[(fc*NcJ+gc)*dim+df]*tmpBasisJ[gidx];
2060:             for (dg = 0; dg < dim; ++dg) {
2061:               elemMat[fOff] += tmpBasisDerI[fidx*dim+df]*g3[((fc*NcJ+gc)*dim+df)*dim+dg]*tmpBasisDerJ[gidx*dim+dg];
2062:             }
2063:           }
2064:         }
2065:       }
2066:     }
2067:   }
2068:   return(0);
2069: }

2072: {
2073:   PetscDualSpace  dsp;
2074:   DM              dm;
2076:   PetscInt        dim, cdim, Nq;
2077:   PetscErrorCode  ierr;

2080:   PetscFEGetDualSpace(fe, &dsp);
2081:   PetscDualSpaceGetDM(dsp, &dm);
2082:   DMGetDimension(dm, &dim);
2083:   DMGetCoordinateDim(dm, &cdim);
2087:   PetscMalloc1(Nq*cdim,      &cgeom->v);
2088:   PetscMalloc1(Nq*cdim*cdim, &cgeom->J);
2089:   PetscMalloc1(Nq*cdim*cdim, &cgeom->invJ);
2090:   PetscMalloc1(Nq,           &cgeom->detJ);
2091:   cgeom->dim       = dim;
2092:   cgeom->dimEmbed  = cdim;
2093:   cgeom->numCells  = 1;
2094:   cgeom->numPoints = Nq;
2095:   DMPlexComputeCellGeometryFEM(dm, 0, quad, cgeom->v, cgeom->J, cgeom->invJ, cgeom->detJ);
2096:   return(0);
2097: }

2099: PetscErrorCode PetscFEDestroyCellGeometry(PetscFE fe, PetscFEGeom *cgeom)
2100: {

2104:   PetscFree(cgeom->v);
2105:   PetscFree(cgeom->J);
2106:   PetscFree(cgeom->invJ);
2107:   PetscFree(cgeom->detJ);
2108:   return(0);
2109: }