Actual source code: dualspace.c

petsc-master 2020-05-26
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  1:  #include <petsc/private/petscfeimpl.h>
  2:  #include <petscdmplex.h>

  4: PetscClassId PETSCDUALSPACE_CLASSID = 0;

  6: PetscFunctionList PetscDualSpaceList              = NULL;
  7: PetscBool         PetscDualSpaceRegisterAllCalled = PETSC_FALSE;

  9: const char *const PetscDualSpaceReferenceCells[] = {"SIMPLEX", "TENSOR", "PetscDualSpaceReferenceCell", "PETSCDUALSPACE_REFCELL_",0};

 11: /*
 12:   PetscDualSpaceLatticePointLexicographic_Internal - Returns all tuples of size 'len' with nonnegative integers that sum up to at most 'max'.
 13:                                                      Ordering is lexicographic with lowest index as least significant in ordering.
 14:                                                      e.g. for len == 2 and max == 2, this will return, in order, {0,0}, {1,0}, {2,0}, {0,1}, {1,1}, {0,2}.

 16:   Input Parameters:
 17: + len - The length of the tuple
 18: . max - The maximum sum
 19: - tup - A tuple of length len+1: tup[len] > 0 indicates a stopping condition

 21:   Output Parameter:
 22: . tup - A tuple of len integers whos sum is at most 'max'

 24:   Level: developer

 26: .seealso: PetscDualSpaceTensorPointLexicographic_Internal()
 27: */
 28: PetscErrorCode PetscDualSpaceLatticePointLexicographic_Internal(PetscInt len, PetscInt max, PetscInt tup[])
 29: {
 31:   while (len--) {
 32:     max -= tup[len];
 33:     if (!max) {
 34:       tup[len] = 0;
 35:       break;
 36:     }
 37:   }
 38:   tup[++len]++;
 39:   return(0);
 40: }

 42: /*
 43:   PetscDualSpaceTensorPointLexicographic_Internal - Returns all tuples of size 'len' with nonnegative integers that are all less than or equal to 'max'.
 44:                                                     Ordering is lexicographic with lowest index as least significant in ordering.
 45:                                                     e.g. for len == 2 and max == 2, this will return, in order, {0,0}, {1,0}, {2,0}, {0,1}, {1,1}, {2,1}, {0,2}, {1,2}, {2,2}.

 47:   Input Parameters:
 48: + len - The length of the tuple
 49: . max - The maximum value
 50: - tup - A tuple of length len+1: tup[len] > 0 indicates a stopping condition

 52:   Output Parameter:
 53: . tup - A tuple of len integers whos sum is at most 'max'

 55:   Level: developer

 57: .seealso: PetscDualSpaceLatticePointLexicographic_Internal()
 58: */
 59: PetscErrorCode PetscDualSpaceTensorPointLexicographic_Internal(PetscInt len, PetscInt max, PetscInt tup[])
 60: {
 61:   PetscInt       i;

 64:   for (i = 0; i < len; i++) {
 65:     if (tup[i] < max) {
 66:       break;
 67:     } else {
 68:       tup[i] = 0;
 69:     }
 70:   }
 71:   tup[i]++;
 72:   return(0);
 73: }

 75: /*@C
 76:   PetscDualSpaceRegister - Adds a new PetscDualSpace implementation

 78:   Not Collective

 80:   Input Parameters:
 81: + name        - The name of a new user-defined creation routine
 82: - create_func - The creation routine itself

 84:   Notes:
 85:   PetscDualSpaceRegister() may be called multiple times to add several user-defined PetscDualSpaces

 87:   Sample usage:
 88: .vb
 89:     PetscDualSpaceRegister("my_space", MyPetscDualSpaceCreate);
 90: .ve

 92:   Then, your PetscDualSpace type can be chosen with the procedural interface via
 93: .vb
 94:     PetscDualSpaceCreate(MPI_Comm, PetscDualSpace *);
 95:     PetscDualSpaceSetType(PetscDualSpace, "my_dual_space");
 96: .ve
 97:    or at runtime via the option
 98: .vb
 99:     -petscdualspace_type my_dual_space
100: .ve

102:   Level: advanced

104: .seealso: PetscDualSpaceRegisterAll(), PetscDualSpaceRegisterDestroy()

106: @*/
107: PetscErrorCode PetscDualSpaceRegister(const char sname[], PetscErrorCode (*function)(PetscDualSpace))
108: {

112:   PetscFunctionListAdd(&PetscDualSpaceList, sname, function);
113:   return(0);
114: }

116: /*@C
117:   PetscDualSpaceSetType - Builds a particular PetscDualSpace

119:   Collective on sp

121:   Input Parameters:
122: + sp   - The PetscDualSpace object
123: - name - The kind of space

125:   Options Database Key:
126: . -petscdualspace_type <type> - Sets the PetscDualSpace type; use -help for a list of available types

128:   Level: intermediate

130: .seealso: PetscDualSpaceGetType(), PetscDualSpaceCreate()
131: @*/
132: PetscErrorCode PetscDualSpaceSetType(PetscDualSpace sp, PetscDualSpaceType name)
133: {
134:   PetscErrorCode (*r)(PetscDualSpace);
135:   PetscBool      match;

140:   PetscObjectTypeCompare((PetscObject) sp, name, &match);
141:   if (match) return(0);

143:   if (!PetscDualSpaceRegisterAllCalled) {PetscDualSpaceRegisterAll();}
144:   PetscFunctionListFind(PetscDualSpaceList, name, &r);
145:   if (!r) SETERRQ1(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscDualSpace type: %s", name);

147:   if (sp->ops->destroy) {
148:     (*sp->ops->destroy)(sp);
149:     sp->ops->destroy = NULL;
150:   }
151:   (*r)(sp);
152:   PetscObjectChangeTypeName((PetscObject) sp, name);
153:   return(0);
154: }

156: /*@C
157:   PetscDualSpaceGetType - Gets the PetscDualSpace type name (as a string) from the object.

159:   Not Collective

161:   Input Parameter:
162: . sp  - The PetscDualSpace

164:   Output Parameter:
165: . name - The PetscDualSpace type name

167:   Level: intermediate

169: .seealso: PetscDualSpaceSetType(), PetscDualSpaceCreate()
170: @*/
171: PetscErrorCode PetscDualSpaceGetType(PetscDualSpace sp, PetscDualSpaceType *name)
172: {

178:   if (!PetscDualSpaceRegisterAllCalled) {
179:     PetscDualSpaceRegisterAll();
180:   }
181:   *name = ((PetscObject) sp)->type_name;
182:   return(0);
183: }

185: static PetscErrorCode PetscDualSpaceView_ASCII(PetscDualSpace sp, PetscViewer v)
186: {
187:   PetscViewerFormat format;
188:   PetscInt          pdim, f;
189:   PetscErrorCode    ierr;

192:   PetscDualSpaceGetDimension(sp, &pdim);
193:   PetscObjectPrintClassNamePrefixType((PetscObject) sp, v);
194:   PetscViewerASCIIPushTab(v);
195:   if (sp->k) {
196:     PetscViewerASCIIPrintf(v, "Dual space for %D-forms %swith %D components, size %D\n", PetscAbsInt(sp->k), sp->k < 0 ? "(stored in dual form) ": "", sp->Nc, pdim);
197:   } else {
198:     PetscViewerASCIIPrintf(v, "Dual space with %D components, size %D\n", sp->Nc, pdim);
199:   }
200:   if (sp->ops->view) {(*sp->ops->view)(sp, v);}
201:   PetscViewerGetFormat(v, &format);
202:   if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
203:     PetscViewerASCIIPushTab(v);
204:     for (f = 0; f < pdim; ++f) {
205:       PetscViewerASCIIPrintf(v, "Dual basis vector %D\n", f);
206:       PetscViewerASCIIPushTab(v);
207:       PetscQuadratureView(sp->functional[f], v);
208:       PetscViewerASCIIPopTab(v);
209:     }
210:     PetscViewerASCIIPopTab(v);
211:   }
212:   PetscViewerASCIIPopTab(v);
213:   return(0);
214: }

216: /*@C
217:    PetscDualSpaceViewFromOptions - View from Options

219:    Collective on PetscDualSpace

221:    Input Parameters:
222: +  A - the PetscDualSpace object
223: .  obj - Optional object, proivides prefix
224: -  name - command line option

226:    Level: intermediate
227: .seealso:  PetscDualSpace, PetscDualSpaceView(), PetscObjectViewFromOptions(), PetscDualSpaceCreate()
228: @*/
229: PetscErrorCode  PetscDualSpaceViewFromOptions(PetscDualSpace A,PetscObject obj,const char name[])
230: {

235:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
236:   return(0);
237: }

239: /*@
240:   PetscDualSpaceView - Views a PetscDualSpace

242:   Collective on sp

244:   Input Parameter:
245: + sp - the PetscDualSpace object to view
246: - v  - the viewer

248:   Level: beginner

250: .seealso PetscDualSpaceDestroy(), PetscDualSpace
251: @*/
252: PetscErrorCode PetscDualSpaceView(PetscDualSpace sp, PetscViewer v)
253: {
254:   PetscBool      iascii;

260:   if (!v) {PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) sp), &v);}
261:   PetscObjectTypeCompare((PetscObject) v, PETSCVIEWERASCII, &iascii);
262:   if (iascii) {PetscDualSpaceView_ASCII(sp, v);}
263:   return(0);
264: }

266: /*@
267:   PetscDualSpaceSetFromOptions - sets parameters in a PetscDualSpace from the options database

269:   Collective on sp

271:   Input Parameter:
272: . sp - the PetscDualSpace object to set options for

274:   Options Database:
275: . -petscspace_degree the approximation order of the space

277:   Level: intermediate

279: .seealso PetscDualSpaceView(), PetscDualSpace, PetscObjectSetFromOptions()
280: @*/
281: PetscErrorCode PetscDualSpaceSetFromOptions(PetscDualSpace sp)
282: {
283:   PetscDualSpaceReferenceCell refCell = PETSCDUALSPACE_REFCELL_SIMPLEX;
284:   PetscInt                    refDim  = 0;
285:   PetscBool                   flg;
286:   const char                 *defaultType;
287:   char                        name[256];
288:   PetscErrorCode              ierr;

292:   if (!((PetscObject) sp)->type_name) {
293:     defaultType = PETSCDUALSPACELAGRANGE;
294:   } else {
295:     defaultType = ((PetscObject) sp)->type_name;
296:   }
297:   if (!PetscSpaceRegisterAllCalled) {PetscSpaceRegisterAll();}

299:   PetscObjectOptionsBegin((PetscObject) sp);
300:   PetscOptionsFList("-petscdualspace_type", "Dual space", "PetscDualSpaceSetType", PetscDualSpaceList, defaultType, name, 256, &flg);
301:   if (flg) {
302:     PetscDualSpaceSetType(sp, name);
303:   } else if (!((PetscObject) sp)->type_name) {
304:     PetscDualSpaceSetType(sp, defaultType);
305:   }
306:   PetscOptionsBoundedInt("-petscdualspace_order", "The approximation order", "PetscDualSpaceSetOrder", sp->order, &sp->order, NULL,0);
307:   PetscOptionsInt("-petscdualspace_form_degree", "The form degree of the dofs", "PetscDualSpaceSetFormDegree", sp->k, &sp->k, NULL);
308:   PetscOptionsBoundedInt("-petscdualspace_components", "The number of components", "PetscDualSpaceSetNumComponents", sp->Nc, &sp->Nc, NULL,1);
309:   if (sp->ops->setfromoptions) {
310:     (*sp->ops->setfromoptions)(PetscOptionsObject,sp);
311:   }
312:   PetscOptionsBoundedInt("-petscdualspace_refdim", "The spatial dimension of the reference cell", "PetscDualSpaceSetReferenceCell", refDim, &refDim, NULL,0);
313:   PetscOptionsEnum("-petscdualspace_refcell", "Reference cell", "PetscDualSpaceSetReferenceCell", PetscDualSpaceReferenceCells, (PetscEnum) refCell, (PetscEnum *) &refCell, &flg);
314:   if (flg) {
315:     DM K;

317:     if (!refDim) SETERRQ(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_INCOMP, "Reference cell specified without a dimension. Use -petscdualspace_refdim.");
318:     PetscDualSpaceCreateReferenceCell(sp, refDim, refCell == PETSCDUALSPACE_REFCELL_SIMPLEX ? PETSC_TRUE : PETSC_FALSE, &K);
319:     PetscDualSpaceSetDM(sp, K);
320:     DMDestroy(&K);
321:   }

323:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
324:   PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject) sp);
325:   PetscOptionsEnd();
326:   sp->setfromoptionscalled = PETSC_TRUE;
327:   return(0);
328: }

330: /*@
331:   PetscDualSpaceSetUp - Construct a basis for the PetscDualSpace

333:   Collective on sp

335:   Input Parameter:
336: . sp - the PetscDualSpace object to setup

338:   Level: intermediate

340: .seealso PetscDualSpaceView(), PetscDualSpaceDestroy(), PetscDualSpace
341: @*/
342: PetscErrorCode PetscDualSpaceSetUp(PetscDualSpace sp)
343: {

348:   if (sp->setupcalled) return(0);
349:   sp->setupcalled = PETSC_TRUE;
350:   if (sp->ops->setup) {(*sp->ops->setup)(sp);}
351:   if (sp->setfromoptionscalled) {PetscDualSpaceViewFromOptions(sp, NULL, "-petscdualspace_view");}
352:   return(0);
353: }

355: static PetscErrorCode PetscDualSpaceClearDMData_Internal(PetscDualSpace sp, DM dm)
356: {
357:   PetscInt       pStart = -1, pEnd = -1, depth = -1;

361:   if (!dm) return(0);
362:   DMPlexGetChart(dm, &pStart, &pEnd);
363:   DMPlexGetDepth(dm, &depth);

365:   if (sp->pointSpaces) {
366:     PetscInt i;

368:     for (i = 0; i < pEnd - pStart; i++) {
369:       PetscDualSpaceDestroy(&(sp->pointSpaces[i]));
370:     }
371:   }
372:   PetscFree(sp->pointSpaces);

374:   if (sp->heightSpaces) {
375:     PetscInt i;

377:     for (i = 0; i <= depth; i++) {
378:       PetscDualSpaceDestroy(&(sp->heightSpaces[i]));
379:     }
380:   }
381:   PetscFree(sp->heightSpaces);

383:   PetscSectionDestroy(&(sp->pointSection));
384:   PetscQuadratureDestroy(&(sp->intNodes));
385:   VecDestroy(&(sp->intDofValues));
386:   VecDestroy(&(sp->intNodeValues));
387:   MatDestroy(&(sp->intMat));
388:   PetscQuadratureDestroy(&(sp->allNodes));
389:   VecDestroy(&(sp->allDofValues));
390:   VecDestroy(&(sp->allNodeValues));
391:   MatDestroy(&(sp->allMat));
392:   PetscFree(sp->numDof);
393:   return(0);
394: }


397: /*@
398:   PetscDualSpaceDestroy - Destroys a PetscDualSpace object

400:   Collective on sp

402:   Input Parameter:
403: . sp - the PetscDualSpace object to destroy

405:   Level: beginner

407: .seealso PetscDualSpaceView(), PetscDualSpace(), PetscDualSpaceCreate()
408: @*/
409: PetscErrorCode PetscDualSpaceDestroy(PetscDualSpace *sp)
410: {
411:   PetscInt       dim, f;
412:   DM             dm;

416:   if (!*sp) return(0);

419:   if (--((PetscObject)(*sp))->refct > 0) {*sp = 0; return(0);}
420:   ((PetscObject) (*sp))->refct = 0;

422:   PetscDualSpaceGetDimension(*sp, &dim);
423:   dm = (*sp)->dm;

425:   if ((*sp)->ops->destroy) {(*(*sp)->ops->destroy)(*sp);}
426:   PetscDualSpaceClearDMData_Internal(*sp, dm);

428:   for (f = 0; f < dim; ++f) {
429:     PetscQuadratureDestroy(&(*sp)->functional[f]);
430:   }
431:   PetscFree((*sp)->functional);
432:   DMDestroy(&(*sp)->dm);
433:   PetscHeaderDestroy(sp);
434:   return(0);
435: }

437: /*@
438:   PetscDualSpaceCreate - Creates an empty PetscDualSpace object. The type can then be set with PetscDualSpaceSetType().

440:   Collective

442:   Input Parameter:
443: . comm - The communicator for the PetscDualSpace object

445:   Output Parameter:
446: . sp - The PetscDualSpace object

448:   Level: beginner

450: .seealso: PetscDualSpaceSetType(), PETSCDUALSPACELAGRANGE
451: @*/
452: PetscErrorCode PetscDualSpaceCreate(MPI_Comm comm, PetscDualSpace *sp)
453: {
454:   PetscDualSpace s;

459:   PetscCitationsRegister(FECitation,&FEcite);
460:   *sp  = NULL;
461:   PetscFEInitializePackage();

463:   PetscHeaderCreate(s, PETSCDUALSPACE_CLASSID, "PetscDualSpace", "Dual Space", "PetscDualSpace", comm, PetscDualSpaceDestroy, PetscDualSpaceView);

465:   s->order       = 0;
466:   s->Nc          = 1;
467:   s->k           = 0;
468:   s->spdim       = -1;
469:   s->spintdim    = -1;
470:   s->uniform     = PETSC_TRUE;
471:   s->setupcalled = PETSC_FALSE;

473:   *sp = s;
474:   return(0);
475: }

477: /*@
478:   PetscDualSpaceDuplicate - Creates a duplicate PetscDualSpace object, however it is not setup.

480:   Collective on sp

482:   Input Parameter:
483: . sp - The original PetscDualSpace

485:   Output Parameter:
486: . spNew - The duplicate PetscDualSpace

488:   Level: beginner

490: .seealso: PetscDualSpaceCreate(), PetscDualSpaceSetType()
491: @*/
492: PetscErrorCode PetscDualSpaceDuplicate(PetscDualSpace sp, PetscDualSpace *spNew)
493: {
494:   DM             dm;
495:   PetscDualSpaceType type;
496:   const char     *name;

502:   PetscDualSpaceCreate(PetscObjectComm((PetscObject)sp), spNew);
503:   PetscObjectGetName((PetscObject) sp,     &name);
504:   PetscObjectSetName((PetscObject) *spNew,  name);
505:   PetscDualSpaceGetType(sp, &type);
506:   PetscDualSpaceSetType(*spNew, type);
507:   PetscDualSpaceGetDM(sp, &dm);
508:   PetscDualSpaceSetDM(*spNew, dm);

510:   (*spNew)->order   = sp->order;
511:   (*spNew)->k       = sp->k;
512:   (*spNew)->Nc      = sp->Nc;
513:   (*spNew)->uniform = sp->uniform;
514:   if (sp->ops->duplicate) {(*sp->ops->duplicate)(sp, *spNew);}
515:   return(0);
516: }

518: /*@
519:   PetscDualSpaceGetDM - Get the DM representing the reference cell

521:   Not collective

523:   Input Parameter:
524: . sp - The PetscDualSpace

526:   Output Parameter:
527: . dm - The reference cell

529:   Level: intermediate

531: .seealso: PetscDualSpaceSetDM(), PetscDualSpaceCreate()
532: @*/
533: PetscErrorCode PetscDualSpaceGetDM(PetscDualSpace sp, DM *dm)
534: {
538:   *dm = sp->dm;
539:   return(0);
540: }

542: /*@
543:   PetscDualSpaceSetDM - Get the DM representing the reference cell

545:   Not collective

547:   Input Parameters:
548: + sp - The PetscDualSpace
549: - dm - The reference cell

551:   Level: intermediate

553: .seealso: PetscDualSpaceGetDM(), PetscDualSpaceCreate()
554: @*/
555: PetscErrorCode PetscDualSpaceSetDM(PetscDualSpace sp, DM dm)
556: {

562:   if (sp->setupcalled) SETERRQ(PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Cannot change DM after dualspace is set up");
563:   PetscObjectReference((PetscObject) dm);
564:   if (sp->dm && sp->dm != dm) {
565:     PetscDualSpaceClearDMData_Internal(sp, sp->dm);
566:   }
567:   DMDestroy(&sp->dm);
568:   sp->dm = dm;
569:   return(0);
570: }

572: /*@
573:   PetscDualSpaceGetOrder - Get the order of the dual space

575:   Not collective

577:   Input Parameter:
578: . sp - The PetscDualSpace

580:   Output Parameter:
581: . order - The order

583:   Level: intermediate

585: .seealso: PetscDualSpaceSetOrder(), PetscDualSpaceCreate()
586: @*/
587: PetscErrorCode PetscDualSpaceGetOrder(PetscDualSpace sp, PetscInt *order)
588: {
592:   *order = sp->order;
593:   return(0);
594: }

596: /*@
597:   PetscDualSpaceSetOrder - Set the order of the dual space

599:   Not collective

601:   Input Parameters:
602: + sp - The PetscDualSpace
603: - order - The order

605:   Level: intermediate

607: .seealso: PetscDualSpaceGetOrder(), PetscDualSpaceCreate()
608: @*/
609: PetscErrorCode PetscDualSpaceSetOrder(PetscDualSpace sp, PetscInt order)
610: {
613:   if (sp->setupcalled) SETERRQ(PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Cannot change order after dualspace is set up");
614:   sp->order = order;
615:   return(0);
616: }

618: /*@
619:   PetscDualSpaceGetNumComponents - Return the number of components for this space

621:   Input Parameter:
622: . sp - The PetscDualSpace

624:   Output Parameter:
625: . Nc - The number of components

627:   Note: A vector space, for example, will have d components, where d is the spatial dimension

629:   Level: intermediate

631: .seealso: PetscDualSpaceSetNumComponents(), PetscDualSpaceGetDimension(), PetscDualSpaceCreate(), PetscDualSpace
632: @*/
633: PetscErrorCode PetscDualSpaceGetNumComponents(PetscDualSpace sp, PetscInt *Nc)
634: {
638:   *Nc = sp->Nc;
639:   return(0);
640: }

642: /*@
643:   PetscDualSpaceSetNumComponents - Set the number of components for this space

645:   Input Parameters:
646: + sp - The PetscDualSpace
647: - order - The number of components

649:   Level: intermediate

651: .seealso: PetscDualSpaceGetNumComponents(), PetscDualSpaceCreate(), PetscDualSpace
652: @*/
653: PetscErrorCode PetscDualSpaceSetNumComponents(PetscDualSpace sp, PetscInt Nc)
654: {
657:   if (sp->setupcalled) SETERRQ(PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Cannot change number of components after dualspace is set up");
658:   sp->Nc = Nc;
659:   return(0);
660: }

662: /*@
663:   PetscDualSpaceGetFunctional - Get the i-th basis functional in the dual space

665:   Not collective

667:   Input Parameters:
668: + sp - The PetscDualSpace
669: - i  - The basis number

671:   Output Parameter:
672: . functional - The basis functional

674:   Level: intermediate

676: .seealso: PetscDualSpaceGetDimension(), PetscDualSpaceCreate()
677: @*/
678: PetscErrorCode PetscDualSpaceGetFunctional(PetscDualSpace sp, PetscInt i, PetscQuadrature *functional)
679: {
680:   PetscInt       dim;

686:   PetscDualSpaceGetDimension(sp, &dim);
687:   if ((i < 0) || (i >= dim)) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Functional index %d must be in [0, %d)", i, dim);
688:   *functional = sp->functional[i];
689:   return(0);
690: }

692: /*@
693:   PetscDualSpaceGetDimension - Get the dimension of the dual space, i.e. the number of basis functionals

695:   Not collective

697:   Input Parameter:
698: . sp - The PetscDualSpace

700:   Output Parameter:
701: . dim - The dimension

703:   Level: intermediate

705: .seealso: PetscDualSpaceGetFunctional(), PetscDualSpaceCreate()
706: @*/
707: PetscErrorCode PetscDualSpaceGetDimension(PetscDualSpace sp, PetscInt *dim)
708: {

714:   if (sp->spdim < 0) {
715:     PetscSection section;

717:     PetscDualSpaceGetSection(sp, &section);
718:     if (section) {
719:       PetscSectionGetStorageSize(section, &(sp->spdim));
720:     } else sp->spdim = 0;
721:   }
722:   *dim = sp->spdim;
723:   return(0);
724: }

726: /*@
727:   PetscDualSpaceGetInteriorDimension - Get the interior dimension of the dual space, i.e. the number of basis functionals assigned to the interior of the reference domain

729:   Not collective

731:   Input Parameter:
732: . sp - The PetscDualSpace

734:   Output Parameter:
735: . dim - The dimension

737:   Level: intermediate

739: .seealso: PetscDualSpaceGetFunctional(), PetscDualSpaceCreate()
740: @*/
741: PetscErrorCode PetscDualSpaceGetInteriorDimension(PetscDualSpace sp, PetscInt *intdim)
742: {

748:   if (sp->spintdim < 0) {
749:     PetscSection section;

751:     PetscDualSpaceGetSection(sp, &section);
752:     if (section) {
753:       PetscSectionGetConstrainedStorageSize(section, &(sp->spintdim));
754:     } else sp->spintdim = 0;
755:   }
756:   *intdim = sp->spintdim;
757:   return(0);
758: }

760: /*@
761:    PetscDualSpaceGetUniform - Whether this dual space is uniform

763:    Not collective

765:    Input Parameters:
766: .  sp - A dual space

768:    Output Parameters:
769: .  uniform - PETSC_TRUE if (a) the dual space is the same for each point in a stratum of the reference DMPlex, and
770:              (b) every symmetry of each point in the reference DMPlex is also a symmetry of the point's dual space.


773:    Level: advanced

775:    Note: all of the usual spaces on simplex or tensor-product elements will be uniform, only reference cells
776:    with non-uniform strata (like trianguar-prisms) or anisotropic hp dual spaces will not be uniform.

778: .seealso: PetscDualSpaceGetPointSubspace(), PetscDualSpaceGetSymmetries()
779: @*/
780: PetscErrorCode PetscDualSpaceGetUniform(PetscDualSpace sp, PetscBool *uniform)
781: {
785:   *uniform = sp->uniform;
786:   return(0);
787: }


790: /*@C
791:   PetscDualSpaceGetNumDof - Get the number of degrees of freedom for each spatial (topological) dimension

793:   Not collective

795:   Input Parameter:
796: . sp - The PetscDualSpace

798:   Output Parameter:
799: . numDof - An array of length dim+1 which holds the number of dofs for each dimension

801:   Level: intermediate

803: .seealso: PetscDualSpaceGetFunctional(), PetscDualSpaceCreate()
804: @*/
805: PetscErrorCode PetscDualSpaceGetNumDof(PetscDualSpace sp, const PetscInt **numDof)
806: {

812:   if (!sp->uniform) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "A non-uniform space does not have a fixed number of dofs for each height");
813:   if (!sp->numDof) {
814:     DM       dm;
815:     PetscInt depth, d;
816:     PetscSection section;

818:     PetscDualSpaceGetDM(sp, &dm);
819:     DMPlexGetDepth(dm, &depth);
820:     PetscCalloc1(depth+1,&(sp->numDof));
821:     PetscDualSpaceGetSection(sp, &section);
822:     for (d = 0; d <= depth; d++) {
823:       PetscInt dStart, dEnd;

825:       DMPlexGetDepthStratum(dm, d, &dStart, &dEnd);
826:       if (dEnd <= dStart) continue;
827:       PetscSectionGetDof(section, dStart, &(sp->numDof[d]));

829:     }
830:   }
831:   *numDof = sp->numDof;
832:   if (!*numDof) SETERRQ(PetscObjectComm((PetscObject) sp), PETSC_ERR_LIB, "Empty numDof[] returned from dual space implementation");
833:   return(0);
834: }

836: /* create the section of the right size and set a permutation for topological ordering */
837: PetscErrorCode PetscDualSpaceSectionCreate_Internal(PetscDualSpace sp, PetscSection *topSection)
838: {
839:   DM             dm;
840:   PetscInt       pStart, pEnd, cStart, cEnd, c, depth, count, i;
841:   PetscInt       *seen, *perm;
842:   PetscSection   section;

846:   dm = sp->dm;
847:   PetscSectionCreate(PETSC_COMM_SELF, &section);
848:   DMPlexGetChart(dm, &pStart, &pEnd);
849:   PetscSectionSetChart(section, pStart, pEnd);
850:   PetscCalloc1(pEnd - pStart, &seen);
851:   PetscMalloc1(pEnd - pStart, &perm);
852:   DMPlexGetDepth(dm, &depth);
853:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
854:   for (c = cStart, count = 0; c < cEnd; c++) {
855:     PetscInt closureSize = -1, e;
856:     PetscInt *closure = NULL;

858:     perm[count++] = c;
859:     seen[c-pStart] = 1;
860:     DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);
861:     for (e = 0; e < closureSize; e++) {
862:       PetscInt point = closure[2*e];

864:       if (seen[point-pStart]) continue;
865:       perm[count++] = point;
866:       seen[point-pStart] = 1;
867:     }
868:     DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);
869:   }
870:   if (count != pEnd - pStart) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Bad topological ordering");
871:   for (i = 0; i < pEnd - pStart; i++) if (perm[i] != i) break;
872:   if (i < pEnd - pStart) {
873:     IS permIS;

875:     ISCreateGeneral(PETSC_COMM_SELF, pEnd - pStart, perm, PETSC_OWN_POINTER, &permIS);
876:     ISSetPermutation(permIS);
877:     PetscSectionSetPermutation(section, permIS);
878:     ISDestroy(&permIS);
879:   } else {
880:     PetscFree(perm);
881:   }
882:   PetscFree(seen);
883:   *topSection = section;
884:   return(0);
885: }

887: /* mark boundary points and set up */
888: PetscErrorCode PetscDualSpaceSectionSetUp_Internal(PetscDualSpace sp, PetscSection section)
889: {
890:   DM             dm;
891:   DMLabel        boundary;
892:   PetscInt       pStart, pEnd, p;

896:   dm = sp->dm;
897:   DMLabelCreate(PETSC_COMM_SELF,"boundary",&boundary);
898:   PetscDualSpaceGetDM(sp,&dm);
899:   DMPlexMarkBoundaryFaces(dm,1,boundary);
900:   DMPlexLabelComplete(dm,boundary);
901:   DMPlexGetChart(dm, &pStart, &pEnd);
902:   for (p = pStart; p < pEnd; p++) {
903:     PetscInt bval;

905:     DMLabelGetValue(boundary, p, &bval);
906:     if (bval == 1) {
907:       PetscInt dof;

909:       PetscSectionGetDof(section, p, &dof);
910:       PetscSectionSetConstraintDof(section, p, dof);
911:     }
912:   }
913:   DMLabelDestroy(&boundary);
914:   PetscSectionSetUp(section);
915:   return(0);
916: }

918: /*@
919:   PetscDualSpaceGetSection - Create a PetscSection over the reference cell with the layout from this space

921:   Collective on sp

923:   Input Parameters:
924: . sp      - The PetscDualSpace

926:   Output Parameter:
927: . section - The section

929:   Level: advanced

931: .seealso: PetscDualSpaceCreate(), DMPLEX
932: @*/
933: PetscErrorCode PetscDualSpaceGetSection(PetscDualSpace sp, PetscSection *section)
934: {
935:   PetscInt       pStart, pEnd, p;

939:   if (!sp->pointSection) {
940:     /* mark the boundary */
941:     PetscDualSpaceSectionCreate_Internal(sp, &(sp->pointSection));
942:     DMPlexGetChart(sp->dm,&pStart,&pEnd);
943:     for (p = pStart; p < pEnd; p++) {
944:       PetscDualSpace psp;

946:       PetscDualSpaceGetPointSubspace(sp, p, &psp);
947:       if (psp) {
948:         PetscInt dof;

950:         PetscDualSpaceGetInteriorDimension(psp, &dof);
951:         PetscSectionSetDof(sp->pointSection,p,dof);
952:       }
953:     }
954:     PetscDualSpaceSectionSetUp_Internal(sp,sp->pointSection);
955:   }
956:   *section = sp->pointSection;
957:   return(0);
958: }

960: /* this assumes that all of the point dual spaces store their interior dofs first, which is true when the point DMs
961:  * have one cell */
962: PetscErrorCode PetscDualSpacePushForwardSubspaces_Internal(PetscDualSpace sp, PetscInt sStart, PetscInt sEnd)
963: {
964:   PetscReal *sv0, *v0, *J;
965:   PetscSection section;
966:   PetscInt     dim, s, k;
967:   DM             dm;

971:   PetscDualSpaceGetDM(sp, &dm);
972:   DMGetDimension(dm, &dim);
973:   PetscDualSpaceGetSection(sp, &section);
974:   PetscMalloc3(dim, &v0, dim, &sv0, dim*dim, &J);
975:   PetscDualSpaceGetFormDegree(sp, &k);
976:   for (s = sStart; s < sEnd; s++) {
977:     PetscReal detJ, hdetJ;
978:     PetscDualSpace ssp;
979:     PetscInt dof, off, f, sdim;
980:     PetscInt i, j;
981:     DM sdm;

983:     PetscDualSpaceGetPointSubspace(sp, s, &ssp);
984:     if (!ssp) continue;
985:     PetscSectionGetDof(section, s, &dof);
986:     PetscSectionGetOffset(section, s, &off);
987:     /* get the first vertex of the reference cell */
988:     PetscDualSpaceGetDM(ssp, &sdm);
989:     DMGetDimension(sdm, &sdim);
990:     DMPlexComputeCellGeometryAffineFEM(sdm, 0, sv0, NULL, NULL, &hdetJ);
991:     DMPlexComputeCellGeometryAffineFEM(dm, s, v0, J, NULL, &detJ);
992:     /* compactify Jacobian */
993:     for (i = 0; i < dim; i++) for (j = 0; j < sdim; j++) J[i* sdim + j] = J[i * dim + j];
994:     for (f = 0; f < dof; f++) {
995:       PetscQuadrature fn;

997:       PetscDualSpaceGetFunctional(ssp, f, &fn);
998:       PetscQuadraturePushForward(fn, dim, sv0, v0, J, k, &(sp->functional[off+f]));
999:     }
1000:   }
1001:   PetscFree3(v0, sv0, J);
1002:   return(0);
1003: }

1005: /*@
1006:   PetscDualSpaceCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell

1008:   Collective on sp

1010:   Input Parameters:
1011: + sp      - The PetscDualSpace
1012: . dim     - The spatial dimension
1013: - simplex - Flag for simplex, otherwise use a tensor-product cell

1015:   Output Parameter:
1016: . refdm - The reference cell

1018:   Level: intermediate

1020: .seealso: PetscDualSpaceCreate(), DMPLEX
1021: @*/
1022: PetscErrorCode PetscDualSpaceCreateReferenceCell(PetscDualSpace sp, PetscInt dim, PetscBool simplex, DM *refdm)
1023: {

1027:   DMPlexCreateReferenceCell(PetscObjectComm((PetscObject) sp), dim, simplex, refdm);
1028:   return(0);
1029: }

1031: /*@C
1032:   PetscDualSpaceApply - Apply a functional from the dual space basis to an input function

1034:   Input Parameters:
1035: + sp      - The PetscDualSpace object
1036: . f       - The basis functional index
1037: . time    - The time
1038: . cgeom   - A context with geometric information for this cell, we use v0 (the initial vertex) and J (the Jacobian) (or evaluated at the coordinates of the functional)
1039: . numComp - The number of components for the function
1040: . func    - The input function
1041: - ctx     - A context for the function

1043:   Output Parameter:
1044: . value   - numComp output values

1046:   Note: The calling sequence for the callback func is given by:

1048: $ func(PetscInt dim, PetscReal time, const PetscReal x[],
1049: $      PetscInt numComponents, PetscScalar values[], void *ctx)

1051:   Level: beginner

1053: .seealso: PetscDualSpaceCreate()
1054: @*/
1055: PetscErrorCode PetscDualSpaceApply(PetscDualSpace sp, PetscInt f, PetscReal time, PetscFEGeom *cgeom, PetscInt numComp, PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void *ctx, PetscScalar *value)
1056: {

1063:   (*sp->ops->apply)(sp, f, time, cgeom, numComp, func, ctx, value);
1064:   return(0);
1065: }

1067: /*@C
1068:   PetscDualSpaceApplyAll - Apply all functionals from the dual space basis to the result of an evaluation at the points returned by PetscDualSpaceGetAllData()

1070:   Input Parameters:
1071: + sp        - The PetscDualSpace object
1072: - pointEval - Evaluation at the points returned by PetscDualSpaceGetAllData()

1074:   Output Parameter:
1075: . spValue   - The values of all dual space functionals

1077:   Level: beginner

1079: .seealso: PetscDualSpaceCreate()
1080: @*/
1081: PetscErrorCode PetscDualSpaceApplyAll(PetscDualSpace sp, const PetscScalar *pointEval, PetscScalar *spValue)
1082: {

1087:   (*sp->ops->applyall)(sp, pointEval, spValue);
1088:   return(0);
1089: }

1091: /*@C
1092:   PetscDualSpaceApplyInterior - Apply interior functionals from the dual space basis to the result of an evaluation at the points returned by PetscDualSpaceGetInteriorData()

1094:   Input Parameters:
1095: + sp        - The PetscDualSpace object
1096: - pointEval - Evaluation at the points returned by PetscDualSpaceGetInteriorData()

1098:   Output Parameter:
1099: . spValue   - The values of interior dual space functionals

1101:   Level: beginner

1103: .seealso: PetscDualSpaceCreate()
1104: @*/
1105: PetscErrorCode PetscDualSpaceApplyInterior(PetscDualSpace sp, const PetscScalar *pointEval, PetscScalar *spValue)
1106: {

1111:   (*sp->ops->applyint)(sp, pointEval, spValue);
1112:   return(0);
1113: }

1115: /*@C
1116:   PetscDualSpaceApplyDefault - Apply a functional from the dual space basis to an input function by assuming a point evaluation functional.

1118:   Input Parameters:
1119: + sp    - The PetscDualSpace object
1120: . f     - The basis functional index
1121: . time  - The time
1122: . cgeom - A context with geometric information for this cell, we use v0 (the initial vertex) and J (the Jacobian)
1123: . Nc    - The number of components for the function
1124: . func  - The input function
1125: - ctx   - A context for the function

1127:   Output Parameter:
1128: . value   - The output value

1130:   Note: The calling sequence for the callback func is given by:

1132: $ func(PetscInt dim, PetscReal time, const PetscReal x[],
1133: $      PetscInt numComponents, PetscScalar values[], void *ctx)

1135: and the idea is to evaluate the functional as an integral

1137: $ n(f) = int dx n(x) . f(x)

1139: where both n and f have Nc components.

1141:   Level: beginner

1143: .seealso: PetscDualSpaceCreate()
1144: @*/
1145: PetscErrorCode PetscDualSpaceApplyDefault(PetscDualSpace sp, PetscInt f, PetscReal time, PetscFEGeom *cgeom, PetscInt Nc, PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void *ctx, PetscScalar *value)
1146: {
1147:   DM               dm;
1148:   PetscQuadrature  n;
1149:   const PetscReal *points, *weights;
1150:   PetscReal        x[3];
1151:   PetscScalar     *val;
1152:   PetscInt         dim, dE, qNc, c, Nq, q;
1153:   PetscBool        isAffine;
1154:   PetscErrorCode   ierr;

1159:   PetscDualSpaceGetDM(sp, &dm);
1160:   PetscDualSpaceGetFunctional(sp, f, &n);
1161:   PetscQuadratureGetData(n, &dim, &qNc, &Nq, &points, &weights);
1162:   if (dim != cgeom->dim) SETERRQ2(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_SIZ, "The quadrature spatial dimension %D != cell geometry dimension %D", dim, cgeom->dim);
1163:   if (qNc != Nc) SETERRQ2(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_SIZ, "The quadrature components %D != function components %D", qNc, Nc);
1164:   DMGetWorkArray(dm, Nc, MPIU_SCALAR, &val);
1165:   *value = 0.0;
1166:   isAffine = cgeom->isAffine;
1167:   dE = cgeom->dimEmbed;
1168:   for (q = 0; q < Nq; ++q) {
1169:     if (isAffine) {
1170:       CoordinatesRefToReal(dE, cgeom->dim, cgeom->xi, cgeom->v, cgeom->J, &points[q*dim], x);
1171:       (*func)(dE, time, x, Nc, val, ctx);
1172:     } else {
1173:       (*func)(dE, time, &cgeom->v[dE*q], Nc, val, ctx);
1174:     }
1175:     for (c = 0; c < Nc; ++c) {
1176:       *value += val[c]*weights[q*Nc+c];
1177:     }
1178:   }
1179:   DMRestoreWorkArray(dm, Nc, MPIU_SCALAR, &val);
1180:   return(0);
1181: }

1183: /*@C
1184:   PetscDualSpaceApplyAllDefault - Apply all functionals from the dual space basis to the result of an evaluation at the points returned by PetscDualSpaceGetAllData()

1186:   Input Parameters:
1187: + sp        - The PetscDualSpace object
1188: - pointEval - Evaluation at the points returned by PetscDualSpaceGetAllData()

1190:   Output Parameter:
1191: . spValue   - The values of all dual space functionals

1193:   Level: beginner

1195: .seealso: PetscDualSpaceCreate()
1196: @*/
1197: PetscErrorCode PetscDualSpaceApplyAllDefault(PetscDualSpace sp, const PetscScalar *pointEval, PetscScalar *spValue)
1198: {
1199:   Vec              pointValues, dofValues;
1200:   Mat              allMat;
1201:   PetscErrorCode   ierr;

1207:   PetscDualSpaceGetAllData(sp, NULL, &allMat);
1208:   if (!(sp->allNodeValues)) {
1209:     MatCreateVecs(allMat, &(sp->allNodeValues), NULL);
1210:   }
1211:   pointValues = sp->allNodeValues;
1212:   if (!(sp->allDofValues)) {
1213:     MatCreateVecs(allMat, NULL, &(sp->allDofValues));
1214:   }
1215:   dofValues = sp->allDofValues;
1216:   VecPlaceArray(pointValues, pointEval);
1217:   VecPlaceArray(dofValues, spValue);
1218:   MatMult(allMat, pointValues, dofValues);
1219:   VecResetArray(dofValues);
1220:   VecResetArray(pointValues);
1221:   return(0);
1222: }

1224: /*@C
1225:   PetscDualSpaceApplyInteriorDefault - Apply interior functionals from the dual space basis to the result of an evaluation at the points returned by PetscDualSpaceGetInteriorData()

1227:   Input Parameters:
1228: + sp        - The PetscDualSpace object
1229: - pointEval - Evaluation at the points returned by PetscDualSpaceGetInteriorData()

1231:   Output Parameter:
1232: . spValue   - The values of interior dual space functionals

1234:   Level: beginner

1236: .seealso: PetscDualSpaceCreate()
1237: @*/
1238: PetscErrorCode PetscDualSpaceApplyInteriorDefault(PetscDualSpace sp, const PetscScalar *pointEval, PetscScalar *spValue)
1239: {
1240:   Vec              pointValues, dofValues;
1241:   Mat              intMat;
1242:   PetscErrorCode   ierr;

1248:   PetscDualSpaceGetInteriorData(sp, NULL, &intMat);
1249:   if (!(sp->intNodeValues)) {
1250:     MatCreateVecs(intMat, &(sp->intNodeValues), NULL);
1251:   }
1252:   pointValues = sp->intNodeValues;
1253:   if (!(sp->intDofValues)) {
1254:     MatCreateVecs(intMat, NULL, &(sp->intDofValues));
1255:   }
1256:   dofValues = sp->intDofValues;
1257:   VecPlaceArray(pointValues, pointEval);
1258:   VecPlaceArray(dofValues, spValue);
1259:   MatMult(intMat, pointValues, dofValues);
1260:   VecResetArray(dofValues);
1261:   VecResetArray(pointValues);
1262:   return(0);
1263: }

1265: /*@
1266:   PetscDualSpaceGetAllData - Get all quadrature nodes from this space, and the matrix that sends quadrature node values to degree-of-freedom values

1268:   Input Parameter:
1269: . sp - The dualspace

1271:   Output Parameter:
1272: + allNodes - A PetscQuadrature object containing all evaluation nodes
1273: - allMat - A Mat for the node-to-dof transformation

1275:   Level: advanced

1277: .seealso: PetscDualSpaceCreate()
1278: @*/
1279: PetscErrorCode PetscDualSpaceGetAllData(PetscDualSpace sp, PetscQuadrature *allNodes, Mat *allMat)
1280: {

1287:   if ((!sp->allNodes || !sp->allMat) && sp->ops->createalldata) {
1288:     PetscQuadrature qpoints;
1289:     Mat amat;

1291:     (*sp->ops->createalldata)(sp,&qpoints,&amat);
1292:     PetscQuadratureDestroy(&(sp->allNodes));
1293:     MatDestroy(&(sp->allMat));
1294:     sp->allNodes = qpoints;
1295:     sp->allMat = amat;
1296:   }
1297:   if (allNodes) *allNodes = sp->allNodes;
1298:   if (allMat) *allMat = sp->allMat;
1299:   return(0);
1300: }

1302: /*@
1303:   PetscDualSpaceCreateAllDataDefault - Create all evaluation nodes and the node-to-dof matrix by examining functionals

1305:   Input Parameter:
1306: . sp - The dualspace

1308:   Output Parameter:
1309: + allNodes - A PetscQuadrature object containing all evaluation nodes
1310: - allMat - A Mat for the node-to-dof transformation

1312:   Level: advanced

1314: .seealso: PetscDualSpaceCreate()
1315: @*/
1316: PetscErrorCode PetscDualSpaceCreateAllDataDefault(PetscDualSpace sp, PetscQuadrature *allNodes, Mat *allMat)
1317: {
1318:   PetscInt        spdim;
1319:   PetscInt        numPoints, offset;
1320:   PetscReal       *points;
1321:   PetscInt        f, dim;
1322:   PetscInt        Nc, nrows, ncols;
1323:   PetscInt        maxNumPoints;
1324:   PetscQuadrature q;
1325:   Mat             A;
1326:   PetscErrorCode  ierr;

1329:   PetscDualSpaceGetNumComponents(sp, &Nc);
1330:   PetscDualSpaceGetDimension(sp,&spdim);
1331:   if (!spdim) {
1332:     PetscQuadratureCreate(PETSC_COMM_SELF,allNodes);
1333:     PetscQuadratureSetData(*allNodes,0,0,0,NULL,NULL);
1334:   }
1335:   nrows = spdim;
1336:   PetscDualSpaceGetFunctional(sp,0,&q);
1337:   PetscQuadratureGetData(q,&dim,NULL,&numPoints,NULL,NULL);
1338:   maxNumPoints = numPoints;
1339:   for (f = 1; f < spdim; f++) {
1340:     PetscInt Np;

1342:     PetscDualSpaceGetFunctional(sp,f,&q);
1343:     PetscQuadratureGetData(q,NULL,NULL,&Np,NULL,NULL);
1344:     numPoints += Np;
1345:     maxNumPoints = PetscMax(maxNumPoints,Np);
1346:   }
1347:   ncols = numPoints * Nc;
1348:   PetscMalloc1(dim*numPoints,&points);
1349:   MatCreateSeqAIJ(PETSC_COMM_SELF, nrows, ncols, maxNumPoints * Nc, NULL, &A);
1350:   for (f = 0, offset = 0; f < spdim; f++) {
1351:     const PetscReal *p, *w;
1352:     PetscInt        Np, i;
1353:     PetscInt        fnc;

1355:     PetscDualSpaceGetFunctional(sp,f,&q);
1356:     PetscQuadratureGetData(q,NULL,&fnc,&Np,&p,&w);
1357:     if (fnc != Nc) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "functional component mismatch");
1358:     for (i = 0; i < Np * dim; i++) {
1359:       points[offset* dim + i] = p[i];
1360:     }
1361:     for (i = 0; i < Np * Nc; i++) {
1362:       MatSetValue(A, f, offset * Nc, w[i], INSERT_VALUES);
1363:     }
1364:     offset += Np;
1365:   }
1366:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
1367:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
1368:   PetscQuadratureCreate(PETSC_COMM_SELF,allNodes);
1369:   PetscQuadratureSetData(*allNodes,dim,0,numPoints,points,NULL);
1370:   *allMat = A;
1371:   return(0);
1372: }

1374: /*@
1375:   PetscDualSpaceGetInteriorData - Get all quadrature points necessary to compute the interior degrees of freedom from
1376:   this space, as well as the matrix that computes the degrees of freedom from the quadrature values.  Degrees of
1377:   freedom are interior degrees of freedom if they belong (by PetscDualSpaceGetSection()) to interior points in the
1378:   reference DMPlex: complementary boundary degrees of freedom are marked as constrained in the section returned by
1379:   PetscDualSpaceGetSection()).

1381:   Input Parameter:
1382: . sp - The dualspace

1384:   Output Parameter:
1385: + intNodes - A PetscQuadrature object containing all evaluation points needed to evaluate interior degrees of freedom
1386: - intMat   - A matrix that computes dual space values from point values: size [spdim0 x (npoints * nc)], where spdim0 is
1387:              the size of the constrained layout (PetscSectionGetConstrainStorageSize()) of the dual space section,
1388:              npoints is the number of points in intNodes and nc is PetscDualSpaceGetNumComponents().

1390:   Level: advanced

1392: .seealso: PetscDualSpaceCreate(), PetscDualSpaceGetDimension(), PetscDualSpaceGetNumComponents(), PetscQuadratureGetData()
1393: @*/
1394: PetscErrorCode PetscDualSpaceGetInteriorData(PetscDualSpace sp, PetscQuadrature *intNodes, Mat *intMat)
1395: {

1402:   if ((!sp->intNodes || !sp->intMat) && sp->ops->createintdata) {
1403:     PetscQuadrature qpoints;
1404:     Mat imat;

1406:     (*sp->ops->createintdata)(sp,&qpoints,&imat);
1407:     PetscQuadratureDestroy(&(sp->intNodes));
1408:     MatDestroy(&(sp->intMat));
1409:     sp->intNodes = qpoints;
1410:     sp->intMat = imat;
1411:   }
1412:   if (intNodes) *intNodes = sp->intNodes;
1413:   if (intMat) *intMat = sp->intMat;
1414:   return(0);
1415: }

1417: /*@
1418:   PetscDualSpaceCreateInteriorDataDefault - Create quadrature points by examining interior functionals and create the matrix mapping quadrature point values to interior dual space values

1420:   Input Parameter:
1421: . sp - The dualspace

1423:   Output Parameter:
1424: + intNodes - A PetscQuadrature object containing all evaluation points needed to evaluate interior degrees of freedom
1425: - intMat    - A matrix that computes dual space values from point values: size [spdim0 x (npoints * nc)], where spdim0 is
1426:               the size of the constrained layout (PetscSectionGetConstrainStorageSize()) of the dual space section,
1427:               npoints is the number of points in allNodes and nc is PetscDualSpaceGetNumComponents().

1429:   Level: advanced

1431: .seealso: PetscDualSpaceCreate(), PetscDualSpaceGetInteriorData()
1432: @*/
1433: PetscErrorCode PetscDualSpaceCreateInteriorDataDefault(PetscDualSpace sp, PetscQuadrature *intNodes, Mat *intMat)
1434: {
1435:   DM              dm;
1436:   PetscInt        spdim0;
1437:   PetscInt        Nc;
1438:   PetscInt        pStart, pEnd, p, f;
1439:   PetscSection    section;
1440:   PetscInt        numPoints, offset, matoffset;
1441:   PetscReal       *points;
1442:   PetscInt        dim;
1443:   PetscInt        *nnz;
1444:   PetscQuadrature q;
1445:   Mat             imat;
1446:   PetscErrorCode  ierr;

1450:   PetscDualSpaceGetSection(sp, &section);
1451:   PetscSectionGetConstrainedStorageSize(section, &spdim0);
1452:   if (!spdim0) {
1453:     *intNodes = NULL;
1454:     *intMat = NULL;
1455:     return(0);
1456:   }
1457:   PetscDualSpaceGetNumComponents(sp, &Nc);
1458:   PetscSectionGetChart(section, &pStart, &pEnd);
1459:   PetscDualSpaceGetDM(sp, &dm);
1460:   DMGetDimension(dm, &dim);
1461:   PetscMalloc1(spdim0, &nnz);
1462:   for (p = pStart, f = 0, numPoints = 0; p < pEnd; p++) {
1463:     PetscInt dof, cdof, off, d;

1465:     PetscSectionGetDof(section, p, &dof);
1466:     PetscSectionGetConstraintDof(section, p, &cdof);
1467:     if (!(dof - cdof)) continue;
1468:     PetscSectionGetOffset(section, p, &off);
1469:     for (d = 0; d < dof; d++, off++, f++) {
1470:       PetscInt Np;

1472:       PetscDualSpaceGetFunctional(sp,off,&q);
1473:       PetscQuadratureGetData(q,NULL,NULL,&Np,NULL,NULL);
1474:       nnz[f] = Np * Nc;
1475:       numPoints += Np;
1476:     }
1477:   }
1478:   MatCreateSeqAIJ(PETSC_COMM_SELF, spdim0, numPoints * Nc, 0, nnz, &imat);
1479:   PetscFree(nnz);
1480:   PetscMalloc1(dim*numPoints,&points);
1481:   for (p = pStart, f = 0, offset = 0, matoffset = 0; p < pEnd; p++) {
1482:     PetscInt dof, cdof, off, d;

1484:     PetscSectionGetDof(section, p, &dof);
1485:     PetscSectionGetConstraintDof(section, p, &cdof);
1486:     if (!(dof - cdof)) continue;
1487:     PetscSectionGetOffset(section, p, &off);
1488:     for (d = 0; d < dof; d++, off++, f++) {
1489:       const PetscReal *p;
1490:       const PetscReal *w;
1491:       PetscInt        Np, i;

1493:       PetscDualSpaceGetFunctional(sp,off,&q);
1494:       PetscQuadratureGetData(q,NULL,NULL,&Np,&p,&w);
1495:       for (i = 0; i < Np * dim; i++) {
1496:         points[offset + i] = p[i];
1497:       }
1498:       for (i = 0; i < Np * Nc; i++) {
1499:         MatSetValue(imat, f, matoffset + i, w[i],INSERT_VALUES);
1500:       }
1501:       offset += Np * dim;
1502:       matoffset += Np * Nc;
1503:     }
1504:   }
1505:   PetscQuadratureCreate(PETSC_COMM_SELF,intNodes);
1506:   PetscQuadratureSetData(*intNodes,dim,0,numPoints,points,NULL);
1507:   MatAssemblyBegin(imat, MAT_FINAL_ASSEMBLY);
1508:   MatAssemblyEnd(imat, MAT_FINAL_ASSEMBLY);
1509:   *intMat = imat;
1510:   return(0);
1511: }

1513: /*@C
1514:   PetscDualSpaceApplyFVM - Apply a functional from the dual space basis to an input function by assuming a point evaluation functional at the cell centroid.

1516:   Input Parameters:
1517: + sp    - The PetscDualSpace object
1518: . f     - The basis functional index
1519: . time  - The time
1520: . cgeom - A context with geometric information for this cell, we currently just use the centroid
1521: . Nc    - The number of components for the function
1522: . func  - The input function
1523: - ctx   - A context for the function

1525:   Output Parameter:
1526: . value - The output value (scalar)

1528:   Note: The calling sequence for the callback func is given by:

1530: $ func(PetscInt dim, PetscReal time, const PetscReal x[],
1531: $      PetscInt numComponents, PetscScalar values[], void *ctx)

1533: and the idea is to evaluate the functional as an integral

1535: $ n(f) = int dx n(x) . f(x)

1537: where both n and f have Nc components.

1539:   Level: beginner

1541: .seealso: PetscDualSpaceCreate()
1542: @*/
1543: PetscErrorCode PetscDualSpaceApplyFVM(PetscDualSpace sp, PetscInt f, PetscReal time, PetscFVCellGeom *cgeom, PetscInt Nc, PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void *ctx, PetscScalar *value)
1544: {
1545:   DM               dm;
1546:   PetscQuadrature  n;
1547:   const PetscReal *points, *weights;
1548:   PetscScalar     *val;
1549:   PetscInt         dimEmbed, qNc, c, Nq, q;
1550:   PetscErrorCode   ierr;

1555:   PetscDualSpaceGetDM(sp, &dm);
1556:   DMGetCoordinateDim(dm, &dimEmbed);
1557:   PetscDualSpaceGetFunctional(sp, f, &n);
1558:   PetscQuadratureGetData(n, NULL, &qNc, &Nq, &points, &weights);
1559:   if (qNc != Nc) SETERRQ2(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_SIZ, "The quadrature components %D != function components %D", qNc, Nc);
1560:   DMGetWorkArray(dm, Nc, MPIU_SCALAR, &val);
1561:   *value = 0.;
1562:   for (q = 0; q < Nq; ++q) {
1563:     (*func)(dimEmbed, time, cgeom->centroid, Nc, val, ctx);
1564:     for (c = 0; c < Nc; ++c) {
1565:       *value += val[c]*weights[q*Nc+c];
1566:     }
1567:   }
1568:   DMRestoreWorkArray(dm, Nc, MPIU_SCALAR, &val);
1569:   return(0);
1570: }

1572: /*@
1573:   PetscDualSpaceGetHeightSubspace - Get the subset of the dual space basis that is supported on a mesh point of a
1574:   given height.  This assumes that the reference cell is symmetric over points of this height.

1576:   If the dual space is not defined on mesh points of the given height (e.g. if the space is discontinuous and
1577:   pointwise values are not defined on the element boundaries), or if the implementation of PetscDualSpace does not
1578:   support extracting subspaces, then NULL is returned.

1580:   This does not increment the reference count on the returned dual space, and the user should not destroy it.

1582:   Not collective

1584:   Input Parameters:
1585: + sp - the PetscDualSpace object
1586: - height - the height of the mesh point for which the subspace is desired

1588:   Output Parameter:
1589: . subsp - the subspace.  Note that the functionals in the subspace are with respect to the intrinsic geometry of the
1590:   point, which will be of lesser dimension if height > 0.

1592:   Level: advanced

1594: .seealso: PetscSpaceGetHeightSubspace(), PetscDualSpace
1595: @*/
1596: PetscErrorCode PetscDualSpaceGetHeightSubspace(PetscDualSpace sp, PetscInt height, PetscDualSpace *subsp)
1597: {
1598:   PetscInt       depth = -1, cStart, cEnd;
1599:   DM             dm;

1605:   if (!(sp->uniform)) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "A non-uniform dual space does not have a single dual space at each height");
1606:   *subsp = NULL;
1607:   dm = sp->dm;
1608:   DMPlexGetDepth(dm, &depth);
1609:   if (height < 0 || height > depth) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid height");
1610:   DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
1611:   if (height == 0 && cEnd == cStart + 1) {
1612:     *subsp = sp;
1613:     return(0);
1614:   }
1615:   if (!sp->heightSpaces) {
1616:     PetscInt h;
1617:     PetscCalloc1(depth+1, &(sp->heightSpaces));

1619:     for (h = 0; h <= depth; h++) {
1620:       if (h == 0 && cEnd == cStart + 1) continue;
1621:       if (sp->ops->createheightsubspace) {(*sp->ops->createheightsubspace)(sp,height,&(sp->heightSpaces[h]));}
1622:       else if (sp->pointSpaces) {
1623:         PetscInt hStart, hEnd;

1625:         DMPlexGetHeightStratum(dm,h,&hStart,&hEnd);
1626:         if (hEnd > hStart) {
1627:           const char *name;

1629:           PetscObjectReference((PetscObject)(sp->pointSpaces[hStart]));
1630:           if (sp->pointSpaces[hStart]) {
1631:             PetscObjectGetName((PetscObject) sp,                     &name);
1632:             PetscObjectSetName((PetscObject) sp->pointSpaces[hStart], name);
1633:           }
1634:           sp->heightSpaces[h] = sp->pointSpaces[hStart];
1635:         }
1636:       }
1637:     }
1638:   }
1639:   *subsp = sp->heightSpaces[height];
1640:   return(0);
1641: }

1643: /*@
1644:   PetscDualSpaceGetPointSubspace - Get the subset of the dual space basis that is supported on a particular mesh point.

1646:   If the dual space is not defined on the mesh point (e.g. if the space is discontinuous and pointwise values are not
1647:   defined on the element boundaries), or if the implementation of PetscDualSpace does not support extracting
1648:   subspaces, then NULL is returned.

1650:   This does not increment the reference count on the returned dual space, and the user should not destroy it.

1652:   Not collective

1654:   Input Parameters:
1655: + sp - the PetscDualSpace object
1656: - point - the point (in the dual space's DM) for which the subspace is desired

1658:   Output Parameters:
1659:   bdsp - the subspace.  Note that the functionals in the subspace are with respect to the intrinsic geometry of the
1660:   point, which will be of lesser dimension if height > 0.

1662:   Level: advanced

1664: .seealso: PetscDualSpace
1665: @*/
1666: PetscErrorCode PetscDualSpaceGetPointSubspace(PetscDualSpace sp, PetscInt point, PetscDualSpace *bdsp)
1667: {
1668:   PetscInt       pStart = 0, pEnd = 0, cStart, cEnd;
1669:   DM             dm;

1675:   *bdsp = NULL;
1676:   dm = sp->dm;
1677:   DMPlexGetChart(dm, &pStart, &pEnd);
1678:   if (point < pStart || point > pEnd) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid point");
1679:   DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
1680:   if (point == cStart && cEnd == cStart + 1) { /* the dual space is only equivalent to the dual space on a cell if the reference mesh has just one cell */
1681:     *bdsp = sp;
1682:     return(0);
1683:   }
1684:   if (!sp->pointSpaces) {
1685:     PetscInt p;
1686:     PetscCalloc1(pEnd - pStart, &(sp->pointSpaces));

1688:     for (p = 0; p < pEnd - pStart; p++) {
1689:       if (p + pStart == cStart && cEnd == cStart + 1) continue;
1690:       if (sp->ops->createpointsubspace) {(*sp->ops->createpointsubspace)(sp,p+pStart,&(sp->pointSpaces[p]));}
1691:       else if (sp->heightSpaces || sp->ops->createheightsubspace) {
1692:         PetscInt dim, depth, height;
1693:         DMLabel  label;

1695:         DMPlexGetDepth(dm,&dim);
1696:         DMPlexGetDepthLabel(dm,&label);
1697:         DMLabelGetValue(label,p+pStart,&depth);
1698:         height = dim - depth;
1699:         PetscDualSpaceGetHeightSubspace(sp, height, &(sp->pointSpaces[p]));
1700:         PetscObjectReference((PetscObject)sp->pointSpaces[p]);
1701:       }
1702:     }
1703:   }
1704:   *bdsp = sp->pointSpaces[point - pStart];
1705:   return(0);
1706: }

1708: /*@C
1709:   PetscDualSpaceGetSymmetries - Returns a description of the symmetries of this basis

1711:   Not collective

1713:   Input Parameter:
1714: . sp - the PetscDualSpace object

1716:   Output Parameters:
1717: + perms - Permutations of the interior degrees of freedom, parameterized by the point orientation
1718: - flips - Sign reversal of the interior degrees of freedom, parameterized by the point orientation

1720:   Note: The permutation and flip arrays are organized in the following way
1721: $ perms[p][ornt][dof # on point] = new local dof #
1722: $ flips[p][ornt][dof # on point] = reversal or not

1724:   Level: developer

1726: @*/
1727: PetscErrorCode PetscDualSpaceGetSymmetries(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
1728: {

1735:   if (sp->ops->getsymmetries) {(sp->ops->getsymmetries)(sp,perms,flips);}
1736:   return(0);
1737: }

1739: /*@
1740:   PetscDualSpaceGetFormDegree - Get the form degree k for the k-form the describes the pushforwards/pullbacks of this
1741:   dual space's functionals.

1743:   Input Parameter:
1744: . dsp - The PetscDualSpace

1746:   Output Parameter:
1747: . k   - The *signed* degree k of the k.  If k >= 0, this means that the degrees of freedom are k-forms, and are stored
1748:         in lexicographic order according to the basis of k-forms constructed from the wedge product of 1-forms.  So for example,
1749:         the 1-form basis in 3-D is (dx, dy, dz), and the 2-form basis in 3-D is (dx wedge dy, dx wedge dz, dy wedge dz).
1750:         If k < 0, this means that the degrees transform as k-forms, but are stored as (N-k) forms according to the
1751:         Hodge star map.  So for example if k = -2 and N = 3, this means that the degrees of freedom transform as 2-forms
1752:         but are stored as 1-forms.

1754:   Level: developer

1756: .seealso: PetscDTAltV, PetscDualSpacePullback(), PetscDualSpacePushforward(), PetscDualSpaceTransform(), PetscDualSpaceTransformType
1757: @*/
1758: PetscErrorCode PetscDualSpaceGetFormDegree(PetscDualSpace dsp, PetscInt *k)
1759: {
1763:   *k = dsp->k;
1764:   return(0);
1765: }

1767: /*@
1768:   PetscDualSpaceSetFormDegree - Set the form degree k for the k-form the describes the pushforwards/pullbacks of this
1769:   dual space's functionals.

1771:   Input Parameter:
1772: + dsp - The PetscDualSpace
1773: - k   - The *signed* degree k of the k.  If k >= 0, this means that the degrees of freedom are k-forms, and are stored
1774:         in lexicographic order according to the basis of k-forms constructed from the wedge product of 1-forms.  So for example,
1775:         the 1-form basis in 3-D is (dx, dy, dz), and the 2-form basis in 3-D is (dx wedge dy, dx wedge dz, dy wedge dz).
1776:         If k < 0, this means that the degrees transform as k-forms, but are stored as (N-k) forms according to the
1777:         Hodge star map.  So for example if k = -2 and N = 3, this means that the degrees of freedom transform as 2-forms
1778:         but are stored as 1-forms.

1780:   Level: developer

1782: .seealso: PetscDTAltV, PetscDualSpacePullback(), PetscDualSpacePushforward(), PetscDualSpaceTransform(), PetscDualSpaceTransformType
1783: @*/
1784: PetscErrorCode PetscDualSpaceSetFormDegree(PetscDualSpace dsp, PetscInt k)
1785: {
1786:   PetscInt dim;

1790:   if (dsp->setupcalled) SETERRQ(PetscObjectComm((PetscObject)dsp), PETSC_ERR_ARG_WRONGSTATE, "Cannot change number of components after dualspace is set up");
1791:   dim = dsp->dm->dim;
1792:   if (k < -dim || k > dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported %D-form on %D-dimensional reference cell", PetscAbsInt(k), dim);
1793:   dsp->k = k;
1794:   return(0);
1795: }

1797: /*@
1798:   PetscDualSpaceGetDeRahm - Get the k-simplex associated with the functionals in this dual space

1800:   Input Parameter:
1801: . dsp - The PetscDualSpace

1803:   Output Parameter:
1804: . k   - The simplex dimension

1806:   Level: developer

1808:   Note: Currently supported values are
1809: $ 0: These are H_1 methods that only transform coordinates
1810: $ 1: These are Hcurl methods that transform functions using the covariant Piola transform (COVARIANT_PIOLA_TRANSFORM)
1811: $ 2: These are the same as 1
1812: $ 3: These are Hdiv methods that transform functions using the contravariant Piola transform (CONTRAVARIANT_PIOLA_TRANSFORM)

1814: .seealso: PetscDualSpacePullback(), PetscDualSpacePushforward(), PetscDualSpaceTransform(), PetscDualSpaceTransformType
1815: @*/
1816: PetscErrorCode PetscDualSpaceGetDeRahm(PetscDualSpace dsp, PetscInt *k)
1817: {
1818:   PetscInt dim;

1823:   dim = dsp->dm->dim;
1824:   if (!dsp->k) *k = IDENTITY_TRANSFORM;
1825:   else if (dsp->k == 1) *k = COVARIANT_PIOLA_TRANSFORM;
1826:   else if (dsp->k == -(dim - 1)) *k = CONTRAVARIANT_PIOLA_TRANSFORM;
1827:   else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported transformation");
1828:   return(0);
1829: }

1831: /*@C
1832:   PetscDualSpaceTransform - Transform the function values

1834:   Input Parameters:
1835: + dsp       - The PetscDualSpace
1836: . trans     - The type of transform
1837: . isInverse - Flag to invert the transform
1838: . fegeom    - The cell geometry
1839: . Nv        - The number of function samples
1840: . Nc        - The number of function components
1841: - vals      - The function values

1843:   Output Parameter:
1844: . vals      - The transformed function values

1846:   Level: intermediate

1848:   Note: This only handles tranformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

1850: .seealso: PetscDualSpaceTransformGradient(), PetscDualSpacePullback(), PetscDualSpacePushforward(), PetscDualSpaceTransformType
1851: @*/
1852: PetscErrorCode PetscDualSpaceTransform(PetscDualSpace dsp, PetscDualSpaceTransformType trans, PetscBool isInverse, PetscFEGeom *fegeom, PetscInt Nv, PetscInt Nc, PetscScalar vals[])
1853: {
1854:   PetscReal Jstar[9] = {0};
1855:   PetscInt dim, v, c, Nk;

1862:   /* TODO: not handling dimEmbed != dim right now */
1863:   dim = dsp->dm->dim;
1864:   /* No change needed for 0-forms */
1865:   if (!dsp->k) return(0);
1866:   PetscDTBinomialInt(dim, PetscAbsInt(dsp->k), &Nk);
1867:   /* TODO: use fegeom->isAffine */
1868:   PetscDTAltVPullbackMatrix(dim, dim, isInverse ? fegeom->J : fegeom->invJ, dsp->k, Jstar);
1869:   for (v = 0; v < Nv; ++v) {
1870:     switch (Nk) {
1871:     case 1:
1872:       for (c = 0; c < Nc; c++) vals[v*Nc + c] *= Jstar[0];
1873:       break;
1874:     case 2:
1875:       for (c = 0; c < Nc; c += 2) DMPlex_Mult2DReal_Internal(Jstar, 1, &vals[v*Nc + c], &vals[v*Nc + c]);
1876:       break;
1877:     case 3:
1878:       for (c = 0; c < Nc; c += 3) DMPlex_Mult3DReal_Internal(Jstar, 1, &vals[v*Nc + c], &vals[v*Nc + c]);
1879:       break;
1880:     default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported form size %D for transformation", Nk);
1881:     }
1882:   }
1883:   return(0);
1884: }

1886: /*@C
1887:   PetscDualSpaceTransformGradient - Transform the function gradient values

1889:   Input Parameters:
1890: + dsp       - The PetscDualSpace
1891: . trans     - The type of transform
1892: . isInverse - Flag to invert the transform
1893: . fegeom    - The cell geometry
1894: . Nv        - The number of function gradient samples
1895: . Nc        - The number of function components
1896: - vals      - The function gradient values

1898:   Output Parameter:
1899: . vals      - The transformed function values

1901:   Level: intermediate

1903:   Note: This only handles tranformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

1905: .seealso: PetscDualSpaceTransform(), PetscDualSpacePullback(), PetscDualSpacePushforward(), PetscDualSpaceTransformType
1906: @*/
1907: PetscErrorCode PetscDualSpaceTransformGradient(PetscDualSpace dsp, PetscDualSpaceTransformType trans, PetscBool isInverse, PetscFEGeom *fegeom, PetscInt Nv, PetscInt Nc, PetscScalar vals[])
1908: {
1909:   const PetscInt dim = dsp->dm->dim, dE = fegeom->dimEmbed;
1910:   PetscInt       v, c, d;

1916: #ifdef PETSC_USE_DEBUG
1917:   if (dE <= 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid embedding dimension %D", dE);
1918: #endif
1919:   /* Transform gradient */
1920:   if (dim == dE) {
1921:     for (v = 0; v < Nv; ++v) {
1922:       for (c = 0; c < Nc; ++c) {
1923:         switch (dim)
1924:         {
1925:           case 1: vals[(v*Nc+c)*dim] *= fegeom->invJ[0];break;
1926:           case 2: DMPlex_MultTranspose2DReal_Internal(fegeom->invJ, 1, &vals[(v*Nc+c)*dim], &vals[(v*Nc+c)*dim]);break;
1927:           case 3: DMPlex_MultTranspose3DReal_Internal(fegeom->invJ, 1, &vals[(v*Nc+c)*dim], &vals[(v*Nc+c)*dim]);break;
1928:           default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dim %D for transformation", dim);
1929:         }
1930:       }
1931:     }
1932:   } else {
1933:     for (v = 0; v < Nv; ++v) {
1934:       for (c = 0; c < Nc; ++c) {
1935:         DMPlex_MultTransposeReal_Internal(fegeom->invJ, dim, dE, 1, &vals[(v*Nc+c)*dE], &vals[(v*Nc+c)*dE]);
1936:       }
1937:     }
1938:   }
1939:   /* Assume its a vector, otherwise assume its a bunch of scalars */
1940:   if (Nc == 1 || Nc != dim) return(0);
1941:   switch (trans) {
1942:     case IDENTITY_TRANSFORM: break;
1943:     case COVARIANT_PIOLA_TRANSFORM: /* Covariant Piola mapping $\sigma^*(F) = J^{-T} F \circ \phi^{-1)$ */
1944:     if (isInverse) {
1945:       for (v = 0; v < Nv; ++v) {
1946:         for (d = 0; d < dim; ++d) {
1947:           switch (dim)
1948:           {
1949:             case 2: DMPlex_MultTranspose2DReal_Internal(fegeom->J, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1950:             case 3: DMPlex_MultTranspose3DReal_Internal(fegeom->J, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1951:             default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dim %D for transformation", dim);
1952:           }
1953:         }
1954:       }
1955:     } else {
1956:       for (v = 0; v < Nv; ++v) {
1957:         for (d = 0; d < dim; ++d) {
1958:           switch (dim)
1959:           {
1960:             case 2: DMPlex_MultTranspose2DReal_Internal(fegeom->invJ, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1961:             case 3: DMPlex_MultTranspose3DReal_Internal(fegeom->invJ, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1962:             default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dim %D for transformation", dim);
1963:           }
1964:         }
1965:       }
1966:     }
1967:     break;
1968:     case CONTRAVARIANT_PIOLA_TRANSFORM: /* Contravariant Piola mapping $\sigma^*(F) = \frac{1}{|\det J|} J F \circ \phi^{-1}$ */
1969:     if (isInverse) {
1970:       for (v = 0; v < Nv; ++v) {
1971:         for (d = 0; d < dim; ++d) {
1972:           switch (dim)
1973:           {
1974:             case 2: DMPlex_Mult2DReal_Internal(fegeom->invJ, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1975:             case 3: DMPlex_Mult3DReal_Internal(fegeom->invJ, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1976:             default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dim %D for transformation", dim);
1977:           }
1978:           for (c = 0; c < Nc; ++c) vals[(v*Nc+c)*dim+d] *= fegeom->detJ[0];
1979:         }
1980:       }
1981:     } else {
1982:       for (v = 0; v < Nv; ++v) {
1983:         for (d = 0; d < dim; ++d) {
1984:           switch (dim)
1985:           {
1986:             case 2: DMPlex_Mult2DReal_Internal(fegeom->J, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1987:             case 3: DMPlex_Mult3DReal_Internal(fegeom->J, dim, &vals[v*Nc*dim+d], &vals[v*Nc*dim+d]);break;
1988:             default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dim %D for transformation", dim);
1989:           }
1990:           for (c = 0; c < Nc; ++c) vals[(v*Nc+c)*dim+d] /= fegeom->detJ[0];
1991:         }
1992:       }
1993:     }
1994:     break;
1995:   }
1996:   return(0);
1997: }

1999: /*@C
2000:   PetscDualSpacePullback - Transform the given functional so that it operates on real space, rather than the reference element. Operationally, this means that we map the function evaluations depending on continuity requirements of our finite element method.

2002:   Input Parameters:
2003: + dsp        - The PetscDualSpace
2004: . fegeom     - The geometry for this cell
2005: . Nq         - The number of function samples
2006: . Nc         - The number of function components
2007: - pointEval  - The function values

2009:   Output Parameter:
2010: . pointEval  - The transformed function values

2012:   Level: advanced

2014:   Note: Functions transform in a complementary way (pushforward) to functionals, so that the scalar product is invariant. The type of transform is dependent on the associated k-simplex from the DeRahm complex.

2016:   Note: This only handles tranformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

2018: .seealso: PetscDualSpacePushforward(), PetscDualSpaceTransform(), PetscDualSpaceGetDeRahm()
2019: @*/
2020: PetscErrorCode PetscDualSpacePullback(PetscDualSpace dsp, PetscFEGeom *fegeom, PetscInt Nq, PetscInt Nc, PetscScalar pointEval[])
2021: {
2022:   PetscDualSpaceTransformType trans;
2023:   PetscInt                    k;
2024:   PetscErrorCode              ierr;

2030:   /* The dualspace dofs correspond to some simplex in the DeRahm complex, which we label by k.
2031:      This determines their transformation properties. */
2032:   PetscDualSpaceGetDeRahm(dsp, &k);
2033:   switch (k)
2034:   {
2035:     case 0: /* H^1 point evaluations */
2036:     trans = IDENTITY_TRANSFORM;break;
2037:     case 1: /* Hcurl preserves tangential edge traces  */
2038:     trans = COVARIANT_PIOLA_TRANSFORM;break;
2039:     case 2:
2040:     case 3: /* Hdiv preserve normal traces */
2041:     trans = CONTRAVARIANT_PIOLA_TRANSFORM;break;
2042:     default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported simplex dim %D for transformation", k);
2043:   }
2044:   PetscDualSpaceTransform(dsp, trans, PETSC_TRUE, fegeom, Nq, Nc, pointEval);
2045:   return(0);
2046: }

2048: /*@C
2049:   PetscDualSpacePushforward - Transform the given function so that it operates on real space, rather than the reference element. Operationally, this means that we map the function evaluations depending on continuity requirements of our finite element method.

2051:   Input Parameters:
2052: + dsp        - The PetscDualSpace
2053: . fegeom     - The geometry for this cell
2054: . Nq         - The number of function samples
2055: . Nc         - The number of function components
2056: - pointEval  - The function values

2058:   Output Parameter:
2059: . pointEval  - The transformed function values

2061:   Level: advanced

2063:   Note: Functionals transform in a complementary way (pullback) to functions, so that the scalar product is invariant. The type of transform is dependent on the associated k-simplex from the DeRahm complex.

2065:   Note: This only handles tranformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

2067: .seealso: PetscDualSpacePullback(), PetscDualSpaceTransform(), PetscDualSpaceGetDeRahm()
2068: @*/
2069: PetscErrorCode PetscDualSpacePushforward(PetscDualSpace dsp, PetscFEGeom *fegeom, PetscInt Nq, PetscInt Nc, PetscScalar pointEval[])
2070: {
2071:   PetscDualSpaceTransformType trans;
2072:   PetscInt                    k;
2073:   PetscErrorCode              ierr;

2079:   /* The dualspace dofs correspond to some simplex in the DeRahm complex, which we label by k.
2080:      This determines their transformation properties. */
2081:   PetscDualSpaceGetDeRahm(dsp, &k);
2082:   switch (k)
2083:   {
2084:     case 0: /* H^1 point evaluations */
2085:     trans = IDENTITY_TRANSFORM;break;
2086:     case 1: /* Hcurl preserves tangential edge traces  */
2087:     trans = COVARIANT_PIOLA_TRANSFORM;break;
2088:     case 2:
2089:     case 3: /* Hdiv preserve normal traces */
2090:     trans = CONTRAVARIANT_PIOLA_TRANSFORM;break;
2091:     default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported simplex dim %D for transformation", k);
2092:   }
2093:   PetscDualSpaceTransform(dsp, trans, PETSC_FALSE, fegeom, Nq, Nc, pointEval);
2094:   return(0);
2095: }

2097: /*@C
2098:   PetscDualSpacePushforwardGradient - Transform the given function gradient so that it operates on real space, rather than the reference element. Operationally, this means that we map the function evaluations depending on continuity requirements of our finite element method.

2100:   Input Parameters:
2101: + dsp        - The PetscDualSpace
2102: . fegeom     - The geometry for this cell
2103: . Nq         - The number of function gradient samples
2104: . Nc         - The number of function components
2105: - pointEval  - The function gradient values

2107:   Output Parameter:
2108: . pointEval  - The transformed function gradient values

2110:   Level: advanced

2112:   Note: Functionals transform in a complementary way (pullback) to functions, so that the scalar product is invariant. The type of transform is dependent on the associated k-simplex from the DeRahm complex.

2114:   Note: This only handles tranformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

2116: .seealso: PetscDualSpacePushforward(), PPetscDualSpacePullback(), PetscDualSpaceTransform(), PetscDualSpaceGetDeRahm()
2117: @*/
2118: PetscErrorCode PetscDualSpacePushforwardGradient(PetscDualSpace dsp, PetscFEGeom *fegeom, PetscInt Nq, PetscInt Nc, PetscScalar pointEval[])
2119: {
2120:   PetscDualSpaceTransformType trans;
2121:   PetscInt                    k;
2122:   PetscErrorCode              ierr;

2128:   /* The dualspace dofs correspond to some simplex in the DeRahm complex, which we label by k.
2129:      This determines their transformation properties. */
2130:   PetscDualSpaceGetDeRahm(dsp, &k);
2131:   switch (k)
2132:   {
2133:     case 0: /* H^1 point evaluations */
2134:     trans = IDENTITY_TRANSFORM;break;
2135:     case 1: /* Hcurl preserves tangential edge traces  */
2136:     trans = COVARIANT_PIOLA_TRANSFORM;break;
2137:     case 2:
2138:     case 3: /* Hdiv preserve normal traces */
2139:     trans = CONTRAVARIANT_PIOLA_TRANSFORM;break;
2140:     default: SETERRQ1(PetscObjectComm((PetscObject) dsp), PETSC_ERR_ARG_OUTOFRANGE, "Unsupported simplex dim %D for transformation", k);
2141:   }
2142:   PetscDualSpaceTransformGradient(dsp, trans, PETSC_FALSE, fegeom, Nq, Nc, pointEval);
2143:   return(0);
2144: }