Actual source code: fe.c
petsc-3.13.0 2020-03-29
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
83: Level: advanced
85: .seealso: PetscFERegisterAll(), PetscFERegisterDestroy()
87: @*/
88: PetscErrorCode PetscFERegister(const char sname[], PetscErrorCode (*function)(PetscFE))
89: {
93: PetscFunctionListAdd(&PetscFEList, sname, function);
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: }
261: /* process any options handlers added with PetscObjectAddOptionsHandler() */
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);
328: PetscQuadratureDestroy(&(*fem)->quadrature);
329: PetscQuadratureDestroy(&(*fem)->faceQuadrature);
331: if ((*fem)->ops->destroy) {(*(*fem)->ops->destroy)(*fem);}
332: PetscHeaderDestroy(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;
372: PetscArrayzero(&f->quadrature, 1);
373: PetscArrayzero(&f->faceQuadrature, 1);
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: /*@
617: PetscFEGetQuadrature - Returns the PetscQuadrature used to calculate inner products
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: @*/
631: PetscErrorCode PetscFEGetQuadrature(PetscFE fem, PetscQuadrature *q)
632: {
636: *q = fem->quadrature;
637: return(0);
638: }
640: /*@
641: PetscFESetQuadrature - Sets the PetscQuadrature used to calculate inner products
643: Not collective
645: Input Parameters:
646: + fem - The PetscFE object
647: - q - The PetscQuadrature object
649: Level: intermediate
651: .seealso: PetscFECreate()
652: @*/
653: PetscErrorCode PetscFESetQuadrature(PetscFE fem, PetscQuadrature q)
654: {
655: PetscInt Nc, qNc;
660: PetscFEGetNumComponents(fem, &Nc);
661: PetscQuadratureGetNumComponents(q, &qNc);
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);
665: PetscQuadratureDestroy(&fem->quadrature);
666: fem->quadrature = q;
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: @*/
686: PetscErrorCode PetscFEGetFaceQuadrature(PetscFE fem, PetscQuadrature *q)
687: {
691: *q = fem->faceQuadrature;
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: @*/
708: PetscErrorCode PetscFESetFaceQuadrature(PetscFE fem, PetscQuadrature q)
709: {
710: PetscInt Nc, qNc;
715: PetscFEGetNumComponents(fem, &Nc);
716: PetscQuadratureGetNumComponents(q, &qNc);
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);
719: PetscQuadratureDestroy(&fem->faceQuadrature);
720: fem->faceQuadrature = q;
721: PetscObjectReference((PetscObject) q);
722: return(0);
723: }
725: /*@
726: PetscFECopyQuadrature - Copy both volumetric and surface quadrature
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
736: .seealso: PetscFECreate(), PetscFESetQuadrature(), PetscFESetFaceQuadrature()
737: @*/
738: PetscErrorCode PetscFECopyQuadrature(PetscFE sfe, PetscFE tfe)
739: {
740: PetscQuadrature q;
741: PetscErrorCode ierr;
746: PetscFEGetQuadrature(sfe, &q);
747: PetscFESetQuadrature(tfe, q);
748: PetscFEGetFaceQuadrature(sfe, &q);
749: PetscFESetFaceQuadrature(tfe, q);
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;
844: PetscQuadrature fq;
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);
857: PetscFEGetFaceQuadrature(fem, &fq);
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, ¢roids);
911: for (f = 0; f < numFaces; ++f) {DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, ¢roids[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.
1586: Level: advanced
1588: .seealso: PetscFECreateDefault()
1589: @*/
1590: PetscErrorCode PetscFEGetHeightSubspace(PetscFE fe, PetscInt height, PetscFE *subfe)
1591: {
1592: PetscSpace P, subP;
1593: PetscDualSpace Q, subQ;
1594: PetscQuadrature 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);
1609: PetscFEGetFaceQuadrature(fe, &subq);
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);
1629: PetscFESetQuadrature(sub, subq);
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
1652: Level: advanced
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;
1661: PetscQuadrature q, qref;
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);
1671: PetscFEGetQuadrature(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);
1699: /* Create quadrature */
1700: PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL);
1701: PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref);
1702: PetscFESetQuadrature(*feRef, qref);
1703: PetscQuadratureDestroy(&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: {
1732: PetscQuadrature q, fq;
1733: DM K;
1734: PetscSpace P;
1735: PetscDualSpace Q;
1736: PetscInt order, quadPointsPerEdge;
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);
1776: PetscOptionsBoundedInt("-petscfe_default_quadrature_order","Quadrature order is one less than quadrature points per edge","PetscFECreateDefault",qorder,&qorder,NULL,0);
1777: PetscOptionsEnd();
1778: quadPointsPerEdge = PetscMax(qorder + 1,1);
1779: if (isSimplex) {
1780: PetscDTStroudConicalQuadrature(dim, 1, quadPointsPerEdge, -1.0, 1.0, &q);
1781: PetscDTStroudConicalQuadrature(dim-1, 1, quadPointsPerEdge, -1.0, 1.0, &fq);
1782: } else {
1783: PetscDTGaussTensorQuadrature(dim, 1, quadPointsPerEdge, -1.0, 1.0, &q);
1784: PetscDTGaussTensorQuadrature(dim-1, 1, quadPointsPerEdge, -1.0, 1.0, &fq);
1785: }
1786: PetscFESetQuadrature(*fem, q);
1787: PetscFESetFaceQuadrature(*fem, fq);
1788: PetscQuadratureDestroy(&q);
1789: PetscQuadratureDestroy(&fq);
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: {
1818: PetscQuadrature q, fq;
1819: DM K;
1820: PetscSpace P;
1821: PetscDualSpace Q;
1822: PetscInt quadPointsPerEdge;
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) {
1861: PetscDTStroudConicalQuadrature(dim, 1, quadPointsPerEdge, -1.0, 1.0, &q);
1862: PetscDTStroudConicalQuadrature(dim-1, 1, quadPointsPerEdge, -1.0, 1.0, &fq);
1863: } else {
1864: PetscDTGaussTensorQuadrature(dim, 1, quadPointsPerEdge, -1.0, 1.0, &q);
1865: PetscDTGaussTensorQuadrature(dim-1, 1, quadPointsPerEdge, -1.0, 1.0, &fq);
1866: }
1867: PetscFESetQuadrature(*fem, q);
1868: PetscFESetFaceQuadrature(*fem, fq);
1869: PetscQuadratureDestroy(&q);
1870: PetscQuadratureDestroy(&fq);
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]);
1929: PetscFEPushforwardGradient(fe, fegeom, 1, &u_x[fOffset*cdim]);
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);
1996: PetscFEPushforwardGradient(fe, fegeom, Nb, tmpBasisDer);
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);
2035: PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI);
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);
2045: PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ);
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: }
2071: PetscErrorCode PetscFECreateCellGeometry(PetscFE fe, PetscQuadrature quad, PetscFEGeom *cgeom)
2072: {
2073: PetscDualSpace dsp;
2074: DM dm;
2075: PetscQuadrature quadDef;
2076: PetscInt dim, cdim, Nq;
2077: PetscErrorCode ierr;
2080: PetscFEGetDualSpace(fe, &dsp);
2081: PetscDualSpaceGetDM(dsp, &dm);
2082: DMGetDimension(dm, &dim);
2083: DMGetCoordinateDim(dm, &cdim);
2084: PetscFEGetQuadrature(fe, &quadDef);
2085: quad = quad ? quad : quadDef;
2086: PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL);
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: }