Actual source code: dtfe.c

petsc-3.6.0 2015-06-09
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  1: /* Basis Jet Tabulation

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

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

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

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

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

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

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

 22:    \alpha = V^{-1}

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

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

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

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

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

 55: PetscClassId PETSCSPACE_CLASSID = 0;

 57: PetscFunctionList PetscSpaceList              = NULL;
 58: PetscBool         PetscSpaceRegisterAllCalled = PETSC_FALSE;

 62: /*@C
 63:   PetscSpaceRegister - Adds a new PetscSpace implementation

 65:   Not Collective

 67:   Input Parameters:
 68: + name        - The name of a new user-defined creation routine
 69: - create_func - The creation routine itself

 71:   Notes:
 72:   PetscSpaceRegister() may be called multiple times to add several user-defined PetscSpaces

 74:   Sample usage:
 75: .vb
 76:     PetscSpaceRegister("my_space", MyPetscSpaceCreate);
 77: .ve

 79:   Then, your PetscSpace type can be chosen with the procedural interface via
 80: .vb
 81:     PetscSpaceCreate(MPI_Comm, PetscSpace *);
 82:     PetscSpaceSetType(PetscSpace, "my_space");
 83: .ve
 84:    or at runtime via the option
 85: .vb
 86:     -petscspace_type my_space
 87: .ve

 89:   Level: advanced

 91: .keywords: PetscSpace, register
 92: .seealso: PetscSpaceRegisterAll(), PetscSpaceRegisterDestroy()

 94: @*/
 95: PetscErrorCode PetscSpaceRegister(const char sname[], PetscErrorCode (*function)(PetscSpace))
 96: {

100:   PetscFunctionListAdd(&PetscSpaceList, sname, function);
101:   return(0);
102: }

106: /*@C
107:   PetscSpaceSetType - Builds a particular PetscSpace

109:   Collective on PetscSpace

111:   Input Parameters:
112: + sp   - The PetscSpace object
113: - name - The kind of space

115:   Options Database Key:
116: . -petscspace_type <type> - Sets the PetscSpace type; use -help for a list of available types

118:   Level: intermediate

120: .keywords: PetscSpace, set, type
121: .seealso: PetscSpaceGetType(), PetscSpaceCreate()
122: @*/
123: PetscErrorCode PetscSpaceSetType(PetscSpace sp, PetscSpaceType name)
124: {
125:   PetscErrorCode (*r)(PetscSpace);
126:   PetscBool      match;

131:   PetscObjectTypeCompare((PetscObject) sp, name, &match);
132:   if (match) return(0);

134:   PetscSpaceRegisterAll();
135:   PetscFunctionListFind(PetscSpaceList, name, &r);
136:   if (!r) SETERRQ1(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscSpace type: %s", name);

138:   if (sp->ops->destroy) {
139:     (*sp->ops->destroy)(sp);
140:     sp->ops->destroy = NULL;
141:   }
142:   (*r)(sp);
143:   PetscObjectChangeTypeName((PetscObject) sp, name);
144:   return(0);
145: }

149: /*@C
150:   PetscSpaceGetType - Gets the PetscSpace type name (as a string) from the object.

152:   Not Collective

154:   Input Parameter:
155: . sp  - The PetscSpace

157:   Output Parameter:
158: . name - The PetscSpace type name

160:   Level: intermediate

162: .keywords: PetscSpace, get, type, name
163: .seealso: PetscSpaceSetType(), PetscSpaceCreate()
164: @*/
165: PetscErrorCode PetscSpaceGetType(PetscSpace sp, PetscSpaceType *name)
166: {

172:   if (!PetscSpaceRegisterAllCalled) {
173:     PetscSpaceRegisterAll();
174:   }
175:   *name = ((PetscObject) sp)->type_name;
176:   return(0);
177: }

181: /*@C
182:   PetscSpaceView - Views a PetscSpace

184:   Collective on PetscSpace

186:   Input Parameter:
187: + sp - the PetscSpace object to view
188: - v  - the viewer

190:   Level: developer

192: .seealso PetscSpaceDestroy()
193: @*/
194: PetscErrorCode PetscSpaceView(PetscSpace sp, PetscViewer v)
195: {

200:   if (!v) {
201:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) sp), &v);
202:   }
203:   if (sp->ops->view) {
204:     (*sp->ops->view)(sp, v);
205:   }
206:   return(0);
207: }

211: /*@
212:   PetscSpaceSetFromOptions - sets parameters in a PetscSpace from the options database

214:   Collective on PetscSpace

216:   Input Parameter:
217: . sp - the PetscSpace object to set options for

219:   Options Database:
220: . -petscspace_order the approximation order of the space

222:   Level: developer

224: .seealso PetscSpaceView()
225: @*/
226: PetscErrorCode PetscSpaceSetFromOptions(PetscSpace sp)
227: {
228:   const char    *defaultType;
229:   char           name[256];
230:   PetscBool      flg;

235:   if (!((PetscObject) sp)->type_name) {
236:     defaultType = PETSCSPACEPOLYNOMIAL;
237:   } else {
238:     defaultType = ((PetscObject) sp)->type_name;
239:   }
240:   if (!PetscSpaceRegisterAllCalled) {PetscSpaceRegisterAll();}

242:   PetscObjectOptionsBegin((PetscObject) sp);
243:   PetscOptionsFList("-petscspace_type", "Linear space", "PetscSpaceSetType", PetscSpaceList, defaultType, name, 256, &flg);
244:   if (flg) {
245:     PetscSpaceSetType(sp, name);
246:   } else if (!((PetscObject) sp)->type_name) {
247:     PetscSpaceSetType(sp, defaultType);
248:   }
249:   PetscOptionsInt("-petscspace_order", "The approximation order", "PetscSpaceSetOrder", sp->order, &sp->order, NULL);
250:   if (sp->ops->setfromoptions) {
251:     (*sp->ops->setfromoptions)(PetscOptionsObject,sp);
252:   }
253:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
254:   PetscObjectProcessOptionsHandlers((PetscObject) sp);
255:   PetscOptionsEnd();
256:   PetscSpaceViewFromOptions(sp, NULL, "-petscspace_view");
257:   return(0);
258: }

262: /*@C
263:   PetscSpaceSetUp - Construct data structures for the PetscSpace

265:   Collective on PetscSpace

267:   Input Parameter:
268: . sp - the PetscSpace object to setup

270:   Level: developer

272: .seealso PetscSpaceView(), PetscSpaceDestroy()
273: @*/
274: PetscErrorCode PetscSpaceSetUp(PetscSpace sp)
275: {

280:   if (sp->ops->setup) {(*sp->ops->setup)(sp);}
281:   return(0);
282: }

286: /*@
287:   PetscSpaceDestroy - Destroys a PetscSpace object

289:   Collective on PetscSpace

291:   Input Parameter:
292: . sp - the PetscSpace object to destroy

294:   Level: developer

296: .seealso PetscSpaceView()
297: @*/
298: PetscErrorCode PetscSpaceDestroy(PetscSpace *sp)
299: {

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

306:   if (--((PetscObject)(*sp))->refct > 0) {*sp = 0; return(0);}
307:   ((PetscObject) (*sp))->refct = 0;
308:   DMDestroy(&(*sp)->dm);

310:   (*(*sp)->ops->destroy)(*sp);
311:   PetscHeaderDestroy(sp);
312:   return(0);
313: }

317: /*@
318:   PetscSpaceCreate - Creates an empty PetscSpace object. The type can then be set with PetscSpaceSetType().

320:   Collective on MPI_Comm

322:   Input Parameter:
323: . comm - The communicator for the PetscSpace object

325:   Output Parameter:
326: . sp - The PetscSpace object

328:   Level: beginner

330: .seealso: PetscSpaceSetType(), PETSCSPACEPOLYNOMIAL
331: @*/
332: PetscErrorCode PetscSpaceCreate(MPI_Comm comm, PetscSpace *sp)
333: {
334:   PetscSpace     s;

339:   PetscCitationsRegister(FECitation,&FEcite);
340:   *sp  = NULL;
341:   PetscFEInitializePackage();

343:   PetscHeaderCreate(s, PETSCSPACE_CLASSID, "PetscSpace", "Linear Space", "PetscSpace", comm, PetscSpaceDestroy, PetscSpaceView);

345:   s->order = 0;
346:   DMShellCreate(comm, &s->dm);

348:   *sp = s;
349:   return(0);
350: }

354: /* Dimension of the space, i.e. number of basis vectors */
355: PetscErrorCode PetscSpaceGetDimension(PetscSpace sp, PetscInt *dim)
356: {

362:   *dim = 0;
363:   if (sp->ops->getdimension) {(*sp->ops->getdimension)(sp, dim);}
364:   return(0);
365: }

369: /*@
370:   PetscSpaceGetOrder - Return the order of approximation for this space

372:   Input Parameter:
373: . sp - The PetscSpace

375:   Output Parameter:
376: . order - The approximation order

378:   Level: intermediate

380: .seealso: PetscSpaceSetOrder(), PetscSpaceCreate(), PetscSpace
381: @*/
382: PetscErrorCode PetscSpaceGetOrder(PetscSpace sp, PetscInt *order)
383: {
387:   *order = sp->order;
388:   return(0);
389: }

393: /*@
394:   PetscSpaceSetOrder - Set the order of approximation for this space

396:   Input Parameters:
397: + sp - The PetscSpace
398: - order - The approximation order

400:   Level: intermediate

402: .seealso: PetscSpaceGetOrder(), PetscSpaceCreate(), PetscSpace
403: @*/
404: PetscErrorCode PetscSpaceSetOrder(PetscSpace sp, PetscInt order)
405: {
408:   sp->order = order;
409:   return(0);
410: }

414: /*@C
415:   PetscSpaceEvaluate - Evaluate the basis functions and their derivatives (jet) at each point

417:   Input Parameters:
418: + sp      - The PetscSpace
419: . npoints - The number of evaluation points
420: - points  - The point coordinates

422:   Output Parameters:
423: + B - The function evaluations in a npoints x nfuncs array
424: . D - The derivative evaluations in a npoints x nfuncs x dim array
425: - H - The second derivative evaluations in a npoints x nfuncs x dim x dim array

427:   Level: advanced

429: .seealso: PetscFEGetTabulation(), PetscFEGetDefaultTabulation(), PetscSpaceCreate()
430: @*/
431: PetscErrorCode PetscSpaceEvaluate(PetscSpace sp, PetscInt npoints, const PetscReal points[], PetscReal B[], PetscReal D[], PetscReal H[])
432: {

441:   if (sp->ops->evaluate) {(*sp->ops->evaluate)(sp, npoints, points, B, D, H);}
442:   return(0);
443: }

447: PetscErrorCode PetscSpaceSetFromOptions_Polynomial(PetscOptions *PetscOptionsObject,PetscSpace sp)
448: {
449:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;
450:   PetscErrorCode   ierr;

453:   PetscOptionsHead(PetscOptionsObject,"PetscSpace polynomial options");
454:   PetscOptionsInt("-petscspace_poly_num_variables", "The number of different variables, e.g. x and y", "PetscSpacePolynomialSetNumVariables", poly->numVariables, &poly->numVariables, NULL);
455:   PetscOptionsBool("-petscspace_poly_sym", "Use only symmetric polynomials", "PetscSpacePolynomialSetSymmetric", poly->symmetric, &poly->symmetric, NULL);
456:   PetscOptionsBool("-petscspace_poly_tensor", "Use the tensor product polynomials", "PetscSpacePolynomialSetTensor", poly->tensor, &poly->tensor, NULL);
457:   PetscOptionsTail();
458:   return(0);
459: }

463: static PetscErrorCode PetscSpacePolynomialView_Ascii(PetscSpace sp, PetscViewer viewer)
464: {
465:   PetscSpace_Poly  *poly = (PetscSpace_Poly *) sp->data;
466:   PetscViewerFormat format;
467:   PetscErrorCode    ierr;

470:   PetscViewerGetFormat(viewer, &format);
471:   if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
472:     if (poly->tensor) {PetscViewerASCIIPrintf(viewer, "Tensor polynomial space in %d variables of order %d\n", poly->numVariables, sp->order);}
473:     else              {PetscViewerASCIIPrintf(viewer, "Polynomial space in %d variables of order %d\n", poly->numVariables, sp->order);}
474:   } else {
475:     if (poly->tensor) {PetscViewerASCIIPrintf(viewer, "Tensor polynomial space in %d variables of order %d\n", poly->numVariables, sp->order);}
476:     else              {PetscViewerASCIIPrintf(viewer, "Polynomial space in %d variables of order %d\n", poly->numVariables, sp->order);}
477:   }
478:   return(0);
479: }

483: PetscErrorCode PetscSpaceView_Polynomial(PetscSpace sp, PetscViewer viewer)
484: {
485:   PetscBool      iascii;

491:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
492:   if (iascii) {PetscSpacePolynomialView_Ascii(sp, viewer);}
493:   return(0);
494: }

498: PetscErrorCode PetscSpaceSetUp_Polynomial(PetscSpace sp)
499: {
500:   PetscSpace_Poly *poly    = (PetscSpace_Poly *) sp->data;
501:   PetscInt         ndegree = sp->order+1;
502:   PetscInt         deg;
503:   PetscErrorCode   ierr;

506:   PetscMalloc1(ndegree, &poly->degrees);
507:   for (deg = 0; deg < ndegree; ++deg) poly->degrees[deg] = deg;
508:   return(0);
509: }

513: PetscErrorCode PetscSpaceDestroy_Polynomial(PetscSpace sp)
514: {
515:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;
516:   PetscErrorCode   ierr;

519:   PetscFree(poly->degrees);
520:   PetscFree(poly);
521:   return(0);
522: }

526: PetscErrorCode PetscSpaceGetDimension_Polynomial(PetscSpace sp, PetscInt *dim)
527: {
528:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;
529:   PetscInt         deg  = sp->order;
530:   PetscInt         n    = poly->numVariables, i;
531:   PetscReal        D    = 1.0;

534:   if (poly->tensor) {
535:     *dim = 1;
536:     for (i = 0; i < n; ++i) *dim *= (deg+1);
537:   } else {
538:     for (i = 1; i <= n; ++i) {
539:       D *= ((PetscReal) (deg+i))/i;
540:     }
541:     *dim = (PetscInt) (D + 0.5);
542:   }
543:   return(0);
544: }

548: /*
549:   LatticePoint_Internal - Returns all tuples of size 'len' with nonnegative integers that sum up to 'sum'.

551:   Input Parameters:
552: + len - The length of the tuple
553: . sum - The sum of all entries in the tuple
554: - ind - The current multi-index of the tuple, initialized to the 0 tuple

556:   Output Parameter:
557: + ind - The multi-index of the tuple, -1 indicates the iteration has terminated
558: . tup - A tuple of len integers addig to sum

560:   Level: developer

562: .seealso: 
563: */
564: static PetscErrorCode LatticePoint_Internal(PetscInt len, PetscInt sum, PetscInt ind[], PetscInt tup[])
565: {
566:   PetscInt       i;

570:   if (len == 1) {
571:     ind[0] = -1;
572:     tup[0] = sum;
573:   } else if (sum == 0) {
574:     for (i = 0; i < len; ++i) {ind[0] = -1; tup[i] = 0;}
575:   } else {
576:     tup[0] = sum - ind[0];
577:     LatticePoint_Internal(len-1, ind[0], &ind[1], &tup[1]);
578:     if (ind[1] < 0) {
579:       if (ind[0] == sum) {ind[0] = -1;}
580:       else               {ind[1] = 0; ++ind[0];}
581:     }
582:   }
583:   return(0);
584: }

588: /*
589:   TensorPoint_Internal - Returns all tuples of size 'len' with nonnegative integers that are less than 'max'.

591:   Input Parameters:
592: + len - The length of the tuple
593: . max - The max for all entries in the tuple
594: - ind - The current multi-index of the tuple, initialized to the 0 tuple

596:   Output Parameter:
597: + ind - The multi-index of the tuple, -1 indicates the iteration has terminated
598: . tup - A tuple of len integers less than max

600:   Level: developer

602: .seealso: 
603: */
604: static PetscErrorCode TensorPoint_Internal(PetscInt len, PetscInt max, PetscInt ind[], PetscInt tup[])
605: {
606:   PetscInt       i;

610:   if (len == 1) {
611:     tup[0] = ind[0]++;
612:     ind[0] = ind[0] >= max ? -1 : ind[0];
613:   } else if (max == 0) {
614:     for (i = 0; i < len; ++i) {ind[0] = -1; tup[i] = 0;}
615:   } else {
616:     tup[0] = ind[0];
617:     TensorPoint_Internal(len-1, max, &ind[1], &tup[1]);
618:     if (ind[1] < 0) {
619:       ind[1] = 0;
620:       if (ind[0] == max-1) {ind[0] = -1;}
621:       else                 {++ind[0];}
622:     }
623:   }
624:   return(0);
625: }

629: PetscErrorCode PetscSpaceEvaluate_Polynomial(PetscSpace sp, PetscInt npoints, const PetscReal points[], PetscReal B[], PetscReal D[], PetscReal H[])
630: {
631:   PetscSpace_Poly *poly    = (PetscSpace_Poly *) sp->data;
632:   DM               dm      = sp->dm;
633:   PetscInt         ndegree = sp->order+1;
634:   PetscInt        *degrees = poly->degrees;
635:   PetscInt         dim     = poly->numVariables;
636:   PetscReal       *lpoints, *tmp, *LB, *LD, *LH;
637:   PetscInt        *ind, *tup;
638:   PetscInt         pdim, d, der, i, p, deg, o;
639:   PetscErrorCode   ierr;

642:   PetscSpaceGetDimension(sp, &pdim);
643:   DMGetWorkArray(dm, npoints, PETSC_REAL, &lpoints);
644:   DMGetWorkArray(dm, npoints*ndegree*3, PETSC_REAL, &tmp);
645:   if (B) {DMGetWorkArray(dm, npoints*dim*ndegree, PETSC_REAL, &LB);}
646:   if (D) {DMGetWorkArray(dm, npoints*dim*ndegree, PETSC_REAL, &LD);}
647:   if (H) {DMGetWorkArray(dm, npoints*dim*ndegree, PETSC_REAL, &LH);}
648:   for (d = 0; d < dim; ++d) {
649:     for (p = 0; p < npoints; ++p) {
650:       lpoints[p] = points[p*dim+d];
651:     }
652:     PetscDTLegendreEval(npoints, lpoints, ndegree, degrees, tmp, &tmp[1*npoints*ndegree], &tmp[2*npoints*ndegree]);
653:     /* LB, LD, LH (ndegree * dim x npoints) */
654:     for (deg = 0; deg < ndegree; ++deg) {
655:       for (p = 0; p < npoints; ++p) {
656:         if (B) LB[(deg*dim + d)*npoints + p] = tmp[(0*npoints + p)*ndegree+deg];
657:         if (D) LD[(deg*dim + d)*npoints + p] = tmp[(1*npoints + p)*ndegree+deg];
658:         if (H) LH[(deg*dim + d)*npoints + p] = tmp[(2*npoints + p)*ndegree+deg];
659:       }
660:     }
661:   }
662:   /* Multiply by A (pdim x ndegree * dim) */
663:   PetscMalloc2(dim,&ind,dim,&tup);
664:   if (B) {
665:     /* B (npoints x pdim) */
666:     if (poly->tensor) {
667:       i = 0;
668:       PetscMemzero(ind, dim * sizeof(PetscInt));
669:       while (ind[0] >= 0) {
670:         TensorPoint_Internal(dim, sp->order+1, ind, tup);
671:         for (p = 0; p < npoints; ++p) {
672:           B[p*pdim + i] = 1.0;
673:           for (d = 0; d < dim; ++d) {
674:             B[p*pdim + i] *= LB[(tup[d]*dim + d)*npoints + p];
675:           }
676:         }
677:         ++i;
678:       }
679:     } else {
680:       i = 0;
681:       for (o = 0; o <= sp->order; ++o) {
682:         PetscMemzero(ind, dim * sizeof(PetscInt));
683:         while (ind[0] >= 0) {
684:           LatticePoint_Internal(dim, o, ind, tup);
685:           for (p = 0; p < npoints; ++p) {
686:             B[p*pdim + i] = 1.0;
687:             for (d = 0; d < dim; ++d) {
688:               B[p*pdim + i] *= LB[(tup[d]*dim + d)*npoints + p];
689:             }
690:           }
691:           ++i;
692:         }
693:       }
694:     }
695:   }
696:   if (D) {
697:     /* D (npoints x pdim x dim) */
698:     if (poly->tensor) {
699:       i = 0;
700:       PetscMemzero(ind, dim * sizeof(PetscInt));
701:       while (ind[0] >= 0) {
702:         TensorPoint_Internal(dim, sp->order+1, ind, tup);
703:         for (p = 0; p < npoints; ++p) {
704:           for (der = 0; der < dim; ++der) {
705:             D[(p*pdim + i)*dim + der] = 1.0;
706:             for (d = 0; d < dim; ++d) {
707:               if (d == der) {
708:                 D[(p*pdim + i)*dim + der] *= LD[(tup[d]*dim + d)*npoints + p];
709:               } else {
710:                 D[(p*pdim + i)*dim + der] *= LB[(tup[d]*dim + d)*npoints + p];
711:               }
712:             }
713:           }
714:         }
715:         ++i;
716:       }
717:     } else {
718:       i = 0;
719:       for (o = 0; o <= sp->order; ++o) {
720:         PetscMemzero(ind, dim * sizeof(PetscInt));
721:         while (ind[0] >= 0) {
722:           LatticePoint_Internal(dim, o, ind, tup);
723:           for (p = 0; p < npoints; ++p) {
724:             for (der = 0; der < dim; ++der) {
725:               D[(p*pdim + i)*dim + der] = 1.0;
726:               for (d = 0; d < dim; ++d) {
727:                 if (d == der) {
728:                   D[(p*pdim + i)*dim + der] *= LD[(tup[d]*dim + d)*npoints + p];
729:                 } else {
730:                   D[(p*pdim + i)*dim + der] *= LB[(tup[d]*dim + d)*npoints + p];
731:                 }
732:               }
733:             }
734:           }
735:           ++i;
736:         }
737:       }
738:     }
739:   }
740:   if (H) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Too lazy to code second derivatives");
741:   PetscFree2(ind,tup);
742:   if (B) {DMRestoreWorkArray(dm, npoints*dim*ndegree, PETSC_REAL, &LB);}
743:   if (D) {DMRestoreWorkArray(dm, npoints*dim*ndegree, PETSC_REAL, &LD);}
744:   if (H) {DMRestoreWorkArray(dm, npoints*dim*ndegree, PETSC_REAL, &LH);}
745:   DMRestoreWorkArray(dm, npoints*ndegree*3, PETSC_REAL, &tmp);
746:   DMRestoreWorkArray(dm, npoints, PETSC_REAL, &lpoints);
747:   return(0);
748: }

752: PetscErrorCode PetscSpaceInitialize_Polynomial(PetscSpace sp)
753: {
755:   sp->ops->setfromoptions = PetscSpaceSetFromOptions_Polynomial;
756:   sp->ops->setup          = PetscSpaceSetUp_Polynomial;
757:   sp->ops->view           = PetscSpaceView_Polynomial;
758:   sp->ops->destroy        = PetscSpaceDestroy_Polynomial;
759:   sp->ops->getdimension   = PetscSpaceGetDimension_Polynomial;
760:   sp->ops->evaluate       = PetscSpaceEvaluate_Polynomial;
761:   return(0);
762: }

764: /*MC
765:   PETSCSPACEPOLYNOMIAL = "poly" - A PetscSpace object that encapsulates a polynomial space, e.g. P1 is the space of linear polynomials.

767:   Level: intermediate

769: .seealso: PetscSpaceType, PetscSpaceCreate(), PetscSpaceSetType()
770: M*/

774: PETSC_EXTERN PetscErrorCode PetscSpaceCreate_Polynomial(PetscSpace sp)
775: {
776:   PetscSpace_Poly *poly;
777:   PetscErrorCode   ierr;

781:   PetscNewLog(sp,&poly);
782:   sp->data = poly;

784:   poly->numVariables = 0;
785:   poly->symmetric    = PETSC_FALSE;
786:   poly->tensor       = PETSC_FALSE;
787:   poly->degrees      = NULL;

789:   PetscSpaceInitialize_Polynomial(sp);
790:   return(0);
791: }

795: PetscErrorCode PetscSpacePolynomialSetSymmetric(PetscSpace sp, PetscBool sym)
796: {
797:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;

801:   poly->symmetric = sym;
802:   return(0);
803: }

807: PetscErrorCode PetscSpacePolynomialGetSymmetric(PetscSpace sp, PetscBool *sym)
808: {
809:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;

814:   *sym = poly->symmetric;
815:   return(0);
816: }

820: /*@
821:   PetscSpacePolynomialSetTensor - Set whether a function space is a space of tensor polynomials (the space is spanned
822:   by polynomials whose degree in each variabl is bounded by the given order), as opposed to polynomials (the space is
823:   spanned by polynomials whose total degree---summing over all variables---is bounded by the given order).

825:   Input Parameters:
826: + sp     - the function space object
827: - tensor - PETSC_TRUE for a tensor polynomial space, PETSC_FALSE for a polynomial space

829:   Level: beginner

831: .seealso: PetscSpacePolynomialGetTensor(), PetscSpaceSetOrder(), PetscSpacePolynomialSetNumVariables()
832: @*/
833: PetscErrorCode PetscSpacePolynomialSetTensor(PetscSpace sp, PetscBool tensor)
834: {
835:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;

839:   poly->tensor = tensor;
840:   return(0);
841: }

845: /*@
846:   PetscSpacePolynomialGetTensor - Get whether a function space is a space of tensor polynomials (the space is spanned
847:   by polynomials whose degree in each variabl is bounded by the given order), as opposed to polynomials (the space is
848:   spanned by polynomials whose total degree---summing over all variables---is bounded by the given order).

850:   Input Parameters:
851: . sp     - the function space object

853:   Output Parameters:
854: . tensor - PETSC_TRUE for a tensor polynomial space, PETSC_FALSE for a polynomial space

856:   Level: beginner

858: .seealso: PetscSpacePolynomialSetTensor(), PetscSpaceSetOrder(), PetscSpacePolynomialSetNumVariables()
859: @*/
860: PetscErrorCode PetscSpacePolynomialGetTensor(PetscSpace sp, PetscBool *tensor)
861: {
862:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;

867:   *tensor = poly->tensor;
868:   return(0);
869: }

873: PetscErrorCode PetscSpacePolynomialSetNumVariables(PetscSpace sp, PetscInt n)
874: {
875:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;

879:   poly->numVariables = n;
880:   return(0);
881: }

885: PetscErrorCode PetscSpacePolynomialGetNumVariables(PetscSpace sp, PetscInt *n)
886: {
887:   PetscSpace_Poly *poly = (PetscSpace_Poly *) sp->data;

892:   *n = poly->numVariables;
893:   return(0);
894: }

898: PetscErrorCode PetscSpaceSetFromOptions_DG(PetscOptions *PetscOptionsObject,PetscSpace sp)
899: {
900:   PetscSpace_DG *dg = (PetscSpace_DG *) sp->data;

904:   PetscOptionsHead(PetscOptionsObject,"PetscSpace DG options");
905:   PetscOptionsInt("-petscspace_dg_num_variables", "The number of different variables, e.g. x and y", "PetscSpaceDGSetNumVariables", dg->numVariables, &dg->numVariables, NULL);
906:   PetscOptionsTail();
907:   return(0);
908: }

912: PetscErrorCode PetscSpaceDGView_Ascii(PetscSpace sp, PetscViewer viewer)
913: {
914:   PetscSpace_DG    *dg = (PetscSpace_DG *) sp->data;
915:   PetscViewerFormat format;
916:   PetscErrorCode    ierr;

919:   PetscViewerGetFormat(viewer, &format);
920:   if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
921:     PetscViewerASCIIPrintf(viewer, "DG space in dimension %d:\n", dg->numVariables);
922:     PetscViewerASCIIPushTab(viewer);
923:     PetscQuadratureView(dg->quad, viewer);
924:     PetscViewerASCIIPopTab(viewer);
925:   } else {
926:     PetscViewerASCIIPrintf(viewer, "DG space in dimension %d on %d points\n", dg->numVariables, dg->quad->numPoints);
927:   }
928:   return(0);
929: }

933: PetscErrorCode PetscSpaceView_DG(PetscSpace sp, PetscViewer viewer)
934: {
935:   PetscBool      iascii;

941:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
942:   if (iascii) {PetscSpaceDGView_Ascii(sp, viewer);}
943:   return(0);
944: }

948: PetscErrorCode PetscSpaceSetUp_DG(PetscSpace sp)
949: {
950:   PetscSpace_DG *dg = (PetscSpace_DG *) sp->data;

954:   if (!dg->quad->points && sp->order) {
955:     PetscDTGaussJacobiQuadrature(dg->numVariables, sp->order, -1.0, 1.0, &dg->quad);
956:   }
957:   return(0);
958: }

962: PetscErrorCode PetscSpaceDestroy_DG(PetscSpace sp)
963: {
964:   PetscSpace_DG *dg = (PetscSpace_DG *) sp->data;

968:   PetscQuadratureDestroy(&dg->quad);
969:   return(0);
970: }

974: PetscErrorCode PetscSpaceGetDimension_DG(PetscSpace sp, PetscInt *dim)
975: {
976:   PetscSpace_DG *dg = (PetscSpace_DG *) sp->data;

979:   *dim = dg->quad->numPoints;
980:   return(0);
981: }

985: PetscErrorCode PetscSpaceEvaluate_DG(PetscSpace sp, PetscInt npoints, const PetscReal points[], PetscReal B[], PetscReal D[], PetscReal H[])
986: {
987:   PetscSpace_DG *dg  = (PetscSpace_DG *) sp->data;
988:   PetscInt       dim = dg->numVariables, d, p;

992:   if (D || H) SETERRQ(PetscObjectComm((PetscObject) sp), PETSC_ERR_SUP, "Cannot calculate derivatives for a DG space");
993:   if (npoints != dg->quad->numPoints) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot evaluate DG space on %d points != %d size", npoints, dg->quad->numPoints);
994:   PetscMemzero(B, npoints*npoints * sizeof(PetscReal));
995:   for (p = 0; p < npoints; ++p) {
996:     for (d = 0; d < dim; ++d) {
997:       if (PetscAbsReal(points[p*dim+d] - dg->quad->points[p*dim+d]) > 1.0e-10) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot evaluate DG point (%d, %d) %g != %g", p, d, points[p*dim+d], dg->quad->points[p*dim+d]);
998:     }
999:     B[p*npoints+p] = 1.0;
1000:   }
1001:   return(0);
1002: }

1006: PetscErrorCode PetscSpaceInitialize_DG(PetscSpace sp)
1007: {
1009:   sp->ops->setfromoptions = PetscSpaceSetFromOptions_DG;
1010:   sp->ops->setup          = PetscSpaceSetUp_DG;
1011:   sp->ops->view           = PetscSpaceView_DG;
1012:   sp->ops->destroy        = PetscSpaceDestroy_DG;
1013:   sp->ops->getdimension   = PetscSpaceGetDimension_DG;
1014:   sp->ops->evaluate       = PetscSpaceEvaluate_DG;
1015:   return(0);
1016: }

1018: /*MC
1019:   PETSCSPACEDG = "dg" - A PetscSpace object that encapsulates functions defined on a set of quadrature points.

1021:   Level: intermediate

1023: .seealso: PetscSpaceType, PetscSpaceCreate(), PetscSpaceSetType()
1024: M*/

1028: PETSC_EXTERN PetscErrorCode PetscSpaceCreate_DG(PetscSpace sp)
1029: {
1030:   PetscSpace_DG *dg;

1035:   PetscNewLog(sp,&dg);
1036:   sp->data = dg;

1038:   dg->numVariables    = 0;
1039:   dg->quad->dim       = 0;
1040:   dg->quad->numPoints = 0;
1041:   dg->quad->points    = NULL;
1042:   dg->quad->weights   = NULL;

1044:   PetscSpaceInitialize_DG(sp);
1045:   return(0);
1046: }


1049: PetscClassId PETSCDUALSPACE_CLASSID = 0;

1051: PetscFunctionList PetscDualSpaceList              = NULL;
1052: PetscBool         PetscDualSpaceRegisterAllCalled = PETSC_FALSE;

1056: /*@C
1057:   PetscDualSpaceRegister - Adds a new PetscDualSpace implementation

1059:   Not Collective

1061:   Input Parameters:
1062: + name        - The name of a new user-defined creation routine
1063: - create_func - The creation routine itself

1065:   Notes:
1066:   PetscDualSpaceRegister() may be called multiple times to add several user-defined PetscDualSpaces

1068:   Sample usage:
1069: .vb
1070:     PetscDualSpaceRegister("my_space", MyPetscDualSpaceCreate);
1071: .ve

1073:   Then, your PetscDualSpace type can be chosen with the procedural interface via
1074: .vb
1075:     PetscDualSpaceCreate(MPI_Comm, PetscDualSpace *);
1076:     PetscDualSpaceSetType(PetscDualSpace, "my_dual_space");
1077: .ve
1078:    or at runtime via the option
1079: .vb
1080:     -petscdualspace_type my_dual_space
1081: .ve

1083:   Level: advanced

1085: .keywords: PetscDualSpace, register
1086: .seealso: PetscDualSpaceRegisterAll(), PetscDualSpaceRegisterDestroy()

1088: @*/
1089: PetscErrorCode PetscDualSpaceRegister(const char sname[], PetscErrorCode (*function)(PetscDualSpace))
1090: {

1094:   PetscFunctionListAdd(&PetscDualSpaceList, sname, function);
1095:   return(0);
1096: }

1100: /*@C
1101:   PetscDualSpaceSetType - Builds a particular PetscDualSpace

1103:   Collective on PetscDualSpace

1105:   Input Parameters:
1106: + sp   - The PetscDualSpace object
1107: - name - The kind of space

1109:   Options Database Key:
1110: . -petscdualspace_type <type> - Sets the PetscDualSpace type; use -help for a list of available types

1112:   Level: intermediate

1114: .keywords: PetscDualSpace, set, type
1115: .seealso: PetscDualSpaceGetType(), PetscDualSpaceCreate()
1116: @*/
1117: PetscErrorCode PetscDualSpaceSetType(PetscDualSpace sp, PetscDualSpaceType name)
1118: {
1119:   PetscErrorCode (*r)(PetscDualSpace);
1120:   PetscBool      match;

1125:   PetscObjectTypeCompare((PetscObject) sp, name, &match);
1126:   if (match) return(0);

1128:   if (!PetscDualSpaceRegisterAllCalled) {PetscDualSpaceRegisterAll();}
1129:   PetscFunctionListFind(PetscDualSpaceList, name, &r);
1130:   if (!r) SETERRQ1(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscDualSpace type: %s", name);

1132:   if (sp->ops->destroy) {
1133:     (*sp->ops->destroy)(sp);
1134:     sp->ops->destroy = NULL;
1135:   }
1136:   (*r)(sp);
1137:   PetscObjectChangeTypeName((PetscObject) sp, name);
1138:   return(0);
1139: }

1143: /*@C
1144:   PetscDualSpaceGetType - Gets the PetscDualSpace type name (as a string) from the object.

1146:   Not Collective

1148:   Input Parameter:
1149: . sp  - The PetscDualSpace

1151:   Output Parameter:
1152: . name - The PetscDualSpace type name

1154:   Level: intermediate

1156: .keywords: PetscDualSpace, get, type, name
1157: .seealso: PetscDualSpaceSetType(), PetscDualSpaceCreate()
1158: @*/
1159: PetscErrorCode PetscDualSpaceGetType(PetscDualSpace sp, PetscDualSpaceType *name)
1160: {

1166:   if (!PetscDualSpaceRegisterAllCalled) {
1167:     PetscDualSpaceRegisterAll();
1168:   }
1169:   *name = ((PetscObject) sp)->type_name;
1170:   return(0);
1171: }

1175: /*@
1176:   PetscDualSpaceView - Views a PetscDualSpace

1178:   Collective on PetscDualSpace

1180:   Input Parameter:
1181: + sp - the PetscDualSpace object to view
1182: - v  - the viewer

1184:   Level: developer

1186: .seealso PetscDualSpaceDestroy()
1187: @*/
1188: PetscErrorCode PetscDualSpaceView(PetscDualSpace sp, PetscViewer v)
1189: {

1194:   if (!v) {
1195:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) sp), &v);
1196:   }
1197:   if (sp->ops->view) {
1198:     (*sp->ops->view)(sp, v);
1199:   }
1200:   return(0);
1201: }

1205: /*@
1206:   PetscDualSpaceSetFromOptions - sets parameters in a PetscDualSpace from the options database

1208:   Collective on PetscDualSpace

1210:   Input Parameter:
1211: . sp - the PetscDualSpace object to set options for

1213:   Options Database:
1214: . -petscspace_order the approximation order of the space

1216:   Level: developer

1218: .seealso PetscDualSpaceView()
1219: @*/
1220: PetscErrorCode PetscDualSpaceSetFromOptions(PetscDualSpace sp)
1221: {
1222:   const char    *defaultType;
1223:   char           name[256];
1224:   PetscBool      flg;

1229:   if (!((PetscObject) sp)->type_name) {
1230:     defaultType = PETSCDUALSPACELAGRANGE;
1231:   } else {
1232:     defaultType = ((PetscObject) sp)->type_name;
1233:   }
1234:   if (!PetscSpaceRegisterAllCalled) {PetscSpaceRegisterAll();}

1236:   PetscObjectOptionsBegin((PetscObject) sp);
1237:   PetscOptionsFList("-petscdualspace_type", "Dual space", "PetscDualSpaceSetType", PetscDualSpaceList, defaultType, name, 256, &flg);
1238:   if (flg) {
1239:     PetscDualSpaceSetType(sp, name);
1240:   } else if (!((PetscObject) sp)->type_name) {
1241:     PetscDualSpaceSetType(sp, defaultType);
1242:   }
1243:   PetscOptionsInt("-petscdualspace_order", "The approximation order", "PetscDualSpaceSetOrder", sp->order, &sp->order, NULL);
1244:   if (sp->ops->setfromoptions) {
1245:     (*sp->ops->setfromoptions)(PetscOptionsObject,sp);
1246:   }
1247:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
1248:   PetscObjectProcessOptionsHandlers((PetscObject) sp);
1249:   PetscOptionsEnd();
1250:   PetscDualSpaceViewFromOptions(sp, NULL, "-petscdualspace_view");
1251:   return(0);
1252: }

1256: /*@
1257:   PetscDualSpaceSetUp - Construct a basis for the PetscDualSpace

1259:   Collective on PetscDualSpace

1261:   Input Parameter:
1262: . sp - the PetscDualSpace object to setup

1264:   Level: developer

1266: .seealso PetscDualSpaceView(), PetscDualSpaceDestroy()
1267: @*/
1268: PetscErrorCode PetscDualSpaceSetUp(PetscDualSpace sp)
1269: {

1274:   if (sp->ops->setup) {(*sp->ops->setup)(sp);}
1275:   return(0);
1276: }

1280: /*@
1281:   PetscDualSpaceDestroy - Destroys a PetscDualSpace object

1283:   Collective on PetscDualSpace

1285:   Input Parameter:
1286: . sp - the PetscDualSpace object to destroy

1288:   Level: developer

1290: .seealso PetscDualSpaceView()
1291: @*/
1292: PetscErrorCode PetscDualSpaceDestroy(PetscDualSpace *sp)
1293: {
1294:   PetscInt       dim, f;

1298:   if (!*sp) return(0);

1301:   if (--((PetscObject)(*sp))->refct > 0) {*sp = 0; return(0);}
1302:   ((PetscObject) (*sp))->refct = 0;

1304:   PetscDualSpaceGetDimension(*sp, &dim);
1305:   for (f = 0; f < dim; ++f) {
1306:     PetscQuadratureDestroy(&(*sp)->functional[f]);
1307:   }
1308:   PetscFree((*sp)->functional);
1309:   DMDestroy(&(*sp)->dm);

1311:   if ((*sp)->ops->destroy) {(*(*sp)->ops->destroy)(*sp);}
1312:   PetscHeaderDestroy(sp);
1313:   return(0);
1314: }

1318: /*@
1319:   PetscDualSpaceCreate - Creates an empty PetscDualSpace object. The type can then be set with PetscDualSpaceSetType().

1321:   Collective on MPI_Comm

1323:   Input Parameter:
1324: . comm - The communicator for the PetscDualSpace object

1326:   Output Parameter:
1327: . sp - The PetscDualSpace object

1329:   Level: beginner

1331: .seealso: PetscDualSpaceSetType(), PETSCDUALSPACELAGRANGE
1332: @*/
1333: PetscErrorCode PetscDualSpaceCreate(MPI_Comm comm, PetscDualSpace *sp)
1334: {
1335:   PetscDualSpace s;

1340:   PetscCitationsRegister(FECitation,&FEcite);
1341:   *sp  = NULL;
1342:   PetscFEInitializePackage();

1344:   PetscHeaderCreate(s, PETSCDUALSPACE_CLASSID, "PetscDualSpace", "Dual Space", "PetscDualSpace", comm, PetscDualSpaceDestroy, PetscDualSpaceView);

1346:   s->order = 0;

1348:   *sp = s;
1349:   return(0);
1350: }

1354: /*@
1355:   PetscDualSpaceDuplicate - Creates a duplicate PetscDualSpace object, however it is not setup.

1357:   Collective on PetscDualSpace

1359:   Input Parameter:
1360: . sp - The original PetscDualSpace

1362:   Output Parameter:
1363: . spNew - The duplicate PetscDualSpace

1365:   Level: beginner

1367: .seealso: PetscDualSpaceCreate(), PetscDualSpaceSetType()
1368: @*/
1369: PetscErrorCode PetscDualSpaceDuplicate(PetscDualSpace sp, PetscDualSpace *spNew)
1370: {

1376:   (*sp->ops->duplicate)(sp, spNew);
1377:   return(0);
1378: }

1382: /*@
1383:   PetscDualSpaceGetDM - Get the DM representing the reference cell

1385:   Not collective

1387:   Input Parameter:
1388: . sp - The PetscDualSpace

1390:   Output Parameter:
1391: . dm - The reference cell

1393:   Level: intermediate

1395: .seealso: PetscDualSpaceSetDM(), PetscDualSpaceCreate()
1396: @*/
1397: PetscErrorCode PetscDualSpaceGetDM(PetscDualSpace sp, DM *dm)
1398: {
1402:   *dm = sp->dm;
1403:   return(0);
1404: }

1408: /*@
1409:   PetscDualSpaceSetDM - Get the DM representing the reference cell

1411:   Not collective

1413:   Input Parameters:
1414: + sp - The PetscDualSpace
1415: - dm - The reference cell

1417:   Level: intermediate

1419: .seealso: PetscDualSpaceGetDM(), PetscDualSpaceCreate()
1420: @*/
1421: PetscErrorCode PetscDualSpaceSetDM(PetscDualSpace sp, DM dm)
1422: {

1428:   DMDestroy(&sp->dm);
1429:   PetscObjectReference((PetscObject) dm);
1430:   sp->dm = dm;
1431:   return(0);
1432: }

1436: /*@
1437:   PetscDualSpaceGetOrder - Get the order of the dual space

1439:   Not collective

1441:   Input Parameter:
1442: . sp - The PetscDualSpace

1444:   Output Parameter:
1445: . order - The order

1447:   Level: intermediate

1449: .seealso: PetscDualSpaceSetOrder(), PetscDualSpaceCreate()
1450: @*/
1451: PetscErrorCode PetscDualSpaceGetOrder(PetscDualSpace sp, PetscInt *order)
1452: {
1456:   *order = sp->order;
1457:   return(0);
1458: }

1462: /*@
1463:   PetscDualSpaceSetOrder - Set the order of the dual space

1465:   Not collective

1467:   Input Parameters:
1468: + sp - The PetscDualSpace
1469: - order - The order

1471:   Level: intermediate

1473: .seealso: PetscDualSpaceGetOrder(), PetscDualSpaceCreate()
1474: @*/
1475: PetscErrorCode PetscDualSpaceSetOrder(PetscDualSpace sp, PetscInt order)
1476: {
1479:   sp->order = order;
1480:   return(0);
1481: }

1485: /*@
1486:   PetscDualSpaceGetFunctional - Get the i-th basis functional in the dual space

1488:   Not collective

1490:   Input Parameters:
1491: + sp - The PetscDualSpace
1492: - i  - The basis number

1494:   Output Parameter:
1495: . functional - The basis functional

1497:   Level: intermediate

1499: .seealso: PetscDualSpaceGetDimension(), PetscDualSpaceCreate()
1500: @*/
1501: PetscErrorCode PetscDualSpaceGetFunctional(PetscDualSpace sp, PetscInt i, PetscQuadrature *functional)
1502: {
1503:   PetscInt       dim;

1509:   PetscDualSpaceGetDimension(sp, &dim);
1510:   if ((i < 0) || (i >= dim)) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Functional index %d must be in [0, %d)", i, dim);
1511:   *functional = sp->functional[i];
1512:   return(0);
1513: }

1517: /*@
1518:   PetscDualSpaceGetDimension - Get the dimension of the dual space, i.e. the number of basis functionals

1520:   Not collective

1522:   Input Parameter:
1523: . sp - The PetscDualSpace

1525:   Output Parameter:
1526: . dim - The dimension

1528:   Level: intermediate

1530: .seealso: PetscDualSpaceGetFunctional(), PetscDualSpaceCreate()
1531: @*/
1532: PetscErrorCode PetscDualSpaceGetDimension(PetscDualSpace sp, PetscInt *dim)
1533: {

1539:   *dim = 0;
1540:   if (sp->ops->getdimension) {(*sp->ops->getdimension)(sp, dim);}
1541:   return(0);
1542: }

1546: /*@C
1547:   PetscDualSpaceGetNumDof - Get the number of degrees of freedom for each spatial (topological) dimension

1549:   Not collective

1551:   Input Parameter:
1552: . sp - The PetscDualSpace

1554:   Output Parameter:
1555: . numDof - An array of length dim+1 which holds the number of dofs for each dimension

1557:   Level: intermediate

1559: .seealso: PetscDualSpaceGetFunctional(), PetscDualSpaceCreate()
1560: @*/
1561: PetscErrorCode PetscDualSpaceGetNumDof(PetscDualSpace sp, const PetscInt **numDof)
1562: {

1568:   *numDof = NULL;
1569:   if (sp->ops->getnumdof) {(*sp->ops->getnumdof)(sp, numDof);}
1570:   return(0);
1571: }

1575: /*@
1576:   PetscDualSpaceCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell

1578:   Collective on PetscDualSpace

1580:   Input Parameters:
1581: + sp      - The PetscDualSpace
1582: . dim     - The spatial dimension
1583: - simplex - Flag for simplex, otherwise use a tensor-product cell

1585:   Output Parameter:
1586: . refdm - The reference cell

1588:   Level: advanced

1590: .keywords: PetscDualSpace, reference cell
1591: .seealso: PetscDualSpaceCreate(), DMPLEX
1592: @*/
1593: PetscErrorCode PetscDualSpaceCreateReferenceCell(PetscDualSpace sp, PetscInt dim, PetscBool simplex, DM *refdm)
1594: {

1598:   DMPlexCreateReferenceCell(PetscObjectComm((PetscObject) sp), dim, simplex, refdm);
1599:   return(0);
1600: }

1604: /*@C
1605:   PetscDualSpaceApply - Apply a functional from the dual space basis to an input function

1607:   Input Parameters:
1608: + sp      - The PetscDualSpace object
1609: . f       - The basis functional index
1610: . geom    - A context with geometric information for this cell, we use v0 (the initial vertex) and J (the Jacobian)
1611: . numComp - The number of components for the function
1612: . func    - The input function
1613: - ctx     - A context for the function

1615:   Output Parameter:
1616: . value   - numComp output values

1618:   Level: developer

1620: .seealso: PetscDualSpaceCreate()
1621: @*/
1622: PetscErrorCode PetscDualSpaceApply(PetscDualSpace sp, PetscInt f, PetscFECellGeom *geom, PetscInt numComp, PetscErrorCode (*func)(PetscInt, const PetscReal [], PetscInt, PetscScalar *, void *), void *ctx, PetscScalar *value)
1623: {
1624:   DM               dm;
1625:   PetscQuadrature  quad;
1626:   PetscReal        x[3];
1627:   PetscScalar     *val;
1628:   PetscInt         dim, q, c;
1629:   PetscErrorCode   ierr;

1634:   dim  = geom->dim;
1635:   PetscDualSpaceGetDM(sp, &dm);
1636:   PetscDualSpaceGetFunctional(sp, f, &quad);
1637:   DMGetWorkArray(dm, numComp, PETSC_SCALAR, &val);
1638:   for (c = 0; c < numComp; ++c) value[c] = 0.0;
1639:   for (q = 0; q < quad->numPoints; ++q) {
1640:     CoordinatesRefToReal(geom->dimEmbed, dim, geom->v0, geom->J, &quad->points[q*dim], x);
1641:     (*func)(geom->dimEmbed, x, numComp, val, ctx);
1642:     for (c = 0; c < numComp; ++c) {
1643:       value[c] += val[c]*quad->weights[q];
1644:     }
1645:   }
1646:   DMRestoreWorkArray(dm, numComp, PETSC_SCALAR, &val);
1647:   return(0);
1648: }

1652: /*@
1653:   PetscDualSpaceGetHeightSubspace - Get the subset of the dual space basis that is supported on a mesh point of a given height.

1655:   If the dual space is not defined on mesh points of the given height (e.g. if the space is discontinuous and
1656:   pointwise values are not defined on the element boundaries), or if the implementation of PetscDualSpace does not
1657:   support extracting subspaces, then NULL is returned.

1659:   Input Parameters:
1660: + sp - the PetscDualSpace object
1661: - height - the height of the mesh point for which the subspace is desired

1663:   Output Parameters:
1664:   bdsp - the subspace: must be destroyed by the user

1666:   Level: advanced

1668: .seealso: PetscDualSpace
1669: @*/
1670: PetscErrorCode PetscDualSpaceGetHeightSubspace(PetscDualSpace sp, PetscInt height, PetscDualSpace *bdsp)
1671: {

1677:   *bdsp = NULL;
1678:   if (sp->ops->getheightsubspace) {
1679:     (*sp->ops->getheightsubspace)(sp,height,bdsp);
1680:   }
1681:   return(0);
1682: }

1686: static PetscErrorCode PetscDualSpaceGetDimension_SingleCell_Lagrange(PetscDualSpace sp, PetscInt order, PetscInt *dim)
1687: {
1688:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
1689:   PetscReal           D   = 1.0;
1690:   PetscInt            n, i;
1691:   PetscErrorCode      ierr;

1694:   *dim = -1;                    /* Ensure that the compiler knows *dim is set. */
1695:   DMGetDimension(sp->dm, &n);
1696:   if (lag->simplex || !lag->continuous) {
1697:     for (i = 1; i <= n; ++i) {
1698:       D *= ((PetscReal) (order+i))/i;
1699:     }
1700:     *dim = (PetscInt) (D + 0.5);
1701:   } else {
1702:     *dim = 1;
1703:     for (i = 0; i < n; ++i) *dim *= (order+1);
1704:   }
1705:   return(0);
1706: }

1710: PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
1711: {
1712:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
1713:   DM                  dm    = sp->dm;
1714:   PetscInt            order = sp->order;
1715:   PetscBool           disc  = lag->continuous ? PETSC_FALSE : PETSC_TRUE;
1716:   PetscSection        csection;
1717:   Vec                 coordinates;
1718:   PetscReal          *qpoints, *qweights;
1719:   PetscInt           *closure = NULL, closureSize, c;
1720:   PetscInt            depth, dim, pdimMax, pMax = 0, *pStart, *pEnd, cell, coneSize, d, n, f = 0;
1721:   PetscBool           simplex;
1722:   PetscErrorCode      ierr;

1725:   /* Classify element type */
1726:   DMGetDimension(dm, &dim);
1727:   DMPlexGetDepth(dm, &depth);
1728:   PetscCalloc1(dim+1, &lag->numDof);
1729:   PetscMalloc2(depth+1,&pStart,depth+1,&pEnd);
1730:   for (d = 0; d <= depth; ++d) {DMPlexGetDepthStratum(dm, d, &pStart[d], &pEnd[d]);}
1731:   DMPlexGetConeSize(dm, pStart[depth], &coneSize);
1732:   DMGetCoordinateSection(dm, &csection);
1733:   DMGetCoordinatesLocal(dm, &coordinates);
1734:   if (depth == 1) {
1735:     if      (coneSize == dim+1)    simplex = PETSC_TRUE;
1736:     else if (coneSize == 1 << dim) simplex = PETSC_FALSE;
1737:     else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Only support simplices and tensor product cells");
1738:   }
1739:   else if (depth == dim) {
1740:     if      (coneSize == dim+1)   simplex = PETSC_TRUE;
1741:     else if (coneSize == 2 * dim) simplex = PETSC_FALSE;
1742:     else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Only support simplices and tensor product cells");
1743:   }
1744:   else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Only support cell-vertex meshes or interpolated meshes");
1745:   lag->simplex = simplex;
1746:   PetscDualSpaceGetDimension_SingleCell_Lagrange(sp, sp->order, &pdimMax);
1747:   pdimMax *= (pEnd[dim] - pStart[dim]);
1748:   PetscMalloc1(pdimMax, &sp->functional);
1749:   for (d = 0; d <= depth; d++) {
1750:     pMax = PetscMax(pMax,pEnd[d]);
1751:   }
1752:   if (!dim) {
1753:     PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]);
1754:     PetscMalloc1(1, &qpoints);
1755:     PetscMalloc1(1, &qweights);
1756:     PetscQuadratureSetOrder(sp->functional[f], 0);
1757:     PetscQuadratureSetData(sp->functional[f], PETSC_DETERMINE, 1, qpoints, qweights);
1758:     qpoints[0]  = 0.0;
1759:     qweights[0] = 1.0;
1760:     ++f;
1761:     lag->numDof[0] = 1;
1762:   } else {
1763:     PetscBT seen;

1765:     PetscBTCreate(pMax, &seen);
1766:     PetscBTMemzero(pMax, seen);
1767:     for (cell = pStart[depth]; cell < pEnd[depth]; ++cell) {
1768:       DMPlexGetTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);
1769:       for (c = 0; c < closureSize*2; c += 2) {
1770:         const PetscInt p = closure[c];

1772:         if (PetscBTLookup(seen, p)) continue;
1773:         PetscBTSet(seen, p);
1774:         if ((p >= pStart[0]) && (p < pEnd[0])) {
1775:           /* Vertices */
1776:           const PetscScalar *coords;
1777:           PetscInt           dof, off, d;

1779:           if (order < 1 || disc) continue;
1780:           PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]);
1781:           PetscMalloc1(dim, &qpoints);
1782:           PetscMalloc1(1, &qweights);
1783:           PetscQuadratureSetOrder(sp->functional[f], 0);
1784:           PetscQuadratureSetData(sp->functional[f], dim, 1, qpoints, qweights);
1785:           VecGetArrayRead(coordinates, &coords);
1786:           PetscSectionGetDof(csection, p, &dof);
1787:           PetscSectionGetOffset(csection, p, &off);
1788:           if (dof != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of coordinates %d does not match spatial dimension %d", dof, dim);
1789:           for (d = 0; d < dof; ++d) {qpoints[d] = PetscRealPart(coords[off+d]);}
1790:           qweights[0] = 1.0;
1791:           ++f;
1792:           VecRestoreArrayRead(coordinates, &coords);
1793:           lag->numDof[0] = 1;
1794:         } else if ((p >= pStart[1]) && (p < pEnd[1])) {
1795:           /* Edges */
1796:           PetscScalar *coords;
1797:           PetscInt     num = ((dim == 1) && !order) ? 1 : order-1, k;

1799:           if (num < 1 || disc) continue;
1800:           coords = NULL;
1801:           DMPlexVecGetClosure(dm, csection, coordinates, p, &n, &coords);
1802:           if (n != dim*2) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Point %d has %d coordinate values instead of %d", p, n, dim*2);
1803:           for (k = 1; k <= num; ++k) {
1804:             PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]);
1805:             PetscMalloc1(dim, &qpoints);
1806:             PetscMalloc1(1, &qweights);
1807:             PetscQuadratureSetOrder(sp->functional[f], 0);
1808:             PetscQuadratureSetData(sp->functional[f], dim, 1, qpoints, qweights);
1809:             for (d = 0; d < dim; ++d) {qpoints[d] = k*PetscRealPart(coords[1*dim+d] - coords[0*dim+d])/order + PetscRealPart(coords[0*dim+d]);}
1810:             qweights[0] = 1.0;
1811:             ++f;
1812:           }
1813:           DMPlexVecRestoreClosure(dm, csection, coordinates, p, &n, &coords);
1814:           lag->numDof[1] = num;
1815:         } else if ((p >= pStart[depth-1]) && (p < pEnd[depth-1])) {
1816:           /* Faces */

1818:           if (disc) continue;
1819:           if ( simplex && (order < 3)) continue;
1820:           if (!simplex && (order < 2)) continue;
1821:           lag->numDof[depth-1] = 0;
1822:           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Too lazy to implement faces");
1823:         } else if ((p >= pStart[depth]) && (p < pEnd[depth])) {
1824:           /* Cells */
1825:           PetscInt     orderEff = lag->continuous && order ? (simplex ? order-3 : order-2) : order;
1826:           PetscReal    denom    = order ? (lag->continuous ? order : (simplex ? order+3 : order+2)) : (simplex ? 3 : 2);
1827:           PetscScalar *coords   = NULL;
1828:           PetscReal    dx = 2.0/denom, *v0, *J, *invJ, detJ;
1829:           PetscInt    *ind, *tup;
1830:           PetscInt     cdim, csize, d, d2, o;

1832:           lag->numDof[depth] = 0;
1833:           if (orderEff < 0) continue;
1834:           PetscDualSpaceGetDimension_SingleCell_Lagrange(sp, orderEff, &cdim);
1835:           DMPlexVecGetClosure(dm, csection, coordinates, p, &csize, &coords);
1836:           if (csize%dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Coordinate size %d is not divisible by spatial dimension %d", csize, dim);

1838:           PetscCalloc5(dim,&ind,dim,&tup,dim,&v0,dim*dim,&J,dim*dim,&invJ);
1839:           DMPlexComputeCellGeometryFEM(dm, p, NULL, v0, J, invJ, &detJ);
1840:           if (simplex || disc) {
1841:             for (o = 0; o <= orderEff; ++o) {
1842:               PetscMemzero(ind, dim*sizeof(PetscInt));
1843:               while (ind[0] >= 0) {
1844:                 PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]);
1845:                 PetscMalloc1(dim, &qpoints);
1846:                 PetscMalloc1(1,   &qweights);
1847:                 PetscQuadratureSetOrder(sp->functional[f], 0);
1848:                 PetscQuadratureSetData(sp->functional[f], dim, 1, qpoints, qweights);
1849:                 LatticePoint_Internal(dim, o, ind, tup);
1850:                 for (d = 0; d < dim; ++d) {
1851:                   qpoints[d] = v0[d];
1852:                   for (d2 = 0; d2 < dim; ++d2) qpoints[d] += J[d*dim+d2]*((tup[d2]+1)*dx);
1853:                 }
1854:                 qweights[0] = 1.0;
1855:                 ++f;
1856:               }
1857:             }
1858:           } else {
1859:             while (ind[0] >= 0) {
1860:               PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]);
1861:               PetscMalloc1(dim, &qpoints);
1862:               PetscMalloc1(1,   &qweights);
1863:               PetscQuadratureSetOrder(sp->functional[f], 0);
1864:               PetscQuadratureSetData(sp->functional[f], dim, 1, qpoints, qweights);
1865:               TensorPoint_Internal(dim, orderEff+1, ind, tup);
1866:               for (d = 0; d < dim; ++d) {
1867:                 qpoints[d] = v0[d];
1868:                 for (d2 = 0; d2 < dim; ++d2) qpoints[d] += J[d*dim+d2]*((tup[d]+1)*dx);
1869:               }
1870:               qweights[0] = 1.0;
1871:               ++f;
1872:             }
1873:           }
1874:           PetscFree5(ind,tup,v0,J,invJ);
1875:           DMPlexVecRestoreClosure(dm, csection, coordinates, p, &csize, &coords);
1876:           lag->numDof[depth] = cdim;
1877:         }
1878:       }
1879:       DMPlexRestoreTransitiveClosure(dm, pStart[depth], PETSC_TRUE, &closureSize, &closure);
1880:     }
1881:     PetscBTDestroy(&seen);
1882:   }
1883:   if (pEnd[dim] == 1 && f != pdimMax) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of dual basis vectors %d not equal to dimension %d", f, pdimMax);
1884:   PetscFree2(pStart,pEnd);
1885:   if (f > pdimMax) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of dual basis vectors %d is greater than dimension %d", f, pdimMax);
1886:   return(0);
1887: }

1891: PetscErrorCode PetscDualSpaceDestroy_Lagrange(PetscDualSpace sp)
1892: {
1893:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
1894:   PetscErrorCode      ierr;

1897:   PetscFree(lag->numDof);
1898:   PetscFree(lag);
1899:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetContinuity_C", NULL);
1900:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetContinuity_C", NULL);
1901:   return(0);
1902: }

1906: PetscErrorCode PetscDualSpaceDuplicate_Lagrange(PetscDualSpace sp, PetscDualSpace *spNew)
1907: {
1908:   PetscInt       order;
1909:   PetscBool      cont;

1913:   PetscDualSpaceCreate(PetscObjectComm((PetscObject) sp), spNew);
1914:   PetscDualSpaceSetType(*spNew, PETSCDUALSPACELAGRANGE);
1915:   PetscDualSpaceGetOrder(sp, &order);
1916:   PetscDualSpaceSetOrder(*spNew, order);
1917:   PetscDualSpaceLagrangeGetContinuity(sp, &cont);
1918:   PetscDualSpaceLagrangeSetContinuity(*spNew, cont);
1919:   return(0);
1920: }

1924: PetscErrorCode PetscDualSpaceSetFromOptions_Lagrange(PetscOptions *PetscOptionsObject,PetscDualSpace sp)
1925: {
1926:   PetscBool      continuous, flg;

1930:   PetscDualSpaceLagrangeGetContinuity(sp, &continuous);
1931:   PetscOptionsHead(PetscOptionsObject,"PetscDualSpace Lagrange Options");
1932:   PetscOptionsBool("-petscdualspace_lagrange_continuity", "Flag for continuous element", "PetscDualSpaceLagrangeSetContinuity", continuous, &continuous, &flg);
1933:   if (flg) {PetscDualSpaceLagrangeSetContinuity(sp, continuous);}
1934:   PetscOptionsTail();
1935:   return(0);
1936: }

1940: PetscErrorCode PetscDualSpaceGetDimension_Lagrange(PetscDualSpace sp, PetscInt *dim)
1941: {
1942:   DM              K;
1943:   const PetscInt *numDof;
1944:   PetscInt        spatialDim, Nc, size = 0, d;
1945:   PetscErrorCode  ierr;

1948:   PetscDualSpaceGetDM(sp, &K);
1949:   PetscDualSpaceGetNumDof(sp, &numDof);
1950:   DMGetDimension(K, &spatialDim);
1951:   DMPlexGetHeightStratum(K, 0, NULL, &Nc);
1952:   if (Nc == 1) {PetscDualSpaceGetDimension_SingleCell_Lagrange(sp, sp->order, dim); return(0);}
1953:   for (d = 0; d <= spatialDim; ++d) {
1954:     PetscInt pStart, pEnd;

1956:     DMPlexGetDepthStratum(K, d, &pStart, &pEnd);
1957:     size += (pEnd-pStart)*numDof[d];
1958:   }
1959:   *dim = size;
1960:   return(0);
1961: }

1965: PetscErrorCode PetscDualSpaceGetNumDof_Lagrange(PetscDualSpace sp, const PetscInt **numDof)
1966: {
1967:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;

1970:   *numDof = lag->numDof;
1971:   return(0);
1972: }

1976: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
1977: {
1978:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;

1983:   *continuous = lag->continuous;
1984:   return(0);
1985: }

1989: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
1990: {
1991:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;

1995:   lag->continuous = continuous;
1996:   return(0);
1997: }

2001: /*@
2002:   PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity

2004:   Not Collective

2006:   Input Parameter:
2007: . sp         - the PetscDualSpace

2009:   Output Parameter:
2010: . continuous - flag for element continuity

2012:   Level: intermediate

2014: .keywords: PetscDualSpace, Lagrange, continuous, discontinuous
2015: .seealso: PetscDualSpaceLagrangeSetContinuity()
2016: @*/
2017: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2018: {

2024:   PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace,PetscBool*),(sp,continuous));
2025:   return(0);
2026: }

2030: /*@
2031:   PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous

2033:   Logically Collective on PetscDualSpace

2035:   Input Parameters:
2036: + sp         - the PetscDualSpace
2037: - continuous - flag for element continuity

2039:   Options Database:
2040: . -petscdualspace_lagrange_continuity <bool>

2042:   Level: intermediate

2044: .keywords: PetscDualSpace, Lagrange, continuous, discontinuous
2045: .seealso: PetscDualSpaceLagrangeGetContinuity()
2046: @*/
2047: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2048: {

2054:   PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace,PetscBool),(sp,continuous));
2055:   return(0);
2056: }

2060: PetscErrorCode PetscDualSpaceGetHeightSubspace_Lagrange(PetscDualSpace sp, PetscInt height, PetscDualSpace *bdsp)
2061: {
2062:   PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
2063:   PetscBool          continuous;
2064:   PetscInt           order;
2065:   PetscErrorCode     ierr;

2070:   PetscDualSpaceLagrangeGetContinuity(sp,&continuous);
2071:   PetscDualSpaceGetOrder(sp,&order);
2072:   if (height == 0) {
2073:     PetscObjectReference((PetscObject)sp);
2074:     *bdsp = sp;
2075:   }
2076:   else if (continuous == PETSC_FALSE || !order) {
2077:     *bdsp = NULL;
2078:   }
2079:   else {
2080:     DM dm, K;
2081:     PetscInt dim;

2083:     PetscDualSpaceGetDM(sp,&dm);
2084:     DMGetDimension(dm,&dim);
2085:     if (height > dim || height < 0) {SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Asked for dual space at height %d for dimension %d reference element\n",height,dim);}
2086:     PetscDualSpaceDuplicate(sp,bdsp);
2087:     PetscDualSpaceCreateReferenceCell(*bdsp, dim-height, lag->simplex, &K);
2088:     PetscDualSpaceSetDM(*bdsp, K);
2089:     DMDestroy(&K);
2090:     PetscDualSpaceSetUp(*bdsp);
2091:   }
2092:   return(0);
2093: }

2097: PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
2098: {
2100:   sp->ops->setfromoptions    = PetscDualSpaceSetFromOptions_Lagrange;
2101:   sp->ops->setup             = PetscDualSpaceSetUp_Lagrange;
2102:   sp->ops->view              = NULL;
2103:   sp->ops->destroy           = PetscDualSpaceDestroy_Lagrange;
2104:   sp->ops->duplicate         = PetscDualSpaceDuplicate_Lagrange;
2105:   sp->ops->getdimension      = PetscDualSpaceGetDimension_Lagrange;
2106:   sp->ops->getnumdof         = PetscDualSpaceGetNumDof_Lagrange;
2107:   sp->ops->getheightsubspace = PetscDualSpaceGetHeightSubspace_Lagrange;
2108:   return(0);
2109: }

2111: /*MC
2112:   PETSCDUALSPACELAGRANGE = "lagrange" - A PetscDualSpace object that encapsulates a dual space of pointwise evaluation functionals

2114:   Level: intermediate

2116: .seealso: PetscDualSpaceType, PetscDualSpaceCreate(), PetscDualSpaceSetType()
2117: M*/

2121: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
2122: {
2123:   PetscDualSpace_Lag *lag;
2124:   PetscErrorCode      ierr;

2128:   PetscNewLog(sp,&lag);
2129:   sp->data = lag;

2131:   lag->numDof     = NULL;
2132:   lag->simplex    = PETSC_TRUE;
2133:   lag->continuous = PETSC_TRUE;

2135:   PetscDualSpaceInitialize_Lagrange(sp);
2136:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange);
2137:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange);
2138:   return(0);
2139: }

2143: PetscErrorCode PetscDualSpaceSetUp_Simple(PetscDualSpace sp)
2144: {
2146:   return(0);
2147: }

2151: PetscErrorCode PetscDualSpaceDestroy_Simple(PetscDualSpace sp)
2152: {
2153:   PetscDualSpace_Simple *s = (PetscDualSpace_Simple *) sp->data;
2154:   PetscErrorCode         ierr;

2157:   PetscFree(s);
2158:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceSimpleSetDimension_C", NULL);
2159:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceSimpleSetFunctional_C", NULL);
2160:   return(0);
2161: }

2165: PetscErrorCode PetscDualSpaceDuplicate_Simple(PetscDualSpace sp, PetscDualSpace *spNew)
2166: {
2167:   PetscInt       dim, d;

2171:   PetscDualSpaceCreate(PetscObjectComm((PetscObject) sp), spNew);
2172:   PetscDualSpaceSetType(*spNew, PETSCDUALSPACESIMPLE);
2173:   PetscDualSpaceGetDimension(sp, &dim);
2174:   PetscDualSpaceSimpleSetDimension(*spNew, dim);
2175:   for (d = 0; d < dim; ++d) {
2176:     PetscQuadrature q;

2178:     PetscDualSpaceGetFunctional(sp, d, &q);
2179:     PetscDualSpaceSimpleSetFunctional(*spNew, d, q);
2180:   }
2181:   return(0);
2182: }

2186: PetscErrorCode PetscDualSpaceSetFromOptions_Simple(PetscOptions *PetscOptionsObject,PetscDualSpace sp)
2187: {
2189:   return(0);
2190: }

2194: PetscErrorCode PetscDualSpaceGetDimension_Simple(PetscDualSpace sp, PetscInt *dim)
2195: {
2196:   PetscDualSpace_Simple *s = (PetscDualSpace_Simple *) sp->data;

2199:   *dim = s->dim;
2200:   return(0);
2201: }

2205: PetscErrorCode PetscDualSpaceSimpleSetDimension_Simple(PetscDualSpace sp, const PetscInt dim)
2206: {
2207:   PetscDualSpace_Simple *s = (PetscDualSpace_Simple *) sp->data;
2208:   PetscInt               f;
2209:   PetscErrorCode         ierr;

2212:   for (f = 0; f < s->dim; ++f) {PetscQuadratureDestroy(&sp->functional[f]);}
2213:   PetscFree(sp->functional);
2214:   s->dim = dim;
2215:   PetscCalloc1(s->dim, &sp->functional);
2216:   return(0);
2217: }

2221: PetscErrorCode PetscDualSpaceSimpleSetFunctional_Simple(PetscDualSpace sp, PetscInt f, PetscQuadrature q)
2222: {
2223:   PetscDualSpace_Simple *s   = (PetscDualSpace_Simple *) sp->data;
2224:   PetscReal              vol = 0.0;
2225:   PetscReal             *weights;
2226:   PetscInt               Nq, p;
2227:   PetscErrorCode         ierr;

2230:   if ((f < 0) || (f >= s->dim)) SETERRQ2(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_OUTOFRANGE, "Basis index %d not in [0, %d)", f, s->dim);
2231:   PetscQuadratureDuplicate(q, &sp->functional[f]);
2232:   /* Reweight so that it has unit volume */
2233:   PetscQuadratureGetData(sp->functional[f], NULL, &Nq, NULL, (const PetscReal **) &weights);
2234:   for (p = 0; p < Nq; ++p) vol += weights[p];
2235:   for (p = 0; p < Nq; ++p) weights[p] /= vol;
2236:   return(0);
2237: }

2241: /*@
2242:   PetscDualSpaceSimpleSetDimension - Set the number of functionals in the dual space basis

2244:   Logically Collective on PetscDualSpace

2246:   Input Parameters:
2247: + sp  - the PetscDualSpace
2248: - dim - the basis dimension

2250:   Level: intermediate

2252: .keywords: PetscDualSpace, dimension
2253: .seealso: PetscDualSpaceSimpleSetFunctional()
2254: @*/
2255: PetscErrorCode PetscDualSpaceSimpleSetDimension(PetscDualSpace sp, PetscInt dim)
2256: {

2262:   PetscTryMethod(sp, "PetscDualSpaceSimpleSetDimension_C", (PetscDualSpace,PetscInt),(sp,dim));
2263:   return(0);
2264: }

2268: /*@
2269:   PetscDualSpaceSimpleSetFunctional - Set the given basis element for this dual space

2271:   Not Collective

2273:   Input Parameters:
2274: + sp  - the PetscDualSpace
2275: . f - the basis index
2276: - q - the basis functional

2278:   Level: intermediate

2280:   Note: The quadrature will be reweighted so that it has unit volume.

2282: .keywords: PetscDualSpace, functional
2283: .seealso: PetscDualSpaceSimpleSetDimension()
2284: @*/
2285: PetscErrorCode PetscDualSpaceSimpleSetFunctional(PetscDualSpace sp, PetscInt func, PetscQuadrature q)
2286: {

2291:   PetscTryMethod(sp, "PetscDualSpaceSimpleSetFunctional_C", (PetscDualSpace,PetscInt,PetscQuadrature),(sp,func,q));
2292:   return(0);
2293: }

2297: PetscErrorCode PetscDualSpaceInitialize_Simple(PetscDualSpace sp)
2298: {
2300:   sp->ops->setfromoptions = PetscDualSpaceSetFromOptions_Simple;
2301:   sp->ops->setup          = PetscDualSpaceSetUp_Simple;
2302:   sp->ops->view           = NULL;
2303:   sp->ops->destroy        = PetscDualSpaceDestroy_Simple;
2304:   sp->ops->duplicate      = PetscDualSpaceDuplicate_Simple;
2305:   sp->ops->getdimension   = PetscDualSpaceGetDimension_Simple;
2306:   sp->ops->getnumdof      = NULL;
2307:   return(0);
2308: }

2310: /*MC
2311:   PETSCDUALSPACESIMPLE = "simple" - A PetscDualSpace object that encapsulates a dual space of arbitrary functionals

2313:   Level: intermediate

2315: .seealso: PetscDualSpaceType, PetscDualSpaceCreate(), PetscDualSpaceSetType()
2316: M*/

2320: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Simple(PetscDualSpace sp)
2321: {
2322:   PetscDualSpace_Simple *s;
2323:   PetscErrorCode         ierr;

2327:   PetscNewLog(sp,&s);
2328:   sp->data = s;

2330:   s->dim = 0;

2332:   PetscDualSpaceInitialize_Simple(sp);
2333:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceSimpleSetDimension_C", PetscDualSpaceSimpleSetDimension_Simple);
2334:   PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceSimpleSetFunctional_C", PetscDualSpaceSimpleSetFunctional_Simple);
2335:   return(0);
2336: }


2339: PetscClassId PETSCFE_CLASSID = 0;

2341: PetscFunctionList PetscFEList              = NULL;
2342: PetscBool         PetscFERegisterAllCalled = PETSC_FALSE;

2346: /*@C
2347:   PetscFERegister - Adds a new PetscFE implementation

2349:   Not Collective

2351:   Input Parameters:
2352: + name        - The name of a new user-defined creation routine
2353: - create_func - The creation routine itself

2355:   Notes:
2356:   PetscFERegister() may be called multiple times to add several user-defined PetscFEs

2358:   Sample usage:
2359: .vb
2360:     PetscFERegister("my_fe", MyPetscFECreate);
2361: .ve

2363:   Then, your PetscFE type can be chosen with the procedural interface via
2364: .vb
2365:     PetscFECreate(MPI_Comm, PetscFE *);
2366:     PetscFESetType(PetscFE, "my_fe");
2367: .ve
2368:    or at runtime via the option
2369: .vb
2370:     -petscfe_type my_fe
2371: .ve

2373:   Level: advanced

2375: .keywords: PetscFE, register
2376: .seealso: PetscFERegisterAll(), PetscFERegisterDestroy()

2378: @*/
2379: PetscErrorCode PetscFERegister(const char sname[], PetscErrorCode (*function)(PetscFE))
2380: {

2384:   PetscFunctionListAdd(&PetscFEList, sname, function);
2385:   return(0);
2386: }

2390: /*@C
2391:   PetscFESetType - Builds a particular PetscFE

2393:   Collective on PetscFE

2395:   Input Parameters:
2396: + fem  - The PetscFE object
2397: - name - The kind of FEM space

2399:   Options Database Key:
2400: . -petscfe_type <type> - Sets the PetscFE type; use -help for a list of available types

2402:   Level: intermediate

2404: .keywords: PetscFE, set, type
2405: .seealso: PetscFEGetType(), PetscFECreate()
2406: @*/
2407: PetscErrorCode PetscFESetType(PetscFE fem, PetscFEType name)
2408: {
2409:   PetscErrorCode (*r)(PetscFE);
2410:   PetscBool      match;

2415:   PetscObjectTypeCompare((PetscObject) fem, name, &match);
2416:   if (match) return(0);

2418:   if (!PetscFERegisterAllCalled) {PetscFERegisterAll();}
2419:   PetscFunctionListFind(PetscFEList, name, &r);
2420:   if (!r) SETERRQ1(PetscObjectComm((PetscObject) fem), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscFE type: %s", name);

2422:   if (fem->ops->destroy) {
2423:     (*fem->ops->destroy)(fem);
2424:     fem->ops->destroy = NULL;
2425:   }
2426:   (*r)(fem);
2427:   PetscObjectChangeTypeName((PetscObject) fem, name);
2428:   return(0);
2429: }

2433: /*@C
2434:   PetscFEGetType - Gets the PetscFE type name (as a string) from the object.

2436:   Not Collective

2438:   Input Parameter:
2439: . fem  - The PetscFE

2441:   Output Parameter:
2442: . name - The PetscFE type name

2444:   Level: intermediate

2446: .keywords: PetscFE, get, type, name
2447: .seealso: PetscFESetType(), PetscFECreate()
2448: @*/
2449: PetscErrorCode PetscFEGetType(PetscFE fem, PetscFEType *name)
2450: {

2456:   if (!PetscFERegisterAllCalled) {
2457:     PetscFERegisterAll();
2458:   }
2459:   *name = ((PetscObject) fem)->type_name;
2460:   return(0);
2461: }

2465: /*@C
2466:   PetscFEView - Views a PetscFE

2468:   Collective on PetscFE

2470:   Input Parameter:
2471: + fem - the PetscFE object to view
2472: - v   - the viewer

2474:   Level: developer

2476: .seealso PetscFEDestroy()
2477: @*/
2478: PetscErrorCode PetscFEView(PetscFE fem, PetscViewer v)
2479: {

2484:   if (!v) {
2485:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) fem), &v);
2486:   }
2487:   if (fem->ops->view) {
2488:     (*fem->ops->view)(fem, v);
2489:   }
2490:   return(0);
2491: }

2495: /*@
2496:   PetscFESetFromOptions - sets parameters in a PetscFE from the options database

2498:   Collective on PetscFE

2500:   Input Parameter:
2501: . fem - the PetscFE object to set options for

2503:   Options Database:
2504: . -petscfe_num_blocks  the number of cell blocks to integrate concurrently
2505: . -petscfe_num_batches the number of cell batches to integrate serially

2507:   Level: developer

2509: .seealso PetscFEView()
2510: @*/
2511: PetscErrorCode PetscFESetFromOptions(PetscFE fem)
2512: {
2513:   const char    *defaultType;
2514:   char           name[256];
2515:   PetscBool      flg;

2520:   if (!((PetscObject) fem)->type_name) {
2521:     defaultType = PETSCFEBASIC;
2522:   } else {
2523:     defaultType = ((PetscObject) fem)->type_name;
2524:   }
2525:   if (!PetscFERegisterAllCalled) {PetscFERegisterAll();}

2527:   PetscObjectOptionsBegin((PetscObject) fem);
2528:   PetscOptionsFList("-petscfe_type", "Finite element space", "PetscFESetType", PetscFEList, defaultType, name, 256, &flg);
2529:   if (flg) {
2530:     PetscFESetType(fem, name);
2531:   } else if (!((PetscObject) fem)->type_name) {
2532:     PetscFESetType(fem, defaultType);
2533:   }
2534:   PetscOptionsInt("-petscfe_num_blocks", "The number of cell blocks to integrate concurrently", "PetscSpaceSetTileSizes", fem->numBlocks, &fem->numBlocks, NULL);
2535:   PetscOptionsInt("-petscfe_num_batches", "The number of cell batches to integrate serially", "PetscSpaceSetTileSizes", fem->numBatches, &fem->numBatches, NULL);
2536:   if (fem->ops->setfromoptions) {
2537:     (*fem->ops->setfromoptions)(PetscOptionsObject,fem);
2538:   }
2539:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
2540:   PetscObjectProcessOptionsHandlers((PetscObject) fem);
2541:   PetscOptionsEnd();
2542:   PetscFEViewFromOptions(fem, NULL, "-petscfe_view");
2543:   return(0);
2544: }

2548: /*@C
2549:   PetscFESetUp - Construct data structures for the PetscFE

2551:   Collective on PetscFE

2553:   Input Parameter:
2554: . fem - the PetscFE object to setup

2556:   Level: developer

2558: .seealso PetscFEView(), PetscFEDestroy()
2559: @*/
2560: PetscErrorCode PetscFESetUp(PetscFE fem)
2561: {

2566:   if (fem->ops->setup) {(*fem->ops->setup)(fem);}
2567:   return(0);
2568: }

2572: /*@
2573:   PetscFEDestroy - Destroys a PetscFE object

2575:   Collective on PetscFE

2577:   Input Parameter:
2578: . fem - the PetscFE object to destroy

2580:   Level: developer

2582: .seealso PetscFEView()
2583: @*/
2584: PetscErrorCode PetscFEDestroy(PetscFE *fem)
2585: {

2589:   if (!*fem) return(0);

2592:   if (--((PetscObject)(*fem))->refct > 0) {*fem = 0; return(0);}
2593:   ((PetscObject) (*fem))->refct = 0;

2595:   PetscFree((*fem)->numDof);
2596:   PetscFree((*fem)->invV);
2597:   PetscFERestoreTabulation((*fem), 0, NULL, &(*fem)->B, &(*fem)->D, NULL /*&(*fem)->H*/);
2598:   PetscFERestoreTabulation((*fem), 0, NULL, &(*fem)->F, NULL, NULL);
2599:   PetscSpaceDestroy(&(*fem)->basisSpace);
2600:   PetscDualSpaceDestroy(&(*fem)->dualSpace);
2601:   PetscQuadratureDestroy(&(*fem)->quadrature);

2603:   if ((*fem)->ops->destroy) {(*(*fem)->ops->destroy)(*fem);}
2604:   PetscHeaderDestroy(fem);
2605:   return(0);
2606: }

2610: /*@
2611:   PetscFECreate - Creates an empty PetscFE object. The type can then be set with PetscFESetType().

2613:   Collective on MPI_Comm

2615:   Input Parameter:
2616: . comm - The communicator for the PetscFE object

2618:   Output Parameter:
2619: . fem - The PetscFE object

2621:   Level: beginner

2623: .seealso: PetscFESetType(), PETSCFEGALERKIN
2624: @*/
2625: PetscErrorCode PetscFECreate(MPI_Comm comm, PetscFE *fem)
2626: {
2627:   PetscFE        f;

2632:   PetscCitationsRegister(FECitation,&FEcite);
2633:   *fem = NULL;
2634:   PetscFEInitializePackage();

2636:   PetscHeaderCreate(f, PETSCFE_CLASSID, "PetscFE", "Finite Element", "PetscFE", comm, PetscFEDestroy, PetscFEView);

2638:   f->basisSpace    = NULL;
2639:   f->dualSpace     = NULL;
2640:   f->numComponents = 1;
2641:   f->numDof        = NULL;
2642:   f->invV          = NULL;
2643:   f->B             = NULL;
2644:   f->D             = NULL;
2645:   f->H             = NULL;
2646:   PetscMemzero(&f->quadrature, sizeof(PetscQuadrature));
2647:   f->blockSize     = 0;
2648:   f->numBlocks     = 1;
2649:   f->batchSize     = 0;
2650:   f->numBatches    = 1;

2652:   *fem = f;
2653:   return(0);
2654: }

2658: /*@
2659:   PetscFEGetSpatialDimension - Returns the spatial dimension of the element

2661:   Not collective

2663:   Input Parameter:
2664: . fem - The PetscFE object

2666:   Output Parameter:
2667: . dim - The spatial dimension

2669:   Level: intermediate

2671: .seealso: PetscFECreate()
2672: @*/
2673: PetscErrorCode PetscFEGetSpatialDimension(PetscFE fem, PetscInt *dim)
2674: {
2675:   DM             dm;

2681:   PetscDualSpaceGetDM(fem->dualSpace, &dm);
2682:   DMGetDimension(dm, dim);
2683:   return(0);
2684: }

2688: /*@
2689:   PetscFESetNumComponents - Sets the number of components in the element

2691:   Not collective

2693:   Input Parameters:
2694: + fem - The PetscFE object
2695: - comp - The number of field components

2697:   Level: intermediate

2699: .seealso: PetscFECreate()
2700: @*/
2701: PetscErrorCode PetscFESetNumComponents(PetscFE fem, PetscInt comp)
2702: {
2705:   fem->numComponents = comp;
2706:   return(0);
2707: }

2711: /*@
2712:   PetscFEGetNumComponents - Returns the number of components in the element

2714:   Not collective

2716:   Input Parameter:
2717: . fem - The PetscFE object

2719:   Output Parameter:
2720: . comp - The number of field components

2722:   Level: intermediate

2724: .seealso: PetscFECreate()
2725: @*/
2726: PetscErrorCode PetscFEGetNumComponents(PetscFE fem, PetscInt *comp)
2727: {
2731:   *comp = fem->numComponents;
2732:   return(0);
2733: }

2737: /*@
2738:   PetscFESetTileSizes - Sets the tile sizes for evaluation

2740:   Not collective

2742:   Input Parameters:
2743: + fem - The PetscFE object
2744: . blockSize - The number of elements in a block
2745: . numBlocks - The number of blocks in a batch
2746: . batchSize - The number of elements in a batch
2747: - numBatches - The number of batches in a chunk

2749:   Level: intermediate

2751: .seealso: PetscFECreate()
2752: @*/
2753: PetscErrorCode PetscFESetTileSizes(PetscFE fem, PetscInt blockSize, PetscInt numBlocks, PetscInt batchSize, PetscInt numBatches)
2754: {
2757:   fem->blockSize  = blockSize;
2758:   fem->numBlocks  = numBlocks;
2759:   fem->batchSize  = batchSize;
2760:   fem->numBatches = numBatches;
2761:   return(0);
2762: }

2766: /*@
2767:   PetscFEGetTileSizes - Returns the tile sizes for evaluation

2769:   Not collective

2771:   Input Parameter:
2772: . fem - The PetscFE object

2774:   Output Parameters:
2775: + blockSize - The number of elements in a block
2776: . numBlocks - The number of blocks in a batch
2777: . batchSize - The number of elements in a batch
2778: - numBatches - The number of batches in a chunk

2780:   Level: intermediate

2782: .seealso: PetscFECreate()
2783: @*/
2784: PetscErrorCode PetscFEGetTileSizes(PetscFE fem, PetscInt *blockSize, PetscInt *numBlocks, PetscInt *batchSize, PetscInt *numBatches)
2785: {
2792:   if (blockSize)  *blockSize  = fem->blockSize;
2793:   if (numBlocks)  *numBlocks  = fem->numBlocks;
2794:   if (batchSize)  *batchSize  = fem->batchSize;
2795:   if (numBatches) *numBatches = fem->numBatches;
2796:   return(0);
2797: }

2801: /*@
2802:   PetscFEGetBasisSpace - Returns the PetscSpace used for approximation of the solution

2804:   Not collective

2806:   Input Parameter:
2807: . fem - The PetscFE object

2809:   Output Parameter:
2810: . sp - The PetscSpace object

2812:   Level: intermediate

2814: .seealso: PetscFECreate()
2815: @*/
2816: PetscErrorCode PetscFEGetBasisSpace(PetscFE fem, PetscSpace *sp)
2817: {
2821:   *sp = fem->basisSpace;
2822:   return(0);
2823: }

2827: /*@
2828:   PetscFESetBasisSpace - Sets the PetscSpace used for approximation of the solution

2830:   Not collective

2832:   Input Parameters:
2833: + fem - The PetscFE object
2834: - sp - The PetscSpace object

2836:   Level: intermediate

2838: .seealso: PetscFECreate()
2839: @*/
2840: PetscErrorCode PetscFESetBasisSpace(PetscFE fem, PetscSpace sp)
2841: {

2847:   PetscSpaceDestroy(&fem->basisSpace);
2848:   fem->basisSpace = sp;
2849:   PetscObjectReference((PetscObject) fem->basisSpace);
2850:   return(0);
2851: }

2855: /*@
2856:   PetscFEGetDualSpace - Returns the PetscDualSpace used to define the inner product

2858:   Not collective

2860:   Input Parameter:
2861: . fem - The PetscFE object

2863:   Output Parameter:
2864: . sp - The PetscDualSpace object

2866:   Level: intermediate

2868: .seealso: PetscFECreate()
2869: @*/
2870: PetscErrorCode PetscFEGetDualSpace(PetscFE fem, PetscDualSpace *sp)
2871: {
2875:   *sp = fem->dualSpace;
2876:   return(0);
2877: }

2881: /*@
2882:   PetscFESetDualSpace - Sets the PetscDualSpace used to define the inner product

2884:   Not collective

2886:   Input Parameters:
2887: + fem - The PetscFE object
2888: - sp - The PetscDualSpace object

2890:   Level: intermediate

2892: .seealso: PetscFECreate()
2893: @*/
2894: PetscErrorCode PetscFESetDualSpace(PetscFE fem, PetscDualSpace sp)
2895: {

2901:   PetscDualSpaceDestroy(&fem->dualSpace);
2902:   fem->dualSpace = sp;
2903:   PetscObjectReference((PetscObject) fem->dualSpace);
2904:   return(0);
2905: }

2909: /*@
2910:   PetscFEGetQuadrature - Returns the PetscQuadreture used to calculate inner products

2912:   Not collective

2914:   Input Parameter:
2915: . fem - The PetscFE object

2917:   Output Parameter:
2918: . q - The PetscQuadrature object

2920:   Level: intermediate

2922: .seealso: PetscFECreate()
2923: @*/
2924: PetscErrorCode PetscFEGetQuadrature(PetscFE fem, PetscQuadrature *q)
2925: {
2929:   *q = fem->quadrature;
2930:   return(0);
2931: }

2935: /*@
2936:   PetscFESetQuadrature - Sets the PetscQuadreture used to calculate inner products

2938:   Not collective

2940:   Input Parameters:
2941: + fem - The PetscFE object
2942: - q - The PetscQuadrature object

2944:   Level: intermediate

2946: .seealso: PetscFECreate()
2947: @*/
2948: PetscErrorCode PetscFESetQuadrature(PetscFE fem, PetscQuadrature q)
2949: {

2954:   PetscFERestoreTabulation(fem, 0, NULL, &fem->B, &fem->D, NULL /*&(*fem)->H*/);
2955:   PetscQuadratureDestroy(&fem->quadrature);
2956:   fem->quadrature = q;
2957:   PetscObjectReference((PetscObject) q);
2958:   return(0);
2959: }

2963: PetscErrorCode PetscFEGetNumDof(PetscFE fem, const PetscInt **numDof)
2964: {
2965:   const PetscInt *numDofDual;
2966:   PetscErrorCode  ierr;

2971:   PetscDualSpaceGetNumDof(fem->dualSpace, &numDofDual);
2972:   if (!fem->numDof) {
2973:     DM       dm;
2974:     PetscInt dim, d;

2976:     PetscDualSpaceGetDM(fem->dualSpace, &dm);
2977:     DMGetDimension(dm, &dim);
2978:     PetscMalloc1(dim+1, &fem->numDof);
2979:     for (d = 0; d <= dim; ++d) {
2980:       fem->numDof[d] = fem->numComponents*numDofDual[d];
2981:     }
2982:   }
2983:   *numDof = fem->numDof;
2984:   return(0);
2985: }

2989: PetscErrorCode PetscFEGetDefaultTabulation(PetscFE fem, PetscReal **B, PetscReal **D, PetscReal **H)
2990: {
2991:   PetscInt         npoints;
2992:   const PetscReal *points;
2993:   PetscErrorCode   ierr;

3000:   PetscQuadratureGetData(fem->quadrature, NULL, &npoints, &points, NULL);
3001:   if (!fem->B) {PetscFEGetTabulation(fem, npoints, points, &fem->B, &fem->D, NULL/*&fem->H*/);}
3002:   if (B) *B = fem->B;
3003:   if (D) *D = fem->D;
3004:   if (H) *H = fem->H;
3005:   return(0);
3006: }

3010: PetscErrorCode PetscFEGetFaceTabulation(PetscFE fem, PetscReal **F)
3011: {
3012:   PetscErrorCode   ierr;

3017:   if (!fem->F) {
3018:     PetscDualSpace  sp;
3019:     DM              dm;
3020:     const PetscInt *cone;
3021:     PetscReal      *centroids;
3022:     PetscInt        dim, numFaces, f;

3024:     PetscFEGetDualSpace(fem, &sp);
3025:     PetscDualSpaceGetDM(sp, &dm);
3026:     DMGetDimension(dm, &dim);
3027:     DMPlexGetConeSize(dm, 0, &numFaces);
3028:     DMPlexGetCone(dm, 0, &cone);
3029:     PetscMalloc1(numFaces*dim, &centroids);
3030:     for (f = 0; f < numFaces; ++f) {DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, &centroids[f*dim], NULL);}
3031:     PetscFEGetTabulation(fem, numFaces, centroids, &fem->F, NULL, NULL);
3032:     PetscFree(centroids);
3033:   }
3034:   *F = fem->F;
3035:   return(0);
3036: }

3040: PetscErrorCode PetscFEGetTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscReal **B, PetscReal **D, PetscReal **H)
3041: {
3042:   DM               dm;
3043:   PetscInt         pdim; /* Dimension of FE space P */
3044:   PetscInt         dim;  /* Spatial dimension */
3045:   PetscInt         comp; /* Field components */
3046:   PetscErrorCode   ierr;

3054:   PetscDualSpaceGetDM(fem->dualSpace, &dm);
3055:   DMGetDimension(dm, &dim);
3056:   PetscDualSpaceGetDimension(fem->dualSpace, &pdim);
3057:   PetscFEGetNumComponents(fem, &comp);
3058:   if (B) {DMGetWorkArray(dm, npoints*pdim*comp, PETSC_REAL, B);}
3059:   if (D) {DMGetWorkArray(dm, npoints*pdim*comp*dim, PETSC_REAL, D);}
3060:   if (H) {DMGetWorkArray(dm, npoints*pdim*comp*dim*dim, PETSC_REAL, H);}
3061:   (*fem->ops->gettabulation)(fem, npoints, points, B ? *B : NULL, D ? *D : NULL, H ? *H : NULL);
3062:   return(0);
3063: }

3067: PetscErrorCode PetscFERestoreTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscReal **B, PetscReal **D, PetscReal **H)
3068: {
3069:   DM             dm;

3074:   PetscDualSpaceGetDM(fem->dualSpace, &dm);
3075:   if (B && *B) {DMRestoreWorkArray(dm, 0, PETSC_REAL, B);}
3076:   if (D && *D) {DMRestoreWorkArray(dm, 0, PETSC_REAL, D);}
3077:   if (H && *H) {DMRestoreWorkArray(dm, 0, PETSC_REAL, H);}
3078:   return(0);
3079: }

3083: PetscErrorCode PetscFEDestroy_Basic(PetscFE fem)
3084: {
3085:   PetscFE_Basic *b = (PetscFE_Basic *) fem->data;

3089:   PetscFree(b);
3090:   return(0);
3091: }

3095: PetscErrorCode PetscFEView_Basic_Ascii(PetscFE fe, PetscViewer viewer)
3096: {
3097:   PetscSpace        basis;
3098:   PetscDualSpace    dual;
3099:   PetscQuadrature   q;
3100:   PetscInt          dim, Nq;
3101:   PetscViewerFormat format;
3102:   PetscErrorCode    ierr;

3105:   PetscFEGetBasisSpace(fe, &basis);
3106:   PetscFEGetDualSpace(fe, &dual);
3107:   PetscFEGetQuadrature(fe, &q);
3108:   PetscQuadratureGetData(q, &dim, &Nq, NULL, NULL);
3109:   PetscViewerGetFormat(viewer, &format);
3110:   PetscViewerASCIIPrintf(viewer, "Basic Finite Element:\n");
3111:   if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
3112:     PetscViewerASCIIPrintf(viewer, "  dimension:       %d\n", dim);
3113:     PetscViewerASCIIPrintf(viewer, "  num quad points: %d\n", Nq);
3114:     PetscViewerASCIIPushTab(viewer);
3115:     PetscQuadratureView(q, viewer);
3116:     PetscViewerASCIIPopTab(viewer);
3117:   } else {
3118:     PetscViewerASCIIPrintf(viewer, "  dimension:       %d\n", dim);
3119:     PetscViewerASCIIPrintf(viewer, "  num quad points: %d\n", Nq);
3120:   }
3121:   PetscViewerASCIIPushTab(viewer);
3122:   PetscSpaceView(basis, viewer);
3123:   PetscDualSpaceView(dual, viewer);
3124:   PetscViewerASCIIPopTab(viewer);
3125:   return(0);
3126: }

3130: PetscErrorCode PetscFEView_Basic(PetscFE fe, PetscViewer viewer)
3131: {
3132:   PetscBool      iascii;

3138:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
3139:   if (iascii) {PetscFEView_Basic_Ascii(fe, viewer);}
3140:   return(0);
3141: }

3145: /* Construct the change of basis from prime basis to nodal basis */
3146: PetscErrorCode PetscFESetUp_Basic(PetscFE fem)
3147: {
3148:   PetscScalar   *work, *invVscalar;
3149:   PetscBLASInt  *pivots;
3150:   PetscBLASInt   n, info;
3151:   PetscInt       pdim, j;

3155:   PetscDualSpaceGetDimension(fem->dualSpace, &pdim);
3156:   PetscMalloc1(pdim*pdim,&fem->invV);
3157: #if defined(PETSC_USE_COMPLEX)
3158:   PetscMalloc1(pdim*pdim,&invVscalar);
3159: #else
3160:   invVscalar = fem->invV;
3161: #endif
3162:   for (j = 0; j < pdim; ++j) {
3163:     PetscReal      *Bf;
3164:     PetscQuadrature f;
3165:     PetscInt        q, k;

3167:     PetscDualSpaceGetFunctional(fem->dualSpace, j, &f);
3168:     PetscMalloc1(f->numPoints*pdim,&Bf);
3169:     PetscSpaceEvaluate(fem->basisSpace, f->numPoints, f->points, Bf, NULL, NULL);
3170:     for (k = 0; k < pdim; ++k) {
3171:       /* n_j \cdot \phi_k */
3172:       invVscalar[j*pdim+k] = 0.0;
3173:       for (q = 0; q < f->numPoints; ++q) {
3174:         invVscalar[j*pdim+k] += Bf[q*pdim+k]*f->weights[q];
3175:       }
3176:     }
3177:     PetscFree(Bf);
3178:   }
3179:   PetscMalloc2(pdim,&pivots,pdim,&work);
3180:   n = pdim;
3181:   PetscStackCallBLAS("LAPACKgetrf", LAPACKgetrf_(&n, &n, invVscalar, &n, pivots, &info));
3182:   PetscStackCallBLAS("LAPACKgetri", LAPACKgetri_(&n, invVscalar, &n, pivots, work, &n, &info));
3183: #if defined(PETSC_USE_COMPLEX)
3184:   for (j = 0; j < pdim*pdim; j++) fem->invV[j] = PetscRealPart(invVscalar[j]);
3185:   PetscFree(invVscalar);
3186: #endif
3187:   PetscFree2(pivots,work);
3188:   return(0);
3189: }

3193: PetscErrorCode PetscFEGetDimension_Basic(PetscFE fem, PetscInt *dim)
3194: {

3198:   PetscDualSpaceGetDimension(fem->dualSpace, dim);
3199:   return(0);
3200: }

3204: PetscErrorCode PetscFEGetTabulation_Basic(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscReal *B, PetscReal *D, PetscReal *H)
3205: {
3206:   DM               dm;
3207:   PetscInt         pdim; /* Dimension of FE space P */
3208:   PetscInt         dim;  /* Spatial dimension */
3209:   PetscInt         comp; /* Field components */
3210:   PetscReal       *tmpB, *tmpD, *tmpH;
3211:   PetscInt         p, d, j, k;
3212:   PetscErrorCode   ierr;

3215:   PetscDualSpaceGetDM(fem->dualSpace, &dm);
3216:   DMGetDimension(dm, &dim);
3217:   PetscDualSpaceGetDimension(fem->dualSpace, &pdim);
3218:   PetscFEGetNumComponents(fem, &comp);
3219:   /* Evaluate the prime basis functions at all points */
3220:   if (B) {DMGetWorkArray(dm, npoints*pdim, PETSC_REAL, &tmpB);}
3221:   if (D) {DMGetWorkArray(dm, npoints*pdim*dim, PETSC_REAL, &tmpD);}
3222:   if (H) {DMGetWorkArray(dm, npoints*pdim*dim*dim, PETSC_REAL, &tmpH);}
3223:   PetscSpaceEvaluate(fem->basisSpace, npoints, points, B ? tmpB : NULL, D ? tmpD : NULL, H ? tmpH : NULL);
3224:   /* Translate to the nodal basis */
3225:   for (p = 0; p < npoints; ++p) {
3226:     if (B) {
3227:       /* Multiply by V^{-1} (pdim x pdim) */
3228:       for (j = 0; j < pdim; ++j) {
3229:         const PetscInt i = (p*pdim + j)*comp;
3230:         PetscInt       c;

3232:         B[i] = 0.0;
3233:         for (k = 0; k < pdim; ++k) {
3234:           B[i] += fem->invV[k*pdim+j] * tmpB[p*pdim + k];
3235:         }
3236:         for (c = 1; c < comp; ++c) {
3237:           B[i+c] = B[i];
3238:         }
3239:       }
3240:     }
3241:     if (D) {
3242:       /* Multiply by V^{-1} (pdim x pdim) */
3243:       for (j = 0; j < pdim; ++j) {
3244:         for (d = 0; d < dim; ++d) {
3245:           const PetscInt i = ((p*pdim + j)*comp + 0)*dim + d;
3246:           PetscInt       c;

3248:           D[i] = 0.0;
3249:           for (k = 0; k < pdim; ++k) {
3250:             D[i] += fem->invV[k*pdim+j] * tmpD[(p*pdim + k)*dim + d];
3251:           }
3252:           for (c = 1; c < comp; ++c) {
3253:             D[((p*pdim + j)*comp + c)*dim + d] = D[i];
3254:           }
3255:         }
3256:       }
3257:     }
3258:     if (H) {
3259:       /* Multiply by V^{-1} (pdim x pdim) */
3260:       for (j = 0; j < pdim; ++j) {
3261:         for (d = 0; d < dim*dim; ++d) {
3262:           const PetscInt i = ((p*pdim + j)*comp + 0)*dim*dim + d;
3263:           PetscInt       c;

3265:           H[i] = 0.0;
3266:           for (k = 0; k < pdim; ++k) {
3267:             H[i] += fem->invV[k*pdim+j] * tmpH[(p*pdim + k)*dim*dim + d];
3268:           }
3269:           for (c = 1; c < comp; ++c) {
3270:             H[((p*pdim + j)*comp + c)*dim*dim + d] = H[i];
3271:           }
3272:         }
3273:       }
3274:     }
3275:   }
3276:   if (B) {DMRestoreWorkArray(dm, npoints*pdim, PETSC_REAL, &tmpB);}
3277:   if (D) {DMRestoreWorkArray(dm, npoints*pdim*dim, PETSC_REAL, &tmpD);}
3278:   if (H) {DMRestoreWorkArray(dm, npoints*pdim*dim*dim, PETSC_REAL, &tmpH);}
3279:   return(0);
3280: }

3284: PetscErrorCode PetscFEIntegrate_Basic(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
3285:                                       const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal integral[])
3286: {
3287:   const PetscInt  debug = 0;
3288:   PetscPointFunc  obj_func;
3289:   PetscQuadrature quad;
3290:   PetscScalar    *u, *u_x, *a, *a_x;
3291:   PetscReal      *x;
3292:   PetscInt       *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
3293:   PetscInt        dim, Nf, NfAux = 0, totDim, totDimAux, cOffset = 0, cOffsetAux = 0, e;
3294:   PetscErrorCode  ierr;

3297:   PetscDSGetObjective(prob, field, &obj_func);
3298:   if (!obj_func) return(0);
3299:   PetscFEGetSpatialDimension(fem, &dim);
3300:   PetscFEGetQuadrature(fem, &quad);
3301:   PetscDSGetNumFields(prob, &Nf);
3302:   PetscDSGetTotalDimension(prob, &totDim);
3303:   PetscDSGetComponentOffsets(prob, &uOff);
3304:   PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);
3305:   PetscDSGetEvaluationArrays(prob, &u, NULL, &u_x);
3306:   PetscDSGetRefCoordArrays(prob, &x, NULL);
3307:   if (probAux) {
3308:     PetscDSGetNumFields(probAux, &NfAux);
3309:     PetscDSGetTotalDimension(probAux, &totDimAux);
3310:     PetscDSGetComponentOffsets(probAux, &aOff);
3311:     PetscDSGetComponentDerivativeOffsets(probAux, &aOff_x);
3312:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
3313:   }
3314:   for (e = 0; e < Ne; ++e) {
3315:     const PetscReal *v0   = geom[e].v0;
3316:     const PetscReal *J    = geom[e].J;
3317:     const PetscReal *invJ = geom[e].invJ;
3318:     const PetscReal  detJ = geom[e].detJ;
3319:     const PetscReal *quadPoints, *quadWeights;
3320:     PetscInt         Nq, q;

3322:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
3323:     if (debug > 1) {
3324:       PetscPrintf(PETSC_COMM_SELF, "  detJ: %g\n", detJ);
3325: #ifndef PETSC_USE_COMPLEX
3326:       DMPrintCellMatrix(e, "invJ", dim, dim, invJ);
3327: #endif
3328:     }
3329:     for (q = 0; q < Nq; ++q) {
3330:       PetscScalar integrand;

3332:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
3333:       CoordinatesRefToReal(dim, dim, v0, J, &quadPoints[q*dim], x);
3334:       EvaluateFieldJets(prob,    PETSC_FALSE, q, invJ, &coefficients[cOffset],       NULL, u, u_x, NULL);
3335:       EvaluateFieldJets(probAux, PETSC_FALSE, q, invJ, &coefficientsAux[cOffsetAux], NULL, a, a_x, NULL);
3336:       obj_func(dim, Nf, NfAux, uOff, uOff_x, u, NULL, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, &integrand);
3337:       integrand *= detJ*quadWeights[q];
3338:       integral[field] += PetscRealPart(integrand);
3339:       if (debug > 1) {PetscPrintf(PETSC_COMM_SELF, "    int: %g %g\n", PetscRealPart(integrand), integral[field]);}
3340:     }
3341:     cOffset    += totDim;
3342:     cOffsetAux += totDimAux;
3343:   }
3344:   return(0);
3345: }

3349: PetscErrorCode PetscFEIntegrateResidual_Basic(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
3350:                                               const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemVec[])
3351: {
3352:   const PetscInt  debug = 0;
3353:   PetscPointFunc  f0_func;
3354:   PetscPointFunc  f1_func;
3355:   PetscQuadrature quad;
3356:   PetscReal     **basisField, **basisFieldDer;
3357:   PetscScalar    *f0, *f1, *u, *u_t = NULL, *u_x, *a, *a_x, *refSpaceDer;
3358:   PetscReal      *x;
3359:   PetscInt       *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
3360:   PetscInt        dim, Nf, NfAux = 0, Nb, Nc, totDim, totDimAux = 0, cOffset = 0, cOffsetAux = 0, fOffset, e;
3361:   PetscErrorCode  ierr;

3364:   PetscFEGetSpatialDimension(fem, &dim);
3365:   PetscFEGetQuadrature(fem, &quad);
3366:   PetscFEGetDimension(fem, &Nb);
3367:   PetscFEGetNumComponents(fem, &Nc);
3368:   PetscDSGetNumFields(prob, &Nf);
3369:   PetscDSGetTotalDimension(prob, &totDim);
3370:   PetscDSGetComponentOffsets(prob, &uOff);
3371:   PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);
3372:   PetscDSGetFieldOffset(prob, field, &fOffset);
3373:   PetscDSGetResidual(prob, field, &f0_func, &f1_func);
3374:   PetscDSGetEvaluationArrays(prob, &u, coefficients_t ? &u_t : NULL, &u_x);
3375:   PetscDSGetRefCoordArrays(prob, &x, &refSpaceDer);
3376:   PetscDSGetWeakFormArrays(prob, &f0, &f1, NULL, NULL, NULL, NULL);
3377:   PetscDSGetTabulation(prob, &basisField, &basisFieldDer);
3378:   if (probAux) {
3379:     PetscDSGetNumFields(probAux, &NfAux);
3380:     PetscDSGetTotalDimension(probAux, &totDimAux);
3381:     PetscDSGetComponentOffsets(probAux, &aOff);
3382:     PetscDSGetComponentDerivativeOffsets(probAux, &aOff_x);
3383:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
3384:   }
3385:   for (e = 0; e < Ne; ++e) {
3386:     const PetscReal *v0   = geom[e].v0;
3387:     const PetscReal *J    = geom[e].J;
3388:     const PetscReal *invJ = geom[e].invJ;
3389:     const PetscReal  detJ = geom[e].detJ;
3390:     const PetscReal *quadPoints, *quadWeights;
3391:     PetscInt         Nq, q;

3393:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
3394:     PetscMemzero(f0, Nq*Nc* sizeof(PetscScalar));
3395:     PetscMemzero(f1, Nq*Nc*dim * sizeof(PetscScalar));
3396:     if (debug > 1) {
3397:       PetscPrintf(PETSC_COMM_SELF, "  detJ: %g\n", detJ);
3398: #ifndef PETSC_USE_COMPLEX
3399:       DMPrintCellMatrix(e, "invJ", dim, dim, invJ);
3400: #endif
3401:     }
3402:     for (q = 0; q < Nq; ++q) {
3403:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
3404:       CoordinatesRefToReal(dim, dim, v0, J, &quadPoints[q*dim], x);
3405:       EvaluateFieldJets(prob,    PETSC_FALSE, q, invJ, &coefficients[cOffset],       &coefficients_t[cOffset], u, u_x, u_t);
3406:       EvaluateFieldJets(probAux, PETSC_FALSE, q, invJ, &coefficientsAux[cOffsetAux], NULL,                     a, a_x, NULL);
3407:       if (f0_func) f0_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, &f0[q*Nc]);
3408:       if (f1_func) f1_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, refSpaceDer);
3409:       TransformF(dim, Nc, q, invJ, detJ, quadWeights, refSpaceDer, f0, f1);
3410:     }
3411:     UpdateElementVec(dim, Nq, Nb, Nc, basisField[field], basisFieldDer[field], f0, f1, &elemVec[cOffset+fOffset]);
3412:     cOffset    += totDim;
3413:     cOffsetAux += totDimAux;
3414:   }
3415:   return(0);
3416: }

3420: PetscErrorCode PetscFEIntegrateBdResidual_Basic(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
3421:                                                 const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemVec[])
3422: {
3423:   const PetscInt  debug = 0;
3424:   PetscBdPointFunc f0_func;
3425:   PetscBdPointFunc f1_func;
3426:   PetscQuadrature quad;
3427:   PetscReal     **basisField, **basisFieldDer;
3428:   PetscScalar    *f0, *f1, *u, *u_t = NULL, *u_x, *a, *a_x, *refSpaceDer;
3429:   PetscReal      *x;
3430:   PetscInt       *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
3431:   PetscInt        dim, Nf, NfAux = 0, Nb, Nc, totDim, totDimAux, cOffset = 0, cOffsetAux = 0, fOffset, e;
3432:   PetscErrorCode  ierr;

3435:   PetscFEGetSpatialDimension(fem, &dim);
3436:   dim += 1; /* Spatial dimension is one higher than topological dimension */
3437:   PetscFEGetQuadrature(fem, &quad);
3438:   PetscFEGetDimension(fem, &Nb);
3439:   PetscFEGetNumComponents(fem, &Nc);
3440:   PetscDSGetNumFields(prob, &Nf);
3441:   PetscDSGetTotalBdDimension(prob, &totDim);
3442:   PetscDSGetComponentBdOffsets(prob, &uOff);
3443:   PetscDSGetComponentBdDerivativeOffsets(prob, &uOff_x);
3444:   PetscDSGetBdFieldOffset(prob, field, &fOffset);
3445:   PetscDSGetBdResidual(prob, field, &f0_func, &f1_func);
3446:   PetscDSGetEvaluationArrays(prob, &u, coefficients_t ? &u_t : NULL, &u_x);
3447:   PetscDSGetRefCoordArrays(prob, &x, &refSpaceDer);
3448:   PetscDSGetWeakFormArrays(prob, &f0, &f1, NULL, NULL, NULL, NULL);
3449:   PetscDSGetBdTabulation(prob, &basisField, &basisFieldDer);
3450:   if (probAux) {
3451:     PetscDSGetNumFields(probAux, &NfAux);
3452:     PetscDSGetTotalBdDimension(probAux, &totDimAux);
3453:     PetscDSGetComponentBdOffsets(probAux, &aOff);
3454:     PetscDSGetComponentBdDerivativeOffsets(probAux, &aOff_x);
3455:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
3456:   }
3457:   for (e = 0; e < Ne; ++e) {
3458:     const PetscReal *v0          = geom[e].v0;
3459:     const PetscReal *n           = geom[e].n;
3460:     const PetscReal *J           = geom[e].J;
3461:     const PetscReal *invJ        = geom[e].invJ;
3462:     const PetscReal  detJ        = geom[e].detJ;
3463:     const PetscReal *quadPoints, *quadWeights;
3464:     PetscInt         Nq, q;

3466:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
3467:     PetscMemzero(f0, Nq*Nc* sizeof(PetscScalar));
3468:     PetscMemzero(f1, Nq*Nc*dim * sizeof(PetscScalar));
3469:     if (debug > 1) {
3470:       PetscPrintf(PETSC_COMM_SELF, "  detJ: %g\n", detJ);
3471: #ifndef PETSC_USE_COMPLEX
3472:       DMPrintCellMatrix(e, "invJ", dim, dim, invJ);
3473: #endif
3474:     }
3475:     for (q = 0; q < Nq; ++q) {
3476:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
3477:       CoordinatesRefToReal(dim, dim-1, v0, J, &quadPoints[q*(dim-1)], x);
3478:       EvaluateFieldJets(prob,    PETSC_TRUE, q, invJ, &coefficients[cOffset],       &coefficients_t[cOffset], u, u_x, u_t);
3479:       EvaluateFieldJets(probAux, PETSC_TRUE, q, invJ, &coefficientsAux[cOffsetAux], NULL,                     a, a_x, NULL);
3480:       if (f0_func) f0_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, n, &f0[q*Nc]);
3481:       if (f1_func) f1_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, n, refSpaceDer);
3482:       TransformF(dim, Nc, q, invJ, detJ, quadWeights, refSpaceDer, f0, f1);
3483:     }
3484:     UpdateElementVec(dim-1, Nq, Nb, Nc, basisField[field], basisFieldDer[field], f0, f1, &elemVec[cOffset+fOffset]);
3485:     cOffset    += totDim;
3486:     cOffsetAux += totDimAux;
3487:   }
3488:   return(0);
3489: }

3493: PetscErrorCode PetscFEIntegrateJacobian_Basic(PetscFE fem, PetscDS prob, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFECellGeom *geom,
3494:                                               const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemMat[])
3495: {
3496:   const PetscInt  debug      = 0;
3497:   PetscPointJac   g0_func;
3498:   PetscPointJac   g1_func;
3499:   PetscPointJac   g2_func;
3500:   PetscPointJac   g3_func;
3501:   PetscFE         fe;
3502:   PetscInt        cOffset    = 0; /* Offset into coefficients[] for element e */
3503:   PetscInt        cOffsetAux = 0; /* Offset into coefficientsAux[] for element e */
3504:   PetscInt        eOffset    = 0; /* Offset into elemMat[] for element e */
3505:   PetscInt        offsetI    = 0; /* Offset into an element vector for fieldI */
3506:   PetscInt        offsetJ    = 0; /* Offset into an element vector for fieldJ */
3507:   PetscQuadrature quad;
3508:   PetscScalar    *g0, *g1, *g2, *g3, *u, *u_t = NULL, *u_x, *a, *a_x, *refSpaceDer;
3509:   PetscReal      *x;
3510:   PetscReal     **basisField, **basisFieldDer, *basisI, *basisDerI, *basisJ, *basisDerJ;
3511:   PetscInt       *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
3512:   PetscInt        NbI = 0, NcI = 0, NbJ = 0, NcJ = 0;
3513:   PetscInt        dim, Nf, NfAux = 0, totDim, totDimAux, e;
3514:   PetscErrorCode  ierr;

3517:   PetscFEGetSpatialDimension(fem, &dim);
3518:   PetscFEGetQuadrature(fem, &quad);
3519:   PetscDSGetNumFields(prob, &Nf);
3520:   PetscDSGetTotalDimension(prob, &totDim);
3521:   PetscDSGetComponentOffsets(prob, &uOff);
3522:   PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);
3523:   PetscDSGetJacobian(prob, fieldI, fieldJ, &g0_func, &g1_func, &g2_func, &g3_func);
3524:   PetscDSGetEvaluationArrays(prob, &u, coefficients_t ? &u_t : NULL, &u_x);
3525:   PetscDSGetRefCoordArrays(prob, &x, &refSpaceDer);
3526:   PetscDSGetWeakFormArrays(prob, NULL, NULL, &g0, &g1, &g2, &g3);
3527:   PetscDSGetTabulation(prob, &basisField, &basisFieldDer);
3528:   PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);
3529:   PetscFEGetDimension(fe, &NbI);
3530:   PetscFEGetNumComponents(fe, &NcI);
3531:   PetscDSGetFieldOffset(prob, fieldI, &offsetI);
3532:   PetscDSGetDiscretization(prob, fieldJ, (PetscObject *) &fe);
3533:   PetscFEGetDimension(fe, &NbJ);
3534:   PetscFEGetNumComponents(fe, &NcJ);
3535:   PetscDSGetFieldOffset(prob, fieldJ, &offsetJ);
3536:   if (probAux) {
3537:     PetscDSGetNumFields(probAux, &NfAux);
3538:     PetscDSGetTotalDimension(probAux, &totDimAux);
3539:     PetscDSGetComponentOffsets(probAux, &aOff);
3540:     PetscDSGetComponentDerivativeOffsets(probAux, &aOff_x);
3541:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
3542:   }
3543:   basisI    = basisField[fieldI];
3544:   basisJ    = basisField[fieldJ];
3545:   basisDerI = basisFieldDer[fieldI];
3546:   basisDerJ = basisFieldDer[fieldJ];
3547:   /* Initialize here in case the function is not defined */
3548:   PetscMemzero(g0, NcI*NcJ * sizeof(PetscScalar));
3549:   PetscMemzero(g1, NcI*NcJ*dim * sizeof(PetscScalar));
3550:   PetscMemzero(g2, NcI*NcJ*dim * sizeof(PetscScalar));
3551:   PetscMemzero(g3, NcI*NcJ*dim*dim * sizeof(PetscScalar));
3552:   for (e = 0; e < Ne; ++e) {
3553:     const PetscReal *v0   = geom[e].v0;
3554:     const PetscReal *J    = geom[e].J;
3555:     const PetscReal *invJ = geom[e].invJ;
3556:     const PetscReal  detJ = geom[e].detJ;
3557:     const PetscReal *quadPoints, *quadWeights;
3558:     PetscInt         Nq, q;

3560:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
3561:     for (q = 0; q < Nq; ++q) {
3562:       PetscInt f, g, fc, gc, c;

3564:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
3565:       CoordinatesRefToReal(dim, dim, v0, J, &quadPoints[q*dim], x);
3566:       EvaluateFieldJets(prob,    PETSC_FALSE, q, invJ, &coefficients[cOffset],       &coefficients_t[cOffset], u, u_x, u_t);
3567:       EvaluateFieldJets(probAux, PETSC_FALSE, q, invJ, &coefficientsAux[cOffsetAux], NULL,                     a, a_x, NULL);
3568:       if (g0_func) {
3569:         PetscMemzero(g0, NcI*NcJ * sizeof(PetscScalar));
3570:         g0_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, g0);
3571:         for (c = 0; c < NcI*NcJ; ++c) {g0[c] *= detJ*quadWeights[q];}
3572:       }
3573:       if (g1_func) {
3574:         PetscInt d, d2;
3575:         PetscMemzero(refSpaceDer, NcI*NcJ*dim * sizeof(PetscScalar));
3576:         g1_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, refSpaceDer);
3577:         for (fc = 0; fc < NcI; ++fc) {
3578:           for (gc = 0; gc < NcJ; ++gc) {
3579:             for (d = 0; d < dim; ++d) {
3580:               g1[(fc*NcJ+gc)*dim+d] = 0.0;
3581:               for (d2 = 0; d2 < dim; ++d2) g1[(fc*NcJ+gc)*dim+d] += invJ[d*dim+d2]*refSpaceDer[(fc*NcJ+gc)*dim+d2];
3582:               g1[(fc*NcJ+gc)*dim+d] *= detJ*quadWeights[q];
3583:             }
3584:           }
3585:         }
3586:       }
3587:       if (g2_func) {
3588:         PetscInt d, d2;
3589:         PetscMemzero(refSpaceDer, NcI*NcJ*dim * sizeof(PetscScalar));
3590:         g2_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, refSpaceDer);
3591:         for (fc = 0; fc < NcI; ++fc) {
3592:           for (gc = 0; gc < NcJ; ++gc) {
3593:             for (d = 0; d < dim; ++d) {
3594:               g2[(fc*NcJ+gc)*dim+d] = 0.0;
3595:               for (d2 = 0; d2 < dim; ++d2) g2[(fc*NcJ+gc)*dim+d] += invJ[d*dim+d2]*refSpaceDer[(fc*NcJ+gc)*dim+d2];
3596:               g2[(fc*NcJ+gc)*dim+d] *= detJ*quadWeights[q];
3597:             }
3598:           }
3599:         }
3600:       }
3601:       if (g3_func) {
3602:         PetscInt d, d2, dp, d3;
3603:         PetscMemzero(refSpaceDer, NcI*NcJ*dim*dim * sizeof(PetscScalar));
3604:         g3_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, refSpaceDer);
3605:         for (fc = 0; fc < NcI; ++fc) {
3606:           for (gc = 0; gc < NcJ; ++gc) {
3607:             for (d = 0; d < dim; ++d) {
3608:               for (dp = 0; dp < dim; ++dp) {
3609:                 g3[((fc*NcJ+gc)*dim+d)*dim+dp] = 0.0;
3610:                 for (d2 = 0; d2 < dim; ++d2) {
3611:                   for (d3 = 0; d3 < dim; ++d3) {
3612:                     g3[((fc*NcJ+gc)*dim+d)*dim+dp] += invJ[d*dim+d2]*refSpaceDer[((fc*NcJ+gc)*dim+d2)*dim+d3]*invJ[dp*dim+d3];
3613:                   }
3614:                 }
3615:                 g3[((fc*NcJ+gc)*dim+d)*dim+dp] *= detJ*quadWeights[q];
3616:               }
3617:             }
3618:           }
3619:         }
3620:       }

3622:       for (f = 0; f < NbI; ++f) {
3623:         for (fc = 0; fc < NcI; ++fc) {
3624:           const PetscInt fidx = f*NcI+fc; /* Test function basis index */
3625:           const PetscInt i    = offsetI+fidx; /* Element matrix row */
3626:           for (g = 0; g < NbJ; ++g) {
3627:             for (gc = 0; gc < NcJ; ++gc) {
3628:               const PetscInt gidx = g*NcJ+gc; /* Trial function basis index */
3629:               const PetscInt j    = offsetJ+gidx; /* Element matrix column */
3630:               const PetscInt fOff = eOffset+i*totDim+j;
3631:               PetscInt       d, d2;

3633:               elemMat[fOff] += basisI[q*NbI*NcI+fidx]*g0[fc*NcJ+gc]*basisJ[q*NbJ*NcJ+gidx];
3634:               for (d = 0; d < dim; ++d) {
3635:                 elemMat[fOff] += basisI[q*NbI*NcI+fidx]*g1[(fc*NcJ+gc)*dim+d]*basisDerJ[(q*NbJ*NcJ+gidx)*dim+d];
3636:                 elemMat[fOff] += basisDerI[(q*NbI*NcI+fidx)*dim+d]*g2[(fc*NcJ+gc)*dim+d]*basisJ[q*NbJ*NcJ+gidx];
3637:                 for (d2 = 0; d2 < dim; ++d2) {
3638:                   elemMat[fOff] += basisDerI[(q*NbI*NcI+fidx)*dim+d]*g3[((fc*NcJ+gc)*dim+d)*dim+d2]*basisDerJ[(q*NbJ*NcJ+gidx)*dim+d2];
3639:                 }
3640:               }
3641:             }
3642:           }
3643:         }
3644:       }
3645:     }
3646:     if (debug > 1) {
3647:       PetscInt fc, f, gc, g;

3649:       PetscPrintf(PETSC_COMM_SELF, "Element matrix for fields %d and %d\n", fieldI, fieldJ);
3650:       for (fc = 0; fc < NcI; ++fc) {
3651:         for (f = 0; f < NbI; ++f) {
3652:           const PetscInt i = offsetI + f*NcI+fc;
3653:           for (gc = 0; gc < NcJ; ++gc) {
3654:             for (g = 0; g < NbJ; ++g) {
3655:               const PetscInt j = offsetJ + g*NcJ+gc;
3656:               PetscPrintf(PETSC_COMM_SELF, "    elemMat[%d,%d,%d,%d]: %g\n", f, fc, g, gc, PetscRealPart(elemMat[eOffset+i*totDim+j]));
3657:             }
3658:           }
3659:           PetscPrintf(PETSC_COMM_SELF, "\n");
3660:         }
3661:       }
3662:     }
3663:     cOffset    += totDim;
3664:     cOffsetAux += totDimAux;
3665:     eOffset    += PetscSqr(totDim);
3666:   }
3667:   return(0);
3668: }

3672: PetscErrorCode PetscFEIntegrateBdJacobian_Basic(PetscFE fem, PetscDS prob, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFECellGeom *geom,
3673:                                                 const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemMat[])
3674: {
3675:   const PetscInt  debug      = 0;
3676:   PetscBdPointJac g0_func;
3677:   PetscBdPointJac g1_func;
3678:   PetscBdPointJac g2_func;
3679:   PetscBdPointJac g3_func;
3680:   PetscFE         fe;
3681:   PetscInt        cOffset    = 0; /* Offset into coefficients[] for element e */
3682:   PetscInt        cOffsetAux = 0; /* Offset into coefficientsAux[] for element e */
3683:   PetscInt        eOffset    = 0; /* Offset into elemMat[] for element e */
3684:   PetscInt        offsetI    = 0; /* Offset into an element vector for fieldI */
3685:   PetscInt        offsetJ    = 0; /* Offset into an element vector for fieldJ */
3686:   PetscQuadrature quad;
3687:   PetscScalar    *g0, *g1, *g2, *g3, *u, *u_t = NULL, *u_x, *a, *a_x, *refSpaceDer;
3688:   PetscReal      *x;
3689:   PetscReal     **basisField, **basisFieldDer, *basisI, *basisDerI, *basisJ, *basisDerJ;
3690:   PetscInt       *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
3691:   PetscInt        NbI = 0, NcI = 0, NbJ = 0, NcJ = 0;
3692:   PetscInt        dim, Nf, NfAux = 0, bdim, totDim, totDimAux, e;
3693:   PetscErrorCode  ierr;

3696:   PetscFEGetQuadrature(fem, &quad);
3697:   PetscFEGetSpatialDimension(fem, &dim);
3698:   dim += 1; /* Spatial dimension is one higher than topological dimension */
3699:   bdim = dim-1;
3700:   PetscDSGetNumFields(prob, &Nf);
3701:   PetscDSGetTotalBdDimension(prob, &totDim);
3702:   PetscDSGetComponentBdOffsets(prob, &uOff);
3703:   PetscDSGetComponentBdDerivativeOffsets(prob, &uOff_x);
3704:   PetscDSGetBdJacobian(prob, fieldI, fieldJ, &g0_func, &g1_func, &g2_func, &g3_func);
3705:   PetscDSGetEvaluationArrays(prob, &u, coefficients_t ? &u_t : NULL, &u_x);
3706:   PetscDSGetRefCoordArrays(prob, &x, &refSpaceDer);
3707:   PetscDSGetWeakFormArrays(prob, NULL, NULL, &g0, &g1, &g2, &g3);
3708:   PetscDSGetBdTabulation(prob, &basisField, &basisFieldDer);
3709:   PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);
3710:   PetscFEGetDimension(fe, &NbI);
3711:   PetscFEGetNumComponents(fe, &NcI);
3712:   PetscDSGetBdFieldOffset(prob, fieldI, &offsetI);
3713:   PetscDSGetBdDiscretization(prob, fieldJ, (PetscObject *) &fe);
3714:   PetscFEGetDimension(fe, &NbJ);
3715:   PetscFEGetNumComponents(fe, &NcJ);
3716:   PetscDSGetBdFieldOffset(prob, fieldJ, &offsetJ);
3717:   if (probAux) {
3718:     PetscDSGetNumFields(probAux, &NfAux);
3719:     PetscDSGetTotalBdDimension(probAux, &totDimAux);
3720:     PetscDSGetComponentBdOffsets(probAux, &aOff);
3721:     PetscDSGetComponentBdDerivativeOffsets(probAux, &aOff_x);
3722:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
3723:   }
3724:   basisI    = basisField[fieldI];
3725:   basisJ    = basisField[fieldJ];
3726:   basisDerI = basisFieldDer[fieldI];
3727:   basisDerJ = basisFieldDer[fieldJ];
3728:   /* Initialize here in case the function is not defined */
3729:   PetscMemzero(g0, NcI*NcJ * sizeof(PetscScalar));
3730:   PetscMemzero(g1, NcI*NcJ*dim * sizeof(PetscScalar));
3731:   PetscMemzero(g2, NcI*NcJ*dim * sizeof(PetscScalar));
3732:   PetscMemzero(g3, NcI*NcJ*dim*dim * sizeof(PetscScalar));
3733:   for (e = 0; e < Ne; ++e) {
3734:     const PetscReal *v0   = geom[e].v0;
3735:     const PetscReal *n    = geom[e].n;
3736:     const PetscReal *J    = geom[e].J;
3737:     const PetscReal *invJ = geom[e].invJ;
3738:     const PetscReal  detJ = geom[e].detJ;
3739:     const PetscReal *quadPoints, *quadWeights;
3740:     PetscInt         Nq, q;

3742:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
3743:     for (q = 0; q < Nq; ++q) {
3744:       PetscInt f, g, fc, gc, c;

3746:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
3747:       CoordinatesRefToReal(dim, bdim, v0, J, &quadPoints[q*bdim], x);
3748:       EvaluateFieldJets(prob,    PETSC_TRUE, q, invJ, &coefficients[cOffset],       &coefficients_t[cOffset], u, u_x, u_t);
3749:       EvaluateFieldJets(probAux, PETSC_TRUE, q, invJ, &coefficientsAux[cOffsetAux], NULL,                     a, a_x, NULL);
3750:       /* TODO: I think I have a mistake in the dim loops here */
3751:       if (g0_func) {
3752:         PetscMemzero(g0, NcI*NcJ * sizeof(PetscScalar));
3753:         g0_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, n, g0);
3754:         for (c = 0; c < NcI*NcJ; ++c) {g0[c] *= detJ*quadWeights[q];}
3755:       }
3756:       if (g1_func) {
3757:         PetscInt d, d2;
3758:         PetscMemzero(refSpaceDer, NcI*NcJ*dim * sizeof(PetscScalar));
3759:         g1_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, n, refSpaceDer);
3760:         for (fc = 0; fc < NcI; ++fc) {
3761:           for (gc = 0; gc < NcJ; ++gc) {
3762:             for (d = 0; d < dim; ++d) {
3763:               g1[(fc*NcJ+gc)*dim+d] = 0.0;
3764:               for (d2 = 0; d2 < dim; ++d2) g1[(fc*NcJ+gc)*dim+d] += invJ[d*dim+d2]*refSpaceDer[(fc*NcJ+gc)*dim+d2];
3765:               g1[(fc*NcJ+gc)*dim+d] *= detJ*quadWeights[q];
3766:             }
3767:           }
3768:         }
3769:       }
3770:       if (g2_func) {
3771:         PetscInt d, d2;
3772:         PetscMemzero(refSpaceDer, NcI*NcJ*dim * sizeof(PetscScalar));
3773:         g2_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, n, refSpaceDer);
3774:         for (fc = 0; fc < NcI; ++fc) {
3775:           for (gc = 0; gc < NcJ; ++gc) {
3776:             for (d = 0; d < dim; ++d) {
3777:               g2[(fc*NcJ+gc)*dim+d] = 0.0;
3778:               for (d2 = 0; d2 < dim; ++d2) g2[(fc*NcJ+gc)*dim+d] += invJ[d*dim+d2]*refSpaceDer[(fc*NcJ+gc)*dim+d2];
3779:               g2[(fc*NcJ+gc)*dim+d] *= detJ*quadWeights[q];
3780:             }
3781:           }
3782:         }
3783:       }
3784:       if (g3_func) {
3785:         PetscInt d, d2, dp, d3;
3786:         PetscMemzero(refSpaceDer, NcI*NcJ*dim*dim * sizeof(PetscScalar));
3787:         g3_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, n, g3);
3788:         for (fc = 0; fc < NcI; ++fc) {
3789:           for (gc = 0; gc < NcJ; ++gc) {
3790:             for (d = 0; d < dim; ++d) {
3791:               for (dp = 0; dp < dim; ++dp) {
3792:                 g3[((fc*NcJ+gc)*dim+d)*dim+dp] = 0.0;
3793:                 for (d2 = 0; d2 < dim; ++d2) {
3794:                   for (d3 = 0; d3 < dim; ++d3) {
3795:                     g3[((fc*NcJ+gc)*dim+d)*dim+dp] += invJ[d*dim+d2]*refSpaceDer[((fc*NcJ+gc)*dim+d2)*dim+d3]*invJ[dp*dim+d3];
3796:                   }
3797:                 }
3798:                 g3[((fc*NcJ+gc)*dim+d)*dim+dp] *= detJ*quadWeights[q];
3799:               }
3800:             }
3801:           }
3802:         }
3803:       }

3805:       for (f = 0; f < NbI; ++f) {
3806:         for (fc = 0; fc < NcI; ++fc) {
3807:           const PetscInt fidx = f*NcI+fc; /* Test function basis index */
3808:           const PetscInt i    = offsetI+fidx; /* Element matrix row */
3809:           for (g = 0; g < NbJ; ++g) {
3810:             for (gc = 0; gc < NcJ; ++gc) {
3811:               const PetscInt gidx = g*NcJ+gc; /* Trial function basis index */
3812:               const PetscInt j    = offsetJ+gidx; /* Element matrix column */
3813:               const PetscInt fOff = eOffset+i*totDim+j;
3814:               PetscInt       d, d2;

3816:               elemMat[fOff] += basisI[q*NbI*NcI+fidx]*g0[fc*NcJ+gc]*basisJ[q*NbJ*NcJ+gidx];
3817:               for (d = 0; d < bdim; ++d) {
3818:                 elemMat[fOff] += basisI[q*NbI*NcI+fidx]*g1[(fc*NcJ+gc)*bdim+d]*basisDerJ[(q*NbJ*NcJ+gidx)*bdim+d];
3819:                 elemMat[fOff] += basisDerI[(q*NbI*NcI+fidx)*bdim+d]*g2[(fc*NcJ+gc)*bdim+d]*basisJ[q*NbJ*NcJ+gidx];
3820:                 for (d2 = 0; d2 < bdim; ++d2) {
3821:                   elemMat[fOff] += basisDerI[(q*NbI*NcI+fidx)*bdim+d]*g3[((fc*NcJ+gc)*bdim+d)*bdim+d2]*basisDerJ[(q*NbJ*NcJ+gidx)*bdim+d2];
3822:                 }
3823:               }
3824:             }
3825:           }
3826:         }
3827:       }
3828:     }
3829:     if (debug > 1) {
3830:       PetscInt fc, f, gc, g;

3832:       PetscPrintf(PETSC_COMM_SELF, "Element matrix for fields %d and %d\n", fieldI, fieldJ);
3833:       for (fc = 0; fc < NcI; ++fc) {
3834:         for (f = 0; f < NbI; ++f) {
3835:           const PetscInt i = offsetI + f*NcI+fc;
3836:           for (gc = 0; gc < NcJ; ++gc) {
3837:             for (g = 0; g < NbJ; ++g) {
3838:               const PetscInt j = offsetJ + g*NcJ+gc;
3839:               PetscPrintf(PETSC_COMM_SELF, "    elemMat[%d,%d,%d,%d]: %g\n", f, fc, g, gc, PetscRealPart(elemMat[eOffset+i*totDim+j]));
3840:             }
3841:           }
3842:           PetscPrintf(PETSC_COMM_SELF, "\n");
3843:         }
3844:       }
3845:     }
3846:     cOffset    += totDim;
3847:     cOffsetAux += totDimAux;
3848:     eOffset    += PetscSqr(totDim);
3849:   }
3850:   return(0);
3851: }

3855: PetscErrorCode PetscFEInitialize_Basic(PetscFE fem)
3856: {
3858:   fem->ops->setfromoptions          = NULL;
3859:   fem->ops->setup                   = PetscFESetUp_Basic;
3860:   fem->ops->view                    = PetscFEView_Basic;
3861:   fem->ops->destroy                 = PetscFEDestroy_Basic;
3862:   fem->ops->getdimension            = PetscFEGetDimension_Basic;
3863:   fem->ops->gettabulation           = PetscFEGetTabulation_Basic;
3864:   fem->ops->integrate               = PetscFEIntegrate_Basic;
3865:   fem->ops->integrateresidual       = PetscFEIntegrateResidual_Basic;
3866:   fem->ops->integratebdresidual     = PetscFEIntegrateBdResidual_Basic;
3867:   fem->ops->integratejacobianaction = NULL/* PetscFEIntegrateJacobianAction_Basic */;
3868:   fem->ops->integratejacobian       = PetscFEIntegrateJacobian_Basic;
3869:   fem->ops->integratebdjacobian     = PetscFEIntegrateBdJacobian_Basic;
3870:   return(0);
3871: }

3873: /*MC
3874:   PETSCFEBASIC = "basic" - A PetscFE object that integrates with basic tiling and no vectorization

3876:   Level: intermediate

3878: .seealso: PetscFEType, PetscFECreate(), PetscFESetType()
3879: M*/

3883: PETSC_EXTERN PetscErrorCode PetscFECreate_Basic(PetscFE fem)
3884: {
3885:   PetscFE_Basic *b;

3890:   PetscNewLog(fem,&b);
3891:   fem->data = b;

3893:   PetscFEInitialize_Basic(fem);
3894:   return(0);
3895: }

3899: PetscErrorCode PetscFEDestroy_Nonaffine(PetscFE fem)
3900: {
3901:   PetscFE_Nonaffine *na = (PetscFE_Nonaffine *) fem->data;

3905:   PetscFree(na);
3906:   return(0);
3907: }

3911: PetscErrorCode PetscFEIntegrateResidual_Nonaffine(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
3912:                                                   const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemVec[])
3913: {
3914:   const PetscInt  debug = 0;
3915:   PetscPointFunc  f0_func;
3916:   PetscPointFunc  f1_func;
3917:   PetscQuadrature quad;
3918:   PetscReal     **basisField, **basisFieldDer;
3919:   PetscScalar    *f0, *f1, *u, *u_t, *u_x, *a, *a_x, *refSpaceDer;
3920:   PetscReal      *x;
3921:   PetscInt       *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
3922:   PetscInt        dim, Nf, NfAux = 0, Nb, Nc, totDim, totDimAux = 0, cOffset = 0, cOffsetAux = 0, fOffset, e;
3923:   PetscErrorCode  ierr;

3926:   PetscFEGetSpatialDimension(fem, &dim);
3927:   PetscFEGetQuadrature(fem, &quad);
3928:   PetscFEGetDimension(fem, &Nb);
3929:   PetscFEGetNumComponents(fem, &Nc);
3930:   PetscDSGetNumFields(prob, &Nf);
3931:   PetscDSGetTotalDimension(prob, &totDim);
3932:   PetscDSGetComponentOffsets(prob, &uOff);
3933:   PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);
3934:   PetscDSGetFieldOffset(prob, field, &fOffset);
3935:   PetscDSGetResidual(prob, field, &f0_func, &f1_func);
3936:   PetscDSGetEvaluationArrays(prob, &u, &u_t, &u_x);
3937:   PetscDSGetRefCoordArrays(prob, &x, &refSpaceDer);
3938:   PetscDSGetWeakFormArrays(prob, &f0, &f1, NULL, NULL, NULL, NULL);
3939:   PetscDSGetTabulation(prob, &basisField, &basisFieldDer);
3940:   if (probAux) {
3941:     PetscDSGetNumFields(probAux, &NfAux);
3942:     PetscDSGetTotalDimension(probAux, &totDimAux);
3943:     PetscDSGetComponentOffsets(probAux, &aOff);
3944:     PetscDSGetComponentDerivativeOffsets(probAux, &aOff_x);
3945:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
3946:   }
3947:   for (e = 0; e < Ne; ++e) {
3948:     const PetscReal *quadPoints, *quadWeights;
3949:     PetscInt         Nq, q;

3951:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
3952:     PetscMemzero(f0, Nq*Nc* sizeof(PetscScalar));
3953:     PetscMemzero(f1, Nq*Nc*dim * sizeof(PetscScalar));
3954:     for (q = 0; q < Nq; ++q) {
3955:       const PetscReal *v0   = geom[e*Nq+q].v0;
3956:       const PetscReal *J    = geom[e*Nq+q].J;
3957:       const PetscReal *invJ = geom[e*Nq+q].invJ;
3958:       const PetscReal  detJ = geom[e*Nq+q].detJ;

3960:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
3961:       CoordinatesRefToReal(dim, dim, v0, J, &quadPoints[q*dim], x);
3962:       EvaluateFieldJets(prob,    PETSC_FALSE, q, invJ, &coefficients[cOffset],       &coefficients_t[cOffset], u, u_x, u_t);
3963:       EvaluateFieldJets(probAux, PETSC_FALSE, q, invJ, &coefficientsAux[cOffsetAux], NULL,                     a, a_x, NULL);
3964:       if (f0_func) f0_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, &f0[q*Nc]);
3965:       if (f1_func) f1_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, refSpaceDer);
3966:       TransformF(dim, Nc, q, invJ, detJ, quadWeights, refSpaceDer, f0, f1);
3967:     }
3968:     UpdateElementVec(dim, Nq, Nb, Nc, basisField[field], basisFieldDer[field], f0, f1, &elemVec[cOffset+fOffset]);
3969:     cOffset    += totDim;
3970:     cOffsetAux += totDimAux;
3971:   }
3972:   return(0);
3973: }

3977: PetscErrorCode PetscFEIntegrateBdResidual_Nonaffine(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
3978:                                                     const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemVec[])
3979: {
3980:   const PetscInt   debug = 0;
3981:   PetscBdPointFunc f0_func;
3982:   PetscBdPointFunc f1_func;
3983:   PetscQuadrature  quad;
3984:   PetscReal      **basisField, **basisFieldDer;
3985:   PetscScalar     *f0, *f1, *u, *u_t, *u_x, *a, *a_x, *refSpaceDer;
3986:   PetscReal       *x;
3987:   PetscInt        *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
3988:   PetscInt         dim, Nf, NfAux = 0, Nb, Nc, totDim, totDimAux, cOffset = 0, cOffsetAux = 0, fOffset, e;
3989:   PetscErrorCode   ierr;

3992:   PetscFEGetSpatialDimension(fem, &dim);
3993:   dim += 1; /* Spatial dimension is one higher than topological dimension */
3994:   PetscFEGetQuadrature(fem, &quad);
3995:   PetscFEGetDimension(fem, &Nb);
3996:   PetscFEGetNumComponents(fem, &Nc);
3997:   PetscDSGetNumFields(prob, &Nf);
3998:   PetscDSGetTotalBdDimension(prob, &totDim);
3999:   PetscDSGetComponentBdOffsets(prob, &uOff);
4000:   PetscDSGetComponentBdDerivativeOffsets(prob, &uOff_x);
4001:   PetscDSGetBdFieldOffset(prob, field, &fOffset);
4002:   PetscDSGetBdResidual(prob, field, &f0_func, &f1_func);
4003:   PetscDSGetEvaluationArrays(prob, &u, &u_t, &u_x);
4004:   PetscDSGetRefCoordArrays(prob, &x, &refSpaceDer);
4005:   PetscDSGetWeakFormArrays(prob, &f0, &f1, NULL, NULL, NULL, NULL);
4006:   PetscDSGetBdTabulation(prob, &basisField, &basisFieldDer);
4007:   if (probAux) {
4008:     PetscDSGetNumFields(probAux, &NfAux);
4009:     PetscDSGetTotalBdDimension(probAux, &totDimAux);
4010:     PetscDSGetComponentBdOffsets(probAux, &aOff);
4011:     PetscDSGetComponentBdDerivativeOffsets(probAux, &aOff_x);
4012:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
4013:   }
4014:   for (e = 0; e < Ne; ++e) {
4015:     const PetscReal *quadPoints, *quadWeights;
4016:     PetscInt         Nq, q;

4018:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
4019:     PetscMemzero(f0, Nq*Nc* sizeof(PetscScalar));
4020:     PetscMemzero(f1, Nq*Nc*dim * sizeof(PetscScalar));
4021:     for (q = 0; q < Nq; ++q) {
4022:       const PetscReal *v0   = geom[e*Nq+q].v0;
4023:       const PetscReal *n    = geom[e*Nq+q].n;
4024:       const PetscReal *J    = geom[e*Nq+q].J;
4025:       const PetscReal *invJ = geom[e*Nq+q].invJ;
4026:       const PetscReal  detJ = geom[e*Nq+q].detJ;

4028:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
4029:       CoordinatesRefToReal(dim, dim-1, v0, J, &quadPoints[q*(dim-1)], x);
4030:       EvaluateFieldJets(prob,    PETSC_TRUE, q, invJ, &coefficients[cOffset],       &coefficients_t[cOffset], u, u_x, u_t);
4031:       EvaluateFieldJets(probAux, PETSC_TRUE, q, invJ, &coefficientsAux[cOffsetAux], NULL,                     a, a_x, NULL);
4032:       if (f0_func) f0_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, n, &f0[q*Nc]);
4033:       if (f1_func) f1_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, x, n, refSpaceDer);
4034:       TransformF(dim, Nc, q, invJ, detJ, quadWeights, refSpaceDer, f0, f1);
4035:     }
4036:     UpdateElementVec(dim, Nq, Nb, Nc, basisField[field], basisFieldDer[field], f0, f1, &elemVec[cOffset+fOffset]);
4037:     cOffset    += totDim;
4038:     cOffsetAux += totDimAux;
4039:   }
4040:   return(0);
4041: }

4045: PetscErrorCode PetscFEIntegrateJacobian_Nonaffine(PetscFE fem, PetscDS prob, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFECellGeom *geom,
4046:                                                   const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemMat[])
4047: {
4048:   const PetscInt  debug      = 0;
4049:   PetscPointJac   g0_func;
4050:   PetscPointJac   g1_func;
4051:   PetscPointJac   g2_func;
4052:   PetscPointJac   g3_func;
4053:   PetscFE         fe;
4054:   PetscInt        cOffset    = 0; /* Offset into coefficients[] for element e */
4055:   PetscInt        cOffsetAux = 0; /* Offset into coefficientsAux[] for element e */
4056:   PetscInt        eOffset    = 0; /* Offset into elemMat[] for element e */
4057:   PetscInt        offsetI    = 0; /* Offset into an element vector for fieldI */
4058:   PetscInt        offsetJ    = 0; /* Offset into an element vector for fieldJ */
4059:   PetscQuadrature quad;
4060:   PetscScalar    *g0, *g1, *g2, *g3, *u, *u_t, *u_x, *a, *a_x, *refSpaceDer;
4061:   PetscReal      *x;
4062:   PetscReal     **basisField, **basisFieldDer, *basisI, *basisDerI, *basisJ, *basisDerJ;
4063:   PetscInt        NbI = 0, NcI = 0, NbJ = 0, NcJ = 0;
4064:   PetscInt       *uOff, *uOff_x, *aOff = NULL, *aOff_x = NULL;
4065:   PetscInt        dim, Nf, NfAux = 0, totDim, totDimAux, e;
4066:   PetscErrorCode  ierr;

4069:   PetscFEGetSpatialDimension(fem, &dim);
4070:   PetscFEGetQuadrature(fem, &quad);
4071:   PetscDSGetNumFields(prob, &Nf);
4072:   PetscDSGetTotalDimension(prob, &totDim);
4073:   PetscDSGetComponentOffsets(prob, &uOff);
4074:   PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);
4075:   PetscDSGetJacobian(prob, fieldI, fieldJ, &g0_func, &g1_func, &g2_func, &g3_func);
4076:   PetscDSGetEvaluationArrays(prob, &u, &u_t, &u_x);
4077:   PetscDSGetRefCoordArrays(prob, &x, &refSpaceDer);
4078:   PetscDSGetWeakFormArrays(prob, NULL, NULL, &g0, &g1, &g2, &g3);
4079:   PetscDSGetTabulation(prob, &basisField, &basisFieldDer);
4080:   PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);
4081:   PetscFEGetDimension(fe, &NbI);
4082:   PetscFEGetNumComponents(fe, &NcI);
4083:   PetscDSGetFieldOffset(prob, fieldI, &offsetI);
4084:   PetscDSGetDiscretization(prob, fieldJ, (PetscObject *) &fe);
4085:   PetscFEGetDimension(fe, &NbJ);
4086:   PetscFEGetNumComponents(fe, &NcJ);
4087:   PetscDSGetFieldOffset(prob, fieldJ, &offsetJ);
4088:   if (probAux) {
4089:     PetscDSGetNumFields(probAux, &NfAux);
4090:     PetscDSGetTotalDimension(probAux, &totDimAux);
4091:     PetscDSGetComponentOffsets(probAux, &aOff);
4092:     PetscDSGetComponentDerivativeOffsets(probAux, &aOff_x);
4093:     PetscDSGetEvaluationArrays(probAux, &a, NULL, &a_x);
4094:   }
4095:   basisI    = basisField[fieldI];
4096:   basisJ    = basisField[fieldJ];
4097:   basisDerI = basisFieldDer[fieldI];
4098:   basisDerJ = basisFieldDer[fieldJ];
4099:   /* Initialize here in case the function is not defined */
4100:   PetscMemzero(g0, NcI*NcJ * sizeof(PetscScalar));
4101:   PetscMemzero(g1, NcI*NcJ*dim * sizeof(PetscScalar));
4102:   PetscMemzero(g2, NcI*NcJ*dim * sizeof(PetscScalar));
4103:   PetscMemzero(g3, NcI*NcJ*dim*dim * sizeof(PetscScalar));
4104:   for (e = 0; e < Ne; ++e) {
4105:     const PetscReal *quadPoints, *quadWeights;
4106:     PetscInt         Nq, q;

4108:     PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);
4109:     for (q = 0; q < Nq; ++q) {
4110:       const PetscReal *v0   = geom[e*Nq+q].v0;
4111:       const PetscReal *J    = geom[e*Nq+q].J;
4112:       const PetscReal *invJ = geom[e*Nq+q].invJ;
4113:       const PetscReal  detJ = geom[e*Nq+q].detJ;
4114:       PetscInt         f, g, fc, gc, c;

4116:       if (debug) {PetscPrintf(PETSC_COMM_SELF, "  quad point %d\n", q);}
4117:       CoordinatesRefToReal(dim, dim, v0, J, &quadPoints[q*dim], x);
4118:       EvaluateFieldJets(prob,    PETSC_FALSE, q, invJ, &coefficients[cOffset],       &coefficients_t[cOffset], u, u_x, u_t);
4119:       EvaluateFieldJets(probAux, PETSC_FALSE, q, invJ, &coefficientsAux[cOffsetAux], NULL,                     a, a_x, NULL);
4120:       if (g0_func) {
4121:         PetscMemzero(g0, NcI*NcJ * sizeof(PetscScalar));
4122:         g0_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, g0);
4123:         for (c = 0; c < NcI*NcJ; ++c) {g0[c] *= detJ*quadWeights[q];}
4124:       }
4125:       if (g1_func) {
4126:         PetscInt d, d2;
4127:         PetscMemzero(refSpaceDer, NcI*NcJ*dim * sizeof(PetscScalar));
4128:         g1_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, refSpaceDer);
4129:         for (fc = 0; fc < NcI; ++fc) {
4130:           for (gc = 0; gc < NcJ; ++gc) {
4131:             for (d = 0; d < dim; ++d) {
4132:               g1[(fc*NcJ+gc)*dim+d] = 0.0;
4133:               for (d2 = 0; d2 < dim; ++d2) g1[(fc*NcJ+gc)*dim+d] += invJ[d*dim+d2]*refSpaceDer[(fc*NcJ+gc)*dim+d2];
4134:               g1[(fc*NcJ+gc)*dim+d] *= detJ*quadWeights[q];
4135:             }
4136:           }
4137:         }
4138:       }
4139:       if (g2_func) {
4140:         PetscInt d, d2;
4141:         PetscMemzero(refSpaceDer, NcI*NcJ*dim * sizeof(PetscScalar));
4142:         g2_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, refSpaceDer);
4143:         for (fc = 0; fc < NcI; ++fc) {
4144:           for (gc = 0; gc < NcJ; ++gc) {
4145:             for (d = 0; d < dim; ++d) {
4146:               g2[(fc*NcJ+gc)*dim+d] = 0.0;
4147:               for (d2 = 0; d2 < dim; ++d2) g2[(fc*NcJ+gc)*dim+d] += invJ[d*dim+d2]*refSpaceDer[(fc*NcJ+gc)*dim+d2];
4148:               g2[(fc*NcJ+gc)*dim+d] *= detJ*quadWeights[q];
4149:             }
4150:           }
4151:         }
4152:       }
4153:       if (g3_func) {
4154:         PetscInt d, d2, dp, d3;
4155:         PetscMemzero(refSpaceDer, NcI*NcJ*dim*dim * sizeof(PetscScalar));
4156:         g3_func(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, NULL, a_x, 0.0, 0.0, x, refSpaceDer);
4157:         for (fc = 0; fc < NcI; ++fc) {
4158:           for (gc = 0; gc < NcJ; ++gc) {
4159:             for (d = 0; d < dim; ++d) {
4160:               for (dp = 0; dp < dim; ++dp) {
4161:                 g3[((fc*NcJ+gc)*dim+d)*dim+dp] = 0.0;
4162:                 for (d2 = 0; d2 < dim; ++d2) {
4163:                   for (d3 = 0; d3 < dim; ++d3) {
4164:                     g3[((fc*NcJ+gc)*dim+d)*dim+dp] += invJ[d*dim+d2]*refSpaceDer[((fc*NcJ+gc)*dim+d2)*dim+d3]*invJ[dp*dim+d3];
4165:                   }
4166:                 }
4167:                 g3[((fc*NcJ+gc)*dim+d)*dim+dp] *= detJ*quadWeights[q];
4168:               }
4169:             }
4170:           }
4171:         }
4172:       }

4174:       for (f = 0; f < NbI; ++f) {
4175:         for (fc = 0; fc < NcI; ++fc) {
4176:           const PetscInt fidx = f*NcI+fc; /* Test function basis index */
4177:           const PetscInt i    = offsetI+fidx; /* Element matrix row */
4178:           for (g = 0; g < NbJ; ++g) {
4179:             for (gc = 0; gc < NcJ; ++gc) {
4180:               const PetscInt gidx = g*NcJ+gc; /* Trial function basis index */
4181:               const PetscInt j    = offsetJ+gidx; /* Element matrix column */
4182:               const PetscInt fOff = eOffset+i*totDim+j;
4183:               PetscInt       d, d2;

4185:               elemMat[fOff] += basisI[q*NbI*NcI+fidx]*g0[fc*NcJ+gc]*basisJ[q*NbJ*NcJ+gidx];
4186:               for (d = 0; d < dim; ++d) {
4187:                 elemMat[fOff] += basisI[q*NbI*NcI+fidx]*g1[(fc*NcJ+gc)*dim+d]*basisDerJ[(q*NbJ*NcJ+gidx)*dim+d];
4188:                 elemMat[fOff] += basisDerI[(q*NbI*NcI+fidx)*dim+d]*g2[(fc*NcJ+gc)*dim+d]*basisJ[q*NbJ*NcJ+gidx];
4189:                 for (d2 = 0; d2 < dim; ++d2) {
4190:                   elemMat[fOff] += basisDerI[(q*NbI*NcI+fidx)*dim+d]*g3[((fc*NcJ+gc)*dim+d)*dim+d2]*basisDerJ[(q*NbJ*NcJ+gidx)*dim+d2];
4191:                 }
4192:               }
4193:             }
4194:           }
4195:         }
4196:       }
4197:     }
4198:     if (debug > 1) {
4199:       PetscInt fc, f, gc, g;

4201:       PetscPrintf(PETSC_COMM_SELF, "Element matrix for fields %d and %d\n", fieldI, fieldJ);
4202:       for (fc = 0; fc < NcI; ++fc) {
4203:         for (f = 0; f < NbI; ++f) {
4204:           const PetscInt i = offsetI + f*NcI+fc;
4205:           for (gc = 0; gc < NcJ; ++gc) {
4206:             for (g = 0; g < NbJ; ++g) {
4207:               const PetscInt j = offsetJ + g*NcJ+gc;
4208:               PetscPrintf(PETSC_COMM_SELF, "    elemMat[%d,%d,%d,%d]: %g\n", f, fc, g, gc, PetscRealPart(elemMat[eOffset+i*totDim+j]));
4209:             }
4210:           }
4211:           PetscPrintf(PETSC_COMM_SELF, "\n");
4212:         }
4213:       }
4214:     }
4215:     cOffset    += totDim;
4216:     cOffsetAux += totDimAux;
4217:     eOffset    += PetscSqr(totDim);
4218:   }
4219:   return(0);
4220: }

4224: PetscErrorCode PetscFEInitialize_Nonaffine(PetscFE fem)
4225: {
4227:   fem->ops->setfromoptions          = NULL;
4228:   fem->ops->setup                   = PetscFESetUp_Basic;
4229:   fem->ops->view                    = NULL;
4230:   fem->ops->destroy                 = PetscFEDestroy_Nonaffine;
4231:   fem->ops->getdimension            = PetscFEGetDimension_Basic;
4232:   fem->ops->gettabulation           = PetscFEGetTabulation_Basic;
4233:   fem->ops->integrateresidual       = PetscFEIntegrateResidual_Nonaffine;
4234:   fem->ops->integratebdresidual     = PetscFEIntegrateBdResidual_Nonaffine;
4235:   fem->ops->integratejacobianaction = NULL/* PetscFEIntegrateJacobianAction_Nonaffine */;
4236:   fem->ops->integratejacobian       = PetscFEIntegrateJacobian_Nonaffine;
4237:   return(0);
4238: }

4240: /*MC
4241:   PETSCFENONAFFINE = "nonaffine" - A PetscFE object that integrates with basic tiling and no vectorization for non-affine mappings

4243:   Level: intermediate

4245: .seealso: PetscFEType, PetscFECreate(), PetscFESetType()
4246: M*/

4250: PETSC_EXTERN PetscErrorCode PetscFECreate_Nonaffine(PetscFE fem)
4251: {
4252:   PetscFE_Nonaffine *na;
4253:   PetscErrorCode     ierr;

4257:   PetscNewLog(fem, &na);
4258:   fem->data = na;

4260:   PetscFEInitialize_Nonaffine(fem);
4261:   return(0);
4262: }

4264: #ifdef PETSC_HAVE_OPENCL

4268: PetscErrorCode PetscFEDestroy_OpenCL(PetscFE fem)
4269: {
4270:   PetscFE_OpenCL *ocl = (PetscFE_OpenCL *) fem->data;
4271:   PetscErrorCode  ierr;

4274:   clReleaseCommandQueue(ocl->queue_id);
4275:   ocl->queue_id = 0;
4276:   clReleaseContext(ocl->ctx_id);
4277:   ocl->ctx_id = 0;
4278:   PetscFree(ocl);
4279:   return(0);
4280: }

4282: #define STRING_ERROR_CHECK(MSG) do { string_tail += count; if (string_tail == end_of_buffer) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, MSG);} while(0)
4283: enum {LAPLACIAN = 0, ELASTICITY = 1};

4287: /* dim     Number of spatial dimensions:          2                   */
4288: /* N_b     Number of basis functions:             generated           */
4289: /* N_{bt}  Number of total basis functions:       N_b * N_{comp}      */
4290: /* N_q     Number of quadrature points:           generated           */
4291: /* N_{bs}  Number of block cells                  LCM(N_b, N_q)       */
4292: /* N_{bst} Number of block cell components        LCM(N_{bt}, N_q)    */
4293: /* N_{bl}  Number of concurrent blocks            generated           */
4294: /* N_t     Number of threads:                     N_{bl} * N_{bs}     */
4295: /* N_{cbc} Number of concurrent basis      cells: N_{bl} * N_q        */
4296: /* N_{cqc} Number of concurrent quadrature cells: N_{bl} * N_b        */
4297: /* N_{sbc} Number of serial     basis      cells: N_{bs} / N_q        */
4298: /* N_{sqc} Number of serial     quadrature cells: N_{bs} / N_b        */
4299: /* N_{cb}  Number of serial cell batches:         input               */
4300: /* N_c     Number of total cells:                 N_{cb}*N_{t}/N_{comp} */
4301: PetscErrorCode PetscFEOpenCLGenerateIntegrationCode(PetscFE fem, char **string_buffer, PetscInt buffer_length, PetscBool useAux, PetscInt N_bl)
4302: {
4303:   PetscFE_OpenCL *ocl = (PetscFE_OpenCL *) fem->data;
4304:   PetscQuadrature q;
4305:   char           *string_tail   = *string_buffer;
4306:   char           *end_of_buffer = *string_buffer + buffer_length;
4307:   char            float_str[]   = "float", double_str[]  = "double";
4308:   char           *numeric_str   = &(float_str[0]);
4309:   PetscInt        op            = ocl->op;
4310:   PetscBool       useField      = PETSC_FALSE;
4311:   PetscBool       useFieldDer   = PETSC_TRUE;
4312:   PetscBool       useFieldAux   = useAux;
4313:   PetscBool       useFieldDerAux= PETSC_FALSE;
4314:   PetscBool       useF0         = PETSC_TRUE;
4315:   PetscBool       useF1         = PETSC_TRUE;
4316:   PetscReal      *basis, *basisDer;
4317:   PetscInt        dim, N_b, N_c, N_q, N_t, p, d, b, c;
4318:   size_t          count;
4319:   PetscErrorCode  ierr;

4322:   PetscFEGetSpatialDimension(fem, &dim);
4323:   PetscFEGetDimension(fem, &N_b);
4324:   PetscFEGetNumComponents(fem, &N_c);
4325:   PetscFEGetQuadrature(fem, &q);
4326:   N_q  = q->numPoints;
4327:   N_t  = N_b * N_c * N_q * N_bl;
4328:   /* Enable device extension for double precision */
4329:   if (ocl->realType == PETSC_DOUBLE) {
4330:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4331: "#if defined(cl_khr_fp64)\n"
4332: "#  pragma OPENCL EXTENSION cl_khr_fp64: enable\n"
4333: "#elif defined(cl_amd_fp64)\n"
4334: "#  pragma OPENCL EXTENSION cl_amd_fp64: enable\n"
4335: "#endif\n",
4336:                               &count);STRING_ERROR_CHECK("Message to short");
4337:     numeric_str  = &(double_str[0]);
4338:   }
4339:   /* Kernel API */
4340:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4341: "\n"
4342: "__kernel void integrateElementQuadrature(int N_cb, __global %s *coefficients, __global %s *coefficientsAux, __global %s *jacobianInverses, __global %s *jacobianDeterminants, __global %s *elemVec)\n"
4343: "{\n",
4344:                        &count, numeric_str, numeric_str, numeric_str, numeric_str, numeric_str);STRING_ERROR_CHECK("Message to short");
4345:   /* Quadrature */
4346:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4347: "  /* Quadrature points\n"
4348: "   - (x1,y1,x2,y2,...) */\n"
4349: "  const %s points[%d] = {\n",
4350:                        &count, numeric_str, N_q*dim);STRING_ERROR_CHECK("Message to short");
4351:   for (p = 0; p < N_q; ++p) {
4352:     for (d = 0; d < dim; ++d) {
4353:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "%g,\n", &count, q->points[p*dim+d]);STRING_ERROR_CHECK("Message to short");
4354:     }
4355:   }
4356:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "};\n", &count);STRING_ERROR_CHECK("Message to short");
4357:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4358: "  /* Quadrature weights\n"
4359: "   - (v1,v2,...) */\n"
4360: "  const %s weights[%d] = {\n",
4361:                        &count, numeric_str, N_q);STRING_ERROR_CHECK("Message to short");
4362:   for (p = 0; p < N_q; ++p) {
4363:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "%g,\n", &count, q->weights[p]);STRING_ERROR_CHECK("Message to short");
4364:   }
4365:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "};\n", &count);STRING_ERROR_CHECK("Message to short");
4366:   /* Basis Functions */
4367:   PetscFEGetDefaultTabulation(fem, &basis, &basisDer, NULL);
4368:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4369: "  /* Nodal basis function evaluations\n"
4370: "    - basis component is fastest varying, the basis function, then point */\n"
4371: "  const %s Basis[%d] = {\n",
4372:                        &count, numeric_str, N_q*N_b*N_c);STRING_ERROR_CHECK("Message to short");
4373:   for (p = 0; p < N_q; ++p) {
4374:     for (b = 0; b < N_b; ++b) {
4375:       for (c = 0; c < N_c; ++c) {
4376:         PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "%g,\n", &count, basis[(p*N_b + b)*N_c + c]);STRING_ERROR_CHECK("Message to short");
4377:       }
4378:     }
4379:   }
4380:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "};\n", &count);STRING_ERROR_CHECK("Message to short");
4381:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4382: "\n"
4383: "  /* Nodal basis function derivative evaluations,\n"
4384: "      - derivative direction is fastest varying, then basis component, then basis function, then point */\n"
4385: "  const %s%d BasisDerivatives[%d] = {\n",
4386:                        &count, numeric_str, dim, N_q*N_b*N_c);STRING_ERROR_CHECK("Message to short");
4387:   for (p = 0; p < N_q; ++p) {
4388:     for (b = 0; b < N_b; ++b) {
4389:       for (c = 0; c < N_c; ++c) {
4390:         PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "(%s%d)(", &count, numeric_str, dim);STRING_ERROR_CHECK("Message to short");
4391:         for (d = 0; d < dim; ++d) {
4392:           if (d > 0) {
4393:             PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, ", %g", &count, basisDer[((p*N_b + b)*dim + d)*N_c + c]);STRING_ERROR_CHECK("Message to short");
4394:           } else {
4395:             PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "%g", &count, basisDer[((p*N_b + b)*dim + d)*N_c + c]);STRING_ERROR_CHECK("Message to short");
4396:           }
4397:         }
4398:         PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "),\n", &count);STRING_ERROR_CHECK("Message to short");
4399:       }
4400:     }
4401:   }
4402:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "};\n", &count);STRING_ERROR_CHECK("Message to short");
4403:   /* Sizes */
4404:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4405: "  const int dim    = %d;                           // The spatial dimension\n"
4406: "  const int N_bl   = %d;                           // The number of concurrent blocks\n"
4407: "  const int N_b    = %d;                           // The number of basis functions\n"
4408: "  const int N_comp = %d;                           // The number of basis function components\n"
4409: "  const int N_bt   = N_b*N_comp;                    // The total number of scalar basis functions\n"
4410: "  const int N_q    = %d;                           // The number of quadrature points\n"
4411: "  const int N_bst  = N_bt*N_q;                      // The block size, LCM(N_b*N_comp, N_q), Notice that a block is not processed simultaneously\n"
4412: "  const int N_t    = N_bst*N_bl;                    // The number of threads, N_bst * N_bl\n"
4413: "  const int N_bc   = N_t/N_comp;                    // The number of cells per batch (N_b*N_q*N_bl)\n"
4414: "  const int N_sbc  = N_bst / (N_q * N_comp);\n"
4415: "  const int N_sqc  = N_bst / N_bt;\n"
4416: "  /*const int N_c    = N_cb * N_bc;*/\n"
4417: "\n"
4418: "  /* Calculated indices */\n"
4419: "  /*const int tidx    = get_local_id(0) + get_local_size(0)*get_local_id(1);*/\n"
4420: "  const int tidx    = get_local_id(0);\n"
4421: "  const int blidx   = tidx / N_bst;                  // Block number for this thread\n"
4422: "  const int bidx    = tidx %% N_bt;                   // Basis function mapped to this thread\n"
4423: "  const int cidx    = tidx %% N_comp;                 // Basis component mapped to this thread\n"
4424: "  const int qidx    = tidx %% N_q;                    // Quadrature point mapped to this thread\n"
4425: "  const int blbidx  = tidx %% N_q + blidx*N_q;        // Cell mapped to this thread in the basis phase\n"
4426: "  const int blqidx  = tidx %% N_b + blidx*N_b;        // Cell mapped to this thread in the quadrature phase\n"
4427: "  const int gidx    = get_group_id(1)*get_num_groups(0) + get_group_id(0);\n"
4428: "  const int Goffset = gidx*N_cb*N_bc;\n",
4429:                             &count, dim, N_bl, N_b, N_c, N_q);STRING_ERROR_CHECK("Message to short");
4430:   /* Local memory */
4431:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4432: "\n"
4433: "  /* Quadrature data */\n"
4434: "  %s                w;                   // $w_q$, Quadrature weight at $x_q$\n"
4435: "  __local %s         phi_i[%d];    //[N_bt*N_q];  // $\\phi_i(x_q)$, Value of the basis function $i$ at $x_q$\n"
4436: "  __local %s%d       phiDer_i[%d]; //[N_bt*N_q];  // $\\frac{\\partial\\phi_i(x_q)}{\\partial x_d}$, Value of the derivative of basis function $i$ in direction $x_d$ at $x_q$\n"
4437: "  /* Geometric data */\n"
4438: "  __local %s        detJ[%d]; //[N_t];           // $|J(x_q)|$, Jacobian determinant at $x_q$\n"
4439: "  __local %s        invJ[%d];//[N_t*dim*dim];   // $J^{-1}(x_q)$, Jacobian inverse at $x_q$\n",
4440:                             &count, numeric_str, numeric_str, N_b*N_c*N_q, numeric_str, dim, N_b*N_c*N_q, numeric_str, N_t,
4441:                             numeric_str, N_t*dim*dim, numeric_str, N_t*N_b*N_c);STRING_ERROR_CHECK("Message to short");
4442:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4443: "  /* FEM data */\n"
4444: "  __local %s        u_i[%d]; //[N_t*N_bt];       // Coefficients $u_i$ of the field $u|_{\\mathcal{T}} = \\sum_i u_i \\phi_i$\n",
4445:                             &count, numeric_str, N_t*N_b*N_c);STRING_ERROR_CHECK("Message to short");
4446:   if (useAux) {
4447:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4448: "  __local %s        a_i[%d]; //[N_t];            // Coefficients $a_i$ of the auxiliary field $a|_{\\mathcal{T}} = \\sum_i a_i \\phi^R_i$\n",
4449:                             &count, numeric_str, N_t);STRING_ERROR_CHECK("Message to short");
4450:   }
4451:   if (useF0) {
4452:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4453: "  /* Intermediate calculations */\n"
4454: "  __local %s         f_0[%d]; //[N_t*N_sqc];      // $f_0(u(x_q), \\nabla u(x_q)) |J(x_q)| w_q$\n",
4455:                               &count, numeric_str, N_t*N_q);STRING_ERROR_CHECK("Message to short");
4456:   }
4457:   if (useF1) {
4458:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4459: "  __local %s%d       f_1[%d]; //[N_t*N_sqc];      // $f_1(u(x_q), \\nabla u(x_q)) |J(x_q)| w_q$\n",
4460:                               &count, numeric_str, dim, N_t*N_q);STRING_ERROR_CHECK("Message to short");
4461:   }
4462:   /* TODO: If using elasticity, put in mu/lambda coefficients */
4463:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4464: "  /* Output data */\n"
4465: "  %s                e_i;                 // Coefficient $e_i$ of the residual\n\n",
4466:                             &count, numeric_str);STRING_ERROR_CHECK("Message to short");
4467:   /* One-time loads */
4468:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4469: "  /* These should be generated inline */\n"
4470: "  /* Load quadrature weights */\n"
4471: "  w = weights[qidx];\n"
4472: "  /* Load basis tabulation \\phi_i for this cell */\n"
4473: "  if (tidx < N_bt*N_q) {\n"
4474: "    phi_i[tidx]    = Basis[tidx];\n"
4475: "    phiDer_i[tidx] = BasisDerivatives[tidx];\n"
4476: "  }\n\n",
4477:                        &count);STRING_ERROR_CHECK("Message to short");
4478:   /* Batch loads */
4479:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4480: "  for (int batch = 0; batch < N_cb; ++batch) {\n"
4481: "    /* Load geometry */\n"
4482: "    detJ[tidx] = jacobianDeterminants[Goffset+batch*N_bc+tidx];\n"
4483: "    for (int n = 0; n < dim*dim; ++n) {\n"
4484: "      const int offset = n*N_t;\n"
4485: "      invJ[offset+tidx] = jacobianInverses[(Goffset+batch*N_bc)*dim*dim+offset+tidx];\n"
4486: "    }\n"
4487: "    /* Load coefficients u_i for this cell */\n"
4488: "    for (int n = 0; n < N_bt; ++n) {\n"
4489: "      const int offset = n*N_t;\n"
4490: "      u_i[offset+tidx] = coefficients[(Goffset*N_bt)+batch*N_t*N_b+offset+tidx];\n"
4491: "    }\n",
4492:                        &count);STRING_ERROR_CHECK("Message to short");
4493:   if (useAux) {
4494:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4495: "    /* Load coefficients a_i for this cell */\n"
4496: "    /* TODO: This should not be N_t here, it should be N_bc*N_comp_aux */\n"
4497: "    a_i[tidx] = coefficientsAux[Goffset+batch*N_t+tidx];\n",
4498:                             &count);STRING_ERROR_CHECK("Message to short");
4499:   }
4500:   /* Quadrature phase */
4501:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4502: "    barrier(CLK_LOCAL_MEM_FENCE);\n"
4503: "\n"
4504: "    /* Map coefficients to values at quadrature points */\n"
4505: "    for (int c = 0; c < N_sqc; ++c) {\n"
4506: "      const int cell          = c*N_bl*N_b + blqidx;\n"
4507: "      const int fidx          = (cell*N_q + qidx)*N_comp + cidx;\n",
4508:                        &count);STRING_ERROR_CHECK("Message to short");
4509:   if (useField) {
4510:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4511: "      %s  u[%d]; //[N_comp];     // $u(x_q)$, Value of the field at $x_q$\n",
4512:                               &count, numeric_str, N_c);STRING_ERROR_CHECK("Message to short");
4513:   }
4514:   if (useFieldDer) {
4515:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4516: "      %s%d   gradU[%d]; //[N_comp]; // $\\nabla u(x_q)$, Value of the field gradient at $x_q$\n",
4517:                               &count, numeric_str, dim, N_c);STRING_ERROR_CHECK("Message to short");
4518:   }
4519:   if (useFieldAux) {
4520:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4521: "      %s  a[%d]; //[1];     // $a(x_q)$, Value of the auxiliary fields at $x_q$\n",
4522:                               &count, numeric_str, 1);STRING_ERROR_CHECK("Message to short");
4523:   }
4524:   if (useFieldDerAux) {
4525:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4526: "      %s%d   gradA[%d]; //[1]; // $\\nabla a(x_q)$, Value of the auxiliary field gradient at $x_q$\n",
4527:                               &count, numeric_str, dim, 1);STRING_ERROR_CHECK("Message to short");
4528:   }
4529:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4530: "\n"
4531: "      for (int comp = 0; comp < N_comp; ++comp) {\n",
4532:                             &count);STRING_ERROR_CHECK("Message to short");
4533:   if (useField) {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "        u[comp] = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");}
4534:   if (useFieldDer) {
4535:     switch (dim) {
4536:     case 1:
4537:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "        gradU[comp].x = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4538:     case 2:
4539:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "        gradU[comp].x = 0.0; gradU[comp].y = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4540:     case 3:
4541:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "        gradU[comp].x = 0.0; gradU[comp].y = 0.0; gradU[comp].z = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4542:     }
4543:   }
4544:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4545: "      }\n",
4546:                             &count);STRING_ERROR_CHECK("Message to short");
4547:   if (useFieldAux) {
4548:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      a[0] = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");
4549:   }
4550:   if (useFieldDerAux) {
4551:     switch (dim) {
4552:     case 1:
4553:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      gradA[0].x = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4554:     case 2:
4555:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      gradA[0].x = 0.0; gradA[0].y = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4556:     case 3:
4557:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      gradA[0].x = 0.0; gradA[0].y = 0.0; gradA[0].z = 0.0;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4558:     }
4559:   }
4560:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4561: "      /* Get field and derivatives at this quadrature point */\n"
4562: "      for (int i = 0; i < N_b; ++i) {\n"
4563: "        for (int comp = 0; comp < N_comp; ++comp) {\n"
4564: "          const int b    = i*N_comp+comp;\n"
4565: "          const int pidx = qidx*N_bt + b;\n"
4566: "          const int uidx = cell*N_bt + b;\n"
4567: "          %s%d   realSpaceDer;\n\n",
4568:                             &count, numeric_str, dim);STRING_ERROR_CHECK("Message to short");
4569:   if (useField) {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,"          u[comp] += u_i[uidx]*phi_i[pidx];\n", &count);STRING_ERROR_CHECK("Message to short");}
4570:   if (useFieldDer) {
4571:     switch (dim) {
4572:     case 2:
4573:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4574: "          realSpaceDer.x = invJ[cell*dim*dim+0*dim+0]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+0]*phiDer_i[pidx].y;\n"
4575: "          gradU[comp].x += u_i[uidx]*realSpaceDer.x;\n"
4576: "          realSpaceDer.y = invJ[cell*dim*dim+0*dim+1]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+1]*phiDer_i[pidx].y;\n"
4577: "          gradU[comp].y += u_i[uidx]*realSpaceDer.y;\n",
4578:                            &count);STRING_ERROR_CHECK("Message to short");break;
4579:     case 3:
4580:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4581: "          realSpaceDer.x = invJ[cell*dim*dim+0*dim+0]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+0]*phiDer_i[pidx].y + invJ[cell*dim*dim+2*dim+0]*phiDer_i[pidx].z;\n"
4582: "          gradU[comp].x += u_i[uidx]*realSpaceDer.x;\n"
4583: "          realSpaceDer.y = invJ[cell*dim*dim+0*dim+1]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+1]*phiDer_i[pidx].y + invJ[cell*dim*dim+2*dim+1]*phiDer_i[pidx].z;\n"
4584: "          gradU[comp].y += u_i[uidx]*realSpaceDer.y;\n"
4585: "          realSpaceDer.z = invJ[cell*dim*dim+0*dim+2]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+2]*phiDer_i[pidx].y + invJ[cell*dim*dim+2*dim+2]*phiDer_i[pidx].z;\n"
4586: "          gradU[comp].z += u_i[uidx]*realSpaceDer.z;\n",
4587:                            &count);STRING_ERROR_CHECK("Message to short");break;
4588:     }
4589:   }
4590:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4591: "        }\n"
4592: "      }\n",
4593:                             &count);STRING_ERROR_CHECK("Message to short");
4594:   if (useFieldAux) {
4595:     PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,"          a[0] += a_i[cell];\n", &count);STRING_ERROR_CHECK("Message to short");
4596:   }
4597:   /* Calculate residual at quadrature points: Should be generated by an weak form egine */
4598:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4599: "      /* Process values at quadrature points */\n",
4600:                             &count);STRING_ERROR_CHECK("Message to short");
4601:   switch (op) {
4602:   case LAPLACIAN:
4603:     if (useF0) {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      f_0[fidx] = 4.0;\n", &count);STRING_ERROR_CHECK("Message to short");}
4604:     if (useF1) {
4605:       if (useAux) {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      f_1[fidx] = a[0]*gradU[cidx];\n", &count);STRING_ERROR_CHECK("Message to short");}
4606:       else        {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      f_1[fidx] = gradU[cidx];\n", &count);STRING_ERROR_CHECK("Message to short");}
4607:     }
4608:     break;
4609:   case ELASTICITY:
4610:     if (useF0) {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail, "      f_0[fidx] = 4.0;\n", &count);STRING_ERROR_CHECK("Message to short");}
4611:     if (useF1) {
4612:     switch (dim) {
4613:     case 2:
4614:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4615: "      switch (cidx) {\n"
4616: "      case 0:\n"
4617: "        f_1[fidx].x = lambda*(gradU[0].x + gradU[1].y) + mu*(gradU[0].x + gradU[0].x);\n"
4618: "        f_1[fidx].y = lambda*(gradU[0].x + gradU[1].y) + mu*(gradU[0].y + gradU[1].x);\n"
4619: "        break;\n"
4620: "      case 1:\n"
4621: "        f_1[fidx].x = lambda*(gradU[0].x + gradU[1].y) + mu*(gradU[1].x + gradU[0].y);\n"
4622: "        f_1[fidx].y = lambda*(gradU[0].x + gradU[1].y) + mu*(gradU[1].y + gradU[1].y);\n"
4623: "      }\n",
4624:                            &count);STRING_ERROR_CHECK("Message to short");break;
4625:     case 3:
4626:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4627: "      switch (cidx) {\n"
4628: "      case 0:\n"
4629: "        f_1[fidx].x = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[0].x + gradU[0].x);\n"
4630: "        f_1[fidx].y = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[0].y + gradU[1].x);\n"
4631: "        f_1[fidx].z = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[0].z + gradU[2].x);\n"
4632: "        break;\n"
4633: "      case 1:\n"
4634: "        f_1[fidx].x = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[1].x + gradU[0].y);\n"
4635: "        f_1[fidx].y = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[1].y + gradU[1].y);\n"
4636: "        f_1[fidx].z = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[1].y + gradU[2].y);\n"
4637: "        break;\n"
4638: "      case 2:\n"
4639: "        f_1[fidx].x = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[2].x + gradU[0].z);\n"
4640: "        f_1[fidx].y = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[2].y + gradU[1].z);\n"
4641: "        f_1[fidx].z = lambda*(gradU[0].x + gradU[1].y + gradU[2].z) + mu*(gradU[2].y + gradU[2].z);\n"
4642: "      }\n",
4643:                            &count);STRING_ERROR_CHECK("Message to short");break;
4644:     }}
4645:     break;
4646:   default:
4647:     SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_SUP, "PDE operator %d is not supported", op);
4648:   }
4649:   if (useF0) {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,"      f_0[fidx] *= detJ[cell]*w;\n", &count);STRING_ERROR_CHECK("Message to short");}
4650:   if (useF1) {
4651:     switch (dim) {
4652:     case 1:
4653:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,"      f_1[fidx].x *= detJ[cell]*w;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4654:     case 2:
4655:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,"      f_1[fidx].x *= detJ[cell]*w; f_1[fidx].y *= detJ[cell]*w;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4656:     case 3:
4657:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,"      f_1[fidx].x *= detJ[cell]*w; f_1[fidx].y *= detJ[cell]*w; f_1[fidx].z *= detJ[cell]*w;\n", &count);STRING_ERROR_CHECK("Message to short");break;
4658:     }
4659:   }
4660:   /* Thread transpose */
4661:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4662: "    }\n\n"
4663: "    /* ==== TRANSPOSE THREADS ==== */\n"
4664: "    barrier(CLK_LOCAL_MEM_FENCE);\n\n",
4665:                        &count);STRING_ERROR_CHECK("Message to short");
4666:   /* Basis phase */
4667:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4668: "    /* Map values at quadrature points to coefficients */\n"
4669: "    for (int c = 0; c < N_sbc; ++c) {\n"
4670: "      const int cell = c*N_bl*N_q + blbidx; /* Cell number in batch */\n"
4671: "\n"
4672: "      e_i = 0.0;\n"
4673: "      for (int q = 0; q < N_q; ++q) {\n"
4674: "        const int pidx = q*N_bt + bidx;\n"
4675: "        const int fidx = (cell*N_q + q)*N_comp + cidx;\n"
4676: "        %s%d   realSpaceDer;\n\n",
4677:                        &count, numeric_str, dim);STRING_ERROR_CHECK("Message to short");

4679:   if (useF0) {PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,"        e_i += phi_i[pidx]*f_0[fidx];\n", &count);STRING_ERROR_CHECK("Message to short");}
4680:   if (useF1) {
4681:     switch (dim) {
4682:     case 2:
4683:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4684: "        realSpaceDer.x = invJ[cell*dim*dim+0*dim+0]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+0]*phiDer_i[pidx].y;\n"
4685: "        e_i           += realSpaceDer.x*f_1[fidx].x;\n"
4686: "        realSpaceDer.y = invJ[cell*dim*dim+0*dim+1]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+1]*phiDer_i[pidx].y;\n"
4687: "        e_i           += realSpaceDer.y*f_1[fidx].y;\n",
4688:                            &count);STRING_ERROR_CHECK("Message to short");break;
4689:     case 3:
4690:       PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4691: "        realSpaceDer.x = invJ[cell*dim*dim+0*dim+0]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+0]*phiDer_i[pidx].y + invJ[cell*dim*dim+2*dim+0]*phiDer_i[pidx].z;\n"
4692: "        e_i           += realSpaceDer.x*f_1[fidx].x;\n"
4693: "        realSpaceDer.y = invJ[cell*dim*dim+0*dim+1]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+1]*phiDer_i[pidx].y + invJ[cell*dim*dim+2*dim+1]*phiDer_i[pidx].z;\n"
4694: "        e_i           += realSpaceDer.y*f_1[fidx].y;\n"
4695: "        realSpaceDer.z = invJ[cell*dim*dim+0*dim+2]*phiDer_i[pidx].x + invJ[cell*dim*dim+1*dim+2]*phiDer_i[pidx].y + invJ[cell*dim*dim+2*dim+2]*phiDer_i[pidx].z;\n"
4696: "        e_i           += realSpaceDer.z*f_1[fidx].z;\n",
4697:                            &count);STRING_ERROR_CHECK("Message to short");break;
4698:     }
4699:   }
4700:   PetscSNPrintfCount(string_tail, end_of_buffer - string_tail,
4701: "      }\n"
4702: "      /* Write element vector for N_{cbc} cells at a time */\n"
4703: "      elemVec[(Goffset + batch*N_bc + c*N_bl*N_q)*N_bt + tidx] = e_i;\n"
4704: "    }\n"
4705: "    /* ==== Could do one write per batch ==== */\n"
4706: "  }\n"
4707: "  return;\n"
4708: "}\n",
4709:                        &count);STRING_ERROR_CHECK("Message to short");
4710:   return(0);
4711: }

4715: PetscErrorCode PetscFEOpenCLGetIntegrationKernel(PetscFE fem, PetscBool useAux, cl_program *ocl_prog, cl_kernel *ocl_kernel)
4716: {
4717:   PetscFE_OpenCL *ocl = (PetscFE_OpenCL *) fem->data;
4718:   PetscInt        dim, N_bl;
4719:   PetscBool       flg;
4720:   char           *buffer;
4721:   size_t          len;
4722:   char            errMsg[8192];
4723:   cl_int          ierr2;
4724:   PetscErrorCode  ierr;

4727:   PetscFEGetSpatialDimension(fem, &dim);
4728:   PetscMalloc1(8192, &buffer);
4729:   PetscFEGetTileSizes(fem, NULL, &N_bl, NULL, NULL);
4730:   PetscFEOpenCLGenerateIntegrationCode(fem, &buffer, 8192, useAux, N_bl);
4731:   PetscOptionsHasName(fem->hdr.prefix, "-petscfe_opencl_kernel_print", &flg);
4732:   if (flg) {PetscPrintf(PetscObjectComm((PetscObject) fem), "OpenCL FE Integration Kernel:\n%s\n", buffer);}
4733:   len  = strlen(buffer);
4734:   *ocl_prog = clCreateProgramWithSource(ocl->ctx_id, 1, (const char **) &buffer, &len, &ierr2);CHKERRQ(ierr2);
4735:   clBuildProgram(*ocl_prog, 0, NULL, NULL, NULL, NULL);
4736:   if (ierr != CL_SUCCESS) {
4737:     clGetProgramBuildInfo(*ocl_prog, ocl->dev_id, CL_PROGRAM_BUILD_LOG, 8192*sizeof(char), &errMsg, NULL);
4738:     SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Build failed! Log:\n %s", errMsg);
4739:   }
4740:   PetscFree(buffer);
4741:   *ocl_kernel = clCreateKernel(*ocl_prog, "integrateElementQuadrature", &ierr);
4742:   return(0);
4743: }

4747: PetscErrorCode PetscFEOpenCLCalculateGrid(PetscFE fem, PetscInt N, PetscInt blockSize, size_t *x, size_t *y, size_t *z)
4748: {
4749:   const PetscInt Nblocks = N/blockSize;

4752:   if (N % blockSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Invalid block size %d for %d elements", blockSize, N);
4753:   *z = 1;
4754:   for (*x = (size_t) (PetscSqrtReal(Nblocks) + 0.5); *x > 0; --*x) {
4755:     *y = Nblocks / *x;
4756:     if (*x * *y == Nblocks) break;
4757:   }
4758:   if (*x * *y != Nblocks) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Could not find partition for %d with block size %d", N, blockSize);
4759:   return(0);
4760: }

4764: PetscErrorCode PetscFEOpenCLLogResidual(PetscFE fem, PetscLogDouble time, PetscLogDouble flops)
4765: {
4766:   PetscFE_OpenCL   *ocl = (PetscFE_OpenCL *) fem->data;
4767:   PetscStageLog     stageLog;
4768:   PetscEventPerfLog eventLog = NULL;
4769:   PetscInt          stage;
4770:   PetscErrorCode    ierr;

4773:   PetscLogGetStageLog(&stageLog);
4774:   PetscStageLogGetCurrent(stageLog, &stage);
4775:   PetscStageLogGetEventPerfLog(stageLog, stage, &eventLog);
4776:     /* Log performance info */
4777:   eventLog->eventInfo[ocl->residualEvent].count++;
4778:   eventLog->eventInfo[ocl->residualEvent].time  += time;
4779:   eventLog->eventInfo[ocl->residualEvent].flops += flops;
4780:   return(0);
4781: }

4785: PetscErrorCode PetscFEIntegrateResidual_OpenCL(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
4786:                                                const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemVec[])
4787: {
4788:   /* Nbc = batchSize */
4789:   PetscFE_OpenCL   *ocl = (PetscFE_OpenCL *) fem->data;
4790:   PetscPointFunc    f0_func;
4791:   PetscPointFunc    f1_func;
4792:   PetscQuadrature   q;
4793:   PetscInt          dim;
4794:   PetscInt          N_b;    /* The number of basis functions */
4795:   PetscInt          N_comp; /* The number of basis function components */
4796:   PetscInt          N_bt;   /* The total number of scalar basis functions */
4797:   PetscInt          N_q;    /* The number of quadrature points */
4798:   PetscInt          N_bst;  /* The block size, LCM(N_bt, N_q), Notice that a block is not process simultaneously */
4799:   PetscInt          N_t;    /* The number of threads, N_bst * N_bl */
4800:   PetscInt          N_bl;   /* The number of blocks */
4801:   PetscInt          N_bc;   /* The batch size, N_bl*N_q*N_b */
4802:   PetscInt          N_cb;   /* The number of batches */
4803:   PetscInt          numFlops, f0Flops = 0, f1Flops = 0;
4804:   PetscBool         useAux      = probAux ? PETSC_TRUE : PETSC_FALSE;
4805:   PetscBool         useField    = PETSC_FALSE;
4806:   PetscBool         useFieldDer = PETSC_TRUE;
4807:   PetscBool         useF0       = PETSC_TRUE;
4808:   PetscBool         useF1       = PETSC_TRUE;
4809:   /* OpenCL variables */
4810:   cl_program        ocl_prog;
4811:   cl_kernel         ocl_kernel;
4812:   cl_event          ocl_ev;         /* The event for tracking kernel execution */
4813:   cl_ulong          ns_start;       /* Nanoseconds counter on GPU at kernel start */
4814:   cl_ulong          ns_end;         /* Nanoseconds counter on GPU at kernel stop */
4815:   cl_mem            o_jacobianInverses, o_jacobianDeterminants;
4816:   cl_mem            o_coefficients, o_coefficientsAux, o_elemVec;
4817:   float            *f_coeff = NULL, *f_coeffAux = NULL, *f_invJ = NULL, *f_detJ = NULL;
4818:   double           *d_coeff = NULL, *d_coeffAux = NULL, *d_invJ = NULL, *d_detJ = NULL;
4819:   PetscReal        *r_invJ = NULL, *r_detJ = NULL;
4820:   void             *oclCoeff, *oclCoeffAux, *oclInvJ, *oclDetJ;
4821:   size_t            local_work_size[3], global_work_size[3];
4822:   size_t            realSize, x, y, z;
4823:   PetscErrorCode    ierr;

4826:   if (!Ne) {PetscFEOpenCLLogResidual(fem, 0.0, 0.0); return(0);}
4827:   PetscFEGetSpatialDimension(fem, &dim);
4828:   PetscFEGetQuadrature(fem, &q);
4829:   PetscFEGetDimension(fem, &N_b);
4830:   PetscFEGetNumComponents(fem, &N_comp);
4831:   PetscDSGetResidual(prob, field, &f0_func, &f1_func);
4832:   PetscFEGetTileSizes(fem, NULL, &N_bl, &N_bc, &N_cb);
4833:   N_bt  = N_b*N_comp;
4834:   N_q   = q->numPoints;
4835:   N_bst = N_bt*N_q;
4836:   N_t   = N_bst*N_bl;
4837:   if (N_bc*N_comp != N_t) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of threads %d should be %d * %d", N_t, N_bc, N_comp);
4838:   /* Calculate layout */
4839:   if (Ne % (N_cb*N_bc)) { /* Remainder cells */
4840:     PetscFEIntegrateResidual_Basic(fem, prob, field, Ne, geom, coefficients, coefficients_t, probAux, coefficientsAux, elemVec);
4841:     return(0);
4842:   }
4843:   PetscFEOpenCLCalculateGrid(fem, Ne, N_cb*N_bc, &x, &y, &z);
4844:   local_work_size[0]  = N_bc*N_comp;
4845:   local_work_size[1]  = 1;
4846:   local_work_size[2]  = 1;
4847:   global_work_size[0] = x * local_work_size[0];
4848:   global_work_size[1] = y * local_work_size[1];
4849:   global_work_size[2] = z * local_work_size[2];
4850:   PetscInfo7(fem, "GPU layout grid(%d,%d,%d) block(%d,%d,%d) with %d batches\n", x, y, z, local_work_size[0], local_work_size[1], local_work_size[2], N_cb);
4851:   PetscInfo2(fem, " N_t: %d, N_cb: %d\n", N_t, N_cb);
4852:   /* Generate code */
4853:   if (probAux) {
4854:     PetscSpace P;
4855:     PetscInt   NfAux, order, f;

4857:     PetscDSGetNumFields(probAux, &NfAux);
4858:     for (f = 0; f < NfAux; ++f) {
4859:       PetscFE feAux;

4861:       PetscDSGetDiscretization(probAux, f, (PetscObject *) &feAux);
4862:       PetscFEGetBasisSpace(feAux, &P);
4863:       PetscSpaceGetOrder(P, &order);
4864:       if (order > 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Can only handle P0 coefficient fields");
4865:     }
4866:   }
4867:   PetscFEOpenCLGetIntegrationKernel(fem, useAux, &ocl_prog, &ocl_kernel);
4868:   /* Create buffers on the device and send data over */
4869:   PetscDataTypeGetSize(ocl->realType, &realSize);
4870:   if (sizeof(PetscReal) != realSize) {
4871:     switch (ocl->realType) {
4872:     case PETSC_FLOAT:
4873:     {
4874:       PetscInt c, b, d;

4876:       PetscMalloc4(Ne*N_bt,&f_coeff,Ne,&f_coeffAux,Ne*dim*dim,&f_invJ,Ne,&f_detJ);
4877:       for (c = 0; c < Ne; ++c) {
4878:         f_detJ[c] = (float) geom[c].detJ;
4879:         for (d = 0; d < dim*dim; ++d) {
4880:           f_invJ[c*dim*dim+d] = (float) geom[c].invJ[d];
4881:         }
4882:         for (b = 0; b < N_bt; ++b) {
4883:           f_coeff[c*N_bt+b] = (float) coefficients[c*N_bt+b];
4884:         }
4885:       }
4886:       if (coefficientsAux) { /* Assume P0 */
4887:         for (c = 0; c < Ne; ++c) {
4888:           f_coeffAux[c] = (float) coefficientsAux[c];
4889:         }
4890:       }
4891:       oclCoeff      = (void *) f_coeff;
4892:       if (coefficientsAux) {
4893:         oclCoeffAux = (void *) f_coeffAux;
4894:       } else {
4895:         oclCoeffAux = NULL;
4896:       }
4897:       oclInvJ       = (void *) f_invJ;
4898:       oclDetJ       = (void *) f_detJ;
4899:     }
4900:     break;
4901:     case PETSC_DOUBLE:
4902:     {
4903:       PetscInt c, b, d;

4905:       PetscMalloc4(Ne*N_bt,&d_coeff,Ne,&d_coeffAux,Ne*dim*dim,&d_invJ,Ne,&d_detJ);
4906:       for (c = 0; c < Ne; ++c) {
4907:         d_detJ[c] = (double) geom[c].detJ;
4908:         for (d = 0; d < dim*dim; ++d) {
4909:           d_invJ[c*dim*dim+d] = (double) geom[c].invJ[d];
4910:         }
4911:         for (b = 0; b < N_bt; ++b) {
4912:           d_coeff[c*N_bt+b] = (double) coefficients[c*N_bt+b];
4913:         }
4914:       }
4915:       if (coefficientsAux) { /* Assume P0 */
4916:         for (c = 0; c < Ne; ++c) {
4917:           d_coeffAux[c] = (double) coefficientsAux[c];
4918:         }
4919:       }
4920:       oclCoeff      = (void *) d_coeff;
4921:       if (coefficientsAux) {
4922:         oclCoeffAux = (void *) d_coeffAux;
4923:       } else {
4924:         oclCoeffAux = NULL;
4925:       }
4926:       oclInvJ       = (void *) d_invJ;
4927:       oclDetJ       = (void *) d_detJ;
4928:     }
4929:     break;
4930:     default:
4931:       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unsupported PETSc type %d", ocl->realType);
4932:     }
4933:   } else {
4934:     PetscInt c, d;

4936:     PetscMalloc2(Ne*dim*dim,&r_invJ,Ne,&r_detJ);
4937:     for (c = 0; c < Ne; ++c) {
4938:       r_detJ[c] = geom[c].detJ;
4939:       for (d = 0; d < dim*dim; ++d) {
4940:         r_invJ[c*dim*dim+d] = geom[c].invJ[d];
4941:       }
4942:     }
4943:     oclCoeff    = (void *) coefficients;
4944:     oclCoeffAux = (void *) coefficientsAux;
4945:     oclInvJ     = (void *) r_invJ;
4946:     oclDetJ     = (void *) r_detJ;
4947:   }
4948:   o_coefficients         = clCreateBuffer(ocl->ctx_id, CL_MEM_READ_ONLY | CL_MEM_COPY_HOST_PTR, Ne*N_bt    * realSize, oclCoeff,    &ierr);
4949:   if (coefficientsAux) {
4950:     o_coefficientsAux    = clCreateBuffer(ocl->ctx_id, CL_MEM_READ_ONLY | CL_MEM_COPY_HOST_PTR, Ne         * realSize, oclCoeffAux, &ierr);
4951:   } else {
4952:     o_coefficientsAux    = clCreateBuffer(ocl->ctx_id, CL_MEM_READ_ONLY,                        Ne         * realSize, oclCoeffAux, &ierr);
4953:   }
4954:   o_jacobianInverses     = clCreateBuffer(ocl->ctx_id, CL_MEM_READ_ONLY | CL_MEM_COPY_HOST_PTR, Ne*dim*dim * realSize, oclInvJ,     &ierr);
4955:   o_jacobianDeterminants = clCreateBuffer(ocl->ctx_id, CL_MEM_READ_ONLY | CL_MEM_COPY_HOST_PTR, Ne         * realSize, oclDetJ,     &ierr);
4956:   o_elemVec              = clCreateBuffer(ocl->ctx_id, CL_MEM_WRITE_ONLY,                       Ne*N_bt    * realSize, NULL,        &ierr);
4957:   /* Kernel launch */
4958:   clSetKernelArg(ocl_kernel, 0, sizeof(cl_int), (void*) &N_cb);
4959:   clSetKernelArg(ocl_kernel, 1, sizeof(cl_mem), (void*) &o_coefficients);
4960:   clSetKernelArg(ocl_kernel, 2, sizeof(cl_mem), (void*) &o_coefficientsAux);
4961:   clSetKernelArg(ocl_kernel, 3, sizeof(cl_mem), (void*) &o_jacobianInverses);
4962:   clSetKernelArg(ocl_kernel, 4, sizeof(cl_mem), (void*) &o_jacobianDeterminants);
4963:   clSetKernelArg(ocl_kernel, 5, sizeof(cl_mem), (void*) &o_elemVec);
4964:   clEnqueueNDRangeKernel(ocl->queue_id, ocl_kernel, 3, NULL, global_work_size, local_work_size, 0, NULL, &ocl_ev);
4965:   /* Read data back from device */
4966:   if (sizeof(PetscReal) != realSize) {
4967:     switch (ocl->realType) {
4968:     case PETSC_FLOAT:
4969:     {
4970:       float   *elem;
4971:       PetscInt c, b;

4973:       PetscFree4(f_coeff,f_coeffAux,f_invJ,f_detJ);
4974:       PetscMalloc1(Ne*N_bt, &elem);
4975:       clEnqueueReadBuffer(ocl->queue_id, o_elemVec, CL_TRUE, 0, Ne*N_bt * realSize, elem, 0, NULL, NULL);
4976:       for (c = 0; c < Ne; ++c) {
4977:         for (b = 0; b < N_bt; ++b) {
4978:           elemVec[c*N_bt+b] = (PetscScalar) elem[c*N_bt+b];
4979:         }
4980:       }
4981:       PetscFree(elem);
4982:     }
4983:     break;
4984:     case PETSC_DOUBLE:
4985:     {
4986:       double  *elem;
4987:       PetscInt c, b;

4989:       PetscFree4(d_coeff,d_coeffAux,d_invJ,d_detJ);
4990:       PetscMalloc1(Ne*N_bt, &elem);
4991:       clEnqueueReadBuffer(ocl->queue_id, o_elemVec, CL_TRUE, 0, Ne*N_bt * realSize, elem, 0, NULL, NULL);
4992:       for (c = 0; c < Ne; ++c) {
4993:         for (b = 0; b < N_bt; ++b) {
4994:           elemVec[c*N_bt+b] = (PetscScalar) elem[c*N_bt+b];
4995:         }
4996:       }
4997:       PetscFree(elem);
4998:     }
4999:     break;
5000:     default:
5001:       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unsupported PETSc type %d", ocl->realType);
5002:     }
5003:   } else {
5004:     PetscFree2(r_invJ,r_detJ);
5005:     clEnqueueReadBuffer(ocl->queue_id, o_elemVec, CL_TRUE, 0, Ne*N_bt * realSize, elemVec, 0, NULL, NULL);
5006:   }
5007:   /* Log performance */
5008:   clGetEventProfilingInfo(ocl_ev, CL_PROFILING_COMMAND_START, sizeof(cl_ulong), &ns_start, NULL);
5009:   clGetEventProfilingInfo(ocl_ev, CL_PROFILING_COMMAND_END,   sizeof(cl_ulong), &ns_end,   NULL);
5010:   f0Flops = 0;
5011:   switch (ocl->op) {
5012:   case LAPLACIAN:
5013:     f1Flops = useAux ? dim : 0;break;
5014:   case ELASTICITY:
5015:     f1Flops = 2*dim*dim;break;
5016:   }
5017:   numFlops = Ne*(
5018:     N_q*(
5019:       N_b*N_comp*((useField ? 2 : 0) + (useFieldDer ? 2*dim*(dim + 1) : 0))
5020:       /*+
5021:        N_ba*N_compa*((useFieldAux ? 2 : 0) + (useFieldDerAux ? 2*dim*(dim + 1) : 0))*/
5022:       +
5023:       N_comp*((useF0 ? f0Flops + 2 : 0) + (useF1 ? f1Flops + 2*dim : 0)))
5024:     +
5025:     N_b*((useF0 ? 2 : 0) + (useF1 ? 2*dim*(dim + 1) : 0)));
5026:   PetscFEOpenCLLogResidual(fem, (ns_end - ns_start)*1.0e-9, numFlops);
5027:   /* Cleanup */
5028:   clReleaseMemObject(o_coefficients);
5029:   clReleaseMemObject(o_coefficientsAux);
5030:   clReleaseMemObject(o_jacobianInverses);
5031:   clReleaseMemObject(o_jacobianDeterminants);
5032:   clReleaseMemObject(o_elemVec);
5033:   clReleaseKernel(ocl_kernel);
5034:   clReleaseProgram(ocl_prog);
5035:   return(0);
5036: }

5040: PetscErrorCode PetscFEInitialize_OpenCL(PetscFE fem)
5041: {
5043:   fem->ops->setfromoptions          = NULL;
5044:   fem->ops->setup                   = PetscFESetUp_Basic;
5045:   fem->ops->view                    = NULL;
5046:   fem->ops->destroy                 = PetscFEDestroy_OpenCL;
5047:   fem->ops->getdimension            = PetscFEGetDimension_Basic;
5048:   fem->ops->gettabulation           = PetscFEGetTabulation_Basic;
5049:   fem->ops->integrateresidual       = PetscFEIntegrateResidual_OpenCL;
5050:   fem->ops->integratebdresidual     = NULL/* PetscFEIntegrateBdResidual_OpenCL */;
5051:   fem->ops->integratejacobianaction = NULL/* PetscFEIntegrateJacobianAction_OpenCL */;
5052:   fem->ops->integratejacobian       = PetscFEIntegrateJacobian_Basic;
5053:   return(0);
5054: }

5056: /*MC
5057:   PETSCFEOPENCL = "opencl" - A PetscFE object that integrates using a vectorized OpenCL implementation

5059:   Level: intermediate

5061: .seealso: PetscFEType, PetscFECreate(), PetscFESetType()
5062: M*/

5066: PETSC_EXTERN PetscErrorCode PetscFECreate_OpenCL(PetscFE fem)
5067: {
5068:   PetscFE_OpenCL *ocl;
5069:   cl_uint         num_platforms;
5070:   cl_platform_id  platform_ids[42];
5071:   cl_uint         num_devices;
5072:   cl_device_id    device_ids[42];
5073:   cl_int          ierr2;
5074:   PetscErrorCode  ierr;

5078:   PetscNewLog(fem,&ocl);
5079:   fem->data = ocl;

5081:   /* Init Platform */
5082:   clGetPlatformIDs(42, platform_ids, &num_platforms);
5083:   if (!num_platforms) SETERRQ(PetscObjectComm((PetscObject) fem), PETSC_ERR_SUP, "No OpenCL platform found.");
5084:   ocl->pf_id = platform_ids[0];
5085:   /* Init Device */
5086:   clGetDeviceIDs(ocl->pf_id, CL_DEVICE_TYPE_ALL, 42, device_ids, &num_devices);
5087:   if (!num_devices) SETERRQ(PetscObjectComm((PetscObject) fem), PETSC_ERR_SUP, "No OpenCL device found.");
5088:   ocl->dev_id = device_ids[0];
5089:   /* Create context with one command queue */
5090:   ocl->ctx_id   = clCreateContext(0, 1, &(ocl->dev_id), NULL, NULL, &ierr2);CHKERRQ(ierr2);
5091:   ocl->queue_id = clCreateCommandQueue(ocl->ctx_id, ocl->dev_id, CL_QUEUE_PROFILING_ENABLE, &ierr2);CHKERRQ(ierr2);
5092:   /* Types */
5093:   ocl->realType = PETSC_FLOAT;
5094:   /* Register events */
5095:   PetscLogEventRegister("OpenCL FEResidual", PETSCFE_CLASSID, &ocl->residualEvent);
5096:   /* Equation handling */
5097:   ocl->op = LAPLACIAN;

5099:   PetscFEInitialize_OpenCL(fem);
5100:   return(0);
5101: }

5105: PetscErrorCode PetscFEOpenCLSetRealType(PetscFE fem, PetscDataType realType)
5106: {
5107:   PetscFE_OpenCL *ocl = (PetscFE_OpenCL *) fem->data;

5111:   ocl->realType = realType;
5112:   return(0);
5113: }

5117: PetscErrorCode PetscFEOpenCLGetRealType(PetscFE fem, PetscDataType *realType)
5118: {
5119:   PetscFE_OpenCL *ocl = (PetscFE_OpenCL *) fem->data;

5124:   *realType = ocl->realType;
5125:   return(0);
5126: }

5128: #endif /* PETSC_HAVE_OPENCL */

5132: PetscErrorCode PetscFEDestroy_Composite(PetscFE fem)
5133: {
5134:   PetscFE_Composite *cmp = (PetscFE_Composite *) fem->data;
5135:   PetscErrorCode     ierr;

5138:   CellRefinerRestoreAffineTransforms_Internal(cmp->cellRefiner, &cmp->numSubelements, &cmp->v0, &cmp->jac, &cmp->invjac);
5139:   PetscFree(cmp->embedding);
5140:   PetscFree(cmp);
5141:   return(0);
5142: }

5146: PetscErrorCode PetscFESetUp_Composite(PetscFE fem)
5147: {
5148:   PetscFE_Composite *cmp = (PetscFE_Composite *) fem->data;
5149:   DM                 K;
5150:   PetscReal         *subpoint;
5151:   PetscBLASInt      *pivots;
5152:   PetscBLASInt       n, info;
5153:   PetscScalar       *work, *invVscalar;
5154:   PetscInt           dim, pdim, spdim, j, s;
5155:   PetscErrorCode     ierr;

5158:   /* Get affine mapping from reference cell to each subcell */
5159:   PetscDualSpaceGetDM(fem->dualSpace, &K);
5160:   DMGetDimension(K, &dim);
5161:   DMPlexGetCellRefiner_Internal(K, &cmp->cellRefiner);
5162:   CellRefinerGetAffineTransforms_Internal(cmp->cellRefiner, &cmp->numSubelements, &cmp->v0, &cmp->jac, &cmp->invjac);
5163:   /* Determine dof embedding into subelements */
5164:   PetscDualSpaceGetDimension(fem->dualSpace, &pdim);
5165:   PetscSpaceGetDimension(fem->basisSpace, &spdim);
5166:   PetscMalloc1(cmp->numSubelements*spdim,&cmp->embedding);
5167:   DMGetWorkArray(K, dim, PETSC_REAL, &subpoint);
5168:   for (s = 0; s < cmp->numSubelements; ++s) {
5169:     PetscInt sd = 0;

5171:     for (j = 0; j < pdim; ++j) {
5172:       PetscBool       inside;
5173:       PetscQuadrature f;
5174:       PetscInt        d, e;

5176:       PetscDualSpaceGetFunctional(fem->dualSpace, j, &f);
5177:       /* Apply transform to first point, and check that point is inside subcell */
5178:       for (d = 0; d < dim; ++d) {
5179:         subpoint[d] = -1.0;
5180:         for (e = 0; e < dim; ++e) subpoint[d] += cmp->invjac[(s*dim + d)*dim+e]*(f->points[e] - cmp->v0[s*dim+e]);
5181:       }
5182:       CellRefinerInCellTest_Internal(cmp->cellRefiner, subpoint, &inside);
5183:       if (inside) {cmp->embedding[s*spdim+sd++] = j;}
5184:     }
5185:     if (sd != spdim) SETERRQ3(PetscObjectComm((PetscObject) fem), PETSC_ERR_PLIB, "Subelement %d has %d dual basis vectors != %d", s, sd, spdim);
5186:   }
5187:   DMRestoreWorkArray(K, dim, PETSC_REAL, &subpoint);
5188:   /* Construct the change of basis from prime basis to nodal basis for each subelement */
5189:   PetscMalloc1(cmp->numSubelements*spdim*spdim,&fem->invV);
5190:   PetscMalloc2(spdim,&pivots,spdim,&work);
5191: #if defined(PETSC_USE_COMPLEX)
5192:   PetscMalloc1(cmp->numSubelements*spdim*spdim,&invVscalar);
5193: #else
5194:   invVscalar = fem->invV;
5195: #endif
5196:   for (s = 0; s < cmp->numSubelements; ++s) {
5197:     for (j = 0; j < spdim; ++j) {
5198:       PetscReal      *Bf;
5199:       PetscQuadrature f;
5200:       PetscInt        q, k;

5202:       PetscDualSpaceGetFunctional(fem->dualSpace, cmp->embedding[s*spdim+j], &f);
5203:       PetscMalloc1(f->numPoints*spdim,&Bf);
5204:       PetscSpaceEvaluate(fem->basisSpace, f->numPoints, f->points, Bf, NULL, NULL);
5205:       for (k = 0; k < spdim; ++k) {
5206:         /* n_j \cdot \phi_k */
5207:         invVscalar[(s*spdim + j)*spdim+k] = 0.0;
5208:         for (q = 0; q < f->numPoints; ++q) {
5209:           invVscalar[(s*spdim + j)*spdim+k] += Bf[q*spdim+k]*f->weights[q];
5210:         }
5211:       }
5212:       PetscFree(Bf);
5213:     }
5214:     n = spdim;
5215:     PetscStackCallBLAS("LAPACKgetrf", LAPACKgetrf_(&n, &n, &invVscalar[s*spdim*spdim], &n, pivots, &info));
5216:     PetscStackCallBLAS("LAPACKgetri", LAPACKgetri_(&n, &invVscalar[s*spdim*spdim], &n, pivots, work, &n, &info));
5217:   }
5218: #if defined(PETSC_USE_COMPLEX)
5219:   for (s = 0; s <cmp->numSubelements*spdim*spdim; s++) fem->invV[s] = PetscRealPart(invVscalar[s]);
5220:   PetscFree(invVscalar);
5221: #endif
5222:   PetscFree2(pivots,work);
5223:   return(0);
5224: }

5228: PetscErrorCode PetscFEGetTabulation_Composite(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscReal *B, PetscReal *D, PetscReal *H)
5229: {
5230:   PetscFE_Composite *cmp = (PetscFE_Composite *) fem->data;
5231:   DM                 dm;
5232:   PetscInt           pdim;  /* Dimension of FE space P */
5233:   PetscInt           spdim; /* Dimension of subelement FE space P */
5234:   PetscInt           dim;   /* Spatial dimension */
5235:   PetscInt           comp;  /* Field components */
5236:   PetscInt          *subpoints;
5237:   PetscReal         *tmpB, *tmpD, *tmpH, *subpoint;
5238:   PetscInt           p, s, d, e, j, k;
5239:   PetscErrorCode     ierr;

5242:   PetscDualSpaceGetDM(fem->dualSpace, &dm);
5243:   DMGetDimension(dm, &dim);
5244:   PetscSpaceGetDimension(fem->basisSpace, &spdim);
5245:   PetscDualSpaceGetDimension(fem->dualSpace, &pdim);
5246:   PetscFEGetNumComponents(fem, &comp);
5247:   /* Divide points into subelements */
5248:   DMGetWorkArray(dm, npoints, PETSC_INT, &subpoints);
5249:   DMGetWorkArray(dm, dim, PETSC_REAL, &subpoint);
5250:   for (p = 0; p < npoints; ++p) {
5251:     for (s = 0; s < cmp->numSubelements; ++s) {
5252:       PetscBool inside;

5254:       /* Apply transform, and check that point is inside cell */
5255:       for (d = 0; d < dim; ++d) {
5256:         subpoint[d] = -1.0;
5257:         for (e = 0; e < dim; ++e) subpoint[d] += cmp->invjac[(s*dim + d)*dim+e]*(points[p*dim+e] - cmp->v0[s*dim+e]);
5258:       }
5259:       CellRefinerInCellTest_Internal(cmp->cellRefiner, subpoint, &inside);
5260:       if (inside) {subpoints[p] = s; break;}
5261:     }
5262:     if (s >= cmp->numSubelements) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Point %d was not found in any subelement", p);
5263:   }
5264:   DMRestoreWorkArray(dm, dim, PETSC_REAL, &subpoint);
5265:   /* Evaluate the prime basis functions at all points */
5266:   if (B) {DMGetWorkArray(dm, npoints*spdim, PETSC_REAL, &tmpB);}
5267:   if (D) {DMGetWorkArray(dm, npoints*spdim*dim, PETSC_REAL, &tmpD);}
5268:   if (H) {DMGetWorkArray(dm, npoints*spdim*dim*dim, PETSC_REAL, &tmpH);}
5269:   PetscSpaceEvaluate(fem->basisSpace, npoints, points, B ? tmpB : NULL, D ? tmpD : NULL, H ? tmpH : NULL);
5270:   /* Translate to the nodal basis */
5271:   if (B) {PetscMemzero(B, npoints*pdim*comp * sizeof(PetscReal));}
5272:   if (D) {PetscMemzero(D, npoints*pdim*comp*dim * sizeof(PetscReal));}
5273:   if (H) {PetscMemzero(H, npoints*pdim*comp*dim*dim * sizeof(PetscReal));}
5274:   for (p = 0; p < npoints; ++p) {
5275:     const PetscInt s = subpoints[p];

5277:     if (B) {
5278:       /* Multiply by V^{-1} (spdim x spdim) */
5279:       for (j = 0; j < spdim; ++j) {
5280:         const PetscInt i = (p*pdim + cmp->embedding[s*spdim+j])*comp;
5281:         PetscInt       c;

5283:         B[i] = 0.0;
5284:         for (k = 0; k < spdim; ++k) {
5285:           B[i] += fem->invV[(s*spdim + k)*spdim+j] * tmpB[p*spdim + k];
5286:         }
5287:         for (c = 1; c < comp; ++c) {
5288:           B[i+c] = B[i];
5289:         }
5290:       }
5291:     }
5292:     if (D) {
5293:       /* Multiply by V^{-1} (spdim x spdim) */
5294:       for (j = 0; j < spdim; ++j) {
5295:         for (d = 0; d < dim; ++d) {
5296:           const PetscInt i = ((p*pdim + cmp->embedding[s*spdim+j])*comp + 0)*dim + d;
5297:           PetscInt       c;

5299:           D[i] = 0.0;
5300:           for (k = 0; k < spdim; ++k) {
5301:             D[i] += fem->invV[(s*spdim + k)*spdim+j] * tmpD[(p*spdim + k)*dim + d];
5302:           }
5303:           for (c = 1; c < comp; ++c) {
5304:             D[((p*pdim + cmp->embedding[s*spdim+j])*comp + c)*dim + d] = D[i];
5305:           }
5306:         }
5307:       }
5308:     }
5309:     if (H) {
5310:       /* Multiply by V^{-1} (pdim x pdim) */
5311:       for (j = 0; j < spdim; ++j) {
5312:         for (d = 0; d < dim*dim; ++d) {
5313:           const PetscInt i = ((p*pdim + cmp->embedding[s*spdim+j])*comp + 0)*dim*dim + d;
5314:           PetscInt       c;

5316:           H[i] = 0.0;
5317:           for (k = 0; k < spdim; ++k) {
5318:             H[i] += fem->invV[(s*spdim + k)*spdim+j] * tmpH[(p*spdim + k)*dim*dim + d];
5319:           }
5320:           for (c = 1; c < comp; ++c) {
5321:             H[((p*pdim + cmp->embedding[s*spdim+j])*comp + c)*dim*dim + d] = H[i];
5322:           }
5323:         }
5324:       }
5325:     }
5326:   }
5327:   DMRestoreWorkArray(dm, npoints, PETSC_INT, &subpoints);
5328:   if (B) {DMRestoreWorkArray(dm, npoints*spdim, PETSC_REAL, &tmpB);}
5329:   if (D) {DMRestoreWorkArray(dm, npoints*spdim*dim, PETSC_REAL, &tmpD);}
5330:   if (H) {DMRestoreWorkArray(dm, npoints*spdim*dim*dim, PETSC_REAL, &tmpH);}
5331:   return(0);
5332: }

5336: PetscErrorCode PetscFEInitialize_Composite(PetscFE fem)
5337: {
5339:   fem->ops->setfromoptions          = NULL;
5340:   fem->ops->setup                   = PetscFESetUp_Composite;
5341:   fem->ops->view                    = NULL;
5342:   fem->ops->destroy                 = PetscFEDestroy_Composite;
5343:   fem->ops->getdimension            = PetscFEGetDimension_Basic;
5344:   fem->ops->gettabulation           = PetscFEGetTabulation_Composite;
5345:   fem->ops->integrateresidual       = PetscFEIntegrateResidual_Basic;
5346:   fem->ops->integratebdresidual     = PetscFEIntegrateBdResidual_Basic;
5347:   fem->ops->integratejacobianaction = NULL/* PetscFEIntegrateJacobianAction_Basic */;
5348:   fem->ops->integratejacobian       = PetscFEIntegrateJacobian_Basic;
5349:   return(0);
5350: }

5352: /*MC
5353:   PETSCFECOMPOSITE = "composite" - A PetscFE object that represents a composite element

5355:   Level: intermediate

5357: .seealso: PetscFEType, PetscFECreate(), PetscFESetType()
5358: M*/

5362: PETSC_EXTERN PetscErrorCode PetscFECreate_Composite(PetscFE fem)
5363: {
5364:   PetscFE_Composite *cmp;
5365:   PetscErrorCode     ierr;

5369:   PetscNewLog(fem, &cmp);
5370:   fem->data = cmp;

5372:   cmp->cellRefiner    = REFINER_NOOP;
5373:   cmp->numSubelements = -1;
5374:   cmp->v0             = NULL;
5375:   cmp->jac            = NULL;

5377:   PetscFEInitialize_Composite(fem);
5378:   return(0);
5379: }

5383: /*@C
5384:   PetscFECompositeGetMapping - Returns the mappings from the reference element to each subelement

5386:   Not collective

5388:   Input Parameter:
5389: . fem - The PetscFE object

5391:   Output Parameters:
5392: + blockSize - The number of elements in a block
5393: . numBlocks - The number of blocks in a batch
5394: . batchSize - The number of elements in a batch
5395: - numBatches - The number of batches in a chunk

5397:   Level: intermediate

5399: .seealso: PetscFECreate()
5400: @*/
5401: PetscErrorCode PetscFECompositeGetMapping(PetscFE fem, PetscInt *numSubelements, const PetscReal *v0[], const PetscReal *jac[], const PetscReal *invjac[])
5402: {
5403:   PetscFE_Composite *cmp = (PetscFE_Composite *) fem->data;

5411:   return(0);
5412: }

5416: /*@
5417:   PetscFEGetDimension - Get the dimension of the finite element space on a cell

5419:   Not collective

5421:   Input Parameter:
5422: . fe - The PetscFE

5424:   Output Parameter:
5425: . dim - The dimension

5427:   Level: intermediate

5429: .seealso: PetscFECreate(), PetscSpaceGetDimension(), PetscDualSpaceGetDimension()
5430: @*/
5431: PetscErrorCode PetscFEGetDimension(PetscFE fem, PetscInt *dim)
5432: {

5438:   if (fem->ops->getdimension) {(*fem->ops->getdimension)(fem, dim);}
5439:   return(0);
5440: }

5442: /*
5443: Purpose: Compute element vector for chunk of elements

5445: Input:
5446:   Sizes:
5447:      Ne:  number of elements
5448:      Nf:  number of fields
5449:      PetscFE
5450:        dim: spatial dimension
5451:        Nb:  number of basis functions
5452:        Nc:  number of field components
5453:        PetscQuadrature
5454:          Nq:  number of quadrature points

5456:   Geometry:
5457:      PetscFECellGeom[Ne] possibly *Nq
5458:        PetscReal v0s[dim]
5459:        PetscReal n[dim]
5460:        PetscReal jacobians[dim*dim]
5461:        PetscReal jacobianInverses[dim*dim]
5462:        PetscReal jacobianDeterminants
5463:   FEM:
5464:      PetscFE
5465:        PetscQuadrature
5466:          PetscReal   quadPoints[Nq*dim]
5467:          PetscReal   quadWeights[Nq]
5468:        PetscReal   basis[Nq*Nb*Nc]
5469:        PetscReal   basisDer[Nq*Nb*Nc*dim]
5470:      PetscScalar coefficients[Ne*Nb*Nc]
5471:      PetscScalar elemVec[Ne*Nb*Nc]

5473:   Problem:
5474:      PetscInt f: the active field
5475:      f0, f1

5477:   Work Space:
5478:      PetscFE
5479:        PetscScalar f0[Nq*dim];
5480:        PetscScalar f1[Nq*dim*dim];
5481:        PetscScalar u[Nc];
5482:        PetscScalar gradU[Nc*dim];
5483:        PetscReal   x[dim];
5484:        PetscScalar realSpaceDer[dim];

5486: Purpose: Compute element vector for N_cb batches of elements

5488: Input:
5489:   Sizes:
5490:      N_cb: Number of serial cell batches

5492:   Geometry:
5493:      PetscReal v0s[Ne*dim]
5494:      PetscReal jacobians[Ne*dim*dim]        possibly *Nq
5495:      PetscReal jacobianInverses[Ne*dim*dim] possibly *Nq
5496:      PetscReal jacobianDeterminants[Ne]     possibly *Nq
5497:   FEM:
5498:      static PetscReal   quadPoints[Nq*dim]
5499:      static PetscReal   quadWeights[Nq]
5500:      static PetscReal   basis[Nq*Nb*Nc]
5501:      static PetscReal   basisDer[Nq*Nb*Nc*dim]
5502:      PetscScalar coefficients[Ne*Nb*Nc]
5503:      PetscScalar elemVec[Ne*Nb*Nc]

5505: ex62.c:
5506:   PetscErrorCode PetscFEIntegrateResidualBatch(PetscInt Ne, PetscInt numFields, PetscInt field, PetscQuadrature quad[], const PetscScalar coefficients[],
5507:                                                const PetscReal v0s[], const PetscReal jacobians[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[],
5508:                                                void (*f0_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]),
5509:                                                void (*f1_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]), PetscScalar elemVec[])

5511: ex52.c:
5512:   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)
5513:   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)

5515: ex52_integrateElement.cu
5516: __global__ void integrateElementQuadrature(int N_cb, realType *coefficients, realType *jacobianInverses, realType *jacobianDeterminants, realType *elemVec)

5518: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt Nbl, const PetscScalar coefficients[],
5519:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
5520:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

5522: ex52_integrateElementOpenCL.c:
5523: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt N_bl, const PetscScalar coefficients[],
5524:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
5525:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

5527: __kernel void integrateElementQuadrature(int N_cb, __global float *coefficients, __global float *jacobianInverses, __global float *jacobianDeterminants, __global float *elemVec)
5528: */

5532: /*@C
5533:   PetscFEIntegrate - Produce the integral for the given field for a chunk of elements by quadrature integration

5535:   Not collective

5537:   Input Parameters:
5538: + fem          - The PetscFE object for the field being integrated
5539: . prob         - The PetscDS specifing the discretizations and continuum functions
5540: . field        - The field being integrated
5541: . Ne           - The number of elements in the chunk
5542: . geom         - The cell geometry for each cell in the chunk
5543: . coefficients - The array of FEM basis coefficients for the elements
5544: . probAux      - The PetscDS specifing the auxiliary discretizations
5545: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

5547:   Output Parameter
5548: . integral     - the integral for this field

5550:   Level: developer

5552: .seealso: PetscFEIntegrateResidual()
5553: @*/
5554: PetscErrorCode PetscFEIntegrate(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
5555:                                 const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal integral[])
5556: {

5562:   if (fem->ops->integrate) {(*fem->ops->integrate)(fem, prob, field, Ne, geom, coefficients, probAux, coefficientsAux, integral);}
5563:   return(0);
5564: }

5568: /*@C
5569:   PetscFEIntegrateResidual - Produce the element residual vector for a chunk of elements by quadrature integration

5571:   Not collective

5573:   Input Parameters:
5574: + fem          - The PetscFE object for the field being integrated
5575: . prob         - The PetscDS specifing the discretizations and continuum functions
5576: . field        - The field being integrated
5577: . Ne           - The number of elements in the chunk
5578: . geom         - The cell geometry for each cell in the chunk
5579: . coefficients - The array of FEM basis coefficients for the elements
5580: . coefficients_t - The array of FEM basis time derivative coefficients for the elements
5581: . probAux      - The PetscDS specifing the auxiliary discretizations
5582: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

5584:   Output Parameter
5585: . elemVec      - the element residual vectors from each element

5587:   Note:
5588: $ Loop over batch of elements (e):
5589: $   Loop over quadrature points (q):
5590: $     Make u_q and gradU_q (loops over fields,Nb,Ncomp) and x_q
5591: $     Call f_0 and f_1
5592: $   Loop over element vector entries (f,fc --> i):
5593: $     elemVec[i] += \psi^{fc}_f(q) f0_{fc}(u, \nabla u) + \nabla\psi^{fc}_f(q) \cdot f1_{fc,df}(u, \nabla u)

5595:   Level: developer

5597: .seealso: PetscFEIntegrateResidual()
5598: @*/
5599: PetscErrorCode PetscFEIntegrateResidual(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
5600:                                         const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemVec[])
5601: {

5607:   if (fem->ops->integrateresidual) {(*fem->ops->integrateresidual)(fem, prob, field, Ne, geom, coefficients, coefficients_t, probAux, coefficientsAux, elemVec);}
5608:   return(0);
5609: }

5613: /*@C
5614:   PetscFEIntegrateBdResidual - Produce the element residual vector for a chunk of elements by quadrature integration over a boundary

5616:   Not collective

5618:   Input Parameters:
5619: + fem          - The PetscFE object for the field being integrated
5620: . prob         - The PetscDS specifing the discretizations and continuum functions
5621: . field        - The field being integrated
5622: . Ne           - The number of elements in the chunk
5623: . geom         - The cell geometry for each cell in the chunk
5624: . coefficients - The array of FEM basis coefficients for the elements
5625: . coefficients_t - The array of FEM basis time derivative coefficients for the elements
5626: . probAux      - The PetscDS specifing the auxiliary discretizations
5627: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

5629:   Output Parameter
5630: . elemVec      - the element residual vectors from each element

5632:   Level: developer

5634: .seealso: PetscFEIntegrateResidual()
5635: @*/
5636: PetscErrorCode PetscFEIntegrateBdResidual(PetscFE fem, PetscDS prob, PetscInt field, PetscInt Ne, PetscFECellGeom *geom,
5637:                                           const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemVec[])
5638: {

5643:   if (fem->ops->integratebdresidual) {(*fem->ops->integratebdresidual)(fem, prob, field, Ne, geom, coefficients, coefficients_t, probAux, coefficientsAux, elemVec);}
5644:   return(0);
5645: }

5649: /*@C
5650:   PetscFEIntegrateJacobian - Produce the element Jacobian for a chunk of elements by quadrature integration

5652:   Not collective

5654:   Input Parameters:
5655: + fem          = The PetscFE object for the field being integrated
5656: . prob         - The PetscDS specifing the discretizations and continuum functions
5657: . fieldI       - The test field being integrated
5658: . fieldJ       - The basis field being integrated
5659: . Ne           - The number of elements in the chunk
5660: . geom         - The cell geometry for each cell in the chunk
5661: . coefficients - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
5662: . coefficients_t - The array of FEM basis time derivative coefficients for the elements
5663: . probAux      - The PetscDS specifing the auxiliary discretizations
5664: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

5666:   Output Parameter
5667: . elemMat      - the element matrices for the Jacobian from each element

5669:   Note:
5670: $ Loop over batch of elements (e):
5671: $   Loop over element matrix entries (f,fc,g,gc --> i,j):
5672: $     Loop over quadrature points (q):
5673: $       Make u_q and gradU_q (loops over fields,Nb,Ncomp)
5674: $         elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
5675: $                      + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
5676: $                      + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
5677: $                      + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
5678: */
5679: PetscErrorCode PetscFEIntegrateJacobian(PetscFE fem, PetscDS prob, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFECellGeom *geom,
5680:                                         const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemMat[])
5681: {

5686:   if (fem->ops->integratejacobian) {(*fem->ops->integratejacobian)(fem, prob, fieldI, fieldJ, Ne, geom, coefficients, coefficients_t, probAux, coefficientsAux, elemMat);}
5687:   return(0);
5688: }

5692: /*C
5693:   PetscFEIntegrateBdJacobian - Produce the boundary element Jacobian for a chunk of elements by quadrature integration

5695:   Not collective

5697:   Input Parameters:
5698: + fem          = The PetscFE object for the field being integrated
5699: . prob         - The PetscDS specifing the discretizations and continuum functions
5700: . fieldI       - The test field being integrated
5701: . fieldJ       - The basis field being integrated
5702: . Ne           - The number of elements in the chunk
5703: . geom         - The cell geometry for each cell in the chunk
5704: . coefficients - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
5705: . coefficients_t - The array of FEM basis time derivative coefficients for the elements
5706: . probAux      - The PetscDS specifing the auxiliary discretizations
5707: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

5709:   Output Parameter
5710: . elemMat              - the element matrices for the Jacobian from each element

5712:   Note:
5713: $ Loop over batch of elements (e):
5714: $   Loop over element matrix entries (f,fc,g,gc --> i,j):
5715: $     Loop over quadrature points (q):
5716: $       Make u_q and gradU_q (loops over fields,Nb,Ncomp)
5717: $         elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
5718: $                      + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
5719: $                      + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
5720: $                      + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
5721: */
5722: PetscErrorCode PetscFEIntegrateBdJacobian(PetscFE fem, PetscDS prob, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFECellGeom *geom,
5723:                                           const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar elemMat[])
5724: {

5729:   if (fem->ops->integratebdjacobian) {(*fem->ops->integratebdjacobian)(fem, prob, fieldI, fieldJ, Ne, geom, coefficients, coefficients_t, probAux, coefficientsAux, elemMat);}
5730:   return(0);
5731: }

5735: /*@
5736:   PetscFERefine - Create a "refined" PetscFE object that refines the reference cell into smaller copies. This is typically used
5737:   to precondition a higher order method with a lower order method on a refined mesh having the same number of dofs (but more
5738:   sparsity). It is also used to create an interpolation between regularly refined meshes.

5740:   Input Parameter:
5741: . fe - The initial PetscFE

5743:   Output Parameter:
5744: . feRef - The refined PetscFE

5746:   Level: developer

5748: .seealso: PetscFEType, PetscFECreate(), PetscFESetType()
5749: @*/
5750: PetscErrorCode PetscFERefine(PetscFE fe, PetscFE *feRef)
5751: {
5752:   PetscSpace       P, Pref;
5753:   PetscDualSpace   Q, Qref;
5754:   DM               K, Kref;
5755:   PetscQuadrature  q, qref;
5756:   const PetscReal *v0, *jac;
5757:   PetscInt         numComp, numSubelements;
5758:   PetscErrorCode   ierr;

5761:   PetscFEGetBasisSpace(fe, &P);
5762:   PetscFEGetDualSpace(fe, &Q);
5763:   PetscFEGetQuadrature(fe, &q);
5764:   PetscDualSpaceGetDM(Q, &K);
5765:   /* Create space */
5766:   PetscObjectReference((PetscObject) P);
5767:   Pref = P;
5768:   /* Create dual space */
5769:   PetscDualSpaceDuplicate(Q, &Qref);
5770:   DMRefine(K, PetscObjectComm((PetscObject) fe), &Kref);
5771:   PetscDualSpaceSetDM(Qref, Kref);
5772:   DMDestroy(&Kref);
5773:   PetscDualSpaceSetUp(Qref);
5774:   /* Create element */
5775:   PetscFECreate(PetscObjectComm((PetscObject) fe), feRef);
5776:   PetscFESetType(*feRef, PETSCFECOMPOSITE);
5777:   PetscFESetBasisSpace(*feRef, Pref);
5778:   PetscFESetDualSpace(*feRef, Qref);
5779:   PetscFEGetNumComponents(fe,    &numComp);
5780:   PetscFESetNumComponents(*feRef, numComp);
5781:   PetscFESetUp(*feRef);
5782:   PetscSpaceDestroy(&Pref);
5783:   PetscDualSpaceDestroy(&Qref);
5784:   /* Create quadrature */
5785:   PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL);
5786:   PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref);
5787:   PetscFESetQuadrature(*feRef, qref);
5788:   PetscQuadratureDestroy(&qref);
5789:   return(0);
5790: }

5794: /*@
5795:   PetscFECreateDefault - Create a PetscFE for basic FEM computation

5797:   Collective on DM

5799:   Input Parameters:
5800: + dm         - The underlying DM for the domain
5801: . dim        - The spatial dimension
5802: . numComp    - The number of components
5803: . isSimplex  - Flag for simplex reference cell, otherwise its a tensor product
5804: . prefix     - The options prefix, or NULL
5805: - qorder     - The quadrature order

5807:   Output Parameter:
5808: . fem - The PetscFE object

5810:   Level: beginner

5812: .keywords: PetscFE, finite element
5813: .seealso: PetscFECreate(), PetscSpaceCreate(), PetscDualSpaceCreate()
5814: @*/
5815: PetscErrorCode PetscFECreateDefault(DM dm, PetscInt dim, PetscInt numComp, PetscBool isSimplex, const char prefix[], PetscInt qorder, PetscFE *fem)
5816: {
5817:   PetscQuadrature q;
5818:   DM              K;
5819:   PetscSpace      P;
5820:   PetscDualSpace  Q;
5821:   PetscInt        order;
5822:   PetscErrorCode  ierr;

5825:   /* Create space */
5826:   PetscSpaceCreate(PetscObjectComm((PetscObject) dm), &P);
5827:   PetscObjectSetOptionsPrefix((PetscObject) P, prefix);
5828:   PetscSpaceSetFromOptions(P);
5829:   PetscSpacePolynomialSetNumVariables(P, dim);
5830:   PetscSpaceSetUp(P);
5831:   PetscSpaceGetOrder(P, &order);
5832:   /* Create dual space */
5833:   PetscDualSpaceCreate(PetscObjectComm((PetscObject) dm), &Q);
5834:   PetscObjectSetOptionsPrefix((PetscObject) Q, prefix);
5835:   PetscDualSpaceCreateReferenceCell(Q, dim, isSimplex, &K);
5836:   PetscDualSpaceSetDM(Q, K);
5837:   DMDestroy(&K);
5838:   PetscDualSpaceSetOrder(Q, order);
5839:   PetscDualSpaceSetFromOptions(Q);
5840:   PetscDualSpaceSetUp(Q);
5841:   /* Create element */
5842:   PetscFECreate(PetscObjectComm((PetscObject) dm), fem);
5843:   PetscObjectSetOptionsPrefix((PetscObject) *fem, prefix);
5844:   PetscFESetFromOptions(*fem);
5845:   PetscFESetBasisSpace(*fem, P);
5846:   PetscFESetDualSpace(*fem, Q);
5847:   PetscFESetNumComponents(*fem, numComp);
5848:   PetscFESetUp(*fem);
5849:   PetscSpaceDestroy(&P);
5850:   PetscDualSpaceDestroy(&Q);
5851:   /* Create quadrature (with specified order if given) */
5852:   if (isSimplex) {PetscDTGaussJacobiQuadrature(dim, PetscMax(qorder > 0 ? qorder : order, 1), -1.0, 1.0, &q);}
5853:   else           {PetscDTGaussTensorQuadrature(dim, PetscMax(qorder > 0 ? qorder : order, 1), -1.0, 1.0, &q);}
5854:   PetscFESetQuadrature(*fem, q);
5855:   PetscQuadratureDestroy(&q);
5856:   return(0);
5857: }