Date: 2026-03-31T05:46:05+00:00

Actual source code: fe.c

      1: /* Basis Jet Tabulation

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

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

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

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

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

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

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

     22:    \alpha = V^{-1}

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

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

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

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

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

     51: PetscClassId PETSCFE_CLASSID = 0;

     53: PetscLogEvent PETSCFE_SetUp;

     55: PetscFunctionList PetscFEList              = NULL;
     56: PetscBool         PetscFERegisterAllCalled = PETSC_FALSE;

     58: /*@C
     59:   PetscFERegister - Adds a new `PetscFEType`

     61:   Not Collective, No Fortran Support

     63:   Input Parameters:
     64: + sname    - The name of a new user-defined creation routine
     65: - function - The creation routine

     67:   Example Usage:
     68: .vb
     69:     PetscFERegister("my_fe", MyPetscFECreate);
     70: .ve

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

     82:   Level: advanced

     84:   Note:
     85:   `PetscFERegister()` may be called multiple times to add several user-defined `PetscFE`s

     87: .seealso: `PetscFE`, `PetscFEType`, `PetscFERegisterAll()`, `PetscFERegisterDestroy()`
     88: @*/
     89: PetscErrorCode PetscFERegister(const char sname[], PetscErrorCode (*function)(PetscFE))
     90: {
     91:   PetscFunctionBegin;
     92:   PetscCall(PetscFunctionListAdd(&PetscFEList, sname, function));
     93:   PetscFunctionReturn(PETSC_SUCCESS);
     94: }

     96: /*@
     97:   PetscFESetType - Builds a particular `PetscFE`

     99:   Collective

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

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

    108:   Level: intermediate

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

    117:   PetscFunctionBegin;
    119:   PetscCall(PetscObjectTypeCompare((PetscObject)fem, name, &match));
    120:   if (match) PetscFunctionReturn(PETSC_SUCCESS);

    122:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());
    123:   PetscCall(PetscFunctionListFind(PetscFEList, name, &r));
    124:   PetscCheck(r, PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscFE type: %s", name);

    126:   PetscTryTypeMethod(fem, destroy);
    127:   fem->ops->destroy = NULL;

    129:   PetscCall((*r)(fem));
    130:   PetscCall(PetscObjectChangeTypeName((PetscObject)fem, name));
    131:   PetscFunctionReturn(PETSC_SUCCESS);
    132: }

    134: /*@
    135:   PetscFEGetType - Gets the `PetscFEType` (as a string) from the `PetscFE` object.

    137:   Not Collective

    139:   Input Parameter:
    140: . fem - The `PetscFE`

    142:   Output Parameter:
    143: . name - The `PetscFEType` name

    145:   Level: intermediate

    147: .seealso: `PetscFEType`, `PetscFE`, `PetscFESetType()`, `PetscFECreate()`
    148: @*/
    149: PetscErrorCode PetscFEGetType(PetscFE fem, PetscFEType *name)
    150: {
    151:   PetscFunctionBegin;
    153:   PetscAssertPointer(name, 2);
    154:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());
    155:   *name = ((PetscObject)fem)->type_name;
    156:   PetscFunctionReturn(PETSC_SUCCESS);
    157: }

    159: /*@
    160:   PetscFEViewFromOptions - View from a `PetscFE` based on values in the options database

    162:   Collective

    164:   Input Parameters:
    165: + A    - the `PetscFE` object
    166: . obj  - Optional object that provides the options prefix, pass `NULL` to use the options prefix of `A`
    167: - name - command line option name

    169:   Level: intermediate

    171: .seealso: `PetscFE`, `PetscFEView()`, `PetscObjectViewFromOptions()`, `PetscFECreate()`
    172: @*/
    173: PetscErrorCode PetscFEViewFromOptions(PetscFE A, PeOp PetscObject obj, const char name[])
    174: {
    175:   PetscFunctionBegin;
    177:   PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
    178:   PetscFunctionReturn(PETSC_SUCCESS);
    179: }

    181: /*@
    182:   PetscFEView - Views a `PetscFE`

    184:   Collective

    186:   Input Parameters:
    187: + fem    - the `PetscFE` object to view
    188: - viewer - the viewer

    190:   Level: beginner

    192: .seealso: `PetscFE`, `PetscViewer`, `PetscFEDestroy()`, `PetscFEViewFromOptions()`
    193: @*/
    194: PetscErrorCode PetscFEView(PetscFE fem, PetscViewer viewer)
    195: {
    196:   PetscBool isascii;

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

    208: /*@
    209:   PetscFESetFromOptions - sets parameters in a `PetscFE` from the options database

    211:   Collective

    213:   Input Parameter:
    214: . fem - the `PetscFE` object to set options for

    216:   Options Database Keys:
    217: + -petscfe_num_blocks  - the number of cell blocks to integrate concurrently
    218: - -petscfe_num_batches - the number of cell batches to integrate serially

    220:   Level: intermediate

    222: .seealso: `PetscFE`, `PetscFEView()`
    223: @*/
    224: PetscErrorCode PetscFESetFromOptions(PetscFE fem)
    225: {
    226:   const char *defaultType;
    227:   char        name[256];
    228:   PetscBool   flg;

    230:   PetscFunctionBegin;
    232:   if (!((PetscObject)fem)->type_name) defaultType = PETSCFEBASIC;
    233:   else defaultType = ((PetscObject)fem)->type_name;
    234:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());

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

    250: /*@
    251:   PetscFESetUp - Construct data structures for the `PetscFE` after the `PetscFEType` has been set

    253:   Collective

    255:   Input Parameter:
    256: . fem - the `PetscFE` object to setup

    258:   Level: intermediate

    260: .seealso: `PetscFE`, `PetscFEView()`, `PetscFEDestroy()`
    261: @*/
    262: PetscErrorCode PetscFESetUp(PetscFE fem)
    263: {
    264:   PetscFunctionBegin;
    266:   if (fem->setupcalled) PetscFunctionReturn(PETSC_SUCCESS);
    267:   PetscCall(PetscLogEventBegin(PETSCFE_SetUp, fem, 0, 0, 0));
    268:   fem->setupcalled = PETSC_TRUE;
    269:   PetscTryTypeMethod(fem, setup);
    270:   PetscCall(PetscLogEventEnd(PETSCFE_SetUp, fem, 0, 0, 0));
    271:   PetscFunctionReturn(PETSC_SUCCESS);
    272: }

    274: /*@
    275:   PetscFEDestroy - Destroys a `PetscFE` object

    277:   Collective

    279:   Input Parameter:
    280: . fem - the `PetscFE` object to destroy

    282:   Level: beginner

    284: .seealso: `PetscFE`, `PetscFEView()`
    285: @*/
    286: PetscErrorCode PetscFEDestroy(PetscFE *fem)
    287: {
    288:   PetscFunctionBegin;
    289:   if (!*fem) PetscFunctionReturn(PETSC_SUCCESS);

    292:   if (--((PetscObject)*fem)->refct > 0) {
    293:     *fem = NULL;
    294:     PetscFunctionReturn(PETSC_SUCCESS);
    295:   }
    296:   ((PetscObject)*fem)->refct = 0;

    298:   if ((*fem)->subspaces) {
    299:     PetscInt dim, d;

    301:     PetscCall(PetscDualSpaceGetDimension((*fem)->dualSpace, &dim));
    302:     for (d = 0; d < dim; ++d) PetscCall(PetscFEDestroy(&(*fem)->subspaces[d]));
    303:   }
    304:   PetscCall(PetscFree((*fem)->subspaces));
    305:   PetscCall(PetscFree((*fem)->invV));
    306:   PetscCall(PetscTabulationDestroy(&(*fem)->T));
    307:   PetscCall(PetscTabulationDestroy(&(*fem)->Tf));
    308:   PetscCall(PetscTabulationDestroy(&(*fem)->Tc));
    309:   PetscCall(PetscSpaceDestroy(&(*fem)->basisSpace));
    310:   PetscCall(PetscDualSpaceDestroy(&(*fem)->dualSpace));
    311:   PetscCall(PetscQuadratureDestroy(&(*fem)->quadrature));
    312:   PetscCall(PetscQuadratureDestroy(&(*fem)->faceQuadrature));
    313: #ifdef PETSC_HAVE_LIBCEED
    314:   PetscCallCEED(CeedBasisDestroy(&(*fem)->ceedBasis));
    315:   PetscCallCEED(CeedDestroy(&(*fem)->ceed));
    316: #endif

    318:   PetscTryTypeMethod(*fem, destroy);
    319:   PetscCall(PetscHeaderDestroy(fem));
    320:   PetscFunctionReturn(PETSC_SUCCESS);
    321: }

    323: /*@
    324:   PetscFECreate - Creates an empty `PetscFE` object. The type can then be set with `PetscFESetType()`.

    326:   Collective

    328:   Input Parameter:
    329: . comm - The communicator for the `PetscFE` object

    331:   Output Parameter:
    332: . fem - The `PetscFE` object

    334:   Level: beginner

    336: .seealso: `PetscFE`, `PetscFEType`, `PetscFESetType()`, `PetscFECreateDefault()`, `PETSCFEGALERKIN`
    337: @*/
    338: PetscErrorCode PetscFECreate(MPI_Comm comm, PetscFE *fem)
    339: {
    340:   PetscFE f;

    342:   PetscFunctionBegin;
    343:   PetscAssertPointer(fem, 2);
    344:   PetscCall(PetscCitationsRegister(FECitation, &FEcite));
    345:   PetscCall(PetscFEInitializePackage());

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

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

    364:   *fem = f;
    365:   PetscFunctionReturn(PETSC_SUCCESS);
    366: }

    368: /*@
    369:   PetscFEGetSpatialDimension - Returns the spatial dimension of the element

    371:   Not Collective

    373:   Input Parameter:
    374: . fem - The `PetscFE` object

    376:   Output Parameter:
    377: . dim - The spatial dimension

    379:   Level: intermediate

    381: .seealso: `PetscFE`, `PetscFECreate()`
    382: @*/
    383: PetscErrorCode PetscFEGetSpatialDimension(PetscFE fem, PetscInt *dim)
    384: {
    385:   DM dm;

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

    395: /*@
    396:   PetscFESetNumComponents - Sets the number of field components in the element

    398:   Not Collective

    400:   Input Parameters:
    401: + fem  - The `PetscFE` object
    402: - comp - The number of field components

    404:   Level: intermediate

    406: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`, `PetscFEGetNumComponents()`
    407: @*/
    408: PetscErrorCode PetscFESetNumComponents(PetscFE fem, PetscInt comp)
    409: {
    410:   PetscFunctionBegin;
    412:   fem->numComponents = comp;
    413:   PetscFunctionReturn(PETSC_SUCCESS);
    414: }

    416: /*@
    417:   PetscFEGetNumComponents - Returns the number of components in the element

    419:   Not Collective

    421:   Input Parameter:
    422: . fem - The `PetscFE` object

    424:   Output Parameter:
    425: . comp - The number of field components

    427:   Level: intermediate

    429: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`
    430: @*/
    431: PetscErrorCode PetscFEGetNumComponents(PetscFE fem, PetscInt *comp)
    432: {
    433:   PetscFunctionBegin;
    435:   PetscAssertPointer(comp, 2);
    436:   *comp = fem->numComponents;
    437:   PetscFunctionReturn(PETSC_SUCCESS);
    438: }

    440: /*@
    441:   PetscFESetTileSizes - Sets the tile sizes for evaluation

    443:   Not Collective

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

    452:   Level: intermediate

    454: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetTileSizes()`
    455: @*/
    456: PetscErrorCode PetscFESetTileSizes(PetscFE fem, PetscInt blockSize, PetscInt numBlocks, PetscInt batchSize, PetscInt numBatches)
    457: {
    458:   PetscFunctionBegin;
    460:   fem->blockSize  = blockSize;
    461:   fem->numBlocks  = numBlocks;
    462:   fem->batchSize  = batchSize;
    463:   fem->numBatches = numBatches;
    464:   PetscFunctionReturn(PETSC_SUCCESS);
    465: }

    467: /*@
    468:   PetscFEGetTileSizes - Returns the tile sizes for evaluation

    470:   Not Collective

    472:   Input Parameter:
    473: . fem - The `PetscFE` object

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

    481:   Level: intermediate

    483: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFESetTileSizes()`
    484: @*/
    485: PetscErrorCode PetscFEGetTileSizes(PetscFE fem, PeOp PetscInt *blockSize, PeOp PetscInt *numBlocks, PeOp PetscInt *batchSize, PeOp PetscInt *numBatches)
    486: {
    487:   PetscFunctionBegin;
    489:   if (blockSize) PetscAssertPointer(blockSize, 2);
    490:   if (numBlocks) PetscAssertPointer(numBlocks, 3);
    491:   if (batchSize) PetscAssertPointer(batchSize, 4);
    492:   if (numBatches) PetscAssertPointer(numBatches, 5);
    493:   if (blockSize) *blockSize = fem->blockSize;
    494:   if (numBlocks) *numBlocks = fem->numBlocks;
    495:   if (batchSize) *batchSize = fem->batchSize;
    496:   if (numBatches) *numBatches = fem->numBatches;
    497:   PetscFunctionReturn(PETSC_SUCCESS);
    498: }

    500: /*@
    501:   PetscFEGetBasisSpace - Returns the `PetscSpace` used for the approximation of the solution for the `PetscFE`

    503:   Not Collective

    505:   Input Parameter:
    506: . fem - The `PetscFE` object

    508:   Output Parameter:
    509: . sp - The `PetscSpace` object

    511:   Level: intermediate

    513: .seealso: `PetscFE`, `PetscSpace`, `PetscFECreate()`
    514: @*/
    515: PetscErrorCode PetscFEGetBasisSpace(PetscFE fem, PetscSpace *sp)
    516: {
    517:   PetscFunctionBegin;
    519:   PetscAssertPointer(sp, 2);
    520:   *sp = fem->basisSpace;
    521:   PetscFunctionReturn(PETSC_SUCCESS);
    522: }

    524: /*@
    525:   PetscFESetBasisSpace - Sets the `PetscSpace` used for the approximation of the solution

    527:   Not Collective

    529:   Input Parameters:
    530: + fem - The `PetscFE` object
    531: - sp  - The `PetscSpace` object

    533:   Level: intermediate

    535:   Developer Notes:
    536:   There is `PetscFESetBasisSpace()` but the `PetscFESetDualSpace()`, likely the Basis is unneeded in the function name

    538: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetDualSpace()`
    539: @*/
    540: PetscErrorCode PetscFESetBasisSpace(PetscFE fem, PetscSpace sp)
    541: {
    542:   PetscFunctionBegin;
    545:   PetscCall(PetscSpaceDestroy(&fem->basisSpace));
    546:   fem->basisSpace = sp;
    547:   PetscCall(PetscObjectReference((PetscObject)fem->basisSpace));
    548:   PetscFunctionReturn(PETSC_SUCCESS);
    549: }

    551: /*@
    552:   PetscFEGetDualSpace - Returns the `PetscDualSpace` used to define the inner product for a `PetscFE`

    554:   Not Collective

    556:   Input Parameter:
    557: . fem - The `PetscFE` object

    559:   Output Parameter:
    560: . sp - The `PetscDualSpace` object

    562:   Level: intermediate

    564: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
    565: @*/
    566: PetscErrorCode PetscFEGetDualSpace(PetscFE fem, PetscDualSpace *sp)
    567: {
    568:   PetscFunctionBegin;
    570:   PetscAssertPointer(sp, 2);
    571:   *sp = fem->dualSpace;
    572:   PetscFunctionReturn(PETSC_SUCCESS);
    573: }

    575: /*@
    576:   PetscFESetDualSpace - Sets the `PetscDualSpace` used to define the inner product

    578:   Not Collective

    580:   Input Parameters:
    581: + fem - The `PetscFE` object
    582: - sp  - The `PetscDualSpace` object

    584:   Level: intermediate

    586: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetBasisSpace()`
    587: @*/
    588: PetscErrorCode PetscFESetDualSpace(PetscFE fem, PetscDualSpace sp)
    589: {
    590:   PetscFunctionBegin;
    593:   PetscCall(PetscDualSpaceDestroy(&fem->dualSpace));
    594:   fem->dualSpace = sp;
    595:   PetscCall(PetscObjectReference((PetscObject)fem->dualSpace));
    596:   PetscFunctionReturn(PETSC_SUCCESS);
    597: }

    599: /*@
    600:   PetscFEGetQuadrature - Returns the `PetscQuadrature` used to calculate inner products

    602:   Not Collective

    604:   Input Parameter:
    605: . fem - The `PetscFE` object

    607:   Output Parameter:
    608: . q - The `PetscQuadrature` object

    610:   Level: intermediate

    612: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`
    613: @*/
    614: PetscErrorCode PetscFEGetQuadrature(PetscFE fem, PetscQuadrature *q)
    615: {
    616:   PetscFunctionBegin;
    618:   PetscAssertPointer(q, 2);
    619:   *q = fem->quadrature;
    620:   PetscFunctionReturn(PETSC_SUCCESS);
    621: }

    623: /*@
    624:   PetscFESetQuadrature - Sets the `PetscQuadrature` used to calculate inner products

    626:   Not Collective

    628:   Input Parameters:
    629: + fem - The `PetscFE` object
    630: - q   - The `PetscQuadrature` object

    632:   Level: intermediate

    634: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFEGetFaceQuadrature()`
    635: @*/
    636: PetscErrorCode PetscFESetQuadrature(PetscFE fem, PetscQuadrature q)
    637: {
    638:   PetscInt Nc, qNc;

    640:   PetscFunctionBegin;
    642:   if (q == fem->quadrature) PetscFunctionReturn(PETSC_SUCCESS);
    643:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
    644:   PetscCall(PetscQuadratureGetNumComponents(q, &qNc));
    645:   PetscCheck(!(qNc != 1) || !(Nc != qNc), PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_SIZ, "FE components %" PetscInt_FMT " != Quadrature components %" PetscInt_FMT " and non-scalar quadrature", Nc, qNc);
    646:   PetscCall(PetscTabulationDestroy(&fem->T));
    647:   PetscCall(PetscTabulationDestroy(&fem->Tc));
    648:   PetscCall(PetscObjectReference((PetscObject)q));
    649:   PetscCall(PetscQuadratureDestroy(&fem->quadrature));
    650:   fem->quadrature = q;
    651:   PetscFunctionReturn(PETSC_SUCCESS);
    652: }

    654: /*@
    655:   PetscFEGetFaceQuadrature - Returns the `PetscQuadrature` used to calculate inner products on faces

    657:   Not Collective

    659:   Input Parameter:
    660: . fem - The `PetscFE` object

    662:   Output Parameter:
    663: . q - The `PetscQuadrature` object

    665:   Level: intermediate

    667:   Developer Notes:
    668:   There is a special face quadrature but not edge, likely this API would benefit from a refactorization

    670: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
    671: @*/
    672: PetscErrorCode PetscFEGetFaceQuadrature(PetscFE fem, PetscQuadrature *q)
    673: {
    674:   PetscFunctionBegin;
    676:   PetscAssertPointer(q, 2);
    677:   *q = fem->faceQuadrature;
    678:   PetscFunctionReturn(PETSC_SUCCESS);
    679: }

    681: /*@
    682:   PetscFESetFaceQuadrature - Sets the `PetscQuadrature` used to calculate inner products on faces

    684:   Not Collective

    686:   Input Parameters:
    687: + fem - The `PetscFE` object
    688: - q   - The `PetscQuadrature` object

    690:   Level: intermediate

    692: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`
    693: @*/
    694: PetscErrorCode PetscFESetFaceQuadrature(PetscFE fem, PetscQuadrature q)
    695: {
    696:   PetscInt Nc, qNc;

    698:   PetscFunctionBegin;
    700:   if (q == fem->faceQuadrature) PetscFunctionReturn(PETSC_SUCCESS);
    701:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
    702:   PetscCall(PetscQuadratureGetNumComponents(q, &qNc));
    703:   PetscCheck(!(qNc != 1) || !(Nc != qNc), PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_SIZ, "FE components %" PetscInt_FMT " != Quadrature components %" PetscInt_FMT " and non-scalar quadrature", Nc, qNc);
    704:   PetscCall(PetscTabulationDestroy(&fem->Tf));
    705:   PetscCall(PetscObjectReference((PetscObject)q));
    706:   PetscCall(PetscQuadratureDestroy(&fem->faceQuadrature));
    707:   fem->faceQuadrature = q;
    708:   PetscFunctionReturn(PETSC_SUCCESS);
    709: }

    711: /*@
    712:   PetscFECopyQuadrature - Copy both volumetric and surface quadrature to a new `PetscFE`

    714:   Not Collective

    716:   Input Parameters:
    717: + sfe - The `PetscFE` source for the quadratures
    718: - tfe - The `PetscFE` target for the quadratures

    720:   Level: intermediate

    722: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
    723: @*/
    724: PetscErrorCode PetscFECopyQuadrature(PetscFE sfe, PetscFE tfe)
    725: {
    726:   PetscQuadrature q;

    728:   PetscFunctionBegin;
    731:   PetscCall(PetscFEGetQuadrature(sfe, &q));
    732:   PetscCall(PetscFESetQuadrature(tfe, q));
    733:   PetscCall(PetscFEGetFaceQuadrature(sfe, &q));
    734:   PetscCall(PetscFESetFaceQuadrature(tfe, q));
    735:   PetscFunctionReturn(PETSC_SUCCESS);
    736: }

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

    741:   Not Collective

    743:   Input Parameter:
    744: . fem - The `PetscFE` object

    746:   Output Parameter:
    747: . numDof - Array of length `dim` with the number of dofs in each dimension

    749:   Level: intermediate

    751: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
    752: @*/
    753: PetscErrorCode PetscFEGetNumDof(PetscFE fem, const PetscInt *numDof[])
    754: {
    755:   PetscFunctionBegin;
    757:   PetscAssertPointer(numDof, 2);
    758:   PetscCall(PetscDualSpaceGetNumDof(fem->dualSpace, numDof));
    759:   PetscFunctionReturn(PETSC_SUCCESS);
    760: }

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

    765:   Not Collective

    767:   Input Parameters:
    768: + fem - The `PetscFE` object
    769: - k   - The highest derivative we need to tabulate, very often 1

    771:   Output Parameter:
    772: . T - The basis function values and derivatives at quadrature points

    774:   Level: intermediate

    776:   Note:
    777: .vb
    778:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    779:   T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
    780:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e
    781: .ve

    783: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
    784: @*/
    785: PetscErrorCode PetscFEGetCellTabulation(PetscFE fem, PetscInt k, PetscTabulation *T)
    786: {
    787:   PetscInt         npoints;
    788:   const PetscReal *points;

    790:   PetscFunctionBegin;
    792:   PetscAssertPointer(T, 3);
    793:   PetscCall(PetscQuadratureGetData(fem->quadrature, NULL, NULL, &npoints, &points, NULL));
    794:   if (!fem->T) PetscCall(PetscFECreateTabulation(fem, 1, npoints, points, k, &fem->T));
    795:   PetscCheck(!fem->T || k <= fem->T->K || (!fem->T->cdim && !fem->T->K), PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_OUTOFRANGE, "Requested %" PetscInt_FMT " derivatives, but only tabulated %" PetscInt_FMT, k, fem->T->K);
    796:   *T = fem->T;
    797:   PetscFunctionReturn(PETSC_SUCCESS);
    798: }

    800: PetscErrorCode PetscFEExpandFaceQuadrature(PetscFE fe, PetscQuadrature fq, PetscQuadrature *efq)
    801: {
    802:   DM               dm;
    803:   PetscDualSpace   sp;
    804:   const PetscInt  *faces;
    805:   const PetscReal *points, *weights;
    806:   DMPolytopeType   ct;
    807:   PetscReal       *facePoints, *faceWeights;
    808:   PetscInt         dim, cStart, Nf, Nc, Np, order;

    810:   PetscFunctionBegin;
    811:   PetscCall(PetscFEGetDualSpace(fe, &sp));
    812:   PetscCall(PetscDualSpaceGetDM(sp, &dm));
    813:   PetscCall(DMGetDimension(dm, &dim));
    814:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
    815:   PetscCall(DMPlexGetConeSize(dm, cStart, &Nf));
    816:   PetscCall(DMPlexGetCone(dm, cStart, &faces));
    817:   PetscCall(PetscQuadratureGetData(fq, NULL, &Nc, &Np, &points, &weights));
    818:   PetscCall(PetscMalloc1(Nf * Np * dim, &facePoints));
    819:   PetscCall(PetscMalloc1(Nf * Np * Nc, &faceWeights));
    820:   for (PetscInt f = 0; f < Nf; ++f) {
    821:     const PetscReal xi0[3] = {-1., -1., -1.};
    822:     PetscReal       v0[3], J[9], detJ;

    824:     PetscCall(DMPlexComputeCellGeometryFEM(dm, faces[f], NULL, v0, J, NULL, &detJ));
    825:     for (PetscInt q = 0; q < Np; ++q) {
    826:       CoordinatesRefToReal(dim, dim - 1, xi0, v0, J, &points[q * (dim - 1)], &facePoints[(f * Np + q) * dim]);
    827:       for (PetscInt c = 0; c < Nc; ++c) faceWeights[(f * Np + q) * Nc + c] = weights[q * Nc + c];
    828:     }
    829:   }
    830:   PetscCall(PetscQuadratureCreate(PetscObjectComm((PetscObject)fq), efq));
    831:   PetscCall(PetscQuadratureGetCellType(fq, &ct));
    832:   PetscCall(PetscQuadratureSetCellType(*efq, ct));
    833:   PetscCall(PetscQuadratureGetOrder(fq, &order));
    834:   PetscCall(PetscQuadratureSetOrder(*efq, order));
    835:   PetscCall(PetscQuadratureSetData(*efq, dim, Nc, Nf * Np, facePoints, faceWeights));
    836:   PetscFunctionReturn(PETSC_SUCCESS);
    837: }

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

    842:   Not Collective

    844:   Input Parameters:
    845: + fem - The `PetscFE` object
    846: - k   - The highest derivative we need to tabulate, very often 1

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

    851:   Level: intermediate

    853:   Note:
    854: .vb
    855:   T->T[0] = Bf[((f*Nq + q)*pdim + i)*Nc + c] is the value at point f,q for basis function i and component c
    856:   T->T[1] = Df[(((f*Nq + q)*pdim + i)*Nc + c)*dim + d] is the derivative value at point f,q for basis function i, component c, in direction d
    857:   T->T[2] = Hf[((((f*Nq + q)*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point f,q for basis function i, component c, in directions d and e
    858: .ve

    860: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
    861: @*/
    862: PetscErrorCode PetscFEGetFaceTabulation(PetscFE fem, PetscInt k, PetscTabulation *Tf)
    863: {
    864:   PetscFunctionBegin;
    866:   PetscAssertPointer(Tf, 3);
    867:   if (!fem->Tf) {
    868:     PetscQuadrature fq;

    870:     PetscCall(PetscFEGetFaceQuadrature(fem, &fq));
    871:     if (fq) {
    872:       PetscQuadrature  efq;
    873:       const PetscReal *facePoints;
    874:       PetscInt         Np, eNp;

    876:       PetscCall(PetscFEExpandFaceQuadrature(fem, fq, &efq));
    877:       PetscCall(PetscQuadratureGetData(fq, NULL, NULL, &Np, NULL, NULL));
    878:       PetscCall(PetscQuadratureGetData(efq, NULL, NULL, &eNp, &facePoints, NULL));
    879:       if (PetscDefined(USE_DEBUG)) {
    880:         PetscDualSpace sp;
    881:         DM             dm;
    882:         PetscInt       cStart, Nf;

    884:         PetscCall(PetscFEGetDualSpace(fem, &sp));
    885:         PetscCall(PetscDualSpaceGetDM(sp, &dm));
    886:         PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
    887:         PetscCall(DMPlexGetConeSize(dm, cStart, &Nf));
    888:         PetscCheck(Nf == eNp / Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of faces %" PetscInt_FMT " != %" PetscInt_FMT " number of quadrature replicas", Nf, eNp / Np);
    889:       }
    890:       PetscCall(PetscFECreateTabulation(fem, eNp / Np, Np, facePoints, k, &fem->Tf));
    891:       PetscCall(PetscQuadratureDestroy(&efq));
    892:     }
    893:   }
    894:   PetscCheck(!fem->Tf || k <= fem->Tf->K, PetscObjectComm((PetscObject)fem), PETSC_ERR_ARG_OUTOFRANGE, "Requested %" PetscInt_FMT " derivatives, but only tabulated %" PetscInt_FMT, k, fem->Tf->K);
    895:   *Tf = fem->Tf;
    896:   PetscFunctionReturn(PETSC_SUCCESS);
    897: }

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

    902:   Not Collective

    904:   Input Parameter:
    905: . fem - The `PetscFE` object

    907:   Output Parameter:
    908: . Tc - The basis function values at face centroid points

    910:   Level: intermediate

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

    917: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetFaceTabulation()`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
    918: @*/
    919: PetscErrorCode PetscFEGetFaceCentroidTabulation(PetscFE fem, PetscTabulation *Tc)
    920: {
    921:   PetscFunctionBegin;
    923:   PetscAssertPointer(Tc, 2);
    924:   if (!fem->Tc) {
    925:     PetscDualSpace  sp;
    926:     DM              dm;
    927:     const PetscInt *cone;
    928:     PetscReal      *centroids;
    929:     PetscInt        dim, numFaces, f;

    931:     PetscCall(PetscFEGetDualSpace(fem, &sp));
    932:     PetscCall(PetscDualSpaceGetDM(sp, &dm));
    933:     PetscCall(DMGetDimension(dm, &dim));
    934:     PetscCall(DMPlexGetConeSize(dm, 0, &numFaces));
    935:     PetscCall(DMPlexGetCone(dm, 0, &cone));
    936:     PetscCall(PetscMalloc1(numFaces * dim, &centroids));
    937:     for (f = 0; f < numFaces; ++f) PetscCall(DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, &centroids[f * dim], NULL));
    938:     PetscCall(PetscFECreateTabulation(fem, 1, numFaces, centroids, 0, &fem->Tc));
    939:     PetscCall(PetscFree(centroids));
    940:   }
    941:   *Tc = fem->Tc;
    942:   PetscFunctionReturn(PETSC_SUCCESS);
    943: }

    945: /*@C
    946:   PetscFECreateTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided.

    948:   Not Collective

    950:   Input Parameters:
    951: + fem     - The `PetscFE` object
    952: . nrepl   - The number of replicas
    953: . npoints - The number of tabulation points in a replica
    954: . points  - The tabulation point coordinates
    955: - K       - The number of derivatives calculated

    957:   Output Parameter:
    958: . T - The basis function values and derivatives at tabulation points

    960:   Level: intermediate

    962:   Note:
    963: .vb
    964:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    965:   T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
    966:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis
    967:   T->function i, component c, in directions d and e
    968: .ve

    970: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`
    971: @*/
    972: PetscErrorCode PetscFECreateTabulation(PetscFE fem, PetscInt nrepl, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation *T)
    973: {
    974:   DM             dm;
    975:   PetscDualSpace Q;
    976:   PetscInt       Nb;   /* Dimension of FE space P */
    977:   PetscInt       Nc;   /* Field components */
    978:   PetscInt       cdim; /* Reference coordinate dimension */
    979:   PetscInt       k;

    981:   PetscFunctionBegin;
    982:   if (!npoints || !fem->dualSpace || K < 0) {
    983:     *T = NULL;
    984:     PetscFunctionReturn(PETSC_SUCCESS);
    985:   }
    987:   PetscAssertPointer(points, 4);
    988:   PetscAssertPointer(T, 6);
    989:   PetscCall(PetscFEGetDualSpace(fem, &Q));
    990:   PetscCall(PetscDualSpaceGetDM(Q, &dm));
    991:   PetscCall(DMGetDimension(dm, &cdim));
    992:   PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
    993:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
    994:   PetscCall(PetscMalloc1(1, T));
    995:   (*T)->K    = !cdim ? 0 : K;
    996:   (*T)->Nr   = nrepl;
    997:   (*T)->Np   = npoints;
    998:   (*T)->Nb   = Nb;
    999:   (*T)->Nc   = Nc;
    1000:   (*T)->cdim = cdim;
    1001:   PetscCall(PetscMalloc1((*T)->K + 1, &(*T)->T));
    1002:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscCalloc1(nrepl * npoints * Nb * Nc * PetscPowInt(cdim, k), &(*T)->T[k]));
    1003:   PetscUseTypeMethod(fem, computetabulation, nrepl * npoints, points, K, *T);
    1004:   PetscFunctionReturn(PETSC_SUCCESS);
    1005: }

    1007: /*@C
    1008:   PetscFEComputeTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided.

    1010:   Not Collective

    1012:   Input Parameters:
    1013: + fem     - The `PetscFE` object
    1014: . npoints - The number of tabulation points
    1015: . points  - The tabulation point coordinates
    1016: . K       - The number of derivatives calculated
    1017: - T       - An existing tabulation object with enough allocated space

    1019:   Output Parameter:
    1020: . T - The basis function values and derivatives at tabulation points

    1022:   Level: intermediate

    1024:   Note:
    1025: .vb
    1026:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    1027:   T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
    1028:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e
    1029: .ve

    1031: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`
    1032: @*/
    1033: PetscErrorCode PetscFEComputeTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation T)
    1034: {
    1035:   PetscFunctionBeginHot;
    1036:   if (!npoints || !fem->dualSpace || K < 0) PetscFunctionReturn(PETSC_SUCCESS);
    1038:   PetscAssertPointer(points, 3);
    1039:   PetscAssertPointer(T, 5);
    1040:   if (PetscDefined(USE_DEBUG)) {
    1041:     DM             dm;
    1042:     PetscDualSpace Q;
    1043:     PetscInt       Nb;   /* Dimension of FE space P */
    1044:     PetscInt       Nc;   /* Field components */
    1045:     PetscInt       cdim; /* Reference coordinate dimension */

    1047:     PetscCall(PetscFEGetDualSpace(fem, &Q));
    1048:     PetscCall(PetscDualSpaceGetDM(Q, &dm));
    1049:     PetscCall(DMGetDimension(dm, &cdim));
    1050:     PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
    1051:     PetscCall(PetscFEGetNumComponents(fem, &Nc));
    1052:     PetscCheck(T->K == (!cdim ? 0 : K), PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation K %" PetscInt_FMT " must match requested K %" PetscInt_FMT, T->K, !cdim ? 0 : K);
    1053:     PetscCheck(T->Nb == Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nb %" PetscInt_FMT " must match requested Nb %" PetscInt_FMT, T->Nb, Nb);
    1054:     PetscCheck(T->Nc == Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nc %" PetscInt_FMT " must match requested Nc %" PetscInt_FMT, T->Nc, Nc);
    1055:     PetscCheck(T->cdim == cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation cdim %" PetscInt_FMT " must match requested cdim %" PetscInt_FMT, T->cdim, cdim);
    1056:   }
    1057:   T->Nr = 1;
    1058:   T->Np = npoints;
    1059:   PetscUseTypeMethod(fem, computetabulation, npoints, points, K, T);
    1060:   PetscFunctionReturn(PETSC_SUCCESS);
    1061: }

    1063: /*@
    1064:   PetscTabulationDestroy - Frees memory from the associated tabulation.

    1066:   Not Collective

    1068:   Input Parameter:
    1069: . T - The tabulation

    1071:   Level: intermediate

    1073: .seealso: `PetscTabulation`, `PetscFECreateTabulation()`, `PetscFEGetCellTabulation()`
    1074: @*/
    1075: PetscErrorCode PetscTabulationDestroy(PetscTabulation *T)
    1076: {
    1077:   PetscInt k;

    1079:   PetscFunctionBegin;
    1080:   PetscAssertPointer(T, 1);
    1081:   if (!T || !*T) PetscFunctionReturn(PETSC_SUCCESS);
    1082:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscFree((*T)->T[k]));
    1083:   PetscCall(PetscFree((*T)->T));
    1084:   PetscCall(PetscFree(*T));
    1085:   *T = NULL;
    1086:   PetscFunctionReturn(PETSC_SUCCESS);
    1087: }

    1089: static PetscErrorCode PetscFECreatePointTraceDefault_Internal(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
    1090: {
    1091:   PetscSpace      bsp, bsubsp;
    1092:   PetscDualSpace  dsp, dsubsp;
    1093:   PetscInt        dim, depth, numComp, i, j, coneSize, order;
    1094:   DM              dm;
    1095:   DMLabel         label;
    1096:   PetscReal      *xi, *v, *J, detJ;
    1097:   const char     *name;
    1098:   PetscQuadrature origin, fullQuad, subQuad;

    1100:   PetscFunctionBegin;
    1101:   PetscCall(PetscFEGetBasisSpace(fe, &bsp));
    1102:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    1103:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    1104:   PetscCall(DMGetDimension(dm, &dim));
    1105:   PetscCall(DMPlexGetDepthLabel(dm, &label));
    1106:   PetscCall(DMLabelGetValue(label, refPoint, &depth));
    1107:   PetscCall(PetscCalloc1(depth, &xi));
    1108:   PetscCall(PetscMalloc1(dim, &v));
    1109:   PetscCall(PetscMalloc1(dim * dim, &J));
    1110:   for (i = 0; i < depth; i++) xi[i] = 0.;
    1111:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &origin));
    1112:   PetscCall(PetscQuadratureSetData(origin, depth, 0, 1, xi, NULL));
    1113:   PetscCall(DMPlexComputeCellGeometryFEM(dm, refPoint, origin, v, J, NULL, &detJ));
    1114:   /* CellGeometryFEM computes the expanded Jacobian, we want the true jacobian */
    1115:   for (i = 1; i < dim; i++) {
    1116:     for (j = 0; j < depth; j++) J[i * depth + j] = J[i * dim + j];
    1117:   }
    1118:   PetscCall(PetscQuadratureDestroy(&origin));
    1119:   PetscCall(PetscDualSpaceGetPointSubspace(dsp, refPoint, &dsubsp));
    1120:   PetscCall(PetscSpaceCreateSubspace(bsp, dsubsp, v, J, NULL, NULL, PETSC_OWN_POINTER, &bsubsp));
    1121:   PetscCall(PetscSpaceSetUp(bsubsp));
    1122:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), trFE));
    1123:   PetscCall(PetscFESetType(*trFE, PETSCFEBASIC));
    1124:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    1125:   PetscCall(PetscFESetNumComponents(*trFE, numComp));
    1126:   PetscCall(PetscFESetBasisSpace(*trFE, bsubsp));
    1127:   PetscCall(PetscFESetDualSpace(*trFE, dsubsp));
    1128:   PetscCall(PetscObjectGetName((PetscObject)fe, &name));
    1129:   if (name) PetscCall(PetscFESetName(*trFE, name));
    1130:   PetscCall(PetscFEGetQuadrature(fe, &fullQuad));
    1131:   PetscCall(PetscQuadratureGetOrder(fullQuad, &order));
    1132:   PetscCall(DMPlexGetConeSize(dm, refPoint, &coneSize));
    1133:   if (coneSize == 2 * depth) PetscCall(PetscDTGaussTensorQuadrature(depth, 1, (order + 2) / 2, -1., 1., &subQuad));
    1134:   else PetscCall(PetscDTSimplexQuadrature(depth, order, PETSCDTSIMPLEXQUAD_DEFAULT, &subQuad));
    1135:   PetscCall(PetscFESetQuadrature(*trFE, subQuad));
    1136:   PetscCall(PetscFESetUp(*trFE));
    1137:   PetscCall(PetscQuadratureDestroy(&subQuad));
    1138:   PetscCall(PetscSpaceDestroy(&bsubsp));
    1139:   PetscFunctionReturn(PETSC_SUCCESS);
    1140: }

    1142: PETSC_EXTERN PetscErrorCode PetscFECreatePointTrace(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
    1143: {
    1144:   PetscFunctionBegin;
    1146:   PetscAssertPointer(trFE, 3);
    1147:   if (fe->ops->createpointtrace) PetscUseTypeMethod(fe, createpointtrace, refPoint, trFE);
    1148:   else PetscCall(PetscFECreatePointTraceDefault_Internal(fe, refPoint, trFE));
    1149:   PetscFunctionReturn(PETSC_SUCCESS);
    1150: }

    1152: PetscErrorCode PetscFECreateHeightTrace(PetscFE fe, PetscInt height, PetscFE *trFE)
    1153: {
    1154:   PetscInt       hStart, hEnd;
    1155:   PetscDualSpace dsp;
    1156:   DM             dm;

    1158:   PetscFunctionBegin;
    1160:   PetscAssertPointer(trFE, 3);
    1161:   *trFE = NULL;
    1162:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    1163:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    1164:   PetscCall(DMPlexGetHeightStratum(dm, height, &hStart, &hEnd));
    1165:   if (hEnd <= hStart) PetscFunctionReturn(PETSC_SUCCESS);
    1166:   PetscCall(PetscFECreatePointTrace(fe, hStart, trFE));
    1167:   PetscFunctionReturn(PETSC_SUCCESS);
    1168: }

    1170: /*@
    1171:   PetscFEGetDimension - Get the dimension of the finite element space on a cell

    1173:   Not Collective

    1175:   Input Parameter:
    1176: . fem - The `PetscFE`

    1178:   Output Parameter:
    1179: . dim - The dimension

    1181:   Level: intermediate

    1183: .seealso: `PetscFE`, `PetscFECreate()`, `PetscSpaceGetDimension()`, `PetscDualSpaceGetDimension()`
    1184: @*/
    1185: PetscErrorCode PetscFEGetDimension(PetscFE fem, PetscInt *dim)
    1186: {
    1187:   PetscFunctionBegin;
    1189:   PetscAssertPointer(dim, 2);
    1190:   PetscTryTypeMethod(fem, getdimension, dim);
    1191:   PetscFunctionReturn(PETSC_SUCCESS);
    1192: }

    1194: /*@
    1195:   PetscFEPushforward - Map the reference element function to real space

    1197:   Input Parameters:
    1198: + fe     - The `PetscFE`
    1199: . fegeom - The cell geometry
    1200: . Nv     - The number of function values
    1201: - vals   - The function values

    1203:   Output Parameter:
    1204: . vals - The transformed function values

    1206:   Level: advanced

    1208:   Notes:
    1209:   This just forwards the call onto `PetscDualSpacePushforward()`.

    1211:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1213: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscDualSpacePushforward()`
    1214: @*/
    1215: PetscErrorCode PetscFEPushforward(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1216: {
    1217:   PetscFunctionBeginHot;
    1218:   PetscCall(PetscDualSpacePushforward(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1219:   PetscFunctionReturn(PETSC_SUCCESS);
    1220: }

    1222: /*@
    1223:   PetscFEPushforwardGradient - Map the reference element function gradient to real space

    1225:   Input Parameters:
    1226: + fe     - The `PetscFE`
    1227: . fegeom - The cell geometry
    1228: . Nv     - The number of function gradient values
    1229: - vals   - The function gradient values

    1231:   Output Parameter:
    1232: . vals - The transformed function gradient values

    1234:   Level: advanced

    1236:   Notes:
    1237:   This just forwards the call onto `PetscDualSpacePushforwardGradient()`.

    1239:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1241: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardGradient()`, `PetscDualSpacePushforward()`
    1242: @*/
    1243: PetscErrorCode PetscFEPushforwardGradient(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1244: {
    1245:   PetscFunctionBeginHot;
    1246:   PetscCall(PetscDualSpacePushforwardGradient(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1247:   PetscFunctionReturn(PETSC_SUCCESS);
    1248: }

    1250: /*@
    1251:   PetscFEPushforwardHessian - Map the reference element function Hessian to real space

    1253:   Input Parameters:
    1254: + fe     - The `PetscFE`
    1255: . fegeom - The cell geometry
    1256: . Nv     - The number of function Hessian values
    1257: - vals   - The function Hessian values

    1259:   Output Parameter:
    1260: . vals - The transformed function Hessian values

    1262:   Level: advanced

    1264:   Notes:
    1265:   This just forwards the call onto `PetscDualSpacePushforwardHessian()`.

    1267:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1269:   Developer Notes:
    1270:   It is unclear why all these one line convenience routines are desirable

    1272: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardHessian()`, `PetscDualSpacePushforward()`
    1273: @*/
    1274: PetscErrorCode PetscFEPushforwardHessian(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1275: {
    1276:   PetscFunctionBeginHot;
    1277:   PetscCall(PetscDualSpacePushforwardHessian(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1278:   PetscFunctionReturn(PETSC_SUCCESS);
    1279: }

    1281: /*
    1282: Purpose: Compute element vector for chunk of elements

    1284: Input:
    1285:   Sizes:
    1286:      Ne:  number of elements
    1287:      Nf:  number of fields
    1288:      PetscFE
    1289:        dim: spatial dimension
    1290:        Nb:  number of basis functions
    1291:        Nc:  number of field components
    1292:        PetscQuadrature
    1293:          Nq:  number of quadrature points

    1295:   Geometry:
    1296:      PetscFEGeom[Ne] possibly *Nq
    1297:        PetscReal v0s[dim]
    1298:        PetscReal n[dim]
    1299:        PetscReal jacobians[dim*dim]
    1300:        PetscReal jacobianInverses[dim*dim]
    1301:        PetscReal jacobianDeterminants
    1302:   FEM:
    1303:      PetscFE
    1304:        PetscQuadrature
    1305:          PetscReal   quadPoints[Nq*dim]
    1306:          PetscReal   quadWeights[Nq]
    1307:        PetscReal   basis[Nq*Nb*Nc]
    1308:        PetscReal   basisDer[Nq*Nb*Nc*dim]
    1309:      PetscScalar coefficients[Ne*Nb*Nc]
    1310:      PetscScalar elemVec[Ne*Nb*Nc]

    1312:   Problem:
    1313:      PetscInt f: the active field
    1314:      f0, f1

    1316:   Work Space:
    1317:      PetscFE
    1318:        PetscScalar f0[Nq*dim];
    1319:        PetscScalar f1[Nq*dim*dim];
    1320:        PetscScalar u[Nc];
    1321:        PetscScalar gradU[Nc*dim];
    1322:        PetscReal   x[dim];
    1323:        PetscScalar realSpaceDer[dim];

    1325: Purpose: Compute element vector for N_cb batches of elements

    1327: Input:
    1328:   Sizes:
    1329:      N_cb: Number of serial cell batches

    1331:   Geometry:
    1332:      PetscReal v0s[Ne*dim]
    1333:      PetscReal jacobians[Ne*dim*dim]        possibly *Nq
    1334:      PetscReal jacobianInverses[Ne*dim*dim] possibly *Nq
    1335:      PetscReal jacobianDeterminants[Ne]     possibly *Nq
    1336:   FEM:
    1337:      static PetscReal   quadPoints[Nq*dim]
    1338:      static PetscReal   quadWeights[Nq]
    1339:      static PetscReal   basis[Nq*Nb*Nc]
    1340:      static PetscReal   basisDer[Nq*Nb*Nc*dim]
    1341:      PetscScalar coefficients[Ne*Nb*Nc]
    1342:      PetscScalar elemVec[Ne*Nb*Nc]

    1344: ex62.c:
    1345:   PetscErrorCode PetscFEIntegrateResidualBatch(PetscInt Ne, PetscInt numFields, PetscInt field, PetscQuadrature quad[], const PetscScalar coefficients[],
    1346:                                                const PetscReal v0s[], const PetscReal jacobians[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[],
    1347:                                                void (*f0_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]),
    1348:                                                void (*f1_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]), PetscScalar elemVec[])

    1350: ex52.c:
    1351:   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)
    1352:   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)

    1354: ex52_integrateElement.cu
    1355: __global__ void integrateElementQuadrature(int N_cb, realType *coefficients, realType *jacobianInverses, realType *jacobianDeterminants, realType *elemVec)

    1357: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt Nbl, const PetscScalar coefficients[],
    1358:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
    1359:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

    1361: ex52_integrateElementOpenCL.c:
    1362: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt N_bl, const PetscScalar coefficients[],
    1363:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
    1364:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

    1366: __kernel void integrateElementQuadrature(int N_cb, __global float *coefficients, __global float *jacobianInverses, __global float *jacobianDeterminants, __global float *elemVec)
    1367: */

    1369: /*@
    1370:   PetscFEIntegrate - Produce the integral for the given field for a chunk of elements by quadrature integration

    1372:   Not Collective

    1374:   Input Parameters:
    1375: + prob            - The `PetscDS` specifying the discretizations and continuum functions
    1376: . field           - The field being integrated
    1377: . Ne              - The number of elements in the chunk
    1378: . cgeom           - The cell geometry for each cell in the chunk
    1379: . coefficients    - The array of FEM basis coefficients for the elements
    1380: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1381: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

    1383:   Output Parameter:
    1384: . integral - the integral for this field

    1386:   Level: intermediate

    1388:   Developer Notes:
    1389:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

    1391: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrateBd()`
    1392: @*/
    1393: PetscErrorCode PetscFEIntegrate(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[])
    1394: {
    1395:   PetscFE fe;

    1397:   PetscFunctionBegin;
    1399:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    1400:   if (fe->ops->integrate) PetscCall((*fe->ops->integrate)(prob, field, Ne, cgeom, coefficients, probAux, coefficientsAux, integral));
    1401:   PetscFunctionReturn(PETSC_SUCCESS);
    1402: }

    1404: /*@C
    1405:   PetscFEIntegrateBd - Produce the integral for the given field for a chunk of elements by quadrature integration

    1407:   Not Collective

    1409:   Input Parameters:
    1410: + prob            - The `PetscDS` specifying the discretizations and continuum functions
    1411: . field           - The field being integrated
    1412: . obj_func        - The function to be integrated
    1413: . Ne              - The number of elements in the chunk
    1414: . geom            - The face geometry for each face in the chunk
    1415: . coefficients    - The array of FEM basis coefficients for the elements
    1416: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1417: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

    1419:   Output Parameter:
    1420: . integral - the integral for this field

    1422:   Level: intermediate

    1424:   Developer Notes:
    1425:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

    1427: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrate()`
    1428: @*/
    1429: PetscErrorCode PetscFEIntegrateBd(PetscDS prob, PetscInt field, void (*obj_func)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), PetscInt Ne, PetscFEGeom *geom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[])
    1430: {
    1431:   PetscFE fe;

    1433:   PetscFunctionBegin;
    1435:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    1436:   if (fe->ops->integratebd) PetscCall((*fe->ops->integratebd)(prob, field, obj_func, Ne, geom, coefficients, probAux, coefficientsAux, integral));
    1437:   PetscFunctionReturn(PETSC_SUCCESS);
    1438: }

    1440: /*@
    1441:   PetscFEIntegrateResidual - Produce the element residual vector for a chunk of elements by quadrature integration

    1443:   Not Collective

    1445:   Input Parameters:
    1446: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1447: . key             - The (label+value, field) being integrated
    1448: . Ne              - The number of elements in the chunk
    1449: . cgeom           - The cell geometry for each cell in the chunk
    1450: . coefficients    - The array of FEM basis coefficients for the elements
    1451: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1452: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1453: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1454: - t               - The time

    1456:   Output Parameter:
    1457: . elemVec - the element residual vectors from each element

    1459:   Level: intermediate

    1461:   Note:
    1462: .vb
    1463:   Loop over batch of elements (e):
    1464:     Loop over quadrature points (q):
    1465:       Make u_q and gradU_q (loops over fields,Nb,Ncomp) and x_q
    1466:       Call f_0 and f_1
    1467:     Loop over element vector entries (f,fc --> i):
    1468:       elemVec[i] += \psi^{fc}_f(q) f0_{fc}(u, \nabla u) + \nabla\psi^{fc}_f(q) \cdot f1_{fc,df}(u, \nabla u)
    1469: .ve

    1471: .seealso: `PetscFEIntegrateBdResidual()`
    1472: @*/
    1473: PetscErrorCode PetscFEIntegrateResidual(PetscDS ds, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
    1474: {
    1475:   PetscFE fe;

    1477:   PetscFunctionBeginHot;
    1479:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1480:   if (fe->ops->integrateresidual) PetscCall((*fe->ops->integrateresidual)(ds, key, Ne, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1481:   PetscFunctionReturn(PETSC_SUCCESS);
    1482: }

    1484: /*@
    1485:   PetscFEIntegrateBdResidual - Produce the element residual vector for a chunk of elements by quadrature integration over a boundary

    1487:   Not Collective

    1489:   Input Parameters:
    1490: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1491: . wf              - The PetscWeakForm object holding the pointwise functions
    1492: . key             - The (label+value, field) being integrated
    1493: . Ne              - The number of elements in the chunk
    1494: . fgeom           - The face geometry for each cell in the chunk
    1495: . coefficients    - The array of FEM basis coefficients for the elements
    1496: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1497: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1498: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1499: - t               - The time

    1501:   Output Parameter:
    1502: . elemVec - the element residual vectors from each element

    1504:   Level: intermediate

    1506: .seealso: `PetscFEIntegrateResidual()`
    1507: @*/
    1508: PetscErrorCode PetscFEIntegrateBdResidual(PetscDS ds, PetscWeakForm wf, PetscFormKey key, PetscInt Ne, PetscFEGeom *fgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
    1509: {
    1510:   PetscFE fe;

    1512:   PetscFunctionBegin;
    1514:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1515:   if (fe->ops->integratebdresidual) PetscCall((*fe->ops->integratebdresidual)(ds, wf, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1516:   PetscFunctionReturn(PETSC_SUCCESS);
    1517: }

    1519: /*@
    1520:   PetscFEIntegrateHybridResidual - Produce the element residual vector for a chunk of hybrid element faces by quadrature integration

    1522:   Not Collective

    1524:   Input Parameters:
    1525: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1526: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for input
    1527: . key             - The (label+value, field) being integrated
    1528: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
    1529: . Ne              - The number of elements in the chunk
    1530: . fgeom           - The face geometry for each cell in the chunk
    1531: . cgeom           - The cell geometry for each neighbor cell in the chunk
    1532: . coefficients    - The array of FEM basis coefficients for the elements
    1533: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1534: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1535: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1536: - t               - The time

    1538:   Output Parameter:
    1539: . elemVec - the element residual vectors from each element

    1541:   Level: developer

    1543: .seealso: `PetscFEIntegrateResidual()`
    1544: @*/
    1545: PetscErrorCode PetscFEIntegrateHybridResidual(PetscDS ds, PetscDS dsIn, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
    1546: {
    1547:   PetscFE fe;

    1549:   PetscFunctionBegin;
    1552:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1553:   if (fe->ops->integratehybridresidual) PetscCall((*fe->ops->integratehybridresidual)(ds, dsIn, key, s, Ne, fgeom, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1554:   PetscFunctionReturn(PETSC_SUCCESS);
    1555: }

    1557: /*@
    1558:   PetscFEIntegrateJacobian - Produce the element Jacobian for a chunk of elements by quadrature integration

    1560:   Not Collective

    1562:   Input Parameters:
    1563: + rds             - The `PetscDS` specifying the row discretizations and continuum functions
    1564: . cds             - The `PetscDS` specifying the column discretizations
    1565: . jtype           - The type of matrix pointwise functions that should be used
    1566: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1567: . Ne              - The number of elements in the chunk
    1568: . cgeom           - The cell geometry for each cell in the chunk
    1569: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1570: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1571: . dsAux           - The `PetscDS` specifying the auxiliary discretizations
    1572: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1573: . t               - The time
    1574: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1576:   Output Parameter:
    1577: . elemMat - the element matrices for the Jacobian from each element

    1579:   Level: intermediate

    1581:   Note:
    1582: .vb
    1583:   Loop over batch of elements (e):
    1584:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1585:       Loop over quadrature points (q):
    1586:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1587:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1588:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1589:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1590:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1591: .ve

    1593: .seealso: `PetscFEIntegrateResidual()`
    1594: @*/
    1595: PetscErrorCode PetscFEIntegrateJacobian(PetscDS rds, PetscDS cds, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS dsAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
    1596: {
    1597:   PetscFE  fe;
    1598:   PetscInt Nf;

    1600:   PetscFunctionBegin;
    1603:   PetscCall(PetscDSGetNumFields(rds, &Nf));
    1604:   PetscCall(PetscDSGetDiscretization(rds, key.field / Nf, (PetscObject *)&fe));
    1605:   if (fe->ops->integratejacobian) PetscCall((*fe->ops->integratejacobian)(rds, cds, jtype, key, Ne, cgeom, coefficients, coefficients_t, dsAux, coefficientsAux, t, u_tshift, elemMat));
    1606:   PetscFunctionReturn(PETSC_SUCCESS);
    1607: }

    1609: /*@
    1610:   PetscFEIntegrateBdJacobian - Produce the boundary element Jacobian for a chunk of elements by quadrature integration

    1612:   Not Collective

    1614:   Input Parameters:
    1615: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1616: . wf              - The PetscWeakForm holding the pointwise functions
    1617: . jtype           - The type of matrix pointwise functions that should be used
    1618: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1619: . Ne              - The number of elements in the chunk
    1620: . fgeom           - The face geometry for each cell in the chunk
    1621: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1622: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1623: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1624: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1625: . t               - The time
    1626: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1628:   Output Parameter:
    1629: . elemMat - the element matrices for the Jacobian from each element

    1631:   Level: intermediate

    1633:   Note:
    1634: .vb
    1635:   Loop over batch of elements (e):
    1636:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1637:       Loop over quadrature points (q):
    1638:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1639:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1640:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1641:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1642:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1643: .ve

    1645: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
    1646: @*/
    1647: PetscErrorCode PetscFEIntegrateBdJacobian(PetscDS ds, PetscWeakForm wf, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *fgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
    1648: {
    1649:   PetscFE  fe;
    1650:   PetscInt Nf;

    1652:   PetscFunctionBegin;
    1654:   PetscCall(PetscDSGetNumFields(ds, &Nf));
    1655:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
    1656:   if (fe->ops->integratebdjacobian) PetscCall((*fe->ops->integratebdjacobian)(ds, wf, jtype, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
    1657:   PetscFunctionReturn(PETSC_SUCCESS);
    1658: }

    1660: /*@
    1661:   PetscFEIntegrateHybridJacobian - Produce the boundary element Jacobian for a chunk of hybrid elements by quadrature integration

    1663:   Not Collective

    1665:   Input Parameters:
    1666: + ds              - The `PetscDS` specifying the discretizations and continuum functions for the output
    1667: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for the input
    1668: . jtype           - The type of matrix pointwise functions that should be used
    1669: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1670: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
    1671: . Ne              - The number of elements in the chunk
    1672: . fgeom           - The face geometry for each cell in the chunk
    1673: . cgeom           - The cell geometry for each neighbor cell in the chunk
    1674: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1675: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1676: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1677: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1678: . t               - The time
    1679: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1681:   Output Parameter:
    1682: . elemMat - the element matrices for the Jacobian from each element

    1684:   Level: developer

    1686:   Note:
    1687: .vb
    1688:   Loop over batch of elements (e):
    1689:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1690:       Loop over quadrature points (q):
    1691:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1692:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1693:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1694:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1695:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1696: .ve

    1698: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
    1699: @*/
    1700: PetscErrorCode PetscFEIntegrateHybridJacobian(PetscDS ds, PetscDS dsIn, PetscFEJacobianType jtype, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
    1701: {
    1702:   PetscFE  fe;
    1703:   PetscInt Nf;

    1705:   PetscFunctionBegin;
    1707:   PetscCall(PetscDSGetNumFields(ds, &Nf));
    1708:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
    1709:   if (fe->ops->integratehybridjacobian) PetscCall((*fe->ops->integratehybridjacobian)(ds, dsIn, jtype, key, s, Ne, fgeom, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
    1710:   PetscFunctionReturn(PETSC_SUCCESS);
    1711: }

    1713: /*@
    1714:   PetscFEGetHeightSubspace - Get the subspace of this space for a mesh point of a given height

    1716:   Input Parameters:
    1717: + fe     - The finite element space
    1718: - height - The height of the `DMPLEX` point

    1720:   Output Parameter:
    1721: . subfe - The subspace of this `PetscFE` space

    1723:   Level: advanced

    1725:   Note:
    1726:   For example, if we want the subspace of this space for a face, we would choose height = 1.

    1728: .seealso: `PetscFECreateDefault()`
    1729: @*/
    1730: PetscErrorCode PetscFEGetHeightSubspace(PetscFE fe, PetscInt height, PetscFE *subfe)
    1731: {
    1732:   PetscSpace      P, subP;
    1733:   PetscDualSpace  Q, subQ;
    1734:   PetscQuadrature subq;
    1735:   PetscInt        dim, Nc;

    1737:   PetscFunctionBegin;
    1739:   PetscAssertPointer(subfe, 3);
    1740:   if (height == 0) {
    1741:     *subfe = fe;
    1742:     PetscFunctionReturn(PETSC_SUCCESS);
    1743:   }
    1744:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1745:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1746:   PetscCall(PetscFEGetNumComponents(fe, &Nc));
    1747:   PetscCall(PetscFEGetFaceQuadrature(fe, &subq));
    1748:   PetscCall(PetscDualSpaceGetDimension(Q, &dim));
    1749:   PetscCheck(height <= dim && height >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Asked for space at height %" PetscInt_FMT " for dimension %" PetscInt_FMT " space", height, dim);
    1750:   if (!fe->subspaces) PetscCall(PetscCalloc1(dim, &fe->subspaces));
    1751:   if (height <= dim) {
    1752:     if (!fe->subspaces[height - 1]) {
    1753:       PetscFE     sub = NULL;
    1754:       const char *name;

    1756:       PetscCall(PetscSpaceGetHeightSubspace(P, height, &subP));
    1757:       PetscCall(PetscDualSpaceGetHeightSubspace(Q, height, &subQ));
    1758:       if (subQ) {
    1759:         PetscCall(PetscObjectReference((PetscObject)subP));
    1760:         PetscCall(PetscObjectReference((PetscObject)subQ));
    1761:         PetscCall(PetscObjectReference((PetscObject)subq));
    1762:         PetscCall(PetscFECreateFromSpaces(subP, subQ, subq, NULL, &sub));
    1763:       }
    1764:       if (sub) {
    1765:         PetscCall(PetscObjectGetName((PetscObject)fe, &name));
    1766:         if (name) PetscCall(PetscFESetName(sub, name));
    1767:       }
    1768:       fe->subspaces[height - 1] = sub;
    1769:     }
    1770:     *subfe = fe->subspaces[height - 1];
    1771:   } else {
    1772:     *subfe = NULL;
    1773:   }
    1774:   PetscFunctionReturn(PETSC_SUCCESS);
    1775: }

    1777: /*@
    1778:   PetscFERefine - Create a "refined" `PetscFE` object that refines the reference cell into
    1779:   smaller copies.

    1781:   Collective

    1783:   Input Parameter:
    1784: . fe - The initial `PetscFE`

    1786:   Output Parameter:
    1787: . feRef - The refined `PetscFE`

    1789:   Level: advanced

    1791:   Notes:
    1792:   This is typically used to generate a preconditioner for a higher order method from a lower order method on a
    1793:   refined mesh having the same number of dofs (but more sparsity). It is also used to create an
    1794:   interpolation between regularly refined meshes.

    1796: .seealso: `PetscFEType`, `PetscFECreate()`, `PetscFESetType()`
    1797: @*/
    1798: PetscErrorCode PetscFERefine(PetscFE fe, PetscFE *feRef)
    1799: {
    1800:   PetscSpace       P, Pref;
    1801:   PetscDualSpace   Q, Qref;
    1802:   DM               K, Kref;
    1803:   PetscQuadrature  q, qref;
    1804:   const PetscReal *v0, *jac;
    1805:   PetscInt         numComp, numSubelements;
    1806:   PetscInt         cStart, cEnd, c;
    1807:   PetscDualSpace  *cellSpaces;

    1809:   PetscFunctionBegin;
    1810:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1811:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1812:   PetscCall(PetscFEGetQuadrature(fe, &q));
    1813:   PetscCall(PetscDualSpaceGetDM(Q, &K));
    1814:   /* Create space */
    1815:   PetscCall(PetscObjectReference((PetscObject)P));
    1816:   Pref = P;
    1817:   /* Create dual space */
    1818:   PetscCall(PetscDualSpaceDuplicate(Q, &Qref));
    1819:   PetscCall(PetscDualSpaceSetType(Qref, PETSCDUALSPACEREFINED));
    1820:   PetscCall(DMRefine(K, PetscObjectComm((PetscObject)fe), &Kref));
    1821:   PetscCall(DMGetCoordinatesLocalSetUp(Kref));
    1822:   PetscCall(PetscDualSpaceSetDM(Qref, Kref));
    1823:   PetscCall(DMPlexGetHeightStratum(Kref, 0, &cStart, &cEnd));
    1824:   PetscCall(PetscMalloc1(cEnd - cStart, &cellSpaces));
    1825:   /* TODO: fix for non-uniform refinement */
    1826:   for (c = 0; c < cEnd - cStart; c++) cellSpaces[c] = Q;
    1827:   PetscCall(PetscDualSpaceRefinedSetCellSpaces(Qref, cellSpaces));
    1828:   PetscCall(PetscFree(cellSpaces));
    1829:   PetscCall(DMDestroy(&Kref));
    1830:   PetscCall(PetscDualSpaceSetUp(Qref));
    1831:   /* Create element */
    1832:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), feRef));
    1833:   PetscCall(PetscFESetType(*feRef, PETSCFECOMPOSITE));
    1834:   PetscCall(PetscFESetBasisSpace(*feRef, Pref));
    1835:   PetscCall(PetscFESetDualSpace(*feRef, Qref));
    1836:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    1837:   PetscCall(PetscFESetNumComponents(*feRef, numComp));
    1838:   PetscCall(PetscFESetUp(*feRef));
    1839:   PetscCall(PetscSpaceDestroy(&Pref));
    1840:   PetscCall(PetscDualSpaceDestroy(&Qref));
    1841:   /* Create quadrature */
    1842:   PetscCall(PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL));
    1843:   PetscCall(PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref));
    1844:   PetscCall(PetscFESetQuadrature(*feRef, qref));
    1845:   PetscCall(PetscQuadratureDestroy(&qref));
    1846:   PetscFunctionReturn(PETSC_SUCCESS);
    1847: }

    1849: static PetscErrorCode PetscFESetDefaultName_Private(PetscFE fe)
    1850: {
    1851:   PetscSpace     P;
    1852:   PetscDualSpace Q;
    1853:   DM             K;
    1854:   DMPolytopeType ct;
    1855:   PetscInt       degree;
    1856:   char           name[64];

    1858:   PetscFunctionBegin;
    1859:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1860:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
    1861:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1862:   PetscCall(PetscDualSpaceGetDM(Q, &K));
    1863:   PetscCall(DMPlexGetCellType(K, 0, &ct));
    1864:   switch (ct) {
    1865:   case DM_POLYTOPE_SEGMENT:
    1866:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1867:   case DM_POLYTOPE_QUADRILATERAL:
    1868:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1869:   case DM_POLYTOPE_HEXAHEDRON:
    1870:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1871:     PetscCall(PetscSNPrintf(name, sizeof(name), "Q%" PetscInt_FMT, degree));
    1872:     break;
    1873:   case DM_POLYTOPE_TRIANGLE:
    1874:   case DM_POLYTOPE_TETRAHEDRON:
    1875:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT, degree));
    1876:     break;
    1877:   case DM_POLYTOPE_TRI_PRISM:
    1878:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
    1879:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT "xQ%" PetscInt_FMT, degree, degree));
    1880:     break;
    1881:   default:
    1882:     PetscCall(PetscSNPrintf(name, sizeof(name), "FE"));
    1883:   }
    1884:   PetscCall(PetscFESetName(fe, name));
    1885:   PetscFunctionReturn(PETSC_SUCCESS);
    1886: }

    1888: /*@
    1889:   PetscFECreateFromSpaces - Create a `PetscFE` from the basis and dual spaces

    1891:   Collective

    1893:   Input Parameters:
    1894: + P  - The basis space
    1895: . Q  - The dual space
    1896: . q  - The cell quadrature
    1897: - fq - The face quadrature

    1899:   Output Parameter:
    1900: . fem - The `PetscFE` object

    1902:   Level: beginner

    1904:   Note:
    1905:   The `PetscFE` takes ownership of these spaces by calling destroy on each. They should not be used after this call, and for borrowed references from `PetscFEGetSpace()` and the like, the caller must use `PetscObjectReference` before this call.

    1907: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`,
    1908:           `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    1909: @*/
    1910: PetscErrorCode PetscFECreateFromSpaces(PetscSpace P, PetscDualSpace Q, PetscQuadrature q, PetscQuadrature fq, PetscFE *fem)
    1911: {
    1912:   PetscInt    Nc;
    1913:   PetscInt    p_Ns = -1, p_Nc = -1, q_Ns = -1, q_Nc = -1;
    1914:   PetscBool   p_is_uniform_sum = PETSC_FALSE, p_interleave_basis = PETSC_FALSE, p_interleave_components = PETSC_FALSE;
    1915:   PetscBool   q_is_uniform_sum = PETSC_FALSE, q_interleave_basis = PETSC_FALSE, q_interleave_components = PETSC_FALSE;
    1916:   const char *prefix;

    1918:   PetscFunctionBegin;
    1919:   PetscCall(PetscObjectTypeCompare((PetscObject)P, PETSCSPACESUM, &p_is_uniform_sum));
    1920:   if (p_is_uniform_sum) {
    1921:     PetscSpace subsp_0 = NULL;
    1922:     PetscCall(PetscSpaceSumGetNumSubspaces(P, &p_Ns));
    1923:     PetscCall(PetscSpaceGetNumComponents(P, &p_Nc));
    1924:     PetscCall(PetscSpaceSumGetConcatenate(P, &p_is_uniform_sum));
    1925:     PetscCall(PetscSpaceSumGetInterleave(P, &p_interleave_basis, &p_interleave_components));
    1926:     for (PetscInt s = 0; s < p_Ns; s++) {
    1927:       PetscSpace subsp;

    1929:       PetscCall(PetscSpaceSumGetSubspace(P, s, &subsp));
    1930:       if (!s) {
    1931:         subsp_0 = subsp;
    1932:       } else if (subsp != subsp_0) {
    1933:         p_is_uniform_sum = PETSC_FALSE;
    1934:       }
    1935:     }
    1936:   }
    1937:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &q_is_uniform_sum));
    1938:   if (q_is_uniform_sum) {
    1939:     PetscDualSpace subsp_0 = NULL;
    1940:     PetscCall(PetscDualSpaceSumGetNumSubspaces(Q, &q_Ns));
    1941:     PetscCall(PetscDualSpaceGetNumComponents(Q, &q_Nc));
    1942:     PetscCall(PetscDualSpaceSumGetConcatenate(Q, &q_is_uniform_sum));
    1943:     PetscCall(PetscDualSpaceSumGetInterleave(Q, &q_interleave_basis, &q_interleave_components));
    1944:     for (PetscInt s = 0; s < q_Ns; s++) {
    1945:       PetscDualSpace subsp;

    1947:       PetscCall(PetscDualSpaceSumGetSubspace(Q, s, &subsp));
    1948:       if (!s) {
    1949:         subsp_0 = subsp;
    1950:       } else if (subsp != subsp_0) {
    1951:         q_is_uniform_sum = PETSC_FALSE;
    1952:       }
    1953:     }
    1954:   }
    1955:   if (p_is_uniform_sum && q_is_uniform_sum && (p_interleave_basis == q_interleave_basis) && (p_interleave_components == q_interleave_components) && (p_Ns == q_Ns) && (p_Nc == q_Nc)) {
    1956:     PetscSpace     scalar_space;
    1957:     PetscDualSpace scalar_dspace;
    1958:     PetscFE        scalar_fe;

    1960:     PetscCall(PetscSpaceSumGetSubspace(P, 0, &scalar_space));
    1961:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &scalar_dspace));
    1962:     PetscCall(PetscObjectReference((PetscObject)scalar_space));
    1963:     PetscCall(PetscObjectReference((PetscObject)scalar_dspace));
    1964:     PetscCall(PetscObjectReference((PetscObject)q));
    1965:     PetscCall(PetscObjectReference((PetscObject)fq));
    1966:     PetscCall(PetscFECreateFromSpaces(scalar_space, scalar_dspace, q, fq, &scalar_fe));
    1967:     PetscCall(PetscFECreateVector(scalar_fe, p_Ns, p_interleave_basis, p_interleave_components, fem));
    1968:     PetscCall(PetscFEDestroy(&scalar_fe));
    1969:   } else {
    1970:     PetscCall(PetscFECreate(PetscObjectComm((PetscObject)P), fem));
    1971:     PetscCall(PetscFESetType(*fem, PETSCFEBASIC));
    1972:   }
    1973:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    1974:   PetscCall(PetscFESetNumComponents(*fem, Nc));
    1975:   PetscCall(PetscFESetBasisSpace(*fem, P));
    1976:   PetscCall(PetscFESetDualSpace(*fem, Q));
    1977:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)P, &prefix));
    1978:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*fem, prefix));
    1979:   PetscCall(PetscFESetUp(*fem));
    1980:   PetscCall(PetscSpaceDestroy(&P));
    1981:   PetscCall(PetscDualSpaceDestroy(&Q));
    1982:   PetscCall(PetscFESetQuadrature(*fem, q));
    1983:   PetscCall(PetscFESetFaceQuadrature(*fem, fq));
    1984:   PetscCall(PetscQuadratureDestroy(&q));
    1985:   PetscCall(PetscQuadratureDestroy(&fq));
    1986:   PetscCall(PetscFESetDefaultName_Private(*fem));
    1987:   PetscFunctionReturn(PETSC_SUCCESS);
    1988: }

    1990: static PetscErrorCode PetscFECreate_Internal(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt degree, PetscInt qorder, PetscBool setFromOptions, PetscFE *fem)
    1991: {
    1992:   DM              K;
    1993:   PetscSpace      P;
    1994:   PetscDualSpace  Q;
    1995:   PetscQuadrature q, fq;
    1996:   PetscBool       tensor;

    1998:   PetscFunctionBegin;
    1999:   if (prefix) PetscAssertPointer(prefix, 5);
    2000:   PetscAssertPointer(fem, 9);
    2001:   switch (ct) {
    2002:   case DM_POLYTOPE_SEGMENT:
    2003:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2004:   case DM_POLYTOPE_QUADRILATERAL:
    2005:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2006:   case DM_POLYTOPE_HEXAHEDRON:
    2007:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    2008:     tensor = PETSC_TRUE;
    2009:     break;
    2010:   default:
    2011:     tensor = PETSC_FALSE;
    2012:   }
    2013:   /* Create space */
    2014:   PetscCall(PetscSpaceCreate(comm, &P));
    2015:   PetscCall(PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL));
    2016:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)P, prefix));
    2017:   PetscCall(PetscSpacePolynomialSetTensor(P, tensor));
    2018:   PetscCall(PetscSpaceSetNumComponents(P, Nc));
    2019:   PetscCall(PetscSpaceSetNumVariables(P, dim));
    2020:   if (degree >= 0) {
    2021:     PetscCall(PetscSpaceSetDegree(P, degree, PETSC_DETERMINE));
    2022:     if (ct == DM_POLYTOPE_TRI_PRISM || ct == DM_POLYTOPE_TRI_PRISM_TENSOR) {
    2023:       PetscSpace Pend, Pside;

    2025:       PetscCall(PetscSpaceSetNumComponents(P, 1));
    2026:       PetscCall(PetscSpaceCreate(comm, &Pend));
    2027:       PetscCall(PetscSpaceSetType(Pend, PETSCSPACEPOLYNOMIAL));
    2028:       PetscCall(PetscSpacePolynomialSetTensor(Pend, PETSC_FALSE));
    2029:       PetscCall(PetscSpaceSetNumComponents(Pend, 1));
    2030:       PetscCall(PetscSpaceSetNumVariables(Pend, dim - 1));
    2031:       PetscCall(PetscSpaceSetDegree(Pend, degree, PETSC_DETERMINE));
    2032:       PetscCall(PetscSpaceCreate(comm, &Pside));
    2033:       PetscCall(PetscSpaceSetType(Pside, PETSCSPACEPOLYNOMIAL));
    2034:       PetscCall(PetscSpacePolynomialSetTensor(Pside, PETSC_FALSE));
    2035:       PetscCall(PetscSpaceSetNumComponents(Pside, 1));
    2036:       PetscCall(PetscSpaceSetNumVariables(Pside, 1));
    2037:       PetscCall(PetscSpaceSetDegree(Pside, degree, PETSC_DETERMINE));
    2038:       PetscCall(PetscSpaceSetType(P, PETSCSPACETENSOR));
    2039:       PetscCall(PetscSpaceTensorSetNumSubspaces(P, 2));
    2040:       PetscCall(PetscSpaceTensorSetSubspace(P, 0, Pend));
    2041:       PetscCall(PetscSpaceTensorSetSubspace(P, 1, Pside));
    2042:       PetscCall(PetscSpaceDestroy(&Pend));
    2043:       PetscCall(PetscSpaceDestroy(&Pside));

    2045:       if (Nc > 1) {
    2046:         PetscSpace scalar_P = P;

    2048:         PetscCall(PetscSpaceCreate(comm, &P));
    2049:         PetscCall(PetscSpaceSetNumVariables(P, dim));
    2050:         PetscCall(PetscSpaceSetNumComponents(P, Nc));
    2051:         PetscCall(PetscSpaceSetType(P, PETSCSPACESUM));
    2052:         PetscCall(PetscSpaceSumSetNumSubspaces(P, Nc));
    2053:         PetscCall(PetscSpaceSumSetConcatenate(P, PETSC_TRUE));
    2054:         PetscCall(PetscSpaceSumSetInterleave(P, PETSC_TRUE, PETSC_FALSE));
    2055:         for (PetscInt i = 0; i < Nc; i++) PetscCall(PetscSpaceSumSetSubspace(P, i, scalar_P));
    2056:         PetscCall(PetscSpaceDestroy(&scalar_P));
    2057:       }
    2058:     }
    2059:   }
    2060:   if (setFromOptions) PetscCall(PetscSpaceSetFromOptions(P));
    2061:   PetscCall(PetscSpaceSetUp(P));
    2062:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
    2063:   PetscCall(PetscSpacePolynomialGetTensor(P, &tensor));
    2064:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    2065:   /* Create dual space */
    2066:   PetscCall(PetscDualSpaceCreate(comm, &Q));
    2067:   PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
    2068:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)Q, prefix));
    2069:   PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
    2070:   PetscCall(PetscDualSpaceSetDM(Q, K));
    2071:   PetscCall(DMDestroy(&K));
    2072:   PetscCall(PetscDualSpaceSetNumComponents(Q, Nc));
    2073:   PetscCall(PetscDualSpaceSetOrder(Q, degree));
    2074:   PetscCall(PetscDualSpaceLagrangeSetTensor(Q, (tensor || (ct == DM_POLYTOPE_TRI_PRISM)) ? PETSC_TRUE : PETSC_FALSE));
    2075:   if (setFromOptions) PetscCall(PetscDualSpaceSetFromOptions(Q));
    2076:   PetscCall(PetscDualSpaceSetUp(Q));
    2077:   /* Create quadrature */
    2078:   PetscDTSimplexQuadratureType qtype = PETSCDTSIMPLEXQUAD_DEFAULT;

    2080:   qorder = qorder >= 0 ? qorder : degree;
    2081:   if (setFromOptions) {
    2082:     PetscObjectOptionsBegin((PetscObject)P);
    2083:     PetscCall(PetscOptionsBoundedInt("-petscfe_default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "PetscFECreateDefault", qorder, &qorder, NULL, 0));
    2084:     PetscCall(PetscOptionsEnum("-petscfe_default_quadrature_type", "Simplex quadrature type", "PetscDTSimplexQuadratureType", PetscDTSimplexQuadratureTypes, (PetscEnum)qtype, (PetscEnum *)&qtype, NULL));
    2085:     PetscOptionsEnd();
    2086:   }
    2087:   PetscCall(PetscDTCreateQuadratureByCell(ct, qorder, qtype, &q, &fq));
    2088:   /* Create finite element */
    2089:   PetscCall(PetscFECreateFromSpaces(P, Q, q, fq, fem));
    2090:   if (setFromOptions) PetscCall(PetscFESetFromOptions(*fem));
    2091:   PetscFunctionReturn(PETSC_SUCCESS);
    2092: }

    2094: /*@
    2095:   PetscFECreateDefault - Create a `PetscFE` for basic FEM computation

    2097:   Collective

    2099:   Input Parameters:
    2100: + comm      - The MPI comm
    2101: . dim       - The spatial dimension
    2102: . Nc        - The number of components
    2103: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
    2104: . prefix    - The options prefix, or `NULL`
    2105: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2107:   Output Parameter:
    2108: . fem - The `PetscFE` object

    2110:   Level: beginner

    2112:   Note:
    2113:   Each subobject is SetFromOption() during creation, so that the object may be customized from the command line, using the prefix specified above. See the links below for the particular options available.

    2115: .seealso: `PetscFECreateLagrange()`, `PetscFECreateByCell()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2116: @*/
    2117: PetscErrorCode PetscFECreateDefault(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, const char prefix[], PetscInt qorder, PetscFE *fem)
    2118: {
    2119:   PetscFunctionBegin;
    2120:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
    2121:   PetscFunctionReturn(PETSC_SUCCESS);
    2122: }

    2124: /*@
    2125:   PetscFECreateByCell - Create a `PetscFE` for basic FEM computation

    2127:   Collective

    2129:   Input Parameters:
    2130: + comm   - The MPI comm
    2131: . dim    - The spatial dimension
    2132: . Nc     - The number of components
    2133: . ct     - The celltype of the reference cell
    2134: . prefix - The options prefix, or `NULL`
    2135: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2137:   Output Parameter:
    2138: . fem - The `PetscFE` object

    2140:   Level: beginner

    2142:   Note:
    2143:   Each subobject is SetFromOption() during creation, so that the object may be customized from the command line, using the prefix specified above. See the links below for the particular options available.

    2145: .seealso: `PetscFECreateDefault()`, `PetscFECreateLagrange()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2146: @*/
    2147: PetscErrorCode PetscFECreateByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt qorder, PetscFE *fem)
    2148: {
    2149:   PetscFunctionBegin;
    2150:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
    2151:   PetscFunctionReturn(PETSC_SUCCESS);
    2152: }

    2154: /*@
    2155:   PetscFECreateLagrange - Create a `PetscFE` for the basic Lagrange space of degree k

    2157:   Collective

    2159:   Input Parameters:
    2160: + comm      - The MPI comm
    2161: . dim       - The spatial dimension
    2162: . Nc        - The number of components
    2163: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
    2164: . k         - The degree k of the space
    2165: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2167:   Output Parameter:
    2168: . fem - The `PetscFE` object

    2170:   Level: beginner

    2172:   Note:
    2173:   For simplices, this element is the space of maximum polynomial degree k, otherwise it is a tensor product of 1D polynomials, each with maximal degree k.

    2175: .seealso: `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2176: @*/
    2177: PetscErrorCode PetscFECreateLagrange(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, PetscInt k, PetscInt qorder, PetscFE *fem)
    2178: {
    2179:   PetscFunctionBegin;
    2180:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), NULL, k, qorder, PETSC_FALSE, fem));
    2181:   PetscFunctionReturn(PETSC_SUCCESS);
    2182: }

    2184: /*@
    2185:   PetscFECreateLagrangeByCell - Create a `PetscFE` for the basic Lagrange space of degree k

    2187:   Collective

    2189:   Input Parameters:
    2190: + comm   - The MPI comm
    2191: . dim    - The spatial dimension
    2192: . Nc     - The number of components
    2193: . ct     - The celltype of the reference cell
    2194: . k      - The degree k of the space
    2195: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2197:   Output Parameter:
    2198: . fem - The `PetscFE` object

    2200:   Level: beginner

    2202:   Note:
    2203:   For simplices, this element is the space of maximum polynomial degree k, otherwise it is a tensor product of 1D polynomials, each with maximal degree k.

    2205: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2206: @*/
    2207: PetscErrorCode PetscFECreateLagrangeByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, PetscInt k, PetscInt qorder, PetscFE *fem)
    2208: {
    2209:   PetscFunctionBegin;
    2210:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, NULL, k, qorder, PETSC_FALSE, fem));
    2211:   PetscFunctionReturn(PETSC_SUCCESS);
    2212: }

    2214: /*@
    2215:   PetscFELimitDegree - Copy a `PetscFE` but limit the degree to be in the given range

    2217:   Collective

    2219:   Input Parameters:
    2220: + fe        - The `PetscFE`
    2221: . minDegree - The minimum degree, or `PETSC_DETERMINE` for no limit
    2222: - maxDegree - The maximum degree, or `PETSC_DETERMINE` for no limit

    2224:   Output Parameter:
    2225: . newfe - The `PetscFE` object

    2227:   Level: advanced

    2229:   Note:
    2230:   This currently only works for Lagrange elements.

    2232: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2233: @*/
    2234: PetscErrorCode PetscFELimitDegree(PetscFE fe, PetscInt minDegree, PetscInt maxDegree, PetscFE *newfe)
    2235: {
    2236:   PetscDualSpace Q;
    2237:   PetscBool      islag, issum;
    2238:   PetscInt       oldk = 0, k;

    2240:   PetscFunctionBegin;
    2241:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    2242:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &islag));
    2243:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &issum));
    2244:   if (islag) {
    2245:     PetscCall(PetscDualSpaceGetOrder(Q, &oldk));
    2246:   } else if (issum) {
    2247:     PetscDualSpace subQ;

    2249:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &subQ));
    2250:     PetscCall(PetscDualSpaceGetOrder(subQ, &oldk));
    2251:   } else {
    2252:     PetscCall(PetscObjectReference((PetscObject)fe));
    2253:     *newfe = fe;
    2254:     PetscFunctionReturn(PETSC_SUCCESS);
    2255:   }
    2256:   k = oldk;
    2257:   if (minDegree >= 0) k = PetscMax(k, minDegree);
    2258:   if (maxDegree >= 0) k = PetscMin(k, maxDegree);
    2259:   if (k != oldk) {
    2260:     DM              K;
    2261:     PetscSpace      P;
    2262:     PetscQuadrature q;
    2263:     DMPolytopeType  ct;
    2264:     PetscInt        dim, Nc;

    2266:     PetscCall(PetscFEGetBasisSpace(fe, &P));
    2267:     PetscCall(PetscSpaceGetNumVariables(P, &dim));
    2268:     PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    2269:     PetscCall(PetscDualSpaceGetDM(Q, &K));
    2270:     PetscCall(DMPlexGetCellType(K, 0, &ct));
    2271:     PetscCall(PetscFECreateLagrangeByCell(PetscObjectComm((PetscObject)fe), dim, Nc, ct, k, PETSC_DETERMINE, newfe));
    2272:     PetscCall(PetscFEGetQuadrature(fe, &q));
    2273:     PetscCall(PetscFESetQuadrature(*newfe, q));
    2274:   } else {
    2275:     PetscCall(PetscObjectReference((PetscObject)fe));
    2276:     *newfe = fe;
    2277:   }
    2278:   PetscFunctionReturn(PETSC_SUCCESS);
    2279: }

    2281: /*@
    2282:   PetscFECreateBrokenElement - Create a discontinuous version of the input `PetscFE`

    2284:   Collective

    2286:   Input Parameters:
    2287: . cgfe - The continuous `PetscFE` object

    2289:   Output Parameter:
    2290: . dgfe - The discontinuous `PetscFE` object

    2292:   Level: advanced

    2294:   Note:
    2295:   This only works for Lagrange elements.

    2297: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`, `PetscFECreateLagrange()`, `PetscFECreateLagrangeByCell()`, `PetscDualSpaceLagrangeSetContinuity()`
    2298: @*/
    2299: PetscErrorCode PetscFECreateBrokenElement(PetscFE cgfe, PetscFE *dgfe)
    2300: {
    2301:   PetscSpace      P;
    2302:   PetscDualSpace  Q, dgQ;
    2303:   PetscQuadrature q, fq;
    2304:   PetscBool       is_lagrange, is_sum;

    2306:   PetscFunctionBegin;
    2307:   PetscCall(PetscFEGetBasisSpace(cgfe, &P));
    2308:   PetscCall(PetscObjectReference((PetscObject)P));
    2309:   PetscCall(PetscFEGetDualSpace(cgfe, &Q));
    2310:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &is_lagrange));
    2311:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &is_sum));
    2312:   PetscCheck(is_lagrange || is_sum, PETSC_COMM_SELF, PETSC_ERR_SUP, "Can only create broken elements of Lagrange elements");
    2313:   PetscCall(PetscDualSpaceDuplicate(Q, &dgQ));
    2314:   PetscCall(PetscDualSpaceLagrangeSetContinuity(dgQ, PETSC_FALSE));
    2315:   PetscCall(PetscDualSpaceSetUp(dgQ));
    2316:   PetscCall(PetscFEGetQuadrature(cgfe, &q));
    2317:   PetscCall(PetscObjectReference((PetscObject)q));
    2318:   PetscCall(PetscFEGetFaceQuadrature(cgfe, &fq));
    2319:   PetscCall(PetscObjectReference((PetscObject)fq));
    2320:   PetscCall(PetscFECreateFromSpaces(P, dgQ, q, fq, dgfe));
    2321:   PetscFunctionReturn(PETSC_SUCCESS);
    2322: }

    2324: /*@
    2325:   PetscFESetName - Names the `PetscFE` and its subobjects

    2327:   Not Collective

    2329:   Input Parameters:
    2330: + fe   - The `PetscFE`
    2331: - name - The name

    2333:   Level: intermediate

    2335: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2336: @*/
    2337: PetscErrorCode PetscFESetName(PetscFE fe, const char name[])
    2338: {
    2339:   PetscSpace     P;
    2340:   PetscDualSpace Q;

    2342:   PetscFunctionBegin;
    2343:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    2344:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    2345:   PetscCall(PetscObjectSetName((PetscObject)fe, name));
    2346:   PetscCall(PetscObjectSetName((PetscObject)P, name));
    2347:   PetscCall(PetscObjectSetName((PetscObject)Q, name));
    2348:   PetscFunctionReturn(PETSC_SUCCESS);
    2349: }

    2351: PetscErrorCode PetscFEEvaluateFieldJets_Internal(PetscDS ds, PetscInt Nf, PetscInt r, PetscInt q, PetscTabulation T[], PetscFEGeom *fegeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscScalar u[], PetscScalar u_x[], PetscScalar u_t[])
    2352: {
    2353:   PetscInt dOffset = 0, fOffset = 0, f, g;

    2355:   for (f = 0; f < Nf; ++f) {
    2356:     PetscCheck(r < T[f]->Nr, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Replica number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", r, T[f]->Nr);
    2357:     PetscCheck(q < T[f]->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Point number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", q, T[f]->Np);
    2358:     PetscFE          fe;
    2359:     const PetscInt   k       = ds->jetDegree[f];
    2360:     const PetscInt   cdim    = T[f]->cdim;
    2361:     const PetscInt   dE      = fegeom->dimEmbed;
    2362:     const PetscInt   Nq      = T[f]->Np;
    2363:     const PetscInt   Nbf     = T[f]->Nb;
    2364:     const PetscInt   Ncf     = T[f]->Nc;
    2365:     const PetscReal *Bq      = &T[f]->T[0][(r * Nq + q) * Nbf * Ncf];
    2366:     const PetscReal *Dq      = &T[f]->T[1][(r * Nq + q) * Nbf * Ncf * cdim];
    2367:     const PetscReal *Hq      = k > 1 ? &T[f]->T[2][(r * Nq + q) * Nbf * Ncf * cdim * cdim] : NULL;
    2368:     PetscInt         hOffset = 0, b, c, d;

    2370:     PetscCall(PetscDSGetDiscretization(ds, f, (PetscObject *)&fe));
    2371:     for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
    2372:     for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
    2373:     for (b = 0; b < Nbf; ++b) {
    2374:       for (c = 0; c < Ncf; ++c) {
    2375:         const PetscInt cidx = b * Ncf + c;

    2377:         u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
    2378:         for (d = 0; d < cdim; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * cdim + d] * coefficients[dOffset + b];
    2379:       }
    2380:     }
    2381:     if (k > 1) {
    2382:       for (g = 0; g < Nf; ++g) hOffset += T[g]->Nc * dE;
    2383:       for (d = 0; d < dE * dE * Ncf; ++d) u_x[hOffset + fOffset * dE * dE + d] = 0.0;
    2384:       for (b = 0; b < Nbf; ++b) {
    2385:         for (c = 0; c < Ncf; ++c) {
    2386:           const PetscInt cidx = b * Ncf + c;

    2388:           for (d = 0; d < cdim * cdim; ++d) u_x[hOffset + (fOffset + c) * dE * dE + d] += Hq[cidx * cdim * cdim + d] * coefficients[dOffset + b];
    2389:         }
    2390:       }
    2391:       PetscCall(PetscFEPushforwardHessian(fe, fegeom, 1, &u_x[hOffset + fOffset * dE * dE]));
    2392:     }
    2393:     PetscCall(PetscFEPushforward(fe, fegeom, 1, &u[fOffset]));
    2394:     PetscCall(PetscFEPushforwardGradient(fe, fegeom, 1, &u_x[fOffset * dE]));
    2395:     if (u_t) {
    2396:       for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
    2397:       for (b = 0; b < Nbf; ++b) {
    2398:         for (c = 0; c < Ncf; ++c) {
    2399:           const PetscInt cidx = b * Ncf + c;

    2401:           u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
    2402:         }
    2403:       }
    2404:       PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
    2405:     }
    2406:     fOffset += Ncf;
    2407:     dOffset += Nbf;
    2408:   }
    2409:   return PETSC_SUCCESS;
    2410: }

    2412: PetscErrorCode PetscFEEvaluateFieldJets_Hybrid_Internal(PetscDS ds, PetscInt Nf, PetscInt rc, PetscInt qc, PetscTabulation Tab[], const PetscInt rf[], const PetscInt qf[], PetscTabulation Tabf[], PetscFEGeom *fegeom, PetscFEGeom *fegeomNbr, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscScalar u[], PetscScalar u_x[], PetscScalar u_t[])
    2413: {
    2414:   PetscInt dOffset = 0, fOffset = 0, f;

    2416:   /* f is the field number in the DS */
    2417:   for (f = 0; f < Nf; ++f) {
    2418:     PetscBool isCohesive;
    2419:     PetscInt  Ns, s;

    2421:     if (!Tab[f]) continue;
    2422:     PetscCall(PetscDSGetCohesive(ds, f, &isCohesive));
    2423:     Ns = isCohesive ? 1 : 2;
    2424:     {
    2425:       PetscTabulation T   = isCohesive ? Tab[f] : Tabf[f];
    2426:       PetscFE         fe  = (PetscFE)ds->disc[f];
    2427:       const PetscInt  dEt = T->cdim;
    2428:       const PetscInt  dE  = fegeom->dimEmbed;
    2429:       const PetscInt  Nq  = T->Np;
    2430:       const PetscInt  Nbf = T->Nb;
    2431:       const PetscInt  Ncf = T->Nc;

    2433:       for (s = 0; s < Ns; ++s) {
    2434:         const PetscInt   r  = isCohesive ? rc : rf[s];
    2435:         const PetscInt   q  = isCohesive ? qc : qf[s];
    2436:         const PetscReal *Bq = &T->T[0][(r * Nq + q) * Nbf * Ncf];
    2437:         const PetscReal *Dq = &T->T[1][(r * Nq + q) * Nbf * Ncf * dEt];
    2438:         PetscInt         b, c, d;

    2440:         PetscCheck(r < T->Nr, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " Side %" PetscInt_FMT " Replica number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", f, s, r, T->Nr);
    2441:         PetscCheck(q < T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " Side %" PetscInt_FMT " Point number %" PetscInt_FMT " should be in [0, %" PetscInt_FMT ")", f, s, q, T->Np);
    2442:         for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
    2443:         for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
    2444:         for (b = 0; b < Nbf; ++b) {
    2445:           for (c = 0; c < Ncf; ++c) {
    2446:             const PetscInt cidx = b * Ncf + c;

    2448:             u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
    2449:             for (d = 0; d < dEt; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * dEt + d] * coefficients[dOffset + b];
    2450:           }
    2451:         }
    2452:         PetscCall(PetscFEPushforward(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u[fOffset]));
    2453:         PetscCall(PetscFEPushforwardGradient(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u_x[fOffset * dE]));
    2454:         if (u_t) {
    2455:           for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
    2456:           for (b = 0; b < Nbf; ++b) {
    2457:             for (c = 0; c < Ncf; ++c) {
    2458:               const PetscInt cidx = b * Ncf + c;

    2460:               u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
    2461:             }
    2462:           }
    2463:           PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
    2464:         }
    2465:         fOffset += Ncf;
    2466:         dOffset += Nbf;
    2467:       }
    2468:     }
    2469:   }
    2470:   return PETSC_SUCCESS;
    2471: }

    2473: PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS prob, PetscInt field, PetscInt faceLoc, const PetscScalar coefficients[], PetscScalar u[])
    2474: {
    2475:   PetscFE         fe;
    2476:   PetscTabulation Tc;
    2477:   PetscInt        b, c;

    2479:   if (!prob) return PETSC_SUCCESS;
    2480:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    2481:   PetscCall(PetscFEGetFaceCentroidTabulation(fe, &Tc));
    2482:   {
    2483:     const PetscReal *faceBasis = Tc->T[0];
    2484:     const PetscInt   Nb        = Tc->Nb;
    2485:     const PetscInt   Nc        = Tc->Nc;

    2487:     for (c = 0; c < Nc; ++c) u[c] = 0.0;
    2488:     for (b = 0; b < Nb; ++b) {
    2489:       for (c = 0; c < Nc; ++c) u[c] += coefficients[b] * faceBasis[(faceLoc * Nb + b) * Nc + c];
    2490:     }
    2491:   }
    2492:   return PETSC_SUCCESS;
    2493: }

    2495: PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscInt e, PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
    2496: {
    2497:   PetscFEGeom      pgeom;
    2498:   const PetscInt   dEt      = T->cdim;
    2499:   const PetscInt   dE       = fegeom->dimEmbed;
    2500:   const PetscInt   Nq       = T->Np;
    2501:   const PetscInt   Nb       = T->Nb;
    2502:   const PetscInt   Nc       = T->Nc;
    2503:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
    2504:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dEt];
    2505:   PetscInt         q, b, c, d;

    2507:   for (q = 0; q < Nq; ++q) {
    2508:     for (b = 0; b < Nb; ++b) {
    2509:       for (c = 0; c < Nc; ++c) {
    2510:         const PetscInt bcidx = b * Nc + c;

    2512:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
    2513:         for (d = 0; d < dEt; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dEt + bcidx * dEt + d];
    2514:         for (d = dEt; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = 0.0;
    2515:       }
    2516:     }
    2517:     PetscCall(PetscFEGeomGetCellPoint(fegeom, e, q, &pgeom));
    2518:     PetscCall(PetscFEPushforward(fe, &pgeom, Nb, tmpBasis));
    2519:     PetscCall(PetscFEPushforwardGradient(fe, &pgeom, Nb, tmpBasisDer));
    2520:     for (b = 0; b < Nb; ++b) {
    2521:       for (c = 0; c < Nc; ++c) {
    2522:         const PetscInt bcidx = b * Nc + c;
    2523:         const PetscInt qcidx = q * Nc + c;

    2525:         elemVec[b] += tmpBasis[bcidx] * f0[qcidx];
    2526:         for (d = 0; d < dE; ++d) elemVec[b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2527:       }
    2528:     }
    2529:   }
    2530:   return PETSC_SUCCESS;
    2531: }

    2533: PetscErrorCode PetscFEUpdateElementVec_Hybrid_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscInt side, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
    2534: {
    2535:   const PetscInt   dE       = T->cdim;
    2536:   const PetscInt   Nq       = T->Np;
    2537:   const PetscInt   Nb       = T->Nb;
    2538:   const PetscInt   Nc       = T->Nc;
    2539:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
    2540:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dE];

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

    2547:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
    2548:         for (PetscInt d = 0; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dE + bcidx * dE + d];
    2549:       }
    2550:     }
    2551:     PetscCall(PetscFEPushforward(fe, fegeom, Nb, tmpBasis));
    2552:     // TODO This is currently broken since we do not pull the geometry down to the lower dimension
    2553:     // PetscCall(PetscFEPushforwardGradient(fe, fegeom, Nb, tmpBasisDer));
    2554:     if (side == 2) {
    2555:       // Integrating over whole cohesive cell, so insert for both sides
    2556:       for (PetscInt s = 0; s < 2; ++s) {
    2557:         for (PetscInt b = 0; b < Nb; ++b) {
    2558:           for (PetscInt c = 0; c < Nc; ++c) {
    2559:             const PetscInt bcidx = b * Nc + c;
    2560:             const PetscInt qcidx = (q * 2 + s) * Nc + c;

    2562:             elemVec[Nb * s + b] += tmpBasis[bcidx] * f0[qcidx];
    2563:             for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * s + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2564:           }
    2565:         }
    2566:       }
    2567:     } else {
    2568:       // Integrating over endcaps of cohesive cell, so insert for correct side
    2569:       for (PetscInt b = 0; b < Nb; ++b) {
    2570:         for (PetscInt c = 0; c < Nc; ++c) {
    2571:           const PetscInt bcidx = b * Nc + c;
    2572:           const PetscInt qcidx = q * Nc + c;

    2574:           elemVec[Nb * side + b] += tmpBasis[bcidx] * f0[qcidx];
    2575:           for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * side + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2576:         }
    2577:       }
    2578:     }
    2579:   }
    2580:   return PETSC_SUCCESS;
    2581: }

    2583: #define petsc_elemmat_kernel_g1(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2584:   do { \
    2585:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2586:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2587:         const PetscScalar *G = g1 + (fc * (_NcJ) + gc) * _dE; \
    2588:         for (PetscInt f = 0; f < (_NbI); ++f) { \
    2589:           const PetscScalar tBIv = tmpBasisI[f * (_NcI) + fc]; \
    2590:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2591:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
    2592:             PetscScalar        s    = 0.0; \
    2593:             for (PetscInt df = 0; df < _dE; ++df) s += G[df] * tBDJ[df]; \
    2594:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBIv; \
    2595:           } \
    2596:         } \
    2597:       } \
    2598:     } \
    2599:   } while (0)

    2601: #define petsc_elemmat_kernel_g2(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2602:   do { \
    2603:     for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2604:       for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2605:         const PetscScalar *G = g2 + (fc * (_NcJ) + gc) * _dE; \
    2606:         for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2607:           const PetscScalar tBJv = tmpBasisJ[g * (_NcJ) + gc]; \
    2608:           for (PetscInt f = 0; f < (_NbI); ++f) { \
    2609:             const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
    2610:             PetscScalar        s    = 0.0; \
    2611:             for (PetscInt df = 0; df < _dE; ++df) s += tBDI[df] * G[df]; \
    2612:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBJv; \
    2613:           } \
    2614:         } \
    2615:       } \
    2616:     } \
    2617:   } while (0)

    2619: #define petsc_elemmat_kernel_g3(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2620:   do { \
    2621:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2622:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2623:         const PetscScalar *G = g3 + (fc * (_NcJ) + gc) * (_dE) * (_dE); \
    2624:         for (PetscInt f = 0; f < (_NbI); ++f) { \
    2625:           const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
    2626:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2627:             PetscScalar        s    = 0.0; \
    2628:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
    2629:             for (PetscInt df = 0; df < (_dE); ++df) { \
    2630:               for (PetscInt dg = 0; dg < (_dE); ++dg) s += tBDI[df] * G[df * (_dE) + dg] * tBDJ[dg]; \
    2631:             } \
    2632:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s; \
    2633:           } \
    2634:         } \
    2635:       } \
    2636:     } \
    2637:   } while (0)

    2639: PetscErrorCode PetscFEUpdateElementMat_Internal(PetscFE feI, PetscFE feJ, PetscInt r, PetscInt q, PetscTabulation TI, PetscScalar tmpBasisI[], PetscScalar tmpBasisDerI[], PetscTabulation TJ, PetscScalar tmpBasisJ[], PetscScalar tmpBasisDerJ[], PetscFEGeom *fegeom, const PetscScalar g0[], const PetscScalar g1[], const PetscScalar g2[], const PetscScalar g3[], PetscInt totDim, PetscInt offsetI, PetscInt offsetJ, PetscScalar elemMat[])
    2640: {
    2641:   const PetscInt   cdim      = TI->cdim;
    2642:   const PetscInt   dE        = fegeom->dimEmbed;
    2643:   const PetscInt   NqI       = TI->Np;
    2644:   const PetscInt   NbI       = TI->Nb;
    2645:   const PetscInt   NcI       = TI->Nc;
    2646:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
    2647:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * cdim];
    2648:   const PetscInt   NqJ       = TJ->Np;
    2649:   const PetscInt   NbJ       = TJ->Nb;
    2650:   const PetscInt   NcJ       = TJ->Nc;
    2651:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
    2652:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * cdim];

    2654:   for (PetscInt f = 0; f < NbI; ++f) {
    2655:     for (PetscInt fc = 0; fc < NcI; ++fc) {
    2656:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2658:       tmpBasisI[fidx] = basisI[fidx];
    2659:       for (PetscInt df = 0; df < cdim; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * cdim + df];
    2660:     }
    2661:   }
    2662:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
    2663:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
    2664:   if (feI != feJ) {
    2665:     for (PetscInt g = 0; g < NbJ; ++g) {
    2666:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2667:         const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2669:         tmpBasisJ[gidx] = basisJ[gidx];
    2670:         for (PetscInt dg = 0; dg < cdim; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * cdim + dg];
    2671:       }
    2672:     }
    2673:     PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
    2674:     PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
    2675:   } else {
    2676:     tmpBasisJ    = tmpBasisI;
    2677:     tmpBasisDerJ = tmpBasisDerI;
    2678:   }
    2679:   if (PetscUnlikely(g0)) {
    2680:     for (PetscInt f = 0; f < NbI; ++f) {
    2681:       const PetscInt i = offsetI + f; /* Element matrix row */

    2683:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2684:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

    2686:         for (PetscInt g = 0; g < NbJ; ++g) {
    2687:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2688:           const PetscInt fOff = i * totDim + j;

    2690:           for (PetscInt gc = 0; gc < NcJ; ++gc) elemMat[fOff] += bI * g0[fc * NcJ + gc] * tmpBasisJ[g * NcJ + gc];
    2691:         }
    2692:       }
    2693:     }
    2694:   }
    2695:   if (PetscUnlikely(g1)) {
    2696: #if 1
    2697:     if (dE == 2) {
    2698:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 2);
    2699:     } else if (dE == 3) {
    2700:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 3);
    2701:     } else {
    2702:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, dE);
    2703:     }
    2704: #else
    2705:     for (PetscInt f = 0; f < NbI; ++f) {
    2706:       const PetscInt i = offsetI + f; /* Element matrix row */

    2708:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2709:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

    2711:         for (PetscInt g = 0; g < NbJ; ++g) {
    2712:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2713:           const PetscInt fOff = i * totDim + j;

    2715:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2716:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2718:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += bI * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
    2719:           }
    2720:         }
    2721:       }
    2722:     }
    2723: #endif
    2724:   }
    2725:   if (PetscUnlikely(g2)) {
    2726: #if 1
    2727:     if (dE == 2) {
    2728:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 2);
    2729:     } else if (dE == 3) {
    2730:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 3);
    2731:     } else {
    2732:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, dE);
    2733:     }
    2734: #else
    2735:     for (PetscInt g = 0; g < NbJ; ++g) {
    2736:       const PetscInt j = offsetJ + g; /* Element matrix column */

    2738:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2739:         const PetscScalar bJ = tmpBasisJ[g * NcJ + gc]; /* Trial function basis value */

    2741:         for (PetscInt f = 0; f < NbI; ++f) {
    2742:           const PetscInt i    = offsetI + f; /* Element matrix row */
    2743:           const PetscInt fOff = i * totDim + j;

    2745:           for (PetscInt fc = 0; fc < NcI; ++fc) {
    2746:             const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2748:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * bJ;
    2749:           }
    2750:         }
    2751:       }
    2752:     }
    2753: #endif
    2754:   }
    2755:   if (PetscUnlikely(g3)) {
    2756: #if 1
    2757:     if (dE == 2) {
    2758:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 2);
    2759:     } else if (dE == 3) {
    2760:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 3);
    2761:     } else {
    2762:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, dE);
    2763:     }
    2764: #else
    2765:     for (PetscInt f = 0; f < NbI; ++f) {
    2766:       const PetscInt i = offsetI + f; /* Element matrix row */

    2768:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2769:         const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2771:         for (PetscInt g = 0; g < NbJ; ++g) {
    2772:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2773:           const PetscInt fOff = i * totDim + j;

    2775:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2776:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2778:             for (PetscInt df = 0; df < dE; ++df) {
    2779:               for (PetscInt dg = 0; dg < dE; ++dg) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g3[((fc * NcJ + gc) * dE + df) * dE + dg] * tmpBasisDerJ[gidx * dE + dg];
    2780:             }
    2781:           }
    2782:         }
    2783:       }
    2784:     }
    2785: #endif
    2786:   }
    2787:   return PETSC_SUCCESS;
    2788: }

    2790: #undef petsc_elemmat_kernel_g1
    2791: #undef petsc_elemmat_kernel_g2
    2792: #undef petsc_elemmat_kernel_g3

    2794: PetscErrorCode PetscFEUpdateElementMat_Hybrid_Internal(PetscFE feI, PetscBool isHybridI, PetscFE feJ, PetscBool isHybridJ, PetscInt r, PetscInt s, PetscInt t, PetscInt q, PetscTabulation TI, PetscScalar tmpBasisI[], PetscScalar tmpBasisDerI[], PetscTabulation TJ, PetscScalar tmpBasisJ[], PetscScalar tmpBasisDerJ[], PetscFEGeom *fegeom, const PetscScalar g0[], const PetscScalar g1[], const PetscScalar g2[], const PetscScalar g3[], PetscInt eOffset, PetscInt totDim, PetscInt offsetI, PetscInt offsetJ, PetscScalar elemMat[])
    2795: {
    2796:   const PetscInt   dE        = TI->cdim;
    2797:   const PetscInt   NqI       = TI->Np;
    2798:   const PetscInt   NbI       = TI->Nb;
    2799:   const PetscInt   NcI       = TI->Nc;
    2800:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
    2801:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * dE];
    2802:   const PetscInt   NqJ       = TJ->Np;
    2803:   const PetscInt   NbJ       = TJ->Nb;
    2804:   const PetscInt   NcJ       = TJ->Nc;
    2805:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
    2806:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * dE];
    2807:   const PetscInt   so        = isHybridI ? 0 : s;
    2808:   const PetscInt   to        = isHybridJ ? 0 : t;
    2809:   PetscInt         f, fc, g, gc, df, dg;

    2811:   for (f = 0; f < NbI; ++f) {
    2812:     for (fc = 0; fc < NcI; ++fc) {
    2813:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2815:       tmpBasisI[fidx] = basisI[fidx];
    2816:       for (df = 0; df < dE; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * dE + df];
    2817:     }
    2818:   }
    2819:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
    2820:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
    2821:   for (g = 0; g < NbJ; ++g) {
    2822:     for (gc = 0; gc < NcJ; ++gc) {
    2823:       const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2825:       tmpBasisJ[gidx] = basisJ[gidx];
    2826:       for (dg = 0; dg < dE; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * dE + dg];
    2827:     }
    2828:   }
    2829:   PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
    2830:   // TODO This is currently broken since we do not pull the geometry down to the lower dimension
    2831:   // PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
    2832:   for (f = 0; f < NbI; ++f) {
    2833:     for (fc = 0; fc < NcI; ++fc) {
    2834:       const PetscInt fidx = f * NcI + fc;           /* Test function basis index */
    2835:       const PetscInt i    = offsetI + NbI * so + f; /* Element matrix row */
    2836:       for (g = 0; g < NbJ; ++g) {
    2837:         for (gc = 0; gc < NcJ; ++gc) {
    2838:           const PetscInt gidx = g * NcJ + gc;           /* Trial function basis index */
    2839:           const PetscInt j    = offsetJ + NbJ * to + g; /* Element matrix column */
    2840:           const PetscInt fOff = eOffset + i * totDim + j;

    2842:           elemMat[fOff] += tmpBasisI[fidx] * g0[fc * NcJ + gc] * tmpBasisJ[gidx];
    2843:           for (df = 0; df < dE; ++df) {
    2844:             elemMat[fOff] += tmpBasisI[fidx] * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
    2845:             elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * tmpBasisJ[gidx];
    2846:             for (dg = 0; dg < dE; ++dg) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g3[((fc * NcJ + gc) * dE + df) * dE + dg] * tmpBasisDerJ[gidx * dE + dg];
    2847:           }
    2848:         }
    2849:       }
    2850:     }
    2851:   }
    2852:   return PETSC_SUCCESS;
    2853: }

    2855: PetscErrorCode PetscFECreateCellGeometry(PetscFE fe, PetscQuadrature quad, PetscFEGeom *cgeom)
    2856: {
    2857:   PetscDualSpace  dsp;
    2858:   DM              dm;
    2859:   PetscQuadrature quadDef;
    2860:   PetscInt        dim, cdim, Nq;

    2862:   PetscFunctionBegin;
    2863:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    2864:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    2865:   PetscCall(DMGetDimension(dm, &dim));
    2866:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2867:   PetscCall(PetscFEGetQuadrature(fe, &quadDef));
    2868:   quad = quad ? quad : quadDef;
    2869:   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
    2870:   PetscCall(PetscMalloc1(Nq * cdim, &cgeom->v));
    2871:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->J));
    2872:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->invJ));
    2873:   PetscCall(PetscMalloc1(Nq, &cgeom->detJ));
    2874:   cgeom->dim       = dim;
    2875:   cgeom->dimEmbed  = cdim;
    2876:   cgeom->numCells  = 1;
    2877:   cgeom->numPoints = Nq;
    2878:   PetscCall(DMPlexComputeCellGeometryFEM(dm, 0, quad, cgeom->v, cgeom->J, cgeom->invJ, cgeom->detJ));
    2879:   PetscFunctionReturn(PETSC_SUCCESS);
    2880: }

    2882: PetscErrorCode PetscFEDestroyCellGeometry(PetscFE fe, PetscFEGeom *cgeom)
    2883: {
    2884:   PetscFunctionBegin;
    2885:   PetscCall(PetscFree(cgeom->v));
    2886:   PetscCall(PetscFree(cgeom->J));
    2887:   PetscCall(PetscFree(cgeom->invJ));
    2888:   PetscCall(PetscFree(cgeom->detJ));
    2889:   PetscFunctionReturn(PETSC_SUCCESS);
    2890: }

    2892: #if 0
    2893: PetscErrorCode PetscFEUpdateElementMat_Internal_SparseIndices(PetscTabulation TI, PetscTabulation TJ, PetscInt dimEmbed, const PetscInt g0[], const PetscInt g1[], const PetscInt g2[], const PetscInt g3[], PetscInt totDim, PetscInt offsetI, PetscInt offsetJ, PetscInt *n_g0, PetscInt **g0_idxs_out, PetscInt *n_g1, PetscInt **g1_idxs_out, PetscInt *n_g2, PetscInt **g2_idxs_out, PetscInt *n_g3, PetscInt **g3_idxs_out)
    2894: {
    2895:   const PetscInt dE      = dimEmbed;
    2896:   const PetscInt NbI     = TI->Nb;
    2897:   const PetscInt NcI     = TI->Nc;
    2898:   const PetscInt NbJ     = TJ->Nb;
    2899:   const PetscInt NcJ     = TJ->Nc;
    2900:   PetscBool      has_g0  = g0 ? PETSC_TRUE : PETSC_FALSE;
    2901:   PetscBool      has_g1  = g1 ? PETSC_TRUE : PETSC_FALSE;
    2902:   PetscBool      has_g2  = g2 ? PETSC_TRUE : PETSC_FALSE;
    2903:   PetscBool      has_g3  = g3 ? PETSC_TRUE : PETSC_FALSE;
    2904:   PetscInt      *g0_idxs = NULL, *g1_idxs = NULL, *g2_idxs = NULL, *g3_idxs = NULL;
    2905:   PetscInt       g0_i, g1_i, g2_i, g3_i;

    2907:   PetscFunctionBegin;
    2908:   g0_i = g1_i = g2_i = g3_i = 0;
    2909:   if (has_g0)
    2910:     for (PetscInt i = 0; i < NcI * NcJ; i++)
    2911:       if (g0[i]) g0_i += NbI * NbJ;
    2912:   if (has_g1)
    2913:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
    2914:       if (g1[i]) g1_i += NbI * NbJ;
    2915:   if (has_g2)
    2916:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
    2917:       if (g2[i]) g2_i += NbI * NbJ;
    2918:   if (has_g3)
    2919:     for (PetscInt i = 0; i < NcI * NcJ * dE * dE; i++)
    2920:       if (g3[i]) g3_i += NbI * NbJ;
    2921:   if (g0_i == NbI * NbJ * NcI * NcJ) g0_i = 0;
    2922:   if (g1_i == NbI * NbJ * NcI * NcJ * dE) g1_i = 0;
    2923:   if (g2_i == NbI * NbJ * NcI * NcJ * dE) g2_i = 0;
    2924:   if (g3_i == NbI * NbJ * NcI * NcJ * dE * dE) g3_i = 0;
    2925:   has_g0 = g0_i ? PETSC_TRUE : PETSC_FALSE;
    2926:   has_g1 = g1_i ? PETSC_TRUE : PETSC_FALSE;
    2927:   has_g2 = g2_i ? PETSC_TRUE : PETSC_FALSE;
    2928:   has_g3 = g3_i ? PETSC_TRUE : PETSC_FALSE;
    2929:   if (has_g0) PetscCall(PetscMalloc1(4 * g0_i, &g0_idxs));
    2930:   if (has_g1) PetscCall(PetscMalloc1(4 * g1_i, &g1_idxs));
    2931:   if (has_g2) PetscCall(PetscMalloc1(4 * g2_i, &g2_idxs));
    2932:   if (has_g3) PetscCall(PetscMalloc1(4 * g3_i, &g3_idxs));
    2933:   g0_i = g1_i = g2_i = g3_i = 0;

    2935:   for (PetscInt f = 0; f < NbI; ++f) {
    2936:     const PetscInt i = offsetI + f; /* Element matrix row */
    2937:     for (PetscInt fc = 0; fc < NcI; ++fc) {
    2938:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2940:       for (PetscInt g = 0; g < NbJ; ++g) {
    2941:         const PetscInt j    = offsetJ + g; /* Element matrix column */
    2942:         const PetscInt fOff = i * totDim + j;
    2943:         for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2944:           const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2946:           if (has_g0) {
    2947:             if (g0[fc * NcJ + gc]) {
    2948:               g0_idxs[4 * g0_i + 0] = fidx;
    2949:               g0_idxs[4 * g0_i + 1] = fc * NcJ + gc;
    2950:               g0_idxs[4 * g0_i + 2] = gidx;
    2951:               g0_idxs[4 * g0_i + 3] = fOff;
    2952:               g0_i++;
    2953:             }
    2954:           }

    2956:           for (PetscInt df = 0; df < dE; ++df) {
    2957:             if (has_g1) {
    2958:               if (g1[(fc * NcJ + gc) * dE + df]) {
    2959:                 g1_idxs[4 * g1_i + 0] = fidx;
    2960:                 g1_idxs[4 * g1_i + 1] = (fc * NcJ + gc) * dE + df;
    2961:                 g1_idxs[4 * g1_i + 2] = gidx * dE + df;
    2962:                 g1_idxs[4 * g1_i + 3] = fOff;
    2963:                 g1_i++;
    2964:               }
    2965:             }
    2966:             if (has_g2) {
    2967:               if (g2[(fc * NcJ + gc) * dE + df]) {
    2968:                 g2_idxs[4 * g2_i + 0] = fidx * dE + df;
    2969:                 g2_idxs[4 * g2_i + 1] = (fc * NcJ + gc) * dE + df;
    2970:                 g2_idxs[4 * g2_i + 2] = gidx;
    2971:                 g2_idxs[4 * g2_i + 3] = fOff;
    2972:                 g2_i++;
    2973:               }
    2974:             }
    2975:             if (has_g3) {
    2976:               for (PetscInt dg = 0; dg < dE; ++dg) {
    2977:                 if (g3[((fc * NcJ + gc) * dE + df) * dE + dg]) {
    2978:                   g3_idxs[4 * g3_i + 0] = fidx * dE + df;
    2979:                   g3_idxs[4 * g3_i + 1] = ((fc * NcJ + gc) * dE + df) * dE + dg;
    2980:                   g3_idxs[4 * g3_i + 2] = gidx * dE + dg;
    2981:                   g3_idxs[4 * g3_i + 3] = fOff;
    2982:                   g3_i++;
    2983:                 }
    2984:               }
    2985:             }
    2986:           }
    2987:         }
    2988:       }
    2989:     }
    2990:   }
    2991:   *n_g0 = g0_i;
    2992:   *n_g1 = g1_i;
    2993:   *n_g2 = g2_i;
    2994:   *n_g3 = g3_i;

    2996:   *g0_idxs_out = g0_idxs;
    2997:   *g1_idxs_out = g1_idxs;
    2998:   *g2_idxs_out = g2_idxs;
    2999:   *g3_idxs_out = g3_idxs;
    3000:   PetscFunctionReturn(PETSC_SUCCESS);
    3001: }

    3003: //example HOW TO USE
    3004:       for (PetscInt i = 0; i < g0_sparse_n; i++) {
    3005:         PetscInt bM = g0_sparse_idxs[4 * i + 0];
    3006:         PetscInt bN = g0_sparse_idxs[4 * i + 1];
    3007:         PetscInt bK = g0_sparse_idxs[4 * i + 2];
    3008:         PetscInt bO = g0_sparse_idxs[4 * i + 3];
    3009:         elemMat[bO] += tmpBasisI[bM] * g0[bN] * tmpBasisJ[bK];
    3010:       }
    3011: #endif