Date: 2025-03-29T05:58:19+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 iascii;

    198:   PetscFunctionBegin;
    201:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)fem), &viewer));
    202:   PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)fem, viewer));
    203:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    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: `PetscFEV`, `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) {
    233:     defaultType = PETSCFEBASIC;
    234:   } else {
    235:     defaultType = ((PetscObject)fem)->type_name;
    236:   }
    237:   if (!PetscFERegisterAllCalled) PetscCall(PetscFERegisterAll());

    239:   PetscObjectOptionsBegin((PetscObject)fem);
    240:   PetscCall(PetscOptionsFList("-petscfe_type", "Finite element space", "PetscFESetType", PetscFEList, defaultType, name, 256, &flg));
    241:   if (flg) {
    242:     PetscCall(PetscFESetType(fem, name));
    243:   } else if (!((PetscObject)fem)->type_name) {
    244:     PetscCall(PetscFESetType(fem, defaultType));
    245:   }
    246:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_blocks", "The number of cell blocks to integrate concurrently", "PetscSpaceSetTileSizes", fem->numBlocks, &fem->numBlocks, NULL, 1));
    247:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_batches", "The number of cell batches to integrate serially", "PetscSpaceSetTileSizes", fem->numBatches, &fem->numBatches, NULL, 1));
    248:   PetscTryTypeMethod(fem, setfromoptions, PetscOptionsObject);
    249:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
    250:   PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)fem, PetscOptionsObject));
    251:   PetscOptionsEnd();
    252:   PetscCall(PetscFEViewFromOptions(fem, NULL, "-petscfe_view"));
    253:   PetscFunctionReturn(PETSC_SUCCESS);
    254: }

    256: /*@
    257:   PetscFESetUp - Construct data structures for the `PetscFE` after the `PetscFEType` has been set

    259:   Collective

    261:   Input Parameter:
    262: . fem - the `PetscFE` object to setup

    264:   Level: intermediate

    266: .seealso: `PetscFE`, `PetscFEView()`, `PetscFEDestroy()`
    267: @*/
    268: PetscErrorCode PetscFESetUp(PetscFE fem)
    269: {
    270:   PetscFunctionBegin;
    272:   if (fem->setupcalled) PetscFunctionReturn(PETSC_SUCCESS);
    273:   PetscCall(PetscLogEventBegin(PETSCFE_SetUp, fem, 0, 0, 0));
    274:   fem->setupcalled = PETSC_TRUE;
    275:   PetscTryTypeMethod(fem, setup);
    276:   PetscCall(PetscLogEventEnd(PETSCFE_SetUp, fem, 0, 0, 0));
    277:   PetscFunctionReturn(PETSC_SUCCESS);
    278: }

    280: /*@
    281:   PetscFEDestroy - Destroys a `PetscFE` object

    283:   Collective

    285:   Input Parameter:
    286: . fem - the `PetscFE` object to destroy

    288:   Level: beginner

    290: .seealso: `PetscFE`, `PetscFEView()`
    291: @*/
    292: PetscErrorCode PetscFEDestroy(PetscFE *fem)
    293: {
    294:   PetscFunctionBegin;
    295:   if (!*fem) PetscFunctionReturn(PETSC_SUCCESS);

    298:   if (--((PetscObject)*fem)->refct > 0) {
    299:     *fem = NULL;
    300:     PetscFunctionReturn(PETSC_SUCCESS);
    301:   }
    302:   ((PetscObject)*fem)->refct = 0;

    304:   if ((*fem)->subspaces) {
    305:     PetscInt dim, d;

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

    324:   PetscTryTypeMethod(*fem, destroy);
    325:   PetscCall(PetscHeaderDestroy(fem));
    326:   PetscFunctionReturn(PETSC_SUCCESS);
    327: }

    329: /*@
    330:   PetscFECreate - Creates an empty `PetscFE` object. The type can then be set with `PetscFESetType()`.

    332:   Collective

    334:   Input Parameter:
    335: . comm - The communicator for the `PetscFE` object

    337:   Output Parameter:
    338: . fem - The `PetscFE` object

    340:   Level: beginner

    342: .seealso: `PetscFE`, `PetscFEType`, `PetscFESetType()`, `PetscFECreateDefault()`, `PETSCFEGALERKIN`
    343: @*/
    344: PetscErrorCode PetscFECreate(MPI_Comm comm, PetscFE *fem)
    345: {
    346:   PetscFE f;

    348:   PetscFunctionBegin;
    349:   PetscAssertPointer(fem, 2);
    350:   PetscCall(PetscCitationsRegister(FECitation, &FEcite));
    351:   PetscCall(PetscFEInitializePackage());

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

    355:   f->basisSpace    = NULL;
    356:   f->dualSpace     = NULL;
    357:   f->numComponents = 1;
    358:   f->subspaces     = NULL;
    359:   f->invV          = NULL;
    360:   f->T             = NULL;
    361:   f->Tf            = NULL;
    362:   f->Tc            = NULL;
    363:   PetscCall(PetscArrayzero(&f->quadrature, 1));
    364:   PetscCall(PetscArrayzero(&f->faceQuadrature, 1));
    365:   f->blockSize  = 0;
    366:   f->numBlocks  = 1;
    367:   f->batchSize  = 0;
    368:   f->numBatches = 1;

    370:   *fem = f;
    371:   PetscFunctionReturn(PETSC_SUCCESS);
    372: }

    374: /*@
    375:   PetscFEGetSpatialDimension - Returns the spatial dimension of the element

    377:   Not Collective

    379:   Input Parameter:
    380: . fem - The `PetscFE` object

    382:   Output Parameter:
    383: . dim - The spatial dimension

    385:   Level: intermediate

    387: .seealso: `PetscFE`, `PetscFECreate()`
    388: @*/
    389: PetscErrorCode PetscFEGetSpatialDimension(PetscFE fem, PetscInt *dim)
    390: {
    391:   DM dm;

    393:   PetscFunctionBegin;
    395:   PetscAssertPointer(dim, 2);
    396:   PetscCall(PetscDualSpaceGetDM(fem->dualSpace, &dm));
    397:   PetscCall(DMGetDimension(dm, dim));
    398:   PetscFunctionReturn(PETSC_SUCCESS);
    399: }

    401: /*@
    402:   PetscFESetNumComponents - Sets the number of field components in the element

    404:   Not Collective

    406:   Input Parameters:
    407: + fem  - The `PetscFE` object
    408: - comp - The number of field components

    410:   Level: intermediate

    412: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`, `PetscFEGetNumComponents()`
    413: @*/
    414: PetscErrorCode PetscFESetNumComponents(PetscFE fem, PetscInt comp)
    415: {
    416:   PetscFunctionBegin;
    418:   fem->numComponents = comp;
    419:   PetscFunctionReturn(PETSC_SUCCESS);
    420: }

    422: /*@
    423:   PetscFEGetNumComponents - Returns the number of components in the element

    425:   Not Collective

    427:   Input Parameter:
    428: . fem - The `PetscFE` object

    430:   Output Parameter:
    431: . comp - The number of field components

    433:   Level: intermediate

    435: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`
    436: @*/
    437: PetscErrorCode PetscFEGetNumComponents(PetscFE fem, PetscInt *comp)
    438: {
    439:   PetscFunctionBegin;
    441:   PetscAssertPointer(comp, 2);
    442:   *comp = fem->numComponents;
    443:   PetscFunctionReturn(PETSC_SUCCESS);
    444: }

    446: /*@
    447:   PetscFESetTileSizes - Sets the tile sizes for evaluation

    449:   Not Collective

    451:   Input Parameters:
    452: + fem        - The `PetscFE` object
    453: . blockSize  - The number of elements in a block
    454: . numBlocks  - The number of blocks in a batch
    455: . batchSize  - The number of elements in a batch
    456: - numBatches - The number of batches in a chunk

    458:   Level: intermediate

    460: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetTileSizes()`
    461: @*/
    462: PetscErrorCode PetscFESetTileSizes(PetscFE fem, PetscInt blockSize, PetscInt numBlocks, PetscInt batchSize, PetscInt numBatches)
    463: {
    464:   PetscFunctionBegin;
    466:   fem->blockSize  = blockSize;
    467:   fem->numBlocks  = numBlocks;
    468:   fem->batchSize  = batchSize;
    469:   fem->numBatches = numBatches;
    470:   PetscFunctionReturn(PETSC_SUCCESS);
    471: }

    473: /*@
    474:   PetscFEGetTileSizes - Returns the tile sizes for evaluation

    476:   Not Collective

    478:   Input Parameter:
    479: . fem - The `PetscFE` object

    481:   Output Parameters:
    482: + blockSize  - The number of elements in a block, pass `NULL` if not needed
    483: . numBlocks  - The number of blocks in a batch, pass `NULL` if not needed
    484: . batchSize  - The number of elements in a batch, pass `NULL` if not needed
    485: - numBatches - The number of batches in a chunk, pass `NULL` if not needed

    487:   Level: intermediate

    489: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFESetTileSizes()`
    490: @*/
    491: PetscErrorCode PetscFEGetTileSizes(PetscFE fem, PeOp PetscInt *blockSize, PeOp PetscInt *numBlocks, PeOp PetscInt *batchSize, PeOp PetscInt *numBatches)
    492: {
    493:   PetscFunctionBegin;
    495:   if (blockSize) PetscAssertPointer(blockSize, 2);
    496:   if (numBlocks) PetscAssertPointer(numBlocks, 3);
    497:   if (batchSize) PetscAssertPointer(batchSize, 4);
    498:   if (numBatches) PetscAssertPointer(numBatches, 5);
    499:   if (blockSize) *blockSize = fem->blockSize;
    500:   if (numBlocks) *numBlocks = fem->numBlocks;
    501:   if (batchSize) *batchSize = fem->batchSize;
    502:   if (numBatches) *numBatches = fem->numBatches;
    503:   PetscFunctionReturn(PETSC_SUCCESS);
    504: }

    506: /*@
    507:   PetscFEGetBasisSpace - Returns the `PetscSpace` used for the approximation of the solution for the `PetscFE`

    509:   Not Collective

    511:   Input Parameter:
    512: . fem - The `PetscFE` object

    514:   Output Parameter:
    515: . sp - The `PetscSpace` object

    517:   Level: intermediate

    519: .seealso: `PetscFE`, `PetscSpace`, `PetscFECreate()`
    520: @*/
    521: PetscErrorCode PetscFEGetBasisSpace(PetscFE fem, PetscSpace *sp)
    522: {
    523:   PetscFunctionBegin;
    525:   PetscAssertPointer(sp, 2);
    526:   *sp = fem->basisSpace;
    527:   PetscFunctionReturn(PETSC_SUCCESS);
    528: }

    530: /*@
    531:   PetscFESetBasisSpace - Sets the `PetscSpace` used for the approximation of the solution

    533:   Not Collective

    535:   Input Parameters:
    536: + fem - The `PetscFE` object
    537: - sp  - The `PetscSpace` object

    539:   Level: intermediate

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

    544: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetDualSpace()`
    545: @*/
    546: PetscErrorCode PetscFESetBasisSpace(PetscFE fem, PetscSpace sp)
    547: {
    548:   PetscFunctionBegin;
    551:   PetscCall(PetscSpaceDestroy(&fem->basisSpace));
    552:   fem->basisSpace = sp;
    553:   PetscCall(PetscObjectReference((PetscObject)fem->basisSpace));
    554:   PetscFunctionReturn(PETSC_SUCCESS);
    555: }

    557: /*@
    558:   PetscFEGetDualSpace - Returns the `PetscDualSpace` used to define the inner product for a `PetscFE`

    560:   Not Collective

    562:   Input Parameter:
    563: . fem - The `PetscFE` object

    565:   Output Parameter:
    566: . sp - The `PetscDualSpace` object

    568:   Level: intermediate

    570: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
    571: @*/
    572: PetscErrorCode PetscFEGetDualSpace(PetscFE fem, PetscDualSpace *sp)
    573: {
    574:   PetscFunctionBegin;
    576:   PetscAssertPointer(sp, 2);
    577:   *sp = fem->dualSpace;
    578:   PetscFunctionReturn(PETSC_SUCCESS);
    579: }

    581: /*@
    582:   PetscFESetDualSpace - Sets the `PetscDualSpace` used to define the inner product

    584:   Not Collective

    586:   Input Parameters:
    587: + fem - The `PetscFE` object
    588: - sp  - The `PetscDualSpace` object

    590:   Level: intermediate

    592: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetBasisSpace()`
    593: @*/
    594: PetscErrorCode PetscFESetDualSpace(PetscFE fem, PetscDualSpace sp)
    595: {
    596:   PetscFunctionBegin;
    599:   PetscCall(PetscDualSpaceDestroy(&fem->dualSpace));
    600:   fem->dualSpace = sp;
    601:   PetscCall(PetscObjectReference((PetscObject)fem->dualSpace));
    602:   PetscFunctionReturn(PETSC_SUCCESS);
    603: }

    605: /*@
    606:   PetscFEGetQuadrature - Returns the `PetscQuadrature` used to calculate inner products

    608:   Not Collective

    610:   Input Parameter:
    611: . fem - The `PetscFE` object

    613:   Output Parameter:
    614: . q - The `PetscQuadrature` object

    616:   Level: intermediate

    618: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`
    619: @*/
    620: PetscErrorCode PetscFEGetQuadrature(PetscFE fem, PetscQuadrature *q)
    621: {
    622:   PetscFunctionBegin;
    624:   PetscAssertPointer(q, 2);
    625:   *q = fem->quadrature;
    626:   PetscFunctionReturn(PETSC_SUCCESS);
    627: }

    629: /*@
    630:   PetscFESetQuadrature - Sets the `PetscQuadrature` used to calculate inner products

    632:   Not Collective

    634:   Input Parameters:
    635: + fem - The `PetscFE` object
    636: - q   - The `PetscQuadrature` object

    638:   Level: intermediate

    640: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFEGetFaceQuadrature()`
    641: @*/
    642: PetscErrorCode PetscFESetQuadrature(PetscFE fem, PetscQuadrature q)
    643: {
    644:   PetscInt Nc, qNc;

    646:   PetscFunctionBegin;
    648:   if (q == fem->quadrature) PetscFunctionReturn(PETSC_SUCCESS);
    649:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
    650:   PetscCall(PetscQuadratureGetNumComponents(q, &qNc));
    651:   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);
    652:   PetscCall(PetscTabulationDestroy(&fem->T));
    653:   PetscCall(PetscTabulationDestroy(&fem->Tc));
    654:   PetscCall(PetscObjectReference((PetscObject)q));
    655:   PetscCall(PetscQuadratureDestroy(&fem->quadrature));
    656:   fem->quadrature = q;
    657:   PetscFunctionReturn(PETSC_SUCCESS);
    658: }

    660: /*@
    661:   PetscFEGetFaceQuadrature - Returns the `PetscQuadrature` used to calculate inner products on faces

    663:   Not Collective

    665:   Input Parameter:
    666: . fem - The `PetscFE` object

    668:   Output Parameter:
    669: . q - The `PetscQuadrature` object

    671:   Level: intermediate

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

    676: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
    677: @*/
    678: PetscErrorCode PetscFEGetFaceQuadrature(PetscFE fem, PetscQuadrature *q)
    679: {
    680:   PetscFunctionBegin;
    682:   PetscAssertPointer(q, 2);
    683:   *q = fem->faceQuadrature;
    684:   PetscFunctionReturn(PETSC_SUCCESS);
    685: }

    687: /*@
    688:   PetscFESetFaceQuadrature - Sets the `PetscQuadrature` used to calculate inner products on faces

    690:   Not Collective

    692:   Input Parameters:
    693: + fem - The `PetscFE` object
    694: - q   - The `PetscQuadrature` object

    696:   Level: intermediate

    698: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`
    699: @*/
    700: PetscErrorCode PetscFESetFaceQuadrature(PetscFE fem, PetscQuadrature q)
    701: {
    702:   PetscInt Nc, qNc;

    704:   PetscFunctionBegin;
    706:   if (q == fem->faceQuadrature) PetscFunctionReturn(PETSC_SUCCESS);
    707:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
    708:   PetscCall(PetscQuadratureGetNumComponents(q, &qNc));
    709:   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);
    710:   PetscCall(PetscTabulationDestroy(&fem->Tf));
    711:   PetscCall(PetscObjectReference((PetscObject)q));
    712:   PetscCall(PetscQuadratureDestroy(&fem->faceQuadrature));
    713:   fem->faceQuadrature = q;
    714:   PetscFunctionReturn(PETSC_SUCCESS);
    715: }

    717: /*@
    718:   PetscFECopyQuadrature - Copy both volumetric and surface quadrature to a new `PetscFE`

    720:   Not Collective

    722:   Input Parameters:
    723: + sfe - The `PetscFE` source for the quadratures
    724: - tfe - The `PetscFE` target for the quadratures

    726:   Level: intermediate

    728: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
    729: @*/
    730: PetscErrorCode PetscFECopyQuadrature(PetscFE sfe, PetscFE tfe)
    731: {
    732:   PetscQuadrature q;

    734:   PetscFunctionBegin;
    737:   PetscCall(PetscFEGetQuadrature(sfe, &q));
    738:   PetscCall(PetscFESetQuadrature(tfe, q));
    739:   PetscCall(PetscFEGetFaceQuadrature(sfe, &q));
    740:   PetscCall(PetscFESetFaceQuadrature(tfe, q));
    741:   PetscFunctionReturn(PETSC_SUCCESS);
    742: }

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

    747:   Not Collective

    749:   Input Parameter:
    750: . fem - The `PetscFE` object

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

    755:   Level: intermediate

    757: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
    758: @*/
    759: PetscErrorCode PetscFEGetNumDof(PetscFE fem, const PetscInt *numDof[])
    760: {
    761:   PetscFunctionBegin;
    763:   PetscAssertPointer(numDof, 2);
    764:   PetscCall(PetscDualSpaceGetNumDof(fem->dualSpace, numDof));
    765:   PetscFunctionReturn(PETSC_SUCCESS);
    766: }

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

    771:   Not Collective

    773:   Input Parameters:
    774: + fem - The `PetscFE` object
    775: - k   - The highest derivative we need to tabulate, very often 1

    777:   Output Parameter:
    778: . T - The basis function values and derivatives at quadrature points

    780:   Level: intermediate

    782:   Note:
    783: .vb
    784:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    785:   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
    786:   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
    787: .ve

    789: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
    790: @*/
    791: PetscErrorCode PetscFEGetCellTabulation(PetscFE fem, PetscInt k, PetscTabulation *T)
    792: {
    793:   PetscInt         npoints;
    794:   const PetscReal *points;

    796:   PetscFunctionBegin;
    798:   PetscAssertPointer(T, 3);
    799:   PetscCall(PetscQuadratureGetData(fem->quadrature, NULL, NULL, &npoints, &points, NULL));
    800:   if (!fem->T) PetscCall(PetscFECreateTabulation(fem, 1, npoints, points, k, &fem->T));
    801:   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);
    802:   *T = fem->T;
    803:   PetscFunctionReturn(PETSC_SUCCESS);
    804: }

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

    809:   Not Collective

    811:   Input Parameters:
    812: + fem - The `PetscFE` object
    813: - k   - The highest derivative we need to tabulate, very often 1

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

    818:   Level: intermediate

    820:   Note:
    821: .vb
    822:   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
    823:   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
    824:   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
    825: .ve

    827: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
    828: @*/
    829: PetscErrorCode PetscFEGetFaceTabulation(PetscFE fem, PetscInt k, PetscTabulation *Tf)
    830: {
    831:   PetscFunctionBegin;
    833:   PetscAssertPointer(Tf, 3);
    834:   if (!fem->Tf) {
    835:     const PetscReal  xi0[3] = {-1., -1., -1.};
    836:     PetscReal        v0[3], J[9], detJ;
    837:     PetscQuadrature  fq;
    838:     PetscDualSpace   sp;
    839:     DM               dm;
    840:     const PetscInt  *faces;
    841:     PetscInt         dim, numFaces, f, npoints, q;
    842:     const PetscReal *points;
    843:     PetscReal       *facePoints;

    845:     PetscCall(PetscFEGetDualSpace(fem, &sp));
    846:     PetscCall(PetscDualSpaceGetDM(sp, &dm));
    847:     PetscCall(DMGetDimension(dm, &dim));
    848:     PetscCall(DMPlexGetConeSize(dm, 0, &numFaces));
    849:     PetscCall(DMPlexGetCone(dm, 0, &faces));
    850:     PetscCall(PetscFEGetFaceQuadrature(fem, &fq));
    851:     if (fq) {
    852:       PetscCall(PetscQuadratureGetData(fq, NULL, NULL, &npoints, &points, NULL));
    853:       PetscCall(PetscMalloc1(numFaces * npoints * dim, &facePoints));
    854:       for (f = 0; f < numFaces; ++f) {
    855:         PetscCall(DMPlexComputeCellGeometryFEM(dm, faces[f], NULL, v0, J, NULL, &detJ));
    856:         for (q = 0; q < npoints; ++q) CoordinatesRefToReal(dim, dim - 1, xi0, v0, J, &points[q * (dim - 1)], &facePoints[(f * npoints + q) * dim]);
    857:       }
    858:       PetscCall(PetscFECreateTabulation(fem, numFaces, npoints, facePoints, k, &fem->Tf));
    859:       PetscCall(PetscFree(facePoints));
    860:     }
    861:   }
    862:   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);
    863:   *Tf = fem->Tf;
    864:   PetscFunctionReturn(PETSC_SUCCESS);
    865: }

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

    870:   Not Collective

    872:   Input Parameter:
    873: . fem - The `PetscFE` object

    875:   Output Parameter:
    876: . Tc - The basis function values at face centroid points

    878:   Level: intermediate

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

    885: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFEGetFaceTabulation()`, `PetscFEGetCellTabulation()`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
    886: @*/
    887: PetscErrorCode PetscFEGetFaceCentroidTabulation(PetscFE fem, PetscTabulation *Tc)
    888: {
    889:   PetscFunctionBegin;
    891:   PetscAssertPointer(Tc, 2);
    892:   if (!fem->Tc) {
    893:     PetscDualSpace  sp;
    894:     DM              dm;
    895:     const PetscInt *cone;
    896:     PetscReal      *centroids;
    897:     PetscInt        dim, numFaces, f;

    899:     PetscCall(PetscFEGetDualSpace(fem, &sp));
    900:     PetscCall(PetscDualSpaceGetDM(sp, &dm));
    901:     PetscCall(DMGetDimension(dm, &dim));
    902:     PetscCall(DMPlexGetConeSize(dm, 0, &numFaces));
    903:     PetscCall(DMPlexGetCone(dm, 0, &cone));
    904:     PetscCall(PetscMalloc1(numFaces * dim, &centroids));
    905:     for (f = 0; f < numFaces; ++f) PetscCall(DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, &centroids[f * dim], NULL));
    906:     PetscCall(PetscFECreateTabulation(fem, 1, numFaces, centroids, 0, &fem->Tc));
    907:     PetscCall(PetscFree(centroids));
    908:   }
    909:   *Tc = fem->Tc;
    910:   PetscFunctionReturn(PETSC_SUCCESS);
    911: }

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

    916:   Not Collective

    918:   Input Parameters:
    919: + fem     - The `PetscFE` object
    920: . nrepl   - The number of replicas
    921: . npoints - The number of tabulation points in a replica
    922: . points  - The tabulation point coordinates
    923: - K       - The number of derivatives calculated

    925:   Output Parameter:
    926: . T - The basis function values and derivatives at tabulation points

    928:   Level: intermediate

    930:   Note:
    931: .vb
    932:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    933:   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
    934:   T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis
    935:   T->function i, component c, in directions d and e
    936: .ve

    938: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`
    939: @*/
    940: PetscErrorCode PetscFECreateTabulation(PetscFE fem, PetscInt nrepl, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation *T)
    941: {
    942:   DM             dm;
    943:   PetscDualSpace Q;
    944:   PetscInt       Nb;   /* Dimension of FE space P */
    945:   PetscInt       Nc;   /* Field components */
    946:   PetscInt       cdim; /* Reference coordinate dimension */
    947:   PetscInt       k;

    949:   PetscFunctionBegin;
    950:   if (!npoints || !fem->dualSpace || K < 0) {
    951:     *T = NULL;
    952:     PetscFunctionReturn(PETSC_SUCCESS);
    953:   }
    955:   PetscAssertPointer(points, 4);
    956:   PetscAssertPointer(T, 6);
    957:   PetscCall(PetscFEGetDualSpace(fem, &Q));
    958:   PetscCall(PetscDualSpaceGetDM(Q, &dm));
    959:   PetscCall(DMGetDimension(dm, &cdim));
    960:   PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
    961:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
    962:   PetscCall(PetscMalloc1(1, T));
    963:   (*T)->K    = !cdim ? 0 : K;
    964:   (*T)->Nr   = nrepl;
    965:   (*T)->Np   = npoints;
    966:   (*T)->Nb   = Nb;
    967:   (*T)->Nc   = Nc;
    968:   (*T)->cdim = cdim;
    969:   PetscCall(PetscMalloc1((*T)->K + 1, &(*T)->T));
    970:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscCalloc1(nrepl * npoints * Nb * Nc * PetscPowInt(cdim, k), &(*T)->T[k]));
    971:   PetscUseTypeMethod(fem, computetabulation, nrepl * npoints, points, K, *T);
    972:   PetscFunctionReturn(PETSC_SUCCESS);
    973: }

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

    978:   Not Collective

    980:   Input Parameters:
    981: + fem     - The `PetscFE` object
    982: . npoints - The number of tabulation points
    983: . points  - The tabulation point coordinates
    984: . K       - The number of derivatives calculated
    985: - T       - An existing tabulation object with enough allocated space

    987:   Output Parameter:
    988: . T - The basis function values and derivatives at tabulation points

    990:   Level: intermediate

    992:   Note:
    993: .vb
    994:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    995:   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
    996:   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
    997: .ve

    999: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`
    1000: @*/
    1001: PetscErrorCode PetscFEComputeTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation T)
    1002: {
    1003:   PetscFunctionBeginHot;
    1004:   if (!npoints || !fem->dualSpace || K < 0) PetscFunctionReturn(PETSC_SUCCESS);
    1006:   PetscAssertPointer(points, 3);
    1007:   PetscAssertPointer(T, 5);
    1008:   if (PetscDefined(USE_DEBUG)) {
    1009:     DM             dm;
    1010:     PetscDualSpace Q;
    1011:     PetscInt       Nb;   /* Dimension of FE space P */
    1012:     PetscInt       Nc;   /* Field components */
    1013:     PetscInt       cdim; /* Reference coordinate dimension */

    1015:     PetscCall(PetscFEGetDualSpace(fem, &Q));
    1016:     PetscCall(PetscDualSpaceGetDM(Q, &dm));
    1017:     PetscCall(DMGetDimension(dm, &cdim));
    1018:     PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
    1019:     PetscCall(PetscFEGetNumComponents(fem, &Nc));
    1020:     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);
    1021:     PetscCheck(T->Nb == Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nb %" PetscInt_FMT " must match requested Nb %" PetscInt_FMT, T->Nb, Nb);
    1022:     PetscCheck(T->Nc == Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nc %" PetscInt_FMT " must match requested Nc %" PetscInt_FMT, T->Nc, Nc);
    1023:     PetscCheck(T->cdim == cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation cdim %" PetscInt_FMT " must match requested cdim %" PetscInt_FMT, T->cdim, cdim);
    1024:   }
    1025:   T->Nr = 1;
    1026:   T->Np = npoints;
    1027:   PetscUseTypeMethod(fem, computetabulation, npoints, points, K, T);
    1028:   PetscFunctionReturn(PETSC_SUCCESS);
    1029: }

    1031: /*@
    1032:   PetscTabulationDestroy - Frees memory from the associated tabulation.

    1034:   Not Collective

    1036:   Input Parameter:
    1037: . T - The tabulation

    1039:   Level: intermediate

    1041: .seealso: `PetscTabulation`, `PetscFECreateTabulation()`, `PetscFEGetCellTabulation()`
    1042: @*/
    1043: PetscErrorCode PetscTabulationDestroy(PetscTabulation *T)
    1044: {
    1045:   PetscInt k;

    1047:   PetscFunctionBegin;
    1048:   PetscAssertPointer(T, 1);
    1049:   if (!T || !*T) PetscFunctionReturn(PETSC_SUCCESS);
    1050:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscFree((*T)->T[k]));
    1051:   PetscCall(PetscFree((*T)->T));
    1052:   PetscCall(PetscFree(*T));
    1053:   *T = NULL;
    1054:   PetscFunctionReturn(PETSC_SUCCESS);
    1055: }

    1057: static PetscErrorCode PetscFECreatePointTraceDefault_Internal(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
    1058: {
    1059:   PetscSpace      bsp, bsubsp;
    1060:   PetscDualSpace  dsp, dsubsp;
    1061:   PetscInt        dim, depth, numComp, i, j, coneSize, order;
    1062:   DM              dm;
    1063:   DMLabel         label;
    1064:   PetscReal      *xi, *v, *J, detJ;
    1065:   const char     *name;
    1066:   PetscQuadrature origin, fullQuad, subQuad;

    1068:   PetscFunctionBegin;
    1069:   PetscCall(PetscFEGetBasisSpace(fe, &bsp));
    1070:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    1071:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    1072:   PetscCall(DMGetDimension(dm, &dim));
    1073:   PetscCall(DMPlexGetDepthLabel(dm, &label));
    1074:   PetscCall(DMLabelGetValue(label, refPoint, &depth));
    1075:   PetscCall(PetscCalloc1(depth, &xi));
    1076:   PetscCall(PetscMalloc1(dim, &v));
    1077:   PetscCall(PetscMalloc1(dim * dim, &J));
    1078:   for (i = 0; i < depth; i++) xi[i] = 0.;
    1079:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &origin));
    1080:   PetscCall(PetscQuadratureSetData(origin, depth, 0, 1, xi, NULL));
    1081:   PetscCall(DMPlexComputeCellGeometryFEM(dm, refPoint, origin, v, J, NULL, &detJ));
    1082:   /* CellGeometryFEM computes the expanded Jacobian, we want the true jacobian */
    1083:   for (i = 1; i < dim; i++) {
    1084:     for (j = 0; j < depth; j++) J[i * depth + j] = J[i * dim + j];
    1085:   }
    1086:   PetscCall(PetscQuadratureDestroy(&origin));
    1087:   PetscCall(PetscDualSpaceGetPointSubspace(dsp, refPoint, &dsubsp));
    1088:   PetscCall(PetscSpaceCreateSubspace(bsp, dsubsp, v, J, NULL, NULL, PETSC_OWN_POINTER, &bsubsp));
    1089:   PetscCall(PetscSpaceSetUp(bsubsp));
    1090:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), trFE));
    1091:   PetscCall(PetscFESetType(*trFE, PETSCFEBASIC));
    1092:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    1093:   PetscCall(PetscFESetNumComponents(*trFE, numComp));
    1094:   PetscCall(PetscFESetBasisSpace(*trFE, bsubsp));
    1095:   PetscCall(PetscFESetDualSpace(*trFE, dsubsp));
    1096:   PetscCall(PetscObjectGetName((PetscObject)fe, &name));
    1097:   if (name) PetscCall(PetscFESetName(*trFE, name));
    1098:   PetscCall(PetscFEGetQuadrature(fe, &fullQuad));
    1099:   PetscCall(PetscQuadratureGetOrder(fullQuad, &order));
    1100:   PetscCall(DMPlexGetConeSize(dm, refPoint, &coneSize));
    1101:   if (coneSize == 2 * depth) PetscCall(PetscDTGaussTensorQuadrature(depth, 1, (order + 2) / 2, -1., 1., &subQuad));
    1102:   else PetscCall(PetscDTSimplexQuadrature(depth, order, PETSCDTSIMPLEXQUAD_DEFAULT, &subQuad));
    1103:   PetscCall(PetscFESetQuadrature(*trFE, subQuad));
    1104:   PetscCall(PetscFESetUp(*trFE));
    1105:   PetscCall(PetscQuadratureDestroy(&subQuad));
    1106:   PetscCall(PetscSpaceDestroy(&bsubsp));
    1107:   PetscFunctionReturn(PETSC_SUCCESS);
    1108: }

    1110: PETSC_EXTERN PetscErrorCode PetscFECreatePointTrace(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
    1111: {
    1112:   PetscFunctionBegin;
    1114:   PetscAssertPointer(trFE, 3);
    1115:   if (fe->ops->createpointtrace) PetscUseTypeMethod(fe, createpointtrace, refPoint, trFE);
    1116:   else PetscCall(PetscFECreatePointTraceDefault_Internal(fe, refPoint, trFE));
    1117:   PetscFunctionReturn(PETSC_SUCCESS);
    1118: }

    1120: PetscErrorCode PetscFECreateHeightTrace(PetscFE fe, PetscInt height, PetscFE *trFE)
    1121: {
    1122:   PetscInt       hStart, hEnd;
    1123:   PetscDualSpace dsp;
    1124:   DM             dm;

    1126:   PetscFunctionBegin;
    1128:   PetscAssertPointer(trFE, 3);
    1129:   *trFE = NULL;
    1130:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    1131:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    1132:   PetscCall(DMPlexGetHeightStratum(dm, height, &hStart, &hEnd));
    1133:   if (hEnd <= hStart) PetscFunctionReturn(PETSC_SUCCESS);
    1134:   PetscCall(PetscFECreatePointTrace(fe, hStart, trFE));
    1135:   PetscFunctionReturn(PETSC_SUCCESS);
    1136: }

    1138: /*@
    1139:   PetscFEGetDimension - Get the dimension of the finite element space on a cell

    1141:   Not Collective

    1143:   Input Parameter:
    1144: . fem - The `PetscFE`

    1146:   Output Parameter:
    1147: . dim - The dimension

    1149:   Level: intermediate

    1151: .seealso: `PetscFE`, `PetscFECreate()`, `PetscSpaceGetDimension()`, `PetscDualSpaceGetDimension()`
    1152: @*/
    1153: PetscErrorCode PetscFEGetDimension(PetscFE fem, PetscInt *dim)
    1154: {
    1155:   PetscFunctionBegin;
    1157:   PetscAssertPointer(dim, 2);
    1158:   PetscTryTypeMethod(fem, getdimension, dim);
    1159:   PetscFunctionReturn(PETSC_SUCCESS);
    1160: }

    1162: /*@
    1163:   PetscFEPushforward - Map the reference element function to real space

    1165:   Input Parameters:
    1166: + fe     - The `PetscFE`
    1167: . fegeom - The cell geometry
    1168: . Nv     - The number of function values
    1169: - vals   - The function values

    1171:   Output Parameter:
    1172: . vals - The transformed function values

    1174:   Level: advanced

    1176:   Notes:
    1177:   This just forwards the call onto `PetscDualSpacePushforward()`.

    1179:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1181: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscDualSpacePushforward()`
    1182: @*/
    1183: PetscErrorCode PetscFEPushforward(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1184: {
    1185:   PetscFunctionBeginHot;
    1186:   PetscCall(PetscDualSpacePushforward(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1187:   PetscFunctionReturn(PETSC_SUCCESS);
    1188: }

    1190: /*@
    1191:   PetscFEPushforwardGradient - Map the reference element function gradient to real space

    1193:   Input Parameters:
    1194: + fe     - The `PetscFE`
    1195: . fegeom - The cell geometry
    1196: . Nv     - The number of function gradient values
    1197: - vals   - The function gradient values

    1199:   Output Parameter:
    1200: . vals - The transformed function gradient values

    1202:   Level: advanced

    1204:   Notes:
    1205:   This just forwards the call onto `PetscDualSpacePushforwardGradient()`.

    1207:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1209: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardGradient()`, `PetscDualSpacePushforward()`
    1210: @*/
    1211: PetscErrorCode PetscFEPushforwardGradient(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1212: {
    1213:   PetscFunctionBeginHot;
    1214:   PetscCall(PetscDualSpacePushforwardGradient(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1215:   PetscFunctionReturn(PETSC_SUCCESS);
    1216: }

    1218: /*@
    1219:   PetscFEPushforwardHessian - Map the reference element function Hessian to real space

    1221:   Input Parameters:
    1222: + fe     - The `PetscFE`
    1223: . fegeom - The cell geometry
    1224: . Nv     - The number of function Hessian values
    1225: - vals   - The function Hessian values

    1227:   Output Parameter:
    1228: . vals - The transformed function Hessian values

    1230:   Level: advanced

    1232:   Notes:
    1233:   This just forwards the call onto `PetscDualSpacePushforwardHessian()`.

    1235:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1237:   Developer Notes:
    1238:   It is unclear why all these one line convenience routines are desirable

    1240: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardHessian()`, `PetscDualSpacePushforward()`
    1241: @*/
    1242: PetscErrorCode PetscFEPushforwardHessian(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1243: {
    1244:   PetscFunctionBeginHot;
    1245:   PetscCall(PetscDualSpacePushforwardHessian(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1246:   PetscFunctionReturn(PETSC_SUCCESS);
    1247: }

    1249: /*
    1250: Purpose: Compute element vector for chunk of elements

    1252: Input:
    1253:   Sizes:
    1254:      Ne:  number of elements
    1255:      Nf:  number of fields
    1256:      PetscFE
    1257:        dim: spatial dimension
    1258:        Nb:  number of basis functions
    1259:        Nc:  number of field components
    1260:        PetscQuadrature
    1261:          Nq:  number of quadrature points

    1263:   Geometry:
    1264:      PetscFEGeom[Ne] possibly *Nq
    1265:        PetscReal v0s[dim]
    1266:        PetscReal n[dim]
    1267:        PetscReal jacobians[dim*dim]
    1268:        PetscReal jacobianInverses[dim*dim]
    1269:        PetscReal jacobianDeterminants
    1270:   FEM:
    1271:      PetscFE
    1272:        PetscQuadrature
    1273:          PetscReal   quadPoints[Nq*dim]
    1274:          PetscReal   quadWeights[Nq]
    1275:        PetscReal   basis[Nq*Nb*Nc]
    1276:        PetscReal   basisDer[Nq*Nb*Nc*dim]
    1277:      PetscScalar coefficients[Ne*Nb*Nc]
    1278:      PetscScalar elemVec[Ne*Nb*Nc]

    1280:   Problem:
    1281:      PetscInt f: the active field
    1282:      f0, f1

    1284:   Work Space:
    1285:      PetscFE
    1286:        PetscScalar f0[Nq*dim];
    1287:        PetscScalar f1[Nq*dim*dim];
    1288:        PetscScalar u[Nc];
    1289:        PetscScalar gradU[Nc*dim];
    1290:        PetscReal   x[dim];
    1291:        PetscScalar realSpaceDer[dim];

    1293: Purpose: Compute element vector for N_cb batches of elements

    1295: Input:
    1296:   Sizes:
    1297:      N_cb: Number of serial cell batches

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

    1312: ex62.c:
    1313:   PetscErrorCode PetscFEIntegrateResidualBatch(PetscInt Ne, PetscInt numFields, PetscInt field, PetscQuadrature quad[], const PetscScalar coefficients[],
    1314:                                                const PetscReal v0s[], const PetscReal jacobians[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[],
    1315:                                                void (*f0_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]),
    1316:                                                void (*f1_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]), PetscScalar elemVec[])

    1318: ex52.c:
    1319:   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)
    1320:   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)

    1322: ex52_integrateElement.cu
    1323: __global__ void integrateElementQuadrature(int N_cb, realType *coefficients, realType *jacobianInverses, realType *jacobianDeterminants, realType *elemVec)

    1325: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt Nbl, const PetscScalar coefficients[],
    1326:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
    1327:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

    1329: ex52_integrateElementOpenCL.c:
    1330: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt N_bl, const PetscScalar coefficients[],
    1331:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
    1332:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

    1334: __kernel void integrateElementQuadrature(int N_cb, __global float *coefficients, __global float *jacobianInverses, __global float *jacobianDeterminants, __global float *elemVec)
    1335: */

    1337: /*@
    1338:   PetscFEIntegrate - Produce the integral for the given field for a chunk of elements by quadrature integration

    1340:   Not Collective

    1342:   Input Parameters:
    1343: + prob            - The `PetscDS` specifying the discretizations and continuum functions
    1344: . field           - The field being integrated
    1345: . Ne              - The number of elements in the chunk
    1346: . cgeom           - The cell geometry for each cell in the chunk
    1347: . coefficients    - The array of FEM basis coefficients for the elements
    1348: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1349: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

    1351:   Output Parameter:
    1352: . integral - the integral for this field

    1354:   Level: intermediate

    1356:   Developer Notes:
    1357:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

    1359: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrateBd()`
    1360: @*/
    1361: PetscErrorCode PetscFEIntegrate(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[])
    1362: {
    1363:   PetscFE fe;

    1365:   PetscFunctionBegin;
    1367:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    1368:   if (fe->ops->integrate) PetscCall((*fe->ops->integrate)(prob, field, Ne, cgeom, coefficients, probAux, coefficientsAux, integral));
    1369:   PetscFunctionReturn(PETSC_SUCCESS);
    1370: }

    1372: /*@C
    1373:   PetscFEIntegrateBd - Produce the integral for the given field for a chunk of elements by quadrature integration

    1375:   Not Collective

    1377:   Input Parameters:
    1378: + prob            - The `PetscDS` specifying the discretizations and continuum functions
    1379: . field           - The field being integrated
    1380: . obj_func        - The function to be integrated
    1381: . Ne              - The number of elements in the chunk
    1382: . geom            - The face geometry for each face in the chunk
    1383: . coefficients    - The array of FEM basis coefficients for the elements
    1384: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1385: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

    1387:   Output Parameter:
    1388: . integral - the integral for this field

    1390:   Level: intermediate

    1392:   Developer Notes:
    1393:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

    1395: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrate()`
    1396: @*/
    1397: 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[])
    1398: {
    1399:   PetscFE fe;

    1401:   PetscFunctionBegin;
    1403:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    1404:   if (fe->ops->integratebd) PetscCall((*fe->ops->integratebd)(prob, field, obj_func, Ne, geom, coefficients, probAux, coefficientsAux, integral));
    1405:   PetscFunctionReturn(PETSC_SUCCESS);
    1406: }

    1408: /*@
    1409:   PetscFEIntegrateResidual - Produce the element residual vector for a chunk of elements by quadrature integration

    1411:   Not Collective

    1413:   Input Parameters:
    1414: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1415: . key             - The (label+value, field) being integrated
    1416: . Ne              - The number of elements in the chunk
    1417: . cgeom           - The cell geometry for each cell in the chunk
    1418: . coefficients    - The array of FEM basis coefficients for the elements
    1419: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1420: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1421: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1422: - t               - The time

    1424:   Output Parameter:
    1425: . elemVec - the element residual vectors from each element

    1427:   Level: intermediate

    1429:   Note:
    1430: .vb
    1431:   Loop over batch of elements (e):
    1432:     Loop over quadrature points (q):
    1433:       Make u_q and gradU_q (loops over fields,Nb,Ncomp) and x_q
    1434:       Call f_0 and f_1
    1435:     Loop over element vector entries (f,fc --> i):
    1436:       elemVec[i] += \psi^{fc}_f(q) f0_{fc}(u, \nabla u) + \nabla\psi^{fc}_f(q) \cdot f1_{fc,df}(u, \nabla u)
    1437: .ve

    1439: .seealso: `PetscFEIntegrateBdResidual()`
    1440: @*/
    1441: 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[])
    1442: {
    1443:   PetscFE fe;

    1445:   PetscFunctionBeginHot;
    1447:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1448:   if (fe->ops->integrateresidual) PetscCall((*fe->ops->integrateresidual)(ds, key, Ne, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1449:   PetscFunctionReturn(PETSC_SUCCESS);
    1450: }

    1452: /*@
    1453:   PetscFEIntegrateBdResidual - Produce the element residual vector for a chunk of elements by quadrature integration over a boundary

    1455:   Not Collective

    1457:   Input Parameters:
    1458: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1459: . wf              - The PetscWeakForm object holding the pointwise functions
    1460: . key             - The (label+value, field) being integrated
    1461: . Ne              - The number of elements in the chunk
    1462: . fgeom           - The face geometry for each cell in the chunk
    1463: . coefficients    - The array of FEM basis coefficients for the elements
    1464: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1465: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1466: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1467: - t               - The time

    1469:   Output Parameter:
    1470: . elemVec - the element residual vectors from each element

    1472:   Level: intermediate

    1474: .seealso: `PetscFEIntegrateResidual()`
    1475: @*/
    1476: 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[])
    1477: {
    1478:   PetscFE fe;

    1480:   PetscFunctionBegin;
    1482:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1483:   if (fe->ops->integratebdresidual) PetscCall((*fe->ops->integratebdresidual)(ds, wf, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1484:   PetscFunctionReturn(PETSC_SUCCESS);
    1485: }

    1487: /*@
    1488:   PetscFEIntegrateHybridResidual - Produce the element residual vector for a chunk of hybrid element faces by quadrature integration

    1490:   Not Collective

    1492:   Input Parameters:
    1493: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1494: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for input
    1495: . key             - The (label+value, field) being integrated
    1496: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
    1497: . Ne              - The number of elements in the chunk
    1498: . fgeom           - The face geometry for each cell in the chunk
    1499: . coefficients    - The array of FEM basis coefficients for the elements
    1500: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1501: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1502: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1503: - t               - The time

    1505:   Output Parameter:
    1506: . elemVec - the element residual vectors from each element

    1508:   Level: developer

    1510: .seealso: `PetscFEIntegrateResidual()`
    1511: @*/
    1512: PetscErrorCode PetscFEIntegrateHybridResidual(PetscDS ds, PetscDS dsIn, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
    1513: {
    1514:   PetscFE fe;

    1516:   PetscFunctionBegin;
    1519:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1520:   if (fe->ops->integratehybridresidual) PetscCall((*fe->ops->integratehybridresidual)(ds, dsIn, key, s, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1521:   PetscFunctionReturn(PETSC_SUCCESS);
    1522: }

    1524: /*@
    1525:   PetscFEIntegrateJacobian - Produce the element Jacobian for a chunk of elements by quadrature integration

    1527:   Not Collective

    1529:   Input Parameters:
    1530: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1531: . jtype           - The type of matrix pointwise functions that should be used
    1532: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1533: . Ne              - The number of elements in the chunk
    1534: . cgeom           - The cell geometry for each cell in the chunk
    1535: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1536: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1537: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1538: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1539: . t               - The time
    1540: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1542:   Output Parameter:
    1543: . elemMat - the element matrices for the Jacobian from each element

    1545:   Level: intermediate

    1547:   Note:
    1548: .vb
    1549:   Loop over batch of elements (e):
    1550:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1551:       Loop over quadrature points (q):
    1552:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1553:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1554:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1555:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1556:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1557: .ve

    1559: .seealso: `PetscFEIntegrateResidual()`
    1560: @*/
    1561: PetscErrorCode PetscFEIntegrateJacobian(PetscDS ds, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
    1562: {
    1563:   PetscFE  fe;
    1564:   PetscInt Nf;

    1566:   PetscFunctionBegin;
    1568:   PetscCall(PetscDSGetNumFields(ds, &Nf));
    1569:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
    1570:   if (fe->ops->integratejacobian) PetscCall((*fe->ops->integratejacobian)(ds, jtype, key, Ne, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
    1571:   PetscFunctionReturn(PETSC_SUCCESS);
    1572: }

    1574: /*@
    1575:   PetscFEIntegrateBdJacobian - Produce the boundary element Jacobian for a chunk of elements by quadrature integration

    1577:   Not Collective

    1579:   Input Parameters:
    1580: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1581: . wf              - The PetscWeakForm holding the pointwise functions
    1582: . jtype           - The type of matrix pointwise functions that should be used
    1583: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1584: . Ne              - The number of elements in the chunk
    1585: . fgeom           - The face geometry for each cell in the chunk
    1586: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1587: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1588: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1589: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1590: . t               - The time
    1591: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1593:   Output Parameter:
    1594: . elemMat - the element matrices for the Jacobian from each element

    1596:   Level: intermediate

    1598:   Note:
    1599: .vb
    1600:   Loop over batch of elements (e):
    1601:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1602:       Loop over quadrature points (q):
    1603:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1604:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1605:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1606:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1607:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1608: .ve

    1610: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
    1611: @*/
    1612: 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[])
    1613: {
    1614:   PetscFE  fe;
    1615:   PetscInt Nf;

    1617:   PetscFunctionBegin;
    1619:   PetscCall(PetscDSGetNumFields(ds, &Nf));
    1620:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
    1621:   if (fe->ops->integratebdjacobian) PetscCall((*fe->ops->integratebdjacobian)(ds, wf, jtype, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
    1622:   PetscFunctionReturn(PETSC_SUCCESS);
    1623: }

    1625: /*@
    1626:   PetscFEIntegrateHybridJacobian - Produce the boundary element Jacobian for a chunk of hybrid elements by quadrature integration

    1628:   Not Collective

    1630:   Input Parameters:
    1631: + ds              - The `PetscDS` specifying the discretizations and continuum functions for the output
    1632: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for the input
    1633: . jtype           - The type of matrix pointwise functions that should be used
    1634: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1635: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
    1636: . Ne              - The number of elements in the chunk
    1637: . fgeom           - The face geometry for each cell in the chunk
    1638: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1639: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1640: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1641: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1642: . t               - The time
    1643: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1645:   Output Parameter:
    1646: . elemMat - the element matrices for the Jacobian from each element

    1648:   Level: developer

    1650:   Note:
    1651: .vb
    1652:   Loop over batch of elements (e):
    1653:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1654:       Loop over quadrature points (q):
    1655:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1656:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1657:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1658:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1659:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1660: .ve

    1662: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
    1663: @*/
    1664: PetscErrorCode PetscFEIntegrateHybridJacobian(PetscDS ds, PetscDS dsIn, PetscFEJacobianType jtype, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
    1665: {
    1666:   PetscFE  fe;
    1667:   PetscInt Nf;

    1669:   PetscFunctionBegin;
    1671:   PetscCall(PetscDSGetNumFields(ds, &Nf));
    1672:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
    1673:   if (fe->ops->integratehybridjacobian) PetscCall((*fe->ops->integratehybridjacobian)(ds, dsIn, jtype, key, s, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
    1674:   PetscFunctionReturn(PETSC_SUCCESS);
    1675: }

    1677: /*@
    1678:   PetscFEGetHeightSubspace - Get the subspace of this space for a mesh point of a given height

    1680:   Input Parameters:
    1681: + fe     - The finite element space
    1682: - height - The height of the `DMPLEX` point

    1684:   Output Parameter:
    1685: . subfe - The subspace of this `PetscFE` space

    1687:   Level: advanced

    1689:   Note:
    1690:   For example, if we want the subspace of this space for a face, we would choose height = 1.

    1692: .seealso: `PetscFECreateDefault()`
    1693: @*/
    1694: PetscErrorCode PetscFEGetHeightSubspace(PetscFE fe, PetscInt height, PetscFE *subfe)
    1695: {
    1696:   PetscSpace      P, subP;
    1697:   PetscDualSpace  Q, subQ;
    1698:   PetscQuadrature subq;
    1699:   PetscInt        dim, Nc;

    1701:   PetscFunctionBegin;
    1703:   PetscAssertPointer(subfe, 3);
    1704:   if (height == 0) {
    1705:     *subfe = fe;
    1706:     PetscFunctionReturn(PETSC_SUCCESS);
    1707:   }
    1708:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1709:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1710:   PetscCall(PetscFEGetNumComponents(fe, &Nc));
    1711:   PetscCall(PetscFEGetFaceQuadrature(fe, &subq));
    1712:   PetscCall(PetscDualSpaceGetDimension(Q, &dim));
    1713:   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);
    1714:   if (!fe->subspaces) PetscCall(PetscCalloc1(dim, &fe->subspaces));
    1715:   if (height <= dim) {
    1716:     if (!fe->subspaces[height - 1]) {
    1717:       PetscFE     sub = NULL;
    1718:       const char *name;

    1720:       PetscCall(PetscSpaceGetHeightSubspace(P, height, &subP));
    1721:       PetscCall(PetscDualSpaceGetHeightSubspace(Q, height, &subQ));
    1722:       if (subQ) {
    1723:         PetscCall(PetscObjectReference((PetscObject)subP));
    1724:         PetscCall(PetscObjectReference((PetscObject)subQ));
    1725:         PetscCall(PetscObjectReference((PetscObject)subq));
    1726:         PetscCall(PetscFECreateFromSpaces(subP, subQ, subq, NULL, &sub));
    1727:       }
    1728:       if (sub) {
    1729:         PetscCall(PetscObjectGetName((PetscObject)fe, &name));
    1730:         if (name) PetscCall(PetscFESetName(sub, name));
    1731:       }
    1732:       fe->subspaces[height - 1] = sub;
    1733:     }
    1734:     *subfe = fe->subspaces[height - 1];
    1735:   } else {
    1736:     *subfe = NULL;
    1737:   }
    1738:   PetscFunctionReturn(PETSC_SUCCESS);
    1739: }

    1741: /*@
    1742:   PetscFERefine - Create a "refined" `PetscFE` object that refines the reference cell into
    1743:   smaller copies.

    1745:   Collective

    1747:   Input Parameter:
    1748: . fe - The initial `PetscFE`

    1750:   Output Parameter:
    1751: . feRef - The refined `PetscFE`

    1753:   Level: advanced

    1755:   Notes:
    1756:   This is typically used to generate a preconditioner for a higher order method from a lower order method on a
    1757:   refined mesh having the same number of dofs (but more sparsity). It is also used to create an
    1758:   interpolation between regularly refined meshes.

    1760: .seealso: `PetscFEType`, `PetscFECreate()`, `PetscFESetType()`
    1761: @*/
    1762: PetscErrorCode PetscFERefine(PetscFE fe, PetscFE *feRef)
    1763: {
    1764:   PetscSpace       P, Pref;
    1765:   PetscDualSpace   Q, Qref;
    1766:   DM               K, Kref;
    1767:   PetscQuadrature  q, qref;
    1768:   const PetscReal *v0, *jac;
    1769:   PetscInt         numComp, numSubelements;
    1770:   PetscInt         cStart, cEnd, c;
    1771:   PetscDualSpace  *cellSpaces;

    1773:   PetscFunctionBegin;
    1774:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1775:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1776:   PetscCall(PetscFEGetQuadrature(fe, &q));
    1777:   PetscCall(PetscDualSpaceGetDM(Q, &K));
    1778:   /* Create space */
    1779:   PetscCall(PetscObjectReference((PetscObject)P));
    1780:   Pref = P;
    1781:   /* Create dual space */
    1782:   PetscCall(PetscDualSpaceDuplicate(Q, &Qref));
    1783:   PetscCall(PetscDualSpaceSetType(Qref, PETSCDUALSPACEREFINED));
    1784:   PetscCall(DMRefine(K, PetscObjectComm((PetscObject)fe), &Kref));
    1785:   PetscCall(DMGetCoordinatesLocalSetUp(Kref));
    1786:   PetscCall(PetscDualSpaceSetDM(Qref, Kref));
    1787:   PetscCall(DMPlexGetHeightStratum(Kref, 0, &cStart, &cEnd));
    1788:   PetscCall(PetscMalloc1(cEnd - cStart, &cellSpaces));
    1789:   /* TODO: fix for non-uniform refinement */
    1790:   for (c = 0; c < cEnd - cStart; c++) cellSpaces[c] = Q;
    1791:   PetscCall(PetscDualSpaceRefinedSetCellSpaces(Qref, cellSpaces));
    1792:   PetscCall(PetscFree(cellSpaces));
    1793:   PetscCall(DMDestroy(&Kref));
    1794:   PetscCall(PetscDualSpaceSetUp(Qref));
    1795:   /* Create element */
    1796:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), feRef));
    1797:   PetscCall(PetscFESetType(*feRef, PETSCFECOMPOSITE));
    1798:   PetscCall(PetscFESetBasisSpace(*feRef, Pref));
    1799:   PetscCall(PetscFESetDualSpace(*feRef, Qref));
    1800:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    1801:   PetscCall(PetscFESetNumComponents(*feRef, numComp));
    1802:   PetscCall(PetscFESetUp(*feRef));
    1803:   PetscCall(PetscSpaceDestroy(&Pref));
    1804:   PetscCall(PetscDualSpaceDestroy(&Qref));
    1805:   /* Create quadrature */
    1806:   PetscCall(PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL));
    1807:   PetscCall(PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref));
    1808:   PetscCall(PetscFESetQuadrature(*feRef, qref));
    1809:   PetscCall(PetscQuadratureDestroy(&qref));
    1810:   PetscFunctionReturn(PETSC_SUCCESS);
    1811: }

    1813: static PetscErrorCode PetscFESetDefaultName_Private(PetscFE fe)
    1814: {
    1815:   PetscSpace     P;
    1816:   PetscDualSpace Q;
    1817:   DM             K;
    1818:   DMPolytopeType ct;
    1819:   PetscInt       degree;
    1820:   char           name[64];

    1822:   PetscFunctionBegin;
    1823:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1824:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
    1825:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1826:   PetscCall(PetscDualSpaceGetDM(Q, &K));
    1827:   PetscCall(DMPlexGetCellType(K, 0, &ct));
    1828:   switch (ct) {
    1829:   case DM_POLYTOPE_SEGMENT:
    1830:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1831:   case DM_POLYTOPE_QUADRILATERAL:
    1832:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1833:   case DM_POLYTOPE_HEXAHEDRON:
    1834:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1835:     PetscCall(PetscSNPrintf(name, sizeof(name), "Q%" PetscInt_FMT, degree));
    1836:     break;
    1837:   case DM_POLYTOPE_TRIANGLE:
    1838:   case DM_POLYTOPE_TETRAHEDRON:
    1839:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT, degree));
    1840:     break;
    1841:   case DM_POLYTOPE_TRI_PRISM:
    1842:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
    1843:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT "xQ%" PetscInt_FMT, degree, degree));
    1844:     break;
    1845:   default:
    1846:     PetscCall(PetscSNPrintf(name, sizeof(name), "FE"));
    1847:   }
    1848:   PetscCall(PetscFESetName(fe, name));
    1849:   PetscFunctionReturn(PETSC_SUCCESS);
    1850: }

    1852: /*@
    1853:   PetscFECreateFromSpaces - Create a `PetscFE` from the basis and dual spaces

    1855:   Collective

    1857:   Input Parameters:
    1858: + P  - The basis space
    1859: . Q  - The dual space
    1860: . q  - The cell quadrature
    1861: - fq - The face quadrature

    1863:   Output Parameter:
    1864: . fem - The `PetscFE` object

    1866:   Level: beginner

    1868:   Note:
    1869:   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.

    1871: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`,
    1872:           `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    1873: @*/
    1874: PetscErrorCode PetscFECreateFromSpaces(PetscSpace P, PetscDualSpace Q, PetscQuadrature q, PetscQuadrature fq, PetscFE *fem)
    1875: {
    1876:   PetscInt    Nc;
    1877:   PetscInt    p_Ns = -1, p_Nc = -1, q_Ns = -1, q_Nc = -1;
    1878:   PetscBool   p_is_uniform_sum = PETSC_FALSE, p_interleave_basis = PETSC_FALSE, p_interleave_components = PETSC_FALSE;
    1879:   PetscBool   q_is_uniform_sum = PETSC_FALSE, q_interleave_basis = PETSC_FALSE, q_interleave_components = PETSC_FALSE;
    1880:   const char *prefix;

    1882:   PetscFunctionBegin;
    1883:   PetscCall(PetscObjectTypeCompare((PetscObject)P, PETSCSPACESUM, &p_is_uniform_sum));
    1884:   if (p_is_uniform_sum) {
    1885:     PetscSpace subsp_0 = NULL;
    1886:     PetscCall(PetscSpaceSumGetNumSubspaces(P, &p_Ns));
    1887:     PetscCall(PetscSpaceGetNumComponents(P, &p_Nc));
    1888:     PetscCall(PetscSpaceSumGetConcatenate(P, &p_is_uniform_sum));
    1889:     PetscCall(PetscSpaceSumGetInterleave(P, &p_interleave_basis, &p_interleave_components));
    1890:     for (PetscInt s = 0; s < p_Ns; s++) {
    1891:       PetscSpace subsp;

    1893:       PetscCall(PetscSpaceSumGetSubspace(P, s, &subsp));
    1894:       if (!s) {
    1895:         subsp_0 = subsp;
    1896:       } else if (subsp != subsp_0) {
    1897:         p_is_uniform_sum = PETSC_FALSE;
    1898:       }
    1899:     }
    1900:   }
    1901:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &q_is_uniform_sum));
    1902:   if (q_is_uniform_sum) {
    1903:     PetscDualSpace subsp_0 = NULL;
    1904:     PetscCall(PetscDualSpaceSumGetNumSubspaces(Q, &q_Ns));
    1905:     PetscCall(PetscDualSpaceGetNumComponents(Q, &q_Nc));
    1906:     PetscCall(PetscDualSpaceSumGetConcatenate(Q, &q_is_uniform_sum));
    1907:     PetscCall(PetscDualSpaceSumGetInterleave(Q, &q_interleave_basis, &q_interleave_components));
    1908:     for (PetscInt s = 0; s < q_Ns; s++) {
    1909:       PetscDualSpace subsp;

    1911:       PetscCall(PetscDualSpaceSumGetSubspace(Q, s, &subsp));
    1912:       if (!s) {
    1913:         subsp_0 = subsp;
    1914:       } else if (subsp != subsp_0) {
    1915:         q_is_uniform_sum = PETSC_FALSE;
    1916:       }
    1917:     }
    1918:   }
    1919:   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)) {
    1920:     PetscSpace     scalar_space;
    1921:     PetscDualSpace scalar_dspace;
    1922:     PetscFE        scalar_fe;

    1924:     PetscCall(PetscSpaceSumGetSubspace(P, 0, &scalar_space));
    1925:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &scalar_dspace));
    1926:     PetscCall(PetscObjectReference((PetscObject)scalar_space));
    1927:     PetscCall(PetscObjectReference((PetscObject)scalar_dspace));
    1928:     PetscCall(PetscObjectReference((PetscObject)q));
    1929:     PetscCall(PetscObjectReference((PetscObject)fq));
    1930:     PetscCall(PetscFECreateFromSpaces(scalar_space, scalar_dspace, q, fq, &scalar_fe));
    1931:     PetscCall(PetscFECreateVector(scalar_fe, p_Ns, p_interleave_basis, p_interleave_components, fem));
    1932:     PetscCall(PetscFEDestroy(&scalar_fe));
    1933:   } else {
    1934:     PetscCall(PetscFECreate(PetscObjectComm((PetscObject)P), fem));
    1935:     PetscCall(PetscFESetType(*fem, PETSCFEBASIC));
    1936:   }
    1937:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    1938:   PetscCall(PetscFESetNumComponents(*fem, Nc));
    1939:   PetscCall(PetscFESetBasisSpace(*fem, P));
    1940:   PetscCall(PetscFESetDualSpace(*fem, Q));
    1941:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)P, &prefix));
    1942:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*fem, prefix));
    1943:   PetscCall(PetscFESetUp(*fem));
    1944:   PetscCall(PetscSpaceDestroy(&P));
    1945:   PetscCall(PetscDualSpaceDestroy(&Q));
    1946:   PetscCall(PetscFESetQuadrature(*fem, q));
    1947:   PetscCall(PetscFESetFaceQuadrature(*fem, fq));
    1948:   PetscCall(PetscQuadratureDestroy(&q));
    1949:   PetscCall(PetscQuadratureDestroy(&fq));
    1950:   PetscCall(PetscFESetDefaultName_Private(*fem));
    1951:   PetscFunctionReturn(PETSC_SUCCESS);
    1952: }

    1954: static PetscErrorCode PetscFECreate_Internal(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt degree, PetscInt qorder, PetscBool setFromOptions, PetscFE *fem)
    1955: {
    1956:   DM              K;
    1957:   PetscSpace      P;
    1958:   PetscDualSpace  Q;
    1959:   PetscQuadrature q, fq;
    1960:   PetscBool       tensor;

    1962:   PetscFunctionBegin;
    1963:   if (prefix) PetscAssertPointer(prefix, 5);
    1964:   PetscAssertPointer(fem, 9);
    1965:   switch (ct) {
    1966:   case DM_POLYTOPE_SEGMENT:
    1967:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1968:   case DM_POLYTOPE_QUADRILATERAL:
    1969:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1970:   case DM_POLYTOPE_HEXAHEDRON:
    1971:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1972:     tensor = PETSC_TRUE;
    1973:     break;
    1974:   default:
    1975:     tensor = PETSC_FALSE;
    1976:   }
    1977:   /* Create space */
    1978:   PetscCall(PetscSpaceCreate(comm, &P));
    1979:   PetscCall(PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL));
    1980:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)P, prefix));
    1981:   PetscCall(PetscSpacePolynomialSetTensor(P, tensor));
    1982:   PetscCall(PetscSpaceSetNumComponents(P, Nc));
    1983:   PetscCall(PetscSpaceSetNumVariables(P, dim));
    1984:   if (degree >= 0) {
    1985:     PetscCall(PetscSpaceSetDegree(P, degree, PETSC_DETERMINE));
    1986:     if (ct == DM_POLYTOPE_TRI_PRISM || ct == DM_POLYTOPE_TRI_PRISM_TENSOR) {
    1987:       PetscSpace Pend, Pside;

    1989:       PetscCall(PetscSpaceSetNumComponents(P, 1));
    1990:       PetscCall(PetscSpaceCreate(comm, &Pend));
    1991:       PetscCall(PetscSpaceSetType(Pend, PETSCSPACEPOLYNOMIAL));
    1992:       PetscCall(PetscSpacePolynomialSetTensor(Pend, PETSC_FALSE));
    1993:       PetscCall(PetscSpaceSetNumComponents(Pend, 1));
    1994:       PetscCall(PetscSpaceSetNumVariables(Pend, dim - 1));
    1995:       PetscCall(PetscSpaceSetDegree(Pend, degree, PETSC_DETERMINE));
    1996:       PetscCall(PetscSpaceCreate(comm, &Pside));
    1997:       PetscCall(PetscSpaceSetType(Pside, PETSCSPACEPOLYNOMIAL));
    1998:       PetscCall(PetscSpacePolynomialSetTensor(Pside, PETSC_FALSE));
    1999:       PetscCall(PetscSpaceSetNumComponents(Pside, 1));
    2000:       PetscCall(PetscSpaceSetNumVariables(Pside, 1));
    2001:       PetscCall(PetscSpaceSetDegree(Pside, degree, PETSC_DETERMINE));
    2002:       PetscCall(PetscSpaceSetType(P, PETSCSPACETENSOR));
    2003:       PetscCall(PetscSpaceTensorSetNumSubspaces(P, 2));
    2004:       PetscCall(PetscSpaceTensorSetSubspace(P, 0, Pend));
    2005:       PetscCall(PetscSpaceTensorSetSubspace(P, 1, Pside));
    2006:       PetscCall(PetscSpaceDestroy(&Pend));
    2007:       PetscCall(PetscSpaceDestroy(&Pside));

    2009:       if (Nc > 1) {
    2010:         PetscSpace scalar_P = P;

    2012:         PetscCall(PetscSpaceCreate(comm, &P));
    2013:         PetscCall(PetscSpaceSetNumVariables(P, dim));
    2014:         PetscCall(PetscSpaceSetNumComponents(P, Nc));
    2015:         PetscCall(PetscSpaceSetType(P, PETSCSPACESUM));
    2016:         PetscCall(PetscSpaceSumSetNumSubspaces(P, Nc));
    2017:         PetscCall(PetscSpaceSumSetConcatenate(P, PETSC_TRUE));
    2018:         PetscCall(PetscSpaceSumSetInterleave(P, PETSC_TRUE, PETSC_FALSE));
    2019:         for (PetscInt i = 0; i < Nc; i++) PetscCall(PetscSpaceSumSetSubspace(P, i, scalar_P));
    2020:         PetscCall(PetscSpaceDestroy(&scalar_P));
    2021:       }
    2022:     }
    2023:   }
    2024:   if (setFromOptions) PetscCall(PetscSpaceSetFromOptions(P));
    2025:   PetscCall(PetscSpaceSetUp(P));
    2026:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
    2027:   PetscCall(PetscSpacePolynomialGetTensor(P, &tensor));
    2028:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    2029:   /* Create dual space */
    2030:   PetscCall(PetscDualSpaceCreate(comm, &Q));
    2031:   PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
    2032:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)Q, prefix));
    2033:   PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
    2034:   PetscCall(PetscDualSpaceSetDM(Q, K));
    2035:   PetscCall(DMDestroy(&K));
    2036:   PetscCall(PetscDualSpaceSetNumComponents(Q, Nc));
    2037:   PetscCall(PetscDualSpaceSetOrder(Q, degree));
    2038:   PetscCall(PetscDualSpaceLagrangeSetTensor(Q, (tensor || (ct == DM_POLYTOPE_TRI_PRISM)) ? PETSC_TRUE : PETSC_FALSE));
    2039:   if (setFromOptions) PetscCall(PetscDualSpaceSetFromOptions(Q));
    2040:   PetscCall(PetscDualSpaceSetUp(Q));
    2041:   /* Create quadrature */
    2042:   qorder = qorder >= 0 ? qorder : degree;
    2043:   if (setFromOptions) {
    2044:     PetscObjectOptionsBegin((PetscObject)P);
    2045:     PetscCall(PetscOptionsBoundedInt("-petscfe_default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "PetscFECreateDefault", qorder, &qorder, NULL, 0));
    2046:     PetscOptionsEnd();
    2047:   }
    2048:   PetscCall(PetscDTCreateDefaultQuadrature(ct, qorder, &q, &fq));
    2049:   /* Create finite element */
    2050:   PetscCall(PetscFECreateFromSpaces(P, Q, q, fq, fem));
    2051:   if (setFromOptions) PetscCall(PetscFESetFromOptions(*fem));
    2052:   PetscFunctionReturn(PETSC_SUCCESS);
    2053: }

    2055: /*@
    2056:   PetscFECreateDefault - Create a `PetscFE` for basic FEM computation

    2058:   Collective

    2060:   Input Parameters:
    2061: + comm      - The MPI comm
    2062: . dim       - The spatial dimension
    2063: . Nc        - The number of components
    2064: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
    2065: . prefix    - The options prefix, or `NULL`
    2066: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2068:   Output Parameter:
    2069: . fem - The `PetscFE` object

    2071:   Level: beginner

    2073:   Note:
    2074:   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.

    2076: .seealso: `PetscFECreateLagrange()`, `PetscFECreateByCell()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2077: @*/
    2078: PetscErrorCode PetscFECreateDefault(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, const char prefix[], PetscInt qorder, PetscFE *fem)
    2079: {
    2080:   PetscFunctionBegin;
    2081:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
    2082:   PetscFunctionReturn(PETSC_SUCCESS);
    2083: }

    2085: /*@
    2086:   PetscFECreateByCell - Create a `PetscFE` for basic FEM computation

    2088:   Collective

    2090:   Input Parameters:
    2091: + comm   - The MPI comm
    2092: . dim    - The spatial dimension
    2093: . Nc     - The number of components
    2094: . ct     - The celltype of the reference cell
    2095: . prefix - The options prefix, or `NULL`
    2096: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2098:   Output Parameter:
    2099: . fem - The `PetscFE` object

    2101:   Level: beginner

    2103:   Note:
    2104:   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.

    2106: .seealso: `PetscFECreateDefault()`, `PetscFECreateLagrange()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2107: @*/
    2108: PetscErrorCode PetscFECreateByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt qorder, PetscFE *fem)
    2109: {
    2110:   PetscFunctionBegin;
    2111:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
    2112:   PetscFunctionReturn(PETSC_SUCCESS);
    2113: }

    2115: /*@
    2116:   PetscFECreateLagrange - Create a `PetscFE` for the basic Lagrange space of degree k

    2118:   Collective

    2120:   Input Parameters:
    2121: + comm      - The MPI comm
    2122: . dim       - The spatial dimension
    2123: . Nc        - The number of components
    2124: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
    2125: . k         - The degree k of the space
    2126: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2128:   Output Parameter:
    2129: . fem - The `PetscFE` object

    2131:   Level: beginner

    2133:   Note:
    2134:   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.

    2136: .seealso: `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2137: @*/
    2138: PetscErrorCode PetscFECreateLagrange(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, PetscInt k, PetscInt qorder, PetscFE *fem)
    2139: {
    2140:   PetscFunctionBegin;
    2141:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), NULL, k, qorder, PETSC_FALSE, fem));
    2142:   PetscFunctionReturn(PETSC_SUCCESS);
    2143: }

    2145: /*@
    2146:   PetscFECreateLagrangeByCell - Create a `PetscFE` for the basic Lagrange space of degree k

    2148:   Collective

    2150:   Input Parameters:
    2151: + comm   - The MPI comm
    2152: . dim    - The spatial dimension
    2153: . Nc     - The number of components
    2154: . ct     - The celltype of the reference cell
    2155: . k      - The degree k of the space
    2156: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2158:   Output Parameter:
    2159: . fem - The `PetscFE` object

    2161:   Level: beginner

    2163:   Note:
    2164:   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.

    2166: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2167: @*/
    2168: PetscErrorCode PetscFECreateLagrangeByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, PetscInt k, PetscInt qorder, PetscFE *fem)
    2169: {
    2170:   PetscFunctionBegin;
    2171:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, NULL, k, qorder, PETSC_FALSE, fem));
    2172:   PetscFunctionReturn(PETSC_SUCCESS);
    2173: }

    2175: /*@
    2176:   PetscFELimitDegree - Copy a `PetscFE` but limit the degree to be in the given range

    2178:   Collective

    2180:   Input Parameters:
    2181: + fe        - The `PetscFE`
    2182: . minDegree - The minimum degree, or `PETSC_DETERMINE` for no limit
    2183: - maxDegree - The maximum degree, or `PETSC_DETERMINE` for no limit

    2185:   Output Parameter:
    2186: . newfe - The `PetscFE` object

    2188:   Level: advanced

    2190:   Note:
    2191:   This currently only works for Lagrange elements.

    2193: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2194: @*/
    2195: PetscErrorCode PetscFELimitDegree(PetscFE fe, PetscInt minDegree, PetscInt maxDegree, PetscFE *newfe)
    2196: {
    2197:   PetscDualSpace Q;
    2198:   PetscBool      islag, issum;
    2199:   PetscInt       oldk = 0, k;

    2201:   PetscFunctionBegin;
    2202:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    2203:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &islag));
    2204:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &issum));
    2205:   if (islag) {
    2206:     PetscCall(PetscDualSpaceGetOrder(Q, &oldk));
    2207:   } else if (issum) {
    2208:     PetscDualSpace subQ;

    2210:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &subQ));
    2211:     PetscCall(PetscDualSpaceGetOrder(subQ, &oldk));
    2212:   } else {
    2213:     PetscCall(PetscObjectReference((PetscObject)fe));
    2214:     *newfe = fe;
    2215:     PetscFunctionReturn(PETSC_SUCCESS);
    2216:   }
    2217:   k = oldk;
    2218:   if (minDegree >= 0) k = PetscMax(k, minDegree);
    2219:   if (maxDegree >= 0) k = PetscMin(k, maxDegree);
    2220:   if (k != oldk) {
    2221:     DM              K;
    2222:     PetscSpace      P;
    2223:     PetscQuadrature q;
    2224:     DMPolytopeType  ct;
    2225:     PetscInt        dim, Nc;

    2227:     PetscCall(PetscFEGetBasisSpace(fe, &P));
    2228:     PetscCall(PetscSpaceGetNumVariables(P, &dim));
    2229:     PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    2230:     PetscCall(PetscDualSpaceGetDM(Q, &K));
    2231:     PetscCall(DMPlexGetCellType(K, 0, &ct));
    2232:     PetscCall(PetscFECreateLagrangeByCell(PetscObjectComm((PetscObject)fe), dim, Nc, ct, k, PETSC_DETERMINE, newfe));
    2233:     PetscCall(PetscFEGetQuadrature(fe, &q));
    2234:     PetscCall(PetscFESetQuadrature(*newfe, q));
    2235:   } else {
    2236:     PetscCall(PetscObjectReference((PetscObject)fe));
    2237:     *newfe = fe;
    2238:   }
    2239:   PetscFunctionReturn(PETSC_SUCCESS);
    2240: }

    2242: /*@
    2243:   PetscFESetName - Names the `PetscFE` and its subobjects

    2245:   Not Collective

    2247:   Input Parameters:
    2248: + fe   - The `PetscFE`
    2249: - name - The name

    2251:   Level: intermediate

    2253: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2254: @*/
    2255: PetscErrorCode PetscFESetName(PetscFE fe, const char name[])
    2256: {
    2257:   PetscSpace     P;
    2258:   PetscDualSpace Q;

    2260:   PetscFunctionBegin;
    2261:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    2262:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    2263:   PetscCall(PetscObjectSetName((PetscObject)fe, name));
    2264:   PetscCall(PetscObjectSetName((PetscObject)P, name));
    2265:   PetscCall(PetscObjectSetName((PetscObject)Q, name));
    2266:   PetscFunctionReturn(PETSC_SUCCESS);
    2267: }

    2269: 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[])
    2270: {
    2271:   PetscInt dOffset = 0, fOffset = 0, f, g;

    2273:   for (f = 0; f < Nf; ++f) {
    2274:     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);
    2275:     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);
    2276:     PetscFE          fe;
    2277:     const PetscInt   k       = ds->jetDegree[f];
    2278:     const PetscInt   cdim    = T[f]->cdim;
    2279:     const PetscInt   dE      = fegeom->dimEmbed;
    2280:     const PetscInt   Nq      = T[f]->Np;
    2281:     const PetscInt   Nbf     = T[f]->Nb;
    2282:     const PetscInt   Ncf     = T[f]->Nc;
    2283:     const PetscReal *Bq      = &T[f]->T[0][(r * Nq + q) * Nbf * Ncf];
    2284:     const PetscReal *Dq      = &T[f]->T[1][(r * Nq + q) * Nbf * Ncf * cdim];
    2285:     const PetscReal *Hq      = k > 1 ? &T[f]->T[2][(r * Nq + q) * Nbf * Ncf * cdim * cdim] : NULL;
    2286:     PetscInt         hOffset = 0, b, c, d;

    2288:     PetscCall(PetscDSGetDiscretization(ds, f, (PetscObject *)&fe));
    2289:     for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
    2290:     for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
    2291:     for (b = 0; b < Nbf; ++b) {
    2292:       for (c = 0; c < Ncf; ++c) {
    2293:         const PetscInt cidx = b * Ncf + c;

    2295:         u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
    2296:         for (d = 0; d < cdim; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * cdim + d] * coefficients[dOffset + b];
    2297:       }
    2298:     }
    2299:     if (k > 1) {
    2300:       for (g = 0; g < Nf; ++g) hOffset += T[g]->Nc * dE;
    2301:       for (d = 0; d < dE * dE * Ncf; ++d) u_x[hOffset + fOffset * dE * dE + d] = 0.0;
    2302:       for (b = 0; b < Nbf; ++b) {
    2303:         for (c = 0; c < Ncf; ++c) {
    2304:           const PetscInt cidx = b * Ncf + c;

    2306:           for (d = 0; d < cdim * cdim; ++d) u_x[hOffset + (fOffset + c) * dE * dE + d] += Hq[cidx * cdim * cdim + d] * coefficients[dOffset + b];
    2307:         }
    2308:       }
    2309:       PetscCall(PetscFEPushforwardHessian(fe, fegeom, 1, &u_x[hOffset + fOffset * dE * dE]));
    2310:     }
    2311:     PetscCall(PetscFEPushforward(fe, fegeom, 1, &u[fOffset]));
    2312:     PetscCall(PetscFEPushforwardGradient(fe, fegeom, 1, &u_x[fOffset * dE]));
    2313:     if (u_t) {
    2314:       for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
    2315:       for (b = 0; b < Nbf; ++b) {
    2316:         for (c = 0; c < Ncf; ++c) {
    2317:           const PetscInt cidx = b * Ncf + c;

    2319:           u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
    2320:         }
    2321:       }
    2322:       PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
    2323:     }
    2324:     fOffset += Ncf;
    2325:     dOffset += Nbf;
    2326:   }
    2327:   return PETSC_SUCCESS;
    2328: }

    2330: PetscErrorCode PetscFEEvaluateFieldJets_Hybrid_Internal(PetscDS ds, PetscInt Nf, PetscInt rc, PetscInt qc, PetscTabulation Tab[], const PetscInt rf[], const PetscInt qf[], PetscTabulation Tabf[], PetscFEGeom *fegeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscScalar u[], PetscScalar u_x[], PetscScalar u_t[])
    2331: {
    2332:   PetscInt dOffset = 0, fOffset = 0, f, g;

    2334:   /* f is the field number in the DS, g is the field number in u[] */
    2335:   for (f = 0, g = 0; f < Nf; ++f) {
    2336:     PetscBool isCohesive;
    2337:     PetscInt  Ns, s;

    2339:     if (!Tab[f]) continue;
    2340:     PetscCall(PetscDSGetCohesive(ds, f, &isCohesive));
    2341:     Ns = isCohesive ? 1 : 2;
    2342:     {
    2343:       PetscTabulation T   = isCohesive ? Tab[f] : Tabf[f];
    2344:       PetscFE         fe  = (PetscFE)ds->disc[f];
    2345:       const PetscInt  dEt = T->cdim;
    2346:       const PetscInt  dE  = fegeom->dimEmbed;
    2347:       const PetscInt  Nq  = T->Np;
    2348:       const PetscInt  Nbf = T->Nb;
    2349:       const PetscInt  Ncf = T->Nc;

    2351:       for (s = 0; s < Ns; ++s, ++g) {
    2352:         const PetscInt   r  = isCohesive ? rc : rf[s];
    2353:         const PetscInt   q  = isCohesive ? qc : qf[s];
    2354:         const PetscReal *Bq = &T->T[0][(r * Nq + q) * Nbf * Ncf];
    2355:         const PetscReal *Dq = &T->T[1][(r * Nq + q) * Nbf * Ncf * dEt];
    2356:         PetscInt         b, c, d;

    2358:         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);
    2359:         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);
    2360:         for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
    2361:         for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
    2362:         for (b = 0; b < Nbf; ++b) {
    2363:           for (c = 0; c < Ncf; ++c) {
    2364:             const PetscInt cidx = b * Ncf + c;

    2366:             u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
    2367:             for (d = 0; d < dEt; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * dEt + d] * coefficients[dOffset + b];
    2368:           }
    2369:         }
    2370:         PetscCall(PetscFEPushforward(fe, fegeom, 1, &u[fOffset]));
    2371:         PetscCall(PetscFEPushforwardGradient(fe, fegeom, 1, &u_x[fOffset * dE]));
    2372:         if (u_t) {
    2373:           for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
    2374:           for (b = 0; b < Nbf; ++b) {
    2375:             for (c = 0; c < Ncf; ++c) {
    2376:               const PetscInt cidx = b * Ncf + c;

    2378:               u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
    2379:             }
    2380:           }
    2381:           PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
    2382:         }
    2383:         fOffset += Ncf;
    2384:         dOffset += Nbf;
    2385:       }
    2386:     }
    2387:   }
    2388:   return PETSC_SUCCESS;
    2389: }

    2391: PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS prob, PetscInt field, PetscInt faceLoc, const PetscScalar coefficients[], PetscScalar u[])
    2392: {
    2393:   PetscFE         fe;
    2394:   PetscTabulation Tc;
    2395:   PetscInt        b, c;

    2397:   if (!prob) return PETSC_SUCCESS;
    2398:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    2399:   PetscCall(PetscFEGetFaceCentroidTabulation(fe, &Tc));
    2400:   {
    2401:     const PetscReal *faceBasis = Tc->T[0];
    2402:     const PetscInt   Nb        = Tc->Nb;
    2403:     const PetscInt   Nc        = Tc->Nc;

    2405:     for (c = 0; c < Nc; ++c) u[c] = 0.0;
    2406:     for (b = 0; b < Nb; ++b) {
    2407:       for (c = 0; c < Nc; ++c) u[c] += coefficients[b] * faceBasis[(faceLoc * Nb + b) * Nc + c];
    2408:     }
    2409:   }
    2410:   return PETSC_SUCCESS;
    2411: }

    2413: PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscInt e, PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
    2414: {
    2415:   PetscFEGeom      pgeom;
    2416:   const PetscInt   dEt      = T->cdim;
    2417:   const PetscInt   dE       = fegeom->dimEmbed;
    2418:   const PetscInt   Nq       = T->Np;
    2419:   const PetscInt   Nb       = T->Nb;
    2420:   const PetscInt   Nc       = T->Nc;
    2421:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
    2422:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dEt];
    2423:   PetscInt         q, b, c, d;

    2425:   for (q = 0; q < Nq; ++q) {
    2426:     for (b = 0; b < Nb; ++b) {
    2427:       for (c = 0; c < Nc; ++c) {
    2428:         const PetscInt bcidx = b * Nc + c;

    2430:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
    2431:         for (d = 0; d < dEt; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dEt + bcidx * dEt + d];
    2432:         for (d = dEt; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = 0.0;
    2433:       }
    2434:     }
    2435:     PetscCall(PetscFEGeomGetCellPoint(fegeom, e, q, &pgeom));
    2436:     PetscCall(PetscFEPushforward(fe, &pgeom, Nb, tmpBasis));
    2437:     PetscCall(PetscFEPushforwardGradient(fe, &pgeom, Nb, tmpBasisDer));
    2438:     for (b = 0; b < Nb; ++b) {
    2439:       for (c = 0; c < Nc; ++c) {
    2440:         const PetscInt bcidx = b * Nc + c;
    2441:         const PetscInt qcidx = q * Nc + c;

    2443:         elemVec[b] += tmpBasis[bcidx] * f0[qcidx];
    2444:         for (d = 0; d < dE; ++d) elemVec[b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2445:       }
    2446:     }
    2447:   }
    2448:   return PETSC_SUCCESS;
    2449: }

    2451: PetscErrorCode PetscFEUpdateElementVec_Hybrid_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscInt side, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
    2452: {
    2453:   const PetscInt   dE       = T->cdim;
    2454:   const PetscInt   Nq       = T->Np;
    2455:   const PetscInt   Nb       = T->Nb;
    2456:   const PetscInt   Nc       = T->Nc;
    2457:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
    2458:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dE];

    2460:   for (PetscInt q = 0; q < Nq; ++q) {
    2461:     for (PetscInt b = 0; b < Nb; ++b) {
    2462:       for (PetscInt c = 0; c < Nc; ++c) {
    2463:         const PetscInt bcidx = b * Nc + c;

    2465:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
    2466:         for (PetscInt d = 0; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dE + bcidx * dE + d];
    2467:       }
    2468:     }
    2469:     PetscCall(PetscFEPushforward(fe, fegeom, Nb, tmpBasis));
    2470:     // TODO This is currently broken since we do not pull the geometry down to the lower dimension
    2471:     // PetscCall(PetscFEPushforwardGradient(fe, fegeom, Nb, tmpBasisDer));
    2472:     if (side == 2) {
    2473:       // Integrating over whole cohesive cell, so insert for both sides
    2474:       for (PetscInt s = 0; s < 2; ++s) {
    2475:         for (PetscInt b = 0; b < Nb; ++b) {
    2476:           for (PetscInt c = 0; c < Nc; ++c) {
    2477:             const PetscInt bcidx = b * Nc + c;
    2478:             const PetscInt qcidx = (q * 2 + s) * Nc + c;

    2480:             elemVec[Nb * s + b] += tmpBasis[bcidx] * f0[qcidx];
    2481:             for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * s + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2482:           }
    2483:         }
    2484:       }
    2485:     } else {
    2486:       // Integrating over endcaps of cohesive cell, so insert for correct side
    2487:       for (PetscInt b = 0; b < Nb; ++b) {
    2488:         for (PetscInt c = 0; c < Nc; ++c) {
    2489:           const PetscInt bcidx = b * Nc + c;
    2490:           const PetscInt qcidx = q * Nc + c;

    2492:           elemVec[Nb * side + b] += tmpBasis[bcidx] * f0[qcidx];
    2493:           for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * side + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2494:         }
    2495:       }
    2496:     }
    2497:   }
    2498:   return PETSC_SUCCESS;
    2499: }

    2501: #define petsc_elemmat_kernel_g1(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2502:   do { \
    2503:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2504:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2505:         const PetscScalar *G = g1 + (fc * (_NcJ) + gc) * _dE; \
    2506:         for (PetscInt f = 0; f < (_NbI); ++f) { \
    2507:           const PetscScalar tBIv = tmpBasisI[f * (_NcI) + fc]; \
    2508:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2509:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
    2510:             PetscScalar        s    = 0.0; \
    2511:             for (PetscInt df = 0; df < _dE; ++df) { s += G[df] * tBDJ[df]; } \
    2512:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBIv; \
    2513:           } \
    2514:         } \
    2515:       } \
    2516:     } \
    2517:   } while (0)

    2519: #define petsc_elemmat_kernel_g2(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2520:   do { \
    2521:     for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2522:       for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2523:         const PetscScalar *G = g2 + (fc * (_NcJ) + gc) * _dE; \
    2524:         for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2525:           const PetscScalar tBJv = tmpBasisJ[g * (_NcJ) + gc]; \
    2526:           for (PetscInt f = 0; f < (_NbI); ++f) { \
    2527:             const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
    2528:             PetscScalar        s    = 0.0; \
    2529:             for (PetscInt df = 0; df < _dE; ++df) { s += tBDI[df] * G[df]; } \
    2530:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBJv; \
    2531:           } \
    2532:         } \
    2533:       } \
    2534:     } \
    2535:   } while (0)

    2537: #define petsc_elemmat_kernel_g3(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2538:   do { \
    2539:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2540:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2541:         const PetscScalar *G = g3 + (fc * (_NcJ) + gc) * (_dE) * (_dE); \
    2542:         for (PetscInt f = 0; f < (_NbI); ++f) { \
    2543:           const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
    2544:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2545:             PetscScalar        s    = 0.0; \
    2546:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
    2547:             for (PetscInt df = 0; df < (_dE); ++df) { \
    2548:               for (PetscInt dg = 0; dg < (_dE); ++dg) { s += tBDI[df] * G[df * (_dE) + dg] * tBDJ[dg]; } \
    2549:             } \
    2550:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s; \
    2551:           } \
    2552:         } \
    2553:       } \
    2554:     } \
    2555:   } while (0)

    2557: 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[])
    2558: {
    2559:   const PetscInt   cdim      = TI->cdim;
    2560:   const PetscInt   dE        = fegeom->dimEmbed;
    2561:   const PetscInt   NqI       = TI->Np;
    2562:   const PetscInt   NbI       = TI->Nb;
    2563:   const PetscInt   NcI       = TI->Nc;
    2564:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
    2565:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * cdim];
    2566:   const PetscInt   NqJ       = TJ->Np;
    2567:   const PetscInt   NbJ       = TJ->Nb;
    2568:   const PetscInt   NcJ       = TJ->Nc;
    2569:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
    2570:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * cdim];

    2572:   for (PetscInt f = 0; f < NbI; ++f) {
    2573:     for (PetscInt fc = 0; fc < NcI; ++fc) {
    2574:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2576:       tmpBasisI[fidx] = basisI[fidx];
    2577:       for (PetscInt df = 0; df < cdim; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * cdim + df];
    2578:     }
    2579:   }
    2580:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
    2581:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
    2582:   if (feI != feJ) {
    2583:     for (PetscInt g = 0; g < NbJ; ++g) {
    2584:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2585:         const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2587:         tmpBasisJ[gidx] = basisJ[gidx];
    2588:         for (PetscInt dg = 0; dg < cdim; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * cdim + dg];
    2589:       }
    2590:     }
    2591:     PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
    2592:     PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
    2593:   } else {
    2594:     tmpBasisJ    = tmpBasisI;
    2595:     tmpBasisDerJ = tmpBasisDerI;
    2596:   }
    2597:   if (PetscUnlikely(g0)) {
    2598:     for (PetscInt f = 0; f < NbI; ++f) {
    2599:       const PetscInt i = offsetI + f; /* Element matrix row */

    2601:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2602:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

    2604:         for (PetscInt g = 0; g < NbJ; ++g) {
    2605:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2606:           const PetscInt fOff = i * totDim + j;

    2608:           for (PetscInt gc = 0; gc < NcJ; ++gc) { elemMat[fOff] += bI * g0[fc * NcJ + gc] * tmpBasisJ[g * NcJ + gc]; }
    2609:         }
    2610:       }
    2611:     }
    2612:   }
    2613:   if (PetscUnlikely(g1)) {
    2614: #if 1
    2615:     if (dE == 2) {
    2616:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 2);
    2617:     } else if (dE == 3) {
    2618:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 3);
    2619:     } else {
    2620:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, dE);
    2621:     }
    2622: #else
    2623:     for (PetscInt f = 0; f < NbI; ++f) {
    2624:       const PetscInt i = offsetI + f; /* Element matrix row */

    2626:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2627:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

    2629:         for (PetscInt g = 0; g < NbJ; ++g) {
    2630:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2631:           const PetscInt fOff = i * totDim + j;

    2633:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2634:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2636:             for (PetscInt df = 0; df < dE; ++df) { elemMat[fOff] += bI * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df]; }
    2637:           }
    2638:         }
    2639:       }
    2640:     }
    2641: #endif
    2642:   }
    2643:   if (PetscUnlikely(g2)) {
    2644: #if 1
    2645:     if (dE == 2) {
    2646:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 2);
    2647:     } else if (dE == 3) {
    2648:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 3);
    2649:     } else {
    2650:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, dE);
    2651:     }
    2652: #else
    2653:     for (PetscInt g = 0; g < NbJ; ++g) {
    2654:       const PetscInt j = offsetJ + g; /* Element matrix column */

    2656:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2657:         const PetscScalar bJ = tmpBasisJ[g * NcJ + gc]; /* Trial function basis value */

    2659:         for (PetscInt f = 0; f < NbI; ++f) {
    2660:           const PetscInt i    = offsetI + f; /* Element matrix row */
    2661:           const PetscInt fOff = i * totDim + j;

    2663:           for (PetscInt fc = 0; fc < NcI; ++fc) {
    2664:             const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2666:             for (PetscInt df = 0; df < dE; ++df) { elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * bJ; }
    2667:           }
    2668:         }
    2669:       }
    2670:     }
    2671: #endif
    2672:   }
    2673:   if (PetscUnlikely(g3)) {
    2674: #if 1
    2675:     if (dE == 2) {
    2676:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 2);
    2677:     } else if (dE == 3) {
    2678:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 3);
    2679:     } else {
    2680:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, dE);
    2681:     }
    2682: #else
    2683:     for (PetscInt f = 0; f < NbI; ++f) {
    2684:       const PetscInt i = offsetI + f; /* Element matrix row */

    2686:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2687:         const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2689:         for (PetscInt g = 0; g < NbJ; ++g) {
    2690:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2691:           const PetscInt fOff = i * totDim + j;

    2693:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2694:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2696:             for (PetscInt df = 0; df < dE; ++df) {
    2697:               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]; }
    2698:             }
    2699:           }
    2700:         }
    2701:       }
    2702:     }
    2703: #endif
    2704:   }
    2705:   return PETSC_SUCCESS;
    2706: }

    2708: #undef petsc_elemmat_kernel_g1
    2709: #undef petsc_elemmat_kernel_g2
    2710: #undef petsc_elemmat_kernel_g3

    2712: 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[])
    2713: {
    2714:   const PetscInt   dE        = TI->cdim;
    2715:   const PetscInt   NqI       = TI->Np;
    2716:   const PetscInt   NbI       = TI->Nb;
    2717:   const PetscInt   NcI       = TI->Nc;
    2718:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
    2719:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * dE];
    2720:   const PetscInt   NqJ       = TJ->Np;
    2721:   const PetscInt   NbJ       = TJ->Nb;
    2722:   const PetscInt   NcJ       = TJ->Nc;
    2723:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
    2724:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * dE];
    2725:   const PetscInt   so        = isHybridI ? 0 : s;
    2726:   const PetscInt   to        = isHybridJ ? 0 : t;
    2727:   PetscInt         f, fc, g, gc, df, dg;

    2729:   for (f = 0; f < NbI; ++f) {
    2730:     for (fc = 0; fc < NcI; ++fc) {
    2731:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2733:       tmpBasisI[fidx] = basisI[fidx];
    2734:       for (df = 0; df < dE; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * dE + df];
    2735:     }
    2736:   }
    2737:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
    2738:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
    2739:   for (g = 0; g < NbJ; ++g) {
    2740:     for (gc = 0; gc < NcJ; ++gc) {
    2741:       const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2743:       tmpBasisJ[gidx] = basisJ[gidx];
    2744:       for (dg = 0; dg < dE; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * dE + dg];
    2745:     }
    2746:   }
    2747:   PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
    2748:   // TODO This is currently broken since we do not pull the geometry down to the lower dimension
    2749:   // PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
    2750:   for (f = 0; f < NbI; ++f) {
    2751:     for (fc = 0; fc < NcI; ++fc) {
    2752:       const PetscInt fidx = f * NcI + fc;           /* Test function basis index */
    2753:       const PetscInt i    = offsetI + NbI * so + f; /* Element matrix row */
    2754:       for (g = 0; g < NbJ; ++g) {
    2755:         for (gc = 0; gc < NcJ; ++gc) {
    2756:           const PetscInt gidx = g * NcJ + gc;           /* Trial function basis index */
    2757:           const PetscInt j    = offsetJ + NbJ * to + g; /* Element matrix column */
    2758:           const PetscInt fOff = eOffset + i * totDim + j;

    2760:           elemMat[fOff] += tmpBasisI[fidx] * g0[fc * NcJ + gc] * tmpBasisJ[gidx];
    2761:           for (df = 0; df < dE; ++df) {
    2762:             elemMat[fOff] += tmpBasisI[fidx] * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
    2763:             elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * tmpBasisJ[gidx];
    2764:             for (dg = 0; dg < dE; ++dg) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g3[((fc * NcJ + gc) * dE + df) * dE + dg] * tmpBasisDerJ[gidx * dE + dg];
    2765:           }
    2766:         }
    2767:       }
    2768:     }
    2769:   }
    2770:   return PETSC_SUCCESS;
    2771: }

    2773: PetscErrorCode PetscFECreateCellGeometry(PetscFE fe, PetscQuadrature quad, PetscFEGeom *cgeom)
    2774: {
    2775:   PetscDualSpace  dsp;
    2776:   DM              dm;
    2777:   PetscQuadrature quadDef;
    2778:   PetscInt        dim, cdim, Nq;

    2780:   PetscFunctionBegin;
    2781:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    2782:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    2783:   PetscCall(DMGetDimension(dm, &dim));
    2784:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2785:   PetscCall(PetscFEGetQuadrature(fe, &quadDef));
    2786:   quad = quad ? quad : quadDef;
    2787:   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
    2788:   PetscCall(PetscMalloc1(Nq * cdim, &cgeom->v));
    2789:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->J));
    2790:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->invJ));
    2791:   PetscCall(PetscMalloc1(Nq, &cgeom->detJ));
    2792:   cgeom->dim       = dim;
    2793:   cgeom->dimEmbed  = cdim;
    2794:   cgeom->numCells  = 1;
    2795:   cgeom->numPoints = Nq;
    2796:   PetscCall(DMPlexComputeCellGeometryFEM(dm, 0, quad, cgeom->v, cgeom->J, cgeom->invJ, cgeom->detJ));
    2797:   PetscFunctionReturn(PETSC_SUCCESS);
    2798: }

    2800: PetscErrorCode PetscFEDestroyCellGeometry(PetscFE fe, PetscFEGeom *cgeom)
    2801: {
    2802:   PetscFunctionBegin;
    2803:   PetscCall(PetscFree(cgeom->v));
    2804:   PetscCall(PetscFree(cgeom->J));
    2805:   PetscCall(PetscFree(cgeom->invJ));
    2806:   PetscCall(PetscFree(cgeom->detJ));
    2807:   PetscFunctionReturn(PETSC_SUCCESS);
    2808: }

    2810: #if 0
    2811: 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)
    2812: {
    2813:   const PetscInt dE      = dimEmbed;
    2814:   const PetscInt NbI     = TI->Nb;
    2815:   const PetscInt NcI     = TI->Nc;
    2816:   const PetscInt NbJ     = TJ->Nb;
    2817:   const PetscInt NcJ     = TJ->Nc;
    2818:   PetscBool      has_g0  = g0 ? PETSC_TRUE : PETSC_FALSE;
    2819:   PetscBool      has_g1  = g1 ? PETSC_TRUE : PETSC_FALSE;
    2820:   PetscBool      has_g2  = g2 ? PETSC_TRUE : PETSC_FALSE;
    2821:   PetscBool      has_g3  = g3 ? PETSC_TRUE : PETSC_FALSE;
    2822:   PetscInt      *g0_idxs = NULL, *g1_idxs = NULL, *g2_idxs = NULL, *g3_idxs = NULL;
    2823:   PetscInt       g0_i, g1_i, g2_i, g3_i;

    2825:   PetscFunctionBegin;
    2826:   g0_i = g1_i = g2_i = g3_i = 0;
    2827:   if (has_g0)
    2828:     for (PetscInt i = 0; i < NcI * NcJ; i++)
    2829:       if (g0[i]) g0_i += NbI * NbJ;
    2830:   if (has_g1)
    2831:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
    2832:       if (g1[i]) g1_i += NbI * NbJ;
    2833:   if (has_g2)
    2834:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
    2835:       if (g2[i]) g2_i += NbI * NbJ;
    2836:   if (has_g3)
    2837:     for (PetscInt i = 0; i < NcI * NcJ * dE * dE; i++)
    2838:       if (g3[i]) g3_i += NbI * NbJ;
    2839:   if (g0_i == NbI * NbJ * NcI * NcJ) g0_i = 0;
    2840:   if (g1_i == NbI * NbJ * NcI * NcJ * dE) g1_i = 0;
    2841:   if (g2_i == NbI * NbJ * NcI * NcJ * dE) g2_i = 0;
    2842:   if (g3_i == NbI * NbJ * NcI * NcJ * dE * dE) g3_i = 0;
    2843:   has_g0 = g0_i ? PETSC_TRUE : PETSC_FALSE;
    2844:   has_g1 = g1_i ? PETSC_TRUE : PETSC_FALSE;
    2845:   has_g2 = g2_i ? PETSC_TRUE : PETSC_FALSE;
    2846:   has_g3 = g3_i ? PETSC_TRUE : PETSC_FALSE;
    2847:   if (has_g0) PetscCall(PetscMalloc1(4 * g0_i, &g0_idxs));
    2848:   if (has_g1) PetscCall(PetscMalloc1(4 * g1_i, &g1_idxs));
    2849:   if (has_g2) PetscCall(PetscMalloc1(4 * g2_i, &g2_idxs));
    2850:   if (has_g3) PetscCall(PetscMalloc1(4 * g3_i, &g3_idxs));
    2851:   g0_i = g1_i = g2_i = g3_i = 0;

    2853:   for (PetscInt f = 0; f < NbI; ++f) {
    2854:     const PetscInt i = offsetI + f; /* Element matrix row */
    2855:     for (PetscInt fc = 0; fc < NcI; ++fc) {
    2856:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2858:       for (PetscInt g = 0; g < NbJ; ++g) {
    2859:         const PetscInt j    = offsetJ + g; /* Element matrix column */
    2860:         const PetscInt fOff = i * totDim + j;
    2861:         for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2862:           const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2864:           if (has_g0) {
    2865:             if (g0[fc * NcJ + gc]) {
    2866:               g0_idxs[4 * g0_i + 0] = fidx;
    2867:               g0_idxs[4 * g0_i + 1] = fc * NcJ + gc;
    2868:               g0_idxs[4 * g0_i + 2] = gidx;
    2869:               g0_idxs[4 * g0_i + 3] = fOff;
    2870:               g0_i++;
    2871:             }
    2872:           }

    2874:           for (PetscInt df = 0; df < dE; ++df) {
    2875:             if (has_g1) {
    2876:               if (g1[(fc * NcJ + gc) * dE + df]) {
    2877:                 g1_idxs[4 * g1_i + 0] = fidx;
    2878:                 g1_idxs[4 * g1_i + 1] = (fc * NcJ + gc) * dE + df;
    2879:                 g1_idxs[4 * g1_i + 2] = gidx * dE + df;
    2880:                 g1_idxs[4 * g1_i + 3] = fOff;
    2881:                 g1_i++;
    2882:               }
    2883:             }
    2884:             if (has_g2) {
    2885:               if (g2[(fc * NcJ + gc) * dE + df]) {
    2886:                 g2_idxs[4 * g2_i + 0] = fidx * dE + df;
    2887:                 g2_idxs[4 * g2_i + 1] = (fc * NcJ + gc) * dE + df;
    2888:                 g2_idxs[4 * g2_i + 2] = gidx;
    2889:                 g2_idxs[4 * g2_i + 3] = fOff;
    2890:                 g2_i++;
    2891:               }
    2892:             }
    2893:             if (has_g3) {
    2894:               for (PetscInt dg = 0; dg < dE; ++dg) {
    2895:                 if (g3[((fc * NcJ + gc) * dE + df) * dE + dg]) {
    2896:                   g3_idxs[4 * g3_i + 0] = fidx * dE + df;
    2897:                   g3_idxs[4 * g3_i + 1] = ((fc * NcJ + gc) * dE + df) * dE + dg;
    2898:                   g3_idxs[4 * g3_i + 2] = gidx * dE + dg;
    2899:                   g3_idxs[4 * g3_i + 3] = fOff;
    2900:                   g3_i++;
    2901:                 }
    2902:               }
    2903:             }
    2904:           }
    2905:         }
    2906:       }
    2907:     }
    2908:   }
    2909:   *n_g0 = g0_i;
    2910:   *n_g1 = g1_i;
    2911:   *n_g2 = g2_i;
    2912:   *n_g3 = g3_i;

    2914:   *g0_idxs_out = g0_idxs;
    2915:   *g1_idxs_out = g1_idxs;
    2916:   *g2_idxs_out = g2_idxs;
    2917:   *g3_idxs_out = g3_idxs;
    2918:   PetscFunctionReturn(PETSC_SUCCESS);
    2919: }

    2921: //example HOW TO USE
    2922:       for (PetscInt i = 0; i < g0_sparse_n; i++) {
    2923:         PetscInt bM = g0_sparse_idxs[4 * i + 0];
    2924:         PetscInt bN = g0_sparse_idxs[4 * i + 1];
    2925:         PetscInt bK = g0_sparse_idxs[4 * i + 2];
    2926:         PetscInt bO = g0_sparse_idxs[4 * i + 3];
    2927:         elemMat[bO] += tmpBasisI[bM] * g0[bN] * tmpBasisJ[bK];
    2928:       }
    2929: #endif