Date: 2026-06-01T23:13:18+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:   Options Database Key:
    170: . -name [viewertype][:...] - option name and values. See `PetscObjectViewFromOptions()` for the possible arguments

    172:   Level: intermediate

    174: .seealso: `PetscFE`, `PetscFEView()`, `PetscObjectViewFromOptions()`, `PetscFECreate()`
    175: @*/
    176: PetscErrorCode PetscFEViewFromOptions(PetscFE A, PeOp PetscObject obj, const char name[])
    177: {
    178:   PetscFunctionBegin;
    180:   PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
    181:   PetscFunctionReturn(PETSC_SUCCESS);
    182: }

    184: /*@
    185:   PetscFEView - Views a `PetscFE`

    187:   Collective

    189:   Input Parameters:
    190: + fem    - the `PetscFE` object to view
    191: - viewer - the viewer

    193:   Level: beginner

    195: .seealso: `PetscFE`, `PetscViewer`, `PetscFEDestroy()`, `PetscFEViewFromOptions()`
    196: @*/
    197: PetscErrorCode PetscFEView(PetscFE fem, PetscViewer viewer)
    198: {
    199:   PetscBool isascii;

    201:   PetscFunctionBegin;
    204:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)fem), &viewer));
    205:   PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)fem, viewer));
    206:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    207:   PetscTryTypeMethod(fem, view, viewer);
    208:   PetscFunctionReturn(PETSC_SUCCESS);
    209: }

    211: /*@
    212:   PetscFESetFromOptions - sets parameters in a `PetscFE` from the options database

    214:   Collective

    216:   Input Parameter:
    217: . fem - the `PetscFE` object to set options for

    219:   Options Database Keys:
    220: + -petscfe_num_blocks  - the number of cell blocks to integrate concurrently
    221: - -petscfe_num_batches - the number of cell batches to integrate serially

    223:   Level: intermediate

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

    233:   PetscFunctionBegin;
    235:   if (!((PetscObject)fem)->type_name) defaultType = PETSCFEBASIC;
    236:   else defaultType = ((PetscObject)fem)->type_name;
    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) PetscCall(PetscFESetType(fem, name));
    242:   else if (!((PetscObject)fem)->type_name) PetscCall(PetscFESetType(fem, defaultType));
    243:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_blocks", "The number of cell blocks to integrate concurrently", "PetscSpaceSetTileSizes", fem->numBlocks, &fem->numBlocks, NULL, 1));
    244:   PetscCall(PetscOptionsBoundedInt("-petscfe_num_batches", "The number of cell batches to integrate serially", "PetscSpaceSetTileSizes", fem->numBatches, &fem->numBatches, NULL, 1));
    245:   PetscTryTypeMethod(fem, setfromoptions, PetscOptionsObject);
    246:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
    247:   PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)fem, PetscOptionsObject));
    248:   PetscOptionsEnd();
    249:   PetscCall(PetscFEViewFromOptions(fem, NULL, "-petscfe_view"));
    250:   PetscFunctionReturn(PETSC_SUCCESS);
    251: }

    253: /*@
    254:   PetscFESetUp - Construct data structures for the `PetscFE` after the `PetscFEType` has been set

    256:   Collective

    258:   Input Parameter:
    259: . fem - the `PetscFE` object to setup

    261:   Level: intermediate

    263: .seealso: `PetscFE`, `PetscFEView()`, `PetscFEDestroy()`
    264: @*/
    265: PetscErrorCode PetscFESetUp(PetscFE fem)
    266: {
    267:   PetscFunctionBegin;
    269:   if (fem->setupcalled) PetscFunctionReturn(PETSC_SUCCESS);
    270:   PetscCall(PetscLogEventBegin(PETSCFE_SetUp, fem, 0, 0, 0));
    271:   fem->setupcalled = PETSC_TRUE;
    272:   PetscTryTypeMethod(fem, setup);
    273:   PetscCall(PetscLogEventEnd(PETSCFE_SetUp, fem, 0, 0, 0));
    274:   PetscFunctionReturn(PETSC_SUCCESS);
    275: }

    277: /*@
    278:   PetscFEDestroy - Destroys a `PetscFE` object

    280:   Collective

    282:   Input Parameter:
    283: . fem - the `PetscFE` object to destroy

    285:   Level: beginner

    287: .seealso: `PetscFE`, `PetscFEView()`
    288: @*/
    289: PetscErrorCode PetscFEDestroy(PetscFE *fem)
    290: {
    291:   PetscFunctionBegin;
    292:   if (!*fem) PetscFunctionReturn(PETSC_SUCCESS);

    295:   if (--((PetscObject)*fem)->refct > 0) {
    296:     *fem = NULL;
    297:     PetscFunctionReturn(PETSC_SUCCESS);
    298:   }
    299:   ((PetscObject)*fem)->refct = 0;

    301:   if ((*fem)->subspaces) {
    302:     PetscInt dim, d;

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

    321:   PetscTryTypeMethod(*fem, destroy);
    322:   PetscCall(PetscHeaderDestroy(fem));
    323:   PetscFunctionReturn(PETSC_SUCCESS);
    324: }

    326: /*@
    327:   PetscFECreate - Creates an empty `PetscFE` object. The type can then be set with `PetscFESetType()`.

    329:   Collective

    331:   Input Parameter:
    332: . comm - The communicator for the `PetscFE` object

    334:   Output Parameter:
    335: . fem - The `PetscFE` object

    337:   Level: beginner

    339: .seealso: `PetscFE`, `PetscFEType`, `PetscFESetType()`, `PetscFECreateDefault()`, `PETSCFEGALERKIN`
    340: @*/
    341: PetscErrorCode PetscFECreate(MPI_Comm comm, PetscFE *fem)
    342: {
    343:   PetscFE f;

    345:   PetscFunctionBegin;
    346:   PetscAssertPointer(fem, 2);
    347:   PetscCall(PetscCitationsRegister(FECitation, &FEcite));
    348:   PetscCall(PetscFEInitializePackage());

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

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

    367:   *fem = f;
    368:   PetscFunctionReturn(PETSC_SUCCESS);
    369: }

    371: /*@
    372:   PetscFEGetSpatialDimension - Returns the spatial dimension of the element

    374:   Not Collective

    376:   Input Parameter:
    377: . fem - The `PetscFE` object

    379:   Output Parameter:
    380: . dim - The spatial dimension

    382:   Level: intermediate

    384: .seealso: `PetscFE`, `PetscFECreate()`
    385: @*/
    386: PetscErrorCode PetscFEGetSpatialDimension(PetscFE fem, PetscInt *dim)
    387: {
    388:   DM dm;

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

    398: /*@
    399:   PetscFESetNumComponents - Sets the number of field components in the element

    401:   Not Collective

    403:   Input Parameters:
    404: + fem  - The `PetscFE` object
    405: - comp - The number of field components

    407:   Level: intermediate

    409: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`, `PetscFEGetNumComponents()`
    410: @*/
    411: PetscErrorCode PetscFESetNumComponents(PetscFE fem, PetscInt comp)
    412: {
    413:   PetscFunctionBegin;
    415:   fem->numComponents = comp;
    416:   PetscFunctionReturn(PETSC_SUCCESS);
    417: }

    419: /*@
    420:   PetscFEGetNumComponents - Returns the number of components in the element

    422:   Not Collective

    424:   Input Parameter:
    425: . fem - The `PetscFE` object

    427:   Output Parameter:
    428: . comp - The number of field components

    430:   Level: intermediate

    432: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetSpatialDimension()`
    433: @*/
    434: PetscErrorCode PetscFEGetNumComponents(PetscFE fem, PetscInt *comp)
    435: {
    436:   PetscFunctionBegin;
    438:   PetscAssertPointer(comp, 2);
    439:   *comp = fem->numComponents;
    440:   PetscFunctionReturn(PETSC_SUCCESS);
    441: }

    443: /*@
    444:   PetscFESetTileSizes - Sets the tile sizes for evaluation

    446:   Not Collective

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

    455:   Level: intermediate

    457: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFEGetTileSizes()`
    458: @*/
    459: PetscErrorCode PetscFESetTileSizes(PetscFE fem, PetscInt blockSize, PetscInt numBlocks, PetscInt batchSize, PetscInt numBatches)
    460: {
    461:   PetscFunctionBegin;
    463:   fem->blockSize  = blockSize;
    464:   fem->numBlocks  = numBlocks;
    465:   fem->batchSize  = batchSize;
    466:   fem->numBatches = numBatches;
    467:   PetscFunctionReturn(PETSC_SUCCESS);
    468: }

    470: /*@
    471:   PetscFEGetTileSizes - Returns the tile sizes for evaluation

    473:   Not Collective

    475:   Input Parameter:
    476: . fem - The `PetscFE` object

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

    484:   Level: intermediate

    486: .seealso: `PetscFE`, `PetscFECreate()`, `PetscFESetTileSizes()`
    487: @*/
    488: PetscErrorCode PetscFEGetTileSizes(PetscFE fem, PeOp PetscInt *blockSize, PeOp PetscInt *numBlocks, PeOp PetscInt *batchSize, PeOp PetscInt *numBatches)
    489: {
    490:   PetscFunctionBegin;
    492:   if (blockSize) PetscAssertPointer(blockSize, 2);
    493:   if (numBlocks) PetscAssertPointer(numBlocks, 3);
    494:   if (batchSize) PetscAssertPointer(batchSize, 4);
    495:   if (numBatches) PetscAssertPointer(numBatches, 5);
    496:   if (blockSize) *blockSize = fem->blockSize;
    497:   if (numBlocks) *numBlocks = fem->numBlocks;
    498:   if (batchSize) *batchSize = fem->batchSize;
    499:   if (numBatches) *numBatches = fem->numBatches;
    500:   PetscFunctionReturn(PETSC_SUCCESS);
    501: }

    503: /*@
    504:   PetscFEGetBasisSpace - Returns the `PetscSpace` used for the approximation of the solution for the `PetscFE`

    506:   Not Collective

    508:   Input Parameter:
    509: . fem - The `PetscFE` object

    511:   Output Parameter:
    512: . sp - The `PetscSpace` object

    514:   Level: intermediate

    516: .seealso: `PetscFE`, `PetscSpace`, `PetscFECreate()`
    517: @*/
    518: PetscErrorCode PetscFEGetBasisSpace(PetscFE fem, PetscSpace *sp)
    519: {
    520:   PetscFunctionBegin;
    522:   PetscAssertPointer(sp, 2);
    523:   *sp = fem->basisSpace;
    524:   PetscFunctionReturn(PETSC_SUCCESS);
    525: }

    527: /*@
    528:   PetscFESetBasisSpace - Sets the `PetscSpace` used for the approximation of the solution

    530:   Not Collective

    532:   Input Parameters:
    533: + fem - The `PetscFE` object
    534: - sp  - The `PetscSpace` object

    536:   Level: intermediate

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

    541: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetDualSpace()`
    542: @*/
    543: PetscErrorCode PetscFESetBasisSpace(PetscFE fem, PetscSpace sp)
    544: {
    545:   PetscFunctionBegin;
    548:   PetscCall(PetscSpaceDestroy(&fem->basisSpace));
    549:   fem->basisSpace = sp;
    550:   PetscCall(PetscObjectReference((PetscObject)fem->basisSpace));
    551:   PetscFunctionReturn(PETSC_SUCCESS);
    552: }

    554: /*@
    555:   PetscFEGetDualSpace - Returns the `PetscDualSpace` used to define the inner product for a `PetscFE`

    557:   Not Collective

    559:   Input Parameter:
    560: . fem - The `PetscFE` object

    562:   Output Parameter:
    563: . sp - The `PetscDualSpace` object

    565:   Level: intermediate

    567: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
    568: @*/
    569: PetscErrorCode PetscFEGetDualSpace(PetscFE fem, PetscDualSpace *sp)
    570: {
    571:   PetscFunctionBegin;
    573:   PetscAssertPointer(sp, 2);
    574:   *sp = fem->dualSpace;
    575:   PetscFunctionReturn(PETSC_SUCCESS);
    576: }

    578: /*@
    579:   PetscFESetDualSpace - Sets the `PetscDualSpace` used to define the inner product

    581:   Not Collective

    583:   Input Parameters:
    584: + fem - The `PetscFE` object
    585: - sp  - The `PetscDualSpace` object

    587:   Level: intermediate

    589: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`, `PetscFESetBasisSpace()`
    590: @*/
    591: PetscErrorCode PetscFESetDualSpace(PetscFE fem, PetscDualSpace sp)
    592: {
    593:   PetscFunctionBegin;
    596:   PetscCall(PetscDualSpaceDestroy(&fem->dualSpace));
    597:   fem->dualSpace = sp;
    598:   PetscCall(PetscObjectReference((PetscObject)fem->dualSpace));
    599:   PetscFunctionReturn(PETSC_SUCCESS);
    600: }

    602: /*@
    603:   PetscFEGetQuadrature - Returns the `PetscQuadrature` used to calculate inner products

    605:   Not Collective

    607:   Input Parameter:
    608: . fem - The `PetscFE` object

    610:   Output Parameter:
    611: . q - The `PetscQuadrature` object

    613:   Level: intermediate

    615: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`
    616: @*/
    617: PetscErrorCode PetscFEGetQuadrature(PetscFE fem, PetscQuadrature *q)
    618: {
    619:   PetscFunctionBegin;
    621:   PetscAssertPointer(q, 2);
    622:   *q = fem->quadrature;
    623:   PetscFunctionReturn(PETSC_SUCCESS);
    624: }

    626: /*@
    627:   PetscFESetQuadrature - Sets the `PetscQuadrature` used to calculate inner products

    629:   Not Collective

    631:   Input Parameters:
    632: + fem - The `PetscFE` object
    633: - q   - The `PetscQuadrature` object

    635:   Level: intermediate

    637: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFEGetFaceQuadrature()`
    638: @*/
    639: PetscErrorCode PetscFESetQuadrature(PetscFE fem, PetscQuadrature q)
    640: {
    641:   PetscInt Nc, qNc;

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

    657: /*@
    658:   PetscFEGetFaceQuadrature - Returns the `PetscQuadrature` used to calculate inner products on faces

    660:   Not Collective

    662:   Input Parameter:
    663: . fem - The `PetscFE` object

    665:   Output Parameter:
    666: . q - The `PetscQuadrature` object

    668:   Level: intermediate

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

    673: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
    674: @*/
    675: PetscErrorCode PetscFEGetFaceQuadrature(PetscFE fem, PetscQuadrature *q)
    676: {
    677:   PetscFunctionBegin;
    679:   PetscAssertPointer(q, 2);
    680:   *q = fem->faceQuadrature;
    681:   PetscFunctionReturn(PETSC_SUCCESS);
    682: }

    684: /*@
    685:   PetscFESetFaceQuadrature - Sets the `PetscQuadrature` used to calculate inner products on faces

    687:   Not Collective

    689:   Input Parameters:
    690: + fem - The `PetscFE` object
    691: - q   - The `PetscQuadrature` object

    693:   Level: intermediate

    695: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`
    696: @*/
    697: PetscErrorCode PetscFESetFaceQuadrature(PetscFE fem, PetscQuadrature q)
    698: {
    699:   PetscInt Nc, qNc;

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

    714: /*@
    715:   PetscFECopyQuadrature - Copy both volumetric and surface quadrature to a new `PetscFE`

    717:   Not Collective

    719:   Input Parameters:
    720: + sfe - The `PetscFE` source for the quadratures
    721: - tfe - The `PetscFE` target for the quadratures

    723:   Level: intermediate

    725: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`, `PetscFECreate()`, `PetscFESetQuadrature()`, `PetscFESetFaceQuadrature()`
    726: @*/
    727: PetscErrorCode PetscFECopyQuadrature(PetscFE sfe, PetscFE tfe)
    728: {
    729:   PetscQuadrature q;

    731:   PetscFunctionBegin;
    734:   PetscCall(PetscFEGetQuadrature(sfe, &q));
    735:   PetscCall(PetscFESetQuadrature(tfe, q));
    736:   PetscCall(PetscFEGetFaceQuadrature(sfe, &q));
    737:   PetscCall(PetscFESetFaceQuadrature(tfe, q));
    738:   PetscFunctionReturn(PETSC_SUCCESS);
    739: }

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

    744:   Not Collective

    746:   Input Parameter:
    747: . fem - The `PetscFE` object

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

    752:   Level: intermediate

    754: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscFECreate()`
    755: @*/
    756: PetscErrorCode PetscFEGetNumDof(PetscFE fem, const PetscInt *numDof[])
    757: {
    758:   PetscFunctionBegin;
    760:   PetscAssertPointer(numDof, 2);
    761:   PetscCall(PetscDualSpaceGetNumDof(fem->dualSpace, numDof));
    762:   PetscFunctionReturn(PETSC_SUCCESS);
    763: }

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

    768:   Not Collective

    770:   Input Parameters:
    771: + fem - The `PetscFE` object
    772: - k   - The highest derivative we need to tabulate, very often 1

    774:   Output Parameter:
    775: . T - The basis function values and derivatives at quadrature points

    777:   Level: intermediate

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

    786: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscTabulation`, `PetscFECreateTabulation()`, `PetscTabulationDestroy()`
    787: @*/
    788: PetscErrorCode PetscFEGetCellTabulation(PetscFE fem, PetscInt k, PetscTabulation *T)
    789: {
    790:   PetscInt         npoints;
    791:   const PetscReal *points;

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

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

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

    827:     PetscCall(DMPlexComputeCellGeometryFEM(dm, faces[f], NULL, v0, J, NULL, &detJ));
    828:     for (PetscInt q = 0; q < Np; ++q) {
    829:       CoordinatesRefToReal(dim, dim - 1, xi0, v0, J, &points[q * (dim - 1)], &facePoints[(f * Np + q) * dim]);
    830:       for (PetscInt c = 0; c < Nc; ++c) faceWeights[(f * Np + q) * Nc + c] = weights[q * Nc + c];
    831:     }
    832:   }
    833:   PetscCall(PetscQuadratureCreate(PetscObjectComm((PetscObject)fq), efq));
    834:   PetscCall(PetscQuadratureGetCellType(fq, &ct));
    835:   PetscCall(PetscQuadratureSetCellType(*efq, ct));
    836:   PetscCall(PetscQuadratureGetOrder(fq, &order));
    837:   PetscCall(PetscQuadratureSetOrder(*efq, order));
    838:   PetscCall(PetscQuadratureSetData(*efq, dim, Nc, Nf * Np, facePoints, faceWeights));
    839:   PetscFunctionReturn(PETSC_SUCCESS);
    840: }

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

    845:   Not Collective

    847:   Input Parameters:
    848: + fem - The `PetscFE` object
    849: - k   - The highest derivative we need to tabulate, very often 1

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

    854:   Level: intermediate

    856:   Note:
    857: .vb
    858:   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
    859:   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
    860:   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
    861: .ve

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

    873:     PetscCall(PetscFEGetFaceQuadrature(fem, &fq));
    874:     if (fq) {
    875:       PetscQuadrature  efq;
    876:       const PetscReal *facePoints;
    877:       PetscInt         Np, eNp;

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

    887:         PetscCall(PetscFEGetDualSpace(fem, &sp));
    888:         PetscCall(PetscDualSpaceGetDM(sp, &dm));
    889:         PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
    890:         PetscCall(DMPlexGetConeSize(dm, cStart, &Nf));
    891:         PetscCheck(Nf == eNp / Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of faces %" PetscInt_FMT " != %" PetscInt_FMT " number of quadrature replicas", Nf, eNp / Np);
    892:       }
    893:       PetscCall(PetscFECreateTabulation(fem, eNp / Np, Np, facePoints, k, &fem->Tf));
    894:       PetscCall(PetscQuadratureDestroy(&efq));
    895:     }
    896:   }
    897:   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);
    898:   *Tf = fem->Tf;
    899:   PetscFunctionReturn(PETSC_SUCCESS);
    900: }

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

    905:   Not Collective

    907:   Input Parameter:
    908: . fem - The `PetscFE` object

    910:   Output Parameter:
    911: . Tc - The basis function values at face centroid points

    913:   Level: intermediate

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

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

    934:     PetscCall(PetscFEGetDualSpace(fem, &sp));
    935:     PetscCall(PetscDualSpaceGetDM(sp, &dm));
    936:     PetscCall(DMGetDimension(dm, &dim));
    937:     PetscCall(DMPlexGetConeSize(dm, 0, &numFaces));
    938:     PetscCall(DMPlexGetCone(dm, 0, &cone));
    939:     PetscCall(PetscMalloc1(numFaces * dim, &centroids));
    940:     for (f = 0; f < numFaces; ++f) PetscCall(DMPlexComputeCellGeometryFVM(dm, cone[f], NULL, &centroids[f * dim], NULL));
    941:     PetscCall(PetscFECreateTabulation(fem, 1, numFaces, centroids, 0, &fem->Tc));
    942:     PetscCall(PetscFree(centroids));
    943:   }
    944:   *Tc = fem->Tc;
    945:   PetscFunctionReturn(PETSC_SUCCESS);
    946: }

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

    951:   Not Collective

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

    960:   Output Parameter:
    961: . T - The basis function values and derivatives at tabulation points

    963:   Level: intermediate

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

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

    984:   PetscFunctionBegin;
    985:   if (!npoints || !fem->dualSpace || K < 0) {
    986:     *T = NULL;
    987:     PetscFunctionReturn(PETSC_SUCCESS);
    988:   }
    990:   PetscAssertPointer(points, 4);
    991:   PetscAssertPointer(T, 6);
    992:   PetscCall(PetscFEGetDualSpace(fem, &Q));
    993:   PetscCall(PetscDualSpaceGetDM(Q, &dm));
    994:   PetscCall(DMGetDimension(dm, &cdim));
    995:   PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
    996:   PetscCall(PetscFEGetNumComponents(fem, &Nc));
    997:   PetscCall(PetscMalloc1(1, T));
    998:   (*T)->K    = !cdim ? 0 : K;
    999:   (*T)->Nr   = nrepl;
    1000:   (*T)->Np   = npoints;
    1001:   (*T)->Nb   = Nb;
    1002:   (*T)->Nc   = Nc;
    1003:   (*T)->cdim = cdim;
    1004:   PetscCall(PetscMalloc1((*T)->K + 1, &(*T)->T));
    1005:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscCalloc1(nrepl * npoints * Nb * Nc * PetscPowInt(cdim, k), &(*T)->T[k]));
    1006:   PetscUseTypeMethod(fem, computetabulation, nrepl * npoints, points, K, *T);
    1007:   PetscFunctionReturn(PETSC_SUCCESS);
    1008: }

    1010: /*@C
    1011:   PetscFEComputeTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided.

    1013:   Not Collective

    1015:   Input Parameters:
    1016: + fem     - The `PetscFE` object
    1017: . npoints - The number of tabulation points
    1018: . points  - The tabulation point coordinates
    1019: . K       - The number of derivatives calculated
    1020: - T       - An existing tabulation object with enough allocated space

    1022:   Output Parameter:
    1023: . T - The basis function values and derivatives at tabulation points

    1025:   Level: intermediate

    1027:   Note:
    1028: .vb
    1029:   T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    1030:   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
    1031:   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
    1032: .ve

    1034: .seealso: `PetscTabulation`, `PetscFEGetCellTabulation()`, `PetscTabulationDestroy()`
    1035: @*/
    1036: PetscErrorCode PetscFEComputeTabulation(PetscFE fem, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation T)
    1037: {
    1038:   PetscFunctionBeginHot;
    1039:   if (!npoints || !fem->dualSpace || K < 0) PetscFunctionReturn(PETSC_SUCCESS);
    1041:   PetscAssertPointer(points, 3);
    1042:   PetscAssertPointer(T, 5);
    1043:   if (PetscDefined(USE_DEBUG)) {
    1044:     DM             dm;
    1045:     PetscDualSpace Q;
    1046:     PetscInt       Nb;   /* Dimension of FE space P */
    1047:     PetscInt       Nc;   /* Field components */
    1048:     PetscInt       cdim; /* Reference coordinate dimension */

    1050:     PetscCall(PetscFEGetDualSpace(fem, &Q));
    1051:     PetscCall(PetscDualSpaceGetDM(Q, &dm));
    1052:     PetscCall(DMGetDimension(dm, &cdim));
    1053:     PetscCall(PetscDualSpaceGetDimension(Q, &Nb));
    1054:     PetscCall(PetscFEGetNumComponents(fem, &Nc));
    1055:     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);
    1056:     PetscCheck(T->Nb == Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nb %" PetscInt_FMT " must match requested Nb %" PetscInt_FMT, T->Nb, Nb);
    1057:     PetscCheck(T->Nc == Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation Nc %" PetscInt_FMT " must match requested Nc %" PetscInt_FMT, T->Nc, Nc);
    1058:     PetscCheck(T->cdim == cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Tabulation cdim %" PetscInt_FMT " must match requested cdim %" PetscInt_FMT, T->cdim, cdim);
    1059:   }
    1060:   T->Nr = 1;
    1061:   T->Np = npoints;
    1062:   PetscUseTypeMethod(fem, computetabulation, npoints, points, K, T);
    1063:   PetscFunctionReturn(PETSC_SUCCESS);
    1064: }

    1066: /*@
    1067:   PetscTabulationDestroy - Frees memory from the associated tabulation.

    1069:   Not Collective

    1071:   Input Parameter:
    1072: . T - The tabulation

    1074:   Level: intermediate

    1076: .seealso: `PetscTabulation`, `PetscFECreateTabulation()`, `PetscFEGetCellTabulation()`
    1077: @*/
    1078: PetscErrorCode PetscTabulationDestroy(PetscTabulation *T)
    1079: {
    1080:   PetscInt k;

    1082:   PetscFunctionBegin;
    1083:   PetscAssertPointer(T, 1);
    1084:   if (!T || !*T) PetscFunctionReturn(PETSC_SUCCESS);
    1085:   for (k = 0; k <= (*T)->K; ++k) PetscCall(PetscFree((*T)->T[k]));
    1086:   PetscCall(PetscFree((*T)->T));
    1087:   PetscCall(PetscFree(*T));
    1088:   *T = NULL;
    1089:   PetscFunctionReturn(PETSC_SUCCESS);
    1090: }

    1092: static PetscErrorCode PetscFECreatePointTraceDefault_Internal(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
    1093: {
    1094:   PetscSpace      bsp, bsubsp;
    1095:   PetscDualSpace  dsp, dsubsp;
    1096:   PetscInt        dim, depth, numComp, i, j, coneSize, order;
    1097:   DM              dm;
    1098:   DMLabel         label;
    1099:   PetscReal      *xi, *v, *J, detJ;
    1100:   const char     *name;
    1101:   PetscQuadrature origin, fullQuad, subQuad;

    1103:   PetscFunctionBegin;
    1104:   PetscCall(PetscFEGetBasisSpace(fe, &bsp));
    1105:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    1106:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    1107:   PetscCall(DMGetDimension(dm, &dim));
    1108:   PetscCall(DMPlexGetDepthLabel(dm, &label));
    1109:   PetscCall(DMLabelGetValue(label, refPoint, &depth));
    1110:   PetscCall(PetscCalloc1(depth, &xi));
    1111:   PetscCall(PetscMalloc1(dim, &v));
    1112:   PetscCall(PetscMalloc1(dim * dim, &J));
    1113:   for (i = 0; i < depth; i++) xi[i] = 0.;
    1114:   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &origin));
    1115:   PetscCall(PetscQuadratureSetData(origin, depth, 0, 1, xi, NULL));
    1116:   PetscCall(DMPlexComputeCellGeometryFEM(dm, refPoint, origin, v, J, NULL, &detJ));
    1117:   /* CellGeometryFEM computes the expanded Jacobian, we want the true jacobian */
    1118:   for (i = 1; i < dim; i++) {
    1119:     for (j = 0; j < depth; j++) J[i * depth + j] = J[i * dim + j];
    1120:   }
    1121:   PetscCall(PetscQuadratureDestroy(&origin));
    1122:   PetscCall(PetscDualSpaceGetPointSubspace(dsp, refPoint, &dsubsp));
    1123:   PetscCall(PetscSpaceCreateSubspace(bsp, dsubsp, v, J, NULL, NULL, PETSC_OWN_POINTER, &bsubsp));
    1124:   PetscCall(PetscSpaceSetUp(bsubsp));
    1125:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), trFE));
    1126:   PetscCall(PetscFESetType(*trFE, PETSCFEBASIC));
    1127:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    1128:   PetscCall(PetscFESetNumComponents(*trFE, numComp));
    1129:   PetscCall(PetscFESetBasisSpace(*trFE, bsubsp));
    1130:   PetscCall(PetscFESetDualSpace(*trFE, dsubsp));
    1131:   PetscCall(PetscObjectGetName((PetscObject)fe, &name));
    1132:   if (name) PetscCall(PetscFESetName(*trFE, name));
    1133:   PetscCall(PetscFEGetQuadrature(fe, &fullQuad));
    1134:   PetscCall(PetscQuadratureGetOrder(fullQuad, &order));
    1135:   PetscCall(DMPlexGetConeSize(dm, refPoint, &coneSize));
    1136:   if (coneSize == 2 * depth) PetscCall(PetscDTGaussTensorQuadrature(depth, 1, (order + 2) / 2, -1., 1., &subQuad));
    1137:   else PetscCall(PetscDTSimplexQuadrature(depth, order, PETSCDTSIMPLEXQUAD_DEFAULT, &subQuad));
    1138:   PetscCall(PetscFESetQuadrature(*trFE, subQuad));
    1139:   PetscCall(PetscFESetUp(*trFE));
    1140:   PetscCall(PetscQuadratureDestroy(&subQuad));
    1141:   PetscCall(PetscSpaceDestroy(&bsubsp));
    1142:   PetscFunctionReturn(PETSC_SUCCESS);
    1143: }

    1145: PETSC_EXTERN PetscErrorCode PetscFECreatePointTrace(PetscFE fe, PetscInt refPoint, PetscFE *trFE)
    1146: {
    1147:   PetscFunctionBegin;
    1149:   PetscAssertPointer(trFE, 3);
    1150:   if (fe->ops->createpointtrace) PetscUseTypeMethod(fe, createpointtrace, refPoint, trFE);
    1151:   else PetscCall(PetscFECreatePointTraceDefault_Internal(fe, refPoint, trFE));
    1152:   PetscFunctionReturn(PETSC_SUCCESS);
    1153: }

    1155: PetscErrorCode PetscFECreateHeightTrace(PetscFE fe, PetscInt height, PetscFE *trFE)
    1156: {
    1157:   PetscInt       hStart, hEnd;
    1158:   PetscDualSpace dsp;
    1159:   DM             dm;

    1161:   PetscFunctionBegin;
    1163:   PetscAssertPointer(trFE, 3);
    1164:   *trFE = NULL;
    1165:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    1166:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    1167:   PetscCall(DMPlexGetHeightStratum(dm, height, &hStart, &hEnd));
    1168:   if (hEnd <= hStart) PetscFunctionReturn(PETSC_SUCCESS);
    1169:   PetscCall(PetscFECreatePointTrace(fe, hStart, trFE));
    1170:   PetscFunctionReturn(PETSC_SUCCESS);
    1171: }

    1173: /*@
    1174:   PetscFEGetDimension - Get the dimension of the finite element space on a cell

    1176:   Not Collective

    1178:   Input Parameter:
    1179: . fem - The `PetscFE`

    1181:   Output Parameter:
    1182: . dim - The dimension

    1184:   Level: intermediate

    1186: .seealso: `PetscFE`, `PetscFECreate()`, `PetscSpaceGetDimension()`, `PetscDualSpaceGetDimension()`
    1187: @*/
    1188: PetscErrorCode PetscFEGetDimension(PetscFE fem, PetscInt *dim)
    1189: {
    1190:   PetscFunctionBegin;
    1192:   PetscAssertPointer(dim, 2);
    1193:   PetscTryTypeMethod(fem, getdimension, dim);
    1194:   PetscFunctionReturn(PETSC_SUCCESS);
    1195: }

    1197: /*@
    1198:   PetscFEPushforward - Map the reference element function to real space

    1200:   Input Parameters:
    1201: + fe     - The `PetscFE`
    1202: . fegeom - The cell geometry
    1203: . Nv     - The number of function values
    1204: - vals   - The function values

    1206:   Output Parameter:
    1207: . vals - The transformed function values

    1209:   Level: advanced

    1211:   Notes:
    1212:   This just forwards the call onto `PetscDualSpacePushforward()`.

    1214:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1216: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscDualSpacePushforward()`
    1217: @*/
    1218: PetscErrorCode PetscFEPushforward(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1219: {
    1220:   PetscFunctionBeginHot;
    1221:   PetscCall(PetscDualSpacePushforward(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1222:   PetscFunctionReturn(PETSC_SUCCESS);
    1223: }

    1225: /*@
    1226:   PetscFEPushforwardGradient - Map the reference element function gradient to real space

    1228:   Input Parameters:
    1229: + fe     - The `PetscFE`
    1230: . fegeom - The cell geometry
    1231: . Nv     - The number of function gradient values
    1232: - vals   - The function gradient values

    1234:   Output Parameter:
    1235: . vals - The transformed function gradient values

    1237:   Level: advanced

    1239:   Notes:
    1240:   This just forwards the call onto `PetscDualSpacePushforwardGradient()`.

    1242:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1244: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardGradient()`, `PetscDualSpacePushforward()`
    1245: @*/
    1246: PetscErrorCode PetscFEPushforwardGradient(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1247: {
    1248:   PetscFunctionBeginHot;
    1249:   PetscCall(PetscDualSpacePushforwardGradient(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1250:   PetscFunctionReturn(PETSC_SUCCESS);
    1251: }

    1253: /*@
    1254:   PetscFEPushforwardHessian - Map the reference element function Hessian to real space

    1256:   Input Parameters:
    1257: + fe     - The `PetscFE`
    1258: . fegeom - The cell geometry
    1259: . Nv     - The number of function Hessian values
    1260: - vals   - The function Hessian values

    1262:   Output Parameter:
    1263: . vals - The transformed function Hessian values

    1265:   Level: advanced

    1267:   Notes:
    1268:   This just forwards the call onto `PetscDualSpacePushforwardHessian()`.

    1270:   It only handles transformations when the embedding dimension of the geometry in fegeom is the same as the reference dimension.

    1272:   Developer Notes:
    1273:   It is unclear why all these one line convenience routines are desirable

    1275: .seealso: `PetscFE`, `PetscFEGeom`, `PetscDualSpace`, `PetscFEPushforward()`, `PetscDualSpacePushforwardHessian()`, `PetscDualSpacePushforward()`
    1276: @*/
    1277: PetscErrorCode PetscFEPushforwardHessian(PetscFE fe, PetscFEGeom *fegeom, PetscInt Nv, PetscScalar vals[])
    1278: {
    1279:   PetscFunctionBeginHot;
    1280:   PetscCall(PetscDualSpacePushforwardHessian(fe->dualSpace, fegeom, Nv, fe->numComponents, vals));
    1281:   PetscFunctionReturn(PETSC_SUCCESS);
    1282: }

    1284: /*
    1285: Purpose: Compute element vector for chunk of elements

    1287: Input:
    1288:   Sizes:
    1289:      Ne:  number of elements
    1290:      Nf:  number of fields
    1291:      PetscFE
    1292:        dim: spatial dimension
    1293:        Nb:  number of basis functions
    1294:        Nc:  number of field components
    1295:        PetscQuadrature
    1296:          Nq:  number of quadrature points

    1298:   Geometry:
    1299:      PetscFEGeom[Ne] possibly *Nq
    1300:        PetscReal v0s[dim]
    1301:        PetscReal n[dim]
    1302:        PetscReal jacobians[dim*dim]
    1303:        PetscReal jacobianInverses[dim*dim]
    1304:        PetscReal jacobianDeterminants
    1305:   FEM:
    1306:      PetscFE
    1307:        PetscQuadrature
    1308:          PetscReal   quadPoints[Nq*dim]
    1309:          PetscReal   quadWeights[Nq]
    1310:        PetscReal   basis[Nq*Nb*Nc]
    1311:        PetscReal   basisDer[Nq*Nb*Nc*dim]
    1312:      PetscScalar coefficients[Ne*Nb*Nc]
    1313:      PetscScalar elemVec[Ne*Nb*Nc]

    1315:   Problem:
    1316:      PetscInt f: the active field
    1317:      f0, f1

    1319:   Work Space:
    1320:      PetscFE
    1321:        PetscScalar f0[Nq*dim];
    1322:        PetscScalar f1[Nq*dim*dim];
    1323:        PetscScalar u[Nc];
    1324:        PetscScalar gradU[Nc*dim];
    1325:        PetscReal   x[dim];
    1326:        PetscScalar realSpaceDer[dim];

    1328: Purpose: Compute element vector for N_cb batches of elements

    1330: Input:
    1331:   Sizes:
    1332:      N_cb: Number of serial cell batches

    1334:   Geometry:
    1335:      PetscReal v0s[Ne*dim]
    1336:      PetscReal jacobians[Ne*dim*dim]        possibly *Nq
    1337:      PetscReal jacobianInverses[Ne*dim*dim] possibly *Nq
    1338:      PetscReal jacobianDeterminants[Ne]     possibly *Nq
    1339:   FEM:
    1340:      static PetscReal   quadPoints[Nq*dim]
    1341:      static PetscReal   quadWeights[Nq]
    1342:      static PetscReal   basis[Nq*Nb*Nc]
    1343:      static PetscReal   basisDer[Nq*Nb*Nc*dim]
    1344:      PetscScalar coefficients[Ne*Nb*Nc]
    1345:      PetscScalar elemVec[Ne*Nb*Nc]

    1347: ex62.c:
    1348:   PetscErrorCode PetscFEIntegrateResidualBatch(PetscInt Ne, PetscInt numFields, PetscInt field, PetscQuadrature quad[], const PetscScalar coefficients[],
    1349:                                                const PetscReal v0s[], const PetscReal jacobians[], const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[],
    1350:                                                void (*f0_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]),
    1351:                                                void (*f1_func)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]), PetscScalar elemVec[])

    1353: ex52.c:
    1354:   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)
    1355:   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)

    1357: ex52_integrateElement.cu
    1358: __global__ void integrateElementQuadrature(int N_cb, realType *coefficients, realType *jacobianInverses, realType *jacobianDeterminants, realType *elemVec)

    1360: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt Nbl, const PetscScalar coefficients[],
    1361:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
    1362:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

    1364: ex52_integrateElementOpenCL.c:
    1365: PETSC_EXTERN PetscErrorCode IntegrateElementBatchGPU(PetscInt spatial_dim, PetscInt Ne, PetscInt Ncb, PetscInt Nbc, PetscInt N_bl, const PetscScalar coefficients[],
    1366:                                                      const PetscReal jacobianInverses[], const PetscReal jacobianDeterminants[], PetscScalar elemVec[],
    1367:                                                      PetscLogEvent event, PetscInt debug, PetscInt pde_op)

    1369: __kernel void integrateElementQuadrature(int N_cb, __global float *coefficients, __global float *jacobianInverses, __global float *jacobianDeterminants, __global float *elemVec)
    1370: */

    1372: /*@
    1373:   PetscFEIntegrate - 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: . Ne              - The number of elements in the chunk
    1381: . cgeom           - The cell geometry for each cell in the chunk
    1382: . coefficients    - The array of FEM basis coefficients for the elements
    1383: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1384: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

    1386:   Output Parameter:
    1387: . integral - the integral for this field

    1389:   Level: intermediate

    1391:   Developer Notes:
    1392:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

    1394: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrateBd()`
    1395: @*/
    1396: PetscErrorCode PetscFEIntegrate(PetscDS prob, PetscInt field, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscScalar integral[])
    1397: {
    1398:   PetscFE fe;

    1400:   PetscFunctionBegin;
    1402:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    1403:   if (fe->ops->integrate) PetscCall((*fe->ops->integrate)(prob, field, Ne, cgeom, coefficients, probAux, coefficientsAux, integral));
    1404:   PetscFunctionReturn(PETSC_SUCCESS);
    1405: }

    1407: /*@C
    1408:   PetscFEIntegrateBd - Produce the integral for the given field for a chunk of elements by quadrature integration

    1410:   Not Collective

    1412:   Input Parameters:
    1413: + prob            - The `PetscDS` specifying the discretizations and continuum functions
    1414: . field           - The field being integrated
    1415: . obj_func        - The function to be integrated
    1416: . Ne              - The number of elements in the chunk
    1417: . geom            - The face geometry for each face in the chunk
    1418: . coefficients    - The array of FEM basis coefficients for the elements
    1419: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1420: - coefficientsAux - The array of FEM auxiliary basis coefficients for the elements

    1422:   Output Parameter:
    1423: . integral - the integral for this field

    1425:   Level: intermediate

    1427:   Developer Notes:
    1428:   The function name begins with `PetscFE` and yet the first argument is `PetscDS` and it has no `PetscFE` arguments.

    1430: .seealso: `PetscFE`, `PetscDS`, `PetscFEIntegrateResidual()`, `PetscFEIntegrate()`
    1431: @*/
    1432: 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[])
    1433: {
    1434:   PetscFE fe;

    1436:   PetscFunctionBegin;
    1438:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    1439:   if (fe->ops->integratebd) PetscCall((*fe->ops->integratebd)(prob, field, obj_func, Ne, geom, coefficients, probAux, coefficientsAux, integral));
    1440:   PetscFunctionReturn(PETSC_SUCCESS);
    1441: }

    1443: /*@
    1444:   PetscFEIntegrateResidual - Produce the element residual vector for a chunk of elements by quadrature integration

    1446:   Not Collective

    1448:   Input Parameters:
    1449: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1450: . key             - The (label+value, field) being integrated
    1451: . Ne              - The number of elements in the chunk
    1452: . cgeom           - The cell geometry for each cell in the chunk
    1453: . coefficients    - The array of FEM basis coefficients for the elements
    1454: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1455: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1456: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1457: - t               - The time

    1459:   Output Parameter:
    1460: . elemVec - the element residual vectors from each element

    1462:   Level: intermediate

    1464:   Note:
    1465: .vb
    1466:   Loop over batch of elements (e):
    1467:     Loop over quadrature points (q):
    1468:       Make u_q and gradU_q (loops over fields,Nb,Ncomp) and x_q
    1469:       Call f_0 and f_1
    1470:     Loop over element vector entries (f,fc --> i):
    1471:       elemVec[i] += \psi^{fc}_f(q) f0_{fc}(u, \nabla u) + \nabla\psi^{fc}_f(q) \cdot f1_{fc,df}(u, \nabla u)
    1472: .ve

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

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

    1487: /*@
    1488:   PetscFEIntegrateBdResidual - Produce the element residual vector for a chunk of elements by quadrature integration over a boundary

    1490:   Not Collective

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

    1504:   Output Parameter:
    1505: . elemVec - the element residual vectors from each element

    1507:   Level: intermediate

    1509: .seealso: `PetscFEIntegrateResidual()`
    1510: @*/
    1511: 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[])
    1512: {
    1513:   PetscFE fe;

    1515:   PetscFunctionBegin;
    1517:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1518:   if (fe->ops->integratebdresidual) PetscCall((*fe->ops->integratebdresidual)(ds, wf, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1519:   PetscFunctionReturn(PETSC_SUCCESS);
    1520: }

    1522: /*@
    1523:   PetscFEIntegrateHybridResidual - Produce the element residual vector for a chunk of hybrid element faces by quadrature integration

    1525:   Not Collective

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

    1541:   Output Parameter:
    1542: . elemVec - the element residual vectors from each element

    1544:   Level: developer

    1546: .seealso: `PetscFEIntegrateResidual()`
    1547: @*/
    1548: PetscErrorCode PetscFEIntegrateHybridResidual(PetscDS ds, PetscDS dsIn, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscScalar elemVec[])
    1549: {
    1550:   PetscFE fe;

    1552:   PetscFunctionBegin;
    1555:   PetscCall(PetscDSGetDiscretization(ds, key.field, (PetscObject *)&fe));
    1556:   if (fe->ops->integratehybridresidual) PetscCall((*fe->ops->integratehybridresidual)(ds, dsIn, key, s, Ne, fgeom, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, elemVec));
    1557:   PetscFunctionReturn(PETSC_SUCCESS);
    1558: }

    1560: /*@
    1561:   PetscFEIntegrateJacobian - Produce the element Jacobian for a chunk of elements by quadrature integration

    1563:   Not Collective

    1565:   Input Parameters:
    1566: + rds             - The `PetscDS` specifying the row discretizations and continuum functions
    1567: . cds             - The `PetscDS` specifying the column discretizations
    1568: . jtype           - The type of matrix pointwise functions that should be used
    1569: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1570: . Ne              - The number of elements in the chunk
    1571: . cgeom           - The cell geometry for each cell in the chunk
    1572: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1573: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1574: . dsAux           - The `PetscDS` specifying the auxiliary discretizations
    1575: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1576: . t               - The time
    1577: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1579:   Output Parameter:
    1580: . elemMat - the element matrices for the Jacobian from each element

    1582:   Level: intermediate

    1584:   Note:
    1585: .vb
    1586:   Loop over batch of elements (e):
    1587:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1588:       Loop over quadrature points (q):
    1589:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1590:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1591:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1592:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1593:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1594: .ve

    1596: .seealso: `PetscFEIntegrateResidual()`
    1597: @*/
    1598: PetscErrorCode PetscFEIntegrateJacobian(PetscDS rds, PetscDS cds, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS dsAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
    1599: {
    1600:   PetscFE  fe;
    1601:   PetscInt Nf;

    1603:   PetscFunctionBegin;
    1606:   PetscCall(PetscDSGetNumFields(rds, &Nf));
    1607:   PetscCall(PetscDSGetDiscretization(rds, key.field / Nf, (PetscObject *)&fe));
    1608:   if (fe->ops->integratejacobian) PetscCall((*fe->ops->integratejacobian)(rds, cds, jtype, key, Ne, cgeom, coefficients, coefficients_t, dsAux, coefficientsAux, t, u_tshift, elemMat));
    1609:   PetscFunctionReturn(PETSC_SUCCESS);
    1610: }

    1612: /*@
    1613:   PetscFEIntegrateBdJacobian - Produce the boundary element Jacobian for a chunk of elements by quadrature integration

    1615:   Not Collective

    1617:   Input Parameters:
    1618: + ds              - The `PetscDS` specifying the discretizations and continuum functions
    1619: . wf              - The PetscWeakForm holding the pointwise functions
    1620: . jtype           - The type of matrix pointwise functions that should be used
    1621: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1622: . Ne              - The number of elements in the chunk
    1623: . fgeom           - The face geometry for each cell in the chunk
    1624: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1625: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1626: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1627: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1628: . t               - The time
    1629: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1631:   Output Parameter:
    1632: . elemMat - the element matrices for the Jacobian from each element

    1634:   Level: intermediate

    1636:   Note:
    1637: .vb
    1638:   Loop over batch of elements (e):
    1639:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1640:       Loop over quadrature points (q):
    1641:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1642:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1643:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1644:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1645:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1646: .ve

    1648: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
    1649: @*/
    1650: 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[])
    1651: {
    1652:   PetscFE  fe;
    1653:   PetscInt Nf;

    1655:   PetscFunctionBegin;
    1657:   PetscCall(PetscDSGetNumFields(ds, &Nf));
    1658:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
    1659:   if (fe->ops->integratebdjacobian) PetscCall((*fe->ops->integratebdjacobian)(ds, wf, jtype, key, Ne, fgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
    1660:   PetscFunctionReturn(PETSC_SUCCESS);
    1661: }

    1663: /*@
    1664:   PetscFEIntegrateHybridJacobian - Produce the boundary element Jacobian for a chunk of hybrid elements by quadrature integration

    1666:   Not Collective

    1668:   Input Parameters:
    1669: + ds              - The `PetscDS` specifying the discretizations and continuum functions for the output
    1670: . dsIn            - The `PetscDS` specifying the discretizations and continuum functions for the input
    1671: . jtype           - The type of matrix pointwise functions that should be used
    1672: . key             - The (label+value, fieldI*Nf + fieldJ) being integrated
    1673: . s               - The side of the cell being integrated, 0 for negative and 1 for positive
    1674: . Ne              - The number of elements in the chunk
    1675: . fgeom           - The face geometry for each cell in the chunk
    1676: . cgeom           - The cell geometry for each neighbor cell in the chunk
    1677: . coefficients    - The array of FEM basis coefficients for the elements for the Jacobian evaluation point
    1678: . coefficients_t  - The array of FEM basis time derivative coefficients for the elements
    1679: . probAux         - The `PetscDS` specifying the auxiliary discretizations
    1680: . coefficientsAux - The array of FEM auxiliary basis coefficients for the elements
    1681: . t               - The time
    1682: - u_tshift        - A multiplier for the dF/du_t term (as opposed to the dF/du term)

    1684:   Output Parameter:
    1685: . elemMat - the element matrices for the Jacobian from each element

    1687:   Level: developer

    1689:   Note:
    1690: .vb
    1691:   Loop over batch of elements (e):
    1692:     Loop over element matrix entries (f,fc,g,gc --> i,j):
    1693:       Loop over quadrature points (q):
    1694:         Make u_q and gradU_q (loops over fields,Nb,Ncomp)
    1695:           elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
    1696:                        + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1697:                        + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
    1698:                        + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
    1699: .ve

    1701: .seealso: `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`
    1702: @*/
    1703: PetscErrorCode PetscFEIntegrateHybridJacobian(PetscDS ds, PetscDS dsIn, PetscFEJacobianType jtype, PetscFormKey key, PetscInt s, PetscInt Ne, PetscFEGeom *fgeom, PetscFEGeom *cgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
    1704: {
    1705:   PetscFE  fe;
    1706:   PetscInt Nf;

    1708:   PetscFunctionBegin;
    1710:   PetscCall(PetscDSGetNumFields(ds, &Nf));
    1711:   PetscCall(PetscDSGetDiscretization(ds, key.field / Nf, (PetscObject *)&fe));
    1712:   if (fe->ops->integratehybridjacobian) PetscCall((*fe->ops->integratehybridjacobian)(ds, dsIn, jtype, key, s, Ne, fgeom, cgeom, coefficients, coefficients_t, probAux, coefficientsAux, t, u_tshift, elemMat));
    1713:   PetscFunctionReturn(PETSC_SUCCESS);
    1714: }

    1716: /*@
    1717:   PetscFEGetHeightSubspace - Get the subspace of this space for a mesh point of a given height

    1719:   Input Parameters:
    1720: + fe     - The finite element space
    1721: - height - The height of the `DMPLEX` point

    1723:   Output Parameter:
    1724: . subfe - The subspace of this `PetscFE` space

    1726:   Level: advanced

    1728:   Note:
    1729:   For example, if we want the subspace of this space for a face, we would choose height = 1.

    1731: .seealso: `PetscFECreateDefault()`
    1732: @*/
    1733: PetscErrorCode PetscFEGetHeightSubspace(PetscFE fe, PetscInt height, PetscFE *subfe)
    1734: {
    1735:   PetscSpace      P, subP;
    1736:   PetscDualSpace  Q, subQ;
    1737:   PetscQuadrature subq;
    1738:   PetscInt        dim, Nc;

    1740:   PetscFunctionBegin;
    1742:   PetscAssertPointer(subfe, 3);
    1743:   if (height == 0) {
    1744:     *subfe = fe;
    1745:     PetscFunctionReturn(PETSC_SUCCESS);
    1746:   }
    1747:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1748:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1749:   PetscCall(PetscFEGetNumComponents(fe, &Nc));
    1750:   PetscCall(PetscFEGetFaceQuadrature(fe, &subq));
    1751:   PetscCall(PetscDualSpaceGetDimension(Q, &dim));
    1752:   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);
    1753:   if (!fe->subspaces) PetscCall(PetscCalloc1(dim, &fe->subspaces));
    1754:   if (height <= dim) {
    1755:     if (!fe->subspaces[height - 1]) {
    1756:       PetscFE     sub = NULL;
    1757:       const char *name;

    1759:       PetscCall(PetscSpaceGetHeightSubspace(P, height, &subP));
    1760:       PetscCall(PetscDualSpaceGetHeightSubspace(Q, height, &subQ));
    1761:       if (subQ) {
    1762:         PetscCall(PetscObjectReference((PetscObject)subP));
    1763:         PetscCall(PetscObjectReference((PetscObject)subQ));
    1764:         PetscCall(PetscObjectReference((PetscObject)subq));
    1765:         PetscCall(PetscFECreateFromSpaces(subP, subQ, subq, NULL, &sub));
    1766:       }
    1767:       if (sub) {
    1768:         PetscCall(PetscObjectGetName((PetscObject)fe, &name));
    1769:         if (name) PetscCall(PetscFESetName(sub, name));
    1770:       }
    1771:       fe->subspaces[height - 1] = sub;
    1772:     }
    1773:     *subfe = fe->subspaces[height - 1];
    1774:   } else {
    1775:     *subfe = NULL;
    1776:   }
    1777:   PetscFunctionReturn(PETSC_SUCCESS);
    1778: }

    1780: /*@
    1781:   PetscFERefine - Create a "refined" `PetscFE` object that refines the reference cell into
    1782:   smaller copies.

    1784:   Collective

    1786:   Input Parameter:
    1787: . fe - The initial `PetscFE`

    1789:   Output Parameter:
    1790: . feRef - The refined `PetscFE`

    1792:   Level: advanced

    1794:   Notes:
    1795:   This is typically used to generate a preconditioner for a higher order method from a lower order method on a
    1796:   refined mesh having the same number of dofs (but more sparsity). It is also used to create an
    1797:   interpolation between regularly refined meshes.

    1799: .seealso: `PetscFEType`, `PetscFECreate()`, `PetscFESetType()`
    1800: @*/
    1801: PetscErrorCode PetscFERefine(PetscFE fe, PetscFE *feRef)
    1802: {
    1803:   PetscSpace       P, Pref;
    1804:   PetscDualSpace   Q, Qref;
    1805:   DM               K, Kref;
    1806:   PetscQuadrature  q, qref;
    1807:   const PetscReal *v0, *jac;
    1808:   PetscInt         numComp, numSubelements;
    1809:   PetscInt         cStart, cEnd, c;
    1810:   PetscDualSpace  *cellSpaces;

    1812:   PetscFunctionBegin;
    1813:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1814:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1815:   PetscCall(PetscFEGetQuadrature(fe, &q));
    1816:   PetscCall(PetscDualSpaceGetDM(Q, &K));
    1817:   /* Create space */
    1818:   PetscCall(PetscObjectReference((PetscObject)P));
    1819:   Pref = P;
    1820:   /* Create dual space */
    1821:   PetscCall(PetscDualSpaceDuplicate(Q, &Qref));
    1822:   PetscCall(PetscDualSpaceSetType(Qref, PETSCDUALSPACEREFINED));
    1823:   PetscCall(DMRefine(K, PetscObjectComm((PetscObject)fe), &Kref));
    1824:   PetscCall(DMGetCoordinatesLocalSetUp(Kref));
    1825:   PetscCall(PetscDualSpaceSetDM(Qref, Kref));
    1826:   PetscCall(DMPlexGetHeightStratum(Kref, 0, &cStart, &cEnd));
    1827:   PetscCall(PetscMalloc1(cEnd - cStart, &cellSpaces));
    1828:   /* TODO: fix for non-uniform refinement */
    1829:   for (c = 0; c < cEnd - cStart; c++) cellSpaces[c] = Q;
    1830:   PetscCall(PetscDualSpaceRefinedSetCellSpaces(Qref, cellSpaces));
    1831:   PetscCall(PetscFree(cellSpaces));
    1832:   PetscCall(DMDestroy(&Kref));
    1833:   PetscCall(PetscDualSpaceSetUp(Qref));
    1834:   /* Create element */
    1835:   PetscCall(PetscFECreate(PetscObjectComm((PetscObject)fe), feRef));
    1836:   PetscCall(PetscFESetType(*feRef, PETSCFECOMPOSITE));
    1837:   PetscCall(PetscFESetBasisSpace(*feRef, Pref));
    1838:   PetscCall(PetscFESetDualSpace(*feRef, Qref));
    1839:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
    1840:   PetscCall(PetscFESetNumComponents(*feRef, numComp));
    1841:   PetscCall(PetscFESetUp(*feRef));
    1842:   PetscCall(PetscSpaceDestroy(&Pref));
    1843:   PetscCall(PetscDualSpaceDestroy(&Qref));
    1844:   /* Create quadrature */
    1845:   PetscCall(PetscFECompositeGetMapping(*feRef, &numSubelements, &v0, &jac, NULL));
    1846:   PetscCall(PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref));
    1847:   PetscCall(PetscFESetQuadrature(*feRef, qref));
    1848:   PetscCall(PetscQuadratureDestroy(&qref));
    1849:   PetscFunctionReturn(PETSC_SUCCESS);
    1850: }

    1852: static PetscErrorCode PetscFESetDefaultName_Private(PetscFE fe)
    1853: {
    1854:   PetscSpace     P;
    1855:   PetscDualSpace Q;
    1856:   DM             K;
    1857:   DMPolytopeType ct;
    1858:   PetscInt       degree;
    1859:   char           name[64];

    1861:   PetscFunctionBegin;
    1862:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    1863:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
    1864:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    1865:   PetscCall(PetscDualSpaceGetDM(Q, &K));
    1866:   PetscCall(DMPlexGetCellType(K, 0, &ct));
    1867:   switch (ct) {
    1868:   case DM_POLYTOPE_SEGMENT:
    1869:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    1870:   case DM_POLYTOPE_QUADRILATERAL:
    1871:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    1872:   case DM_POLYTOPE_HEXAHEDRON:
    1873:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    1874:     PetscCall(PetscSNPrintf(name, sizeof(name), "Q%" PetscInt_FMT, degree));
    1875:     break;
    1876:   case DM_POLYTOPE_TRIANGLE:
    1877:   case DM_POLYTOPE_TETRAHEDRON:
    1878:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT, degree));
    1879:     break;
    1880:   case DM_POLYTOPE_TRI_PRISM:
    1881:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
    1882:     PetscCall(PetscSNPrintf(name, sizeof(name), "P%" PetscInt_FMT "xQ%" PetscInt_FMT, degree, degree));
    1883:     break;
    1884:   default:
    1885:     PetscCall(PetscSNPrintf(name, sizeof(name), "FE"));
    1886:   }
    1887:   PetscCall(PetscFESetName(fe, name));
    1888:   PetscFunctionReturn(PETSC_SUCCESS);
    1889: }

    1891: /*@
    1892:   PetscFECreateFromSpaces - Create a `PetscFE` from the basis and dual spaces

    1894:   Collective

    1896:   Input Parameters:
    1897: + P  - The basis space
    1898: . Q  - The dual space
    1899: . q  - The cell quadrature
    1900: - fq - The face quadrature

    1902:   Output Parameter:
    1903: . fem - The `PetscFE` object

    1905:   Level: beginner

    1907:   Note:
    1908:   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.

    1910: .seealso: `PetscFE`, `PetscSpace`, `PetscDualSpace`, `PetscQuadrature`,
    1911:           `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    1912: @*/
    1913: PetscErrorCode PetscFECreateFromSpaces(PetscSpace P, PetscDualSpace Q, PetscQuadrature q, PetscQuadrature fq, PetscFE *fem)
    1914: {
    1915:   PetscInt    Nc;
    1916:   PetscInt    p_Ns = -1, p_Nc = -1, q_Ns = -1, q_Nc = -1;
    1917:   PetscBool   p_is_uniform_sum = PETSC_FALSE, p_interleave_basis = PETSC_FALSE, p_interleave_components = PETSC_FALSE;
    1918:   PetscBool   q_is_uniform_sum = PETSC_FALSE, q_interleave_basis = PETSC_FALSE, q_interleave_components = PETSC_FALSE;
    1919:   const char *prefix;

    1921:   PetscFunctionBegin;
    1922:   PetscCall(PetscObjectTypeCompare((PetscObject)P, PETSCSPACESUM, &p_is_uniform_sum));
    1923:   if (p_is_uniform_sum) {
    1924:     PetscSpace subsp_0 = NULL;
    1925:     PetscCall(PetscSpaceSumGetNumSubspaces(P, &p_Ns));
    1926:     PetscCall(PetscSpaceGetNumComponents(P, &p_Nc));
    1927:     PetscCall(PetscSpaceSumGetConcatenate(P, &p_is_uniform_sum));
    1928:     PetscCall(PetscSpaceSumGetInterleave(P, &p_interleave_basis, &p_interleave_components));
    1929:     for (PetscInt s = 0; s < p_Ns; s++) {
    1930:       PetscSpace subsp;

    1932:       PetscCall(PetscSpaceSumGetSubspace(P, s, &subsp));
    1933:       if (!s) {
    1934:         subsp_0 = subsp;
    1935:       } else if (subsp != subsp_0) {
    1936:         p_is_uniform_sum = PETSC_FALSE;
    1937:       }
    1938:     }
    1939:   }
    1940:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &q_is_uniform_sum));
    1941:   if (q_is_uniform_sum) {
    1942:     PetscDualSpace subsp_0 = NULL;
    1943:     PetscCall(PetscDualSpaceSumGetNumSubspaces(Q, &q_Ns));
    1944:     PetscCall(PetscDualSpaceGetNumComponents(Q, &q_Nc));
    1945:     PetscCall(PetscDualSpaceSumGetConcatenate(Q, &q_is_uniform_sum));
    1946:     PetscCall(PetscDualSpaceSumGetInterleave(Q, &q_interleave_basis, &q_interleave_components));
    1947:     for (PetscInt s = 0; s < q_Ns; s++) {
    1948:       PetscDualSpace subsp;

    1950:       PetscCall(PetscDualSpaceSumGetSubspace(Q, s, &subsp));
    1951:       if (!s) {
    1952:         subsp_0 = subsp;
    1953:       } else if (subsp != subsp_0) {
    1954:         q_is_uniform_sum = PETSC_FALSE;
    1955:       }
    1956:     }
    1957:   }
    1958:   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)) {
    1959:     PetscSpace     scalar_space;
    1960:     PetscDualSpace scalar_dspace;
    1961:     PetscFE        scalar_fe;

    1963:     PetscCall(PetscSpaceSumGetSubspace(P, 0, &scalar_space));
    1964:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &scalar_dspace));
    1965:     PetscCall(PetscObjectReference((PetscObject)scalar_space));
    1966:     PetscCall(PetscObjectReference((PetscObject)scalar_dspace));
    1967:     PetscCall(PetscObjectReference((PetscObject)q));
    1968:     PetscCall(PetscObjectReference((PetscObject)fq));
    1969:     PetscCall(PetscFECreateFromSpaces(scalar_space, scalar_dspace, q, fq, &scalar_fe));
    1970:     PetscCall(PetscFECreateVector(scalar_fe, p_Ns, p_interleave_basis, p_interleave_components, fem));
    1971:     PetscCall(PetscFEDestroy(&scalar_fe));
    1972:   } else {
    1973:     PetscCall(PetscFECreate(PetscObjectComm((PetscObject)P), fem));
    1974:     PetscCall(PetscFESetType(*fem, PETSCFEBASIC));
    1975:   }
    1976:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    1977:   PetscCall(PetscFESetNumComponents(*fem, Nc));
    1978:   PetscCall(PetscFESetBasisSpace(*fem, P));
    1979:   PetscCall(PetscFESetDualSpace(*fem, Q));
    1980:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)P, &prefix));
    1981:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*fem, prefix));
    1982:   PetscCall(PetscFESetUp(*fem));
    1983:   PetscCall(PetscSpaceDestroy(&P));
    1984:   PetscCall(PetscDualSpaceDestroy(&Q));
    1985:   PetscCall(PetscFESetQuadrature(*fem, q));
    1986:   PetscCall(PetscFESetFaceQuadrature(*fem, fq));
    1987:   PetscCall(PetscQuadratureDestroy(&q));
    1988:   PetscCall(PetscQuadratureDestroy(&fq));
    1989:   PetscCall(PetscFESetDefaultName_Private(*fem));
    1990:   PetscFunctionReturn(PETSC_SUCCESS);
    1991: }

    1993: static PetscErrorCode PetscFECreate_Internal(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt degree, PetscInt qorder, PetscBool setFromOptions, PetscFE *fem)
    1994: {
    1995:   DM              K;
    1996:   PetscSpace      P;
    1997:   PetscDualSpace  Q;
    1998:   PetscQuadrature q, fq;
    1999:   PetscBool       tensor;

    2001:   PetscFunctionBegin;
    2002:   if (prefix) PetscAssertPointer(prefix, 5);
    2003:   PetscAssertPointer(fem, 9);
    2004:   switch (ct) {
    2005:   case DM_POLYTOPE_SEGMENT:
    2006:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
    2007:   case DM_POLYTOPE_QUADRILATERAL:
    2008:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
    2009:   case DM_POLYTOPE_HEXAHEDRON:
    2010:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    2011:     tensor = PETSC_TRUE;
    2012:     break;
    2013:   default:
    2014:     tensor = PETSC_FALSE;
    2015:   }
    2016:   /* Create space */
    2017:   PetscCall(PetscSpaceCreate(comm, &P));
    2018:   PetscCall(PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL));
    2019:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)P, prefix));
    2020:   PetscCall(PetscSpacePolynomialSetTensor(P, tensor));
    2021:   PetscCall(PetscSpaceSetNumComponents(P, Nc));
    2022:   PetscCall(PetscSpaceSetNumVariables(P, dim));
    2023:   if (degree >= 0) {
    2024:     PetscCall(PetscSpaceSetDegree(P, degree, PETSC_DETERMINE));
    2025:     if (ct == DM_POLYTOPE_TRI_PRISM || ct == DM_POLYTOPE_TRI_PRISM_TENSOR) {
    2026:       PetscSpace Pend, Pside;

    2028:       PetscCall(PetscSpaceSetNumComponents(P, 1));
    2029:       PetscCall(PetscSpaceCreate(comm, &Pend));
    2030:       PetscCall(PetscSpaceSetType(Pend, PETSCSPACEPOLYNOMIAL));
    2031:       PetscCall(PetscSpacePolynomialSetTensor(Pend, PETSC_FALSE));
    2032:       PetscCall(PetscSpaceSetNumComponents(Pend, 1));
    2033:       PetscCall(PetscSpaceSetNumVariables(Pend, dim - 1));
    2034:       PetscCall(PetscSpaceSetDegree(Pend, degree, PETSC_DETERMINE));
    2035:       PetscCall(PetscSpaceCreate(comm, &Pside));
    2036:       PetscCall(PetscSpaceSetType(Pside, PETSCSPACEPOLYNOMIAL));
    2037:       PetscCall(PetscSpacePolynomialSetTensor(Pside, PETSC_FALSE));
    2038:       PetscCall(PetscSpaceSetNumComponents(Pside, 1));
    2039:       PetscCall(PetscSpaceSetNumVariables(Pside, 1));
    2040:       PetscCall(PetscSpaceSetDegree(Pside, degree, PETSC_DETERMINE));
    2041:       PetscCall(PetscSpaceSetType(P, PETSCSPACETENSOR));
    2042:       PetscCall(PetscSpaceTensorSetNumSubspaces(P, 2));
    2043:       PetscCall(PetscSpaceTensorSetSubspace(P, 0, Pend));
    2044:       PetscCall(PetscSpaceTensorSetSubspace(P, 1, Pside));
    2045:       PetscCall(PetscSpaceDestroy(&Pend));
    2046:       PetscCall(PetscSpaceDestroy(&Pside));

    2048:       if (Nc > 1) {
    2049:         PetscSpace scalar_P = P;

    2051:         PetscCall(PetscSpaceCreate(comm, &P));
    2052:         PetscCall(PetscSpaceSetNumVariables(P, dim));
    2053:         PetscCall(PetscSpaceSetNumComponents(P, Nc));
    2054:         PetscCall(PetscSpaceSetType(P, PETSCSPACESUM));
    2055:         PetscCall(PetscSpaceSumSetNumSubspaces(P, Nc));
    2056:         PetscCall(PetscSpaceSumSetConcatenate(P, PETSC_TRUE));
    2057:         PetscCall(PetscSpaceSumSetInterleave(P, PETSC_TRUE, PETSC_FALSE));
    2058:         for (PetscInt i = 0; i < Nc; i++) PetscCall(PetscSpaceSumSetSubspace(P, i, scalar_P));
    2059:         PetscCall(PetscSpaceDestroy(&scalar_P));
    2060:       }
    2061:     }
    2062:   }
    2063:   if (setFromOptions) PetscCall(PetscSpaceSetFromOptions(P));
    2064:   PetscCall(PetscSpaceSetUp(P));
    2065:   PetscCall(PetscSpaceGetDegree(P, &degree, NULL));
    2066:   PetscCall(PetscSpacePolynomialGetTensor(P, &tensor));
    2067:   PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    2068:   /* Create dual space */
    2069:   PetscCall(PetscDualSpaceCreate(comm, &Q));
    2070:   PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
    2071:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)Q, prefix));
    2072:   PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
    2073:   PetscCall(PetscDualSpaceSetDM(Q, K));
    2074:   PetscCall(DMDestroy(&K));
    2075:   PetscCall(PetscDualSpaceSetNumComponents(Q, Nc));
    2076:   PetscCall(PetscDualSpaceSetOrder(Q, degree));
    2077:   PetscCall(PetscDualSpaceLagrangeSetTensor(Q, (tensor || (ct == DM_POLYTOPE_TRI_PRISM)) ? PETSC_TRUE : PETSC_FALSE));
    2078:   if (setFromOptions) PetscCall(PetscDualSpaceSetFromOptions(Q));
    2079:   PetscCall(PetscDualSpaceSetUp(Q));
    2080:   /* Create quadrature */
    2081:   PetscDTSimplexQuadratureType qtype = PETSCDTSIMPLEXQUAD_DEFAULT;

    2083:   qorder = qorder >= 0 ? qorder : degree;
    2084:   if (setFromOptions) {
    2085:     PetscObjectOptionsBegin((PetscObject)P);
    2086:     PetscCall(PetscOptionsBoundedInt("-petscfe_default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "PetscFECreateDefault", qorder, &qorder, NULL, 0));
    2087:     PetscCall(PetscOptionsEnum("-petscfe_default_quadrature_type", "Simplex quadrature type", "PetscDTSimplexQuadratureType", PetscDTSimplexQuadratureTypes, (PetscEnum)qtype, (PetscEnum *)&qtype, NULL));
    2088:     PetscOptionsEnd();
    2089:   }
    2090:   PetscCall(PetscDTCreateQuadratureByCell(ct, qorder, qtype, &q, &fq));
    2091:   /* Create finite element */
    2092:   PetscCall(PetscFECreateFromSpaces(P, Q, q, fq, fem));
    2093:   if (setFromOptions) PetscCall(PetscFESetFromOptions(*fem));
    2094:   PetscFunctionReturn(PETSC_SUCCESS);
    2095: }

    2097: /*@
    2098:   PetscFECreateDefault - Create a `PetscFE` for basic FEM computation

    2100:   Collective

    2102:   Input Parameters:
    2103: + comm      - The MPI comm
    2104: . dim       - The spatial dimension
    2105: . Nc        - The number of components
    2106: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
    2107: . prefix    - The options prefix, or `NULL`
    2108: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2110:   Output Parameter:
    2111: . fem - The `PetscFE` object

    2113:   Level: beginner

    2115:   Note:
    2116:   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.

    2118: .seealso: `PetscFECreateLagrange()`, `PetscFECreateByCell()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2119: @*/
    2120: PetscErrorCode PetscFECreateDefault(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, const char prefix[], PetscInt qorder, PetscFE *fem)
    2121: {
    2122:   PetscFunctionBegin;
    2123:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
    2124:   PetscFunctionReturn(PETSC_SUCCESS);
    2125: }

    2127: /*@
    2128:   PetscFECreateByCell - Create a `PetscFE` for basic FEM computation

    2130:   Collective

    2132:   Input Parameters:
    2133: + comm   - The MPI comm
    2134: . dim    - The spatial dimension
    2135: . Nc     - The number of components
    2136: . ct     - The celltype of the reference cell
    2137: . prefix - The options prefix, or `NULL`
    2138: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2140:   Output Parameter:
    2141: . fem - The `PetscFE` object

    2143:   Level: beginner

    2145:   Note:
    2146:   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.

    2148: .seealso: `PetscFECreateDefault()`, `PetscFECreateLagrange()`, `PetscSpaceSetFromOptions()`, `PetscDualSpaceSetFromOptions()`, `PetscFESetFromOptions()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2149: @*/
    2150: PetscErrorCode PetscFECreateByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, const char prefix[], PetscInt qorder, PetscFE *fem)
    2151: {
    2152:   PetscFunctionBegin;
    2153:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, prefix, PETSC_DECIDE, qorder, PETSC_TRUE, fem));
    2154:   PetscFunctionReturn(PETSC_SUCCESS);
    2155: }

    2157: /*@
    2158:   PetscFECreateLagrange - Create a `PetscFE` for the basic Lagrange space of degree k

    2160:   Collective

    2162:   Input Parameters:
    2163: + comm      - The MPI comm
    2164: . dim       - The spatial dimension
    2165: . Nc        - The number of components
    2166: . isSimplex - Flag for simplex reference cell, otherwise its a tensor product
    2167: . k         - The degree k of the space
    2168: - qorder    - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2170:   Output Parameter:
    2171: . fem - The `PetscFE` object

    2173:   Level: beginner

    2175:   Note:
    2176:   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.

    2178: .seealso: `PetscFECreateLagrangeByCell()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2179: @*/
    2180: PetscErrorCode PetscFECreateLagrange(MPI_Comm comm, PetscInt dim, PetscInt Nc, PetscBool isSimplex, PetscInt k, PetscInt qorder, PetscFE *fem)
    2181: {
    2182:   PetscFunctionBegin;
    2183:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, DMPolytopeTypeSimpleShape(dim, isSimplex), NULL, k, qorder, PETSC_FALSE, fem));
    2184:   PetscFunctionReturn(PETSC_SUCCESS);
    2185: }

    2187: /*@
    2188:   PetscFECreateLagrangeByCell - Create a `PetscFE` for the basic Lagrange space of degree k

    2190:   Collective

    2192:   Input Parameters:
    2193: + comm   - The MPI comm
    2194: . dim    - The spatial dimension
    2195: . Nc     - The number of components
    2196: . ct     - The celltype of the reference cell
    2197: . k      - The degree k of the space
    2198: - qorder - The quadrature order or `PETSC_DETERMINE` to use `PetscSpace` polynomial degree

    2200:   Output Parameter:
    2201: . fem - The `PetscFE` object

    2203:   Level: beginner

    2205:   Note:
    2206:   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.

    2208: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2209: @*/
    2210: PetscErrorCode PetscFECreateLagrangeByCell(MPI_Comm comm, PetscInt dim, PetscInt Nc, DMPolytopeType ct, PetscInt k, PetscInt qorder, PetscFE *fem)
    2211: {
    2212:   PetscFunctionBegin;
    2213:   PetscCall(PetscFECreate_Internal(comm, dim, Nc, ct, NULL, k, qorder, PETSC_FALSE, fem));
    2214:   PetscFunctionReturn(PETSC_SUCCESS);
    2215: }

    2217: /*@
    2218:   PetscFELimitDegree - Copy a `PetscFE` but limit the degree to be in the given range

    2220:   Collective

    2222:   Input Parameters:
    2223: + fe        - The `PetscFE`
    2224: . minDegree - The minimum degree, or `PETSC_DETERMINE` for no limit
    2225: - maxDegree - The maximum degree, or `PETSC_DETERMINE` for no limit

    2227:   Output Parameter:
    2228: . newfe - The `PetscFE` object

    2230:   Level: advanced

    2232:   Note:
    2233:   This currently only works for Lagrange elements.

    2235: .seealso: `PetscFECreateLagrange()`, `PetscFECreateDefault()`, `PetscFECreateByCell()`, `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2236: @*/
    2237: PetscErrorCode PetscFELimitDegree(PetscFE fe, PetscInt minDegree, PetscInt maxDegree, PetscFE *newfe)
    2238: {
    2239:   PetscDualSpace Q;
    2240:   PetscBool      islag, issum;
    2241:   PetscInt       oldk = 0, k;

    2243:   PetscFunctionBegin;
    2244:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    2245:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &islag));
    2246:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &issum));
    2247:   if (islag) {
    2248:     PetscCall(PetscDualSpaceGetOrder(Q, &oldk));
    2249:   } else if (issum) {
    2250:     PetscDualSpace subQ;

    2252:     PetscCall(PetscDualSpaceSumGetSubspace(Q, 0, &subQ));
    2253:     PetscCall(PetscDualSpaceGetOrder(subQ, &oldk));
    2254:   } else {
    2255:     PetscCall(PetscObjectReference((PetscObject)fe));
    2256:     *newfe = fe;
    2257:     PetscFunctionReturn(PETSC_SUCCESS);
    2258:   }
    2259:   k = oldk;
    2260:   if (minDegree >= 0) k = PetscMax(k, minDegree);
    2261:   if (maxDegree >= 0) k = PetscMin(k, maxDegree);
    2262:   if (k != oldk) {
    2263:     DM              K;
    2264:     PetscSpace      P;
    2265:     PetscQuadrature q;
    2266:     DMPolytopeType  ct;
    2267:     PetscInt        dim, Nc;

    2269:     PetscCall(PetscFEGetBasisSpace(fe, &P));
    2270:     PetscCall(PetscSpaceGetNumVariables(P, &dim));
    2271:     PetscCall(PetscSpaceGetNumComponents(P, &Nc));
    2272:     PetscCall(PetscDualSpaceGetDM(Q, &K));
    2273:     PetscCall(DMPlexGetCellType(K, 0, &ct));
    2274:     PetscCall(PetscFECreateLagrangeByCell(PetscObjectComm((PetscObject)fe), dim, Nc, ct, k, PETSC_DETERMINE, newfe));
    2275:     PetscCall(PetscFEGetQuadrature(fe, &q));
    2276:     PetscCall(PetscFESetQuadrature(*newfe, q));
    2277:   } else {
    2278:     PetscCall(PetscObjectReference((PetscObject)fe));
    2279:     *newfe = fe;
    2280:   }
    2281:   PetscFunctionReturn(PETSC_SUCCESS);
    2282: }

    2284: /*@
    2285:   PetscFECreateBrokenElement - Create a discontinuous version of the input `PetscFE`

    2287:   Collective

    2289:   Input Parameters:
    2290: . cgfe - The continuous `PetscFE` object

    2292:   Output Parameter:
    2293: . dgfe - The discontinuous `PetscFE` object

    2295:   Level: advanced

    2297:   Note:
    2298:   This only works for Lagrange elements.

    2300: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`, `PetscFECreateLagrange()`, `PetscFECreateLagrangeByCell()`, `PetscDualSpaceLagrangeSetContinuity()`
    2301: @*/
    2302: PetscErrorCode PetscFECreateBrokenElement(PetscFE cgfe, PetscFE *dgfe)
    2303: {
    2304:   PetscSpace      P;
    2305:   PetscDualSpace  Q, dgQ;
    2306:   PetscQuadrature q, fq;
    2307:   PetscBool       is_lagrange, is_sum;

    2309:   PetscFunctionBegin;
    2310:   PetscCall(PetscFEGetBasisSpace(cgfe, &P));
    2311:   PetscCall(PetscObjectReference((PetscObject)P));
    2312:   PetscCall(PetscFEGetDualSpace(cgfe, &Q));
    2313:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACELAGRANGE, &is_lagrange));
    2314:   PetscCall(PetscObjectTypeCompare((PetscObject)Q, PETSCDUALSPACESUM, &is_sum));
    2315:   PetscCheck(is_lagrange || is_sum, PETSC_COMM_SELF, PETSC_ERR_SUP, "Can only create broken elements of Lagrange elements");
    2316:   PetscCall(PetscDualSpaceDuplicate(Q, &dgQ));
    2317:   PetscCall(PetscDualSpaceLagrangeSetContinuity(dgQ, PETSC_FALSE));
    2318:   PetscCall(PetscDualSpaceSetUp(dgQ));
    2319:   PetscCall(PetscFEGetQuadrature(cgfe, &q));
    2320:   PetscCall(PetscObjectReference((PetscObject)q));
    2321:   PetscCall(PetscFEGetFaceQuadrature(cgfe, &fq));
    2322:   PetscCall(PetscObjectReference((PetscObject)fq));
    2323:   PetscCall(PetscFECreateFromSpaces(P, dgQ, q, fq, dgfe));
    2324:   PetscFunctionReturn(PETSC_SUCCESS);
    2325: }

    2327: /*@
    2328:   PetscFESetName - Names the `PetscFE` and its subobjects

    2330:   Not Collective

    2332:   Input Parameters:
    2333: + fe   - The `PetscFE`
    2334: - name - The name

    2336:   Level: intermediate

    2338: .seealso: `PetscFECreate()`, `PetscSpaceCreate()`, `PetscDualSpaceCreate()`
    2339: @*/
    2340: PetscErrorCode PetscFESetName(PetscFE fe, const char name[])
    2341: {
    2342:   PetscSpace     P;
    2343:   PetscDualSpace Q;

    2345:   PetscFunctionBegin;
    2346:   PetscCall(PetscFEGetBasisSpace(fe, &P));
    2347:   PetscCall(PetscFEGetDualSpace(fe, &Q));
    2348:   PetscCall(PetscObjectSetName((PetscObject)fe, name));
    2349:   PetscCall(PetscObjectSetName((PetscObject)P, name));
    2350:   PetscCall(PetscObjectSetName((PetscObject)Q, name));
    2351:   PetscFunctionReturn(PETSC_SUCCESS);
    2352: }

    2354: 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[])
    2355: {
    2356:   PetscInt dOffset = 0, fOffset = 0, f, g;

    2358:   for (f = 0; f < Nf; ++f) {
    2359:     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);
    2360:     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);
    2361:     PetscFE          fe;
    2362:     const PetscInt   k       = ds->jetDegree[f];
    2363:     const PetscInt   cdim    = T[f]->cdim;
    2364:     const PetscInt   dE      = fegeom->dimEmbed;
    2365:     const PetscInt   Nq      = T[f]->Np;
    2366:     const PetscInt   Nbf     = T[f]->Nb;
    2367:     const PetscInt   Ncf     = T[f]->Nc;
    2368:     const PetscReal *Bq      = &T[f]->T[0][(r * Nq + q) * Nbf * Ncf];
    2369:     const PetscReal *Dq      = &T[f]->T[1][(r * Nq + q) * Nbf * Ncf * cdim];
    2370:     const PetscReal *Hq      = k > 1 ? &T[f]->T[2][(r * Nq + q) * Nbf * Ncf * cdim * cdim] : NULL;
    2371:     PetscInt         hOffset = 0, b, c, d;

    2373:     PetscCall(PetscDSGetDiscretization(ds, f, (PetscObject *)&fe));
    2374:     for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
    2375:     for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
    2376:     for (b = 0; b < Nbf; ++b) {
    2377:       for (c = 0; c < Ncf; ++c) {
    2378:         const PetscInt cidx = b * Ncf + c;

    2380:         u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
    2381:         for (d = 0; d < cdim; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * cdim + d] * coefficients[dOffset + b];
    2382:       }
    2383:     }
    2384:     if (k > 1) {
    2385:       for (g = 0; g < Nf; ++g) hOffset += T[g]->Nc * dE;
    2386:       for (d = 0; d < dE * dE * Ncf; ++d) u_x[hOffset + fOffset * dE * dE + d] = 0.0;
    2387:       for (b = 0; b < Nbf; ++b) {
    2388:         for (c = 0; c < Ncf; ++c) {
    2389:           const PetscInt cidx = b * Ncf + c;

    2391:           for (d = 0; d < cdim * cdim; ++d) u_x[hOffset + (fOffset + c) * dE * dE + d] += Hq[cidx * cdim * cdim + d] * coefficients[dOffset + b];
    2392:         }
    2393:       }
    2394:       PetscCall(PetscFEPushforwardHessian(fe, fegeom, 1, &u_x[hOffset + fOffset * dE * dE]));
    2395:     }
    2396:     PetscCall(PetscFEPushforward(fe, fegeom, 1, &u[fOffset]));
    2397:     PetscCall(PetscFEPushforwardGradient(fe, fegeom, 1, &u_x[fOffset * dE]));
    2398:     if (u_t) {
    2399:       for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
    2400:       for (b = 0; b < Nbf; ++b) {
    2401:         for (c = 0; c < Ncf; ++c) {
    2402:           const PetscInt cidx = b * Ncf + c;

    2404:           u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
    2405:         }
    2406:       }
    2407:       PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
    2408:     }
    2409:     fOffset += Ncf;
    2410:     dOffset += Nbf;
    2411:   }
    2412:   return PETSC_SUCCESS;
    2413: }

    2415: PetscErrorCode PetscFEEvaluateFieldJets_Hybrid_Internal(PetscDS ds, PetscInt Nf, PetscInt rc, PetscInt qc, PetscTabulation Tab[], const PetscInt rf[], const PetscInt qf[], PetscTabulation Tabf[], PetscFEGeom *fegeom, PetscFEGeom *fegeomNbr, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscScalar u[], PetscScalar u_x[], PetscScalar u_t[])
    2416: {
    2417:   PetscInt dOffset = 0, fOffset = 0, f;

    2419:   /* f is the field number in the DS */
    2420:   for (f = 0; f < Nf; ++f) {
    2421:     PetscBool isCohesive;
    2422:     PetscInt  Ns, s;

    2424:     if (!Tab[f]) continue;
    2425:     PetscCall(PetscDSGetCohesive(ds, f, &isCohesive));
    2426:     Ns = isCohesive ? 1 : 2;
    2427:     {
    2428:       PetscTabulation T   = isCohesive ? Tab[f] : Tabf[f];
    2429:       PetscFE         fe  = (PetscFE)ds->disc[f];
    2430:       const PetscInt  dEt = T->cdim;
    2431:       const PetscInt  dE  = fegeom->dimEmbed;
    2432:       const PetscInt  Nq  = T->Np;
    2433:       const PetscInt  Nbf = T->Nb;
    2434:       const PetscInt  Ncf = T->Nc;

    2436:       for (s = 0; s < Ns; ++s) {
    2437:         const PetscInt   r  = isCohesive ? rc : rf[s];
    2438:         const PetscInt   q  = isCohesive ? qc : qf[s];
    2439:         const PetscReal *Bq = &T->T[0][(r * Nq + q) * Nbf * Ncf];
    2440:         const PetscReal *Dq = &T->T[1][(r * Nq + q) * Nbf * Ncf * dEt];
    2441:         PetscInt         b, c, d;

    2443:         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);
    2444:         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);
    2445:         for (c = 0; c < Ncf; ++c) u[fOffset + c] = 0.0;
    2446:         for (d = 0; d < dE * Ncf; ++d) u_x[fOffset * dE + d] = 0.0;
    2447:         for (b = 0; b < Nbf; ++b) {
    2448:           for (c = 0; c < Ncf; ++c) {
    2449:             const PetscInt cidx = b * Ncf + c;

    2451:             u[fOffset + c] += Bq[cidx] * coefficients[dOffset + b];
    2452:             for (d = 0; d < dEt; ++d) u_x[(fOffset + c) * dE + d] += Dq[cidx * dEt + d] * coefficients[dOffset + b];
    2453:           }
    2454:         }
    2455:         PetscCall(PetscFEPushforward(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u[fOffset]));
    2456:         PetscCall(PetscFEPushforwardGradient(fe, isCohesive ? fegeom : &fegeomNbr[s], 1, &u_x[fOffset * dE]));
    2457:         if (u_t) {
    2458:           for (c = 0; c < Ncf; ++c) u_t[fOffset + c] = 0.0;
    2459:           for (b = 0; b < Nbf; ++b) {
    2460:             for (c = 0; c < Ncf; ++c) {
    2461:               const PetscInt cidx = b * Ncf + c;

    2463:               u_t[fOffset + c] += Bq[cidx] * coefficients_t[dOffset + b];
    2464:             }
    2465:           }
    2466:           PetscCall(PetscFEPushforward(fe, fegeom, 1, &u_t[fOffset]));
    2467:         }
    2468:         fOffset += Ncf;
    2469:         dOffset += Nbf;
    2470:       }
    2471:     }
    2472:   }
    2473:   return PETSC_SUCCESS;
    2474: }

    2476: PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS prob, PetscInt field, PetscInt faceLoc, const PetscScalar coefficients[], PetscScalar u[])
    2477: {
    2478:   PetscFE         fe;
    2479:   PetscTabulation Tc;
    2480:   PetscInt        b, c;

    2482:   if (!prob) return PETSC_SUCCESS;
    2483:   PetscCall(PetscDSGetDiscretization(prob, field, (PetscObject *)&fe));
    2484:   PetscCall(PetscFEGetFaceCentroidTabulation(fe, &Tc));
    2485:   {
    2486:     const PetscReal *faceBasis = Tc->T[0];
    2487:     const PetscInt   Nb        = Tc->Nb;
    2488:     const PetscInt   Nc        = Tc->Nc;

    2490:     for (c = 0; c < Nc; ++c) u[c] = 0.0;
    2491:     for (b = 0; b < Nb; ++b) {
    2492:       for (c = 0; c < Nc; ++c) u[c] += coefficients[b] * faceBasis[(faceLoc * Nb + b) * Nc + c];
    2493:     }
    2494:   }
    2495:   return PETSC_SUCCESS;
    2496: }

    2498: PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscInt e, PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
    2499: {
    2500:   PetscFEGeom      pgeom;
    2501:   const PetscInt   dEt      = T->cdim;
    2502:   const PetscInt   dE       = fegeom->dimEmbed;
    2503:   const PetscInt   Nq       = T->Np;
    2504:   const PetscInt   Nb       = T->Nb;
    2505:   const PetscInt   Nc       = T->Nc;
    2506:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
    2507:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dEt];
    2508:   PetscInt         q, b, c, d;

    2510:   for (q = 0; q < Nq; ++q) {
    2511:     for (b = 0; b < Nb; ++b) {
    2512:       for (c = 0; c < Nc; ++c) {
    2513:         const PetscInt bcidx = b * Nc + c;

    2515:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
    2516:         for (d = 0; d < dEt; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dEt + bcidx * dEt + d];
    2517:         for (d = dEt; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = 0.0;
    2518:       }
    2519:     }
    2520:     PetscCall(PetscFEGeomGetCellPoint(fegeom, e, q, &pgeom));
    2521:     PetscCall(PetscFEPushforward(fe, &pgeom, Nb, tmpBasis));
    2522:     PetscCall(PetscFEPushforwardGradient(fe, &pgeom, Nb, tmpBasisDer));
    2523:     for (b = 0; b < Nb; ++b) {
    2524:       for (c = 0; c < Nc; ++c) {
    2525:         const PetscInt bcidx = b * Nc + c;
    2526:         const PetscInt qcidx = q * Nc + c;

    2528:         elemVec[b] += tmpBasis[bcidx] * f0[qcidx];
    2529:         for (d = 0; d < dE; ++d) elemVec[b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2530:       }
    2531:     }
    2532:   }
    2533:   return PETSC_SUCCESS;
    2534: }

    2536: PetscErrorCode PetscFEUpdateElementVec_Hybrid_Internal(PetscFE fe, PetscTabulation T, PetscInt r, PetscInt side, PetscScalar tmpBasis[], PetscScalar tmpBasisDer[], PetscFEGeom *fegeom, PetscScalar f0[], PetscScalar f1[], PetscScalar elemVec[])
    2537: {
    2538:   const PetscInt   dE       = T->cdim;
    2539:   const PetscInt   Nq       = T->Np;
    2540:   const PetscInt   Nb       = T->Nb;
    2541:   const PetscInt   Nc       = T->Nc;
    2542:   const PetscReal *basis    = &T->T[0][r * Nq * Nb * Nc];
    2543:   const PetscReal *basisDer = &T->T[1][r * Nq * Nb * Nc * dE];

    2545:   for (PetscInt q = 0; q < Nq; ++q) {
    2546:     for (PetscInt b = 0; b < Nb; ++b) {
    2547:       for (PetscInt c = 0; c < Nc; ++c) {
    2548:         const PetscInt bcidx = b * Nc + c;

    2550:         tmpBasis[bcidx] = basis[q * Nb * Nc + bcidx];
    2551:         for (PetscInt d = 0; d < dE; ++d) tmpBasisDer[bcidx * dE + d] = basisDer[q * Nb * Nc * dE + bcidx * dE + d];
    2552:       }
    2553:     }
    2554:     PetscCall(PetscFEPushforward(fe, fegeom, Nb, tmpBasis));
    2555:     // TODO This is currently broken since we do not pull the geometry down to the lower dimension
    2556:     // PetscCall(PetscFEPushforwardGradient(fe, fegeom, Nb, tmpBasisDer));
    2557:     if (side == 2) {
    2558:       // Integrating over whole cohesive cell, so insert for both sides
    2559:       for (PetscInt s = 0; s < 2; ++s) {
    2560:         for (PetscInt b = 0; b < Nb; ++b) {
    2561:           for (PetscInt c = 0; c < Nc; ++c) {
    2562:             const PetscInt bcidx = b * Nc + c;
    2563:             const PetscInt qcidx = (q * 2 + s) * Nc + c;

    2565:             elemVec[Nb * s + b] += tmpBasis[bcidx] * f0[qcidx];
    2566:             for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * s + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2567:           }
    2568:         }
    2569:       }
    2570:     } else {
    2571:       // Integrating over endcaps of cohesive cell, so insert for correct side
    2572:       for (PetscInt b = 0; b < Nb; ++b) {
    2573:         for (PetscInt c = 0; c < Nc; ++c) {
    2574:           const PetscInt bcidx = b * Nc + c;
    2575:           const PetscInt qcidx = q * Nc + c;

    2577:           elemVec[Nb * side + b] += tmpBasis[bcidx] * f0[qcidx];
    2578:           for (PetscInt d = 0; d < dE; ++d) elemVec[Nb * side + b] += tmpBasisDer[bcidx * dE + d] * f1[qcidx * dE + d];
    2579:         }
    2580:       }
    2581:     }
    2582:   }
    2583:   return PETSC_SUCCESS;
    2584: }

    2586: #define petsc_elemmat_kernel_g1(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2587:   do { \
    2588:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2589:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2590:         const PetscScalar *G = g1 + (fc * (_NcJ) + gc) * _dE; \
    2591:         for (PetscInt f = 0; f < (_NbI); ++f) { \
    2592:           const PetscScalar tBIv = tmpBasisI[f * (_NcI) + fc]; \
    2593:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2594:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
    2595:             PetscScalar        s    = 0.0; \
    2596:             for (PetscInt df = 0; df < _dE; ++df) s += G[df] * tBDJ[df]; \
    2597:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBIv; \
    2598:           } \
    2599:         } \
    2600:       } \
    2601:     } \
    2602:   } while (0)

    2604: #define petsc_elemmat_kernel_g2(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2605:   do { \
    2606:     for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2607:       for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2608:         const PetscScalar *G = g2 + (fc * (_NcJ) + gc) * _dE; \
    2609:         for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2610:           const PetscScalar tBJv = tmpBasisJ[g * (_NcJ) + gc]; \
    2611:           for (PetscInt f = 0; f < (_NbI); ++f) { \
    2612:             const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
    2613:             PetscScalar        s    = 0.0; \
    2614:             for (PetscInt df = 0; df < _dE; ++df) s += tBDI[df] * G[df]; \
    2615:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s * tBJv; \
    2616:           } \
    2617:         } \
    2618:       } \
    2619:     } \
    2620:   } while (0)

    2622: #define petsc_elemmat_kernel_g3(_NbI, _NcI, _NbJ, _NcJ, _dE) \
    2623:   do { \
    2624:     for (PetscInt fc = 0; fc < (_NcI); ++fc) { \
    2625:       for (PetscInt gc = 0; gc < (_NcJ); ++gc) { \
    2626:         const PetscScalar *G = g3 + (fc * (_NcJ) + gc) * (_dE) * (_dE); \
    2627:         for (PetscInt f = 0; f < (_NbI); ++f) { \
    2628:           const PetscScalar *tBDI = tmpBasisDerI + (f * (_NcI) + fc) * (_dE); \
    2629:           for (PetscInt g = 0; g < (_NbJ); ++g) { \
    2630:             PetscScalar        s    = 0.0; \
    2631:             const PetscScalar *tBDJ = tmpBasisDerJ + (g * (_NcJ) + gc) * (_dE); \
    2632:             for (PetscInt df = 0; df < (_dE); ++df) { \
    2633:               for (PetscInt dg = 0; dg < (_dE); ++dg) s += tBDI[df] * G[df * (_dE) + dg] * tBDJ[dg]; \
    2634:             } \
    2635:             elemMat[(offsetI + f) * totDim + (offsetJ + g)] += s; \
    2636:           } \
    2637:         } \
    2638:       } \
    2639:     } \
    2640:   } while (0)

    2642: 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[])
    2643: {
    2644:   const PetscInt   cdim      = TI->cdim;
    2645:   const PetscInt   dE        = fegeom->dimEmbed;
    2646:   const PetscInt   NqI       = TI->Np;
    2647:   const PetscInt   NbI       = TI->Nb;
    2648:   const PetscInt   NcI       = TI->Nc;
    2649:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
    2650:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * cdim];
    2651:   const PetscInt   NqJ       = TJ->Np;
    2652:   const PetscInt   NbJ       = TJ->Nb;
    2653:   const PetscInt   NcJ       = TJ->Nc;
    2654:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
    2655:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * cdim];

    2657:   for (PetscInt f = 0; f < NbI; ++f) {
    2658:     for (PetscInt fc = 0; fc < NcI; ++fc) {
    2659:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2661:       tmpBasisI[fidx] = basisI[fidx];
    2662:       for (PetscInt df = 0; df < cdim; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * cdim + df];
    2663:     }
    2664:   }
    2665:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
    2666:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
    2667:   if (feI != feJ) {
    2668:     for (PetscInt g = 0; g < NbJ; ++g) {
    2669:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2670:         const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2672:         tmpBasisJ[gidx] = basisJ[gidx];
    2673:         for (PetscInt dg = 0; dg < cdim; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * cdim + dg];
    2674:       }
    2675:     }
    2676:     PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
    2677:     PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
    2678:   } else {
    2679:     tmpBasisJ    = tmpBasisI;
    2680:     tmpBasisDerJ = tmpBasisDerI;
    2681:   }
    2682:   if (PetscUnlikely(g0)) {
    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 PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

    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) elemMat[fOff] += bI * g0[fc * NcJ + gc] * tmpBasisJ[g * NcJ + gc];
    2694:         }
    2695:       }
    2696:     }
    2697:   }
    2698:   if (PetscUnlikely(g1)) {
    2699: #if 1
    2700:     if (dE == 2) {
    2701:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 2);
    2702:     } else if (dE == 3) {
    2703:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, 3);
    2704:     } else {
    2705:       petsc_elemmat_kernel_g1(NbI, NcI, NbJ, NcJ, dE);
    2706:     }
    2707: #else
    2708:     for (PetscInt f = 0; f < NbI; ++f) {
    2709:       const PetscInt i = offsetI + f; /* Element matrix row */

    2711:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2712:         const PetscScalar bI = tmpBasisI[f * NcI + fc]; /* Test function basis value */

    2714:         for (PetscInt g = 0; g < NbJ; ++g) {
    2715:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2716:           const PetscInt fOff = i * totDim + j;

    2718:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2719:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2721:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += bI * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
    2722:           }
    2723:         }
    2724:       }
    2725:     }
    2726: #endif
    2727:   }
    2728:   if (PetscUnlikely(g2)) {
    2729: #if 1
    2730:     if (dE == 2) {
    2731:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 2);
    2732:     } else if (dE == 3) {
    2733:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, 3);
    2734:     } else {
    2735:       petsc_elemmat_kernel_g2(NbI, NcI, NbJ, NcJ, dE);
    2736:     }
    2737: #else
    2738:     for (PetscInt g = 0; g < NbJ; ++g) {
    2739:       const PetscInt j = offsetJ + g; /* Element matrix column */

    2741:       for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2742:         const PetscScalar bJ = tmpBasisJ[g * NcJ + gc]; /* Trial function basis value */

    2744:         for (PetscInt f = 0; f < NbI; ++f) {
    2745:           const PetscInt i    = offsetI + f; /* Element matrix row */
    2746:           const PetscInt fOff = i * totDim + j;

    2748:           for (PetscInt fc = 0; fc < NcI; ++fc) {
    2749:             const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2751:             for (PetscInt df = 0; df < dE; ++df) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * bJ;
    2752:           }
    2753:         }
    2754:       }
    2755:     }
    2756: #endif
    2757:   }
    2758:   if (PetscUnlikely(g3)) {
    2759: #if 1
    2760:     if (dE == 2) {
    2761:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 2);
    2762:     } else if (dE == 3) {
    2763:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, 3);
    2764:     } else {
    2765:       petsc_elemmat_kernel_g3(NbI, NcI, NbJ, NcJ, dE);
    2766:     }
    2767: #else
    2768:     for (PetscInt f = 0; f < NbI; ++f) {
    2769:       const PetscInt i = offsetI + f; /* Element matrix row */

    2771:       for (PetscInt fc = 0; fc < NcI; ++fc) {
    2772:         const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2774:         for (PetscInt g = 0; g < NbJ; ++g) {
    2775:           const PetscInt j    = offsetJ + g; /* Element matrix column */
    2776:           const PetscInt fOff = i * totDim + j;

    2778:           for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2779:             const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2781:             for (PetscInt df = 0; df < dE; ++df) {
    2782:               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];
    2783:             }
    2784:           }
    2785:         }
    2786:       }
    2787:     }
    2788: #endif
    2789:   }
    2790:   return PETSC_SUCCESS;
    2791: }

    2793: #undef petsc_elemmat_kernel_g1
    2794: #undef petsc_elemmat_kernel_g2
    2795: #undef petsc_elemmat_kernel_g3

    2797: 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[])
    2798: {
    2799:   const PetscInt   dE        = TI->cdim;
    2800:   const PetscInt   NqI       = TI->Np;
    2801:   const PetscInt   NbI       = TI->Nb;
    2802:   const PetscInt   NcI       = TI->Nc;
    2803:   const PetscReal *basisI    = &TI->T[0][(r * NqI + q) * NbI * NcI];
    2804:   const PetscReal *basisDerI = &TI->T[1][(r * NqI + q) * NbI * NcI * dE];
    2805:   const PetscInt   NqJ       = TJ->Np;
    2806:   const PetscInt   NbJ       = TJ->Nb;
    2807:   const PetscInt   NcJ       = TJ->Nc;
    2808:   const PetscReal *basisJ    = &TJ->T[0][(r * NqJ + q) * NbJ * NcJ];
    2809:   const PetscReal *basisDerJ = &TJ->T[1][(r * NqJ + q) * NbJ * NcJ * dE];
    2810:   const PetscInt   so        = isHybridI ? 0 : s;
    2811:   const PetscInt   to        = isHybridJ ? 0 : t;
    2812:   PetscInt         f, fc, g, gc, df, dg;

    2814:   for (f = 0; f < NbI; ++f) {
    2815:     for (fc = 0; fc < NcI; ++fc) {
    2816:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2818:       tmpBasisI[fidx] = basisI[fidx];
    2819:       for (df = 0; df < dE; ++df) tmpBasisDerI[fidx * dE + df] = basisDerI[fidx * dE + df];
    2820:     }
    2821:   }
    2822:   PetscCall(PetscFEPushforward(feI, fegeom, NbI, tmpBasisI));
    2823:   PetscCall(PetscFEPushforwardGradient(feI, fegeom, NbI, tmpBasisDerI));
    2824:   for (g = 0; g < NbJ; ++g) {
    2825:     for (gc = 0; gc < NcJ; ++gc) {
    2826:       const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2828:       tmpBasisJ[gidx] = basisJ[gidx];
    2829:       for (dg = 0; dg < dE; ++dg) tmpBasisDerJ[gidx * dE + dg] = basisDerJ[gidx * dE + dg];
    2830:     }
    2831:   }
    2832:   PetscCall(PetscFEPushforward(feJ, fegeom, NbJ, tmpBasisJ));
    2833:   // TODO This is currently broken since we do not pull the geometry down to the lower dimension
    2834:   // PetscCall(PetscFEPushforwardGradient(feJ, fegeom, NbJ, tmpBasisDerJ));
    2835:   for (f = 0; f < NbI; ++f) {
    2836:     for (fc = 0; fc < NcI; ++fc) {
    2837:       const PetscInt fidx = f * NcI + fc;           /* Test function basis index */
    2838:       const PetscInt i    = offsetI + NbI * so + f; /* Element matrix row */
    2839:       for (g = 0; g < NbJ; ++g) {
    2840:         for (gc = 0; gc < NcJ; ++gc) {
    2841:           const PetscInt gidx = g * NcJ + gc;           /* Trial function basis index */
    2842:           const PetscInt j    = offsetJ + NbJ * to + g; /* Element matrix column */
    2843:           const PetscInt fOff = eOffset + i * totDim + j;

    2845:           elemMat[fOff] += tmpBasisI[fidx] * g0[fc * NcJ + gc] * tmpBasisJ[gidx];
    2846:           for (df = 0; df < dE; ++df) {
    2847:             elemMat[fOff] += tmpBasisI[fidx] * g1[(fc * NcJ + gc) * dE + df] * tmpBasisDerJ[gidx * dE + df];
    2848:             elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g2[(fc * NcJ + gc) * dE + df] * tmpBasisJ[gidx];
    2849:             for (dg = 0; dg < dE; ++dg) elemMat[fOff] += tmpBasisDerI[fidx * dE + df] * g3[((fc * NcJ + gc) * dE + df) * dE + dg] * tmpBasisDerJ[gidx * dE + dg];
    2850:           }
    2851:         }
    2852:       }
    2853:     }
    2854:   }
    2855:   return PETSC_SUCCESS;
    2856: }

    2858: PetscErrorCode PetscFECreateCellGeometry(PetscFE fe, PetscQuadrature quad, PetscFEGeom *cgeom)
    2859: {
    2860:   PetscDualSpace  dsp;
    2861:   DM              dm;
    2862:   PetscQuadrature quadDef;
    2863:   PetscInt        dim, cdim, Nq;

    2865:   PetscFunctionBegin;
    2866:   PetscCall(PetscFEGetDualSpace(fe, &dsp));
    2867:   PetscCall(PetscDualSpaceGetDM(dsp, &dm));
    2868:   PetscCall(DMGetDimension(dm, &dim));
    2869:   PetscCall(DMGetCoordinateDim(dm, &cdim));
    2870:   PetscCall(PetscFEGetQuadrature(fe, &quadDef));
    2871:   quad = quad ? quad : quadDef;
    2872:   PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, NULL, NULL));
    2873:   PetscCall(PetscMalloc1(Nq * cdim, &cgeom->v));
    2874:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->J));
    2875:   PetscCall(PetscMalloc1(Nq * cdim * cdim, &cgeom->invJ));
    2876:   PetscCall(PetscMalloc1(Nq, &cgeom->detJ));
    2877:   cgeom->dim       = dim;
    2878:   cgeom->dimEmbed  = cdim;
    2879:   cgeom->numCells  = 1;
    2880:   cgeom->numPoints = Nq;
    2881:   PetscCall(DMPlexComputeCellGeometryFEM(dm, 0, quad, cgeom->v, cgeom->J, cgeom->invJ, cgeom->detJ));
    2882:   PetscFunctionReturn(PETSC_SUCCESS);
    2883: }

    2885: PetscErrorCode PetscFEDestroyCellGeometry(PetscFE fe, PetscFEGeom *cgeom)
    2886: {
    2887:   PetscFunctionBegin;
    2888:   PetscCall(PetscFree(cgeom->v));
    2889:   PetscCall(PetscFree(cgeom->J));
    2890:   PetscCall(PetscFree(cgeom->invJ));
    2891:   PetscCall(PetscFree(cgeom->detJ));
    2892:   PetscFunctionReturn(PETSC_SUCCESS);
    2893: }

    2895: #if 0
    2896: 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)
    2897: {
    2898:   const PetscInt dE      = dimEmbed;
    2899:   const PetscInt NbI     = TI->Nb;
    2900:   const PetscInt NcI     = TI->Nc;
    2901:   const PetscInt NbJ     = TJ->Nb;
    2902:   const PetscInt NcJ     = TJ->Nc;
    2903:   PetscBool      has_g0  = g0 ? PETSC_TRUE : PETSC_FALSE;
    2904:   PetscBool      has_g1  = g1 ? PETSC_TRUE : PETSC_FALSE;
    2905:   PetscBool      has_g2  = g2 ? PETSC_TRUE : PETSC_FALSE;
    2906:   PetscBool      has_g3  = g3 ? PETSC_TRUE : PETSC_FALSE;
    2907:   PetscInt      *g0_idxs = NULL, *g1_idxs = NULL, *g2_idxs = NULL, *g3_idxs = NULL;
    2908:   PetscInt       g0_i, g1_i, g2_i, g3_i;

    2910:   PetscFunctionBegin;
    2911:   g0_i = g1_i = g2_i = g3_i = 0;
    2912:   if (has_g0)
    2913:     for (PetscInt i = 0; i < NcI * NcJ; i++)
    2914:       if (g0[i]) g0_i += NbI * NbJ;
    2915:   if (has_g1)
    2916:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
    2917:       if (g1[i]) g1_i += NbI * NbJ;
    2918:   if (has_g2)
    2919:     for (PetscInt i = 0; i < NcI * NcJ * dE; i++)
    2920:       if (g2[i]) g2_i += NbI * NbJ;
    2921:   if (has_g3)
    2922:     for (PetscInt i = 0; i < NcI * NcJ * dE * dE; i++)
    2923:       if (g3[i]) g3_i += NbI * NbJ;
    2924:   if (g0_i == NbI * NbJ * NcI * NcJ) g0_i = 0;
    2925:   if (g1_i == NbI * NbJ * NcI * NcJ * dE) g1_i = 0;
    2926:   if (g2_i == NbI * NbJ * NcI * NcJ * dE) g2_i = 0;
    2927:   if (g3_i == NbI * NbJ * NcI * NcJ * dE * dE) g3_i = 0;
    2928:   has_g0 = g0_i ? PETSC_TRUE : PETSC_FALSE;
    2929:   has_g1 = g1_i ? PETSC_TRUE : PETSC_FALSE;
    2930:   has_g2 = g2_i ? PETSC_TRUE : PETSC_FALSE;
    2931:   has_g3 = g3_i ? PETSC_TRUE : PETSC_FALSE;
    2932:   if (has_g0) PetscCall(PetscMalloc1(4 * g0_i, &g0_idxs));
    2933:   if (has_g1) PetscCall(PetscMalloc1(4 * g1_i, &g1_idxs));
    2934:   if (has_g2) PetscCall(PetscMalloc1(4 * g2_i, &g2_idxs));
    2935:   if (has_g3) PetscCall(PetscMalloc1(4 * g3_i, &g3_idxs));
    2936:   g0_i = g1_i = g2_i = g3_i = 0;

    2938:   for (PetscInt f = 0; f < NbI; ++f) {
    2939:     const PetscInt i = offsetI + f; /* Element matrix row */
    2940:     for (PetscInt fc = 0; fc < NcI; ++fc) {
    2941:       const PetscInt fidx = f * NcI + fc; /* Test function basis index */

    2943:       for (PetscInt g = 0; g < NbJ; ++g) {
    2944:         const PetscInt j    = offsetJ + g; /* Element matrix column */
    2945:         const PetscInt fOff = i * totDim + j;
    2946:         for (PetscInt gc = 0; gc < NcJ; ++gc) {
    2947:           const PetscInt gidx = g * NcJ + gc; /* Trial function basis index */

    2949:           if (has_g0) {
    2950:             if (g0[fc * NcJ + gc]) {
    2951:               g0_idxs[4 * g0_i + 0] = fidx;
    2952:               g0_idxs[4 * g0_i + 1] = fc * NcJ + gc;
    2953:               g0_idxs[4 * g0_i + 2] = gidx;
    2954:               g0_idxs[4 * g0_i + 3] = fOff;
    2955:               g0_i++;
    2956:             }
    2957:           }

    2959:           for (PetscInt df = 0; df < dE; ++df) {
    2960:             if (has_g1) {
    2961:               if (g1[(fc * NcJ + gc) * dE + df]) {
    2962:                 g1_idxs[4 * g1_i + 0] = fidx;
    2963:                 g1_idxs[4 * g1_i + 1] = (fc * NcJ + gc) * dE + df;
    2964:                 g1_idxs[4 * g1_i + 2] = gidx * dE + df;
    2965:                 g1_idxs[4 * g1_i + 3] = fOff;
    2966:                 g1_i++;
    2967:               }
    2968:             }
    2969:             if (has_g2) {
    2970:               if (g2[(fc * NcJ + gc) * dE + df]) {
    2971:                 g2_idxs[4 * g2_i + 0] = fidx * dE + df;
    2972:                 g2_idxs[4 * g2_i + 1] = (fc * NcJ + gc) * dE + df;
    2973:                 g2_idxs[4 * g2_i + 2] = gidx;
    2974:                 g2_idxs[4 * g2_i + 3] = fOff;
    2975:                 g2_i++;
    2976:               }
    2977:             }
    2978:             if (has_g3) {
    2979:               for (PetscInt dg = 0; dg < dE; ++dg) {
    2980:                 if (g3[((fc * NcJ + gc) * dE + df) * dE + dg]) {
    2981:                   g3_idxs[4 * g3_i + 0] = fidx * dE + df;
    2982:                   g3_idxs[4 * g3_i + 1] = ((fc * NcJ + gc) * dE + df) * dE + dg;
    2983:                   g3_idxs[4 * g3_i + 2] = gidx * dE + dg;
    2984:                   g3_idxs[4 * g3_i + 3] = fOff;
    2985:                   g3_i++;
    2986:                 }
    2987:               }
    2988:             }
    2989:           }
    2990:         }
    2991:       }
    2992:     }
    2993:   }
    2994:   *n_g0 = g0_i;
    2995:   *n_g1 = g1_i;
    2996:   *n_g2 = g2_i;
    2997:   *n_g3 = g3_i;

    2999:   *g0_idxs_out = g0_idxs;
    3000:   *g1_idxs_out = g1_idxs;
    3001:   *g2_idxs_out = g2_idxs;
    3002:   *g3_idxs_out = g3_idxs;
    3003:   PetscFunctionReturn(PETSC_SUCCESS);
    3004: }

    3006: //example HOW TO USE
    3007:       for (PetscInt i = 0; i < g0_sparse_n; i++) {
    3008:         PetscInt bM = g0_sparse_idxs[4 * i + 0];
    3009:         PetscInt bN = g0_sparse_idxs[4 * i + 1];
    3010:         PetscInt bK = g0_sparse_idxs[4 * i + 2];
    3011:         PetscInt bO = g0_sparse_idxs[4 * i + 3];
    3012:         elemMat[bO] += tmpBasisI[bM] * g0[bN] * tmpBasisJ[bK];
    3013:       }
    3014: #endif