Date: 2022-03-31T04:49:13+00:00

Actual source code: petscfeimpl.h

      1: #if !defined(PETSCFEIMPL_H)
      2: #define PETSCFEIMPL_H

      4: #include <petscfe.h>
      5: #ifdef PETSC_HAVE_LIBCEED
      6: #include <petscfeceed.h>
      7: #endif
      8: #include <petscds.h>
      9: #include <petsc/private/petscimpl.h>
     10: #include <petsc/private/dmpleximpl.h>

     12: PETSC_EXTERN PetscBool PetscSpaceRegisterAllCalled;
     13: PETSC_EXTERN PetscBool PetscDualSpaceRegisterAllCalled;
     14: PETSC_EXTERN PetscBool PetscFERegisterAllCalled;
     15: PETSC_EXTERN PetscErrorCode PetscSpaceRegisterAll(void);
     16: PETSC_EXTERN PetscErrorCode PetscDualSpaceRegisterAll(void);
     17: PETSC_EXTERN PetscErrorCode PetscFERegisterAll(void);

     19: PETSC_EXTERN PetscBool FEcite;
     20: PETSC_EXTERN const char FECitation[];

     22: PETSC_EXTERN PetscLogEvent PETSCDUALSPACE_SetUp;
     23: PETSC_EXTERN PetscLogEvent PETSCFE_SetUp;

     25: typedef struct _PetscSpaceOps *PetscSpaceOps;
     26: struct _PetscSpaceOps {
     27:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,PetscSpace);
     28:   PetscErrorCode (*setup)(PetscSpace);
     29:   PetscErrorCode (*view)(PetscSpace,PetscViewer);
     30:   PetscErrorCode (*destroy)(PetscSpace);

     32:   PetscErrorCode (*getdimension)(PetscSpace,PetscInt*);
     33:   PetscErrorCode (*evaluate)(PetscSpace,PetscInt,const PetscReal*,PetscReal*,PetscReal*,PetscReal*);
     34:   PetscErrorCode (*getheightsubspace)(PetscSpace,PetscInt,PetscSpace *);
     35: };

     37: struct _p_PetscSpace {
     38:   PETSCHEADER(struct _PetscSpaceOps);
     39:   void                   *data;          /* Implementation object */
     40:   PetscInt                degree;        /* The approximation order of the space */
     41:   PetscInt                maxDegree;     /* The containing approximation order of the space */
     42:   PetscInt                Nc;            /* The number of components */
     43:   PetscInt                Nv;            /* The number of variables in the space, e.g. x and y */
     44:   PetscInt                dim;           /* The dimension of the space */
     45:   DM                      dm;            /* Shell to use for temp allocation */
     46: };

     48: typedef struct {
     49:   PetscBool   tensor;      /* Flag for tensor product */
     50:   PetscBool   setupCalled;
     51:   PetscSpace *subspaces;   /* Subspaces for each dimension */
     52: } PetscSpace_Poly;

     54: typedef struct {
     55:   PetscInt    formDegree;
     56:   PetscBool   setupCalled;
     57:   PetscSpace *subspaces;
     58: } PetscSpace_Ptrimmed;

     60: typedef struct {
     61:   PetscSpace *tensspaces;
     62:   PetscInt    numTensSpaces;
     63:   PetscInt    dim;
     64:   PetscBool   uniform;
     65:   PetscBool   setupCalled;
     66:   PetscSpace *heightsubspaces;    /* Height subspaces */
     67: } PetscSpace_Tensor;

     69: typedef struct {
     70:   PetscSpace *sumspaces;
     71:   PetscInt    numSumSpaces;
     72:   PetscBool   uniform;
     73:   PetscBool   concatenate;
     74:   PetscBool   setupCalled;
     75:   PetscSpace *heightsubspaces;    /* Height subspaces */
     76: } PetscSpace_Sum;

     78: typedef struct {
     79:   PetscQuadrature quad;         /* The points defining the space */
     80: } PetscSpace_Point;

     82: typedef struct {
     83:   PetscBool setupCalled;
     84: } PetscSpace_WXY;

     86: typedef struct _PetscDualSpaceOps *PetscDualSpaceOps;
     87: struct _PetscDualSpaceOps {
     88:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,PetscDualSpace);
     89:   PetscErrorCode (*setup)(PetscDualSpace);
     90:   PetscErrorCode (*view)(PetscDualSpace,PetscViewer);
     91:   PetscErrorCode (*destroy)(PetscDualSpace);

     93:   PetscErrorCode (*duplicate)(PetscDualSpace,PetscDualSpace);
     94:   PetscErrorCode (*createheightsubspace)(PetscDualSpace,PetscInt,PetscDualSpace *);
     95:   PetscErrorCode (*createpointsubspace)(PetscDualSpace,PetscInt,PetscDualSpace *);
     96:   PetscErrorCode (*getsymmetries)(PetscDualSpace,const PetscInt****,const PetscScalar****);
     97:   PetscErrorCode (*apply)(PetscDualSpace, PetscInt, PetscReal, PetscFEGeom *, PetscInt, PetscErrorCode (*)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void *, PetscScalar *);
     98:   PetscErrorCode (*applyall)(PetscDualSpace, const PetscScalar *, PetscScalar *);
     99:   PetscErrorCode (*applyint)(PetscDualSpace, const PetscScalar *, PetscScalar *);
    100:   PetscErrorCode (*createalldata)(PetscDualSpace, PetscQuadrature *, Mat *);
    101:   PetscErrorCode (*createintdata)(PetscDualSpace, PetscQuadrature *, Mat *);
    102: };

    104: struct _p_PetscDualSpace {
    105:   PETSCHEADER(struct _PetscDualSpaceOps);
    106:   void            *data;       /* Implementation object */
    107:   DM               dm;         /* The integration region K */
    108:   PetscInt         order;      /* The approximation order of the space */
    109:   PetscInt         Nc;         /* The number of components */
    110:   PetscQuadrature *functional; /* The basis of functionals for this space */
    111:   Mat              allMat;
    112:   PetscQuadrature  allNodes;   /* Collects all quadrature points representing functionals in the basis */
    113:   Vec              allNodeValues;
    114:   Vec              allDofValues;
    115:   Mat              intMat;
    116:   PetscQuadrature  intNodes;   /* Collects all quadrature points representing functionals in the basis in the interior of the cell */
    117:   Vec              intNodeValues;
    118:   Vec              intDofValues;
    119:   PetscInt         spdim;      /* The dual-space dimension */
    120:   PetscInt         spintdim;   /* The dual-space interior dimension */
    121:   PetscInt         k;          /* k-simplex corresponding to the dofs in this basis (we always use the 3D complex right now) */
    122:   PetscBool        uniform;
    123:   PetscBool        setupcalled;
    124:   PetscBool        setfromoptionscalled;
    125:   PetscSection     pointSection;
    126:   PetscDualSpace  *pointSpaces;
    127:   PetscDualSpace  *heightSpaces;
    128:   PetscInt        *numDof;
    129: };

    131: typedef struct _n_Petsc1DNodeFamily *Petsc1DNodeFamily;
    132: typedef struct _n_PetscLagNodeIndices *PetscLagNodeIndices;

    134: PETSC_EXTERN PetscErrorCode PetscLagNodeIndicesGetData_Internal(PetscLagNodeIndices, PetscInt *, PetscInt *, PetscInt *, const PetscInt *[], const PetscReal *[]);
    135: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat);

    137: typedef struct {
    138:   /* these describe the types of dual spaces implemented */
    139:   PetscBool         tensorCell;  /* Flag for tensor product cell */
    140:   PetscBool         tensorSpace; /* Flag for tensor product space of polynomials, as opposed to a space of maximum degree */
    141:   PetscBool         trimmed;     /* Flag for dual space of trimmed polynomial spaces */
    142:   PetscBool         continuous;  /* Flag for a continuous basis, as opposed to discontinuous across element boundaries */

    144:   PetscBool         interiorOnly; /* To make setup faster for tensor elements, only construct interior dofs in recursive calls */

    146:   /* these keep track of symmetries */
    147:   PetscInt       ***symperms;
    148:   PetscScalar    ***symflips;
    149:   PetscInt          numSelfSym;
    150:   PetscInt          selfSymOff;
    151:   PetscBool         symComputed;

    153:   /* these describe different schemes of placing nodes in a simplex, from
    154:    * which are derived all dofs in Lagrange dual spaces */
    155:   PetscDTNodeType   nodeType;
    156:   PetscBool         endNodes;
    157:   PetscReal         nodeExponent;
    158:   PetscInt          numNodeSkip; /* The number of end nodes from the 1D Node family to skip */
    159:   Petsc1DNodeFamily nodeFamily;

    161:   PetscInt          numCopies;

    163:   PetscBool         useMoments;  /* Use moments for functionals */
    164:   PetscInt          momentOrder; /* Order for moment quadrature */

    166:   /* these are ways of indexing nodes in a way that makes
    167:    * the computation of symmetries programmatic */
    168:   PetscLagNodeIndices vertIndices;
    169:   PetscLagNodeIndices intNodeIndices;
    170:   PetscLagNodeIndices allNodeIndices;
    171: } PetscDualSpace_Lag;

    173: typedef struct {
    174:   PetscInt  dim;
    175:   PetscInt *numDof;
    176: } PetscDualSpace_Simple;

    178: typedef struct _PetscFEOps *PetscFEOps;
    179: struct _PetscFEOps {
    180:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,PetscFE);
    181:   PetscErrorCode (*setup)(PetscFE);
    182:   PetscErrorCode (*view)(PetscFE,PetscViewer);
    183:   PetscErrorCode (*destroy)(PetscFE);
    184:   PetscErrorCode (*getdimension)(PetscFE,PetscInt*);
    185:   PetscErrorCode (*createtabulation)(PetscFE,PetscInt,const PetscReal*,PetscInt,PetscTabulation);
    186:   /* Element integration */
    187:   PetscErrorCode (*integrate)(PetscDS, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], PetscDS, const PetscScalar[], PetscScalar[]);
    188:   PetscErrorCode (*integratebd)(PetscDS, PetscInt, PetscBdPointFunc, PetscInt, PetscFEGeom *, const PetscScalar[], PetscDS, const PetscScalar[], PetscScalar[]);
    189:   PetscErrorCode (*integrateresidual)(PetscDS, PetscFormKey, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscScalar[]);
    190:   PetscErrorCode (*integratebdresidual)(PetscDS, PetscWeakForm, PetscFormKey, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscScalar[]);
    191:   PetscErrorCode (*integratehybridresidual)(PetscDS, PetscFormKey, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscScalar[]);
    192:   PetscErrorCode (*integratejacobianaction)(PetscFE, PetscDS, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    193:   PetscErrorCode (*integratejacobian)(PetscDS, PetscFEJacobianType, PetscFormKey, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    194:   PetscErrorCode (*integratebdjacobian)(PetscDS, PetscWeakForm, PetscFormKey, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    195:   PetscErrorCode (*integratehybridjacobian)(PetscDS, PetscFEJacobianType, PetscFormKey, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    196: };

    198: struct _p_PetscFE {
    199:   PETSCHEADER(struct _PetscFEOps);
    200:   void           *data;                  /* Implementation object */
    201:   PetscSpace      basisSpace;            /* The basis space P */
    202:   PetscDualSpace  dualSpace;             /* The dual space P' */
    203:   PetscInt        numComponents;         /* The number of field components */
    204:   PetscQuadrature quadrature;            /* Suitable quadrature on K */
    205:   PetscQuadrature faceQuadrature;        /* Suitable face quadrature on \partial K */
    206:   PetscFE        *subspaces;             /* Subspaces for each dimension */
    207:   PetscReal      *invV;                  /* Change of basis matrix, from prime to nodal basis set */
    208:   PetscTabulation T;                     /* Tabulation of basis and derivatives at quadrature points */
    209:   PetscTabulation Tf;                    /* Tabulation of basis and derivatives at quadrature points on each face */
    210:   PetscTabulation Tc;                    /* Tabulation of basis at face centroids */
    211:   PetscInt        blockSize, numBlocks;  /* Blocks are processed concurrently */
    212:   PetscInt        batchSize, numBatches; /* A batch is made up of blocks, Batches are processed in serial */
    213:   PetscBool       setupcalled;
    214: #ifdef PETSC_HAVE_LIBCEED
    215:   Ceed            ceed;                  /* The LibCEED context, usually set by the DM */
    216:   CeedBasis       ceedBasis;             /* Basis for libCEED matching this element */
    217: #endif
    218: };

    220: typedef struct {
    221:   PetscInt cellType;
    222: } PetscFE_Basic;

    224: #ifdef PETSC_HAVE_OPENCL

    226: #ifdef __APPLE__
    227: #include <OpenCL/cl.h>
    228: #else
    229: #include <CL/cl.h>
    230: #endif

    232: typedef struct {
    233:   cl_platform_id   pf_id;
    234:   cl_device_id     dev_id;
    235:   cl_context       ctx_id;
    236:   cl_command_queue queue_id;
    237:   PetscDataType    realType;
    238:   PetscLogEvent    residualEvent;
    239:   PetscInt         op; /* ANDY: Stand-in for real equation code generation */
    240: } PetscFE_OpenCL;
    241: #endif

    243: typedef struct {
    244:   PetscInt   numSubelements; /* The number of subelements */
    245:   PetscReal *v0;             /* The affine transformation for each subelement */
    246:   PetscReal *jac, *invjac;
    247:   PetscInt  *embedding;      /* Map from subelements dofs to element dofs */
    248: } PetscFE_Composite;

    250: /* Utility functions */
    251: static inline void CoordinatesRefToReal(PetscInt dimReal, PetscInt dimRef, const PetscReal xi0[], const PetscReal v0[], const PetscReal J[], const PetscReal xi[], PetscReal x[])
    252: {
    253:   PetscInt d, e;

    255:   for (d = 0; d < dimReal; ++d) {
    256:     x[d] = v0[d];
    257:     for (e = 0; e < dimRef; ++e) {
    258:       x[d] += J[d*dimReal+e]*(xi[e] - xi0[e]);
    259:     }
    260:   }
    261: }

    263: static inline void CoordinatesRealToRef(PetscInt dimReal, PetscInt dimRef, const PetscReal xi0[], const PetscReal v0[], const PetscReal invJ[], const PetscReal x[], PetscReal xi[])
    264: {
    265:   PetscInt d, e;

    267:   for (d = 0; d < dimRef; ++d) {
    268:     xi[d] = xi0[d];
    269:     for (e = 0; e < dimReal; ++e) {
    270:       xi[d] += invJ[d*dimReal+e]*(x[e] - v0[e]);
    271:     }
    272:   }
    273: }

    275: static inline PetscErrorCode PetscFEInterpolate_Static(PetscFE fe, const PetscScalar x[], PetscFEGeom *fegeom, PetscInt q, PetscScalar interpolant[])
    276: {
    277:   PetscTabulation T;

    280:   PetscFEGetCellTabulation(fe, 0, &T);
    281:   {
    282:     const PetscReal *basis = T->T[0];
    283:     const PetscInt   Nb    = T->Nb;
    284:     const PetscInt   Nc    = T->Nc;
    285:     for (PetscInt fc = 0; fc < Nc; ++fc) {
    286:       interpolant[fc] = 0.0;
    287:       for (PetscInt f = 0; f < Nb; ++f) interpolant[fc] += x[f]*basis[(q*Nb + f)*Nc + fc];
    288:     }
    289:   }
    290:   PetscFEPushforward(fe, fegeom, 1, interpolant);
    291:   return 0;
    292: }

    294: static inline PetscErrorCode PetscFEInterpolateGradient_Static(PetscFE fe, PetscInt k, const PetscScalar x[], PetscFEGeom *fegeom, PetscInt q, PetscScalar interpolant[])
    295: {
    296:   PetscTabulation T;
    297:   PetscInt        fc, f, d;

    300:   PetscFEGetCellTabulation(fe, k, &T);
    301:   {
    302:     const PetscReal *basisDer = T->T[1];
    303:     const PetscReal *basisHes = k > 1 ? T->T[2] : NULL;
    304:     const PetscInt   Nb       = T->Nb;
    305:     const PetscInt   Nc       = T->Nc;
    306:     const PetscInt   cdim     = T->cdim;

    309:     for (fc = 0; fc < Nc; ++fc) {
    310:       for (d = 0; d < cdim; ++d) interpolant[fc*cdim+d] = 0.0;
    311:       for (f = 0; f < Nb; ++f) {
    312:         for (d = 0; d < cdim; ++d) {
    313:           interpolant[fc*cdim+d] += x[f]*basisDer[((q*Nb + f)*Nc + fc)*cdim + d];
    314:         }
    315:       }
    316:     }
    317:     if (k > 1) {
    318:       const PetscInt off = Nc*cdim;

    320:       for (fc = 0; fc < Nc; ++fc) {
    321:         for (d = 0; d < cdim*cdim; ++d) interpolant[off+fc*cdim*cdim+d] = 0.0;
    322:         for (f = 0; f < Nb; ++f) {
    323:           for (d = 0; d < cdim*cdim; ++d) interpolant[off+fc*cdim+d] += x[f]*basisHes[((q*Nb + f)*Nc + fc)*cdim*cdim + d];
    324:         }
    325:       }
    326:     }
    327:   }
    328:   PetscFEPushforwardGradient(fe, fegeom, 1, interpolant);
    329:   return 0;
    330: }

    332: static inline PetscErrorCode PetscFEFreeInterpolateGradient_Static(PetscFE fe, const PetscReal basisDer[], const PetscScalar x[], PetscInt dim, const PetscReal invJ[], const PetscReal n[], PetscInt q, PetscScalar interpolant[])
    333: {
    334:  PetscReal      realSpaceDer[3];
    335:  PetscScalar    compGradient[3];
    336:  PetscInt       Nb, Nc, fc, f=0, d, g;

    339:  PetscFEGetDimension(fe, &Nb);
    340:  PetscFEGetNumComponents(fe, &Nc);

    342:  for (fc = 0; fc < Nc; ++fc) {
    343:    interpolant[fc] = 0.0;
    344:    for (d = 0; d < dim; ++d) compGradient[d] = 0.0;
    345:    for (d = 0; d < dim; ++d) {
    346:       for (d = 0; d < dim; ++d) {
    347:         realSpaceDer[d] = 0.0;
    348:         for (g = 0; g < dim; ++g) {
    349:           realSpaceDer[d] += invJ[g*dim+d]*basisDer[((q*Nb + f)*Nc + fc)*dim + g];
    350:         }
    351:         compGradient[d] += x[f]*realSpaceDer[d];
    352:       }
    353:    }
    354:    if (n) {
    355:      for (d = 0; d < dim; ++d) interpolant[fc] += compGradient[d]*n[d];
    356:    } else {
    357:      for (d = 0; d < dim; ++d) interpolant[d] = compGradient[d];
    358:    }
    359:  }
    360:  return 0;
    361: }

    363: static inline PetscErrorCode PetscFEInterpolateFieldAndGradient_Static(PetscFE fe, PetscInt k, const PetscScalar x[], PetscFEGeom *fegeom, PetscInt q, PetscScalar interpolant[], PetscScalar interpolantGrad[])
    364: {
    365:   PetscTabulation T;
    366:   PetscInt        fc, f, d;

    369:   PetscFEGetCellTabulation(fe, k, &T);
    370:   {
    371:     const PetscReal *basis    = T->T[0];
    372:     const PetscReal *basisDer = T->T[1];
    373:     const PetscReal *basisHes = k > 1 ? T->T[2] : NULL;
    374:     const PetscInt   Nb       = T->Nb;
    375:     const PetscInt   Nc       = T->Nc;
    376:     const PetscInt   cdim     = T->cdim;

    379:     for (fc = 0; fc < Nc; ++fc) {
    380:       interpolant[fc] = 0.0;
    381:       for (d = 0; d < cdim; ++d) interpolantGrad[fc*cdim+d] = 0.0;
    382:       for (f = 0; f < Nb; ++f) {
    383:         interpolant[fc] += x[f]*basis[(q*Nb + f)*Nc + fc];
    384:         for (d = 0; d < cdim; ++d) interpolantGrad[fc*cdim+d] += x[f]*basisDer[((q*Nb + f)*Nc + fc)*cdim + d];
    385:       }
    386:     }
    387:     if (k > 1) {
    388:       const PetscInt off = Nc*cdim;

    390:       for (fc = 0; fc < Nc; ++fc) {
    391:         for (d = 0; d < cdim*cdim; ++d) interpolantGrad[off+fc*cdim*cdim+d] = 0.0;
    392:         for (f = 0; f < Nb; ++f) {
    393:           for (d = 0; d < cdim*cdim; ++d) interpolantGrad[off+fc*cdim+d] += x[f]*basisHes[((q*Nb + f)*Nc + fc)*cdim*cdim + d];
    394:         }
    395:       }
    396:       PetscFEPushforwardHessian(fe, fegeom, 1, &interpolantGrad[off]);
    397:     }
    398:   }
    399:   PetscFEPushforward(fe, fegeom, 1, interpolant);
    400:   PetscFEPushforwardGradient(fe, fegeom, 1, interpolantGrad);
    401:   return 0;
    402: }

    404: PETSC_INTERN PetscErrorCode PetscDualSpaceLatticePointLexicographic_Internal(PetscInt, PetscInt, PetscInt[]);
    405: PETSC_INTERN PetscErrorCode PetscDualSpaceTensorPointLexicographic_Internal(PetscInt, PetscInt, PetscInt[]);

    407: PETSC_INTERN PetscErrorCode PetscDualSpaceSectionCreate_Internal(PetscDualSpace, PetscSection*);
    408: PETSC_INTERN PetscErrorCode PetscDualSpaceSectionSetUp_Internal(PetscDualSpace, PetscSection);
    409: PETSC_INTERN PetscErrorCode PetscDualSpacePushForwardSubspaces_Internal(PetscDualSpace, PetscInt, PetscInt);

    411: PETSC_INTERN PetscErrorCode PetscFEEvaluateFieldJets_Internal(PetscDS, PetscInt, PetscInt, PetscInt, PetscTabulation[], PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscScalar[], PetscScalar[], PetscScalar[]);
    412: PETSC_INTERN PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS, PetscInt, PetscInt, const PetscScalar[], PetscScalar[]);
    413: PETSC_INTERN PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE, PetscTabulation, PetscInt, PetscScalar[], PetscScalar[], PetscInt, PetscFEGeom *, PetscScalar[], PetscScalar[], PetscScalar[]);
    414: PETSC_INTERN PetscErrorCode PetscFEUpdateElementMat_Internal(PetscFE, PetscFE, PetscInt, PetscInt, PetscTabulation, PetscScalar[], PetscScalar[], PetscTabulation, PetscScalar[], PetscScalar[], PetscFEGeom *, const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar[]);

    416: PETSC_INTERN PetscErrorCode PetscFEEvaluateFieldJets_Hybrid_Internal(PetscDS, PetscInt, PetscInt, PetscInt, PetscTabulation[], PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscScalar[], PetscScalar[], PetscScalar[]);
    417: PETSC_INTERN PetscErrorCode PetscFEUpdateElementVec_Hybrid_Internal(PetscFE, PetscTabulation, PetscInt, PetscInt, PetscScalar[], PetscScalar[], PetscFEGeom *, PetscScalar[], PetscScalar[], PetscScalar[]);
    418: PETSC_INTERN PetscErrorCode PetscFEUpdateElementMat_Hybrid_Internal(PetscFE, PetscBool, PetscFE, PetscBool, PetscInt, PetscInt, PetscInt, PetscTabulation, PetscScalar[], PetscScalar[], PetscTabulation, PetscScalar[], PetscScalar[], PetscFEGeom *, const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar[]);

    420: PETSC_EXTERN PetscErrorCode PetscFEGetDimension_Basic(PetscFE, PetscInt *);
    421: PETSC_EXTERN PetscErrorCode PetscFEIntegrateResidual_Basic(PetscDS, PetscFormKey, PetscInt, PetscFEGeom *, const PetscScalar [], const PetscScalar [], PetscDS, const PetscScalar [], PetscReal, PetscScalar []);
    422: PETSC_EXTERN PetscErrorCode PetscFEIntegrateBdResidual_Basic(PetscDS, PetscWeakForm, PetscFormKey, PetscInt, PetscFEGeom *, const PetscScalar [], const PetscScalar [], PetscDS, const PetscScalar [], PetscReal, PetscScalar[]);
    423: PETSC_EXTERN PetscErrorCode PetscFEIntegrateJacobian_Basic(PetscDS, PetscFEJacobianType, PetscFormKey, PetscInt, PetscFEGeom *, const PetscScalar [], const PetscScalar [], PetscDS, const PetscScalar [], PetscReal, PetscReal, PetscScalar []);
    424: #endif