Actual source code: petscfeimpl.h

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

      4: #include <petscfe.h>
      5: #include <petscds.h>
      6: #include <petsc/private/petscimpl.h>
      7: #include <petsc/private/dmpleximpl.h>

      9: PETSC_EXTERN PetscBool PetscSpaceRegisterAllCalled;
     10: PETSC_EXTERN PetscBool PetscDualSpaceRegisterAllCalled;
     11: PETSC_EXTERN PetscBool PetscFERegisterAllCalled;
     12: PETSC_EXTERN PetscErrorCode PetscSpaceRegisterAll(void);
     13: PETSC_EXTERN PetscErrorCode PetscDualSpaceRegisterAll(void);
     14: PETSC_EXTERN PetscErrorCode PetscFERegisterAll(void);

     16: PETSC_EXTERN PetscBool FEcite;
     17: PETSC_EXTERN const char FECitation[];

     19: PETSC_EXTERN PetscLogEvent PETSCDUALSPACE_SetUp;
     20: PETSC_EXTERN PetscLogEvent PETSCFE_SetUp;

     22: typedef struct _PetscSpaceOps *PetscSpaceOps;
     23: struct _PetscSpaceOps {
     24:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,PetscSpace);
     25:   PetscErrorCode (*setup)(PetscSpace);
     26:   PetscErrorCode (*view)(PetscSpace,PetscViewer);
     27:   PetscErrorCode (*destroy)(PetscSpace);

     29:   PetscErrorCode (*getdimension)(PetscSpace,PetscInt*);
     30:   PetscErrorCode (*evaluate)(PetscSpace,PetscInt,const PetscReal*,PetscReal*,PetscReal*,PetscReal*);
     31:   PetscErrorCode (*getheightsubspace)(PetscSpace,PetscInt,PetscSpace *);
     32: };

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

     45: typedef struct {
     46:   PetscBool                symmetric;   /* Use only symmetric polynomials */
     47:   PetscBool                tensor;      /* Flag for tensor product */
     48:   PetscInt                *degrees;     /* Degrees of single variable which we need to compute */
     49:   PetscSpacePolynomialType ptype;       /* Allows us to make the Hdiv and Hcurl spaces */
     50:   PetscBool                setupCalled;
     51:   PetscSpace              *subspaces;   /* Subspaces for each dimension */
     52: } PetscSpace_Poly;

     54: typedef struct {
     55:   PetscSpace *tensspaces;
     56:   PetscInt    numTensSpaces;
     57:   PetscInt    dim;
     58:   PetscBool   uniform;
     59:   PetscBool   setupCalled;
     60:   PetscSpace *heightsubspaces;    /* Height subspaces */
     61: } PetscSpace_Tensor;

     63: typedef struct {
     64:   PetscSpace *sumspaces;
     65:   PetscInt    numSumSpaces;
     66:   PetscBool   concatenate;
     67:   PetscBool   setupCalled;
     68: } PetscSpace_Sum;

     70: typedef struct {
     71:   PetscQuadrature quad;         /* The points defining the space */
     72: } PetscSpace_Point;

     74: typedef struct _PetscDualSpaceOps *PetscDualSpaceOps;
     75: struct _PetscDualSpaceOps {
     76:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,PetscDualSpace);
     77:   PetscErrorCode (*setup)(PetscDualSpace);
     78:   PetscErrorCode (*view)(PetscDualSpace,PetscViewer);
     79:   PetscErrorCode (*destroy)(PetscDualSpace);

     81:   PetscErrorCode (*duplicate)(PetscDualSpace,PetscDualSpace);
     82:   PetscErrorCode (*createheightsubspace)(PetscDualSpace,PetscInt,PetscDualSpace *);
     83:   PetscErrorCode (*createpointsubspace)(PetscDualSpace,PetscInt,PetscDualSpace *);
     84:   PetscErrorCode (*getsymmetries)(PetscDualSpace,const PetscInt****,const PetscScalar****);
     85:   PetscErrorCode (*apply)(PetscDualSpace, PetscInt, PetscReal, PetscFEGeom *, PetscInt, PetscErrorCode (*)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void *, PetscScalar *);
     86:   PetscErrorCode (*applyall)(PetscDualSpace, const PetscScalar *, PetscScalar *);
     87:   PetscErrorCode (*applyint)(PetscDualSpace, const PetscScalar *, PetscScalar *);
     88:   PetscErrorCode (*createalldata)(PetscDualSpace, PetscQuadrature *, Mat *);
     89:   PetscErrorCode (*createintdata)(PetscDualSpace, PetscQuadrature *, Mat *);
     90: };

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

    119: typedef struct _n_Petsc1DNodeFamily *Petsc1DNodeFamily;
    120: typedef struct _n_PetscLagNodeIndices *PetscLagNodeIndices;

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

    125: typedef struct {
    126:   /* these describe the types of dual spaces implemented */
    127:   PetscBool         tensorCell;  /* Flag for tensor product cell */
    128:   PetscBool         tensorSpace; /* Flag for tensor product space of polynomials, as opposed to a space of maximum degree */
    129:   PetscBool         trimmed;     /* Flag for dual space of trimmed polynomial spaces */
    130:   PetscBool         continuous;  /* Flag for a continuous basis, as opposed to discontinuous across element boundaries */

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

    134:   /* these keep track of symmetries */
    135:   PetscInt       ***symperms;
    136:   PetscScalar    ***symflips;
    137:   PetscInt          numSelfSym;
    138:   PetscInt          selfSymOff;
    139:   PetscBool         symComputed;

    141:   /* these describe different schemes of placing nodes in a simplex, from
    142:    * which are derived all dofs in Lagrange dual spaces */
    143:   PetscDTNodeType   nodeType;
    144:   PetscBool         endNodes;
    145:   PetscReal         nodeExponent;
    146:   PetscInt          numNodeSkip; /* The number of end nodes from the 1D Node family to skip */
    147:   Petsc1DNodeFamily nodeFamily;

    149:   PetscInt          numCopies;

    151:   PetscBool         useMoments;  /* Use moments for functionals */
    152:   PetscInt          momentOrder; /* Order for moment quadrature */

    154:   /* these are ways of indexing nodes in a way that makes
    155:    * the computation of symmetries programmatic */
    156:   PetscLagNodeIndices vertIndices;
    157:   PetscLagNodeIndices intNodeIndices;
    158:   PetscLagNodeIndices allNodeIndices;
    159: } PetscDualSpace_Lag;

    161: typedef struct {
    162:   PetscInt  dim;
    163:   PetscInt *numDof;
    164: } PetscDualSpace_Simple;

    166: typedef struct _PetscFEOps *PetscFEOps;
    167: struct _PetscFEOps {
    168:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,PetscFE);
    169:   PetscErrorCode (*setup)(PetscFE);
    170:   PetscErrorCode (*view)(PetscFE,PetscViewer);
    171:   PetscErrorCode (*destroy)(PetscFE);
    172:   PetscErrorCode (*getdimension)(PetscFE,PetscInt*);
    173:   PetscErrorCode (*createtabulation)(PetscFE,PetscInt,const PetscReal*,PetscInt,PetscTabulation);
    174:   /* Element integration */
    175:   PetscErrorCode (*integrate)(PetscDS, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], PetscDS, const PetscScalar[], PetscScalar[]);
    176:   PetscErrorCode (*integratebd)(PetscDS, PetscInt, PetscBdPointFunc, PetscInt, PetscFEGeom *, const PetscScalar[], PetscDS, const PetscScalar[], PetscScalar[]);
    177:   PetscErrorCode (*integrateresidual)(PetscDS, PetscHashFormKey, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscScalar[]);
    178:   PetscErrorCode (*integratebdresidual)(PetscDS, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscScalar[]);
    179:   PetscErrorCode (*integratehybridresidual)(PetscDS, PetscHashFormKey, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscScalar[]);
    180:   PetscErrorCode (*integratejacobianaction)(PetscFE, PetscDS, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    181:   PetscErrorCode (*integratejacobian)(PetscDS, PetscFEJacobianType, PetscHashFormKey, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    182:   PetscErrorCode (*integratebdjacobian)(PetscDS, PetscInt, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    183:   PetscErrorCode (*integratehybridjacobian)(PetscDS, PetscFEJacobianType, PetscInt, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscDS, const PetscScalar[], PetscReal, PetscReal, PetscScalar[]);
    184: };

    186: struct _p_PetscFE {
    187:   PETSCHEADER(struct _PetscFEOps);
    188:   void           *data;                  /* Implementation object */
    189:   PetscSpace      basisSpace;            /* The basis space P */
    190:   PetscDualSpace  dualSpace;             /* The dual space P' */
    191:   PetscInt        numComponents;         /* The number of field components */
    192:   PetscQuadrature quadrature;            /* Suitable quadrature on K */
    193:   PetscQuadrature faceQuadrature;        /* Suitable face quadrature on \partial K */
    194:   PetscFE        *subspaces;             /* Subspaces for each dimension */
    195:   PetscReal      *invV;                  /* Change of basis matrix, from prime to nodal basis set */
    196:   PetscTabulation T;                     /* Tabulation of basis and derivatives at quadrature points */
    197:   PetscTabulation Tf;                    /* Tabulation of basis and derivatives at quadrature points on each face */
    198:   PetscTabulation Tc;                    /* Tabulation of basis at face centroids */
    199:   PetscInt        blockSize, numBlocks;  /* Blocks are processed concurrently */
    200:   PetscInt        batchSize, numBatches; /* A batch is made up of blocks, Batches are processed in serial */
    201:   PetscBool       setupcalled;
    202: };

    204: typedef struct {
    205:   PetscInt cellType;
    206: } PetscFE_Basic;

    208: #ifdef PETSC_HAVE_OPENCL

    210: #ifdef __APPLE__
    211: #include <OpenCL/cl.h>
    212: #else
    213: #include <CL/cl.h>
    214: #endif

    216: typedef struct {
    217:   cl_platform_id   pf_id;
    218:   cl_device_id     dev_id;
    219:   cl_context       ctx_id;
    220:   cl_command_queue queue_id;
    221:   PetscDataType    realType;
    222:   PetscLogEvent    residualEvent;
    223:   PetscInt         op; /* ANDY: Stand-in for real equation code generation */
    224: } PetscFE_OpenCL;
    225: #endif

    227: typedef struct {
    228:   PetscInt   numSubelements; /* The number of subelements */
    229:   PetscReal *v0;             /* The affine transformation for each subelement */
    230:   PetscReal *jac, *invjac;
    231:   PetscInt  *embedding;      /* Map from subelements dofs to element dofs */
    232: } PetscFE_Composite;

    234: /* Utility functions */
    235: PETSC_STATIC_INLINE void CoordinatesRefToReal(PetscInt dimReal, PetscInt dimRef, const PetscReal xi0[], const PetscReal v0[], const PetscReal J[], const PetscReal xi[], PetscReal x[])
    236: {
    237:   PetscInt d, e;

    239:   for (d = 0; d < dimReal; ++d) {
    240:     x[d] = v0[d];
    241:     for (e = 0; e < dimRef; ++e) {
    242:       x[d] += J[d*dimReal+e]*(xi[e] - xi0[e]);
    243:     }
    244:   }
    245: }

    247: PETSC_STATIC_INLINE void CoordinatesRealToRef(PetscInt dimReal, PetscInt dimRef, const PetscReal xi0[], const PetscReal v0[], const PetscReal invJ[], const PetscReal x[], PetscReal xi[])
    248: {
    249:   PetscInt d, e;

    251:   for (d = 0; d < dimRef; ++d) {
    252:     xi[d] = xi0[d];
    253:     for (e = 0; e < dimReal; ++e) {
    254:       xi[d] += invJ[d*dimReal+e]*(x[e] - v0[e]);
    255:     }
    256:   }
    257: }

    259: PETSC_STATIC_INLINE PetscErrorCode PetscFEInterpolate_Static(PetscFE fe, const PetscScalar x[], PetscFEGeom *fegeom, PetscInt q, PetscScalar interpolant[])
    260: {
    261:   PetscTabulation T;
    262:   PetscInt        fc, f;
    263:   PetscErrorCode  ierr;

    266:   PetscFEGetCellTabulation(fe, 0, &T);
    267:   {
    268:     const PetscReal *basis = T->T[0];
    269:     const PetscInt   Nb    = T->Nb;
    270:     const PetscInt   Nc    = T->Nc;
    271:     for (fc = 0; fc < Nc; ++fc) {
    272:       interpolant[fc] = 0.0;
    273:       for (f = 0; f < Nb; ++f) {
    274:         interpolant[fc] += x[f]*basis[(q*Nb + f)*Nc + fc];
    275:       }
    276:     }
    277:   }
    278:   PetscFEPushforward(fe, fegeom, 1, interpolant);
    279:   return(0);
    280: }

    282: PETSC_STATIC_INLINE PetscErrorCode PetscFEInterpolateGradient_Static(PetscFE fe, PetscInt k, const PetscScalar x[], PetscFEGeom *fegeom, PetscInt q, PetscScalar interpolant[])
    283: {
    284:   PetscTabulation T;
    285:   PetscInt        fc, f, d;
    286:   PetscErrorCode  ierr;

    289:   PetscFEGetCellTabulation(fe, k, &T);
    290:   {
    291:     const PetscReal *basisDer = T->T[1];
    292:     const PetscReal *basisHes = k > 1 ? T->T[2] : NULL;
    293:     const PetscInt   Nb       = T->Nb;
    294:     const PetscInt   Nc       = T->Nc;
    295:     const PetscInt   cdim     = T->cdim;

    297:     if (cdim != fegeom->dimEmbed) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Geometry dim %D must match tabulation dim %D", fegeom->dimEmbed, cdim);
    298:     for (fc = 0; fc < Nc; ++fc) {
    299:       for (d = 0; d < cdim; ++d) interpolant[fc*cdim+d] = 0.0;
    300:       for (f = 0; f < Nb; ++f) {
    301:         for (d = 0; d < cdim; ++d) {
    302:           interpolant[fc*cdim+d] += x[f]*basisDer[((q*Nb + f)*Nc + fc)*cdim + d];
    303:         }
    304:       }
    305:     }
    306:     if (k > 1) {
    307:       const PetscInt off = Nc*cdim;

    309:       for (fc = 0; fc < Nc; ++fc) {
    310:         for (d = 0; d < cdim*cdim; ++d) interpolant[off+fc*cdim*cdim+d] = 0.0;
    311:         for (f = 0; f < Nb; ++f) {
    312:           for (d = 0; d < cdim*cdim; ++d) interpolant[off+fc*cdim+d] += x[f]*basisHes[((q*Nb + f)*Nc + fc)*cdim*cdim + d];
    313:         }
    314:       }
    315:     }
    316:   }
    317:   PetscFEPushforwardGradient(fe, fegeom, 1, interpolant);
    318:   return(0);
    319: }

    321: PETSC_STATIC_INLINE PetscErrorCode PetscFEInterpolateFieldAndGradient_Static(PetscFE fe, PetscInt k, const PetscScalar x[], PetscFEGeom *fegeom, PetscInt q, PetscScalar interpolant[], PetscScalar interpolantGrad[])
    322: {
    323:   PetscTabulation T;
    324:   PetscInt        fc, f, d;
    325:   PetscErrorCode  ierr;

    328:   PetscFEGetCellTabulation(fe, k, &T);
    329:   {
    330:     const PetscReal *basis    = T->T[0];
    331:     const PetscReal *basisDer = T->T[1];
    332:     const PetscReal *basisHes = k > 1 ? T->T[2] : NULL;
    333:     const PetscInt   Nb       = T->Nb;
    334:     const PetscInt   Nc       = T->Nc;
    335:     const PetscInt   cdim     = T->cdim;

    337:     if (cdim != fegeom->dimEmbed) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Geometry dim %D must match tabulation dim %D", fegeom->dimEmbed, cdim);
    338:     for (fc = 0; fc < Nc; ++fc) {
    339:       interpolant[fc] = 0.0;
    340:       for (d = 0; d < cdim; ++d) interpolantGrad[fc*cdim+d] = 0.0;
    341:       for (f = 0; f < Nb; ++f) {
    342:         interpolant[fc] += x[f]*basis[(q*Nb + f)*Nc + fc];
    343:         for (d = 0; d < cdim; ++d) interpolantGrad[fc*cdim+d] += x[f]*basisDer[((q*Nb + f)*Nc + fc)*cdim + d];
    344:       }
    345:     }
    346:     if (k > 1) {
    347:       const PetscInt off = Nc*cdim;

    349:       for (fc = 0; fc < Nc; ++fc) {
    350:         for (d = 0; d < cdim*cdim; ++d) interpolantGrad[off+fc*cdim*cdim+d] = 0.0;
    351:         for (f = 0; f < Nb; ++f) {
    352:           for (d = 0; d < cdim*cdim; ++d) interpolantGrad[off+fc*cdim+d] += x[f]*basisHes[((q*Nb + f)*Nc + fc)*cdim*cdim + d];
    353:         }
    354:       }
    355:       PetscFEPushforwardHessian(fe, fegeom, 1, &interpolantGrad[off]);
    356:     }
    357:   }
    358:   PetscFEPushforward(fe, fegeom, 1, interpolant);
    359:   PetscFEPushforwardGradient(fe, fegeom, 1, interpolantGrad);
    360:   return(0);
    361: }

    363: PETSC_INTERN PetscErrorCode PetscDualSpaceLatticePointLexicographic_Internal(PetscInt, PetscInt, PetscInt[]);
    364: PETSC_INTERN PetscErrorCode PetscDualSpaceTensorPointLexicographic_Internal(PetscInt, PetscInt, PetscInt[]);

    366: PETSC_INTERN PetscErrorCode PetscDualSpaceSectionCreate_Internal(PetscDualSpace, PetscSection*);
    367: PETSC_INTERN PetscErrorCode PetscDualSpaceSectionSetUp_Internal(PetscDualSpace, PetscSection);
    368: PETSC_INTERN PetscErrorCode PetscDualSpacePushForwardSubspaces_Internal(PetscDualSpace, PetscInt, PetscInt);

    370: PETSC_INTERN PetscErrorCode PetscFEEvaluateFieldJets_Internal(PetscDS, PetscInt, PetscInt, PetscInt, PetscTabulation[], PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscScalar[], PetscScalar[], PetscScalar[]);
    371: PETSC_INTERN PetscErrorCode PetscFEEvaluateFaceFields_Internal(PetscDS, PetscInt, PetscInt, const PetscScalar[], PetscScalar[]);
    372: PETSC_INTERN PetscErrorCode PetscFEUpdateElementVec_Internal(PetscFE, PetscTabulation, PetscInt, PetscScalar[], PetscScalar[], PetscFEGeom *, PetscScalar[], PetscScalar[], PetscScalar[]);
    373: 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[]);

    375: PETSC_INTERN PetscErrorCode PetscFEEvaluateFieldJets_Hybrid_Internal(PetscDS, PetscInt, PetscInt, PetscInt, PetscTabulation[], PetscFEGeom *, const PetscScalar[], const PetscScalar[], PetscScalar[], PetscScalar[], PetscScalar[]);
    376: PETSC_INTERN PetscErrorCode PetscFEUpdateElementVec_Hybrid_Internal(PetscFE, PetscTabulation, PetscInt, PetscScalar[], PetscScalar[], PetscFEGeom *, PetscScalar[], PetscScalar[], PetscScalar[]);
    377: PETSC_INTERN PetscErrorCode PetscFEUpdateElementMat_Hybrid_Internal(PetscFE, PetscBool, PetscFE, PetscBool, PetscInt, PetscInt, PetscTabulation, PetscScalar[], PetscScalar[], PetscTabulation, PetscScalar[], PetscScalar[], PetscFEGeom *, const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscInt, PetscInt, PetscInt, PetscInt, PetscScalar[]);

    379: PETSC_EXTERN PetscErrorCode PetscFEGetDimension_Basic(PetscFE, PetscInt *);
    380: PETSC_EXTERN PetscErrorCode PetscFEIntegrateResidual_Basic(PetscDS, PetscHashFormKey, PetscInt, PetscFEGeom *, const PetscScalar [], const PetscScalar [], PetscDS, const PetscScalar [], PetscReal, PetscScalar []);
    381: PETSC_EXTERN PetscErrorCode PetscFEIntegrateBdResidual_Basic(PetscDS, PetscInt, PetscInt, PetscFEGeom *, const PetscScalar [], const PetscScalar [], PetscDS, const PetscScalar [], PetscReal, PetscScalar[]);
    382: PETSC_EXTERN PetscErrorCode PetscFEIntegrateJacobian_Basic(PetscDS, PetscFEJacobianType, PetscHashFormKey, PetscInt, PetscFEGeom *, const PetscScalar [], const PetscScalar [], PetscDS, const PetscScalar [], PetscReal, PetscReal, PetscScalar []);
    383: #endif