xref: /petsc/src/dm/impls/plex/plexfem.c (revision c110b1eed3fc6d435822e10a4aa5917ffc8efa18) 
1 #include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 
3 #include <petscfe.h>
4 
5 #undef __FUNCT__
6 #define __FUNCT__ "DMPlexGetScale"
7 PetscErrorCode DMPlexGetScale(DM dm, PetscUnit unit, PetscReal *scale)
8 {
9   DM_Plex *mesh = (DM_Plex*) dm->data;
10 
11   PetscFunctionBegin;
12   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
13   PetscValidPointer(scale, 3);
14   *scale = mesh->scale[unit];
15   PetscFunctionReturn(0);
16 }
17 
18 #undef __FUNCT__
19 #define __FUNCT__ "DMPlexSetScale"
20 PetscErrorCode DMPlexSetScale(DM dm, PetscUnit unit, PetscReal scale)
21 {
22   DM_Plex *mesh = (DM_Plex*) dm->data;
23 
24   PetscFunctionBegin;
25   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
26   mesh->scale[unit] = scale;
27   PetscFunctionReturn(0);
28 }
29 
30 PETSC_STATIC_INLINE PetscInt epsilon(PetscInt i, PetscInt j, PetscInt k)
31 {
32   switch (i) {
33   case 0:
34     switch (j) {
35     case 0: return 0;
36     case 1:
37       switch (k) {
38       case 0: return 0;
39       case 1: return 0;
40       case 2: return 1;
41       }
42     case 2:
43       switch (k) {
44       case 0: return 0;
45       case 1: return -1;
46       case 2: return 0;
47       }
48     }
49   case 1:
50     switch (j) {
51     case 0:
52       switch (k) {
53       case 0: return 0;
54       case 1: return 0;
55       case 2: return -1;
56       }
57     case 1: return 0;
58     case 2:
59       switch (k) {
60       case 0: return 1;
61       case 1: return 0;
62       case 2: return 0;
63       }
64     }
65   case 2:
66     switch (j) {
67     case 0:
68       switch (k) {
69       case 0: return 0;
70       case 1: return 1;
71       case 2: return 0;
72       }
73     case 1:
74       switch (k) {
75       case 0: return -1;
76       case 1: return 0;
77       case 2: return 0;
78       }
79     case 2: return 0;
80     }
81   }
82   return 0;
83 }
84 
85 #undef __FUNCT__
86 #define __FUNCT__ "DMPlexCreateRigidBody"
87 /*@C
88   DMPlexCreateRigidBody - create rigid body modes from coordinates
89 
90   Collective on DM
91 
92   Input Arguments:
93 + dm - the DM
94 . section - the local section associated with the rigid field, or NULL for the default section
95 - globalSection - the global section associated with the rigid field, or NULL for the default section
96 
97   Output Argument:
98 . sp - the null space
99 
100   Note: This is necessary to take account of Dirichlet conditions on the displacements
101 
102   Level: advanced
103 
104 .seealso: MatNullSpaceCreate()
105 @*/
106 PetscErrorCode DMPlexCreateRigidBody(DM dm, PetscSection section, PetscSection globalSection, MatNullSpace *sp)
107 {
108   MPI_Comm       comm;
109   Vec            coordinates, localMode, mode[6];
110   PetscSection   coordSection;
111   PetscScalar   *coords;
112   PetscInt       dim, vStart, vEnd, v, n, m, d, i, j;
113   PetscErrorCode ierr;
114 
115   PetscFunctionBegin;
116   ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
117   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
118   if (dim == 1) {
119     ierr = MatNullSpaceCreate(comm, PETSC_TRUE, 0, NULL, sp);CHKERRQ(ierr);
120     PetscFunctionReturn(0);
121   }
122   if (!section)       {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
123   if (!globalSection) {ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);}
124   ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
125   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
126   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
127   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
128   m    = (dim*(dim+1))/2;
129   ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
130   ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
131   ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
132   for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
133   /* Assume P1 */
134   ierr = DMGetLocalVector(dm, &localMode);CHKERRQ(ierr);
135   for (d = 0; d < dim; ++d) {
136     PetscScalar values[3] = {0.0, 0.0, 0.0};
137 
138     values[d] = 1.0;
139     ierr      = VecSet(localMode, 0.0);CHKERRQ(ierr);
140     for (v = vStart; v < vEnd; ++v) {
141       ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
142     }
143     ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
144     ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
145   }
146   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
147   for (d = dim; d < dim*(dim+1)/2; ++d) {
148     PetscInt i, j, k = dim > 2 ? d - dim : d;
149 
150     ierr = VecSet(localMode, 0.0);CHKERRQ(ierr);
151     for (v = vStart; v < vEnd; ++v) {
152       PetscScalar values[3] = {0.0, 0.0, 0.0};
153       PetscInt    off;
154 
155       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
156       for (i = 0; i < dim; ++i) {
157         for (j = 0; j < dim; ++j) {
158           values[j] += epsilon(i, j, k)*PetscRealPart(coords[off+i]);
159         }
160       }
161       ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
162     }
163     ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
164     ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
165   }
166   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
167   ierr = DMRestoreLocalVector(dm, &localMode);CHKERRQ(ierr);
168   for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
169   /* Orthonormalize system */
170   for (i = dim; i < m; ++i) {
171     PetscScalar dots[6];
172 
173     ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
174     for (j = 0; j < i; ++j) dots[j] *= -1.0;
175     ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
176     ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
177   }
178   ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
179   for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
180   PetscFunctionReturn(0);
181 }
182 
183 #undef __FUNCT__
184 #define __FUNCT__ "DMPlexProjectFunctionLocal"
185 PetscErrorCode DMPlexProjectFunctionLocal(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
186 {
187   PetscDualSpace *sp;
188   PetscSection    section;
189   PetscScalar    *values;
190   PetscReal      *v0, *J, detJ;
191   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, c, f, d, v;
192   PetscErrorCode  ierr;
193 
194   PetscFunctionBegin;
195   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
196   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
197   ierr = PetscMalloc1(numFields, &sp);CHKERRQ(ierr);
198   for (f = 0; f < numFields; ++f) {
199     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
200     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
201     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
202     totDim += spDim*numComp;
203   }
204   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
205   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
206   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
207   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
208   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
209   ierr = PetscMalloc2(dim,&v0,dim*dim,&J);CHKERRQ(ierr);
210   for (c = cStart; c < cEnd; ++c) {
211     PetscCellGeometry geom;
212 
213     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
214     geom.v0   = v0;
215     geom.J    = J;
216     geom.detJ = &detJ;
217     for (f = 0, v = 0; f < numFields; ++f) {
218       void * const ctx = ctxs ? ctxs[f] : NULL;
219       ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
220       ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
221       for (d = 0; d < spDim; ++d) {
222         ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
223         v += numComp;
224       }
225     }
226     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
227   }
228   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
229   ierr = PetscFree2(v0,J);CHKERRQ(ierr);
230   ierr = PetscFree(sp);CHKERRQ(ierr);
231   PetscFunctionReturn(0);
232 }
233 
234 #undef __FUNCT__
235 #define __FUNCT__ "DMPlexProjectFunction"
236 /*@C
237   DMPlexProjectFunction - This projects the given function into the function space provided.
238 
239   Input Parameters:
240 + dm      - The DM
241 . fe      - The PetscFE associated with the field
242 . funcs   - The coordinate functions to evaluate, one per field
243 . ctxs    - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
244 - mode    - The insertion mode for values
245 
246   Output Parameter:
247 . X - vector
248 
249   Level: developer
250 
251 .seealso: DMPlexComputeL2Diff()
252 @*/
253 PetscErrorCode DMPlexProjectFunction(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec X)
254 {
255   Vec            localX;
256   PetscErrorCode ierr;
257 
258   PetscFunctionBegin;
259   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
260   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
261   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, mode, localX);CHKERRQ(ierr);
262   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
263   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
264   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
265   PetscFunctionReturn(0);
266 }
267 
268 #undef __FUNCT__
269 #define __FUNCT__ "DMPlexComputeL2Diff"
270 /*@C
271   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
272 
273   Input Parameters:
274 + dm    - The DM
275 . fe    - The PetscFE object for each field
276 . funcs - The functions to evaluate for each field component
277 . ctxs  - Optional array of contexts to pass to each function.  ctxs itself may be null.
278 - X     - The coefficient vector u_h
279 
280   Output Parameter:
281 . diff - The diff ||u - u_h||_2
282 
283   Level: developer
284 
285 .seealso: DMPlexProjectFunction()
286 @*/
287 PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
288 {
289   const PetscInt  debug = 0;
290   PetscSection    section;
291   PetscQuadrature quad;
292   Vec             localX;
293   PetscScalar    *funcVal;
294   PetscReal      *coords, *v0, *J, *invJ, detJ;
295   PetscReal       localDiff = 0.0;
296   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
297   PetscErrorCode  ierr;
298 
299   PetscFunctionBegin;
300   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
301   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
302   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
303   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
304   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
305   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
306   for (field = 0; field < numFields; ++field) {
307     PetscInt Nc;
308 
309     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
310     numComponents += Nc;
311   }
312   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
313   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
314   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
315   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
316   for (c = cStart; c < cEnd; ++c) {
317     PetscScalar *x = NULL;
318     PetscReal    elemDiff = 0.0;
319 
320     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
321     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
322     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
323 
324     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
325       void * const     ctx           = ctxs ? ctxs[field] : NULL;
326       const PetscInt   numQuadPoints = quad.numPoints;
327       const PetscReal *quadPoints    = quad.points;
328       const PetscReal *quadWeights   = quad.weights;
329       PetscReal       *basis;
330       PetscInt         numBasisFuncs, numBasisComps, q, d, e, fc, f;
331 
332       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
333       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
334       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
335       if (debug) {
336         char title[1024];
337         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
338         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
339       }
340       for (q = 0; q < numQuadPoints; ++q) {
341         for (d = 0; d < dim; d++) {
342           coords[d] = v0[d];
343           for (e = 0; e < dim; e++) {
344             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
345           }
346         }
347         (*funcs[field])(coords, funcVal, ctx);
348         for (fc = 0; fc < numBasisComps; ++fc) {
349           PetscScalar interpolant = 0.0;
350 
351           for (f = 0; f < numBasisFuncs; ++f) {
352             const PetscInt fidx = f*numBasisComps+fc;
353             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
354           }
355           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ);CHKERRQ(ierr);}
356           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
357         }
358       }
359       comp        += numBasisComps;
360       fieldOffset += numBasisFuncs*numBasisComps;
361     }
362     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
363     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
364     localDiff += elemDiff;
365   }
366   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
367   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
368   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
369   *diff = PetscSqrtReal(*diff);
370   PetscFunctionReturn(0);
371 }
372 
373 #if 0
374 
375 #undef __FUNCT__
376 #define __FUNCT__ "DMPlexComputeResidualFEM"
377 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
378 {
379   DM_Plex         *mesh   = (DM_Plex *) dm->data;
380   PetscFEM        *fem    = (PetscFEM *) user;
381   PetscQuadrature *quad   = fem->quad;
382   PetscQuadrature *quadBd = fem->quadBd;
383   PetscSection     section;
384   PetscReal       *v0, *n, *J, *invJ, *detJ;
385   PetscScalar     *elemVec, *u;
386   PetscInt         dim, numFields, field, numBatchesTmp = 1, numCells, cStart, cEnd, c;
387   PetscInt         cellDof, numComponents;
388   PetscBool        has;
389   PetscErrorCode   ierr;
390 
391   PetscFunctionBegin;
392   if (has && quadBd) {
393     DMLabel         label;
394     IS              pointIS;
395     const PetscInt *points;
396     PetscInt        numPoints, p;
397 
398     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
399     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
400     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
401     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
402     for (field = 0, cellDof = 0, numComponents = 0; field < numFields; ++field) {
403       cellDof       += quadBd[field].numBasisFuncs*quadBd[field].numComponents;
404       numComponents += quadBd[field].numComponents;
405     }
406     ierr = PetscMalloc7(numPoints*cellDof,&u,numPoints*dim,&v0,numPoints*dim,&n,numPoints*dim*dim,&J,numPoints*dim*dim,&invJ,numPoints,&detJ,numPoints*cellDof,&elemVec);CHKERRQ(ierr);
407     for (p = 0; p < numPoints; ++p) {
408       const PetscInt point = points[p];
409       PetscScalar   *x;
410       PetscInt       i;
411 
412       /* TODO: Add normal determination here */
413       ierr = DMPlexComputeCellGeometry(dm, point, &v0[p*dim], &J[p*dim*dim], &invJ[p*dim*dim], &detJ[p]);CHKERRQ(ierr);
414       if (detJ[p] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[p], point);
415       ierr = DMPlexVecGetClosure(dm, NULL, X, point, NULL, &x);CHKERRQ(ierr);
416 
417       for (i = 0; i < cellDof; ++i) u[p*cellDof+i] = x[i];
418       ierr = DMPlexVecRestoreClosure(dm, NULL, X, point, NULL, &x);CHKERRQ(ierr);
419     }
420     for (field = 0; field < numFields; ++field) {
421       const PetscInt numQuadPoints = quadBd[field].numQuadPoints;
422       const PetscInt numBasisFuncs = quadBd[field].numBasisFuncs;
423       void           (*f0)(const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[field];
424       void           (*f1)(const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[field];
425       /* Conforming batches */
426       PetscInt blockSize  = numBasisFuncs*numQuadPoints;
427       PetscInt numBlocks  = 1;
428       PetscInt batchSize  = numBlocks * blockSize;
429       PetscInt numBatches = numBatchesTmp;
430       PetscInt numChunks  = numPoints / (numBatches*batchSize);
431       /* Remainder */
432       PetscInt numRemainder = numPoints % (numBatches * batchSize);
433       PetscInt offset       = numPoints - numRemainder;
434 
435       ierr = (*mesh->integrateBdResidualFEM)(numChunks*numBatches*batchSize, numFields, field, quadBd, u, v0, n, J, invJ, detJ, f0, f1, elemVec);CHKERRQ(ierr);
436       ierr = (*mesh->integrateBdResidualFEM)(numRemainder, numFields, field, quadBd, &u[offset*cellDof], &v0[offset*dim], &n[offset*dim], &J[offset*dim*dim], &invJ[offset*dim*dim], &detJ[offset],
437                                              f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
438     }
439     for (p = 0; p < numPoints; ++p) {
440       const PetscInt point = points[p];
441 
442       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "Residual", cellDof, &elemVec[p*cellDof]);CHKERRQ(ierr);}
443       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[p*cellDof], ADD_VALUES);CHKERRQ(ierr);
444     }
445     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
446     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
447     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
448   }
449   PetscFunctionReturn(0);
450 }
451 
452 #else
453 
454 #undef __FUNCT__
455 #define __FUNCT__ "DMPlexComputeResidualFEM"
456 /*@
457   DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
458 
459   Input Parameters:
460 + dm - The mesh
461 . X  - Local input vector
462 - user - The user context
463 
464   Output Parameter:
465 . F  - Local output vector
466 
467   Note:
468   The second member of the user context must be an FEMContext.
469 
470   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
471   like a GPU, or vectorize on a multicore machine.
472 
473   Level: developer
474 
475 .seealso: DMPlexComputeJacobianActionFEM()
476 @*/
477 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
478 {
479   DM_Plex          *mesh  = (DM_Plex *) dm->data;
480   PetscFEM         *fem   = (PetscFEM *) user;
481   PetscFE          *fe    = fem->fe;
482   PetscFE          *feAux = fem->feAux;
483   PetscFE          *feBd  = fem->feBd;
484   const char       *name  = "Residual";
485   DM                dmAux;
486   Vec               A;
487   PetscQuadrature   q;
488   PetscCellGeometry geom;
489   PetscSection      section, sectionAux;
490   PetscReal        *v0, *J, *invJ, *detJ;
491   PetscScalar      *elemVec, *u, *a;
492   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
493   PetscInt          cellDof = 0, numComponents = 0;
494   PetscInt          cellDofAux = 0, numComponentsAux = 0;
495   PetscErrorCode    ierr;
496 
497   PetscFunctionBegin;
498   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
499   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
500   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
501   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
502   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
503   numCells = cEnd - cStart;
504   for (f = 0; f < Nf; ++f) {
505     PetscInt Nb, Nc;
506 
507     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
508     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
509     cellDof       += Nb*Nc;
510     numComponents += Nc;
511   }
512   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
513   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
514   if (dmAux) {
515     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
516     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
517   }
518   for (f = 0; f < NfAux; ++f) {
519     PetscInt Nb, Nc;
520 
521     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
522     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
523     cellDofAux       += Nb*Nc;
524     numComponentsAux += Nc;
525   }
526   ierr = DMPlexProjectFunctionLocal(dm, fe, fem->bcFuncs, fem->bcCtxs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
527   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
528   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
529   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
530   for (c = cStart; c < cEnd; ++c) {
531     PetscScalar *x = NULL;
532     PetscInt     i;
533 
534     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
535     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
536     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
537     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
538     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
539     if (dmAux) {
540       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
541       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
542       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
543     }
544   }
545   for (f = 0; f < Nf; ++f) {
546     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0Funcs[f];
547     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1Funcs[f];
548     PetscInt Nb;
549     /* Conforming batches */
550     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
551     /* Remainder */
552     PetscInt Nr, offset;
553 
554     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
555     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
556     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
557     blockSize = Nb*q.numPoints;
558     batchSize = numBlocks * blockSize;
559     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
560     numChunks = numCells / (numBatches*batchSize);
561     Ne        = numChunks*numBatches*batchSize;
562     Nr        = numCells % (numBatches*batchSize);
563     offset    = numCells - Nr;
564     geom.v0   = v0;
565     geom.J    = J;
566     geom.invJ = invJ;
567     geom.detJ = detJ;
568     ierr = PetscFEIntegrateResidual(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
569     geom.v0   = &v0[offset*dim];
570     geom.J    = &J[offset*dim*dim];
571     geom.invJ = &invJ[offset*dim*dim];
572     geom.detJ = &detJ[offset];
573     ierr = PetscFEIntegrateResidual(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
574   }
575   for (c = cStart; c < cEnd; ++c) {
576     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
577     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
578   }
579   ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
580   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
581   if (feBd) {
582     DMLabel         label, depth;
583     IS              pointIS;
584     const PetscInt *points;
585     PetscInt        dep, numPoints, p, numFaces;
586     PetscReal      *n;
587 
588     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
589     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
590     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
591     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
592     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
593     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
594       PetscInt Nb, Nc;
595 
596       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
597       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
598       cellDof       += Nb*Nc;
599       numComponents += Nc;
600     }
601     for (p = 0, numFaces = 0; p < numPoints; ++p) {
602       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
603       if (dep == dim-1) ++numFaces;
604     }
605     ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof,&elemVec);CHKERRQ(ierr);
606     for (p = 0, f = 0; p < numPoints; ++p) {
607       const PetscInt point = points[p];
608       PetscScalar   *x     = NULL;
609       PetscInt       i;
610 
611       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
612       if (dep != dim-1) continue;
613       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
614       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
615       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
616       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
617       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
618       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
619       ++f;
620     }
621     for (f = 0; f < Nf; ++f) {
622       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
623       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
624       PetscInt Nb;
625       /* Conforming batches */
626       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
627       /* Remainder */
628       PetscInt Nr, offset;
629 
630       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
631       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
632       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
633       blockSize = Nb*q.numPoints;
634       batchSize = numBlocks * blockSize;
635       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
636       numChunks = numFaces / (numBatches*batchSize);
637       Ne        = numChunks*numBatches*batchSize;
638       Nr        = numFaces % (numBatches*batchSize);
639       offset    = numFaces - Nr;
640       geom.v0   = v0;
641       geom.n    = n;
642       geom.J    = J;
643       geom.invJ = invJ;
644       geom.detJ = detJ;
645       ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
646       geom.v0   = &v0[offset*dim];
647       geom.n    = &n[offset*dim];
648       geom.J    = &J[offset*dim*dim];
649       geom.invJ = &invJ[offset*dim*dim];
650       geom.detJ = &detJ[offset];
651       ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
652     }
653     for (p = 0, f = 0; p < numPoints; ++p) {
654       const PetscInt point = points[p];
655 
656       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
657       if (dep != dim-1) continue;
658       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
659       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
660       ++f;
661     }
662     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
663     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
664     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
665   }
666   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
667   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
668   PetscFunctionReturn(0);
669 }
670 
671 #endif
672 
673 #undef __FUNCT__
674 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
675 /*@C
676   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
677 
678   Input Parameters:
679 + dm - The mesh
680 . J  - The Jacobian shell matrix
681 . X  - Local input vector
682 - user - The user context
683 
684   Output Parameter:
685 . F  - Local output vector
686 
687   Note:
688   The second member of the user context must be an FEMContext.
689 
690   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
691   like a GPU, or vectorize on a multicore machine.
692 
693   Level: developer
694 
695 .seealso: DMPlexComputeResidualFEM()
696 @*/
697 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
698 {
699   DM_Plex          *mesh = (DM_Plex *) dm->data;
700   PetscFEM         *fem  = (PetscFEM *) user;
701   PetscFE          *fe   = fem->fe;
702   PetscQuadrature   quad;
703   PetscCellGeometry geom;
704   PetscSection      section;
705   JacActionCtx     *jctx;
706   PetscReal        *v0, *J, *invJ, *detJ;
707   PetscScalar      *elemVec, *u, *a;
708   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
709   PetscInt          cellDof = 0;
710   PetscErrorCode    ierr;
711 
712   PetscFunctionBegin;
713   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
714   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
715   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
716   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
717   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
718   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
719   numCells = cEnd - cStart;
720   for (field = 0; field < numFields; ++field) {
721     PetscInt Nb, Nc;
722 
723     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
724     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
725     cellDof += Nb*Nc;
726   }
727   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
728   ierr = PetscMalloc7(numCells*cellDof,&u,numCells*cellDof,&a,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
729   for (c = cStart; c < cEnd; ++c) {
730     PetscScalar *x = NULL;
731     PetscInt     i;
732 
733     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
734     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
735     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
736     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
737     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
738     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
739     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
740     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
741   }
742   for (field = 0; field < numFields; ++field) {
743     PetscInt Nb;
744     /* Conforming batches */
745     PetscInt numBlocks  = 1;
746     PetscInt numBatches = 1;
747     PetscInt numChunks, Ne, blockSize, batchSize;
748     /* Remainder */
749     PetscInt Nr, offset;
750 
751     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
752     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
753     blockSize = Nb*quad.numPoints;
754     batchSize = numBlocks * blockSize;
755     numChunks = numCells / (numBatches*batchSize);
756     Ne        = numChunks*numBatches*batchSize;
757     Nr        = numCells % (numBatches*batchSize);
758     offset    = numCells - Nr;
759     geom.v0   = v0;
760     geom.J    = J;
761     geom.invJ = invJ;
762     geom.detJ = detJ;
763     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
764     geom.v0   = &v0[offset*dim];
765     geom.J    = &J[offset*dim*dim];
766     geom.invJ = &invJ[offset*dim*dim];
767     geom.detJ = &detJ[offset];
768     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
769                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
770   }
771   for (c = cStart; c < cEnd; ++c) {
772     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
773     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
774   }
775   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
776   if (mesh->printFEM) {
777     PetscMPIInt rank, numProcs;
778     PetscInt    p;
779 
780     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
781     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
782     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
783     for (p = 0; p < numProcs; ++p) {
784       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
785       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
786     }
787   }
788   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
789   PetscFunctionReturn(0);
790 }
791 
792 #undef __FUNCT__
793 #define __FUNCT__ "DMPlexComputeJacobianFEM"
794 /*@
795   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
796 
797   Input Parameters:
798 + dm - The mesh
799 . X  - Local input vector
800 - user - The user context
801 
802   Output Parameter:
803 . Jac  - Jacobian matrix
804 
805   Note:
806   The second member of the user context must be an FEMContext.
807 
808   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
809   like a GPU, or vectorize on a multicore machine.
810 
811   Level: developer
812 
813 .seealso: FormFunctionLocal()
814 @*/
815 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP, MatStructure *str,void *user)
816 {
817   DM_Plex          *mesh  = (DM_Plex *) dm->data;
818   PetscFEM         *fem   = (PetscFEM *) user;
819   PetscFE          *fe    = fem->fe;
820   PetscFE          *feAux = fem->feAux;
821   const char       *name  = "Jacobian";
822   DM                dmAux;
823   Vec               A;
824   PetscQuadrature   quad;
825   PetscCellGeometry geom;
826   PetscSection      section, globalSection, sectionAux;
827   PetscReal        *v0, *J, *invJ, *detJ;
828   PetscScalar      *elemMat, *u, *a;
829   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
830   PetscInt          cellDof = 0, numComponents = 0;
831   PetscInt          cellDofAux = 0, numComponentsAux = 0;
832   PetscBool         isShell;
833   PetscErrorCode    ierr;
834 
835   PetscFunctionBegin;
836   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
837   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
838   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
839   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
840   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
841   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
842   numCells = cEnd - cStart;
843   for (f = 0; f < Nf; ++f) {
844     PetscInt Nb, Nc;
845 
846     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
847     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
848     cellDof       += Nb*Nc;
849     numComponents += Nc;
850   }
851   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
852   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
853   if (dmAux) {
854     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
855     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
856   }
857   for (f = 0; f < NfAux; ++f) {
858     PetscInt Nb, Nc;
859 
860     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
861     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
862     cellDofAux       += Nb*Nc;
863     numComponentsAux += Nc;
864   }
865   ierr = DMPlexProjectFunctionLocal(dm, fe, fem->bcFuncs, fem->bcCtxs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
866   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
867   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
868   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
869   for (c = cStart; c < cEnd; ++c) {
870     PetscScalar *x = NULL;
871     PetscInt     i;
872 
873     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
874     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
875     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
876     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
877     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
878     if (dmAux) {
879       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
880       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
881       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
882     }
883   }
884   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
885   for (fieldI = 0; fieldI < Nf; ++fieldI) {
886     PetscInt Nb;
887     /* Conforming batches */
888     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
889     /* Remainder */
890     PetscInt Nr, offset;
891 
892     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
893     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
894     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
895     blockSize = Nb*quad.numPoints;
896     batchSize = numBlocks * blockSize;
897     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
898     numChunks = numCells / (numBatches*batchSize);
899     Ne        = numChunks*numBatches*batchSize;
900     Nr        = numCells % (numBatches*batchSize);
901     offset    = numCells - Nr;
902     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
903       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
904       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
905       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
906       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
907 
908       geom.v0   = v0;
909       geom.J    = J;
910       geom.invJ = invJ;
911       geom.detJ = detJ;
912       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
913       geom.v0   = &v0[offset*dim];
914       geom.J    = &J[offset*dim*dim];
915       geom.invJ = &invJ[offset*dim*dim];
916       geom.detJ = &detJ[offset];
917       ierr = PetscFEIntegrateJacobian(fe[fieldI], Nr, Nf, fe, fieldI, fieldJ, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], g0, g1, g2, g3, &elemMat[offset*cellDof*cellDof]);CHKERRQ(ierr);
918     }
919   }
920   for (c = cStart; c < cEnd; ++c) {
921     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
922     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
923   }
924   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
925   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
926   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
927   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
928   if (mesh->printFEM) {
929     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
930     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
931     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
932   }
933   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
934   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
935   if (isShell) {
936     JacActionCtx *jctx;
937 
938     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
939     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
940   }
941   *str = SAME_NONZERO_PATTERN;
942   PetscFunctionReturn(0);
943 }
944