xref: /petsc/src/dm/impls/plex/plexfem.c (revision 1f6798043ba3915ee8b4a00dc4c31979120e7f4c) ! 
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 *), 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 = PetscMalloc(numFields * sizeof(PetscDualSpace), &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,PetscReal,&v0,dim*dim,PetscReal,&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       ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
219       ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
220       for (d = 0; d < spDim; ++d) {
221         ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], &values[v]);CHKERRQ(ierr);
222         v += numComp;
223       }
224     }
225     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
226   }
227   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
228   ierr = PetscFree2(v0,J);CHKERRQ(ierr);
229   ierr = PetscFree(sp);CHKERRQ(ierr);
230   PetscFunctionReturn(0);
231 }
232 
233 #undef __FUNCT__
234 #define __FUNCT__ "DMPlexProjectFunction"
235 /*@C
236   DMPlexProjectFunction - This projects the given function into the function space provided.
237 
238   Input Parameters:
239 + dm      - The DM
240 . fe      - The PetscFE associated with the field
241 . funcs   - The coordinate functions to evaluate, one per field
242 - mode    - The insertion mode for values
243 
244   Output Parameter:
245 . X - vector
246 
247   Level: developer
248 
249 .seealso: DMPlexComputeL2Diff()
250 @*/
251 PetscErrorCode DMPlexProjectFunction(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *), InsertMode mode, Vec X)
252 {
253   Vec            localX;
254   PetscErrorCode ierr;
255 
256   PetscFunctionBegin;
257   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
258   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
259   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, mode, localX);CHKERRQ(ierr);
260   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
261   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
262   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
263   PetscFunctionReturn(0);
264 }
265 
266 #undef __FUNCT__
267 #define __FUNCT__ "DMPlexComputeL2Diff"
268 /*@C
269   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
270 
271   Input Parameters:
272 + dm    - The DM
273 . fe    - The PetscFE object for each field
274 . funcs - The functions to evaluate for each field component
275 - X     - The coefficient vector u_h
276 
277   Output Parameter:
278 . diff - The diff ||u - u_h||_2
279 
280   Level: developer
281 
282 .seealso: DMPlexProjectFunction()
283 @*/
284 PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *), Vec X, PetscReal *diff)
285 {
286   const PetscInt  debug = 0;
287   PetscSection    section;
288   PetscQuadrature quad;
289   Vec             localX;
290   PetscScalar    *funcVal;
291   PetscReal      *coords, *v0, *J, *invJ, detJ;
292   PetscReal       localDiff = 0.0;
293   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
294   PetscErrorCode  ierr;
295 
296   PetscFunctionBegin;
297   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
298   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
299   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
300   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
301   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
302   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
303   for (field = 0; field < numFields; ++field) {
304     PetscInt Nc;
305 
306     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
307     numComponents += Nc;
308   }
309   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
310   ierr = PetscMalloc5(numComponents,PetscScalar,&funcVal,dim,PetscReal,&coords,dim,PetscReal,&v0,dim*dim,PetscReal,&J,dim*dim,PetscReal,&invJ);CHKERRQ(ierr);
311   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
312   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
313   for (c = cStart; c < cEnd; ++c) {
314     PetscScalar *x = NULL;
315     PetscReal    elemDiff = 0.0;
316 
317     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
318     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
319     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
320 
321     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
322       const PetscInt   numQuadPoints = quad.numPoints;
323       const PetscReal *quadPoints    = quad.points;
324       const PetscReal *quadWeights   = quad.weights;
325       PetscReal       *basis;
326       PetscInt         numBasisFuncs, numBasisComps, q, d, e, fc, f;
327 
328       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
329       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
330       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
331       if (debug) {
332         char title[1024];
333         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
334         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
335       }
336       for (q = 0; q < numQuadPoints; ++q) {
337         for (d = 0; d < dim; d++) {
338           coords[d] = v0[d];
339           for (e = 0; e < dim; e++) {
340             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
341           }
342         }
343         (*funcs[field])(coords, funcVal);
344         for (fc = 0; fc < numBasisComps; ++fc) {
345           PetscScalar interpolant = 0.0;
346 
347           for (f = 0; f < numBasisFuncs; ++f) {
348             const PetscInt fidx = f*numBasisComps+fc;
349             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
350           }
351           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);}
352           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
353         }
354       }
355       comp        += numBasisComps;
356       fieldOffset += numBasisFuncs*numBasisComps;
357     }
358     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
359     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
360     localDiff += elemDiff;
361   }
362   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
363   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
364   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
365   *diff = PetscSqrtReal(*diff);
366   PetscFunctionReturn(0);
367 }
368 
369 #if 0
370 
371 #undef __FUNCT__
372 #define __FUNCT__ "DMPlexComputeResidualFEM"
373 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
374 {
375   DM_Plex         *mesh   = (DM_Plex *) dm->data;
376   PetscFEM        *fem    = (PetscFEM *) user;
377   PetscQuadrature *quad   = fem->quad;
378   PetscQuadrature *quadBd = fem->quadBd;
379   PetscSection     section;
380   PetscReal       *v0, *n, *J, *invJ, *detJ;
381   PetscScalar     *elemVec, *u;
382   PetscInt         dim, numFields, field, numBatchesTmp = 1, numCells, cStart, cEnd, c;
383   PetscInt         cellDof, numComponents;
384   PetscBool        has;
385   PetscErrorCode   ierr;
386 
387   PetscFunctionBegin;
388   if (has && quadBd) {
389     DMLabel         label;
390     IS              pointIS;
391     const PetscInt *points;
392     PetscInt        numPoints, p;
393 
394     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
395     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
396     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
397     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
398     for (field = 0, cellDof = 0, numComponents = 0; field < numFields; ++field) {
399       cellDof       += quadBd[field].numBasisFuncs*quadBd[field].numComponents;
400       numComponents += quadBd[field].numComponents;
401     }
402     ierr = PetscMalloc7(numPoints*cellDof,PetscScalar,&u,numPoints*dim,PetscReal,&v0,numPoints*dim,PetscReal,&n,numPoints*dim*dim,PetscReal,&J,numPoints*dim*dim,PetscReal,&invJ,numPoints,PetscReal,&detJ,numPoints*cellDof,PetscScalar,&elemVec);CHKERRQ(ierr);
403     for (p = 0; p < numPoints; ++p) {
404       const PetscInt point = points[p];
405       PetscScalar   *x;
406       PetscInt       i;
407 
408       /* TODO: Add normal determination here */
409       ierr = DMPlexComputeCellGeometry(dm, point, &v0[p*dim], &J[p*dim*dim], &invJ[p*dim*dim], &detJ[p]);CHKERRQ(ierr);
410       if (detJ[p] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[p], point);
411       ierr = DMPlexVecGetClosure(dm, NULL, X, point, NULL, &x);CHKERRQ(ierr);
412 
413       for (i = 0; i < cellDof; ++i) u[p*cellDof+i] = x[i];
414       ierr = DMPlexVecRestoreClosure(dm, NULL, X, point, NULL, &x);CHKERRQ(ierr);
415     }
416     for (field = 0; field < numFields; ++field) {
417       const PetscInt numQuadPoints = quadBd[field].numQuadPoints;
418       const PetscInt numBasisFuncs = quadBd[field].numBasisFuncs;
419       void           (*f0)(const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[field];
420       void           (*f1)(const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[field];
421       /* Conforming batches */
422       PetscInt blockSize  = numBasisFuncs*numQuadPoints;
423       PetscInt numBlocks  = 1;
424       PetscInt batchSize  = numBlocks * blockSize;
425       PetscInt numBatches = numBatchesTmp;
426       PetscInt numChunks  = numPoints / (numBatches*batchSize);
427       /* Remainder */
428       PetscInt numRemainder = numPoints % (numBatches * batchSize);
429       PetscInt offset       = numPoints - numRemainder;
430 
431       ierr = (*mesh->integrateBdResidualFEM)(numChunks*numBatches*batchSize, numFields, field, quadBd, u, v0, n, J, invJ, detJ, f0, f1, elemVec);CHKERRQ(ierr);
432       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],
433                                              f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
434     }
435     for (p = 0; p < numPoints; ++p) {
436       const PetscInt point = points[p];
437 
438       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "Residual", cellDof, &elemVec[p*cellDof]);CHKERRQ(ierr);}
439       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[p*cellDof], ADD_VALUES);CHKERRQ(ierr);
440     }
441     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
442     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
443     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
444   }
445   PetscFunctionReturn(0);
446 }
447 
448 #else
449 
450 #undef __FUNCT__
451 #define __FUNCT__ "DMPlexComputeResidualFEM"
452 /*@
453   DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
454 
455   Input Parameters:
456 + dm - The mesh
457 . X  - Local input vector
458 - user - The user context
459 
460   Output Parameter:
461 . F  - Local output vector
462 
463   Note:
464   The second member of the user context must be an FEMContext.
465 
466   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
467   like a GPU, or vectorize on a multicore machine.
468 
469   Level: developer
470 
471 .seealso: DMPlexComputeJacobianActionFEM()
472 @*/
473 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
474 {
475   DM_Plex          *mesh  = (DM_Plex *) dm->data;
476   PetscFEM         *fem   = (PetscFEM *) user;
477   PetscFE          *fe    = fem->fe;
478   PetscFE          *feAux = fem->feAux;
479   PetscFE          *feBd  = fem->feBd;
480   const char       *name  = "Residual";
481   DM                dmAux;
482   Vec               A;
483   PetscQuadrature   q;
484   PetscCellGeometry geom;
485   PetscSection      section, sectionAux;
486   PetscReal        *v0, *J, *invJ, *detJ;
487   PetscScalar      *elemVec, *u, *a;
488   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
489   PetscInt          cellDof = 0, numComponents = 0;
490   PetscInt          cellDofAux = 0, numComponentsAux = 0;
491   PetscErrorCode    ierr;
492 
493   PetscFunctionBegin;
494   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
495   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
496   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
497   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
498   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
499   numCells = cEnd - cStart;
500   for (f = 0; f < Nf; ++f) {
501     PetscInt Nb, Nc;
502 
503     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
504     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
505     cellDof       += Nb*Nc;
506     numComponents += Nc;
507   }
508   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
509   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
510   if (dmAux) {
511     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
512     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
513   }
514   for (f = 0; f < NfAux; ++f) {
515     PetscInt Nb, Nc;
516 
517     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
518     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
519     cellDofAux       += Nb*Nc;
520     numComponentsAux += Nc;
521   }
522   ierr = DMPlexProjectFunctionLocal(dm, fe, fem->bcFuncs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
523   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
524   ierr = PetscMalloc6(numCells*cellDof,PetscScalar,&u,numCells*dim,PetscReal,&v0,numCells*dim*dim,PetscReal,&J,numCells*dim*dim,PetscReal,&invJ,numCells,PetscReal,&detJ,numCells*cellDof,PetscScalar,&elemVec);CHKERRQ(ierr);
525   if (dmAux) {ierr = PetscMalloc(numCells*cellDofAux * sizeof(PetscScalar), &a);CHKERRQ(ierr);}
526   for (c = cStart; c < cEnd; ++c) {
527     PetscScalar *x = NULL;
528     PetscInt     i;
529 
530     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
531     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
532     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
533     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
534     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
535     if (dmAux) {
536       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
537       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
538       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
539     }
540   }
541   for (f = 0; f < Nf; ++f) {
542     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0Funcs[f];
543     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1Funcs[f];
544     PetscInt Nb;
545     /* Conforming batches */
546     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
547     /* Remainder */
548     PetscInt Nr, offset;
549 
550     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
551     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
552     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
553     blockSize = Nb*q.numPoints;
554     batchSize = numBlocks * blockSize;
555     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
556     numChunks = numCells / (numBatches*batchSize);
557     Ne        = numChunks*numBatches*batchSize;
558     Nr        = numCells % (numBatches*batchSize);
559     offset    = numCells - Nr;
560     geom.v0   = v0;
561     geom.J    = J;
562     geom.invJ = invJ;
563     geom.detJ = detJ;
564     ierr = PetscFEIntegrateResidual(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
565     geom.v0   = &v0[offset*dim];
566     geom.J    = &J[offset*dim*dim];
567     geom.invJ = &invJ[offset*dim*dim];
568     geom.detJ = &detJ[offset];
569     ierr = PetscFEIntegrateResidual(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
570   }
571   for (c = cStart; c < cEnd; ++c) {
572     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
573     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
574   }
575   ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
576   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
577   if (feBd) {
578     DMLabel         label;
579     IS              pointIS;
580     const PetscInt *points;
581     PetscInt        numPoints, p;
582     PetscReal      *n;
583 
584     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
585     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
586     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
587     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
588     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
589       PetscInt Nb, Nc;
590 
591       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
592       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
593       cellDof       += Nb*Nc;
594       numComponents += Nc;
595     }
596     ierr = PetscMalloc7(numPoints*cellDof,PetscScalar,&u,numPoints*dim,PetscReal,&v0,numPoints*dim,PetscReal,&n,numPoints*dim*dim,PetscReal,&J,numPoints*dim*dim,PetscReal,&invJ,numPoints,PetscReal,&detJ,numPoints*cellDof,PetscScalar,&elemVec);CHKERRQ(ierr);
597     for (p = 0; p < numPoints; ++p) {
598       const PetscInt point = points[p];
599       PetscScalar   *x     = NULL;
600       PetscInt       i;
601 
602       /* TODO: Add normal determination here */
603       ierr = DMPlexComputeCellGeometry(dm, point, &v0[p*dim], &J[p*dim*dim], &invJ[p*dim*dim], &detJ[p]);CHKERRQ(ierr);
604       if (detJ[p] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[p], point);
605       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
606       for (i = 0; i < cellDof; ++i) u[p*cellDof+i] = x[i];
607       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
608     }
609     for (f = 0; f < Nf; ++f) {
610       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
611       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
612       PetscInt Nb;
613       /* Conforming batches */
614       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
615       /* Remainder */
616       PetscInt Nr, offset;
617 
618       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
619       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
620       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
621       blockSize = Nb*q.numPoints;
622       batchSize = numBlocks * blockSize;
623       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
624       numChunks = numPoints / (numBatches*batchSize);
625       Ne        = numChunks*numBatches*batchSize;
626       Nr        = numPoints % (numBatches*batchSize);
627       offset    = numPoints - Nr;
628       geom.v0   = v0;
629       geom.n    = n;
630       geom.J    = J;
631       geom.invJ = invJ;
632       geom.detJ = detJ;
633       ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
634       geom.v0   = &v0[offset*dim];
635       geom.n    = &n[offset*dim];
636       geom.J    = &J[offset*dim*dim];
637       geom.invJ = &invJ[offset*dim*dim];
638       geom.detJ = &detJ[offset];
639       ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
640     }
641     for (p = 0; p < numPoints; ++p) {
642       const PetscInt point = points[p];
643 
644       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[p*cellDof]);CHKERRQ(ierr);}
645       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[p*cellDof], ADD_VALUES);CHKERRQ(ierr);
646     }
647     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
648     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
649     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
650   }
651   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
652   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
653   PetscFunctionReturn(0);
654 }
655 
656 #endif
657 
658 #undef __FUNCT__
659 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
660 /*@C
661   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
662 
663   Input Parameters:
664 + dm - The mesh
665 . J  - The Jacobian shell matrix
666 . X  - Local input vector
667 - user - The user context
668 
669   Output Parameter:
670 . F  - Local output vector
671 
672   Note:
673   The second member of the user context must be an FEMContext.
674 
675   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
676   like a GPU, or vectorize on a multicore machine.
677 
678   Level: developer
679 
680 .seealso: DMPlexComputeResidualFEM()
681 @*/
682 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
683 {
684   DM_Plex          *mesh = (DM_Plex *) dm->data;
685   PetscFEM         *fem  = (PetscFEM *) user;
686   PetscFE          *fe   = fem->fe;
687   PetscQuadrature   quad;
688   PetscCellGeometry geom;
689   PetscSection      section;
690   JacActionCtx     *jctx;
691   PetscReal        *v0, *J, *invJ, *detJ;
692   PetscScalar      *elemVec, *u, *a;
693   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
694   PetscInt          cellDof = 0;
695   PetscErrorCode    ierr;
696 
697   PetscFunctionBegin;
698   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
699   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
700   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
701   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
702   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
703   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
704   numCells = cEnd - cStart;
705   for (field = 0; field < numFields; ++field) {
706     PetscInt Nb, Nc;
707 
708     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
709     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
710     cellDof += Nb*Nc;
711   }
712   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
713   ierr = PetscMalloc7(numCells*cellDof,PetscScalar,&u,numCells*cellDof,PetscScalar,&a,numCells*dim,PetscReal,&v0,numCells*dim*dim,PetscReal,&J,numCells*dim*dim,PetscReal,&invJ,numCells,PetscReal,&detJ,numCells*cellDof,PetscScalar,&elemVec);CHKERRQ(ierr);
714   for (c = cStart; c < cEnd; ++c) {
715     PetscScalar *x = NULL;
716     PetscInt     i;
717 
718     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
719     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
720     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
721     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
722     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
723     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
724     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
725     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
726   }
727   for (field = 0; field < numFields; ++field) {
728     PetscInt Nb;
729     /* Conforming batches */
730     PetscInt numBlocks  = 1;
731     PetscInt numBatches = 1;
732     PetscInt numChunks, Ne, blockSize, batchSize;
733     /* Remainder */
734     PetscInt Nr, offset;
735 
736     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
737     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
738     blockSize = Nb*quad.numPoints;
739     batchSize = numBlocks * blockSize;
740     numChunks = numCells / (numBatches*batchSize);
741     Ne        = numChunks*numBatches*batchSize;
742     Nr        = numCells % (numBatches*batchSize);
743     offset    = numCells - Nr;
744     geom.v0   = v0;
745     geom.J    = J;
746     geom.invJ = invJ;
747     geom.detJ = detJ;
748     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
749     geom.v0   = &v0[offset*dim];
750     geom.J    = &J[offset*dim*dim];
751     geom.invJ = &invJ[offset*dim*dim];
752     geom.detJ = &detJ[offset];
753     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
754                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
755   }
756   for (c = cStart; c < cEnd; ++c) {
757     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
758     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
759   }
760   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
761   if (mesh->printFEM) {
762     PetscMPIInt rank, numProcs;
763     PetscInt    p;
764 
765     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
766     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
767     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
768     for (p = 0; p < numProcs; ++p) {
769       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
770       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
771     }
772   }
773   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
774   PetscFunctionReturn(0);
775 }
776 
777 #undef __FUNCT__
778 #define __FUNCT__ "DMPlexComputeJacobianFEM"
779 /*@
780   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
781 
782   Input Parameters:
783 + dm - The mesh
784 . X  - Local input vector
785 - user - The user context
786 
787   Output Parameter:
788 . Jac  - Jacobian matrix
789 
790   Note:
791   The second member of the user context must be an FEMContext.
792 
793   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
794   like a GPU, or vectorize on a multicore machine.
795 
796   Level: developer
797 
798 .seealso: FormFunctionLocal()
799 @*/
800 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP, MatStructure *str,void *user)
801 {
802   DM_Plex          *mesh  = (DM_Plex *) dm->data;
803   PetscFEM         *fem   = (PetscFEM *) user;
804   PetscFE          *fe    = fem->fe;
805   PetscFE          *feAux = fem->feAux;
806   const char       *name  = "Jacobian";
807   DM                dmAux;
808   Vec               A;
809   PetscQuadrature   quad;
810   PetscCellGeometry geom;
811   PetscSection      section, globalSection, sectionAux;
812   PetscReal        *v0, *J, *invJ, *detJ;
813   PetscScalar      *elemMat, *u, *a;
814   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
815   PetscInt          cellDof = 0, numComponents = 0;
816   PetscInt          cellDofAux = 0, numComponentsAux = 0;
817   PetscBool         isShell;
818   PetscErrorCode    ierr;
819 
820   PetscFunctionBegin;
821   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
822   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
823   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
824   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
825   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
826   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
827   numCells = cEnd - cStart;
828   for (f = 0; f < Nf; ++f) {
829     PetscInt Nb, Nc;
830 
831     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
832     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
833     cellDof       += Nb*Nc;
834     numComponents += Nc;
835   }
836   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
837   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
838   if (dmAux) {
839     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
840     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
841   }
842   for (f = 0; f < NfAux; ++f) {
843     PetscInt Nb, Nc;
844 
845     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
846     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
847     cellDofAux       += Nb*Nc;
848     numComponentsAux += Nc;
849   }
850   ierr = DMPlexProjectFunctionLocal(dm, fe, fem->bcFuncs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
851   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
852   ierr = PetscMalloc6(numCells*cellDof,PetscScalar,&u,numCells*dim,PetscReal,&v0,numCells*dim*dim,PetscReal,&J,numCells*dim*dim,PetscReal,&invJ,numCells,PetscReal,&detJ,numCells*cellDof*cellDof,PetscScalar,&elemMat);CHKERRQ(ierr);
853   if (dmAux) {ierr = PetscMalloc(numCells*cellDofAux * sizeof(PetscScalar), &a);CHKERRQ(ierr);}
854   for (c = cStart; c < cEnd; ++c) {
855     PetscScalar *x = NULL;
856     PetscInt     i;
857 
858     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
859     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
860     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
861     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
862     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
863     if (dmAux) {
864       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
865       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
866       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
867     }
868   }
869   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
870   for (fieldI = 0; fieldI < Nf; ++fieldI) {
871     PetscInt Nb;
872     /* Conforming batches */
873     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
874     /* Remainder */
875     PetscInt Nr, offset;
876 
877     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
878     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
879     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
880     blockSize = Nb*quad.numPoints;
881     batchSize = numBlocks * blockSize;
882     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
883     numChunks = numCells / (numBatches*batchSize);
884     Ne        = numChunks*numBatches*batchSize;
885     Nr        = numCells % (numBatches*batchSize);
886     offset    = numCells - Nr;
887     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
888       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
889       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
890       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
891       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
892 
893       geom.v0   = v0;
894       geom.J    = J;
895       geom.invJ = invJ;
896       geom.detJ = detJ;
897       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
898       geom.v0   = &v0[offset*dim];
899       geom.J    = &J[offset*dim*dim];
900       geom.invJ = &invJ[offset*dim*dim];
901       geom.detJ = &detJ[offset];
902       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);
903     }
904   }
905   for (c = cStart; c < cEnd; ++c) {
906     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
907     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
908   }
909   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
910   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
911   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
912   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
913   if (mesh->printFEM) {
914     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
915     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
916     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
917   }
918   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
919   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
920   if (isShell) {
921     JacActionCtx *jctx;
922 
923     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
924     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
925   }
926   *str = SAME_NONZERO_PATTERN;
927   PetscFunctionReturn(0);
928 }
929