xref: /petsc/src/dm/impls/plex/plexfem.c (revision dcca6d9d80ebd869fe6029bd05a3aa9faafef49e) 
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 = DMPlexGetCoordinateSection(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,&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       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   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
258   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, mode, localX);CHKERRQ(ierr);
259   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
260   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
261   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
262   PetscFunctionReturn(0);
263 }
264 
265 #undef __FUNCT__
266 #define __FUNCT__ "DMPlexComputeL2Diff"
267 /*@C
268   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
269 
270   Input Parameters:
271 + dm    - The DM
272 . fe    - The PetscFE object for each field
273 . funcs - The functions to evaluate for each field component
274 - X     - The coefficient vector u_h
275 
276   Output Parameter:
277 . diff - The diff ||u - u_h||_2
278 
279   Level: developer
280 
281 .seealso: DMPlexProjectFunction()
282 @*/
283 PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *), Vec X, PetscReal *diff)
284 {
285   const PetscInt  debug = 0;
286   PetscSection    section;
287   PetscQuadrature quad;
288   Vec             localX;
289   PetscScalar    *funcVal;
290   PetscReal      *coords, *v0, *J, *invJ, detJ;
291   PetscReal       localDiff = 0.0;
292   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
293   PetscErrorCode  ierr;
294 
295   PetscFunctionBegin;
296   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
297   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
298   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
299   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
300   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
301   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
302   for (field = 0; field < numFields; ++field) {
303     PetscInt Nc;
304 
305     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
306     numComponents += Nc;
307   }
308   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
309   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
310   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
311   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
312   for (c = cStart; c < cEnd; ++c) {
313     PetscScalar *x = NULL;
314     PetscReal    elemDiff = 0.0;
315 
316     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
317     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
318     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
319 
320     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
321       const PetscInt   numQuadPoints = quad.numPoints;
322       const PetscReal *quadPoints    = quad.points;
323       const PetscReal *quadWeights   = quad.weights;
324       PetscReal       *basis;
325       PetscInt         numBasisFuncs, numBasisComps, q, d, e, fc, f;
326 
327       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
328       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
329       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
330       if (debug) {
331         char title[1024];
332         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
333         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
334       }
335       for (q = 0; q < numQuadPoints; ++q) {
336         for (d = 0; d < dim; d++) {
337           coords[d] = v0[d];
338           for (e = 0; e < dim; e++) {
339             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
340           }
341         }
342         (*funcs[field])(coords, funcVal);
343         for (fc = 0; fc < numBasisComps; ++fc) {
344           PetscScalar interpolant = 0.0;
345 
346           for (f = 0; f < numBasisFuncs; ++f) {
347             const PetscInt fidx = f*numBasisComps+fc;
348             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
349           }
350           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);}
351           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
352         }
353       }
354       comp        += numBasisComps;
355       fieldOffset += numBasisFuncs*numBasisComps;
356     }
357     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
358     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
359     localDiff += elemDiff;
360   }
361   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
362   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
363   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
364   *diff = PetscSqrtReal(*diff);
365   PetscFunctionReturn(0);
366 }
367 
368 #if 0
369 
370 #undef __FUNCT__
371 #define __FUNCT__ "DMPlexComputeResidualFEM"
372 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
373 {
374   DM_Plex         *mesh   = (DM_Plex *) dm->data;
375   PetscFEM        *fem    = (PetscFEM *) user;
376   PetscQuadrature *quad   = fem->quad;
377   PetscQuadrature *quadBd = fem->quadBd;
378   PetscSection     section;
379   PetscReal       *v0, *n, *J, *invJ, *detJ;
380   PetscScalar     *elemVec, *u;
381   PetscInt         dim, numFields, field, numBatchesTmp = 1, numCells, cStart, cEnd, c;
382   PetscInt         cellDof, numComponents;
383   PetscBool        has;
384   PetscErrorCode   ierr;
385 
386   PetscFunctionBegin;
387   if (has && quadBd) {
388     DMLabel         label;
389     IS              pointIS;
390     const PetscInt *points;
391     PetscInt        numPoints, p;
392 
393     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
394     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
395     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
396     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
397     for (field = 0, cellDof = 0, numComponents = 0; field < numFields; ++field) {
398       cellDof       += quadBd[field].numBasisFuncs*quadBd[field].numComponents;
399       numComponents += quadBd[field].numComponents;
400     }
401     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);
402     for (p = 0; p < numPoints; ++p) {
403       const PetscInt point = points[p];
404       PetscScalar   *x;
405       PetscInt       i;
406 
407       /* TODO: Add normal determination here */
408       ierr = DMPlexComputeCellGeometry(dm, point, &v0[p*dim], &J[p*dim*dim], &invJ[p*dim*dim], &detJ[p]);CHKERRQ(ierr);
409       if (detJ[p] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[p], point);
410       ierr = DMPlexVecGetClosure(dm, NULL, X, point, NULL, &x);CHKERRQ(ierr);
411 
412       for (i = 0; i < cellDof; ++i) u[p*cellDof+i] = x[i];
413       ierr = DMPlexVecRestoreClosure(dm, NULL, X, point, NULL, &x);CHKERRQ(ierr);
414     }
415     for (field = 0; field < numFields; ++field) {
416       const PetscInt numQuadPoints = quadBd[field].numQuadPoints;
417       const PetscInt numBasisFuncs = quadBd[field].numBasisFuncs;
418       void           (*f0)(const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[field];
419       void           (*f1)(const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[field];
420       /* Conforming batches */
421       PetscInt blockSize  = numBasisFuncs*numQuadPoints;
422       PetscInt numBlocks  = 1;
423       PetscInt batchSize  = numBlocks * blockSize;
424       PetscInt numBatches = numBatchesTmp;
425       PetscInt numChunks  = numPoints / (numBatches*batchSize);
426       /* Remainder */
427       PetscInt numRemainder = numPoints % (numBatches * batchSize);
428       PetscInt offset       = numPoints - numRemainder;
429 
430       ierr = (*mesh->integrateBdResidualFEM)(numChunks*numBatches*batchSize, numFields, field, quadBd, u, v0, n, J, invJ, detJ, f0, f1, elemVec);CHKERRQ(ierr);
431       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],
432                                              f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
433     }
434     for (p = 0; p < numPoints; ++p) {
435       const PetscInt point = points[p];
436 
437       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "Residual", cellDof, &elemVec[p*cellDof]);CHKERRQ(ierr);}
438       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[p*cellDof], ADD_VALUES);CHKERRQ(ierr);
439     }
440     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
441     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
442     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
443   }
444   PetscFunctionReturn(0);
445 }
446 
447 #else
448 
449 #undef __FUNCT__
450 #define __FUNCT__ "DMPlexComputeResidualFEM"
451 /*@
452   DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
453 
454   Input Parameters:
455 + dm - The mesh
456 . X  - Local input vector
457 - user - The user context
458 
459   Output Parameter:
460 . F  - Local output vector
461 
462   Note:
463   The second member of the user context must be an FEMContext.
464 
465   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
466   like a GPU, or vectorize on a multicore machine.
467 
468   Level: developer
469 
470 .seealso: DMPlexComputeJacobianActionFEM()
471 @*/
472 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
473 {
474   DM_Plex          *mesh  = (DM_Plex *) dm->data;
475   PetscFEM         *fem   = (PetscFEM *) user;
476   PetscFE          *fe    = fem->fe;
477   PetscFE          *feAux = fem->feAux;
478   PetscFE          *feBd  = fem->feBd;
479   const char       *name  = "Residual";
480   DM                dmAux;
481   Vec               A;
482   PetscQuadrature   q;
483   PetscCellGeometry geom;
484   PetscSection      section, sectionAux;
485   PetscReal        *v0, *J, *invJ, *detJ;
486   PetscScalar      *elemVec, *u, *a;
487   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
488   PetscInt          cellDof = 0, numComponents = 0;
489   PetscInt          cellDofAux = 0, numComponentsAux = 0;
490   PetscErrorCode    ierr;
491 
492   PetscFunctionBegin;
493   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
494   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
495   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
496   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
497   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
498   numCells = cEnd - cStart;
499   for (f = 0; f < Nf; ++f) {
500     PetscInt Nb, Nc;
501 
502     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
503     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
504     cellDof       += Nb*Nc;
505     numComponents += Nc;
506   }
507   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
508   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
509   if (dmAux) {
510     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
511     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
512   }
513   for (f = 0; f < NfAux; ++f) {
514     PetscInt Nb, Nc;
515 
516     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
517     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
518     cellDofAux       += Nb*Nc;
519     numComponentsAux += Nc;
520   }
521   ierr = DMPlexProjectFunctionLocal(dm, fe, fem->bcFuncs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
522   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
523   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
524   if (dmAux) {ierr = PetscMalloc(numCells*cellDofAux * sizeof(PetscScalar), &a);CHKERRQ(ierr);}
525   for (c = cStart; c < cEnd; ++c) {
526     PetscScalar *x = NULL;
527     PetscInt     i;
528 
529     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
530     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
531     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
532     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
533     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
534     if (dmAux) {
535       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
536       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
537       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
538     }
539   }
540   for (f = 0; f < Nf; ++f) {
541     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0Funcs[f];
542     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1Funcs[f];
543     PetscInt Nb;
544     /* Conforming batches */
545     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
546     /* Remainder */
547     PetscInt Nr, offset;
548 
549     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
550     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
551     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
552     blockSize = Nb*q.numPoints;
553     batchSize = numBlocks * blockSize;
554     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
555     numChunks = numCells / (numBatches*batchSize);
556     Ne        = numChunks*numBatches*batchSize;
557     Nr        = numCells % (numBatches*batchSize);
558     offset    = numCells - Nr;
559     geom.v0   = v0;
560     geom.J    = J;
561     geom.invJ = invJ;
562     geom.detJ = detJ;
563     ierr = PetscFEIntegrateResidual(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
564     geom.v0   = &v0[offset*dim];
565     geom.J    = &J[offset*dim*dim];
566     geom.invJ = &invJ[offset*dim*dim];
567     geom.detJ = &detJ[offset];
568     ierr = PetscFEIntegrateResidual(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
569   }
570   for (c = cStart; c < cEnd; ++c) {
571     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
572     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
573   }
574   ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
575   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
576   if (feBd) {
577     DMLabel         label, depth;
578     IS              pointIS;
579     const PetscInt *points;
580     PetscInt        dep, numPoints, p, numFaces;
581     PetscReal      *n;
582 
583     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
584     ierr = DMPlexGetDepthLabel(dm, &depth);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     for (p = 0, numFaces = 0; p < numPoints; ++p) {
597       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
598       if (dep == dim-1) ++numFaces;
599     }
600     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);
601     for (p = 0, f = 0; p < numPoints; ++p) {
602       const PetscInt point = points[p];
603       PetscScalar   *x     = NULL;
604       PetscInt       i;
605 
606       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
607       if (dep != dim-1) continue;
608       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
609       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
610       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
611       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
612       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
613       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
614       ++f;
615     }
616     for (f = 0; f < Nf; ++f) {
617       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
618       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
619       PetscInt Nb;
620       /* Conforming batches */
621       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
622       /* Remainder */
623       PetscInt Nr, offset;
624 
625       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
626       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
627       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
628       blockSize = Nb*q.numPoints;
629       batchSize = numBlocks * blockSize;
630       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
631       numChunks = numFaces / (numBatches*batchSize);
632       Ne        = numChunks*numBatches*batchSize;
633       Nr        = numFaces % (numBatches*batchSize);
634       offset    = numFaces - Nr;
635       geom.v0   = v0;
636       geom.n    = n;
637       geom.J    = J;
638       geom.invJ = invJ;
639       geom.detJ = detJ;
640       ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
641       geom.v0   = &v0[offset*dim];
642       geom.n    = &n[offset*dim];
643       geom.J    = &J[offset*dim*dim];
644       geom.invJ = &invJ[offset*dim*dim];
645       geom.detJ = &detJ[offset];
646       ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
647     }
648     for (p = 0, f = 0; p < numPoints; ++p) {
649       const PetscInt point = points[p];
650 
651       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
652       if (dep != dim-1) continue;
653       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
654       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
655       ++f;
656     }
657     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
658     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
659     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
660   }
661   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
662   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
663   PetscFunctionReturn(0);
664 }
665 
666 #endif
667 
668 #undef __FUNCT__
669 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
670 /*@C
671   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
672 
673   Input Parameters:
674 + dm - The mesh
675 . J  - The Jacobian shell matrix
676 . X  - Local input vector
677 - user - The user context
678 
679   Output Parameter:
680 . F  - Local output vector
681 
682   Note:
683   The second member of the user context must be an FEMContext.
684 
685   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
686   like a GPU, or vectorize on a multicore machine.
687 
688   Level: developer
689 
690 .seealso: DMPlexComputeResidualFEM()
691 @*/
692 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
693 {
694   DM_Plex          *mesh = (DM_Plex *) dm->data;
695   PetscFEM         *fem  = (PetscFEM *) user;
696   PetscFE          *fe   = fem->fe;
697   PetscQuadrature   quad;
698   PetscCellGeometry geom;
699   PetscSection      section;
700   JacActionCtx     *jctx;
701   PetscReal        *v0, *J, *invJ, *detJ;
702   PetscScalar      *elemVec, *u, *a;
703   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
704   PetscInt          cellDof = 0;
705   PetscErrorCode    ierr;
706 
707   PetscFunctionBegin;
708   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
709   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
710   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
711   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
712   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
713   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
714   numCells = cEnd - cStart;
715   for (field = 0; field < numFields; ++field) {
716     PetscInt Nb, Nc;
717 
718     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
719     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
720     cellDof += Nb*Nc;
721   }
722   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
723   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);
724   for (c = cStart; c < cEnd; ++c) {
725     PetscScalar *x = NULL;
726     PetscInt     i;
727 
728     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
729     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
730     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
731     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
732     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
733     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
734     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
735     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
736   }
737   for (field = 0; field < numFields; ++field) {
738     PetscInt Nb;
739     /* Conforming batches */
740     PetscInt numBlocks  = 1;
741     PetscInt numBatches = 1;
742     PetscInt numChunks, Ne, blockSize, batchSize;
743     /* Remainder */
744     PetscInt Nr, offset;
745 
746     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
747     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
748     blockSize = Nb*quad.numPoints;
749     batchSize = numBlocks * blockSize;
750     numChunks = numCells / (numBatches*batchSize);
751     Ne        = numChunks*numBatches*batchSize;
752     Nr        = numCells % (numBatches*batchSize);
753     offset    = numCells - Nr;
754     geom.v0   = v0;
755     geom.J    = J;
756     geom.invJ = invJ;
757     geom.detJ = detJ;
758     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
759     geom.v0   = &v0[offset*dim];
760     geom.J    = &J[offset*dim*dim];
761     geom.invJ = &invJ[offset*dim*dim];
762     geom.detJ = &detJ[offset];
763     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
764                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
765   }
766   for (c = cStart; c < cEnd; ++c) {
767     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
768     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
769   }
770   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
771   if (mesh->printFEM) {
772     PetscMPIInt rank, numProcs;
773     PetscInt    p;
774 
775     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
776     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
777     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
778     for (p = 0; p < numProcs; ++p) {
779       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
780       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
781     }
782   }
783   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
784   PetscFunctionReturn(0);
785 }
786 
787 #undef __FUNCT__
788 #define __FUNCT__ "DMPlexComputeJacobianFEM"
789 /*@
790   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
791 
792   Input Parameters:
793 + dm - The mesh
794 . X  - Local input vector
795 - user - The user context
796 
797   Output Parameter:
798 . Jac  - Jacobian matrix
799 
800   Note:
801   The second member of the user context must be an FEMContext.
802 
803   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
804   like a GPU, or vectorize on a multicore machine.
805 
806   Level: developer
807 
808 .seealso: FormFunctionLocal()
809 @*/
810 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP, MatStructure *str,void *user)
811 {
812   DM_Plex          *mesh  = (DM_Plex *) dm->data;
813   PetscFEM         *fem   = (PetscFEM *) user;
814   PetscFE          *fe    = fem->fe;
815   PetscFE          *feAux = fem->feAux;
816   const char       *name  = "Jacobian";
817   DM                dmAux;
818   Vec               A;
819   PetscQuadrature   quad;
820   PetscCellGeometry geom;
821   PetscSection      section, globalSection, sectionAux;
822   PetscReal        *v0, *J, *invJ, *detJ;
823   PetscScalar      *elemMat, *u, *a;
824   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
825   PetscInt          cellDof = 0, numComponents = 0;
826   PetscInt          cellDofAux = 0, numComponentsAux = 0;
827   PetscBool         isShell;
828   PetscErrorCode    ierr;
829 
830   PetscFunctionBegin;
831   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
832   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
833   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
834   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
835   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
836   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
837   numCells = cEnd - cStart;
838   for (f = 0; f < Nf; ++f) {
839     PetscInt Nb, Nc;
840 
841     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
842     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
843     cellDof       += Nb*Nc;
844     numComponents += Nc;
845   }
846   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
847   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
848   if (dmAux) {
849     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
850     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
851   }
852   for (f = 0; f < NfAux; ++f) {
853     PetscInt Nb, Nc;
854 
855     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
856     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
857     cellDofAux       += Nb*Nc;
858     numComponentsAux += Nc;
859   }
860   ierr = DMPlexProjectFunctionLocal(dm, fe, fem->bcFuncs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
861   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
862   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
863   if (dmAux) {ierr = PetscMalloc(numCells*cellDofAux * sizeof(PetscScalar), &a);CHKERRQ(ierr);}
864   for (c = cStart; c < cEnd; ++c) {
865     PetscScalar *x = NULL;
866     PetscInt     i;
867 
868     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
869     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
870     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
871     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
872     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
873     if (dmAux) {
874       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
875       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
876       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
877     }
878   }
879   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
880   for (fieldI = 0; fieldI < Nf; ++fieldI) {
881     PetscInt Nb;
882     /* Conforming batches */
883     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
884     /* Remainder */
885     PetscInt Nr, offset;
886 
887     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
888     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
889     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
890     blockSize = Nb*quad.numPoints;
891     batchSize = numBlocks * blockSize;
892     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
893     numChunks = numCells / (numBatches*batchSize);
894     Ne        = numChunks*numBatches*batchSize;
895     Nr        = numCells % (numBatches*batchSize);
896     offset    = numCells - Nr;
897     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
898       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
899       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
900       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
901       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
902 
903       geom.v0   = v0;
904       geom.J    = J;
905       geom.invJ = invJ;
906       geom.detJ = detJ;
907       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
908       geom.v0   = &v0[offset*dim];
909       geom.J    = &J[offset*dim*dim];
910       geom.invJ = &invJ[offset*dim*dim];
911       geom.detJ = &detJ[offset];
912       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);
913     }
914   }
915   for (c = cStart; c < cEnd; ++c) {
916     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
917     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
918   }
919   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
920   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
921   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
922   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
923   if (mesh->printFEM) {
924     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
925     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
926     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
927   }
928   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
929   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
930   if (isShell) {
931     JacActionCtx *jctx;
932 
933     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
934     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
935   }
936   *str = SAME_NONZERO_PATTERN;
937   PetscFunctionReturn(0);
938 }
939