xref: /petsc/src/dm/impls/plex/plexfem.c (revision ed91c37e759c22f27466ebab4e4819970f7fc0f7) 
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 = 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       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,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&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,&u,numPoints*dim,&v0,numPoints*dim,&n,numPoints*dim*dim,&J,numPoints*dim*dim,&invJ,numPoints,&detJ,numPoints*cellDof,&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 = NULL;
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,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
525   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &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, depth;
579     IS              pointIS;
580     const PetscInt *points;
581     PetscInt        dep, numPoints, p, numFaces;
582     PetscReal      *n;
583 
584     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
585     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
586     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
587     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
588     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
589     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
590       PetscInt Nb, Nc;
591 
592       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
593       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
594       cellDof       += Nb*Nc;
595       numComponents += Nc;
596     }
597     for (p = 0, numFaces = 0; p < numPoints; ++p) {
598       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
599       if (dep == dim-1) ++numFaces;
600     }
601     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);
602     for (p = 0, f = 0; p < numPoints; ++p) {
603       const PetscInt point = points[p];
604       PetscScalar   *x     = NULL;
605       PetscInt       i;
606 
607       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
608       if (dep != dim-1) continue;
609       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
610       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
611       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
612       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
613       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
614       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
615       ++f;
616     }
617     for (f = 0; f < Nf; ++f) {
618       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
619       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
620       PetscInt Nb;
621       /* Conforming batches */
622       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
623       /* Remainder */
624       PetscInt Nr, offset;
625 
626       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
627       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
628       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
629       blockSize = Nb*q.numPoints;
630       batchSize = numBlocks * blockSize;
631       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
632       numChunks = numFaces / (numBatches*batchSize);
633       Ne        = numChunks*numBatches*batchSize;
634       Nr        = numFaces % (numBatches*batchSize);
635       offset    = numFaces - Nr;
636       geom.v0   = v0;
637       geom.n    = n;
638       geom.J    = J;
639       geom.invJ = invJ;
640       geom.detJ = detJ;
641       ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
642       geom.v0   = &v0[offset*dim];
643       geom.n    = &n[offset*dim];
644       geom.J    = &J[offset*dim*dim];
645       geom.invJ = &invJ[offset*dim*dim];
646       geom.detJ = &detJ[offset];
647       ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
648     }
649     for (p = 0, f = 0; p < numPoints; ++p) {
650       const PetscInt point = points[p];
651 
652       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
653       if (dep != dim-1) continue;
654       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
655       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
656       ++f;
657     }
658     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
659     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
660     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
661   }
662   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
663   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
664   PetscFunctionReturn(0);
665 }
666 
667 #endif
668 
669 #undef __FUNCT__
670 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
671 /*@C
672   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
673 
674   Input Parameters:
675 + dm - The mesh
676 . J  - The Jacobian shell matrix
677 . X  - Local input vector
678 - user - The user context
679 
680   Output Parameter:
681 . F  - Local output vector
682 
683   Note:
684   The second member of the user context must be an FEMContext.
685 
686   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
687   like a GPU, or vectorize on a multicore machine.
688 
689   Level: developer
690 
691 .seealso: DMPlexComputeResidualFEM()
692 @*/
693 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
694 {
695   DM_Plex          *mesh = (DM_Plex *) dm->data;
696   PetscFEM         *fem  = (PetscFEM *) user;
697   PetscFE          *fe   = fem->fe;
698   PetscQuadrature   quad;
699   PetscCellGeometry geom;
700   PetscSection      section;
701   JacActionCtx     *jctx;
702   PetscReal        *v0, *J, *invJ, *detJ;
703   PetscScalar      *elemVec, *u, *a;
704   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
705   PetscInt          cellDof = 0;
706   PetscErrorCode    ierr;
707 
708   PetscFunctionBegin;
709   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
710   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
711   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
712   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
713   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
714   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
715   numCells = cEnd - cStart;
716   for (field = 0; field < numFields; ++field) {
717     PetscInt Nb, Nc;
718 
719     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
720     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
721     cellDof += Nb*Nc;
722   }
723   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
724   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);
725   for (c = cStart; c < cEnd; ++c) {
726     PetscScalar *x = NULL;
727     PetscInt     i;
728 
729     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
730     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
731     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
732     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
733     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
734     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
735     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
736     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
737   }
738   for (field = 0; field < numFields; ++field) {
739     PetscInt Nb;
740     /* Conforming batches */
741     PetscInt numBlocks  = 1;
742     PetscInt numBatches = 1;
743     PetscInt numChunks, Ne, blockSize, batchSize;
744     /* Remainder */
745     PetscInt Nr, offset;
746 
747     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
748     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
749     blockSize = Nb*quad.numPoints;
750     batchSize = numBlocks * blockSize;
751     numChunks = numCells / (numBatches*batchSize);
752     Ne        = numChunks*numBatches*batchSize;
753     Nr        = numCells % (numBatches*batchSize);
754     offset    = numCells - Nr;
755     geom.v0   = v0;
756     geom.J    = J;
757     geom.invJ = invJ;
758     geom.detJ = detJ;
759     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
760     geom.v0   = &v0[offset*dim];
761     geom.J    = &J[offset*dim*dim];
762     geom.invJ = &invJ[offset*dim*dim];
763     geom.detJ = &detJ[offset];
764     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
765                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
766   }
767   for (c = cStart; c < cEnd; ++c) {
768     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
769     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
770   }
771   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
772   if (mesh->printFEM) {
773     PetscMPIInt rank, numProcs;
774     PetscInt    p;
775 
776     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
777     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
778     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
779     for (p = 0; p < numProcs; ++p) {
780       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
781       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
782     }
783   }
784   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
785   PetscFunctionReturn(0);
786 }
787 
788 #undef __FUNCT__
789 #define __FUNCT__ "DMPlexComputeJacobianFEM"
790 /*@
791   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
792 
793   Input Parameters:
794 + dm - The mesh
795 . X  - Local input vector
796 - user - The user context
797 
798   Output Parameter:
799 . Jac  - Jacobian matrix
800 
801   Note:
802   The second member of the user context must be an FEMContext.
803 
804   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
805   like a GPU, or vectorize on a multicore machine.
806 
807   Level: developer
808 
809 .seealso: FormFunctionLocal()
810 @*/
811 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP, MatStructure *str,void *user)
812 {
813   DM_Plex          *mesh  = (DM_Plex *) dm->data;
814   PetscFEM         *fem   = (PetscFEM *) user;
815   PetscFE          *fe    = fem->fe;
816   PetscFE          *feAux = fem->feAux;
817   const char       *name  = "Jacobian";
818   DM                dmAux;
819   Vec               A;
820   PetscQuadrature   quad;
821   PetscCellGeometry geom;
822   PetscSection      section, globalSection, sectionAux;
823   PetscReal        *v0, *J, *invJ, *detJ;
824   PetscScalar      *elemMat, *u, *a;
825   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
826   PetscInt          cellDof = 0, numComponents = 0;
827   PetscInt          cellDofAux = 0, numComponentsAux = 0;
828   PetscBool         isShell;
829   PetscErrorCode    ierr;
830 
831   PetscFunctionBegin;
832   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
833   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
834   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
835   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
836   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
837   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
838   numCells = cEnd - cStart;
839   for (f = 0; f < Nf; ++f) {
840     PetscInt Nb, Nc;
841 
842     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
843     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
844     cellDof       += Nb*Nc;
845     numComponents += Nc;
846   }
847   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
848   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
849   if (dmAux) {
850     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
851     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
852   }
853   for (f = 0; f < NfAux; ++f) {
854     PetscInt Nb, Nc;
855 
856     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
857     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
858     cellDofAux       += Nb*Nc;
859     numComponentsAux += Nc;
860   }
861   ierr = DMPlexProjectFunctionLocal(dm, fe, fem->bcFuncs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
862   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
863   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
864   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
865   for (c = cStart; c < cEnd; ++c) {
866     PetscScalar *x = NULL;
867     PetscInt     i;
868 
869     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
870     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
871     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
872     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
873     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
874     if (dmAux) {
875       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
876       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
877       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
878     }
879   }
880   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
881   for (fieldI = 0; fieldI < Nf; ++fieldI) {
882     PetscInt Nb;
883     /* Conforming batches */
884     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
885     /* Remainder */
886     PetscInt Nr, offset;
887 
888     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
889     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
890     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
891     blockSize = Nb*quad.numPoints;
892     batchSize = numBlocks * blockSize;
893     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
894     numChunks = numCells / (numBatches*batchSize);
895     Ne        = numChunks*numBatches*batchSize;
896     Nr        = numCells % (numBatches*batchSize);
897     offset    = numCells - Nr;
898     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
899       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
900       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
901       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
902       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
903 
904       geom.v0   = v0;
905       geom.J    = J;
906       geom.invJ = invJ;
907       geom.detJ = detJ;
908       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
909       geom.v0   = &v0[offset*dim];
910       geom.J    = &J[offset*dim*dim];
911       geom.invJ = &invJ[offset*dim*dim];
912       geom.detJ = &detJ[offset];
913       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);
914     }
915   }
916   for (c = cStart; c < cEnd; ++c) {
917     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
918     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
919   }
920   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
921   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
922   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
923   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
924   if (mesh->printFEM) {
925     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
926     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
927     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
928   }
929   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
930   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
931   if (isShell) {
932     JacActionCtx *jctx;
933 
934     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
935     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
936   }
937   *str = SAME_NONZERO_PATTERN;
938   PetscFunctionReturn(0);
939 }
940