xref: /petsc/src/dm/impls/plex/plexfem.c (revision 95ecbf38f54bf907855fa510dba2b327f79c8484)
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__ "DMPlexProjectFunctionLabelLocal"
185 PetscErrorCode DMPlexProjectFunctionLabelLocal(DM dm, DMLabel label, PetscInt numIds, const PetscInt ids[], PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
186 {
187   PetscDualSpace *sp;
188   PetscSection    section;
189   PetscScalar    *values;
190   PetscReal      *v0, *J, detJ;
191   PetscBool      *fieldActive;
192   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, f, d, v, i, comp;
193   PetscErrorCode  ierr;
194 
195   PetscFunctionBegin;
196   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
197   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
198   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
199   ierr = PetscMalloc3(numFields,&sp,dim,&v0,dim*dim,&J);CHKERRQ(ierr);
200   for (f = 0; f < numFields; ++f) {
201     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
202     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
203     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
204     totDim += spDim*numComp;
205   }
206   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
207   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
208   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
209   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
210   ierr = DMGetWorkArray(dm, numFields, PETSC_BOOL, &fieldActive);CHKERRQ(ierr);
211   for (f = 0; f < numFields; ++f) fieldActive[f] = funcs[f] ? PETSC_TRUE : PETSC_FALSE;
212   for (i = 0; i < numIds; ++i) {
213     IS              pointIS;
214     const PetscInt *points;
215     PetscInt        n, p;
216 
217     ierr = DMLabelGetStratumIS(label, ids[i], &pointIS);CHKERRQ(ierr);
218     ierr = ISGetLocalSize(pointIS, &n);CHKERRQ(ierr);
219     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
220     for (p = 0; p < n; ++p) {
221       const PetscInt    point = points[p];
222       PetscCellGeometry geom;
223 
224       if ((point < cStart) || (point >= cEnd)) continue;
225       ierr = DMPlexComputeCellGeometry(dm, point, v0, J, NULL, &detJ);CHKERRQ(ierr);
226       geom.v0   = v0;
227       geom.J    = J;
228       geom.detJ = &detJ;
229       for (f = 0, v = 0; f < numFields; ++f) {
230         void * const ctx = ctxs ? ctxs[f] : NULL;
231         ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
232         ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
233         for (d = 0; d < spDim; ++d) {
234           if (funcs[f]) {
235             ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
236           } else {
237             for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
238           }
239           v += numComp;
240         }
241       }
242       ierr = DMPlexVecSetFieldClosure_Internal(dm, section, localX, fieldActive, point, values, mode);CHKERRQ(ierr);
243     }
244     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
245     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
246   }
247   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
248   ierr = DMRestoreWorkArray(dm, numFields, PETSC_BOOL, &fieldActive);CHKERRQ(ierr);
249   ierr = PetscFree3(sp,v0,J);CHKERRQ(ierr);
250   PetscFunctionReturn(0);
251 }
252 
253 #undef __FUNCT__
254 #define __FUNCT__ "DMPlexProjectFunctionLocal"
255 PetscErrorCode DMPlexProjectFunctionLocal(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
256 {
257   PetscDualSpace *sp;
258   PetscSection    section;
259   PetscScalar    *values;
260   PetscReal      *v0, *J, detJ;
261   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, c, f, d, v, comp;
262   PetscErrorCode  ierr;
263 
264   PetscFunctionBegin;
265   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
266   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
267   ierr = PetscMalloc1(numFields, &sp);CHKERRQ(ierr);
268   for (f = 0; f < numFields; ++f) {
269     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
270     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
271     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
272     totDim += spDim*numComp;
273   }
274   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
275   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
276   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
277   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
278   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
279   ierr = PetscMalloc2(dim,&v0,dim*dim,&J);CHKERRQ(ierr);
280   for (c = cStart; c < cEnd; ++c) {
281     PetscCellGeometry geom;
282 
283     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
284     geom.v0   = v0;
285     geom.J    = J;
286     geom.detJ = &detJ;
287     for (f = 0, v = 0; f < numFields; ++f) {
288       void * const ctx = ctxs ? ctxs[f] : NULL;
289       ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
290       ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
291       for (d = 0; d < spDim; ++d) {
292         if (funcs[f]) {
293           ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
294         } else {
295           for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
296         }
297         v += numComp;
298       }
299     }
300     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
301   }
302   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
303   ierr = PetscFree2(v0,J);CHKERRQ(ierr);
304   ierr = PetscFree(sp);CHKERRQ(ierr);
305   PetscFunctionReturn(0);
306 }
307 
308 #undef __FUNCT__
309 #define __FUNCT__ "DMPlexProjectFunction"
310 /*@C
311   DMPlexProjectFunction - This projects the given function into the function space provided.
312 
313   Input Parameters:
314 + dm      - The DM
315 . fe      - The PetscFE associated with the field
316 . funcs   - The coordinate functions to evaluate, one per field
317 . ctxs    - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
318 - mode    - The insertion mode for values
319 
320   Output Parameter:
321 . X - vector
322 
323   Level: developer
324 
325 .seealso: DMPlexComputeL2Diff()
326 @*/
327 PetscErrorCode DMPlexProjectFunction(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec X)
328 {
329   Vec            localX;
330   PetscErrorCode ierr;
331 
332   PetscFunctionBegin;
333   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
334   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
335   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, mode, localX);CHKERRQ(ierr);
336   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
337   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
338   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
339   PetscFunctionReturn(0);
340 }
341 
342 #undef __FUNCT__
343 #define __FUNCT__ "DMPlexInsertBoundaryValuesFEM"
344 PetscErrorCode DMPlexInsertBoundaryValuesFEM(DM dm, Vec localX)
345 {
346   void        (**funcs)(const PetscReal x[], PetscScalar *u, void *ctx);
347   void         **ctxs;
348   PetscFE       *fe;
349   PetscInt       numFields, f, numBd, b;
350   PetscErrorCode ierr;
351 
352   PetscFunctionBegin;
353   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
354   PetscValidHeaderSpecific(localX, VEC_CLASSID, 2);
355   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
356   ierr = PetscMalloc3(numFields,&fe,numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
357   for (f = 0; f < numFields; ++f) {ierr = DMGetField(dm, f, (PetscObject *) &fe[f]);CHKERRQ(ierr);}
358   /* OPT: Could attempt to do multiple BCs at once */
359   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
360   for (b = 0; b < numBd; ++b) {
361     DMLabel         label;
362     const PetscInt *ids;
363     const char     *name;
364     PetscInt        numids, field;
365     PetscBool       isEssential;
366     void          (*func)();
367     void           *ctx;
368 
369     /* TODO: We need to set only the part indicated by the ids */
370     ierr = DMPlexGetBoundary(dm, b, &isEssential, &name, &field, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
371     ierr = DMPlexGetLabel(dm, name, &label);CHKERRQ(ierr);
372     for (f = 0; f < numFields; ++f) {
373       funcs[f] = field == f ? (void (*)(const PetscReal[], PetscScalar *, void *)) func : NULL;
374       ctxs[f]  = field == f ? ctx : NULL;
375     }
376     ierr = DMPlexProjectFunctionLabelLocal(dm, label, numids, ids, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
377   }
378   ierr = PetscFree3(fe,funcs,ctxs);CHKERRQ(ierr);
379   PetscFunctionReturn(0);
380 }
381 
382 /* Assuming dim == 3 */
383 typedef struct {
384   PetscScalar normal[3];   /* Area-scaled normals */
385   PetscScalar centroid[3]; /* Location of centroid (quadrature point) */
386   PetscScalar grad[2][3];  /* Face contribution to gradient in left and right cell */
387 } FaceGeom;
388 
389 #undef __FUNCT__
390 #define __FUNCT__ "DMPlexInsertBoundaryValuesFVM"
391 PetscErrorCode DMPlexInsertBoundaryValuesFVM(DM dm, PetscReal time, Vec locX)
392 {
393   DM                 dmFace;
394   Vec                faceGeometry;
395   DMLabel            label;
396   const PetscScalar *facegeom;
397   PetscScalar       *x;
398   PetscInt           numBd, b, fStart, fEnd;
399   PetscErrorCode     ierr;
400 
401   PetscFunctionBegin;
402   /* TODO Pull this geometry calculation into the library */
403   ierr = PetscObjectQuery((PetscObject) dm, "FaceGeometry", (PetscObject *) &faceGeometry);CHKERRQ(ierr);
404   ierr = DMPlexGetLabel(dm, "Face Sets", &label);CHKERRQ(ierr);
405   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
406   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
407   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
408   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
409   ierr = VecGetArray(locX, &x);CHKERRQ(ierr);
410   for (b = 0; b < numBd; ++b) {
411     PetscErrorCode (*func)(PetscReal,const PetscScalar*,const PetscScalar*,const PetscScalar*,PetscScalar*,void*);
412     const PetscInt  *ids;
413     PetscInt         numids, i;
414     void            *ctx;
415 
416     ierr = DMPlexGetBoundary(dm, b, NULL, NULL, NULL, (void (**)()) &func, &numids, &ids, &ctx);CHKERRQ(ierr);
417     for (i = 0; i < numids; ++i) {
418       IS              faceIS;
419       const PetscInt *faces;
420       PetscInt        numFaces, f;
421 
422       ierr = DMLabelGetStratumIS(label, ids[i], &faceIS);CHKERRQ(ierr);
423       if (!faceIS) continue; /* No points with that id on this process */
424       ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
425       ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
426       for (f = 0; f < numFaces; ++f) {
427         const PetscInt     face = faces[f], *cells;
428         const PetscScalar *xI;
429         PetscScalar       *xG;
430         const FaceGeom    *fg;
431 
432         if ((face < fStart) || (face >= fEnd)) continue; /* Refinement adds non-faces to labels */
433         ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
434         ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
435         ierr = DMPlexPointLocalRead(dm, cells[0], x, &xI);CHKERRQ(ierr);
436         ierr = DMPlexPointLocalRef(dm, cells[1], x, &xG);CHKERRQ(ierr);
437         ierr = (*func)(time, fg->centroid, fg->normal, xI, xG, ctx);CHKERRQ(ierr);
438       }
439       ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
440       ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
441     }
442   }
443   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
444   ierr = VecRestoreArray(locX, &x);CHKERRQ(ierr);
445   PetscFunctionReturn(0);
446 }
447 
448 #undef __FUNCT__
449 #define __FUNCT__ "DMPlexComputeL2Diff"
450 /*@C
451   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
452 
453   Input Parameters:
454 + dm    - The DM
455 . fe    - The PetscFE object for each field
456 . funcs - The functions to evaluate for each field component
457 . ctxs  - Optional array of contexts to pass to each function, or NULL.
458 - X     - The coefficient vector u_h
459 
460   Output Parameter:
461 . diff - The diff ||u - u_h||_2
462 
463   Level: developer
464 
465 .seealso: DMPlexProjectFunction(), DMPlexComputeL2GradientDiff()
466 @*/
467 PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
468 {
469   const PetscInt  debug = 0;
470   PetscSection    section;
471   PetscQuadrature quad;
472   Vec             localX;
473   PetscScalar    *funcVal;
474   PetscReal      *coords, *v0, *J, *invJ, detJ;
475   PetscReal       localDiff = 0.0;
476   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
477   PetscErrorCode  ierr;
478 
479   PetscFunctionBegin;
480   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
481   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
482   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
483   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
484   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
485   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
486   for (field = 0; field < numFields; ++field) {
487     PetscInt Nc;
488 
489     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
490     numComponents += Nc;
491   }
492   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
493   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
494   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
495   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
496   for (c = cStart; c < cEnd; ++c) {
497     PetscScalar *x = NULL;
498     PetscReal    elemDiff = 0.0;
499 
500     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
501     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
502     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
503 
504     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
505       void * const     ctx = ctxs ? ctxs[field] : NULL;
506       const PetscReal *quadPoints, *quadWeights;
507       PetscReal       *basis;
508       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
509 
510       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
511       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
512       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
513       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
514       if (debug) {
515         char title[1024];
516         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
517         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
518       }
519       for (q = 0; q < numQuadPoints; ++q) {
520         for (d = 0; d < dim; d++) {
521           coords[d] = v0[d];
522           for (e = 0; e < dim; e++) {
523             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
524           }
525         }
526         (*funcs[field])(coords, funcVal, ctx);
527         for (fc = 0; fc < numBasisComps; ++fc) {
528           PetscScalar interpolant = 0.0;
529 
530           for (f = 0; f < numBasisFuncs; ++f) {
531             const PetscInt fidx = f*numBasisComps+fc;
532             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
533           }
534           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);}
535           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
536         }
537       }
538       comp        += numBasisComps;
539       fieldOffset += numBasisFuncs*numBasisComps;
540     }
541     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
542     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
543     localDiff += elemDiff;
544   }
545   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
546   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
547   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
548   *diff = PetscSqrtReal(*diff);
549   PetscFunctionReturn(0);
550 }
551 
552 #undef __FUNCT__
553 #define __FUNCT__ "DMPlexComputeL2GradientDiff"
554 /*@C
555   DMPlexComputeL2GradientDiff - This function computes the L_2 difference between the gradient of a function u and an FEM interpolant solution grad u_h.
556 
557   Input Parameters:
558 + dm    - The DM
559 . fe    - The PetscFE object for each field
560 . funcs - The gradient functions to evaluate for each field component
561 . ctxs  - Optional array of contexts to pass to each function, or NULL.
562 . X     - The coefficient vector u_h
563 - n     - The vector to project along
564 
565   Output Parameter:
566 . diff - The diff ||(grad u - grad u_h) . n||_2
567 
568   Level: developer
569 
570 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
571 @*/
572 PetscErrorCode DMPlexComputeL2GradientDiff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
573 {
574   const PetscInt  debug = 0;
575   PetscSection    section;
576   PetscQuadrature quad;
577   Vec             localX;
578   PetscScalar    *funcVal, *interpolantVec;
579   PetscReal      *coords, *realSpaceDer, *v0, *J, *invJ, detJ;
580   PetscReal       localDiff = 0.0;
581   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
582   PetscErrorCode  ierr;
583 
584   PetscFunctionBegin;
585   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
586   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
587   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
588   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
589   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
590   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
591   for (field = 0; field < numFields; ++field) {
592     PetscInt Nc;
593 
594     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
595     numComponents += Nc;
596   }
597   /* ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
598   ierr = PetscMalloc7(numComponents,&funcVal,dim,&coords,dim,&realSpaceDer,dim,&v0,dim*dim,&J,dim*dim,&invJ,dim,&interpolantVec);CHKERRQ(ierr);
599   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
600   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
601   for (c = cStart; c < cEnd; ++c) {
602     PetscScalar *x = NULL;
603     PetscReal    elemDiff = 0.0;
604 
605     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
606     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
607     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
608 
609     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
610       void * const     ctx = ctxs ? ctxs[field] : NULL;
611       const PetscReal *quadPoints, *quadWeights;
612       PetscReal       *basisDer;
613       PetscInt         numQuadPoints, Nb, Ncomp, q, d, e, fc, f, g;
614 
615       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
616       ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
617       ierr = PetscFEGetNumComponents(fe[field], &Ncomp);CHKERRQ(ierr);
618       ierr = PetscFEGetDefaultTabulation(fe[field], NULL, &basisDer, NULL);CHKERRQ(ierr);
619       if (debug) {
620         char title[1024];
621         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
622         ierr = DMPrintCellVector(c, title, Nb*Ncomp, &x[fieldOffset]);CHKERRQ(ierr);
623       }
624       for (q = 0; q < numQuadPoints; ++q) {
625         for (d = 0; d < dim; d++) {
626           coords[d] = v0[d];
627           for (e = 0; e < dim; e++) {
628             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
629           }
630         }
631         (*funcs[field])(coords, n, funcVal, ctx);
632         for (fc = 0; fc < Ncomp; ++fc) {
633           PetscScalar interpolant = 0.0;
634 
635           for (d = 0; d < dim; ++d) interpolantVec[d] = 0.0;
636           for (f = 0; f < Nb; ++f) {
637             const PetscInt fidx = f*Ncomp+fc;
638 
639             for (d = 0; d < dim; ++d) {
640               realSpaceDer[d] = 0.0;
641               for (g = 0; g < dim; ++g) {
642                 realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+fidx)*dim+g];
643               }
644               interpolantVec[d] += x[fieldOffset+fidx]*realSpaceDer[d];
645             }
646           }
647           for (d = 0; d < dim; ++d) interpolant += interpolantVec[d]*n[d];
648           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d fieldDer %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ);CHKERRQ(ierr);}
649           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
650         }
651       }
652       comp        += Ncomp;
653       fieldOffset += Nb*Ncomp;
654     }
655     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
656     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
657     localDiff += elemDiff;
658   }
659   ierr  = PetscFree7(funcVal,coords,realSpaceDer,v0,J,invJ,interpolantVec);CHKERRQ(ierr);
660   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
661   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
662   *diff = PetscSqrtReal(*diff);
663   PetscFunctionReturn(0);
664 }
665 
666 #undef __FUNCT__
667 #define __FUNCT__ "DMPlexComputeL2FieldDiff"
668 PetscErrorCode DMPlexComputeL2FieldDiff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal diff[])
669 {
670   const PetscInt  debug = 0;
671   PetscSection    section;
672   PetscQuadrature quad;
673   Vec             localX;
674   PetscScalar    *funcVal;
675   PetscReal      *coords, *v0, *J, *invJ, detJ;
676   PetscReal      *localDiff;
677   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
678   PetscErrorCode  ierr;
679 
680   PetscFunctionBegin;
681   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
682   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
683   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
684   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
685   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
686   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
687   for (field = 0; field < numFields; ++field) {
688     PetscInt Nc;
689 
690     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
691     numComponents += Nc;
692   }
693   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
694   ierr = PetscCalloc6(numFields,&localDiff,numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
695   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
696   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
697   for (c = cStart; c < cEnd; ++c) {
698     PetscScalar *x = NULL;
699 
700     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
701     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
702     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
703 
704     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
705       void * const     ctx = ctxs ? ctxs[field] : NULL;
706       const PetscReal *quadPoints, *quadWeights;
707       PetscReal       *basis, elemDiff = 0.0;
708       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
709 
710       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
711       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
712       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
713       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
714       if (debug) {
715         char title[1024];
716         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
717         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
718       }
719       for (q = 0; q < numQuadPoints; ++q) {
720         for (d = 0; d < dim; d++) {
721           coords[d] = v0[d];
722           for (e = 0; e < dim; e++) {
723             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
724           }
725         }
726         (*funcs[field])(coords, funcVal, ctx);
727         for (fc = 0; fc < numBasisComps; ++fc) {
728           PetscScalar interpolant = 0.0;
729 
730           for (f = 0; f < numBasisFuncs; ++f) {
731             const PetscInt fidx = f*numBasisComps+fc;
732             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
733           }
734           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);}
735           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
736         }
737       }
738       comp        += numBasisComps;
739       fieldOffset += numBasisFuncs*numBasisComps;
740       localDiff[field] += elemDiff;
741     }
742     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
743   }
744   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
745   ierr  = MPI_Allreduce(localDiff, diff, numFields, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
746   for (field = 0; field < numFields; ++field) diff[field] = PetscSqrtReal(diff[field]);
747   ierr  = PetscFree6(localDiff,funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
748   PetscFunctionReturn(0);
749 }
750 
751 #undef __FUNCT__
752 #define __FUNCT__ "DMPlexComputeIntegralFEM"
753 /*@
754   DMPlexComputeIntegralFEM - Form the local integral F from the local input X using pointwise functions specified by the user
755 
756   Input Parameters:
757 + dm - The mesh
758 . X  - Local input vector
759 . obj - The functions to integrate for each field
760 - user - The user context
761 
762   Output Parameter:
763 . integral - Local integral for each field
764 
765   Note:
766   The first member of the user context must be an FEMContext.
767 
768   Level: developer
769 
770 .seealso: DMPlexComputeResidualFEM()
771 @*/
772 PetscErrorCode DMPlexComputeIntegralFEM(DM dm, Vec X, void (**obj)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]), PetscReal *integral, void *user)
773 {
774   DM_Plex          *mesh  = (DM_Plex *) dm->data;
775   PetscFEM         *fem   = (PetscFEM *) user;
776   PetscFE          *fe    = fem->fe;
777   PetscFE          *feAux = fem->feAux;
778   DM                dmAux;
779   Vec               localX, A;
780   PetscQuadrature   q;
781   PetscCellGeometry geom;
782   PetscSection      section, sectionAux;
783   PetscReal        *v0, *J, *invJ, *detJ;
784   PetscScalar      *u, *a = NULL;
785   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
786   PetscInt          cellDof = 0, numComponents = 0;
787   PetscInt          cellDofAux = 0, numComponentsAux = 0;
788   PetscErrorCode    ierr;
789 
790   PetscFunctionBegin;
791   /*ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);*/
792   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
793   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
794   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
795   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
796   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
797   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
798   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
799   numCells = cEnd - cStart;
800   for (f = 0; f < Nf; ++f) {
801     PetscInt Nb, Nc;
802 
803     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
804     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
805     cellDof       += Nb*Nc;
806     numComponents += Nc;
807     integral[f]    = 0.0;
808   }
809   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
810   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
811   if (dmAux) {
812     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
813     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
814   }
815   for (f = 0; f < NfAux; ++f) {
816     PetscInt Nb, Nc;
817 
818     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
819     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
820     cellDofAux       += Nb*Nc;
821     numComponentsAux += Nc;
822   }
823   ierr = DMPlexInsertBoundaryValuesFEM(dm, localX);CHKERRQ(ierr);
824   ierr = PetscMalloc5(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ);CHKERRQ(ierr);
825   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
826   for (c = cStart; c < cEnd; ++c) {
827     PetscScalar *x = NULL;
828     PetscInt     i;
829 
830     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
831     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
832     ierr = DMPlexVecGetClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
833     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
834     ierr = DMPlexVecRestoreClosure(dm, section, localX, c, NULL, &x);CHKERRQ(ierr);
835     if (dmAux) {
836       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
837       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
838       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
839     }
840   }
841   for (f = 0; f < Nf; ++f) {
842     PetscInt numQuadPoints, Nb;
843     /* Conforming batches */
844     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
845     /* Remainder */
846     PetscInt Nr, offset;
847 
848     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
849     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
850     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
851     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
852     blockSize = Nb*numQuadPoints;
853     batchSize = numBlocks * blockSize;
854     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
855     numChunks = numCells / (numBatches*batchSize);
856     Ne        = numChunks*numBatches*batchSize;
857     Nr        = numCells % (numBatches*batchSize);
858     offset    = numCells - Nr;
859     geom.v0   = v0;
860     geom.J    = J;
861     geom.invJ = invJ;
862     geom.detJ = detJ;
863     ierr = PetscFEIntegrate(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, obj[f], integral);CHKERRQ(ierr);
864     geom.v0   = &v0[offset*dim];
865     geom.J    = &J[offset*dim*dim];
866     geom.invJ = &invJ[offset*dim*dim];
867     geom.detJ = &detJ[offset];
868     ierr = PetscFEIntegrate(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], obj[f], integral);CHKERRQ(ierr);
869   }
870   ierr = PetscFree5(u,v0,J,invJ,detJ);CHKERRQ(ierr);
871   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
872   if (mesh->printFEM) {
873     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Local integral:");CHKERRQ(ierr);
874     for (f = 0; f < Nf; ++f) {ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), " %g", integral[f]);CHKERRQ(ierr);}
875     ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "\n");CHKERRQ(ierr);
876   }
877   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
878   /* TODO: Allreduce for integral */
879   /*ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);*/
880   PetscFunctionReturn(0);
881 }
882 
883 #undef __FUNCT__
884 #define __FUNCT__ "DMPlexComputeResidualFEM"
885 /*@
886   DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
887 
888   Input Parameters:
889 + dm - The mesh
890 . X  - Local input vector
891 - user - The user context
892 
893   Output Parameter:
894 . F  - Local output vector
895 
896   Note:
897   The first member of the user context must be an FEMContext.
898 
899   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
900   like a GPU, or vectorize on a multicore machine.
901 
902   Level: developer
903 
904 .seealso: DMPlexComputeJacobianActionFEM()
905 @*/
906 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
907 {
908   DM_Plex          *mesh  = (DM_Plex *) dm->data;
909   PetscFEM         *fem   = (PetscFEM *) user;
910   PetscFE          *fe    = fem->fe;
911   PetscFE          *feAux = fem->feAux;
912   PetscFE          *feBd  = fem->feBd;
913   const char       *name  = "Residual";
914   DM                dmAux;
915   Vec               A;
916   PetscQuadrature   q;
917   PetscCellGeometry geom;
918   PetscSection      section, sectionAux;
919   PetscReal        *v0, *J, *invJ, *detJ;
920   PetscScalar      *elemVec, *u, *a = NULL;
921   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
922   PetscInt          cellDof = 0, numComponents = 0;
923   PetscInt          cellDofAux = 0, numComponentsAux = 0;
924   PetscErrorCode    ierr;
925 
926   PetscFunctionBegin;
927   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
928   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
929   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
930   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
931   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
932   numCells = cEnd - cStart;
933   for (f = 0; f < Nf; ++f) {
934     PetscInt Nb, Nc;
935 
936     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
937     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
938     cellDof       += Nb*Nc;
939     numComponents += Nc;
940   }
941   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
942   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
943   if (dmAux) {
944     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
945     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
946   }
947   for (f = 0; f < NfAux; ++f) {
948     PetscInt Nb, Nc;
949 
950     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
951     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
952     cellDofAux       += Nb*Nc;
953     numComponentsAux += Nc;
954   }
955   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
956   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
957   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
958   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
959   for (c = cStart; c < cEnd; ++c) {
960     PetscScalar *x = NULL;
961     PetscInt     i;
962 
963     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
964     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
965     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
966     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
967     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
968     if (dmAux) {
969       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
970       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
971       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
972     }
973   }
974   for (f = 0; f < Nf; ++f) {
975     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0Funcs[f];
976     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1Funcs[f];
977     PetscInt numQuadPoints, Nb;
978     /* Conforming batches */
979     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
980     /* Remainder */
981     PetscInt Nr, offset;
982 
983     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
984     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
985     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
986     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
987     blockSize = Nb*numQuadPoints;
988     batchSize = numBlocks * blockSize;
989     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
990     numChunks = numCells / (numBatches*batchSize);
991     Ne        = numChunks*numBatches*batchSize;
992     Nr        = numCells % (numBatches*batchSize);
993     offset    = numCells - Nr;
994     geom.v0   = v0;
995     geom.J    = J;
996     geom.invJ = invJ;
997     geom.detJ = detJ;
998     ierr = PetscFEIntegrateResidual(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
999     geom.v0   = &v0[offset*dim];
1000     geom.J    = &J[offset*dim*dim];
1001     geom.invJ = &invJ[offset*dim*dim];
1002     geom.detJ = &detJ[offset];
1003     ierr = PetscFEIntegrateResidual(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1004   }
1005   for (c = cStart; c < cEnd; ++c) {
1006     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1007     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1008   }
1009   ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1010   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1011   if (feBd) {
1012     DMLabel  depth;
1013     PetscInt numBd, bd;
1014 
1015     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
1016       PetscInt Nb, Nc;
1017 
1018       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1019       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
1020       cellDof       += Nb*Nc;
1021       numComponents += Nc;
1022     }
1023     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1024     ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1025     for (bd = 0; bd < numBd; ++bd) {
1026       const char     *bdLabel;
1027       DMLabel         label;
1028       IS              pointIS;
1029       const PetscInt *points;
1030       const PetscInt *values;
1031       PetscReal      *n;
1032       PetscInt        field, numValues, numPoints, p, dep, numFaces;
1033       PetscBool       isEssential;
1034 
1035       ierr = DMPlexGetBoundary(dm, bd, &isEssential, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1036       if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1037       ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1038       ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1039       ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1040       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1041       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1042         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1043         if (dep == dim-1) ++numFaces;
1044       }
1045       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);
1046       for (p = 0, f = 0; p < numPoints; ++p) {
1047         const PetscInt point = points[p];
1048         PetscScalar   *x     = NULL;
1049         PetscInt       i;
1050 
1051         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1052         if (dep != dim-1) continue;
1053         ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1054         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1055         if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1056         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1057         for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
1058         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1059         ++f;
1060       }
1061       for (f = 0; f < Nf; ++f) {
1062         void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
1063         void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
1064         PetscInt numQuadPoints, Nb;
1065         /* Conforming batches */
1066         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1067         /* Remainder */
1068         PetscInt Nr, offset;
1069 
1070         ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
1071         ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1072         ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1073         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1074         blockSize = Nb*numQuadPoints;
1075         batchSize = numBlocks * blockSize;
1076         ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1077         numChunks = numFaces / (numBatches*batchSize);
1078         Ne        = numChunks*numBatches*batchSize;
1079         Nr        = numFaces % (numBatches*batchSize);
1080         offset    = numFaces - Nr;
1081         geom.v0   = v0;
1082         geom.n    = n;
1083         geom.J    = J;
1084         geom.invJ = invJ;
1085         geom.detJ = detJ;
1086         ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
1087         geom.v0   = &v0[offset*dim];
1088         geom.n    = &n[offset*dim];
1089         geom.J    = &J[offset*dim*dim];
1090         geom.invJ = &invJ[offset*dim*dim];
1091         geom.detJ = &detJ[offset];
1092         ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1093       }
1094       for (p = 0, f = 0; p < numPoints; ++p) {
1095         const PetscInt point = points[p];
1096 
1097         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1098         if (dep != dim-1) continue;
1099         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
1100         ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
1101         ++f;
1102       }
1103       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1104       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1105       ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1106     }
1107   }
1108   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
1109   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1110   PetscFunctionReturn(0);
1111 }
1112 
1113 #undef __FUNCT__
1114 #define __FUNCT__ "DMPlexComputeIFunctionFEM"
1115 /*@
1116   DMPlexComputeIFunctionFEM - Form the local implicit function F from the local input X, X_t using pointwise functions specified by the user
1117 
1118   Input Parameters:
1119 + dm - The mesh
1120 . time - The current time
1121 . X  - Local input vector
1122 . X_t  - Time derivative of the local input vector
1123 - user - The user context
1124 
1125   Output Parameter:
1126 . F  - Local output vector
1127 
1128   Note:
1129   The first member of the user context must be an FEMContext.
1130 
1131   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1132   like a GPU, or vectorize on a multicore machine.
1133 
1134   Level: developer
1135 
1136 .seealso: DMPlexComputeResidualFEM()
1137 @*/
1138 PetscErrorCode DMPlexComputeIFunctionFEM(DM dm, PetscReal time, Vec X, Vec X_t, Vec F, void *user)
1139 {
1140   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1141   PetscFEM         *fem   = (PetscFEM *) user;
1142   PetscFE          *fe    = fem->fe;
1143   PetscFE          *feAux = fem->feAux;
1144   PetscFE          *feBd  = fem->feBd;
1145   const char       *name  = "Residual";
1146   DM                dmAux;
1147   Vec               A;
1148   PetscQuadrature   q;
1149   PetscCellGeometry geom;
1150   PetscSection      section, sectionAux;
1151   PetscReal        *v0, *J, *invJ, *detJ;
1152   PetscScalar      *elemVec, *u, *u_t, *a = NULL;
1153   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
1154   PetscInt          cellDof = 0, numComponents = 0;
1155   PetscInt          cellDofAux = 0, numComponentsAux = 0;
1156   PetscErrorCode    ierr;
1157 
1158   PetscFunctionBegin;
1159   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1160   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1161   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1162   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1163   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1164   numCells = cEnd - cStart;
1165   for (f = 0; f < Nf; ++f) {
1166     PetscInt Nb, Nc;
1167 
1168     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
1169     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1170     cellDof       += Nb*Nc;
1171     numComponents += Nc;
1172   }
1173   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1174   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1175   if (dmAux) {
1176     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1177     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
1178   }
1179   for (f = 0; f < NfAux; ++f) {
1180     PetscInt Nb, Nc;
1181 
1182     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
1183     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
1184     cellDofAux       += Nb*Nc;
1185     numComponentsAux += Nc;
1186   }
1187   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1188   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1189   ierr = PetscMalloc7(numCells*cellDof,&u,numCells*cellDof,&u_t,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
1190   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
1191   for (c = cStart; c < cEnd; ++c) {
1192     PetscScalar *x = NULL, *x_t = NULL;
1193     PetscInt     i;
1194 
1195     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1196     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1197     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1198     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1199     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1200     ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1201     for (i = 0; i < cellDof; ++i) u_t[c*cellDof+i] = x_t[i];
1202     ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1203     if (dmAux) {
1204       PetscScalar *x_a = NULL;
1205       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
1206       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x_a[i];
1207       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
1208     }
1209   }
1210   for (f = 0; f < Nf; ++f) {
1211     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0IFuncs[f];
1212     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1IFuncs[f];
1213     PetscInt numQuadPoints, Nb;
1214     /* Conforming batches */
1215     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1216     /* Remainder */
1217     PetscInt Nr, offset;
1218 
1219     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
1220     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
1221     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1222     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1223     blockSize = Nb*numQuadPoints;
1224     batchSize = numBlocks * blockSize;
1225     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1226     numChunks = numCells / (numBatches*batchSize);
1227     Ne        = numChunks*numBatches*batchSize;
1228     Nr        = numCells % (numBatches*batchSize);
1229     offset    = numCells - Nr;
1230     geom.v0   = v0;
1231     geom.J    = J;
1232     geom.invJ = invJ;
1233     geom.detJ = detJ;
1234     ierr = PetscFEIntegrateIFunction(fe[f], Ne, Nf, fe, f, geom, u, u_t, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
1235     geom.v0   = &v0[offset*dim];
1236     geom.J    = &J[offset*dim*dim];
1237     geom.invJ = &invJ[offset*dim*dim];
1238     geom.detJ = &detJ[offset];
1239     ierr = PetscFEIntegrateIFunction(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], &u_t[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1240   }
1241   for (c = cStart; c < cEnd; ++c) {
1242     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1243     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1244   }
1245   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1246   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1247   if (feBd) {
1248     DMLabel         label, depth;
1249     IS              pointIS;
1250     const PetscInt *points;
1251     PetscInt        dep, numPoints, p, numFaces;
1252     PetscReal      *n;
1253 
1254     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
1255     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1256     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1257     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1258     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1259     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
1260       PetscInt Nb, Nc;
1261 
1262       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1263       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
1264       cellDof       += Nb*Nc;
1265       numComponents += Nc;
1266     }
1267     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1268       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1269       if (dep == dim-1) ++numFaces;
1270     }
1271     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);
1272     ierr = PetscMalloc1(numFaces*cellDof,&u_t);CHKERRQ(ierr);
1273     for (p = 0, f = 0; p < numPoints; ++p) {
1274       const PetscInt point = points[p];
1275       PetscScalar   *x     = NULL;
1276       PetscInt       i;
1277 
1278       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1279       if (dep != dim-1) continue;
1280       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1281       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1282       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1283       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1284       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
1285       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1286       ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1287       for (i = 0; i < cellDof; ++i) u_t[f*cellDof+i] = x[i];
1288       ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1289       ++f;
1290     }
1291     for (f = 0; f < Nf; ++f) {
1292       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdIFuncs[f];
1293       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdIFuncs[f];
1294       PetscInt numQuadPoints, Nb;
1295       /* Conforming batches */
1296       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1297       /* Remainder */
1298       PetscInt Nr, offset;
1299 
1300       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
1301       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1302       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1303       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1304       blockSize = Nb*numQuadPoints;
1305       batchSize = numBlocks * blockSize;
1306       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1307       numChunks = numFaces / (numBatches*batchSize);
1308       Ne        = numChunks*numBatches*batchSize;
1309       Nr        = numFaces % (numBatches*batchSize);
1310       offset    = numFaces - Nr;
1311       geom.v0   = v0;
1312       geom.n    = n;
1313       geom.J    = J;
1314       geom.invJ = invJ;
1315       geom.detJ = detJ;
1316       ierr = PetscFEIntegrateBdIFunction(feBd[f], Ne, Nf, feBd, f, geom, u, u_t, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
1317       geom.v0   = &v0[offset*dim];
1318       geom.n    = &n[offset*dim];
1319       geom.J    = &J[offset*dim*dim];
1320       geom.invJ = &invJ[offset*dim*dim];
1321       geom.detJ = &detJ[offset];
1322       ierr = PetscFEIntegrateBdIFunction(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], &u_t[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1323     }
1324     for (p = 0, f = 0; p < numPoints; ++p) {
1325       const PetscInt point = points[p];
1326 
1327       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1328       if (dep != dim-1) continue;
1329       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
1330       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
1331       ++f;
1332     }
1333     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1334     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1335     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1336     ierr = PetscFree(u_t);CHKERRQ(ierr);
1337   }
1338   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
1339   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1340   PetscFunctionReturn(0);
1341 }
1342 
1343 #undef __FUNCT__
1344 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
1345 /*@C
1346   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
1347 
1348   Input Parameters:
1349 + dm - The mesh
1350 . J  - The Jacobian shell matrix
1351 . X  - Local input vector
1352 - user - The user context
1353 
1354   Output Parameter:
1355 . F  - Local output vector
1356 
1357   Note:
1358   The first member of the user context must be an FEMContext.
1359 
1360   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1361   like a GPU, or vectorize on a multicore machine.
1362 
1363   Level: developer
1364 
1365 .seealso: DMPlexComputeResidualFEM()
1366 @*/
1367 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
1368 {
1369   DM_Plex          *mesh = (DM_Plex *) dm->data;
1370   PetscFEM         *fem  = (PetscFEM *) user;
1371   PetscFE          *fe   = fem->fe;
1372   PetscQuadrature   quad;
1373   PetscCellGeometry geom;
1374   PetscSection      section;
1375   JacActionCtx     *jctx;
1376   PetscReal        *v0, *J, *invJ, *detJ;
1377   PetscScalar      *elemVec, *u, *a;
1378   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
1379   PetscInt          cellDof = 0;
1380   PetscErrorCode    ierr;
1381 
1382   PetscFunctionBegin;
1383   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1384   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1385   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1386   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1387   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1388   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1389   numCells = cEnd - cStart;
1390   for (field = 0; field < numFields; ++field) {
1391     PetscInt Nb, Nc;
1392 
1393     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1394     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
1395     cellDof += Nb*Nc;
1396   }
1397   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1398   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);
1399   for (c = cStart; c < cEnd; ++c) {
1400     PetscScalar *x = NULL;
1401     PetscInt     i;
1402 
1403     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1404     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1405     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1406     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1407     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1408     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1409     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
1410     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1411   }
1412   for (field = 0; field < numFields; ++field) {
1413     PetscInt numQuadPoints, Nb;
1414     /* Conforming batches */
1415     PetscInt numBlocks  = 1;
1416     PetscInt numBatches = 1;
1417     PetscInt numChunks, Ne, blockSize, batchSize;
1418     /* Remainder */
1419     PetscInt Nr, offset;
1420 
1421     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
1422     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1423     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1424     blockSize = Nb*numQuadPoints;
1425     batchSize = numBlocks * blockSize;
1426     numChunks = numCells / (numBatches*batchSize);
1427     Ne        = numChunks*numBatches*batchSize;
1428     Nr        = numCells % (numBatches*batchSize);
1429     offset    = numCells - Nr;
1430     geom.v0   = v0;
1431     geom.J    = J;
1432     geom.invJ = invJ;
1433     geom.detJ = detJ;
1434     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
1435     geom.v0   = &v0[offset*dim];
1436     geom.J    = &J[offset*dim*dim];
1437     geom.invJ = &invJ[offset*dim*dim];
1438     geom.detJ = &detJ[offset];
1439     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
1440                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1441   }
1442   for (c = cStart; c < cEnd; ++c) {
1443     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1444     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1445   }
1446   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1447   if (mesh->printFEM) {
1448     PetscMPIInt rank, numProcs;
1449     PetscInt    p;
1450 
1451     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
1452     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
1453     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
1454     for (p = 0; p < numProcs; ++p) {
1455       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
1456       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
1457     }
1458   }
1459   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1460   PetscFunctionReturn(0);
1461 }
1462 
1463 #undef __FUNCT__
1464 #define __FUNCT__ "DMPlexComputeJacobianFEM"
1465 /*@
1466   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
1467 
1468   Input Parameters:
1469 + dm - The mesh
1470 . X  - Local input vector
1471 - user - The user context
1472 
1473   Output Parameter:
1474 . Jac  - Jacobian matrix
1475 
1476   Note:
1477   The first member of the user context must be an FEMContext.
1478 
1479   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1480   like a GPU, or vectorize on a multicore machine.
1481 
1482   Level: developer
1483 
1484 .seealso: FormFunctionLocal()
1485 @*/
1486 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
1487 {
1488   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1489   PetscFEM         *fem   = (PetscFEM *) user;
1490   PetscFE          *fe    = fem->fe;
1491   PetscFE          *feAux = fem->feAux;
1492   PetscFE          *feBd  = fem->feBd;
1493   const char       *name  = "Jacobian";
1494   DM                dmAux;
1495   Vec               A;
1496   PetscQuadrature   quad;
1497   PetscCellGeometry geom;
1498   PetscSection      section, globalSection, sectionAux;
1499   PetscReal        *v0, *J, *invJ, *detJ;
1500   PetscScalar      *elemMat, *u, *a;
1501   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1502   PetscInt          cellDof = 0, numComponents = 0;
1503   PetscInt          cellDofAux = 0, numComponentsAux = 0;
1504   PetscBool         isShell;
1505   PetscErrorCode    ierr;
1506 
1507   PetscFunctionBegin;
1508   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1509   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1510   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1511   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1512   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1513   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1514   numCells = cEnd - cStart;
1515   for (f = 0; f < Nf; ++f) {
1516     PetscInt Nb, Nc;
1517 
1518     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
1519     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1520     cellDof       += Nb*Nc;
1521     numComponents += Nc;
1522   }
1523   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1524   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1525   if (dmAux) {
1526     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1527     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
1528   }
1529   for (f = 0; f < NfAux; ++f) {
1530     PetscInt Nb, Nc;
1531 
1532     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
1533     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
1534     cellDofAux       += Nb*Nc;
1535     numComponentsAux += Nc;
1536   }
1537   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1538   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
1539   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
1540   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
1541   for (c = cStart; c < cEnd; ++c) {
1542     PetscScalar *x = NULL;
1543     PetscInt     i;
1544 
1545     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1546     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1547     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1548     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1549     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1550     if (dmAux) {
1551       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1552       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
1553       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1554     }
1555   }
1556   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1557   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1558     PetscInt numQuadPoints, Nb;
1559     /* Conforming batches */
1560     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1561     /* Remainder */
1562     PetscInt Nr, offset;
1563 
1564     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
1565     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
1566     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1567     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1568     blockSize = Nb*numQuadPoints;
1569     batchSize = numBlocks * blockSize;
1570     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1571     numChunks = numCells / (numBatches*batchSize);
1572     Ne        = numChunks*numBatches*batchSize;
1573     Nr        = numCells % (numBatches*batchSize);
1574     offset    = numCells - Nr;
1575     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1576       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
1577       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
1578       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
1579       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
1580 
1581       geom.v0   = v0;
1582       geom.J    = J;
1583       geom.invJ = invJ;
1584       geom.detJ = detJ;
1585       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
1586       geom.v0   = &v0[offset*dim];
1587       geom.J    = &J[offset*dim*dim];
1588       geom.invJ = &invJ[offset*dim*dim];
1589       geom.detJ = &detJ[offset];
1590       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);
1591     }
1592   }
1593   for (c = cStart; c < cEnd; ++c) {
1594     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
1595     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
1596   }
1597   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1598   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1599   if (feBd) {
1600     DMLabel  depth;
1601     PetscInt numBd, bd;
1602 
1603     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
1604       PetscInt Nb, Nc;
1605 
1606       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1607       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
1608       cellDof       += Nb*Nc;
1609       numComponents += Nc;
1610     }
1611     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1612     ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1613     for (bd = 0; bd < numBd; ++bd) {
1614       const char     *bdLabel;
1615       DMLabel         label;
1616       IS              pointIS;
1617       const PetscInt *points;
1618       const PetscInt *values;
1619       PetscReal      *n;
1620       PetscInt        field, numValues, numPoints, p, dep, numFaces;
1621       PetscBool       isEssential;
1622 
1623       ierr = DMPlexGetBoundary(dm, bd, &isEssential, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1624       if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
1625       ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1626       ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1627       ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1628       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1629       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1630         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1631         if (dep == dim-1) ++numFaces;
1632       }
1633       ierr = PetscMalloc7(numFaces*cellDof,&u,numFaces*dim,&v0,numFaces*dim,&n,numFaces*dim*dim,&J,numFaces*dim*dim,&invJ,numFaces,&detJ,numFaces*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
1634       for (p = 0, f = 0; p < numPoints; ++p) {
1635         const PetscInt point = points[p];
1636         PetscScalar   *x     = NULL;
1637         PetscInt       i;
1638 
1639         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1640         if (dep != dim-1) continue;
1641         ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1642         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1643         if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1644         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1645         for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
1646         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1647         ++f;
1648       }
1649       ierr = PetscMemzero(elemMat, numFaces*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1650       for (fieldI = 0; fieldI < Nf; ++fieldI) {
1651         PetscInt numQuadPoints, Nb;
1652         /* Conforming batches */
1653         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1654         /* Remainder */
1655         PetscInt Nr, offset;
1656 
1657         ierr = PetscFEGetQuadrature(feBd[fieldI], &quad);CHKERRQ(ierr);
1658         ierr = PetscFEGetDimension(feBd[fieldI], &Nb);CHKERRQ(ierr);
1659         ierr = PetscFEGetTileSizes(feBd[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1660         ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1661         blockSize = Nb*numQuadPoints;
1662         batchSize = numBlocks * blockSize;
1663         ierr =  PetscFESetTileSizes(feBd[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1664         numChunks = numFaces / (numBatches*batchSize);
1665         Ne        = numChunks*numBatches*batchSize;
1666         Nr        = numFaces % (numBatches*batchSize);
1667         offset    = numFaces - Nr;
1668         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1669           void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g0BdFuncs[fieldI*Nf+fieldJ];
1670           void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g1BdFuncs[fieldI*Nf+fieldJ];
1671           void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g2BdFuncs[fieldI*Nf+fieldJ];
1672           void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->g3BdFuncs[fieldI*Nf+fieldJ];
1673 
1674           geom.v0   = v0;
1675           geom.n    = n;
1676           geom.J    = J;
1677           geom.invJ = invJ;
1678           geom.detJ = detJ;
1679           ierr = PetscFEIntegrateBdJacobian(feBd[fieldI], Ne, Nf, feBd, fieldI, fieldJ, geom, u, 0, NULL, NULL, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
1680           geom.v0   = &v0[offset*dim];
1681           geom.n    = &n[offset*dim];
1682           geom.J    = &J[offset*dim*dim];
1683           geom.invJ = &invJ[offset*dim*dim];
1684           geom.detJ = &detJ[offset];
1685           ierr = PetscFEIntegrateBdJacobian(feBd[fieldI], Nr, Nf, feBd, fieldI, fieldJ, geom, &u[offset*cellDof], 0, NULL, NULL, g0, g1, g2, g3, &elemMat[offset*cellDof*cellDof]);CHKERRQ(ierr);
1686         }
1687       }
1688       for (p = 0, f = 0; p < numPoints; ++p) {
1689         const PetscInt point = points[p];
1690 
1691         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1692         if (dep != dim-1) continue;
1693         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", cellDof, cellDof, &elemMat[f*cellDof*cellDof]);CHKERRQ(ierr);}
1694         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
1695         ++f;
1696       }
1697       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1698       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1699       ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1700     }
1701   }
1702   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1703   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1704   if (mesh->printFEM) {
1705     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1706     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
1707     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1708   }
1709   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1710   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
1711   if (isShell) {
1712     JacActionCtx *jctx;
1713 
1714     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1715     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
1716   }
1717   PetscFunctionReturn(0);
1718 }
1719 
1720 #undef __FUNCT__
1721 #define __FUNCT__ "DMPlexComputeInterpolatorFEM"
1722 /*@
1723   DMPlexComputeInterpolatorFEM - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1724 
1725   Input Parameters:
1726 + dmf  - The fine mesh
1727 . dmc  - The coarse mesh
1728 - user - The user context
1729 
1730   Output Parameter:
1731 . In  - The interpolation matrix
1732 
1733   Note:
1734   The first member of the user context must be an FEMContext.
1735 
1736   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1737   like a GPU, or vectorize on a multicore machine.
1738 
1739   Level: developer
1740 
1741 .seealso: DMPlexComputeJacobianFEM()
1742 @*/
1743 PetscErrorCode DMPlexComputeInterpolatorFEM(DM dmc, DM dmf, Mat In, void *user)
1744 {
1745   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1746   PetscFEM         *fem   = (PetscFEM *) user;
1747   PetscFE          *fe    = fem->fe;
1748   const char       *name  = "Interpolator";
1749   PetscFE          *feRef;
1750   PetscSection      fsection, fglobalSection;
1751   PetscSection      csection, cglobalSection;
1752   PetscScalar      *elemMat;
1753   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, c;
1754   PetscInt          rCellDof = 0, cCellDof = 0;
1755   PetscErrorCode    ierr;
1756 
1757   PetscFunctionBegin;
1758 #if 0
1759   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1760 #endif
1761   ierr = DMPlexGetDimension(dmf, &dim);CHKERRQ(ierr);
1762   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1763   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1764   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1765   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1766   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1767   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1768   ierr = PetscMalloc1(Nf,&feRef);CHKERRQ(ierr);
1769   for (f = 0; f < Nf; ++f) {
1770     PetscInt rNb, cNb, Nc;
1771 
1772     ierr = PetscFERefine(fe[f], &feRef[f]);CHKERRQ(ierr);
1773     ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1774     ierr = PetscFEGetDimension(fe[f], &cNb);CHKERRQ(ierr);
1775     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1776     rCellDof += rNb*Nc;
1777     cCellDof += cNb*Nc;
1778   }
1779   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1780   ierr = PetscMalloc1(rCellDof*cCellDof,&elemMat);CHKERRQ(ierr);
1781   ierr = PetscMemzero(elemMat, rCellDof*cCellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1782   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1783     PetscDualSpace   Qref;
1784     PetscQuadrature  f;
1785     const PetscReal *qpoints, *qweights;
1786     PetscReal       *points;
1787     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1788 
1789     /* Compose points from all dual basis functionals */
1790     ierr = PetscFEGetNumComponents(fe[fieldI], &Nc);CHKERRQ(ierr);
1791     ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1792     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1793     for (i = 0; i < fpdim; ++i) {
1794       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1795       ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1796       npoints += Np;
1797     }
1798     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1799     for (i = 0, k = 0; i < fpdim; ++i) {
1800       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1801       ierr = PetscQuadratureGetData(f, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1802       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1803     }
1804 
1805     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1806       PetscReal *B;
1807       PetscInt   NcJ, cpdim, j;
1808 
1809       /* Evaluate basis at points */
1810       ierr = PetscFEGetNumComponents(fe[fieldJ], &NcJ);CHKERRQ(ierr);
1811       if (Nc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in fine space field %d does not match coarse field %d", Nc, NcJ);
1812       ierr = PetscFEGetDimension(fe[fieldJ], &cpdim);CHKERRQ(ierr);
1813       /* For now, fields only interpolate themselves */
1814       if (fieldI == fieldJ) {
1815         ierr = PetscFEGetTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1816         for (i = 0, k = 0; i < fpdim; ++i) {
1817           ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1818           ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, &qweights);CHKERRQ(ierr);
1819           for (p = 0; p < Np; ++p, ++k) {
1820             for (j = 0; j < cpdim; ++j) {
1821               for (c = 0; c < Nc; ++c) elemMat[(offsetI + i*Nc + c)*cCellDof + offsetJ + j*NcJ + c] += B[k*cpdim*NcJ+j*Nc+c]*qweights[p];
1822             }
1823           }
1824         }
1825         ierr = PetscFERestoreTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1826       }
1827       offsetJ += cpdim*NcJ;
1828     }
1829     offsetI += fpdim*Nc;
1830     ierr = PetscFree(points);CHKERRQ(ierr);
1831   }
1832   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rCellDof, cCellDof, elemMat);CHKERRQ(ierr);}
1833   for (c = cStart; c < cEnd; ++c) {
1834     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1835   }
1836   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1837   ierr = PetscFree(feRef);CHKERRQ(ierr);
1838   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1839   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1840   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1841   if (mesh->printFEM) {
1842     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1843     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1844     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1845   }
1846 #if 0
1847   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1848 #endif
1849   PetscFunctionReturn(0);
1850 }
1851 
1852 #undef __FUNCT__
1853 #define __FUNCT__ "DMPlexAddBoundary"
1854 /* The ids can be overridden by the command line option -bc_<boundary name> */
1855 PetscErrorCode DMPlexAddBoundary(DM dm, PetscBool isEssential, const char name[], PetscInt field, void (*bcFunc)(), PetscInt numids, const PetscInt *ids, void *ctx)
1856 {
1857   DM_Plex       *mesh = (DM_Plex *) dm->data;
1858   DMBoundary     b;
1859   PetscErrorCode ierr;
1860 
1861   PetscFunctionBegin;
1862   ierr = PetscNew(&b);CHKERRQ(ierr);
1863   ierr = PetscStrallocpy(name, (char **) &b->name);CHKERRQ(ierr);
1864   ierr = PetscMalloc1(numids, &b->ids);CHKERRQ(ierr);
1865   ierr = PetscMemcpy(b->ids, ids, numids*sizeof(PetscInt));CHKERRQ(ierr);
1866   b->essential   = isEssential;
1867   b->field       = field;
1868   b->func        = bcFunc;
1869   b->numids      = numids;
1870   b->ctx         = ctx;
1871   b->next        = mesh->boundary;
1872   mesh->boundary = b;
1873   PetscFunctionReturn(0);
1874 }
1875 
1876 #undef __FUNCT__
1877 #define __FUNCT__ "DMPlexGetNumBoundary"
1878 PetscErrorCode DMPlexGetNumBoundary(DM dm, PetscInt *numBd)
1879 {
1880   DM_Plex   *mesh = (DM_Plex *) dm->data;
1881   DMBoundary b    = mesh->boundary;
1882 
1883   PetscFunctionBegin;
1884   *numBd = 0;
1885   while (b) {++(*numBd); b = b->next;}
1886   PetscFunctionReturn(0);
1887 }
1888 
1889 #undef __FUNCT__
1890 #define __FUNCT__ "DMPlexGetBoundary"
1891 PetscErrorCode DMPlexGetBoundary(DM dm, PetscInt bd, PetscBool *isEssential, const char **name, PetscInt *field, void (**func)(), PetscInt *numids, const PetscInt **ids, void **ctx)
1892 {
1893   DM_Plex   *mesh = (DM_Plex *) dm->data;
1894   DMBoundary b    = mesh->boundary;
1895   PetscInt   n    = 0;
1896 
1897   PetscFunctionBegin;
1898   while (b) {
1899     if (n == bd) break;
1900     b = b->next;
1901     ++n;
1902   }
1903   if (n != bd) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %d is not in [0, %d)", bd, n);
1904   if (isEssential) {
1905     PetscValidPointer(isEssential, 3);
1906     *isEssential = b->essential;
1907   }
1908   if (name) {
1909     PetscValidPointer(name, 4);
1910     *name = b->name;
1911   }
1912   if (field) {
1913     PetscValidPointer(field, 5);
1914     *field = b->field;
1915   }
1916   if (func) {
1917     PetscValidPointer(func, 6);
1918     *func = b->func;
1919   }
1920   if (numids) {
1921     PetscValidPointer(numids, 7);
1922     *numids = b->numids;
1923   }
1924   if (ids) {
1925     PetscValidPointer(ids, 8);
1926     *ids = b->ids;
1927   }
1928   if (ctx) {
1929     PetscValidPointer(ctx, 9);
1930     *ctx = b->ctx;
1931   }
1932   PetscFunctionReturn(0);
1933 }
1934