xref: /petsc/src/dm/impls/plex/plexfem.c (revision 45e40e47e89655e6851e72a8f91f9a259b2ebaa9)
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   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, f, d, v, i, comp;
192   PetscErrorCode  ierr;
193 
194   PetscFunctionBegin;
195   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
196   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
197   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
198   ierr = PetscMalloc3(numFields,&sp,dim,&v0,dim*dim,&J);CHKERRQ(ierr);
199   for (f = 0; f < numFields; ++f) {
200     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
201     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
202     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
203     totDim += spDim*numComp;
204   }
205   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
206   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
207   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
208   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
209   for (i = 0; i < numIds; ++i) {
210     IS              pointIS;
211     const PetscInt *points;
212     PetscInt        n, p;
213 
214     ierr = DMLabelGetStratumIS(label, ids[i], &pointIS);CHKERRQ(ierr);
215     ierr = ISGetLocalSize(pointIS, &n);CHKERRQ(ierr);
216     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
217     for (p = 0; p < n; ++p) {
218       const PetscInt    point = points[p];
219       PetscCellGeometry geom;
220 
221       if ((point < cStart) || (point >= cEnd)) continue;
222       ierr = DMPlexComputeCellGeometry(dm, point, v0, J, NULL, &detJ);CHKERRQ(ierr);
223       geom.v0   = v0;
224       geom.J    = J;
225       geom.detJ = &detJ;
226       for (f = 0, v = 0; f < numFields; ++f) {
227         void * const ctx = ctxs ? ctxs[f] : NULL;
228         ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
229         ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
230         for (d = 0; d < spDim; ++d) {
231           if (funcs[f]) {
232             ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
233           } else {
234             for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
235           }
236           v += numComp;
237         }
238       }
239       ierr = DMPlexVecSetClosure(dm, section, localX, point, values, mode);CHKERRQ(ierr);
240     }
241     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
242     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
243   }
244   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
245   ierr = PetscFree3(sp,v0,J);CHKERRQ(ierr);
246   PetscFunctionReturn(0);
247 }
248 
249 #undef __FUNCT__
250 #define __FUNCT__ "DMPlexProjectFunctionLocal"
251 PetscErrorCode DMPlexProjectFunctionLocal(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
252 {
253   PetscDualSpace *sp;
254   PetscSection    section;
255   PetscScalar    *values;
256   PetscReal      *v0, *J, detJ;
257   PetscInt        numFields, numComp, dim, spDim, totDim = 0, numValues, cStart, cEnd, c, f, d, v, comp;
258   PetscErrorCode  ierr;
259 
260   PetscFunctionBegin;
261   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
262   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
263   ierr = PetscMalloc1(numFields, &sp);CHKERRQ(ierr);
264   for (f = 0; f < numFields; ++f) {
265     ierr = PetscFEGetDualSpace(fe[f], &sp[f]);CHKERRQ(ierr);
266     ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
267     ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
268     totDim += spDim*numComp;
269   }
270   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
271   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
272   ierr = DMPlexVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
273   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
274   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
275   ierr = PetscMalloc2(dim,&v0,dim*dim,&J);CHKERRQ(ierr);
276   for (c = cStart; c < cEnd; ++c) {
277     PetscCellGeometry geom;
278 
279     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
280     geom.v0   = v0;
281     geom.J    = J;
282     geom.detJ = &detJ;
283     for (f = 0, v = 0; f < numFields; ++f) {
284       void * const ctx = ctxs ? ctxs[f] : NULL;
285       ierr = PetscFEGetNumComponents(fe[f], &numComp);CHKERRQ(ierr);
286       ierr = PetscDualSpaceGetDimension(sp[f], &spDim);CHKERRQ(ierr);
287       for (d = 0; d < spDim; ++d) {
288         if (funcs[f]) {
289           ierr = PetscDualSpaceApply(sp[f], d, geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
290         } else {
291           for (comp = 0; comp < numComp; ++comp) values[v+comp] = 0.0;
292         }
293         v += numComp;
294       }
295     }
296     ierr = DMPlexVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
297   }
298   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
299   ierr = PetscFree2(v0,J);CHKERRQ(ierr);
300   ierr = PetscFree(sp);CHKERRQ(ierr);
301   PetscFunctionReturn(0);
302 }
303 
304 #undef __FUNCT__
305 #define __FUNCT__ "DMPlexProjectFunction"
306 /*@C
307   DMPlexProjectFunction - This projects the given function into the function space provided.
308 
309   Input Parameters:
310 + dm      - The DM
311 . fe      - The PetscFE associated with the field
312 . funcs   - The coordinate functions to evaluate, one per field
313 . ctxs    - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
314 - mode    - The insertion mode for values
315 
316   Output Parameter:
317 . X - vector
318 
319   Level: developer
320 
321 .seealso: DMPlexComputeL2Diff()
322 @*/
323 PetscErrorCode DMPlexProjectFunction(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec X)
324 {
325   Vec            localX;
326   PetscErrorCode ierr;
327 
328   PetscFunctionBegin;
329   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
330   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
331   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, mode, localX);CHKERRQ(ierr);
332   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
333   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
334   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
335   PetscFunctionReturn(0);
336 }
337 
338 #undef __FUNCT__
339 #define __FUNCT__ "DMPlexInsertBoundaryValuesFEM"
340 PetscErrorCode DMPlexInsertBoundaryValuesFEM(DM dm, Vec localX)
341 {
342   void        (**funcs)(const PetscReal x[], PetscScalar *u, void *ctx);
343   void         **ctxs;
344   PetscFE       *fe;
345   PetscInt       numFields, f, numBd, b;
346   PetscErrorCode ierr;
347 
348   PetscFunctionBegin;
349   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
350   PetscValidHeaderSpecific(localX, VEC_CLASSID, 2);
351   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
352   ierr = PetscMalloc3(numFields,&fe,numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
353   for (f = 0; f < numFields; ++f) {ierr = DMGetField(dm, f, (PetscObject *) &fe[f]);CHKERRQ(ierr);}
354   /* OPT: Could attempt to do multiple BCs at once */
355   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
356   for (b = 0; b < numBd; ++b) {
357     DMLabel         label;
358     const PetscInt *ids;
359     const char     *name;
360     PetscInt        numids, field;
361     PetscBool       isEssential;
362     void          (*func)();
363     void           *ctx;
364 
365     /* TODO: We need to set only the part indicated by the ids */
366     ierr = DMPlexGetBoundary(dm, b, &isEssential, &name, &field, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
367     ierr = DMPlexGetLabel(dm, name, &label);CHKERRQ(ierr);
368     for (f = 0; f < numFields; ++f) {
369       funcs[f] = field == f ? (void (*)(const PetscReal[], PetscScalar *, void *)) func : NULL;
370       ctxs[f]  = field == f ? ctx : NULL;
371     }
372     ierr = DMPlexProjectFunctionLabelLocal(dm, label, numids, ids, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
373   }
374   ierr = PetscFree3(fe,funcs,ctxs);CHKERRQ(ierr);
375   PetscFunctionReturn(0);
376 }
377 
378 /* Assuming dim == 3 */
379 typedef struct {
380   PetscScalar normal[3];   /* Area-scaled normals */
381   PetscScalar centroid[3]; /* Location of centroid (quadrature point) */
382   PetscScalar grad[2][3];  /* Face contribution to gradient in left and right cell */
383 } FaceGeom;
384 
385 #undef __FUNCT__
386 #define __FUNCT__ "DMPlexInsertBoundaryValuesFVM"
387 PetscErrorCode DMPlexInsertBoundaryValuesFVM(DM dm, PetscReal time, Vec locX)
388 {
389   DM                 dmFace;
390   Vec                faceGeometry;
391   DMLabel            label;
392   const PetscScalar *facegeom;
393   PetscScalar       *x;
394   PetscInt           numBd, b;
395   PetscErrorCode     ierr;
396 
397   PetscFunctionBegin;
398   /* TODO Pull this geometry calculation into the library */
399   ierr = PetscObjectQuery((PetscObject) dm, "FaceGeometry", (PetscObject *) &faceGeometry);CHKERRQ(ierr);
400   ierr = DMPlexGetLabel(dm, "Face Sets", &label);CHKERRQ(ierr);
401   ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
402   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
403   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
404   ierr = VecGetArray(locX, &x);CHKERRQ(ierr);
405   for (b = 0; b < numBd; ++b) {
406     PetscErrorCode (*func)(PetscReal,const PetscScalar*,const PetscScalar*,const PetscScalar*,PetscScalar*,void*);
407     const PetscInt  *ids;
408     PetscInt         numids, i;
409     void            *ctx;
410 
411     ierr = DMPlexGetBoundary(dm, b, NULL, NULL, NULL, (void (**)()) &func, &numids, &ids, &ctx);CHKERRQ(ierr);
412     for (i = 0; i < numids; ++i) {
413       IS              faceIS;
414       const PetscInt *faces;
415       PetscInt        numFaces, f;
416 
417       ierr = DMLabelGetStratumIS(label, ids[i], &faceIS);CHKERRQ(ierr);
418       if (!faceIS) continue; /* No points with that id on this process */
419       ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
420       ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
421       for (f = 0; f < numFaces; ++f) {
422         const PetscInt     face = faces[f], *cells;
423         const PetscScalar *xI;
424         PetscScalar       *xG;
425         const FaceGeom    *fg;
426 
427         ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
428         ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
429         ierr = DMPlexPointLocalRead(dm, cells[0], x, &xI);CHKERRQ(ierr);
430         ierr = DMPlexPointLocalRef(dm, cells[1], x, &xG);CHKERRQ(ierr);
431         ierr = (*func)(time, fg->centroid, fg->normal, xI, xG, ctx);CHKERRQ(ierr);
432       }
433       ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
434       ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
435     }
436   }
437   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
438   ierr = VecRestoreArray(locX, &x);CHKERRQ(ierr);
439   PetscFunctionReturn(0);
440 }
441 
442 #undef __FUNCT__
443 #define __FUNCT__ "DMPlexComputeL2Diff"
444 /*@C
445   DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
446 
447   Input Parameters:
448 + dm    - The DM
449 . fe    - The PetscFE object for each field
450 . funcs - The functions to evaluate for each field component
451 . ctxs  - Optional array of contexts to pass to each function, or NULL.
452 - X     - The coefficient vector u_h
453 
454   Output Parameter:
455 . diff - The diff ||u - u_h||_2
456 
457   Level: developer
458 
459 .seealso: DMPlexProjectFunction(), DMPlexComputeL2GradientDiff()
460 @*/
461 PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
462 {
463   const PetscInt  debug = 0;
464   PetscSection    section;
465   PetscQuadrature quad;
466   Vec             localX;
467   PetscScalar    *funcVal;
468   PetscReal      *coords, *v0, *J, *invJ, detJ;
469   PetscReal       localDiff = 0.0;
470   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
471   PetscErrorCode  ierr;
472 
473   PetscFunctionBegin;
474   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
475   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
476   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
477   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
478   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
479   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
480   for (field = 0; field < numFields; ++field) {
481     PetscInt Nc;
482 
483     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
484     numComponents += Nc;
485   }
486   ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
487   ierr = PetscMalloc5(numComponents,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
488   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
489   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
490   for (c = cStart; c < cEnd; ++c) {
491     PetscScalar *x = NULL;
492     PetscReal    elemDiff = 0.0;
493 
494     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
495     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
496     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
497 
498     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
499       void * const     ctx = ctxs ? ctxs[field] : NULL;
500       const PetscReal *quadPoints, *quadWeights;
501       PetscReal       *basis;
502       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
503 
504       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
505       ierr = PetscFEGetDimension(fe[field], &numBasisFuncs);CHKERRQ(ierr);
506       ierr = PetscFEGetNumComponents(fe[field], &numBasisComps);CHKERRQ(ierr);
507       ierr = PetscFEGetDefaultTabulation(fe[field], &basis, NULL, NULL);CHKERRQ(ierr);
508       if (debug) {
509         char title[1024];
510         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
511         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
512       }
513       for (q = 0; q < numQuadPoints; ++q) {
514         for (d = 0; d < dim; d++) {
515           coords[d] = v0[d];
516           for (e = 0; e < dim; e++) {
517             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
518           }
519         }
520         (*funcs[field])(coords, funcVal, ctx);
521         for (fc = 0; fc < numBasisComps; ++fc) {
522           PetscScalar interpolant = 0.0;
523 
524           for (f = 0; f < numBasisFuncs; ++f) {
525             const PetscInt fidx = f*numBasisComps+fc;
526             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
527           }
528           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);}
529           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
530         }
531       }
532       comp        += numBasisComps;
533       fieldOffset += numBasisFuncs*numBasisComps;
534     }
535     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
536     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
537     localDiff += elemDiff;
538   }
539   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
540   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
541   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
542   *diff = PetscSqrtReal(*diff);
543   PetscFunctionReturn(0);
544 }
545 
546 #undef __FUNCT__
547 #define __FUNCT__ "DMPlexComputeL2GradientDiff"
548 /*@C
549   DMPlexComputeL2GradientDiff - This function computes the L_2 difference between the gradient of a function u and an FEM interpolant solution grad u_h.
550 
551   Input Parameters:
552 + dm    - The DM
553 . fe    - The PetscFE object for each field
554 . funcs - The gradient functions to evaluate for each field component
555 . ctxs  - Optional array of contexts to pass to each function, or NULL.
556 . X     - The coefficient vector u_h
557 - n     - The vector to project along
558 
559   Output Parameter:
560 . diff - The diff ||(grad u - grad u_h) . n||_2
561 
562   Level: developer
563 
564 .seealso: DMPlexProjectFunction(), DMPlexComputeL2Diff()
565 @*/
566 PetscErrorCode DMPlexComputeL2GradientDiff(DM dm, PetscFE fe[], void (**funcs)(const PetscReal [], const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
567 {
568   const PetscInt  debug = 0;
569   PetscSection    section;
570   PetscQuadrature quad;
571   Vec             localX;
572   PetscScalar    *funcVal, *interpolantVec;
573   PetscReal      *coords, *realSpaceDer, *v0, *J, *invJ, detJ;
574   PetscReal       localDiff = 0.0;
575   PetscInt        dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
576   PetscErrorCode  ierr;
577 
578   PetscFunctionBegin;
579   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
580   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
581   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
582   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
583   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
584   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
585   for (field = 0; field < numFields; ++field) {
586     PetscInt Nc;
587 
588     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
589     numComponents += Nc;
590   }
591   /* ierr = DMPlexProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
592   ierr = PetscMalloc7(numComponents,&funcVal,dim,&coords,dim,&realSpaceDer,dim,&v0,dim*dim,&J,dim*dim,&invJ,dim,&interpolantVec);CHKERRQ(ierr);
593   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
594   ierr = PetscFEGetQuadrature(fe[0], &quad);CHKERRQ(ierr);
595   for (c = cStart; c < cEnd; ++c) {
596     PetscScalar *x = NULL;
597     PetscReal    elemDiff = 0.0;
598 
599     ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
600     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
601     ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
602 
603     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
604       void * const     ctx = ctxs ? ctxs[field] : NULL;
605       const PetscReal *quadPoints, *quadWeights;
606       PetscReal       *basisDer;
607       PetscInt         numQuadPoints, Nb, Ncomp, q, d, e, fc, f, g;
608 
609       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
610       ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
611       ierr = PetscFEGetNumComponents(fe[field], &Ncomp);CHKERRQ(ierr);
612       ierr = PetscFEGetDefaultTabulation(fe[field], NULL, &basisDer, NULL);CHKERRQ(ierr);
613       if (debug) {
614         char title[1024];
615         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
616         ierr = DMPrintCellVector(c, title, Nb*Ncomp, &x[fieldOffset]);CHKERRQ(ierr);
617       }
618       for (q = 0; q < numQuadPoints; ++q) {
619         for (d = 0; d < dim; d++) {
620           coords[d] = v0[d];
621           for (e = 0; e < dim; e++) {
622             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
623           }
624         }
625         (*funcs[field])(coords, n, funcVal, ctx);
626         for (fc = 0; fc < Ncomp; ++fc) {
627           PetscScalar interpolant = 0.0;
628 
629           for (d = 0; d < dim; ++d) interpolantVec[d] = 0.0;
630           for (f = 0; f < Nb; ++f) {
631             const PetscInt fidx = f*Ncomp+fc;
632 
633             for (d = 0; d < dim; ++d) {
634               realSpaceDer[d] = 0.0;
635               for (g = 0; g < dim; ++g) {
636                 realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Ncomp+fidx)*dim+g];
637               }
638               interpolantVec[d] += x[fieldOffset+fidx]*realSpaceDer[d];
639             }
640           }
641           for (d = 0; d < dim; ++d) interpolant += interpolantVec[d]*n[d];
642           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);}
643           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
644         }
645       }
646       comp        += Ncomp;
647       fieldOffset += Nb*Ncomp;
648     }
649     ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
650     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
651     localDiff += elemDiff;
652   }
653   ierr  = PetscFree7(funcVal,coords,realSpaceDer,v0,J,invJ,interpolantVec);CHKERRQ(ierr);
654   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
655   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
656   *diff = PetscSqrtReal(*diff);
657   PetscFunctionReturn(0);
658 }
659 
660 #undef __FUNCT__
661 #define __FUNCT__ "DMPlexComputeResidualFEM"
662 /*@
663   DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
664 
665   Input Parameters:
666 + dm - The mesh
667 . X  - Local input vector
668 - user - The user context
669 
670   Output Parameter:
671 . F  - Local output vector
672 
673   Note:
674   The first member of the user context must be an FEMContext.
675 
676   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
677   like a GPU, or vectorize on a multicore machine.
678 
679   Level: developer
680 
681 .seealso: DMPlexComputeJacobianActionFEM()
682 @*/
683 PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
684 {
685   DM_Plex          *mesh  = (DM_Plex *) dm->data;
686   PetscFEM         *fem   = (PetscFEM *) user;
687   PetscFE          *fe    = fem->fe;
688   PetscFE          *feAux = fem->feAux;
689   PetscFE          *feBd  = fem->feBd;
690   const char       *name  = "Residual";
691   DM                dmAux;
692   Vec               A;
693   PetscQuadrature   q;
694   PetscCellGeometry geom;
695   PetscSection      section, sectionAux;
696   PetscReal        *v0, *J, *invJ, *detJ;
697   PetscScalar      *elemVec, *u, *a = NULL;
698   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
699   PetscInt          cellDof = 0, numComponents = 0;
700   PetscInt          cellDofAux = 0, numComponentsAux = 0;
701   PetscErrorCode    ierr;
702 
703   PetscFunctionBegin;
704   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
705   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
706   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
707   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
708   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
709   numCells = cEnd - cStart;
710   for (f = 0; f < Nf; ++f) {
711     PetscInt Nb, Nc;
712 
713     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
714     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
715     cellDof       += Nb*Nc;
716     numComponents += Nc;
717   }
718   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
719   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
720   if (dmAux) {
721     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
722     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
723   }
724   for (f = 0; f < NfAux; ++f) {
725     PetscInt Nb, Nc;
726 
727     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
728     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
729     cellDofAux       += Nb*Nc;
730     numComponentsAux += Nc;
731   }
732   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
733   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
734   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof,&elemVec);CHKERRQ(ierr);
735   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
736   for (c = cStart; c < cEnd; ++c) {
737     PetscScalar *x = NULL;
738     PetscInt     i;
739 
740     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
741     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
742     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
743     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
744     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
745     if (dmAux) {
746       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
747       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
748       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
749     }
750   }
751   for (f = 0; f < Nf; ++f) {
752     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0Funcs[f];
753     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1Funcs[f];
754     PetscInt numQuadPoints, Nb;
755     /* Conforming batches */
756     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
757     /* Remainder */
758     PetscInt Nr, offset;
759 
760     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
761     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
762     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
763     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
764     blockSize = Nb*numQuadPoints;
765     batchSize = numBlocks * blockSize;
766     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
767     numChunks = numCells / (numBatches*batchSize);
768     Ne        = numChunks*numBatches*batchSize;
769     Nr        = numCells % (numBatches*batchSize);
770     offset    = numCells - Nr;
771     geom.v0   = v0;
772     geom.J    = J;
773     geom.invJ = invJ;
774     geom.detJ = detJ;
775     ierr = PetscFEIntegrateResidual(fe[f], Ne, Nf, fe, f, geom, u, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
776     geom.v0   = &v0[offset*dim];
777     geom.J    = &J[offset*dim*dim];
778     geom.invJ = &invJ[offset*dim*dim];
779     geom.detJ = &detJ[offset];
780     ierr = PetscFEIntegrateResidual(fe[f], Nr, Nf, fe, f, geom, &u[offset*cellDof], NfAux, feAux, &a[offset*cellDofAux], f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
781   }
782   for (c = cStart; c < cEnd; ++c) {
783     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
784     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
785   }
786   ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
787   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
788   if (feBd) {
789     DMLabel         label, depth;
790     IS              pointIS;
791     const PetscInt *points;
792     PetscInt        dep, numPoints, p, numFaces;
793     PetscReal      *n;
794 
795     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
796     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
797     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
798     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
799     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
800     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
801       PetscInt Nb, Nc;
802 
803       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
804       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
805       cellDof       += Nb*Nc;
806       numComponents += Nc;
807     }
808     for (p = 0, numFaces = 0; p < numPoints; ++p) {
809       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
810       if (dep == dim-1) ++numFaces;
811     }
812     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);
813     for (p = 0, f = 0; p < numPoints; ++p) {
814       const PetscInt point = points[p];
815       PetscScalar   *x     = NULL;
816       PetscInt       i;
817 
818       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
819       if (dep != dim-1) continue;
820       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
821       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
822       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
823       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
824       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
825       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
826       ++f;
827     }
828     for (f = 0; f < Nf; ++f) {
829       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdFuncs[f];
830       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdFuncs[f];
831       PetscInt numQuadPoints, Nb;
832       /* Conforming batches */
833       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
834       /* Remainder */
835       PetscInt Nr, offset;
836 
837       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
838       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
839       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
840       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
841       blockSize = Nb*numQuadPoints;
842       batchSize = numBlocks * blockSize;
843       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
844       numChunks = numFaces / (numBatches*batchSize);
845       Ne        = numChunks*numBatches*batchSize;
846       Nr        = numFaces % (numBatches*batchSize);
847       offset    = numFaces - Nr;
848       geom.v0   = v0;
849       geom.n    = n;
850       geom.J    = J;
851       geom.invJ = invJ;
852       geom.detJ = detJ;
853       ierr = PetscFEIntegrateBdResidual(feBd[f], Ne, Nf, feBd, f, geom, u, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
854       geom.v0   = &v0[offset*dim];
855       geom.n    = &n[offset*dim];
856       geom.J    = &J[offset*dim*dim];
857       geom.invJ = &invJ[offset*dim*dim];
858       geom.detJ = &detJ[offset];
859       ierr = PetscFEIntegrateBdResidual(feBd[f], Nr, Nf, feBd, f, geom, &u[offset*cellDof], 0, NULL, NULL, f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
860     }
861     for (p = 0, f = 0; p < numPoints; ++p) {
862       const PetscInt point = points[p];
863 
864       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
865       if (dep != dim-1) continue;
866       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
867       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
868       ++f;
869     }
870     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
871     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
872     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
873   }
874   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
875   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
876   PetscFunctionReturn(0);
877 }
878 
879 #undef __FUNCT__
880 #define __FUNCT__ "DMPlexComputeIFunctionFEM"
881 /*@
882   DMPlexComputeIFunctionFEM - Form the local implicit function F from the local input X, X_t using pointwise functions specified by the user
883 
884   Input Parameters:
885 + dm - The mesh
886 . time - The current time
887 . X  - Local input vector
888 . X_t  - Time derivative of the local input vector
889 - user - The user context
890 
891   Output Parameter:
892 . F  - Local output vector
893 
894   Note:
895   The first member of the user context must be an FEMContext.
896 
897   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
898   like a GPU, or vectorize on a multicore machine.
899 
900   Level: developer
901 
902 .seealso: DMPlexComputeResidualFEM()
903 @*/
904 PetscErrorCode DMPlexComputeIFunctionFEM(DM dm, PetscReal time, Vec X, Vec X_t, Vec F, void *user)
905 {
906   DM_Plex          *mesh  = (DM_Plex *) dm->data;
907   PetscFEM         *fem   = (PetscFEM *) user;
908   PetscFE          *fe    = fem->fe;
909   PetscFE          *feAux = fem->feAux;
910   PetscFE          *feBd  = fem->feBd;
911   const char       *name  = "Residual";
912   DM                dmAux;
913   Vec               A;
914   PetscQuadrature   q;
915   PetscCellGeometry geom;
916   PetscSection      section, sectionAux;
917   PetscReal        *v0, *J, *invJ, *detJ;
918   PetscScalar      *elemVec, *u, *u_t, *a = NULL;
919   PetscInt          dim, Nf, NfAux = 0, f, numCells, cStart, cEnd, c;
920   PetscInt          cellDof = 0, numComponents = 0;
921   PetscInt          cellDofAux = 0, numComponentsAux = 0;
922   PetscErrorCode    ierr;
923 
924   PetscFunctionBegin;
925   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
926   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
927   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
928   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
929   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
930   numCells = cEnd - cStart;
931   for (f = 0; f < Nf; ++f) {
932     PetscInt Nb, Nc;
933 
934     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
935     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
936     cellDof       += Nb*Nc;
937     numComponents += Nc;
938   }
939   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
940   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
941   if (dmAux) {
942     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
943     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
944   }
945   for (f = 0; f < NfAux; ++f) {
946     PetscInt Nb, Nc;
947 
948     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
949     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
950     cellDofAux       += Nb*Nc;
951     numComponentsAux += Nc;
952   }
953   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
954   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
955   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);
956   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
957   for (c = cStart; c < cEnd; ++c) {
958     PetscScalar *x = NULL, *x_t = NULL;
959     PetscInt     i;
960 
961     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
962     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
963     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
964     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
965     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
966     ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
967     for (i = 0; i < cellDof; ++i) u_t[c*cellDof+i] = x_t[i];
968     ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
969     if (dmAux) {
970       PetscScalar *x_a = NULL;
971       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
972       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x_a[i];
973       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x_a);CHKERRQ(ierr);
974     }
975   }
976   for (f = 0; f < Nf; ++f) {
977     void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f0IFuncs[f];
978     void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->f1IFuncs[f];
979     PetscInt numQuadPoints, Nb;
980     /* Conforming batches */
981     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
982     /* Remainder */
983     PetscInt Nr, offset;
984 
985     ierr = PetscFEGetQuadrature(fe[f], &q);CHKERRQ(ierr);
986     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
987     ierr = PetscFEGetTileSizes(fe[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
988     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
989     blockSize = Nb*numQuadPoints;
990     batchSize = numBlocks * blockSize;
991     ierr =  PetscFESetTileSizes(fe[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
992     numChunks = numCells / (numBatches*batchSize);
993     Ne        = numChunks*numBatches*batchSize;
994     Nr        = numCells % (numBatches*batchSize);
995     offset    = numCells - Nr;
996     geom.v0   = v0;
997     geom.J    = J;
998     geom.invJ = invJ;
999     geom.detJ = detJ;
1000     ierr = PetscFEIntegrateIFunction(fe[f], Ne, Nf, fe, f, geom, u, u_t, NfAux, feAux, a, f0, f1, elemVec);CHKERRQ(ierr);
1001     geom.v0   = &v0[offset*dim];
1002     geom.J    = &J[offset*dim*dim];
1003     geom.invJ = &invJ[offset*dim*dim];
1004     geom.detJ = &detJ[offset];
1005     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);
1006   }
1007   for (c = cStart; c < cEnd; ++c) {
1008     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, name, cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1009     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1010   }
1011   ierr = PetscFree7(u,u_t,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1012   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1013   if (feBd) {
1014     DMLabel         label, depth;
1015     IS              pointIS;
1016     const PetscInt *points;
1017     PetscInt        dep, numPoints, p, numFaces;
1018     PetscReal      *n;
1019 
1020     ierr = DMPlexGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
1021     ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1022     ierr = DMLabelGetStratumSize(label, 1, &numPoints);CHKERRQ(ierr);
1023     ierr = DMLabelGetStratumIS(label, 1, &pointIS);CHKERRQ(ierr);
1024     ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1025     for (f = 0, cellDof = 0, numComponents = 0; f < Nf; ++f) {
1026       PetscInt Nb, Nc;
1027 
1028       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1029       ierr = PetscFEGetNumComponents(feBd[f], &Nc);CHKERRQ(ierr);
1030       cellDof       += Nb*Nc;
1031       numComponents += Nc;
1032     }
1033     for (p = 0, numFaces = 0; p < numPoints; ++p) {
1034       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1035       if (dep == dim-1) ++numFaces;
1036     }
1037     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);
1038     ierr = PetscMalloc1(numFaces*cellDof,&u_t);CHKERRQ(ierr);
1039     for (p = 0, f = 0; p < numPoints; ++p) {
1040       const PetscInt point = points[p];
1041       PetscScalar   *x     = NULL;
1042       PetscInt       i;
1043 
1044       ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1045       if (dep != dim-1) continue;
1046       ierr = DMPlexComputeCellGeometry(dm, point, &v0[f*dim], &J[f*dim*dim], &invJ[f*dim*dim], &detJ[f]);CHKERRQ(ierr);
1047       ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, &n[f*dim]);
1048       if (detJ[f] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", detJ[f], point);
1049       ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1050       for (i = 0; i < cellDof; ++i) u[f*cellDof+i] = x[i];
1051       ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
1052       ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1053       for (i = 0; i < cellDof; ++i) u_t[f*cellDof+i] = x[i];
1054       ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
1055       ++f;
1056     }
1057     for (f = 0; f < Nf; ++f) {
1058       void   (*f0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f0BdIFuncs[f];
1059       void   (*f1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], const PetscReal[], PetscScalar[]) = fem->f1BdIFuncs[f];
1060       PetscInt numQuadPoints, Nb;
1061       /* Conforming batches */
1062       PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1063       /* Remainder */
1064       PetscInt Nr, offset;
1065 
1066       ierr = PetscFEGetQuadrature(feBd[f], &q);CHKERRQ(ierr);
1067       ierr = PetscFEGetDimension(feBd[f], &Nb);CHKERRQ(ierr);
1068       ierr = PetscFEGetTileSizes(feBd[f], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1069       ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1070       blockSize = Nb*numQuadPoints;
1071       batchSize = numBlocks * blockSize;
1072       ierr =  PetscFESetTileSizes(feBd[f], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1073       numChunks = numFaces / (numBatches*batchSize);
1074       Ne        = numChunks*numBatches*batchSize;
1075       Nr        = numFaces % (numBatches*batchSize);
1076       offset    = numFaces - Nr;
1077       geom.v0   = v0;
1078       geom.n    = n;
1079       geom.J    = J;
1080       geom.invJ = invJ;
1081       geom.detJ = detJ;
1082       ierr = PetscFEIntegrateBdIFunction(feBd[f], Ne, Nf, feBd, f, geom, u, u_t, 0, NULL, NULL, f0, f1, elemVec);CHKERRQ(ierr);
1083       geom.v0   = &v0[offset*dim];
1084       geom.n    = &n[offset*dim];
1085       geom.J    = &J[offset*dim*dim];
1086       geom.invJ = &invJ[offset*dim*dim];
1087       geom.detJ = &detJ[offset];
1088       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);
1089     }
1090     for (p = 0, f = 0; p < numPoints; ++p) {
1091       const PetscInt point = points[p];
1092 
1093       ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1094       if (dep != dim-1) continue;
1095       if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", cellDof, &elemVec[f*cellDof]);CHKERRQ(ierr);}
1096       ierr = DMPlexVecSetClosure(dm, NULL, F, point, &elemVec[f*cellDof], ADD_VALUES);CHKERRQ(ierr);
1097       ++f;
1098     }
1099     ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1100     ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1101     ierr = PetscFree7(u,v0,n,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1102     ierr = PetscFree(u_t);CHKERRQ(ierr);
1103   }
1104   if (mesh->printFEM) {ierr = DMPrintLocalVec(dm, name, mesh->printTol, F);CHKERRQ(ierr);}
1105   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1106   PetscFunctionReturn(0);
1107 }
1108 
1109 #undef __FUNCT__
1110 #define __FUNCT__ "DMPlexComputeJacobianActionFEM"
1111 /*@C
1112   DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user
1113 
1114   Input Parameters:
1115 + dm - The mesh
1116 . J  - The Jacobian shell matrix
1117 . X  - Local input vector
1118 - user - The user context
1119 
1120   Output Parameter:
1121 . F  - Local output vector
1122 
1123   Note:
1124   The first member of the user context must be an FEMContext.
1125 
1126   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1127   like a GPU, or vectorize on a multicore machine.
1128 
1129   Level: developer
1130 
1131 .seealso: DMPlexComputeResidualFEM()
1132 @*/
1133 PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
1134 {
1135   DM_Plex          *mesh = (DM_Plex *) dm->data;
1136   PetscFEM         *fem  = (PetscFEM *) user;
1137   PetscFE          *fe   = fem->fe;
1138   PetscQuadrature   quad;
1139   PetscCellGeometry geom;
1140   PetscSection      section;
1141   JacActionCtx     *jctx;
1142   PetscReal        *v0, *J, *invJ, *detJ;
1143   PetscScalar      *elemVec, *u, *a;
1144   PetscInt          dim, numFields, field, numCells, cStart, cEnd, c;
1145   PetscInt          cellDof = 0;
1146   PetscErrorCode    ierr;
1147 
1148   PetscFunctionBegin;
1149   /* ierr = PetscLogEventBegin(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1150   ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1151   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1152   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1153   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1154   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1155   numCells = cEnd - cStart;
1156   for (field = 0; field < numFields; ++field) {
1157     PetscInt Nb, Nc;
1158 
1159     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1160     ierr = PetscFEGetNumComponents(fe[field], &Nc);CHKERRQ(ierr);
1161     cellDof += Nb*Nc;
1162   }
1163   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1164   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);
1165   for (c = cStart; c < cEnd; ++c) {
1166     PetscScalar *x = NULL;
1167     PetscInt     i;
1168 
1169     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1170     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1171     ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1172     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1173     ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
1174     ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1175     for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
1176     ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
1177   }
1178   for (field = 0; field < numFields; ++field) {
1179     PetscInt numQuadPoints, Nb;
1180     /* Conforming batches */
1181     PetscInt numBlocks  = 1;
1182     PetscInt numBatches = 1;
1183     PetscInt numChunks, Ne, blockSize, batchSize;
1184     /* Remainder */
1185     PetscInt Nr, offset;
1186 
1187     ierr = PetscFEGetQuadrature(fe[field], &quad);CHKERRQ(ierr);
1188     ierr = PetscFEGetDimension(fe[field], &Nb);CHKERRQ(ierr);
1189     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1190     blockSize = Nb*numQuadPoints;
1191     batchSize = numBlocks * blockSize;
1192     numChunks = numCells / (numBatches*batchSize);
1193     Ne        = numChunks*numBatches*batchSize;
1194     Nr        = numCells % (numBatches*batchSize);
1195     offset    = numCells - Nr;
1196     geom.v0   = v0;
1197     geom.J    = J;
1198     geom.invJ = invJ;
1199     geom.detJ = detJ;
1200     ierr = PetscFEIntegrateJacobianAction(fe[field], Ne, numFields, fe, field, geom, u, a, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
1201     geom.v0   = &v0[offset*dim];
1202     geom.J    = &J[offset*dim*dim];
1203     geom.invJ = &invJ[offset*dim*dim];
1204     geom.detJ = &detJ[offset];
1205     ierr = PetscFEIntegrateJacobianAction(fe[field], Nr, numFields, fe, field, geom, &u[offset*cellDof], &a[offset*cellDof],
1206                                           fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
1207   }
1208   for (c = cStart; c < cEnd; ++c) {
1209     if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
1210     ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
1211   }
1212   ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
1213   if (mesh->printFEM) {
1214     PetscMPIInt rank, numProcs;
1215     PetscInt    p;
1216 
1217     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
1218     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
1219     ierr = PetscPrintf(PetscObjectComm((PetscObject)dm), "Jacobian Action:\n");CHKERRQ(ierr);
1220     for (p = 0; p < numProcs; ++p) {
1221       if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
1222       ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
1223     }
1224   }
1225   /* ierr = PetscLogEventEnd(DMPLEX_JacobianActionFEM,dm,0,0,0);CHKERRQ(ierr); */
1226   PetscFunctionReturn(0);
1227 }
1228 
1229 #undef __FUNCT__
1230 #define __FUNCT__ "DMPlexComputeJacobianFEM"
1231 /*@
1232   DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
1233 
1234   Input Parameters:
1235 + dm - The mesh
1236 . X  - Local input vector
1237 - user - The user context
1238 
1239   Output Parameter:
1240 . Jac  - Jacobian matrix
1241 
1242   Note:
1243   The first member of the user context must be an FEMContext.
1244 
1245   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1246   like a GPU, or vectorize on a multicore machine.
1247 
1248   Level: developer
1249 
1250 .seealso: FormFunctionLocal()
1251 @*/
1252 PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
1253 {
1254   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1255   PetscFEM         *fem   = (PetscFEM *) user;
1256   PetscFE          *fe    = fem->fe;
1257   PetscFE          *feAux = fem->feAux;
1258   const char       *name  = "Jacobian";
1259   DM                dmAux;
1260   Vec               A;
1261   PetscQuadrature   quad;
1262   PetscCellGeometry geom;
1263   PetscSection      section, globalSection, sectionAux;
1264   PetscReal        *v0, *J, *invJ, *detJ;
1265   PetscScalar      *elemMat, *u, *a;
1266   PetscInt          dim, Nf, NfAux = 0, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1267   PetscInt          cellDof = 0, numComponents = 0;
1268   PetscInt          cellDofAux = 0, numComponentsAux = 0;
1269   PetscBool         isShell;
1270   PetscErrorCode    ierr;
1271 
1272   PetscFunctionBegin;
1273   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1274   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1275   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1276   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
1277   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1278   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1279   numCells = cEnd - cStart;
1280   for (f = 0; f < Nf; ++f) {
1281     PetscInt Nb, Nc;
1282 
1283     ierr = PetscFEGetDimension(fe[f], &Nb);CHKERRQ(ierr);
1284     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1285     cellDof       += Nb*Nc;
1286     numComponents += Nc;
1287   }
1288   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1289   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1290   if (dmAux) {
1291     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1292     ierr = PetscSectionGetNumFields(sectionAux, &NfAux);CHKERRQ(ierr);
1293   }
1294   for (f = 0; f < NfAux; ++f) {
1295     PetscInt Nb, Nc;
1296 
1297     ierr = PetscFEGetDimension(feAux[f], &Nb);CHKERRQ(ierr);
1298     ierr = PetscFEGetNumComponents(feAux[f], &Nc);CHKERRQ(ierr);
1299     cellDofAux       += Nb*Nc;
1300     numComponentsAux += Nc;
1301   }
1302   ierr = DMPlexInsertBoundaryValuesFEM(dm, X);CHKERRQ(ierr);
1303   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
1304   ierr = PetscMalloc6(numCells*cellDof,&u,numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*cellDof*cellDof,&elemMat);CHKERRQ(ierr);
1305   if (dmAux) {ierr = PetscMalloc1(numCells*cellDofAux, &a);CHKERRQ(ierr);}
1306   for (c = cStart; c < cEnd; ++c) {
1307     PetscScalar *x = NULL;
1308     PetscInt     i;
1309 
1310     ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1311     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1312     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1313     for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
1314     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1315     if (dmAux) {
1316       ierr = DMPlexVecGetClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1317       for (i = 0; i < cellDofAux; ++i) a[c*cellDofAux+i] = x[i];
1318       ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1319     }
1320   }
1321   ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1322   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1323     PetscInt numQuadPoints, Nb;
1324     /* Conforming batches */
1325     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1326     /* Remainder */
1327     PetscInt Nr, offset;
1328 
1329     ierr = PetscFEGetQuadrature(fe[fieldI], &quad);CHKERRQ(ierr);
1330     ierr = PetscFEGetDimension(fe[fieldI], &Nb);CHKERRQ(ierr);
1331     ierr = PetscFEGetTileSizes(fe[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1332     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1333     blockSize = Nb*numQuadPoints;
1334     batchSize = numBlocks * blockSize;
1335     ierr = PetscFESetTileSizes(fe[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1336     numChunks = numCells / (numBatches*batchSize);
1337     Ne        = numChunks*numBatches*batchSize;
1338     Nr        = numCells % (numBatches*batchSize);
1339     offset    = numCells - Nr;
1340     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1341       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ];
1342       void   (*g1)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g1Funcs[fieldI*Nf+fieldJ];
1343       void   (*g2)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g2Funcs[fieldI*Nf+fieldJ];
1344       void   (*g3)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g3Funcs[fieldI*Nf+fieldJ];
1345 
1346       geom.v0   = v0;
1347       geom.J    = J;
1348       geom.invJ = invJ;
1349       geom.detJ = detJ;
1350       ierr = PetscFEIntegrateJacobian(fe[fieldI], Ne, Nf, fe, fieldI, fieldJ, geom, u, NfAux, feAux, a, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
1351       geom.v0   = &v0[offset*dim];
1352       geom.J    = &J[offset*dim*dim];
1353       geom.invJ = &invJ[offset*dim*dim];
1354       geom.detJ = &detJ[offset];
1355       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);
1356     }
1357   }
1358   for (c = cStart; c < cEnd; ++c) {
1359     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
1360     ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
1361   }
1362   ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1363   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1364   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1365   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1366   if (mesh->printFEM) {
1367     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1368     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
1369     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1370   }
1371   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
1372   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
1373   if (isShell) {
1374     JacActionCtx *jctx;
1375 
1376     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
1377     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
1378   }
1379   PetscFunctionReturn(0);
1380 }
1381 
1382 #if 0
1383 
1384 static void g0_identity_1d_static(const PetscScalar u[], const PetscScalar gradU[], const PetscScalar a[], const PetscScalar gradA[], const PetscReal x[], PetscScalar g3[])
1385 {
1386   g3[0] = 1.0;
1387 }
1388 
1389 static void g0_identity_2d_static(const PetscScalar u[], const PetscScalar gradU[], const PetscScalar a[], const PetscScalar gradA[], const PetscReal x[], PetscScalar g3[])
1390 {
1391   g3[0] = g3[3] = 1.0;
1392 }
1393 
1394 static void g0_identity_3d_static(const PetscScalar u[], const PetscScalar gradU[], const PetscScalar a[], const PetscScalar gradA[], const PetscReal x[], PetscScalar g3[])
1395 {
1396   g3[0] = g3[4] = g3[8] = 1.0;
1397 }
1398 
1399 #undef __FUNCT__
1400 #define __FUNCT__ "DMPlexComputeInterpolatorFEMBroken"
1401 PetscErrorCode DMPlexComputeInterpolatorFEMBroken(DM dmc, DM dmf, Mat I, void *user)
1402 {
1403   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1404   PetscFEM         *fem   = (PetscFEM *) user;
1405   PetscFE          *fe    = fem->fe;
1406   const char       *name  = "Interpolator";
1407   PetscFE          *feRef;
1408   PetscQuadrature   quad, quadOld;
1409   PetscCellGeometry geom;
1410   PetscSection      fsection, fglobalSection;
1411   PetscSection      csection, cglobalSection;
1412   PetscReal        *v0, *J, *invJ, *detJ;
1413   PetscScalar      *elemMat;
1414   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, cStart, cEnd, c;
1415   PetscInt          rCellDof = 0, cCellDof = 0, numComponents = 0;
1416   PetscErrorCode    ierr;
1417 
1418   PetscFunctionBegin;
1419 #if 0
1420   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1421 #endif
1422   ierr = DMPlexGetDimension(dmf, &dim);CHKERRQ(ierr);
1423   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1424   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1425   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1426   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1427   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1428   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1429   numCells = cEnd - cStart;
1430   ierr = PetscMalloc1(Nf,&feRef);CHKERRQ(ierr);
1431   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1432     ierr = PetscFERefine(fe[fieldI], &feRef[fieldI]);CHKERRQ(ierr);
1433   }
1434   for (f = 0; f < Nf; ++f) {
1435     PetscInt rNb, cNb, Nc;
1436 
1437     ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1438     ierr = PetscFEGetDimension(fe[f], &cNb);CHKERRQ(ierr);
1439     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1440     numComponents += Nc;
1441     rCellDof += rNb*Nc;
1442     cCellDof += cNb*Nc;
1443   }
1444   ierr = MatZeroEntries(I);CHKERRQ(ierr);
1445   ierr = PetscMalloc5(numCells*dim,&v0,numCells*dim*dim,&J,numCells*dim*dim,&invJ,numCells,&detJ,numCells*rCellDof*cCellDof,&elemMat);CHKERRQ(ierr);
1446   for (c = cStart; c < cEnd; ++c) {
1447     ierr = DMPlexComputeCellGeometry(dmc, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
1448     if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
1449   }
1450   ierr = PetscMemzero(elemMat, numCells*rCellDof*cCellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1451   for (fieldI = 0; fieldI < Nf; ++fieldI) {
1452     PetscInt numQuadPoints, Nb;
1453     /* Conforming batches */
1454     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1455     /* Remainder */
1456     PetscInt Nr, offset;
1457 
1458     /* Make new fine FE which refines the ref cell and the quadrature rule */
1459     ierr = PetscFEGetQuadrature(feRef[fieldI], &quad);CHKERRQ(ierr);
1460     ierr = PetscFEGetDimension(feRef[fieldI], &Nb);CHKERRQ(ierr);
1461     ierr = PetscFEGetTileSizes(feRef[fieldI], NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1462     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1463     blockSize = Nb*numQuadPoints;
1464     batchSize = numBlocks * blockSize;
1465     ierr = PetscFESetTileSizes(feRef[fieldI], blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1466     numChunks = numCells / (numBatches*batchSize);
1467     Ne        = numChunks*numBatches*batchSize;
1468     Nr        = numCells % (numBatches*batchSize);
1469     offset    = numCells - Nr;
1470 
1471     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
1472       /* void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = fem->g0Funcs[fieldI*Nf+fieldJ]; */
1473       void   (*g0)(const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]) = g0_identity_2d_static;
1474 
1475       /* Replace quadrature in coarse FE with refined quadrature */
1476       ierr = PetscFEGetQuadrature(fe[fieldJ], &quadOld);CHKERRQ(ierr);
1477       ierr = PetscObjectReference((PetscObject) quadOld);CHKERRQ(ierr);
1478       ierr = PetscFESetQuadrature(fe[fieldJ], quad);CHKERRQ(ierr);
1479       geom.v0   = v0;
1480       geom.J    = J;
1481       geom.invJ = invJ;
1482       geom.detJ = detJ;
1483       ierr = PetscFEIntegrateInterpolator_Basic(feRef[fieldI], Ne, Nf, feRef, fieldI, fe, fieldJ, geom, g0, elemMat);CHKERRQ(ierr);
1484       geom.v0   = &v0[offset*dim];
1485       geom.J    = &J[offset*dim*dim];
1486       geom.invJ = &invJ[offset*dim*dim];
1487       geom.detJ = &detJ[offset];
1488       ierr = PetscFEIntegrateInterpolator_Basic(feRef[fieldI], Nr, Nf, feRef, fieldI, fe, fieldJ, geom, g0, &elemMat[offset*rCellDof*cCellDof]);CHKERRQ(ierr);
1489       ierr = PetscFESetQuadrature(fe[fieldJ], quadOld);CHKERRQ(ierr);
1490     }
1491   }
1492   for (c = cStart; c < cEnd; ++c) {
1493     if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, rCellDof, cCellDof, &elemMat[c*rCellDof*cCellDof]);CHKERRQ(ierr);}
1494     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, I, c, &elemMat[c*rCellDof*cCellDof], ADD_VALUES);CHKERRQ(ierr);
1495   }
1496   ierr = PetscFree5(v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);
1497   ierr = PetscFree(feRef);CHKERRQ(ierr);
1498   ierr = MatAssemblyBegin(I, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1499   ierr = MatAssemblyEnd(I, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1500   if (mesh->printFEM) {
1501     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1502     ierr = MatChop(I, 1.0e-10);CHKERRQ(ierr);
1503     ierr = MatView(I, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1504   }
1505 #if 0
1506   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1507 #endif
1508   PetscFunctionReturn(0);
1509 }
1510 #endif
1511 
1512 #undef __FUNCT__
1513 #define __FUNCT__ "DMPlexComputeInterpolatorFEM"
1514 /*@
1515   DMPlexComputeInterpolatorFEM - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.
1516 
1517   Input Parameters:
1518 + dmf  - The fine mesh
1519 . dmc  - The coarse mesh
1520 - user - The user context
1521 
1522   Output Parameter:
1523 . In  - The interpolation matrix
1524 
1525   Note:
1526   The first member of the user context must be an FEMContext.
1527 
1528   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
1529   like a GPU, or vectorize on a multicore machine.
1530 
1531   Level: developer
1532 
1533 .seealso: DMPlexComputeJacobianFEM()
1534 @*/
1535 PetscErrorCode DMPlexComputeInterpolatorFEM(DM dmc, DM dmf, Mat In, void *user)
1536 {
1537   DM_Plex          *mesh  = (DM_Plex *) dmc->data;
1538   PetscFEM         *fem   = (PetscFEM *) user;
1539   PetscFE          *fe    = fem->fe;
1540   const char       *name  = "Interpolator";
1541   PetscFE          *feRef;
1542   PetscSection      fsection, fglobalSection;
1543   PetscSection      csection, cglobalSection;
1544   PetscScalar      *elemMat;
1545   PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, c;
1546   PetscInt          rCellDof = 0, cCellDof = 0;
1547   PetscErrorCode    ierr;
1548 
1549   PetscFunctionBegin;
1550 #if 0
1551   ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1552 #endif
1553   ierr = DMPlexGetDimension(dmf, &dim);CHKERRQ(ierr);
1554   ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
1555   ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
1556   ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
1557   ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
1558   ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
1559   ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
1560   ierr = PetscMalloc1(Nf,&feRef);CHKERRQ(ierr);
1561   for (f = 0; f < Nf; ++f) {
1562     PetscInt rNb, cNb, Nc;
1563 
1564     ierr = PetscFERefine(fe[f], &feRef[f]);CHKERRQ(ierr);
1565     ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
1566     ierr = PetscFEGetDimension(fe[f], &cNb);CHKERRQ(ierr);
1567     ierr = PetscFEGetNumComponents(fe[f], &Nc);CHKERRQ(ierr);
1568     rCellDof += rNb*Nc;
1569     cCellDof += cNb*Nc;
1570   }
1571   ierr = MatZeroEntries(In);CHKERRQ(ierr);
1572   ierr = PetscMalloc1(rCellDof*cCellDof,&elemMat);CHKERRQ(ierr);
1573   ierr = PetscMemzero(elemMat, rCellDof*cCellDof * sizeof(PetscScalar));CHKERRQ(ierr);
1574   for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
1575     PetscDualSpace   Qref;
1576     PetscQuadrature  f;
1577     const PetscReal *qpoints, *qweights;
1578     PetscReal       *points;
1579     PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;
1580 
1581     /* Compose points from all dual basis functionals */
1582     ierr = PetscFEGetNumComponents(fe[fieldI], &Nc);CHKERRQ(ierr);
1583     ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
1584     ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
1585     for (i = 0; i < fpdim; ++i) {
1586       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1587       ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
1588       npoints += Np;
1589     }
1590     ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
1591     for (i = 0, k = 0; i < fpdim; ++i) {
1592       ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1593       ierr = PetscQuadratureGetData(f, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
1594       for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
1595     }
1596 
1597     for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
1598       PetscReal *B;
1599       PetscInt   NcJ, cpdim, j;
1600 
1601       /* Evaluate basis at points */
1602       ierr = PetscFEGetNumComponents(fe[fieldJ], &NcJ);CHKERRQ(ierr);
1603       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);
1604       ierr = PetscFEGetDimension(fe[fieldJ], &cpdim);CHKERRQ(ierr);
1605       /* For now, fields only interpolate themselves */
1606       if (fieldI == fieldJ) {
1607         ierr = PetscFEGetTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
1608         for (i = 0, k = 0; i < fpdim; ++i) {
1609           ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
1610           ierr = PetscQuadratureGetData(f, NULL, &Np, NULL, &qweights);CHKERRQ(ierr);
1611           for (p = 0; p < Np; ++p, ++k) {
1612             for (j = 0; j < cpdim; ++j) {
1613               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];
1614             }
1615           }
1616         }
1617         ierr = PetscFERestoreTabulation(fe[fieldJ], npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
1618       }
1619       offsetJ += cpdim*NcJ;
1620     }
1621     offsetI += fpdim*Nc;
1622     ierr = PetscFree(points);CHKERRQ(ierr);
1623   }
1624   if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rCellDof, cCellDof, elemMat);CHKERRQ(ierr);}
1625   for (c = cStart; c < cEnd; ++c) {
1626     ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
1627   }
1628   for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
1629   ierr = PetscFree(feRef);CHKERRQ(ierr);
1630   ierr = PetscFree(elemMat);CHKERRQ(ierr);
1631   ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1632   ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1633   if (mesh->printFEM) {
1634     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
1635     ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
1636     ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
1637   }
1638 #if 0
1639   ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
1640 #endif
1641   PetscFunctionReturn(0);
1642 }
1643 
1644 #undef __FUNCT__
1645 #define __FUNCT__ "DMPlexAddBoundary"
1646 /* The ids can be overridden by the command line option -bc_<boundary name> */
1647 PetscErrorCode DMPlexAddBoundary(DM dm, PetscBool isEssential, const char name[], PetscInt field, void (*bcFunc)(), PetscInt numids, const PetscInt *ids, void *ctx)
1648 {
1649   DM_Plex       *mesh = (DM_Plex *) dm->data;
1650   DMBoundary     b;
1651   PetscErrorCode ierr;
1652 
1653   PetscFunctionBegin;
1654   ierr = PetscNew(&b);CHKERRQ(ierr);
1655   ierr = PetscStrallocpy(name, (char **) &b->name);CHKERRQ(ierr);
1656   ierr = PetscMalloc1(numids, &b->ids);CHKERRQ(ierr);
1657   ierr = PetscMemcpy(b->ids, ids, numids*sizeof(PetscInt));CHKERRQ(ierr);
1658   b->essential   = isEssential;
1659   b->field       = field;
1660   b->func        = bcFunc;
1661   b->numids      = numids;
1662   b->ctx         = ctx;
1663   b->next        = mesh->boundary;
1664   mesh->boundary = b;
1665   PetscFunctionReturn(0);
1666 }
1667 
1668 #undef __FUNCT__
1669 #define __FUNCT__ "DMPlexGetNumBoundary"
1670 PetscErrorCode DMPlexGetNumBoundary(DM dm, PetscInt *numBd)
1671 {
1672   DM_Plex   *mesh = (DM_Plex *) dm->data;
1673   DMBoundary b    = mesh->boundary;
1674 
1675   PetscFunctionBegin;
1676   *numBd = 0;
1677   while (b) {++(*numBd); b = b->next;}
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #undef __FUNCT__
1682 #define __FUNCT__ "DMPlexGetBoundary"
1683 PetscErrorCode DMPlexGetBoundary(DM dm, PetscInt bd, PetscBool *isEssential, const char **name, PetscInt *field, void (**func)(), PetscInt *numids, const PetscInt **ids, void **ctx)
1684 {
1685   DM_Plex   *mesh = (DM_Plex *) dm->data;
1686   DMBoundary b    = mesh->boundary;
1687   PetscInt   n    = 0;
1688 
1689   PetscFunctionBegin;
1690   while (b) {
1691     if (n == bd) break;
1692     b = b->next;
1693     ++n;
1694   }
1695   if (n != bd) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Boundary %d is not in [0, %d)", bd, n);
1696   if (isEssential) {
1697     PetscValidPointer(isEssential, 3);
1698     *isEssential = b->essential;
1699   }
1700   if (name) {
1701     PetscValidPointer(name, 4);
1702     *name = b->name;
1703   }
1704   if (field) {
1705     PetscValidPointer(field, 5);
1706     *field = b->field;
1707   }
1708   if (func) {
1709     PetscValidPointer(func, 6);
1710     *func = b->func;
1711   }
1712   if (numids) {
1713     PetscValidPointer(numids, 7);
1714     *numids = b->numids;
1715   }
1716   if (ids) {
1717     PetscValidPointer(ids, 8);
1718     *ids = b->ids;
1719   }
1720   if (ctx) {
1721     PetscValidPointer(ctx, 9);
1722     *ctx = b->ctx;
1723   }
1724   PetscFunctionReturn(0);
1725 }
1726