xref: /petsc/src/snes/utils/dmplexsnes.c (revision 1a2443445f10a6cdb92f6af2ca31cdcaa5f5151b)
1 #include <petsc/private/dmpleximpl.h>   /*I "petscdmplex.h" I*/
2 #include <petsc/private/snesimpl.h>     /*I "petscsnes.h"   I*/
3 #include <petscds.h>
4 #include <petsc/private/petscimpl.h>
5 #include <petsc/private/petscfeimpl.h>
6 
7 /************************** Interpolation *******************************/
8 
9 #undef __FUNCT__
10 #define __FUNCT__ "DMSNESConvertPlex"
11 static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
12 {
13   PetscBool      isPlex;
14   PetscErrorCode ierr;
15 
16   PetscFunctionBegin;
17   ierr = PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);CHKERRQ(ierr);
18   if (isPlex) {
19     *plex = dm;
20     ierr = PetscObjectReference((PetscObject) dm);CHKERRQ(ierr);
21   } else {
22     ierr = PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);CHKERRQ(ierr);
23     if (!*plex) {
24       ierr = DMConvert(dm,DMPLEX,plex);CHKERRQ(ierr);
25       ierr = PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);CHKERRQ(ierr);
26       if (copy) {
27         PetscInt    i;
28         PetscObject obj;
29         const char *comps[3] = {"A","dmAux","dmCh"};
30 
31         ierr = DMCopyDMSNES(dm, *plex);CHKERRQ(ierr);
32         for (i = 0; i < 3; i++) {
33           ierr = PetscObjectQuery((PetscObject) dm, comps[i], &obj);CHKERRQ(ierr);
34           ierr = PetscObjectCompose((PetscObject) *plex, comps[i], obj);CHKERRQ(ierr);
35         }
36       }
37     } else {
38       ierr = PetscObjectReference((PetscObject) *plex);CHKERRQ(ierr);
39     }
40   }
41   PetscFunctionReturn(0);
42 }
43 
44 #undef __FUNCT__
45 #define __FUNCT__ "DMInterpolationCreate"
46 PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
47 {
48   PetscErrorCode ierr;
49 
50   PetscFunctionBegin;
51   PetscValidPointer(ctx, 2);
52   ierr = PetscMalloc(sizeof(struct _DMInterpolationInfo), ctx);CHKERRQ(ierr);
53 
54   (*ctx)->comm   = comm;
55   (*ctx)->dim    = -1;
56   (*ctx)->nInput = 0;
57   (*ctx)->points = NULL;
58   (*ctx)->cells  = NULL;
59   (*ctx)->n      = -1;
60   (*ctx)->coords = NULL;
61   PetscFunctionReturn(0);
62 }
63 
64 #undef __FUNCT__
65 #define __FUNCT__ "DMInterpolationSetDim"
66 PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
67 {
68   PetscFunctionBegin;
69   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
70   ctx->dim = dim;
71   PetscFunctionReturn(0);
72 }
73 
74 #undef __FUNCT__
75 #define __FUNCT__ "DMInterpolationGetDim"
76 PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
77 {
78   PetscFunctionBegin;
79   PetscValidIntPointer(dim, 2);
80   *dim = ctx->dim;
81   PetscFunctionReturn(0);
82 }
83 
84 #undef __FUNCT__
85 #define __FUNCT__ "DMInterpolationSetDof"
86 PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
87 {
88   PetscFunctionBegin;
89   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
90   ctx->dof = dof;
91   PetscFunctionReturn(0);
92 }
93 
94 #undef __FUNCT__
95 #define __FUNCT__ "DMInterpolationGetDof"
96 PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
97 {
98   PetscFunctionBegin;
99   PetscValidIntPointer(dof, 2);
100   *dof = ctx->dof;
101   PetscFunctionReturn(0);
102 }
103 
104 #undef __FUNCT__
105 #define __FUNCT__ "DMInterpolationAddPoints"
106 PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
107 {
108   PetscErrorCode ierr;
109 
110   PetscFunctionBegin;
111   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
112   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
113   ctx->nInput = n;
114 
115   ierr = PetscMalloc1(n*ctx->dim, &ctx->points);CHKERRQ(ierr);
116   ierr = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));CHKERRQ(ierr);
117   PetscFunctionReturn(0);
118 }
119 
120 #undef __FUNCT__
121 #define __FUNCT__ "DMInterpolationSetUp"
122 PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
123 {
124   MPI_Comm          comm = ctx->comm;
125   PetscScalar       *a;
126   PetscInt          p, q, i;
127   PetscMPIInt       rank, size;
128   PetscErrorCode    ierr;
129   Vec               pointVec;
130   PetscSF           cellSF;
131   PetscLayout       layout;
132   PetscReal         *globalPoints;
133   PetscScalar       *globalPointsScalar;
134   const PetscInt    *ranges;
135   PetscMPIInt       *counts, *displs;
136   const PetscSFNode *foundCells;
137   const PetscInt    *foundPoints;
138   PetscMPIInt       *foundProcs, *globalProcs;
139   PetscInt          n, N, numFound;
140 
141   PetscFunctionBegin;
142   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
143   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
144   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
145   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
146   /* Locate points */
147   n = ctx->nInput;
148   if (!redundantPoints) {
149     ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
150     ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
151     ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
152     ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
153     ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
154     /* Communicate all points to all processes */
155     ierr = PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);CHKERRQ(ierr);
156     ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
157     for (p = 0; p < size; ++p) {
158       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
159       displs[p] = ranges[p]*ctx->dim;
160     }
161     ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
162   } else {
163     N = n;
164     globalPoints = ctx->points;
165     counts = displs = NULL;
166     layout = NULL;
167   }
168 #if 0
169   ierr = PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
170   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
171 #else
172 #if defined(PETSC_USE_COMPLEX)
173   ierr = PetscMalloc1(N,&globalPointsScalar);CHKERRQ(ierr);
174   for (i=0; i<N; i++) globalPointsScalar[i] = globalPoints[i];
175 #else
176   globalPointsScalar = globalPoints;
177 #endif
178   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
179   ierr = PetscMalloc2(N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
180   cellSF = NULL;
181   ierr = DMLocatePoints(dm, pointVec, &cellSF);CHKERRQ(ierr);
182   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
183 #endif
184   for (p = 0; p < numFound; ++p) {
185     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
186     else foundProcs[foundPoints ? foundPoints[p] : p] = size;
187   }
188   /* Let the lowest rank process own each point */
189   ierr   = MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
190   ctx->n = 0;
191   for (p = 0; p < N; ++p) {
192     if (globalProcs[p] == size) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, globalPoints[p*ctx->dim+0], ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0, ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0);
193     else if (globalProcs[p] == rank) ctx->n++;
194   }
195   /* Create coordinates vector and array of owned cells */
196   ierr = PetscMalloc1(ctx->n, &ctx->cells);CHKERRQ(ierr);
197   ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
198   ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
199   ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
200   ierr = VecSetType(ctx->coords,VECSTANDARD);CHKERRQ(ierr);
201   ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
202   for (p = 0, q = 0, i = 0; p < N; ++p) {
203     if (globalProcs[p] == rank) {
204       PetscInt d;
205 
206       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
207       ctx->cells[q++] = foundCells[p].index;
208     }
209   }
210   ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
211 #if 0
212   ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
213 #else
214   ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
215   ierr = PetscSFDestroy(&cellSF);CHKERRQ(ierr);
216   ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
217 #endif
218   if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
219   if (!redundantPoints) {ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);}
220   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
221   PetscFunctionReturn(0);
222 }
223 
224 #undef __FUNCT__
225 #define __FUNCT__ "DMInterpolationGetCoordinates"
226 PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
227 {
228   PetscFunctionBegin;
229   PetscValidPointer(coordinates, 2);
230   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
231   *coordinates = ctx->coords;
232   PetscFunctionReturn(0);
233 }
234 
235 #undef __FUNCT__
236 #define __FUNCT__ "DMInterpolationGetVector"
237 PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
238 {
239   PetscErrorCode ierr;
240 
241   PetscFunctionBegin;
242   PetscValidPointer(v, 2);
243   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
244   ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
245   ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
246   ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
247   ierr = VecSetType(*v,VECSTANDARD);CHKERRQ(ierr);
248   PetscFunctionReturn(0);
249 }
250 
251 #undef __FUNCT__
252 #define __FUNCT__ "DMInterpolationRestoreVector"
253 PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
254 {
255   PetscErrorCode ierr;
256 
257   PetscFunctionBegin;
258   PetscValidPointer(v, 2);
259   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
260   ierr = VecDestroy(v);CHKERRQ(ierr);
261   PetscFunctionReturn(0);
262 }
263 
264 #undef __FUNCT__
265 #define __FUNCT__ "DMInterpolate_Triangle_Private"
266 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
267 {
268   PetscReal      *v0, *J, *invJ, detJ;
269   const PetscScalar *coords;
270   PetscScalar    *a;
271   PetscInt       p;
272   PetscErrorCode ierr;
273 
274   PetscFunctionBegin;
275   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
276   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
277   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
278   for (p = 0; p < ctx->n; ++p) {
279     PetscInt     c = ctx->cells[p];
280     PetscScalar *x = NULL;
281     PetscReal    xi[4];
282     PetscInt     d, f, comp;
283 
284     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
285     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
286     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
287     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
288 
289     for (d = 0; d < ctx->dim; ++d) {
290       xi[d] = 0.0;
291       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
292       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[(d+1)*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
293     }
294     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
295   }
296   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
297   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
298   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
299   PetscFunctionReturn(0);
300 }
301 
302 #undef __FUNCT__
303 #define __FUNCT__ "DMInterpolate_Tetrahedron_Private"
304 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
305 {
306   PetscReal      *v0, *J, *invJ, detJ;
307   const PetscScalar *coords;
308   PetscScalar    *a;
309   PetscInt       p;
310   PetscErrorCode ierr;
311 
312   PetscFunctionBegin;
313   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
314   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
315   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
316   for (p = 0; p < ctx->n; ++p) {
317     PetscInt       c = ctx->cells[p];
318     const PetscInt order[3] = {2, 1, 3};
319     PetscScalar   *x = NULL;
320     PetscReal      xi[4];
321     PetscInt       d, f, comp;
322 
323     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
324     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
325     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
326     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
327 
328     for (d = 0; d < ctx->dim; ++d) {
329       xi[d] = 0.0;
330       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
331       for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[order[d]*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
332     }
333     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
334   }
335   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
336   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
337   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
338   PetscFunctionReturn(0);
339 }
340 
341 #undef __FUNCT__
342 #define __FUNCT__ "QuadMap_Private"
343 PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
344 {
345   const PetscScalar *vertices = (const PetscScalar*) ctx;
346   const PetscScalar x0        = vertices[0];
347   const PetscScalar y0        = vertices[1];
348   const PetscScalar x1        = vertices[2];
349   const PetscScalar y1        = vertices[3];
350   const PetscScalar x2        = vertices[4];
351   const PetscScalar y2        = vertices[5];
352   const PetscScalar x3        = vertices[6];
353   const PetscScalar y3        = vertices[7];
354   const PetscScalar f_1       = x1 - x0;
355   const PetscScalar g_1       = y1 - y0;
356   const PetscScalar f_3       = x3 - x0;
357   const PetscScalar g_3       = y3 - y0;
358   const PetscScalar f_01      = x2 - x1 - x3 + x0;
359   const PetscScalar g_01      = y2 - y1 - y3 + y0;
360   const PetscScalar *ref;
361   PetscScalar       *real;
362   PetscErrorCode    ierr;
363 
364   PetscFunctionBegin;
365   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
366   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
367   {
368     const PetscScalar p0 = ref[0];
369     const PetscScalar p1 = ref[1];
370 
371     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
372     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
373   }
374   ierr = PetscLogFlops(28);CHKERRQ(ierr);
375   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
376   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
377   PetscFunctionReturn(0);
378 }
379 
380 #include <petsc/private/dmimpl.h>
381 #undef __FUNCT__
382 #define __FUNCT__ "QuadJacobian_Private"
383 PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
384 {
385   const PetscScalar *vertices = (const PetscScalar*) ctx;
386   const PetscScalar x0        = vertices[0];
387   const PetscScalar y0        = vertices[1];
388   const PetscScalar x1        = vertices[2];
389   const PetscScalar y1        = vertices[3];
390   const PetscScalar x2        = vertices[4];
391   const PetscScalar y2        = vertices[5];
392   const PetscScalar x3        = vertices[6];
393   const PetscScalar y3        = vertices[7];
394   const PetscScalar f_01      = x2 - x1 - x3 + x0;
395   const PetscScalar g_01      = y2 - y1 - y3 + y0;
396   const PetscScalar *ref;
397   PetscErrorCode    ierr;
398 
399   PetscFunctionBegin;
400   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
401   {
402     const PetscScalar x       = ref[0];
403     const PetscScalar y       = ref[1];
404     const PetscInt    rows[2] = {0, 1};
405     PetscScalar       values[4];
406 
407     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
408     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
409     ierr      = MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
410   }
411   ierr = PetscLogFlops(30);CHKERRQ(ierr);
412   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
413   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
414   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
415   PetscFunctionReturn(0);
416 }
417 
418 #undef __FUNCT__
419 #define __FUNCT__ "DMInterpolate_Quad_Private"
420 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
421 {
422   DM             dmCoord;
423   SNES           snes;
424   KSP            ksp;
425   PC             pc;
426   Vec            coordsLocal, r, ref, real;
427   Mat            J;
428   const PetscScalar *coords;
429   PetscScalar    *a;
430   PetscInt       p;
431   PetscErrorCode ierr;
432 
433   PetscFunctionBegin;
434   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
435   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
436   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
437   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
438   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
439   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
440   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
441   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
442   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
443   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
444   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
445   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
446   ierr = MatSetUp(J);CHKERRQ(ierr);
447   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
448   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
449   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
450   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
451   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
452   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
453 
454   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
455   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
456   for (p = 0; p < ctx->n; ++p) {
457     PetscScalar *x = NULL, *vertices = NULL;
458     PetscScalar *xi;
459     PetscReal    xir[2];
460     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
461 
462     /* Can make this do all points at once */
463     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
464     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
465     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
466     if (4*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 4*ctx->dof);
467     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
468     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
469     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
470     xi[0]  = coords[p*ctx->dim+0];
471     xi[1]  = coords[p*ctx->dim+1];
472     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
473     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
474     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
475     xir[0] = PetscRealPart(xi[0]);
476     xir[1] = PetscRealPart(xi[1]);
477     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*ctx->dof+comp]*xir[0]*(1 - xir[1]) + x[2*ctx->dof+comp]*xir[0]*xir[1] + x[3*ctx->dof+comp]*(1 - xir[0])*xir[1];
478 
479     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
480     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
481     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
482   }
483   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
484   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
485 
486   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
487   ierr = VecDestroy(&r);CHKERRQ(ierr);
488   ierr = VecDestroy(&ref);CHKERRQ(ierr);
489   ierr = VecDestroy(&real);CHKERRQ(ierr);
490   ierr = MatDestroy(&J);CHKERRQ(ierr);
491   PetscFunctionReturn(0);
492 }
493 
494 #undef __FUNCT__
495 #define __FUNCT__ "HexMap_Private"
496 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
497 {
498   const PetscScalar *vertices = (const PetscScalar*) ctx;
499   const PetscScalar x0        = vertices[0];
500   const PetscScalar y0        = vertices[1];
501   const PetscScalar z0        = vertices[2];
502   const PetscScalar x1        = vertices[9];
503   const PetscScalar y1        = vertices[10];
504   const PetscScalar z1        = vertices[11];
505   const PetscScalar x2        = vertices[6];
506   const PetscScalar y2        = vertices[7];
507   const PetscScalar z2        = vertices[8];
508   const PetscScalar x3        = vertices[3];
509   const PetscScalar y3        = vertices[4];
510   const PetscScalar z3        = vertices[5];
511   const PetscScalar x4        = vertices[12];
512   const PetscScalar y4        = vertices[13];
513   const PetscScalar z4        = vertices[14];
514   const PetscScalar x5        = vertices[15];
515   const PetscScalar y5        = vertices[16];
516   const PetscScalar z5        = vertices[17];
517   const PetscScalar x6        = vertices[18];
518   const PetscScalar y6        = vertices[19];
519   const PetscScalar z6        = vertices[20];
520   const PetscScalar x7        = vertices[21];
521   const PetscScalar y7        = vertices[22];
522   const PetscScalar z7        = vertices[23];
523   const PetscScalar f_1       = x1 - x0;
524   const PetscScalar g_1       = y1 - y0;
525   const PetscScalar h_1       = z1 - z0;
526   const PetscScalar f_3       = x3 - x0;
527   const PetscScalar g_3       = y3 - y0;
528   const PetscScalar h_3       = z3 - z0;
529   const PetscScalar f_4       = x4 - x0;
530   const PetscScalar g_4       = y4 - y0;
531   const PetscScalar h_4       = z4 - z0;
532   const PetscScalar f_01      = x2 - x1 - x3 + x0;
533   const PetscScalar g_01      = y2 - y1 - y3 + y0;
534   const PetscScalar h_01      = z2 - z1 - z3 + z0;
535   const PetscScalar f_12      = x7 - x3 - x4 + x0;
536   const PetscScalar g_12      = y7 - y3 - y4 + y0;
537   const PetscScalar h_12      = z7 - z3 - z4 + z0;
538   const PetscScalar f_02      = x5 - x1 - x4 + x0;
539   const PetscScalar g_02      = y5 - y1 - y4 + y0;
540   const PetscScalar h_02      = z5 - z1 - z4 + z0;
541   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
542   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
543   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
544   const PetscScalar *ref;
545   PetscScalar       *real;
546   PetscErrorCode    ierr;
547 
548   PetscFunctionBegin;
549   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
550   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
551   {
552     const PetscScalar p0 = ref[0];
553     const PetscScalar p1 = ref[1];
554     const PetscScalar p2 = ref[2];
555 
556     real[0] = x0 + f_1*p0 + f_3*p1 + f_4*p2 + f_01*p0*p1 + f_12*p1*p2 + f_02*p0*p2 + f_012*p0*p1*p2;
557     real[1] = y0 + g_1*p0 + g_3*p1 + g_4*p2 + g_01*p0*p1 + g_01*p0*p1 + g_12*p1*p2 + g_02*p0*p2 + g_012*p0*p1*p2;
558     real[2] = z0 + h_1*p0 + h_3*p1 + h_4*p2 + h_01*p0*p1 + h_01*p0*p1 + h_12*p1*p2 + h_02*p0*p2 + h_012*p0*p1*p2;
559   }
560   ierr = PetscLogFlops(114);CHKERRQ(ierr);
561   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
562   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
563   PetscFunctionReturn(0);
564 }
565 
566 #undef __FUNCT__
567 #define __FUNCT__ "HexJacobian_Private"
568 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
569 {
570   const PetscScalar *vertices = (const PetscScalar*) ctx;
571   const PetscScalar x0        = vertices[0];
572   const PetscScalar y0        = vertices[1];
573   const PetscScalar z0        = vertices[2];
574   const PetscScalar x1        = vertices[9];
575   const PetscScalar y1        = vertices[10];
576   const PetscScalar z1        = vertices[11];
577   const PetscScalar x2        = vertices[6];
578   const PetscScalar y2        = vertices[7];
579   const PetscScalar z2        = vertices[8];
580   const PetscScalar x3        = vertices[3];
581   const PetscScalar y3        = vertices[4];
582   const PetscScalar z3        = vertices[5];
583   const PetscScalar x4        = vertices[12];
584   const PetscScalar y4        = vertices[13];
585   const PetscScalar z4        = vertices[14];
586   const PetscScalar x5        = vertices[15];
587   const PetscScalar y5        = vertices[16];
588   const PetscScalar z5        = vertices[17];
589   const PetscScalar x6        = vertices[18];
590   const PetscScalar y6        = vertices[19];
591   const PetscScalar z6        = vertices[20];
592   const PetscScalar x7        = vertices[21];
593   const PetscScalar y7        = vertices[22];
594   const PetscScalar z7        = vertices[23];
595   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
596   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
597   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
598   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
599   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
600   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
601   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
602   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
603   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
604   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
605   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
606   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
607   const PetscScalar *ref;
608   PetscErrorCode    ierr;
609 
610   PetscFunctionBegin;
611   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
612   {
613     const PetscScalar x       = ref[0];
614     const PetscScalar y       = ref[1];
615     const PetscScalar z       = ref[2];
616     const PetscInt    rows[3] = {0, 1, 2};
617     PetscScalar       values[9];
618 
619     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
620     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
621     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
622     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
623     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
624     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
625     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
626     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
627     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
628 
629     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
630   }
631   ierr = PetscLogFlops(152);CHKERRQ(ierr);
632   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
633   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
634   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
635   PetscFunctionReturn(0);
636 }
637 
638 #undef __FUNCT__
639 #define __FUNCT__ "DMInterpolate_Hex_Private"
640 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
641 {
642   DM             dmCoord;
643   SNES           snes;
644   KSP            ksp;
645   PC             pc;
646   Vec            coordsLocal, r, ref, real;
647   Mat            J;
648   const PetscScalar *coords;
649   PetscScalar    *a;
650   PetscInt       p;
651   PetscErrorCode ierr;
652 
653   PetscFunctionBegin;
654   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
655   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
656   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
657   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
658   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
659   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
660   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
661   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
662   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
663   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
664   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
665   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
666   ierr = MatSetUp(J);CHKERRQ(ierr);
667   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
668   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
669   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
670   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
671   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
672   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
673 
674   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
675   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
676   for (p = 0; p < ctx->n; ++p) {
677     PetscScalar *x = NULL, *vertices = NULL;
678     PetscScalar *xi;
679     PetscReal    xir[3];
680     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
681 
682     /* Can make this do all points at once */
683     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
684     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
685     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
686     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
687     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
688     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
689     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
690     xi[0]  = coords[p*ctx->dim+0];
691     xi[1]  = coords[p*ctx->dim+1];
692     xi[2]  = coords[p*ctx->dim+2];
693     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
694     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
695     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
696     xir[0] = PetscRealPart(xi[0]);
697     xir[1] = PetscRealPart(xi[1]);
698     xir[2] = PetscRealPart(xi[2]);
699     for (comp = 0; comp < ctx->dof; ++comp) {
700       a[p*ctx->dof+comp] =
701         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
702         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
703         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
704         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
705         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
706         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
707         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
708         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
709     }
710     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
711     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
712     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
713   }
714   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
715   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
716 
717   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
718   ierr = VecDestroy(&r);CHKERRQ(ierr);
719   ierr = VecDestroy(&ref);CHKERRQ(ierr);
720   ierr = VecDestroy(&real);CHKERRQ(ierr);
721   ierr = MatDestroy(&J);CHKERRQ(ierr);
722   PetscFunctionReturn(0);
723 }
724 
725 #undef __FUNCT__
726 #define __FUNCT__ "DMInterpolationEvaluate"
727 /*
728   Input Parameters:
729 + ctx - The DMInterpolationInfo context
730 . dm  - The DM
731 - x   - The local vector containing the field to be interpolated
732 
733   Output Parameters:
734 . v   - The vector containing the interpolated values
735 */
736 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
737 {
738   PetscInt       dim, coneSize, n;
739   PetscErrorCode ierr;
740 
741   PetscFunctionBegin;
742   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
743   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
744   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
745   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
746   if (n != ctx->n*ctx->dof) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid input vector size %d should be %d", n, ctx->n*ctx->dof);
747   if (n) {
748     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
749     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
750     if (dim == 2) {
751       if (coneSize == 3) {
752         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
753       } else if (coneSize == 4) {
754         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
755       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
756     } else if (dim == 3) {
757       if (coneSize == 4) {
758         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
759       } else {
760         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
761       }
762     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
763   }
764   PetscFunctionReturn(0);
765 }
766 
767 #undef __FUNCT__
768 #define __FUNCT__ "DMInterpolationDestroy"
769 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
770 {
771   PetscErrorCode ierr;
772 
773   PetscFunctionBegin;
774   PetscValidPointer(ctx, 2);
775   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
776   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
777   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
778   ierr = PetscFree(*ctx);CHKERRQ(ierr);
779   *ctx = NULL;
780   PetscFunctionReturn(0);
781 }
782 
783 #undef __FUNCT__
784 #define __FUNCT__ "SNESMonitorFields"
785 /*@C
786   SNESMonitorFields - Monitors the residual for each field separately
787 
788   Collective on SNES
789 
790   Input Parameters:
791 + snes   - the SNES context
792 . its    - iteration number
793 . fgnorm - 2-norm of residual
794 - vf  - PetscViewerAndFormat of type ASCII
795 
796   Notes:
797   This routine prints the residual norm at each iteration.
798 
799   Level: intermediate
800 
801 .keywords: SNES, nonlinear, default, monitor, norm
802 .seealso: SNESMonitorSet(), SNESMonitorDefault()
803 @*/
804 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
805 {
806   PetscViewer        viewer = vf->viewer;
807   Vec                res;
808   DM                 dm;
809   PetscSection       s;
810   const PetscScalar *r;
811   PetscReal         *lnorms, *norms;
812   PetscInt           numFields, f, pStart, pEnd, p;
813   PetscErrorCode     ierr;
814 
815   PetscFunctionBegin;
816   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
817   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
818   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
819   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
820   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
821   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
822   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
823   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
824   for (p = pStart; p < pEnd; ++p) {
825     for (f = 0; f < numFields; ++f) {
826       PetscInt fdof, foff, d;
827 
828       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
829       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
830       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
831     }
832   }
833   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
834   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
835   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
836   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
837   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
838   for (f = 0; f < numFields; ++f) {
839     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
840     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
841   }
842   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
843   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
844   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
845   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
846   PetscFunctionReturn(0);
847 }
848 
849 /********************* Residual Computation **************************/
850 
851 #undef __FUNCT__
852 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
853 /*@
854   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
855 
856   Input Parameter:
857 . dm - The DM
858 
859   Output Parameters:
860 . cellgeom - The values precomputed from cell geometry
861 
862   Level: developer
863 
864 .seealso: DMPlexSNESSetFunctionLocal()
865 @*/
866 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
867 {
868   DMSNES         dmsnes;
869   PetscObject    obj;
870   PetscErrorCode ierr;
871 
872   PetscFunctionBegin;
873   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
874   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
875   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
876   if (!obj) {
877     Vec cellgeom;
878 
879     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
880     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
881     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
882   }
883   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
884   PetscFunctionReturn(0);
885 }
886 
887 #undef __FUNCT__
888 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
889 /*@
890   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
891 
892   Input Parameter:
893 . dm - The DM
894 
895   Output Parameters:
896 + facegeom - The values precomputed from face geometry
897 . cellgeom - The values precomputed from cell geometry
898 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
899 
900   Level: developer
901 
902 .seealso: DMPlexTSSetRHSFunctionLocal()
903 @*/
904 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
905 {
906   DMSNES         dmsnes;
907   PetscObject    obj;
908   PetscErrorCode ierr;
909 
910   PetscFunctionBegin;
911   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
912   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
913   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", &obj);CHKERRQ(ierr);
914   if (!obj) {
915     Vec cellgeom, facegeom;
916 
917     ierr = DMPlexComputeGeometryFVM(dm, &cellgeom, &facegeom);CHKERRQ(ierr);
918     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject) facegeom);CHKERRQ(ierr);
919     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject) cellgeom);CHKERRQ(ierr);
920     ierr = VecDestroy(&facegeom);CHKERRQ(ierr);
921     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
922   }
923   if (facegeom) {PetscValidPointer(facegeom, 2); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_facegeom_fvm", (PetscObject *) facegeom);CHKERRQ(ierr);}
924   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fvm", (PetscObject *) cellgeom);CHKERRQ(ierr);}
925   if (minRadius) {ierr = DMPlexGetMinRadius(dm, minRadius);CHKERRQ(ierr);}
926   PetscFunctionReturn(0);
927 }
928 
929 #undef __FUNCT__
930 #define __FUNCT__ "DMPlexSNESGetGradientDM"
931 /*@
932   DMPlexSNESGetGradientDM - Return gradient data layout
933 
934   Input Parameters:
935 + dm - The DM
936 - fv - The PetscFV
937 
938   Output Parameter:
939 . dmGrad - The layout for gradient values
940 
941   Level: developer
942 
943 .seealso: DMPlexSNESGetGeometryFVM()
944 @*/
945 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
946 {
947   DMSNES         dmsnes;
948   PetscObject    obj;
949   PetscBool      computeGradients;
950   PetscErrorCode ierr;
951 
952   PetscFunctionBegin;
953   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
954   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
955   PetscValidPointer(dmGrad,3);
956   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
957   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
958   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
959   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", &obj);CHKERRQ(ierr);
960   if (!obj) {
961     DM  dmGrad;
962     Vec faceGeometry, cellGeometry;
963 
964     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometry, &cellGeometry, NULL);CHKERRQ(ierr);
965     ierr = DMPlexComputeGradientFVM(dm, fv, faceGeometry, cellGeometry, &dmGrad);CHKERRQ(ierr);
966     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject) dmGrad);CHKERRQ(ierr);
967     ierr = DMDestroy(&dmGrad);CHKERRQ(ierr);
968   }
969   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_dmgrad_fvm", (PetscObject *) dmGrad);CHKERRQ(ierr);
970   PetscFunctionReturn(0);
971 }
972 
973 #undef __FUNCT__
974 #define __FUNCT__ "DMPlexGetCellFields"
975 /*@C
976   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
977 
978   Input Parameters:
979 + dm     - The DM
980 . cStart - The first cell to include
981 . cEnd   - The first cell to exclude
982 . locX   - A local vector with the solution fields
983 . locX_t - A local vector with solution field time derivatives, or NULL
984 - locA   - A local vector with auxiliary fields, or NULL
985 
986   Output Parameters:
987 + u   - The field coefficients
988 . u_t - The fields derivative coefficients
989 - a   - The auxiliary field coefficients
990 
991   Level: developer
992 
993 .seealso: DMPlexGetFaceFields()
994 @*/
995 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
996 {
997   DM             dmAux;
998   PetscSection   section, sectionAux;
999   PetscDS        prob;
1000   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
1001   PetscErrorCode ierr;
1002 
1003   PetscFunctionBegin;
1004   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1005   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1006   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1007   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
1008   PetscValidPointer(u, 7);
1009   PetscValidPointer(u_t, 8);
1010   PetscValidPointer(a, 9);
1011   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1012   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1013   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1014   if (locA) {
1015     PetscDS probAux;
1016 
1017     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1018     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1019     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1020     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1021   }
1022   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
1023   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1024   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1025   for (c = cStart; c < cEnd; ++c) {
1026     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1027     PetscInt     i;
1028 
1029     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1030     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
1031     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1032     if (locX_t) {
1033       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1034       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
1035       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1036     }
1037     if (locA) {
1038       DM dmAuxPlex;
1039 
1040       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1041       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1042       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
1043       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1044       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1045     }
1046   }
1047   PetscFunctionReturn(0);
1048 }
1049 
1050 #undef __FUNCT__
1051 #define __FUNCT__ "DMPlexRestoreCellFields"
1052 /*@C
1053   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1054 
1055   Input Parameters:
1056 + dm     - The DM
1057 . cStart - The first cell to include
1058 . cEnd   - The first cell to exclude
1059 . locX   - A local vector with the solution fields
1060 . locX_t - A local vector with solution field time derivatives, or NULL
1061 - locA   - A local vector with auxiliary fields, or NULL
1062 
1063   Output Parameters:
1064 + u   - The field coefficients
1065 . u_t - The fields derivative coefficients
1066 - a   - The auxiliary field coefficients
1067 
1068   Level: developer
1069 
1070 .seealso: DMPlexGetFaceFields()
1071 @*/
1072 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1073 {
1074   PetscErrorCode ierr;
1075 
1076   PetscFunctionBegin;
1077   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1078   if (*u_t) {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);}
1079   if (*a)   {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);}
1080   PetscFunctionReturn(0);
1081 }
1082 
1083 #undef __FUNCT__
1084 #define __FUNCT__ "DMPlexGetFaceFields"
1085 /*@C
1086   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1087 
1088   Input Parameters:
1089 + dm     - The DM
1090 . fStart - The first face to include
1091 . fEnd   - The first face to exclude
1092 . locX   - A local vector with the solution fields
1093 . locX_t - A local vector with solution field time derivatives, or NULL
1094 . faceGeometry - A local vector with face geometry
1095 . cellGeometry - A local vector with cell geometry
1096 - locaGrad - A local vector with field gradients, or NULL
1097 
1098   Output Parameters:
1099 + uL - The field values at the left side of the face
1100 - uR - The field values at the right side of the face
1101 
1102   Level: developer
1103 
1104 .seealso: DMPlexGetCellFields()
1105 @*/
1106 PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1107 {
1108   DM                 dmFace, dmCell, dmGrad = NULL;
1109   PetscSection       section;
1110   PetscDS            prob;
1111   DMLabel            ghostLabel;
1112   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1113   PetscBool         *isFE;
1114   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1115   PetscErrorCode     ierr;
1116 
1117   PetscFunctionBegin;
1118   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1119   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1120   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1121   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1122   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1123   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1124   PetscValidPointer(uL, 9);
1125   PetscValidPointer(uR, 10);
1126   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1127   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1128   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1129   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1130   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1131   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1132   for (f = 0; f < Nf; ++f) {
1133     PetscObject  obj;
1134     PetscClassId id;
1135 
1136     ierr = DMGetField(dm, f, &obj);CHKERRQ(ierr);
1137     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1138     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1139     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1140     else                            {isFE[f] = PETSC_FALSE;}
1141   }
1142   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1143   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1144   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1145   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1146   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1147   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1148   if (locGrad) {
1149     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1150     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1151   }
1152   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);CHKERRQ(ierr);
1153   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);CHKERRQ(ierr);
1154   /* Right now just eat the extra work for FE (could make a cell loop) */
1155   for (face = fStart, iface = 0; face < fEnd; ++face) {
1156     const PetscInt        *cells;
1157     PetscFVFaceGeom       *fg;
1158     PetscFVCellGeom       *cgL, *cgR;
1159     PetscScalar           *xL, *xR, *gL, *gR;
1160     PetscScalar           *uLl = *uL, *uRl = *uR;
1161     PetscInt               ghost, nsupp;
1162 
1163     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1164     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1165     if (ghost >= 0) continue;
1166     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1167     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1168     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1169     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1170     for (f = 0; f < Nf; ++f) {
1171       PetscInt off;
1172 
1173       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1174       if (isFE[f]) {
1175         const PetscInt *cone;
1176         PetscInt        comp, coneSize, faceLocL, faceLocR, ldof, rdof, d;
1177 
1178         xL = xR = NULL;
1179         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1180         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1181         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1182         ierr = DMPlexGetConeSize(dm, cells[0], &coneSize);CHKERRQ(ierr);
1183         for (faceLocL = 0; faceLocL < coneSize; ++faceLocL) if (cone[faceLocL] == face) break;
1184         if (faceLocL == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[0]);
1185         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1186         ierr = DMPlexGetConeSize(dm, cells[1], &coneSize);CHKERRQ(ierr);
1187         for (faceLocR = 0; faceLocR < coneSize; ++faceLocR) if (cone[faceLocR] == face) break;
1188         if (faceLocR == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d", face, cells[1]);
1189         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1190         ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1191         if (rdof == ldof) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1192         else              {ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr); for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1193         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1194         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1195       } else {
1196         PetscFV  fv;
1197         PetscInt numComp, c;
1198 
1199         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1200         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1201         if (nsupp > 2) {
1202           for (f = 0; f < Nf; ++f) {
1203             PetscInt off;
1204 
1205             ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1206             ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1207             for (c = 0; c < numComp; ++c) {
1208               uLl[iface*Nc+off+c] = 0.;
1209               uRl[iface*Nc+off+c] = 0.;
1210             }
1211           }
1212           continue;
1213         }
1214         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1215         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1216         if (dmGrad) {
1217           PetscReal dxL[3], dxR[3];
1218 
1219           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1220           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1221           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1222           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1223           for (c = 0; c < numComp; ++c) {
1224             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1225             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1226           }
1227         } else {
1228           for (c = 0; c < numComp; ++c) {
1229             uLl[iface*Nc+off+c] = xL[c];
1230             uRl[iface*Nc+off+c] = xR[c];
1231           }
1232         }
1233       }
1234     }
1235     ++iface;
1236   }
1237   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1238   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1239   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1240   if (locGrad) {
1241     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1242   }
1243   ierr = PetscFree(isFE);CHKERRQ(ierr);
1244   PetscFunctionReturn(0);
1245 }
1246 
1247 #undef __FUNCT__
1248 #define __FUNCT__ "DMPlexRestoreFaceFields"
1249 /*@C
1250   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1251 
1252   Input Parameters:
1253 + dm     - The DM
1254 . fStart - The first face to include
1255 . fEnd   - The first face to exclude
1256 . locX   - A local vector with the solution fields
1257 . locX_t - A local vector with solution field time derivatives, or NULL
1258 . faceGeometry - A local vector with face geometry
1259 . cellGeometry - A local vector with cell geometry
1260 - locaGrad - A local vector with field gradients, or NULL
1261 
1262   Output Parameters:
1263 + uL - The field values at the left side of the face
1264 - uR - The field values at the right side of the face
1265 
1266   Level: developer
1267 
1268 .seealso: DMPlexGetFaceFields()
1269 @*/
1270 PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscScalar **uL, PetscScalar **uR)
1271 {
1272   PetscErrorCode ierr;
1273 
1274   PetscFunctionBegin;
1275   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1276   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1277   PetscFunctionReturn(0);
1278 }
1279 
1280 #undef __FUNCT__
1281 #define __FUNCT__ "DMPlexGetFaceGeometry"
1282 /*@C
1283   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1284 
1285   Input Parameters:
1286 + dm     - The DM
1287 . fStart - The first face to include
1288 . fEnd   - The first face to exclude
1289 . faceGeometry - A local vector with face geometry
1290 - cellGeometry - A local vector with cell geometry
1291 
1292   Output Parameters:
1293 + fgeom - The extract the face centroid and normal
1294 - vol   - The cell volume
1295 
1296   Level: developer
1297 
1298 .seealso: DMPlexGetCellFields()
1299 @*/
1300 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
1301 {
1302   DM                 dmFace, dmCell;
1303   DMLabel            ghostLabel;
1304   const PetscScalar *facegeom, *cellgeom;
1305   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1306   PetscErrorCode     ierr;
1307 
1308   PetscFunctionBegin;
1309   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1310   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1311   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1312   PetscValidPointer(fgeom, 6);
1313   PetscValidPointer(vol, 7);
1314   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1315   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1316   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1317   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1318   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1319   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1320   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1321   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1322   for (face = fStart, iface = 0; face < fEnd; ++face) {
1323     const PetscInt        *cells;
1324     PetscFVFaceGeom       *fg;
1325     PetscFVCellGeom       *cgL, *cgR;
1326     PetscFVFaceGeom       *fgeoml = *fgeom;
1327     PetscReal             *voll   = *vol;
1328     PetscInt               ghost, d;
1329 
1330     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1331     if (ghost >= 0) continue;
1332     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1333     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1334     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1335     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1336     for (d = 0; d < dim; ++d) {
1337       fgeoml[iface].centroid[d] = fg->centroid[d];
1338       fgeoml[iface].normal[d]   = fg->normal[d];
1339     }
1340     voll[iface*2+0] = cgL->volume;
1341     voll[iface*2+1] = cgR->volume;
1342     ++iface;
1343   }
1344   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1345   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1346   PetscFunctionReturn(0);
1347 }
1348 
1349 #undef __FUNCT__
1350 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1351 /*@C
1352   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1353 
1354   Input Parameters:
1355 + dm     - The DM
1356 . fStart - The first face to include
1357 . fEnd   - The first face to exclude
1358 . faceGeometry - A local vector with face geometry
1359 - cellGeometry - A local vector with cell geometry
1360 
1361   Output Parameters:
1362 + fgeom - The extract the face centroid and normal
1363 - vol   - The cell volume
1364 
1365   Level: developer
1366 
1367 .seealso: DMPlexGetFaceFields()
1368 @*/
1369 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscFVFaceGeom **fgeom, PetscReal **vol)
1370 {
1371   PetscErrorCode ierr;
1372 
1373   PetscFunctionBegin;
1374   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1375   ierr = DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);CHKERRQ(ierr);
1376   PetscFunctionReturn(0);
1377 }
1378 
1379 #undef __FUNCT__
1380 #define __FUNCT__ "DMPlexApplyLimiter_Internal"
1381 static PetscErrorCode DMPlexApplyLimiter_Internal (DM dm, DM dmCell, PetscLimiter lim, PetscInt dim, PetscInt totDim, PetscInt cell, PetscInt face, PetscInt fStart, PetscInt fEnd, PetscReal *cellPhi, const PetscScalar *x,
1382                                                    const PetscScalar *cellgeom, const PetscFVCellGeom *cg, const PetscScalar *cx, const PetscScalar *cgrad)
1383 {
1384   const PetscInt        *children;
1385   PetscInt               numChildren;
1386   PetscErrorCode         ierr;
1387 
1388   PetscFunctionBegin;
1389   ierr = DMPlexGetTreeChildren(dm,face,&numChildren,&children);CHKERRQ(ierr);
1390   if (numChildren) {
1391     PetscInt c;
1392 
1393     for (c = 0; c < numChildren; c++) {
1394       PetscInt childFace = children[c];
1395 
1396       if (childFace >= fStart && childFace < fEnd) {
1397         ierr = DMPlexApplyLimiter_Internal(dm,dmCell,lim,dim,totDim,cell,childFace,fStart,fEnd,cellPhi,x,cellgeom,cg,cx,cgrad);CHKERRQ(ierr);
1398       }
1399     }
1400   }
1401   else {
1402     PetscScalar           *ncx;
1403     PetscFVCellGeom       *ncg;
1404     const PetscInt        *fcells;
1405     PetscInt               ncell, d;
1406     PetscReal              v[3];
1407 
1408     ierr  = DMPlexGetSupport(dm, face, &fcells);CHKERRQ(ierr);
1409     ncell = cell == fcells[0] ? fcells[1] : fcells[0];
1410     ierr  = DMPlexPointLocalRead(dm, ncell, x, &ncx);CHKERRQ(ierr);
1411     ierr  = DMPlexPointLocalRead(dmCell, ncell, cellgeom, &ncg);CHKERRQ(ierr);
1412     DMPlex_WaxpyD_Internal(dim, -1, cg->centroid, ncg->centroid, v);
1413     for (d = 0; d < totDim; ++d) {
1414       /* We use the symmetric slope limited form of Berger, Aftosmis, and Murman 2005 */
1415       PetscReal phi, flim = 0.5 * PetscRealPart(ncx[d] - cx[d]) / DMPlex_DotD_Internal(dim, &cgrad[d*dim], v);
1416 
1417       ierr = PetscLimiterLimit(lim, flim, &phi);CHKERRQ(ierr);
1418       cellPhi[d] = PetscMin(cellPhi[d], phi);
1419     }
1420   }
1421   PetscFunctionReturn(0);
1422 }
1423 
1424 #undef __FUNCT__
1425 #define __FUNCT__ "DMPlexReconstructGradients_Internal"
1426 PetscErrorCode DMPlexReconstructGradients_Internal(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, Vec locX, Vec grad)
1427 {
1428   DM                 dmFace, dmCell, dmGrad;
1429   DMLabel            ghostLabel;
1430   PetscDS            prob;
1431   PetscFV            fvm;
1432   PetscLimiter       lim;
1433   const PetscScalar *facegeom, *cellgeom, *x;
1434   PetscScalar       *gr;
1435   PetscReal         *cellPhi;
1436   PetscInt           dim, face, cell, totDim, cStart, cEnd, cEndInterior;
1437   PetscErrorCode     ierr;
1438 
1439   PetscFunctionBegin;
1440   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1441   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1442   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1443   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1444   ierr = PetscDSGetDiscretization(prob, 0, (PetscObject *) &fvm);CHKERRQ(ierr);
1445   ierr = PetscFVGetLimiter(fvm, &lim);CHKERRQ(ierr);
1446   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1447   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1448   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1449   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1450   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1451   ierr = VecGetDM(grad, &dmGrad);CHKERRQ(ierr);
1452   ierr = VecZeroEntries(grad);CHKERRQ(ierr);
1453   ierr = VecGetArray(grad, &gr);CHKERRQ(ierr);
1454   /* Reconstruct gradients */
1455   for (face = fStart; face < fEnd; ++face) {
1456     const PetscInt        *cells;
1457     PetscFVFaceGeom       *fg;
1458     PetscScalar           *cx[2];
1459     PetscScalar           *cgrad[2];
1460     PetscBool              boundary;
1461     PetscInt               ghost, c, pd, d, numChildren, numCells;
1462 
1463     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1464     ierr = DMIsBoundaryPoint(dm, face, &boundary);CHKERRQ(ierr);
1465     ierr = DMPlexGetTreeChildren(dm, face, &numChildren, NULL);CHKERRQ(ierr);
1466     if (ghost >= 0 || boundary || numChildren) continue;
1467     ierr = DMPlexGetSupportSize(dm, face, &numCells);CHKERRQ(ierr);
1468     if (numCells != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "facet %d has %d support points: expected 2",face,numCells);
1469     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1470     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1471     for (c = 0; c < 2; ++c) {
1472       ierr = DMPlexPointLocalRead(dm, cells[c], x, &cx[c]);CHKERRQ(ierr);
1473       ierr = DMPlexPointGlobalRef(dmGrad, cells[c], gr, &cgrad[c]);CHKERRQ(ierr);
1474     }
1475     for (pd = 0; pd < totDim; ++pd) {
1476       PetscScalar delta = cx[1][pd] - cx[0][pd];
1477 
1478       for (d = 0; d < dim; ++d) {
1479         if (cgrad[0]) cgrad[0][pd*dim+d] += fg->grad[0][d] * delta;
1480         if (cgrad[1]) cgrad[1][pd*dim+d] -= fg->grad[1][d] * delta;
1481       }
1482     }
1483   }
1484   /* Limit interior gradients (using cell-based loop because it generalizes better to vector limiters) */
1485   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1486   ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1487   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
1488   ierr = DMGetWorkArray(dm, totDim, PETSC_REAL, &cellPhi);CHKERRQ(ierr);
1489   for (cell = dmGrad && lim ? cStart : cEnd; cell < cEndInterior; ++cell) {
1490     const PetscInt        *faces;
1491     PetscScalar           *cx;
1492     PetscFVCellGeom       *cg;
1493     PetscScalar           *cgrad;
1494     PetscInt               coneSize, f, pd, d;
1495 
1496     ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
1497     ierr = DMPlexGetCone(dm, cell, &faces);CHKERRQ(ierr);
1498     ierr = DMPlexPointLocalRead(dm, cell, x, &cx);CHKERRQ(ierr);
1499     ierr = DMPlexPointLocalRead(dmCell, cell, cellgeom, &cg);CHKERRQ(ierr);
1500     ierr = DMPlexPointGlobalRef(dmGrad, cell, gr, &cgrad);CHKERRQ(ierr);
1501     if (!cgrad) continue; /* Unowned overlap cell, we do not compute */
1502     /* Limiter will be minimum value over all neighbors */
1503     for (d = 0; d < totDim; ++d) cellPhi[d] = PETSC_MAX_REAL;
1504     for (f = 0; f < coneSize; ++f) {
1505       ierr = DMPlexApplyLimiter_Internal(dm,dmCell,lim,dim,totDim,cell,faces[f],fStart,fEnd,cellPhi,x,cellgeom,cg,cx,cgrad);CHKERRQ(ierr);
1506     }
1507     /* Apply limiter to gradient */
1508     for (pd = 0; pd < totDim; ++pd)
1509       /* Scalar limiter applied to each component separately */
1510       for (d = 0; d < dim; ++d) cgrad[pd*dim+d] *= cellPhi[pd];
1511   }
1512   ierr = DMRestoreWorkArray(dm, totDim, PETSC_REAL, &cellPhi);CHKERRQ(ierr);
1513   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1514   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1515   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1516   ierr = VecRestoreArray(grad, &gr);CHKERRQ(ierr);
1517   PetscFunctionReturn(0);
1518 }
1519 
1520 #undef __FUNCT__
1521 #define __FUNCT__ "DMPlexComputeBdResidual_Internal"
1522 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, Vec locF, void *user)
1523 {
1524   DM_Plex         *mesh = (DM_Plex *) dm->data;
1525   PetscSection     section;
1526   PetscDS          prob;
1527   DMLabel          depth;
1528   PetscFECellGeom *cgeom;
1529   PetscScalar     *u = NULL, *u_t = NULL, *elemVec = NULL;
1530   PetscInt         dim, Nf, f, totDimBd, numBd, bd;
1531   PetscErrorCode   ierr;
1532 
1533   PetscFunctionBegin;
1534   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1535   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1536   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1537   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1538   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1539   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1540   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1541   for (bd = 0; bd < numBd; ++bd) {
1542     const char     *bdLabel;
1543     DMLabel         label;
1544     IS              pointIS;
1545     const PetscInt *points;
1546     const PetscInt *values;
1547     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
1548     PetscBool       isEssential;
1549     PetscObject     obj;
1550     PetscClassId    id;
1551 
1552     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1553     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1554     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1555     if ((id != PETSCFE_CLASSID) || isEssential) continue;
1556     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1557     for (v = 0; v < numValues; ++v) {
1558       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
1559       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1560       if (!pointIS) continue; /* No points with that id on this process */
1561       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1562       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1563         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1564         if (dep == dim-1) ++numFaces;
1565       }
1566       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd,&elemVec);CHKERRQ(ierr);
1567       if (locX_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1568       for (p = 0, f = 0; p < numPoints; ++p) {
1569         const PetscInt point = points[p];
1570         PetscScalar   *x     = NULL;
1571         PetscInt       i;
1572 
1573         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1574         if (dep != dim-1) continue;
1575         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
1576         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
1577         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
1578         /* TODO: Matt, this is wrong if feBd does not match fe: i.e., if the order differs. */
1579         ierr = DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1580         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1581         ierr = DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1582         if (locX_t) {
1583           ierr = DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1584           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1585           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1586         }
1587         ++f;
1588       }
1589       for (f = 0; f < Nf; ++f) {
1590         PetscFE         fe;
1591         PetscQuadrature q;
1592         PetscInt        numQuadPoints, Nb;
1593         /* Conforming batches */
1594         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1595         /* Remainder */
1596         PetscInt        Nr, offset;
1597 
1598         ierr = PetscDSGetBdDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1599         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1600         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1601         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1602         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1603         blockSize = Nb*numQuadPoints;
1604         batchSize = numBlocks * blockSize;
1605         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1606         numChunks = numFaces / (numBatches*batchSize);
1607         Ne        = numChunks*numBatches*batchSize;
1608         Nr        = numFaces % (numBatches*batchSize);
1609         offset    = numFaces - Nr;
1610         ierr = PetscFEIntegrateBdResidual(fe, prob, f, Ne, cgeom, u, u_t, NULL, NULL, elemVec);CHKERRQ(ierr);
1611         ierr = PetscFEIntegrateBdResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemVec[offset*totDimBd]);CHKERRQ(ierr);
1612       }
1613       for (p = 0, f = 0; p < numPoints; ++p) {
1614         const PetscInt point = points[p];
1615 
1616         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1617         if (dep != dim-1) continue;
1618         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1619         ierr = DMPlexVecSetClosure(dm, NULL, locF, point, &elemVec[f*totDimBd], ADD_ALL_VALUES);CHKERRQ(ierr);
1620         ++f;
1621       }
1622       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1623       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1624       ierr = PetscFree3(u,cgeom,elemVec);CHKERRQ(ierr);
1625       if (locX_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1626     }
1627   }
1628   PetscFunctionReturn(0);
1629 }
1630 
1631 #undef __FUNCT__
1632 #define __FUNCT__ "DMPlexReconstructGradientsFVM"
1633 /*@
1634   DMPlexReconstructGradientsFVM - reconstruct the gradient of a vector using a finite volume method.
1635 
1636   Input Parameters:
1637 + dm - the mesh
1638 - locX - the local representation of the vector
1639 
1640   Output Parameter:
1641 . grad - the global representation of the gradient
1642 
1643   Level: developer
1644 
1645 .seealso: DMPlexSNESGetGradientDM()
1646 @*/
1647 PetscErrorCode DMPlexReconstructGradientsFVM(DM dm, Vec locX, Vec grad)
1648 {
1649   PetscDS          prob;
1650   PetscInt         Nf, f, fStart, fEnd;
1651   PetscBool        useFVM = PETSC_FALSE;
1652   PetscFV          fvm = NULL;
1653   Vec              faceGeometryFVM, cellGeometryFVM;
1654   PetscFVCellGeom  *cgeomFVM   = NULL;
1655   PetscFVFaceGeom  *fgeomFVM   = NULL;
1656   DM               dmGrad = NULL;
1657   PetscErrorCode   ierr;
1658 
1659   PetscFunctionBegin;
1660   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1661   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1662   for (f = 0; f < Nf; ++f) {
1663     PetscObject  obj;
1664     PetscClassId id;
1665 
1666     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1667     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1668     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1669   }
1670   if (!useFVM) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm does not have a finite volume discretization");
1671   ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1672   if (!dmGrad) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"This dm's finite volume discretization does not reconstruct gradients");
1673   ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1674   ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1675   ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1676   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1677   ierr = DMPlexReconstructGradients_Internal(dm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #undef __FUNCT__
1682 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1683 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, Vec locF, void *user)
1684 {
1685   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1686   const char       *name       = "Residual";
1687   DM                dmAux      = NULL;
1688   DM                dmGrad     = NULL;
1689   DMLabel           ghostLabel = NULL;
1690   PetscDS           prob       = NULL;
1691   PetscDS           probAux    = NULL;
1692   PetscSection      section    = NULL;
1693   PetscBool         useFEM     = PETSC_FALSE;
1694   PetscBool         useFVM     = PETSC_FALSE;
1695   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1696   PetscFV           fvm        = NULL;
1697   PetscFECellGeom  *cgeomFEM   = NULL;
1698   PetscScalar      *cgeomScal;
1699   PetscFVCellGeom  *cgeomFVM   = NULL;
1700   PetscFVFaceGeom  *fgeomFVM   = NULL;
1701   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1702   PetscScalar      *u, *u_t, *a, *uL, *uR;
1703   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1704   PetscErrorCode    ierr;
1705 
1706   PetscFunctionBegin;
1707   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1708   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1709   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1710   /* FEM+FVM */
1711   /* 1: Get sizes from dm and dmAux */
1712   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1713   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1714   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1715   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1716   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1717   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1718   if (locA) {
1719     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1720     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1721     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1722   }
1723   /* 2: Get geometric data */
1724   for (f = 0; f < Nf; ++f) {
1725     PetscObject  obj;
1726     PetscClassId id;
1727     PetscBool    fimp;
1728 
1729     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1730     if (isImplicit != fimp) continue;
1731     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1732     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1733     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1734     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1735   }
1736   if (useFEM) {
1737     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1738     ierr = VecGetArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);
1739     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1740       DM dmCell;
1741       PetscInt c;
1742 
1743       ierr = VecGetDM(cellGeometryFEM,&dmCell);CHKERRQ(ierr);
1744       ierr = PetscMalloc1(cEnd-cStart,&cgeomFEM);CHKERRQ(ierr);
1745       for (c = 0; c < cEnd - cStart; c++) {
1746         PetscScalar *thisgeom;
1747 
1748         ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1749         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
1750       }
1751     }
1752     else {
1753       cgeomFEM = (PetscFECellGeom *) cgeomScal;
1754     }
1755   }
1756   if (useFVM) {
1757     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1758     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1759     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1760     /* Reconstruct and limit cell gradients */
1761     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1762     if (dmGrad) {
1763       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1764       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1765       ierr = DMPlexReconstructGradients_Internal(dm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1766       /* Communicate gradient values */
1767       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1768       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1769       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1770       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1771     }
1772     /* Handle non-essential (e.g. outflow) boundary values */
1773     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1774   }
1775   /* Loop over chunks */
1776   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1777   numChunks     = 1;
1778   cellChunkSize = (cEnd - cStart)/numChunks;
1779   faceChunkSize = (fEnd - fStart)/numChunks;
1780   for (chunk = 0; chunk < numChunks; ++chunk) {
1781     PetscScalar     *elemVec, *fluxL, *fluxR;
1782     PetscReal       *vol;
1783     PetscFVFaceGeom *fgeom;
1784     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1785     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = fE - fS, face;
1786 
1787     /* Extract field coefficients */
1788     if (useFEM) {
1789       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1790       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1791       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1792     }
1793     if (useFVM) {
1794       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1795       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1796       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1797       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1798       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1799       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1800     }
1801     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1802     /* Loop over fields */
1803     for (f = 0; f < Nf; ++f) {
1804       PetscObject  obj;
1805       PetscClassId id;
1806       PetscBool    fimp;
1807       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1808 
1809       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1810       if (isImplicit != fimp) continue;
1811       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1812       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1813       if (id == PETSCFE_CLASSID) {
1814         PetscFE         fe = (PetscFE) obj;
1815         PetscQuadrature q;
1816         PetscInt        Nq, Nb;
1817 
1818         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1819 
1820         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1821         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1822         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1823         blockSize = Nb*Nq;
1824         batchSize = numBlocks * blockSize;
1825         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1826         numChunks = numCells / (numBatches*batchSize);
1827         Ne        = numChunks*numBatches*batchSize;
1828         Nr        = numCells % (numBatches*batchSize);
1829         offset    = numCells - Nr;
1830         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1831         /*   For FV, I think we use a P0 basis and the cell coefficients (for subdivided cells, we can tweak the basis tabulation to be the indicator function) */
1832         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, elemVec);CHKERRQ(ierr);
1833         ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeomFEM[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);CHKERRQ(ierr);
1834       } else if (id == PETSCFV_CLASSID) {
1835         PetscFV fv = (PetscFV) obj;
1836 
1837         Ne = numFaces;
1838         /* Riemann solve over faces (need fields at face centroids) */
1839         /*   We need to evaluate FE fields at those coordinates */
1840         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1841       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1842     }
1843     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1844       ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);
1845     }
1846     else {
1847       cgeomFEM = NULL;
1848     }
1849     if (cellGeometryFEM) {ierr = VecRestoreArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);}
1850     /* Loop over domain */
1851     if (useFEM) {
1852       /* Add elemVec to locX */
1853       for (cell = cS; cell < cE; ++cell) {
1854         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1855         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1856       }
1857     }
1858     if (useFVM) {
1859       PetscScalar *fa;
1860       PetscInt     iface;
1861 
1862       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1863       for (f = 0; f < Nf; ++f) {
1864         PetscFV      fv;
1865         PetscObject  obj;
1866         PetscClassId id;
1867         PetscInt     foff, pdim;
1868 
1869         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1870         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1871         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1872         if (id != PETSCFV_CLASSID) continue;
1873         fv   = (PetscFV) obj;
1874         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1875         /* Accumulate fluxes to cells */
1876         for (face = fS, iface = 0; face < fE; ++face) {
1877           const PetscInt *cells;
1878           PetscScalar    *fL, *fR;
1879           PetscInt        ghost, d, nsupp;
1880 
1881           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1882           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1883           if (ghost >= 0) continue;
1884           if (nsupp > 2) { /* noop */
1885             ++iface;
1886             continue;
1887           }
1888           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1889           ierr = DMPlexPointGlobalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);
1890           ierr = DMPlexPointGlobalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);
1891           for (d = 0; d < pdim; ++d) {
1892             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1893             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1894           }
1895           ++iface;
1896         }
1897       }
1898       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1899     }
1900     /* Handle time derivative */
1901     if (locX_t) {
1902       PetscScalar *x_t, *fa;
1903 
1904       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1905       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1906       for (f = 0; f < Nf; ++f) {
1907         PetscFV      fv;
1908         PetscObject  obj;
1909         PetscClassId id;
1910         PetscInt     pdim, d;
1911 
1912         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1913         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1914         if (id != PETSCFV_CLASSID) continue;
1915         fv   = (PetscFV) obj;
1916         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1917         for (cell = cS; cell < cE; ++cell) {
1918           PetscScalar *u_t, *r;
1919 
1920           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1921           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1922           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1923         }
1924       }
1925       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1926       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1927     }
1928     if (useFEM) {
1929       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1930       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1931     }
1932     if (useFVM) {
1933       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &uL, &uR);CHKERRQ(ierr);
1934       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &fgeom, &vol);CHKERRQ(ierr);
1935       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1936       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1937       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1938     }
1939   }
1940 
1941   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, locF, user);CHKERRQ(ierr);}
1942 
1943   /* FEM */
1944   /* 1: Get sizes from dm and dmAux */
1945   /* 2: Get geometric data */
1946   /* 3: Handle boundary values */
1947   /* 4: Loop over domain */
1948   /*   Extract coefficients */
1949   /* Loop over fields */
1950   /*   Set tiling for FE*/
1951   /*   Integrate FE residual to get elemVec */
1952   /*     Loop over subdomain */
1953   /*       Loop over quad points */
1954   /*         Transform coords to real space */
1955   /*         Evaluate field and aux fields at point */
1956   /*         Evaluate residual at point */
1957   /*         Transform residual to real space */
1958   /*       Add residual to elemVec */
1959   /* Loop over domain */
1960   /*   Add elemVec to locX */
1961 
1962   /* FVM */
1963   /* Get geometric data */
1964   /* If using gradients */
1965   /*   Compute gradient data */
1966   /*   Loop over domain faces */
1967   /*     Count computational faces */
1968   /*     Reconstruct cell gradient */
1969   /*   Loop over domain cells */
1970   /*     Limit cell gradients */
1971   /* Handle boundary values */
1972   /* Loop over domain faces */
1973   /*   Read out field, centroid, normal, volume for each side of face */
1974   /* Riemann solve over faces */
1975   /* Loop over domain faces */
1976   /*   Accumulate fluxes to cells */
1977   /* TODO Change printFEM to printDisc here */
1978   if (mesh->printFEM) {
1979     Vec         locFbc;
1980     PetscInt    pStart, pEnd, p, maxDof;
1981     PetscScalar *zeroes;
1982 
1983     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1984     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1985     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1986     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1987     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1988     for (p = pStart; p < pEnd; p++) {
1989       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1990     }
1991     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1992     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1993     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1994   }
1995   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1996   PetscFunctionReturn(0);
1997 }
1998 
1999 #undef __FUNCT__
2000 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
2001 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, Vec F, void *user)
2002 {
2003   DM                dmCh, dmAux;
2004   Vec               A, cellgeom;
2005   PetscDS           prob, probCh, probAux = NULL;
2006   PetscQuadrature   q;
2007   PetscSection      section, sectionAux;
2008   PetscFECellGeom  *cgeom = NULL;
2009   PetscScalar      *cgeomScal;
2010   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
2011   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
2012   PetscInt          totDim, totDimAux, diffCell = 0;
2013   PetscErrorCode    ierr;
2014 
2015   PetscFunctionBegin;
2016   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2017   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2018   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2019   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2020   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2021   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2022   numCells = cEnd - cStart;
2023   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
2024   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
2025   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2026   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2027   if (dmAux) {
2028     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
2029     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2030     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2031   }
2032   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
2033   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
2034   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
2035   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2036   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2037   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2038   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2039     DM dmCell;
2040 
2041     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2042     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2043     for (c = 0; c < cEnd - cStart; c++) {
2044       PetscScalar *thisgeom;
2045 
2046       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2047       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2048     }
2049   }
2050   else {
2051     cgeom = (PetscFECellGeom *) cgeomScal;
2052   }
2053   for (c = cStart; c < cEnd; ++c) {
2054     PetscScalar *x = NULL, *x_t = NULL;
2055     PetscInt     i;
2056 
2057     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2058     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
2059     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2060     if (X_t) {
2061       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2062       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
2063       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2064     }
2065     if (dmAux) {
2066       DM dmAuxPlex;
2067 
2068       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
2069       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2070       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
2071       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2072       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
2073     }
2074   }
2075   for (f = 0; f < Nf; ++f) {
2076     PetscFE  fe, feCh;
2077     PetscInt numQuadPoints, Nb;
2078     /* Conforming batches */
2079     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2080     /* Remainder */
2081     PetscInt Nr, offset;
2082 
2083     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
2084     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
2085     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
2086     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2087     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2088     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2089     blockSize = Nb*numQuadPoints;
2090     batchSize = numBlocks * blockSize;
2091     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2092     numChunks = numCells / (numBatches*batchSize);
2093     Ne        = numChunks*numBatches*batchSize;
2094     Nr        = numCells % (numBatches*batchSize);
2095     offset    = numCells - Nr;
2096     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, elemVec);CHKERRQ(ierr);
2097     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, elemVecCh);CHKERRQ(ierr);
2098     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVec[offset*totDim]);CHKERRQ(ierr);
2099     ierr = PetscFEIntegrateResidual(feCh, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemVecCh[offset*totDim]);CHKERRQ(ierr);
2100   }
2101   for (c = cStart; c < cEnd; ++c) {
2102     PetscBool diff = PETSC_FALSE;
2103     PetscInt  d;
2104 
2105     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
2106     if (diff) {
2107       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
2108       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
2109       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
2110       ++diffCell;
2111     }
2112     if (diffCell > 9) break;
2113     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
2114   }
2115   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2116     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2117   }
2118   else {
2119     cgeom = NULL;
2120   }
2121   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2122   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
2123   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
2124   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
2125   PetscFunctionReturn(0);
2126 }
2127 
2128 #undef __FUNCT__
2129 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
2130 /*@
2131   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
2132 
2133   Input Parameters:
2134 + dm - The mesh
2135 . X  - Local solution
2136 - user - The user context
2137 
2138   Output Parameter:
2139 . F  - Local output vector
2140 
2141   Level: developer
2142 
2143 .seealso: DMPlexComputeJacobianActionFEM()
2144 @*/
2145 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
2146 {
2147   PetscObject    check;
2148   PetscInt       cStart, cEnd, cEndInterior;
2149   DM             plex;
2150   PetscErrorCode ierr;
2151 
2152   PetscFunctionBegin;
2153   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2154   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2155   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2156   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2157   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
2158   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2159   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, F, user);CHKERRQ(ierr);}
2160   else       {ierr = DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, F, user);CHKERRQ(ierr);}
2161   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2162   PetscFunctionReturn(0);
2163 }
2164 
2165 #undef __FUNCT__
2166 #define __FUNCT__ "DMPlexSNESComputeBoundaryFEM"
2167 /*@
2168   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2169 
2170   Input Parameters:
2171 + dm - The mesh
2172 - user - The user context
2173 
2174   Output Parameter:
2175 . X  - Local solution
2176 
2177   Level: developer
2178 
2179 .seealso: DMPlexComputeJacobianActionFEM()
2180 @*/
2181 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2182 {
2183   DM             plex;
2184   PetscErrorCode ierr;
2185 
2186   PetscFunctionBegin;
2187   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2188   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2189   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2190   PetscFunctionReturn(0);
2191 }
2192 
2193 #undef __FUNCT__
2194 #define __FUNCT__ "DMPlexComputeJacobian_Internal"
2195 PetscErrorCode DMPlexComputeJacobian_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Mat Jac, Mat JacP,void *user)
2196 {
2197   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2198   const char       *name  = "Jacobian";
2199   DM                dmAux, plex;
2200   DMLabel           depth;
2201   Vec               A, cellgeom;
2202   PetscDS           prob, probAux = NULL;
2203   PetscQuadrature   quad;
2204   PetscSection      section, globalSection, sectionAux;
2205   PetscFECellGeom  *cgeom = NULL;
2206   PetscScalar      *cgeomScal;
2207   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2208   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, c;
2209   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
2210   PetscBool         isShell, hasPrec, hasDyn;
2211   PetscErrorCode    ierr;
2212 
2213   PetscFunctionBegin;
2214   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2215   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2216   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2217   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2218   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2219   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2220   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2221   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2222   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2223   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2224   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2225   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2226   numCells = cEnd - cStart;
2227   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2228   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2229   if (dmAux) {
2230     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2231     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2232     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2233     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2234   }
2235   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2236   ierr = PetscMalloc5(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim*totDim,&elemMat,hasPrec ? numCells*totDim*totDim : 0, &elemMatP,hasDyn ? numCells*totDim*totDim : 0, &elemMatD);CHKERRQ(ierr);
2237   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2238   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2239   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2240   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2241     DM dmCell;
2242 
2243     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2244     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2245     for (c = 0; c < cEnd - cStart; c++) {
2246       PetscScalar *thisgeom;
2247 
2248       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2249       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2250     }
2251   }
2252   else {
2253     cgeom = (PetscFECellGeom *) cgeomScal;
2254   }
2255   for (c = cStart; c < cEnd; ++c) {
2256     PetscScalar *x = NULL,  *x_t = NULL;
2257     PetscInt     i;
2258 
2259     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2260     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2261     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2262     if (X_t) {
2263       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2264       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2265       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2266     }
2267     if (dmAux) {
2268       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2269       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2270       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2271     }
2272   }
2273   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2274   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2275   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2276   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2277     PetscFE  fe;
2278     PetscInt numQuadPoints, Nb;
2279     /* Conforming batches */
2280     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2281     /* Remainder */
2282     PetscInt Nr, offset;
2283 
2284     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2285     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2286     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2287     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2288     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2289     blockSize = Nb*numQuadPoints;
2290     batchSize = numBlocks * blockSize;
2291     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2292     numChunks = numCells / (numBatches*batchSize);
2293     Ne        = numChunks*numBatches*batchSize;
2294     Nr        = numCells % (numBatches*batchSize);
2295     offset    = numCells - Nr;
2296     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2297       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, elemMat);CHKERRQ(ierr);
2298       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2299       if (hasPrec) {
2300         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, elemMatP);CHKERRQ(ierr);
2301         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMatP[offset*totDim*totDim]);CHKERRQ(ierr);
2302       }
2303       if (hasDyn) {
2304         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, elemMatD);CHKERRQ(ierr);
2305         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2306       }
2307     }
2308   }
2309   if (hasDyn) {
2310     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2311   }
2312   for (c = cStart; c < cEnd; ++c) {
2313     if (hasPrec) {
2314       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2315       ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2316       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2317       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2318     } else {
2319       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2320       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2321     }
2322   }
2323   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2324     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2325   }
2326   else {
2327     cgeom = NULL;
2328   }
2329   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2330   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2331   if (dmAux) {
2332     ierr = PetscFree(a);CHKERRQ(ierr);
2333     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2334   }
2335   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2336   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2337   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2338   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2339   for (bd = 0; bd < numBd; ++bd) {
2340     const char     *bdLabel;
2341     DMLabel         label;
2342     IS              pointIS;
2343     const PetscInt *points;
2344     const PetscInt *values;
2345     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
2346     PetscBool       isEssential;
2347     PetscObject     obj;
2348     PetscClassId    id;
2349 
2350     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2351     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
2352     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2353     if ((id != PETSCFE_CLASSID) || isEssential) continue;
2354     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2355     for (v = 0; v < numValues; ++v) {
2356       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
2357       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2358       if (!pointIS) continue; /* No points with that id on this process */
2359       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2360       for (p = 0, numFaces = 0; p < numPoints; ++p) {
2361         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2362         if (dep == dim-1) ++numFaces;
2363       }
2364       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd*totDimBd,&elemMat);CHKERRQ(ierr);
2365       if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
2366       for (p = 0, f = 0; p < numPoints; ++p) {
2367         const PetscInt point = points[p];
2368         PetscScalar   *x     = NULL;
2369         PetscInt       i;
2370 
2371         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2372         if (dep != dim-1) continue;
2373         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
2374         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
2375         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
2376         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2377         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
2378         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2379         if (X_t) {
2380           ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2381           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
2382           ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2383         }
2384         ++f;
2385       }
2386       ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
2387       for (fieldI = 0; fieldI < Nf; ++fieldI) {
2388         PetscFE  fe;
2389         PetscInt numQuadPoints, Nb;
2390         /* Conforming batches */
2391         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2392         /* Remainder */
2393         PetscInt Nr, offset;
2394 
2395         ierr = PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2396         ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2397         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2398         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2399         ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2400         blockSize = Nb*numQuadPoints;
2401         batchSize = numBlocks * blockSize;
2402         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2403         numChunks = numFaces / (numBatches*batchSize);
2404         Ne        = numChunks*numBatches*batchSize;
2405         Nr        = numFaces % (numBatches*batchSize);
2406         offset    = numFaces - Nr;
2407         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2408           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, NULL, NULL, elemMat);CHKERRQ(ierr);
2409           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, &elemMat[offset*totDimBd*totDimBd]);CHKERRQ(ierr);
2410         }
2411       }
2412       for (p = 0, f = 0; p < numPoints; ++p) {
2413         const PetscInt point = points[p];
2414 
2415         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2416         if (dep != dim-1) continue;
2417         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
2418         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
2419         ++f;
2420       }
2421       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2422       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2423       ierr = PetscFree3(u,cgeom,elemMat);CHKERRQ(ierr);
2424       if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
2425     }
2426   }
2427   if (hasPrec) {
2428     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2429     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2430   }
2431   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2432   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2433   if (mesh->printFEM) {
2434     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2435     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2436     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2437   }
2438   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2439   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2440   if (isShell) {
2441     JacActionCtx *jctx;
2442 
2443     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2444     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2445   }
2446   PetscFunctionReturn(0);
2447 }
2448 
2449 #undef __FUNCT__
2450 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2451 /*@
2452   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2453 
2454   Input Parameters:
2455 + dm - The mesh
2456 . X  - Local input vector
2457 - user - The user context
2458 
2459   Output Parameter:
2460 . Jac  - Jacobian matrix
2461 
2462   Note:
2463   The first member of the user context must be an FEMContext.
2464 
2465   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2466   like a GPU, or vectorize on a multicore machine.
2467 
2468   Level: developer
2469 
2470 .seealso: FormFunctionLocal()
2471 @*/
2472 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2473 {
2474   PetscInt       cStart, cEnd, cEndInterior;
2475   DM             plex;
2476   PetscErrorCode ierr;
2477 
2478   PetscFunctionBegin;
2479   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2480   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2481   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2482   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2483   ierr = DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2484   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2485   PetscFunctionReturn(0);
2486 }
2487 
2488 #undef __FUNCT__
2489 #define __FUNCT__ "DMPlexSetSNESLocalFEM"
2490 /*@
2491   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2492 
2493   Input Parameters:
2494 + dm - The DM object
2495 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see DMAddBoundary())
2496 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2497 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2498 
2499   Level: developer
2500 @*/
2501 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2502 {
2503   PetscErrorCode ierr;
2504 
2505   PetscFunctionBegin;
2506   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2507   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2508   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2509   PetscFunctionReturn(0);
2510 }
2511 
2512 #undef __FUNCT__
2513 #define __FUNCT__ "DMSNESCheckFromOptions_Internal"
2514 PetscErrorCode DMSNESCheckFromOptions_Internal(SNES snes, DM dm, Vec u, Vec sol, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx), void **ctxs)
2515 {
2516   Mat            J, M;
2517   Vec            r, b;
2518   MatNullSpace   nullSpace;
2519   PetscReal     *error, res = 0.0;
2520   PetscInt       numFields;
2521   PetscErrorCode ierr;
2522 
2523   PetscFunctionBegin;
2524   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2525   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2526   M    = J;
2527   /* TODO Null space for J */
2528   /* Check discretization error */
2529   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2530   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2531   if (numFields > 1) {
2532     PetscInt f;
2533 
2534     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2535     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2536     for (f = 0; f < numFields; ++f) {
2537       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2538       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);CHKERRQ(ierr);}
2539       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2540     }
2541     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2542   } else {
2543     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2544     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);CHKERRQ(ierr);}
2545     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2546   }
2547   ierr = PetscFree(error);CHKERRQ(ierr);
2548   /* Check residual */
2549   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2550   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2551   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
2552   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2553   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2554   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2555   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2556   /* Check Jacobian */
2557   ierr = SNESComputeJacobian(snes, u, M, M);CHKERRQ(ierr);
2558   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2559   if (nullSpace) {
2560     PetscBool isNull;
2561     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2562     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2563   }
2564   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2565   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2566   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2567   ierr = MatMult(M, u, r);CHKERRQ(ierr);
2568   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2569   ierr = VecDestroy(&b);CHKERRQ(ierr);
2570   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2571   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
2572   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2573   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2574   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2575   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2576   ierr = VecDestroy(&r);CHKERRQ(ierr);
2577   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2578   ierr = MatDestroy(&J);CHKERRQ(ierr);
2579   PetscFunctionReturn(0);
2580 }
2581 
2582 #undef __FUNCT__
2583 #define __FUNCT__ "DMSNESCheckFromOptions"
2584 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2585 {
2586   DM             dm;
2587   Vec            sol;
2588   PetscBool      check;
2589   PetscErrorCode ierr;
2590 
2591   PetscFunctionBegin;
2592   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2593   if (!check) PetscFunctionReturn(0);
2594   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2595   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2596   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2597   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2598   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2599   PetscFunctionReturn(0);
2600 }
2601