xref: /petsc/src/snes/utils/dmplexsnes.c (revision 95dccacacae8a8fc0b691f9b4fba69a249b61188)
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 <petscblaslapack.h>
5 #include <petsc/private/petscimpl.h>
6 #include <petsc/private/petscfeimpl.h>
7 
8 /************************** Interpolation *******************************/
9 
10 #undef __FUNCT__
11 #define __FUNCT__ "DMSNESConvertPlex"
12 static PetscErrorCode DMSNESConvertPlex(DM dm, DM *plex, PetscBool copy)
13 {
14   PetscBool      isPlex;
15   PetscErrorCode ierr;
16 
17   PetscFunctionBegin;
18   ierr = PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isPlex);CHKERRQ(ierr);
19   if (isPlex) {
20     *plex = dm;
21     ierr = PetscObjectReference((PetscObject) dm);CHKERRQ(ierr);
22   } else {
23     ierr = PetscObjectQuery((PetscObject) dm, "dm_plex", (PetscObject *) plex);CHKERRQ(ierr);
24     if (!*plex) {
25       ierr = DMConvert(dm,DMPLEX,plex);CHKERRQ(ierr);
26       ierr = PetscObjectCompose((PetscObject) dm, "dm_plex", (PetscObject) *plex);CHKERRQ(ierr);
27       if (copy) {
28         PetscInt    i;
29         PetscObject obj;
30         const char *comps[3] = {"A","dmAux","dmCh"};
31 
32         ierr = DMCopyDMSNES(dm, *plex);CHKERRQ(ierr);
33         for (i = 0; i < 3; i++) {
34           ierr = PetscObjectQuery((PetscObject) dm, comps[i], &obj);CHKERRQ(ierr);
35           ierr = PetscObjectCompose((PetscObject) *plex, comps[i], obj);CHKERRQ(ierr);
36         }
37       }
38     } else {
39       ierr = PetscObjectReference((PetscObject) *plex);CHKERRQ(ierr);
40     }
41   }
42   PetscFunctionReturn(0);
43 }
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "DMInterpolationCreate"
47 PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
48 {
49   PetscErrorCode ierr;
50 
51   PetscFunctionBegin;
52   PetscValidPointer(ctx, 2);
53   ierr = PetscNew(ctx);CHKERRQ(ierr);
54 
55   (*ctx)->comm   = comm;
56   (*ctx)->dim    = -1;
57   (*ctx)->nInput = 0;
58   (*ctx)->points = NULL;
59   (*ctx)->cells  = NULL;
60   (*ctx)->n      = -1;
61   (*ctx)->coords = NULL;
62   PetscFunctionReturn(0);
63 }
64 
65 #undef __FUNCT__
66 #define __FUNCT__ "DMInterpolationSetDim"
67 PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
68 {
69   PetscFunctionBegin;
70   if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
71   ctx->dim = dim;
72   PetscFunctionReturn(0);
73 }
74 
75 #undef __FUNCT__
76 #define __FUNCT__ "DMInterpolationGetDim"
77 PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
78 {
79   PetscFunctionBegin;
80   PetscValidIntPointer(dim, 2);
81   *dim = ctx->dim;
82   PetscFunctionReturn(0);
83 }
84 
85 #undef __FUNCT__
86 #define __FUNCT__ "DMInterpolationSetDof"
87 PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
88 {
89   PetscFunctionBegin;
90   if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
91   ctx->dof = dof;
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "DMInterpolationGetDof"
97 PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
98 {
99   PetscFunctionBegin;
100   PetscValidIntPointer(dof, 2);
101   *dof = ctx->dof;
102   PetscFunctionReturn(0);
103 }
104 
105 #undef __FUNCT__
106 #define __FUNCT__ "DMInterpolationAddPoints"
107 PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
108 {
109   PetscErrorCode ierr;
110 
111   PetscFunctionBegin;
112   if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
113   if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
114   ctx->nInput = n;
115 
116   ierr = PetscMalloc1(n*ctx->dim, &ctx->points);CHKERRQ(ierr);
117   ierr = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));CHKERRQ(ierr);
118   PetscFunctionReturn(0);
119 }
120 
121 #undef __FUNCT__
122 #define __FUNCT__ "DMInterpolationSetUp"
123 PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
124 {
125   MPI_Comm          comm = ctx->comm;
126   PetscScalar       *a;
127   PetscInt          p, q, i;
128   PetscMPIInt       rank, size;
129   PetscErrorCode    ierr;
130   Vec               pointVec;
131   PetscSF           cellSF;
132   PetscLayout       layout;
133   PetscReal         *globalPoints;
134   PetscScalar       *globalPointsScalar;
135   const PetscInt    *ranges;
136   PetscMPIInt       *counts, *displs;
137   const PetscSFNode *foundCells;
138   const PetscInt    *foundPoints;
139   PetscMPIInt       *foundProcs, *globalProcs;
140   PetscInt          n, N, numFound;
141 
142   PetscFunctionBegin;
143   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
144   ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
145   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
146   if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
147   /* Locate points */
148   n = ctx->nInput;
149   if (!redundantPoints) {
150     ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
151     ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
152     ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
153     ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
154     ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
155     /* Communicate all points to all processes */
156     ierr = PetscMalloc3(N*ctx->dim,&globalPoints,size,&counts,size,&displs);CHKERRQ(ierr);
157     ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
158     for (p = 0; p < size; ++p) {
159       counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
160       displs[p] = ranges[p]*ctx->dim;
161     }
162     ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
163   } else {
164     N = n;
165     globalPoints = ctx->points;
166     counts = displs = NULL;
167     layout = NULL;
168   }
169 #if 0
170   ierr = PetscMalloc3(N,&foundCells,N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
171   /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
172 #else
173 #if defined(PETSC_USE_COMPLEX)
174   ierr = PetscMalloc1(N,&globalPointsScalar);CHKERRQ(ierr);
175   for (i=0; i<N; i++) globalPointsScalar[i] = globalPoints[i];
176 #else
177   globalPointsScalar = globalPoints;
178 #endif
179   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
180   ierr = PetscMalloc2(N,&foundProcs,N,&globalProcs);CHKERRQ(ierr);
181   cellSF = NULL;
182   ierr = DMLocatePoints(dm, pointVec, DM_POINTLOCATION_NONE, &cellSF);CHKERRQ(ierr);
183   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
184 #endif
185   for (p = 0; p < numFound; ++p) {
186     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
187     else foundProcs[foundPoints ? foundPoints[p] : p] = size;
188   }
189   /* Let the lowest rank process own each point */
190   ierr   = MPIU_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
191   ctx->n = 0;
192   for (p = 0; p < N; ++p) {
193     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);
194     else if (globalProcs[p] == rank) ctx->n++;
195   }
196   /* Create coordinates vector and array of owned cells */
197   ierr = PetscMalloc1(ctx->n, &ctx->cells);CHKERRQ(ierr);
198   ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
199   ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
200   ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
201   ierr = VecSetType(ctx->coords,VECSTANDARD);CHKERRQ(ierr);
202   ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
203   for (p = 0, q = 0, i = 0; p < N; ++p) {
204     if (globalProcs[p] == rank) {
205       PetscInt d;
206 
207       for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
208       ctx->cells[q++] = foundCells[p].index;
209     }
210   }
211   ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
212 #if 0
213   ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
214 #else
215   ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
216   ierr = PetscSFDestroy(&cellSF);CHKERRQ(ierr);
217   ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
218 #endif
219   if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
220   if (!redundantPoints) {ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);}
221   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
222   PetscFunctionReturn(0);
223 }
224 
225 #undef __FUNCT__
226 #define __FUNCT__ "DMInterpolationGetCoordinates"
227 PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
228 {
229   PetscFunctionBegin;
230   PetscValidPointer(coordinates, 2);
231   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
232   *coordinates = ctx->coords;
233   PetscFunctionReturn(0);
234 }
235 
236 #undef __FUNCT__
237 #define __FUNCT__ "DMInterpolationGetVector"
238 PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
239 {
240   PetscErrorCode ierr;
241 
242   PetscFunctionBegin;
243   PetscValidPointer(v, 2);
244   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
245   ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
246   ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
247   ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
248   ierr = VecSetType(*v,VECSTANDARD);CHKERRQ(ierr);
249   PetscFunctionReturn(0);
250 }
251 
252 #undef __FUNCT__
253 #define __FUNCT__ "DMInterpolationRestoreVector"
254 PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
255 {
256   PetscErrorCode ierr;
257 
258   PetscFunctionBegin;
259   PetscValidPointer(v, 2);
260   if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
261   ierr = VecDestroy(v);CHKERRQ(ierr);
262   PetscFunctionReturn(0);
263 }
264 
265 #undef __FUNCT__
266 #define __FUNCT__ "DMInterpolate_Triangle_Private"
267 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Triangle_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
268 {
269   PetscReal      *v0, *J, *invJ, detJ;
270   const PetscScalar *coords;
271   PetscScalar    *a;
272   PetscInt       p;
273   PetscErrorCode ierr;
274 
275   PetscFunctionBegin;
276   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
277   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
278   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
279   for (p = 0; p < ctx->n; ++p) {
280     PetscInt     c = ctx->cells[p];
281     PetscScalar *x = NULL;
282     PetscReal    xi[4];
283     PetscInt     d, f, comp;
284 
285     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
286     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
287     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
288     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
289 
290     for (d = 0; d < ctx->dim; ++d) {
291       xi[d] = 0.0;
292       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
293       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];
294     }
295     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
296   }
297   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
298   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
299   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
300   PetscFunctionReturn(0);
301 }
302 
303 #undef __FUNCT__
304 #define __FUNCT__ "DMInterpolate_Tetrahedron_Private"
305 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Tetrahedron_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
306 {
307   PetscReal      *v0, *J, *invJ, detJ;
308   const PetscScalar *coords;
309   PetscScalar    *a;
310   PetscInt       p;
311   PetscErrorCode ierr;
312 
313   PetscFunctionBegin;
314   ierr = PetscMalloc3(ctx->dim,&v0,ctx->dim*ctx->dim,&J,ctx->dim*ctx->dim,&invJ);CHKERRQ(ierr);
315   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
316   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
317   for (p = 0; p < ctx->n; ++p) {
318     PetscInt       c = ctx->cells[p];
319     const PetscInt order[3] = {2, 1, 3};
320     PetscScalar   *x = NULL;
321     PetscReal      xi[4];
322     PetscInt       d, f, comp;
323 
324     ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
325     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
326     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
327     for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];
328 
329     for (d = 0; d < ctx->dim; ++d) {
330       xi[d] = 0.0;
331       for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
332       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];
333     }
334     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, NULL, &x);CHKERRQ(ierr);
335   }
336   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
337   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
338   ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
339   PetscFunctionReturn(0);
340 }
341 
342 #undef __FUNCT__
343 #define __FUNCT__ "QuadMap_Private"
344 PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
345 {
346   const PetscScalar *vertices = (const PetscScalar*) ctx;
347   const PetscScalar x0        = vertices[0];
348   const PetscScalar y0        = vertices[1];
349   const PetscScalar x1        = vertices[2];
350   const PetscScalar y1        = vertices[3];
351   const PetscScalar x2        = vertices[4];
352   const PetscScalar y2        = vertices[5];
353   const PetscScalar x3        = vertices[6];
354   const PetscScalar y3        = vertices[7];
355   const PetscScalar f_1       = x1 - x0;
356   const PetscScalar g_1       = y1 - y0;
357   const PetscScalar f_3       = x3 - x0;
358   const PetscScalar g_3       = y3 - y0;
359   const PetscScalar f_01      = x2 - x1 - x3 + x0;
360   const PetscScalar g_01      = y2 - y1 - y3 + y0;
361   const PetscScalar *ref;
362   PetscScalar       *real;
363   PetscErrorCode    ierr;
364 
365   PetscFunctionBegin;
366   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
367   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
368   {
369     const PetscScalar p0 = ref[0];
370     const PetscScalar p1 = ref[1];
371 
372     real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
373     real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
374   }
375   ierr = PetscLogFlops(28);CHKERRQ(ierr);
376   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
377   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
378   PetscFunctionReturn(0);
379 }
380 
381 #include <petsc/private/dmimpl.h>
382 #undef __FUNCT__
383 #define __FUNCT__ "QuadJacobian_Private"
384 PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
385 {
386   const PetscScalar *vertices = (const PetscScalar*) ctx;
387   const PetscScalar x0        = vertices[0];
388   const PetscScalar y0        = vertices[1];
389   const PetscScalar x1        = vertices[2];
390   const PetscScalar y1        = vertices[3];
391   const PetscScalar x2        = vertices[4];
392   const PetscScalar y2        = vertices[5];
393   const PetscScalar x3        = vertices[6];
394   const PetscScalar y3        = vertices[7];
395   const PetscScalar f_01      = x2 - x1 - x3 + x0;
396   const PetscScalar g_01      = y2 - y1 - y3 + y0;
397   const PetscScalar *ref;
398   PetscErrorCode    ierr;
399 
400   PetscFunctionBegin;
401   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
402   {
403     const PetscScalar x       = ref[0];
404     const PetscScalar y       = ref[1];
405     const PetscInt    rows[2] = {0, 1};
406     PetscScalar       values[4];
407 
408     values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
409     values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
410     ierr      = MatSetValues(J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
411   }
412   ierr = PetscLogFlops(30);CHKERRQ(ierr);
413   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
414   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
415   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
416   PetscFunctionReturn(0);
417 }
418 
419 #undef __FUNCT__
420 #define __FUNCT__ "DMInterpolate_Quad_Private"
421 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
422 {
423   DM             dmCoord;
424   SNES           snes;
425   KSP            ksp;
426   PC             pc;
427   Vec            coordsLocal, r, ref, real;
428   Mat            J;
429   const PetscScalar *coords;
430   PetscScalar    *a;
431   PetscInt       p;
432   PetscErrorCode ierr;
433 
434   PetscFunctionBegin;
435   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
436   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
437   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
438   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
439   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
440   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
441   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
442   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
443   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
444   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
445   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
446   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
447   ierr = MatSetUp(J);CHKERRQ(ierr);
448   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
449   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
450   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
451   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
452   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
453   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
454 
455   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
456   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
457   for (p = 0; p < ctx->n; ++p) {
458     PetscScalar *x = NULL, *vertices = NULL;
459     PetscScalar *xi;
460     PetscReal    xir[2];
461     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
462 
463     /* Can make this do all points at once */
464     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
465     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
466     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
467     if (4*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 4*ctx->dof);
468     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
469     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
470     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
471     xi[0]  = coords[p*ctx->dim+0];
472     xi[1]  = coords[p*ctx->dim+1];
473     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
474     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
475     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
476     xir[0] = PetscRealPart(xi[0]);
477     xir[1] = PetscRealPart(xi[1]);
478     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];
479 
480     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
481     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
482     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
483   }
484   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
485   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
486 
487   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
488   ierr = VecDestroy(&r);CHKERRQ(ierr);
489   ierr = VecDestroy(&ref);CHKERRQ(ierr);
490   ierr = VecDestroy(&real);CHKERRQ(ierr);
491   ierr = MatDestroy(&J);CHKERRQ(ierr);
492   PetscFunctionReturn(0);
493 }
494 
495 #undef __FUNCT__
496 #define __FUNCT__ "HexMap_Private"
497 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
498 {
499   const PetscScalar *vertices = (const PetscScalar*) ctx;
500   const PetscScalar x0        = vertices[0];
501   const PetscScalar y0        = vertices[1];
502   const PetscScalar z0        = vertices[2];
503   const PetscScalar x1        = vertices[9];
504   const PetscScalar y1        = vertices[10];
505   const PetscScalar z1        = vertices[11];
506   const PetscScalar x2        = vertices[6];
507   const PetscScalar y2        = vertices[7];
508   const PetscScalar z2        = vertices[8];
509   const PetscScalar x3        = vertices[3];
510   const PetscScalar y3        = vertices[4];
511   const PetscScalar z3        = vertices[5];
512   const PetscScalar x4        = vertices[12];
513   const PetscScalar y4        = vertices[13];
514   const PetscScalar z4        = vertices[14];
515   const PetscScalar x5        = vertices[15];
516   const PetscScalar y5        = vertices[16];
517   const PetscScalar z5        = vertices[17];
518   const PetscScalar x6        = vertices[18];
519   const PetscScalar y6        = vertices[19];
520   const PetscScalar z6        = vertices[20];
521   const PetscScalar x7        = vertices[21];
522   const PetscScalar y7        = vertices[22];
523   const PetscScalar z7        = vertices[23];
524   const PetscScalar f_1       = x1 - x0;
525   const PetscScalar g_1       = y1 - y0;
526   const PetscScalar h_1       = z1 - z0;
527   const PetscScalar f_3       = x3 - x0;
528   const PetscScalar g_3       = y3 - y0;
529   const PetscScalar h_3       = z3 - z0;
530   const PetscScalar f_4       = x4 - x0;
531   const PetscScalar g_4       = y4 - y0;
532   const PetscScalar h_4       = z4 - z0;
533   const PetscScalar f_01      = x2 - x1 - x3 + x0;
534   const PetscScalar g_01      = y2 - y1 - y3 + y0;
535   const PetscScalar h_01      = z2 - z1 - z3 + z0;
536   const PetscScalar f_12      = x7 - x3 - x4 + x0;
537   const PetscScalar g_12      = y7 - y3 - y4 + y0;
538   const PetscScalar h_12      = z7 - z3 - z4 + z0;
539   const PetscScalar f_02      = x5 - x1 - x4 + x0;
540   const PetscScalar g_02      = y5 - y1 - y4 + y0;
541   const PetscScalar h_02      = z5 - z1 - z4 + z0;
542   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
543   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
544   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
545   const PetscScalar *ref;
546   PetscScalar       *real;
547   PetscErrorCode    ierr;
548 
549   PetscFunctionBegin;
550   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
551   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
552   {
553     const PetscScalar p0 = ref[0];
554     const PetscScalar p1 = ref[1];
555     const PetscScalar p2 = ref[2];
556 
557     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;
558     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;
559     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;
560   }
561   ierr = PetscLogFlops(114);CHKERRQ(ierr);
562   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
563   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
564   PetscFunctionReturn(0);
565 }
566 
567 #undef __FUNCT__
568 #define __FUNCT__ "HexJacobian_Private"
569 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
570 {
571   const PetscScalar *vertices = (const PetscScalar*) ctx;
572   const PetscScalar x0        = vertices[0];
573   const PetscScalar y0        = vertices[1];
574   const PetscScalar z0        = vertices[2];
575   const PetscScalar x1        = vertices[9];
576   const PetscScalar y1        = vertices[10];
577   const PetscScalar z1        = vertices[11];
578   const PetscScalar x2        = vertices[6];
579   const PetscScalar y2        = vertices[7];
580   const PetscScalar z2        = vertices[8];
581   const PetscScalar x3        = vertices[3];
582   const PetscScalar y3        = vertices[4];
583   const PetscScalar z3        = vertices[5];
584   const PetscScalar x4        = vertices[12];
585   const PetscScalar y4        = vertices[13];
586   const PetscScalar z4        = vertices[14];
587   const PetscScalar x5        = vertices[15];
588   const PetscScalar y5        = vertices[16];
589   const PetscScalar z5        = vertices[17];
590   const PetscScalar x6        = vertices[18];
591   const PetscScalar y6        = vertices[19];
592   const PetscScalar z6        = vertices[20];
593   const PetscScalar x7        = vertices[21];
594   const PetscScalar y7        = vertices[22];
595   const PetscScalar z7        = vertices[23];
596   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
597   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
598   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
599   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
600   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
601   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
602   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
603   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
604   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
605   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
606   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
607   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
608   const PetscScalar *ref;
609   PetscErrorCode    ierr;
610 
611   PetscFunctionBegin;
612   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
613   {
614     const PetscScalar x       = ref[0];
615     const PetscScalar y       = ref[1];
616     const PetscScalar z       = ref[2];
617     const PetscInt    rows[3] = {0, 1, 2};
618     PetscScalar       values[9];
619 
620     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
621     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
622     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
623     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
624     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
625     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
626     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
627     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
628     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
629 
630     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
631   }
632   ierr = PetscLogFlops(152);CHKERRQ(ierr);
633   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
634   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
635   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
636   PetscFunctionReturn(0);
637 }
638 
639 #undef __FUNCT__
640 #define __FUNCT__ "DMInterpolate_Hex_Private"
641 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
642 {
643   DM             dmCoord;
644   SNES           snes;
645   KSP            ksp;
646   PC             pc;
647   Vec            coordsLocal, r, ref, real;
648   Mat            J;
649   const PetscScalar *coords;
650   PetscScalar    *a;
651   PetscInt       p;
652   PetscErrorCode ierr;
653 
654   PetscFunctionBegin;
655   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
656   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
657   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
658   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
659   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
660   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
661   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
662   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
663   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
664   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
665   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
666   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
667   ierr = MatSetUp(J);CHKERRQ(ierr);
668   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
669   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
670   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
671   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
672   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
673   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
674 
675   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
676   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
677   for (p = 0; p < ctx->n; ++p) {
678     PetscScalar *x = NULL, *vertices = NULL;
679     PetscScalar *xi;
680     PetscReal    xir[3];
681     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
682 
683     /* Can make this do all points at once */
684     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
685     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
686     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
687     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
688     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
689     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
690     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
691     xi[0]  = coords[p*ctx->dim+0];
692     xi[1]  = coords[p*ctx->dim+1];
693     xi[2]  = coords[p*ctx->dim+2];
694     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
695     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
696     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
697     xir[0] = PetscRealPart(xi[0]);
698     xir[1] = PetscRealPart(xi[1]);
699     xir[2] = PetscRealPart(xi[2]);
700     for (comp = 0; comp < ctx->dof; ++comp) {
701       a[p*ctx->dof+comp] =
702         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
703         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
704         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
705         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
706         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
707         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
708         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
709         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
710     }
711     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
712     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
713     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
714   }
715   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
716   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
717 
718   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
719   ierr = VecDestroy(&r);CHKERRQ(ierr);
720   ierr = VecDestroy(&ref);CHKERRQ(ierr);
721   ierr = VecDestroy(&real);CHKERRQ(ierr);
722   ierr = MatDestroy(&J);CHKERRQ(ierr);
723   PetscFunctionReturn(0);
724 }
725 
726 #undef __FUNCT__
727 #define __FUNCT__ "DMInterpolationEvaluate"
728 /*
729   Input Parameters:
730 + ctx - The DMInterpolationInfo context
731 . dm  - The DM
732 - x   - The local vector containing the field to be interpolated
733 
734   Output Parameters:
735 . v   - The vector containing the interpolated values
736 */
737 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
738 {
739   PetscInt       dim, coneSize, n;
740   PetscErrorCode ierr;
741 
742   PetscFunctionBegin;
743   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
744   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
745   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
746   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
747   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);
748   if (n) {
749     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
750     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
751     if (dim == 2) {
752       if (coneSize == 3) {
753         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
754       } else if (coneSize == 4) {
755         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
756       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
757     } else if (dim == 3) {
758       if (coneSize == 4) {
759         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
760       } else {
761         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
762       }
763     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
764   }
765   PetscFunctionReturn(0);
766 }
767 
768 #undef __FUNCT__
769 #define __FUNCT__ "DMInterpolationDestroy"
770 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
771 {
772   PetscErrorCode ierr;
773 
774   PetscFunctionBegin;
775   PetscValidPointer(ctx, 2);
776   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
777   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
778   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
779   ierr = PetscFree(*ctx);CHKERRQ(ierr);
780   *ctx = NULL;
781   PetscFunctionReturn(0);
782 }
783 
784 #undef __FUNCT__
785 #define __FUNCT__ "SNESMonitorFields"
786 /*@C
787   SNESMonitorFields - Monitors the residual for each field separately
788 
789   Collective on SNES
790 
791   Input Parameters:
792 + snes   - the SNES context
793 . its    - iteration number
794 . fgnorm - 2-norm of residual
795 - vf  - PetscViewerAndFormat of type ASCII
796 
797   Notes:
798   This routine prints the residual norm at each iteration.
799 
800   Level: intermediate
801 
802 .keywords: SNES, nonlinear, default, monitor, norm
803 .seealso: SNESMonitorSet(), SNESMonitorDefault()
804 @*/
805 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
806 {
807   PetscViewer        viewer = vf->viewer;
808   Vec                res;
809   DM                 dm;
810   PetscSection       s;
811   const PetscScalar *r;
812   PetscReal         *lnorms, *norms;
813   PetscInt           numFields, f, pStart, pEnd, p;
814   PetscErrorCode     ierr;
815 
816   PetscFunctionBegin;
817   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
818   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
819   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
820   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
821   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
822   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
823   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
824   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
825   for (p = pStart; p < pEnd; ++p) {
826     for (f = 0; f < numFields; ++f) {
827       PetscInt fdof, foff, d;
828 
829       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
830       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
831       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
832     }
833   }
834   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
835   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
836   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
837   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
838   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
839   for (f = 0; f < numFields; ++f) {
840     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
841     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
842   }
843   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
844   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
845   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
846   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
847   PetscFunctionReturn(0);
848 }
849 
850 /********************* Residual Computation **************************/
851 
852 #undef __FUNCT__
853 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
854 /*@
855   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
856 
857   Input Parameter:
858 . dm - The DM
859 
860   Output Parameters:
861 . cellgeom - The values precomputed from cell geometry
862 
863   Level: developer
864 
865 .seealso: DMPlexSNESSetFunctionLocal()
866 @*/
867 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
868 {
869   DMSNES         dmsnes;
870   PetscObject    obj;
871   PetscErrorCode ierr;
872 
873   PetscFunctionBegin;
874   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
875   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
876   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
877   if (!obj) {
878     Vec cellgeom;
879 
880     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
881     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
882     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
883   }
884   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
885   PetscFunctionReturn(0);
886 }
887 
888 #undef __FUNCT__
889 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
890 /*@
891   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
892 
893   Input Parameter:
894 . dm - The DM
895 
896   Output Parameters:
897 + facegeom - The values precomputed from face geometry
898 . cellgeom - The values precomputed from cell geometry
899 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
900 
901   Level: developer
902 
903 .seealso: DMPlexTSSetRHSFunctionLocal()
904 @*/
905 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
906 {
907   DM             plex;
908   PetscErrorCode ierr;
909 
910   PetscFunctionBegin;
911   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
912   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
913   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
914   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
915   ierr = DMDestroy(&plex);CHKERRQ(ierr);
916   PetscFunctionReturn(0);
917 }
918 
919 #undef __FUNCT__
920 #define __FUNCT__ "DMPlexSNESGetGradientDM"
921 /*@
922   DMPlexSNESGetGradientDM - Return gradient data layout
923 
924   Input Parameters:
925 + dm - The DM
926 - fv - The PetscFV
927 
928   Output Parameter:
929 . dmGrad - The layout for gradient values
930 
931   Level: developer
932 
933 .seealso: DMPlexSNESGetGeometryFVM()
934 @*/
935 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
936 {
937   DM             plex;
938   PetscBool      computeGradients;
939   PetscErrorCode ierr;
940 
941   PetscFunctionBegin;
942   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
943   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
944   PetscValidPointer(dmGrad,3);
945   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
946   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
947   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
948   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
949   ierr = DMDestroy(&plex);CHKERRQ(ierr);
950   PetscFunctionReturn(0);
951 }
952 
953 #undef __FUNCT__
954 #define __FUNCT__ "DMPlexGetCellFields"
955 /*@C
956   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
957 
958   Input Parameters:
959 + dm     - The DM
960 . cStart - The first cell to include
961 . cEnd   - The first cell to exclude
962 . locX   - A local vector with the solution fields
963 . locX_t - A local vector with solution field time derivatives, or NULL
964 - locA   - A local vector with auxiliary fields, or NULL
965 
966   Output Parameters:
967 + u   - The field coefficients
968 . u_t - The fields derivative coefficients
969 - a   - The auxiliary field coefficients
970 
971   Level: developer
972 
973 .seealso: DMPlexGetFaceFields()
974 @*/
975 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
976 {
977   DM             dmAux;
978   PetscSection   section, sectionAux;
979   PetscDS        prob;
980   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
981   PetscErrorCode ierr;
982 
983   PetscFunctionBegin;
984   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
985   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
986   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
987   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
988   PetscValidPointer(u, 7);
989   PetscValidPointer(u_t, 8);
990   PetscValidPointer(a, 9);
991   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
992   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
993   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
994   if (locA) {
995     PetscDS probAux;
996 
997     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
998     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
999     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1000     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1001   }
1002   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
1003   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1004   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1005   for (c = cStart; c < cEnd; ++c) {
1006     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1007     PetscInt     i;
1008 
1009     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1010     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
1011     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1012     if (locX_t) {
1013       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1014       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
1015       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1016     }
1017     if (locA) {
1018       DM dmAuxPlex;
1019 
1020       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1021       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1022       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
1023       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1024       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1025     }
1026   }
1027   PetscFunctionReturn(0);
1028 }
1029 
1030 #undef __FUNCT__
1031 #define __FUNCT__ "DMPlexRestoreCellFields"
1032 /*@C
1033   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1034 
1035   Input Parameters:
1036 + dm     - The DM
1037 . cStart - The first cell to include
1038 . cEnd   - The first cell to exclude
1039 . locX   - A local vector with the solution fields
1040 . locX_t - A local vector with solution field time derivatives, or NULL
1041 - locA   - A local vector with auxiliary fields, or NULL
1042 
1043   Output Parameters:
1044 + u   - The field coefficients
1045 . u_t - The fields derivative coefficients
1046 - a   - The auxiliary field coefficients
1047 
1048   Level: developer
1049 
1050 .seealso: DMPlexGetFaceFields()
1051 @*/
1052 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1053 {
1054   PetscErrorCode ierr;
1055 
1056   PetscFunctionBegin;
1057   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1058   if (*u_t) {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);}
1059   if (*a)   {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);}
1060   PetscFunctionReturn(0);
1061 }
1062 
1063 #undef __FUNCT__
1064 #define __FUNCT__ "DMPlexGetFaceFields"
1065 /*@C
1066   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1067 
1068   Input Parameters:
1069 + dm     - The DM
1070 . fStart - The first face to include
1071 . fEnd   - The first face to exclude
1072 . locX   - A local vector with the solution fields
1073 . locX_t - A local vector with solution field time derivatives, or NULL
1074 . faceGeometry - A local vector with face geometry
1075 . cellGeometry - A local vector with cell geometry
1076 - locaGrad - A local vector with field gradients, or NULL
1077 
1078   Output Parameters:
1079 + Nface - The number of faces with field values
1080 . uL - The field values at the left side of the face
1081 - uR - The field values at the right side of the face
1082 
1083   Level: developer
1084 
1085 .seealso: DMPlexGetCellFields()
1086 @*/
1087 PetscErrorCode DMPlexGetFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscInt *Nface, PetscScalar **uL, PetscScalar **uR)
1088 {
1089   DM                 dmFace, dmCell, dmGrad = NULL;
1090   PetscSection       section;
1091   PetscDS            prob;
1092   DMLabel            ghostLabel;
1093   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1094   PetscBool         *isFE;
1095   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1096   PetscErrorCode     ierr;
1097 
1098   PetscFunctionBegin;
1099   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1100   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1101   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1102   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1103   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1104   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1105   PetscValidPointer(uL, 9);
1106   PetscValidPointer(uR, 10);
1107   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1108   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1109   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1110   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1111   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1112   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1113   for (f = 0; f < Nf; ++f) {
1114     PetscObject  obj;
1115     PetscClassId id;
1116 
1117     ierr = DMGetField(dm, f, &obj);CHKERRQ(ierr);
1118     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1119     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1120     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1121     else                            {isFE[f] = PETSC_FALSE;}
1122   }
1123   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1124   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1125   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1126   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1127   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1128   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1129   if (locGrad) {
1130     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1131     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1132   }
1133   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);CHKERRQ(ierr);
1134   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);CHKERRQ(ierr);
1135   /* Right now just eat the extra work for FE (could make a cell loop) */
1136   for (face = fStart, iface = 0; face < fEnd; ++face) {
1137     const PetscInt        *cells;
1138     PetscFVFaceGeom       *fg;
1139     PetscFVCellGeom       *cgL, *cgR;
1140     PetscScalar           *xL, *xR, *gL, *gR;
1141     PetscScalar           *uLl = *uL, *uRl = *uR;
1142     PetscInt               ghost, nsupp, nchild;
1143 
1144     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1145     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1146     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1147     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1148     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1149     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1150     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1151     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1152     for (f = 0; f < Nf; ++f) {
1153       PetscInt off;
1154 
1155       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1156       if (isFE[f]) {
1157         const PetscInt *cone;
1158         PetscInt        comp, coneSizeL, coneSizeR, faceLocL, faceLocR, ldof, rdof, d;
1159 
1160         xL = xR = NULL;
1161         ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1162         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1163         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1164         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1165         ierr = DMPlexGetConeSize(dm, cells[0], &coneSizeL);CHKERRQ(ierr);
1166         for (faceLocL = 0; faceLocL < coneSizeL; ++faceLocL) if (cone[faceLocL] == face) break;
1167         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1168         ierr = DMPlexGetConeSize(dm, cells[1], &coneSizeR);CHKERRQ(ierr);
1169         for (faceLocR = 0; faceLocR < coneSizeR; ++faceLocR) if (cone[faceLocR] == face) break;
1170         if (faceLocL == coneSizeL && faceLocR == coneSizeR) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of cell %d or cell %d", face, cells[0], cells[1]);
1171         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1172         /* TODO: this is a hack that might not be right for nonconforming */
1173         if (faceLocL < coneSizeL) {
1174           ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1175           if (rdof == ldof && faceLocR < coneSizeR) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1176           else              {for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1177         }
1178         else {
1179           ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);
1180           ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1181           for(d = 0; d < comp; ++d) uLl[iface*Nc+off+d] = uRl[iface*Nc+off+d];
1182         }
1183         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1184         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1185       } else {
1186         PetscFV  fv;
1187         PetscInt numComp, c;
1188 
1189         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1190         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1191         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1192         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1193         if (dmGrad) {
1194           PetscReal dxL[3], dxR[3];
1195 
1196           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1197           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1198           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1199           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1200           for (c = 0; c < numComp; ++c) {
1201             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1202             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1203           }
1204         } else {
1205           for (c = 0; c < numComp; ++c) {
1206             uLl[iface*Nc+off+c] = xL[c];
1207             uRl[iface*Nc+off+c] = xR[c];
1208           }
1209         }
1210       }
1211     }
1212     ++iface;
1213   }
1214   *Nface = iface;
1215   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1216   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1217   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1218   if (locGrad) {
1219     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1220   }
1221   ierr = PetscFree(isFE);CHKERRQ(ierr);
1222   PetscFunctionReturn(0);
1223 }
1224 
1225 #undef __FUNCT__
1226 #define __FUNCT__ "DMPlexRestoreFaceFields"
1227 /*@C
1228   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1229 
1230   Input Parameters:
1231 + dm     - The DM
1232 . fStart - The first face to include
1233 . fEnd   - The first face to exclude
1234 . locX   - A local vector with the solution fields
1235 . locX_t - A local vector with solution field time derivatives, or NULL
1236 . faceGeometry - A local vector with face geometry
1237 . cellGeometry - A local vector with cell geometry
1238 - locaGrad - A local vector with field gradients, or NULL
1239 
1240   Output Parameters:
1241 + Nface - The number of faces with field values
1242 . uL - The field values at the left side of the face
1243 - uR - The field values at the right side of the face
1244 
1245   Level: developer
1246 
1247 .seealso: DMPlexGetFaceFields()
1248 @*/
1249 PetscErrorCode DMPlexRestoreFaceFields(DM dm, PetscInt fStart, PetscInt fEnd, Vec locX, Vec locX_t, Vec faceGeometry, Vec cellGeometry, Vec locGrad, PetscInt *Nface, PetscScalar **uL, PetscScalar **uR)
1250 {
1251   PetscErrorCode ierr;
1252 
1253   PetscFunctionBegin;
1254   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1255   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1256   PetscFunctionReturn(0);
1257 }
1258 
1259 #undef __FUNCT__
1260 #define __FUNCT__ "DMPlexGetFaceGeometry"
1261 /*@C
1262   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1263 
1264   Input Parameters:
1265 + dm     - The DM
1266 . fStart - The first face to include
1267 . fEnd   - The first face to exclude
1268 . faceGeometry - A local vector with face geometry
1269 - cellGeometry - A local vector with cell geometry
1270 
1271   Output Parameters:
1272 + Nface - The number of faces with field values
1273 . fgeom - The extract the face centroid and normal
1274 - vol   - The cell volume
1275 
1276   Level: developer
1277 
1278 .seealso: DMPlexGetCellFields()
1279 @*/
1280 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1281 {
1282   DM                 dmFace, dmCell;
1283   DMLabel            ghostLabel;
1284   const PetscScalar *facegeom, *cellgeom;
1285   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1286   PetscErrorCode     ierr;
1287 
1288   PetscFunctionBegin;
1289   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1290   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1291   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1292   PetscValidPointer(fgeom, 6);
1293   PetscValidPointer(vol, 7);
1294   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1295   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1296   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1297   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1298   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1299   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1300   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1301   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1302   for (face = fStart, iface = 0; face < fEnd; ++face) {
1303     const PetscInt        *cells;
1304     PetscFVFaceGeom       *fg;
1305     PetscFVCellGeom       *cgL, *cgR;
1306     PetscFVFaceGeom       *fgeoml = *fgeom;
1307     PetscReal             *voll   = *vol;
1308     PetscInt               ghost, d, nchild, nsupp;
1309 
1310     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1311     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1312     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1313     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1314     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1315     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1316     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1317     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1318     for (d = 0; d < dim; ++d) {
1319       fgeoml[iface].centroid[d] = fg->centroid[d];
1320       fgeoml[iface].normal[d]   = fg->normal[d];
1321     }
1322     voll[iface*2+0] = cgL->volume;
1323     voll[iface*2+1] = cgR->volume;
1324     ++iface;
1325   }
1326   *Nface = iface;
1327   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1328   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1329   PetscFunctionReturn(0);
1330 }
1331 
1332 #undef __FUNCT__
1333 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1334 /*@C
1335   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1336 
1337   Input Parameters:
1338 + dm     - The DM
1339 . fStart - The first face to include
1340 . fEnd   - The first face to exclude
1341 . faceGeometry - A local vector with face geometry
1342 - cellGeometry - A local vector with cell geometry
1343 
1344   Output Parameters:
1345 + Nface - The number of faces with field values
1346 . fgeom - The extract the face centroid and normal
1347 - vol   - The cell volume
1348 
1349   Level: developer
1350 
1351 .seealso: DMPlexGetFaceFields()
1352 @*/
1353 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1354 {
1355   PetscErrorCode ierr;
1356 
1357   PetscFunctionBegin;
1358   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1359   ierr = DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);CHKERRQ(ierr);
1360   PetscFunctionReturn(0);
1361 }
1362 
1363 #undef __FUNCT__
1364 #define __FUNCT__ "DMPlexComputeBdResidual_Internal"
1365 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1366 {
1367   DM_Plex         *mesh = (DM_Plex *) dm->data;
1368   PetscSection     section;
1369   PetscDS          prob;
1370   DMLabel          depth;
1371   PetscFECellGeom *cgeom;
1372   PetscScalar     *u = NULL, *u_t = NULL, *elemVec = NULL;
1373   PetscInt         dim, Nf, f, totDimBd, numBd, bd;
1374   PetscErrorCode   ierr;
1375 
1376   PetscFunctionBegin;
1377   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1378   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1379   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1380   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1381   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
1382   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1383   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
1384   for (bd = 0; bd < numBd; ++bd) {
1385     const char     *bdLabel;
1386     DMLabel         label;
1387     IS              pointIS;
1388     const PetscInt *points;
1389     const PetscInt *values;
1390     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
1391     PetscBool       isEssential;
1392     PetscObject     obj;
1393     PetscClassId    id;
1394 
1395     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1396     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
1397     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1398     if ((id != PETSCFE_CLASSID) || isEssential) continue;
1399     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1400     for (v = 0; v < numValues; ++v) {
1401       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
1402       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1403       if (!pointIS) continue; /* No points with that id on this process */
1404       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1405       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1406         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1407         if (dep == dim-1) ++numFaces;
1408       }
1409       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd,&elemVec);CHKERRQ(ierr);
1410       if (locX_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
1411       for (p = 0, f = 0; p < numPoints; ++p) {
1412         const PetscInt point = points[p];
1413         PetscScalar   *x     = NULL;
1414         PetscInt       i;
1415 
1416         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1417         if (dep != dim-1) continue;
1418         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
1419         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
1420         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
1421         /* TODO: Matt, this is wrong if feBd does not match fe: i.e., if the order differs. */
1422         ierr = DMPlexVecGetClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1423         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
1424         ierr = DMPlexVecRestoreClosure(dm, section, locX, point, NULL, &x);CHKERRQ(ierr);
1425         if (locX_t) {
1426           ierr = DMPlexVecGetClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1427           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
1428           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, point, NULL, &x);CHKERRQ(ierr);
1429         }
1430         ++f;
1431       }
1432       for (f = 0; f < Nf; ++f) {
1433         PetscFE         fe;
1434         PetscQuadrature q;
1435         PetscInt        numQuadPoints, Nb;
1436         /* Conforming batches */
1437         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1438         /* Remainder */
1439         PetscInt        Nr, offset;
1440 
1441         ierr = PetscDSGetBdDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1442         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1443         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1444         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1445         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1446         blockSize = Nb*numQuadPoints;
1447         batchSize = numBlocks * blockSize;
1448         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1449         numChunks = numFaces / (numBatches*batchSize);
1450         Ne        = numChunks*numBatches*batchSize;
1451         Nr        = numFaces % (numBatches*batchSize);
1452         offset    = numFaces - Nr;
1453         ierr = PetscFEIntegrateBdResidual(fe, prob, f, Ne, cgeom, u, u_t, NULL, NULL, t, elemVec);CHKERRQ(ierr);
1454         ierr = PetscFEIntegrateBdResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, t, &elemVec[offset*totDimBd]);CHKERRQ(ierr);
1455       }
1456       for (p = 0, f = 0; p < numPoints; ++p) {
1457         const PetscInt point = points[p];
1458 
1459         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1460         if (dep != dim-1) continue;
1461         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDimBd, &elemVec[f*totDimBd]);CHKERRQ(ierr);}
1462         ierr = DMPlexVecSetClosure(dm, NULL, locF, point, &elemVec[f*totDimBd], ADD_ALL_VALUES);CHKERRQ(ierr);
1463         ++f;
1464       }
1465       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1466       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1467       ierr = PetscFree3(u,cgeom,elemVec);CHKERRQ(ierr);
1468       if (locX_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
1469     }
1470   }
1471   PetscFunctionReturn(0);
1472 }
1473 
1474 #undef __FUNCT__
1475 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1476 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1477 {
1478   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1479   const char       *name       = "Residual";
1480   DM                dmAux      = NULL;
1481   DM                dmGrad     = NULL;
1482   DMLabel           ghostLabel = NULL;
1483   PetscDS           prob       = NULL;
1484   PetscDS           probAux    = NULL;
1485   PetscSection      section    = NULL;
1486   PetscBool         useFEM     = PETSC_FALSE;
1487   PetscBool         useFVM     = PETSC_FALSE;
1488   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1489   PetscFV           fvm        = NULL;
1490   PetscFECellGeom  *cgeomFEM   = NULL;
1491   PetscScalar      *cgeomScal;
1492   PetscFVCellGeom  *cgeomFVM   = NULL;
1493   PetscFVFaceGeom  *fgeomFVM   = NULL;
1494   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1495   PetscScalar      *u = NULL, *u_t, *a, *uL, *uR;
1496   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1497   PetscErrorCode    ierr;
1498 
1499   PetscFunctionBegin;
1500   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1501   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1502   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1503   /* FEM+FVM */
1504   /* 1: Get sizes from dm and dmAux */
1505   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1506   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1507   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1508   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1509   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1510   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1511   if (locA) {
1512     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1513     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1514     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1515   }
1516   /* 2: Get geometric data */
1517   for (f = 0; f < Nf; ++f) {
1518     PetscObject  obj;
1519     PetscClassId id;
1520     PetscBool    fimp;
1521 
1522     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1523     if (isImplicit != fimp) continue;
1524     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1525     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1526     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1527     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1528   }
1529   if (useFEM) {
1530     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1531     ierr = VecGetArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);
1532     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1533       DM dmCell;
1534       PetscInt c;
1535 
1536       ierr = VecGetDM(cellGeometryFEM,&dmCell);CHKERRQ(ierr);
1537       ierr = PetscMalloc1(cEnd-cStart,&cgeomFEM);CHKERRQ(ierr);
1538       for (c = 0; c < cEnd - cStart; c++) {
1539         PetscScalar *thisgeom;
1540 
1541         ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1542         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
1543       }
1544     }
1545     else {
1546       cgeomFEM = (PetscFECellGeom *) cgeomScal;
1547     }
1548   }
1549   if (useFVM) {
1550     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1551     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1552     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1553     /* Reconstruct and limit cell gradients */
1554     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1555     if (dmGrad) {
1556       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1557       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1558       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1559       /* Communicate gradient values */
1560       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1561       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1562       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1563       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1564     }
1565     /* Handle non-essential (e.g. outflow) boundary values */
1566     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1567   }
1568   /* Loop over chunks */
1569   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1570   numChunks     = 1;
1571   cellChunkSize = (cEnd - cStart)/numChunks;
1572   faceChunkSize = (fEnd - fStart)/numChunks;
1573   for (chunk = 0; chunk < numChunks; ++chunk) {
1574     PetscScalar     *elemVec, *fluxL, *fluxR;
1575     PetscReal       *vol;
1576     PetscFVFaceGeom *fgeom;
1577     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1578     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1579 
1580     /* Extract field coefficients */
1581     if (useFEM) {
1582       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1583       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1584       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1585     }
1586     if (useFVM) {
1587       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1588       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1589       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1590       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1591       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1592       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1593     }
1594     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1595     /* Loop over fields */
1596     for (f = 0; f < Nf; ++f) {
1597       PetscObject  obj;
1598       PetscClassId id;
1599       PetscBool    fimp;
1600       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1601 
1602       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1603       if (isImplicit != fimp) continue;
1604       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1605       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1606       if (id == PETSCFE_CLASSID) {
1607         PetscFE         fe = (PetscFE) obj;
1608         PetscQuadrature q;
1609         PetscInt        Nq, Nb;
1610 
1611         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1612 
1613         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1614         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1615         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1616         blockSize = Nb*Nq;
1617         batchSize = numBlocks * blockSize;
1618         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1619         numChunks = numCells / (numBatches*batchSize);
1620         Ne        = numChunks*numBatches*batchSize;
1621         Nr        = numCells % (numBatches*batchSize);
1622         offset    = numCells - Nr;
1623         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1624         /*   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) */
1625         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1626         ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeomFEM[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1627       } else if (id == PETSCFV_CLASSID) {
1628         PetscFV fv = (PetscFV) obj;
1629 
1630         Ne = numFaces;
1631         /* Riemann solve over faces (need fields at face centroids) */
1632         /*   We need to evaluate FE fields at those coordinates */
1633         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1634       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1635     }
1636     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1637       ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);
1638     }
1639     else {
1640       cgeomFEM = NULL;
1641     }
1642     if (cellGeometryFEM) {ierr = VecRestoreArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);}
1643     /* Loop over domain */
1644     if (useFEM) {
1645       /* Add elemVec to locX */
1646       for (cell = cS; cell < cE; ++cell) {
1647         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1648         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1649       }
1650     }
1651     if (useFVM) {
1652       PetscScalar *fa;
1653       PetscInt     iface;
1654 
1655       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1656       for (f = 0; f < Nf; ++f) {
1657         PetscFV      fv;
1658         PetscObject  obj;
1659         PetscClassId id;
1660         PetscInt     foff, pdim;
1661 
1662         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1663         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1664         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1665         if (id != PETSCFV_CLASSID) continue;
1666         fv   = (PetscFV) obj;
1667         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1668         /* Accumulate fluxes to cells */
1669         for (face = fS, iface = 0; face < fE; ++face) {
1670           const PetscInt *cells;
1671           PetscScalar    *fL, *fR;
1672           PetscInt        ghost, d, nsupp, nchild;
1673 
1674           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1675           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1676           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1677           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1678           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1679           ierr = DMPlexPointGlobalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);
1680           ierr = DMPlexPointGlobalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);
1681           for (d = 0; d < pdim; ++d) {
1682             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1683             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1684           }
1685           ++iface;
1686         }
1687       }
1688       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1689     }
1690     /* Handle time derivative */
1691     if (locX_t) {
1692       PetscScalar *x_t, *fa;
1693 
1694       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1695       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1696       for (f = 0; f < Nf; ++f) {
1697         PetscFV      fv;
1698         PetscObject  obj;
1699         PetscClassId id;
1700         PetscInt     pdim, d;
1701 
1702         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1703         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1704         if (id != PETSCFV_CLASSID) continue;
1705         fv   = (PetscFV) obj;
1706         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1707         for (cell = cS; cell < cE; ++cell) {
1708           PetscScalar *u_t, *r;
1709 
1710           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1711           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1712           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1713         }
1714       }
1715       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1716       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1717     }
1718     if (useFEM) {
1719       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1720       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1721     }
1722     if (useFVM) {
1723       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1724       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1725       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1726       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1727       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1728     }
1729   }
1730 
1731   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);}
1732 
1733   /* FEM */
1734   /* 1: Get sizes from dm and dmAux */
1735   /* 2: Get geometric data */
1736   /* 3: Handle boundary values */
1737   /* 4: Loop over domain */
1738   /*   Extract coefficients */
1739   /* Loop over fields */
1740   /*   Set tiling for FE*/
1741   /*   Integrate FE residual to get elemVec */
1742   /*     Loop over subdomain */
1743   /*       Loop over quad points */
1744   /*         Transform coords to real space */
1745   /*         Evaluate field and aux fields at point */
1746   /*         Evaluate residual at point */
1747   /*         Transform residual to real space */
1748   /*       Add residual to elemVec */
1749   /* Loop over domain */
1750   /*   Add elemVec to locX */
1751 
1752   /* FVM */
1753   /* Get geometric data */
1754   /* If using gradients */
1755   /*   Compute gradient data */
1756   /*   Loop over domain faces */
1757   /*     Count computational faces */
1758   /*     Reconstruct cell gradient */
1759   /*   Loop over domain cells */
1760   /*     Limit cell gradients */
1761   /* Handle boundary values */
1762   /* Loop over domain faces */
1763   /*   Read out field, centroid, normal, volume for each side of face */
1764   /* Riemann solve over faces */
1765   /* Loop over domain faces */
1766   /*   Accumulate fluxes to cells */
1767   /* TODO Change printFEM to printDisc here */
1768   if (mesh->printFEM) {
1769     Vec         locFbc;
1770     PetscInt    pStart, pEnd, p, maxDof;
1771     PetscScalar *zeroes;
1772 
1773     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1774     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1775     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1776     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1777     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1778     for (p = pStart; p < pEnd; p++) {
1779       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1780     }
1781     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1782     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1783     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1784   }
1785   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1786   PetscFunctionReturn(0);
1787 }
1788 
1789 #undef __FUNCT__
1790 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
1791 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1792 {
1793   DM                dmCh, dmAux;
1794   Vec               A, cellgeom;
1795   PetscDS           prob, probCh, probAux = NULL;
1796   PetscQuadrature   q;
1797   PetscSection      section, sectionAux;
1798   PetscFECellGeom  *cgeom = NULL;
1799   PetscScalar      *cgeomScal;
1800   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1801   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1802   PetscInt          totDim, totDimAux = 0, diffCell = 0;
1803   PetscErrorCode    ierr;
1804 
1805   PetscFunctionBegin;
1806   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1807   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1808   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1809   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1810   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1811   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1812   numCells = cEnd - cStart;
1813   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1814   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1815   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1816   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1817   if (dmAux) {
1818     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1819     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1820     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1821   }
1822   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1823   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1824   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1825   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1826   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1827   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1828   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1829     DM dmCell;
1830 
1831     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
1832     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
1833     for (c = 0; c < cEnd - cStart; c++) {
1834       PetscScalar *thisgeom;
1835 
1836       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1837       cgeom[c] = *((PetscFECellGeom *) thisgeom);
1838     }
1839   }
1840   else {
1841     cgeom = (PetscFECellGeom *) cgeomScal;
1842   }
1843   for (c = cStart; c < cEnd; ++c) {
1844     PetscScalar *x = NULL, *x_t = NULL;
1845     PetscInt     i;
1846 
1847     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1848     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1849     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1850     if (X_t) {
1851       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1852       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1853       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1854     }
1855     if (dmAux) {
1856       DM dmAuxPlex;
1857 
1858       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1859       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1860       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1861       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1862       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1863     }
1864   }
1865   for (f = 0; f < Nf; ++f) {
1866     PetscFE  fe, feCh;
1867     PetscInt numQuadPoints, Nb;
1868     /* Conforming batches */
1869     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1870     /* Remainder */
1871     PetscInt Nr, offset;
1872 
1873     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1874     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1875     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1876     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1877     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1878     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1879     blockSize = Nb*numQuadPoints;
1880     batchSize = numBlocks * blockSize;
1881     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1882     numChunks = numCells / (numBatches*batchSize);
1883     Ne        = numChunks*numBatches*batchSize;
1884     Nr        = numCells % (numBatches*batchSize);
1885     offset    = numCells - Nr;
1886     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1887     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1888     ierr = PetscFEIntegrateResidual(fe, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1889     ierr = PetscFEIntegrateResidual(feCh, prob, f, Nr, &cgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, &a[offset*totDimAux], t, &elemVecCh[offset*totDim]);CHKERRQ(ierr);
1890   }
1891   for (c = cStart; c < cEnd; ++c) {
1892     PetscBool diff = PETSC_FALSE;
1893     PetscInt  d;
1894 
1895     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1896     if (diff) {
1897       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1898       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1899       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1900       ++diffCell;
1901     }
1902     if (diffCell > 9) break;
1903     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1904   }
1905   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1906     ierr = PetscFree(cgeom);CHKERRQ(ierr);
1907   }
1908   else {
1909     cgeom = NULL;
1910   }
1911   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1912   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1913   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1914   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1915   PetscFunctionReturn(0);
1916 }
1917 
1918 #undef __FUNCT__
1919 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1920 /*@
1921   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1922 
1923   Input Parameters:
1924 + dm - The mesh
1925 . X  - Local solution
1926 - user - The user context
1927 
1928   Output Parameter:
1929 . F  - Local output vector
1930 
1931   Level: developer
1932 
1933 .seealso: DMPlexComputeJacobianActionFEM()
1934 @*/
1935 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1936 {
1937   PetscObject    check;
1938   PetscInt       cStart, cEnd, cEndInterior;
1939   DM             plex;
1940   PetscErrorCode ierr;
1941 
1942   PetscFunctionBegin;
1943   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1944   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
1945   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
1946   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
1947   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
1948   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
1949   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
1950   else       {ierr = DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
1951   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1952   PetscFunctionReturn(0);
1953 }
1954 
1955 #undef __FUNCT__
1956 #define __FUNCT__ "DMPlexSNESComputeBoundaryFEM"
1957 /*@
1958   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
1959 
1960   Input Parameters:
1961 + dm - The mesh
1962 - user - The user context
1963 
1964   Output Parameter:
1965 . X  - Local solution
1966 
1967   Level: developer
1968 
1969 .seealso: DMPlexComputeJacobianActionFEM()
1970 @*/
1971 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
1972 {
1973   DM             plex;
1974   PetscErrorCode ierr;
1975 
1976   PetscFunctionBegin;
1977   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1978   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
1979   ierr = DMDestroy(&plex);CHKERRQ(ierr);
1980   PetscFunctionReturn(0);
1981 }
1982 
1983 #undef __FUNCT__
1984 #define __FUNCT__ "DMPlexComputeJacobian_Internal"
1985 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)
1986 {
1987   DM_Plex          *mesh  = (DM_Plex *) dm->data;
1988   const char       *name  = "Jacobian";
1989   DM                dmAux, plex;
1990   DMLabel           depth;
1991   Vec               A, cellgeom;
1992   PetscDS           prob, probAux = NULL;
1993   PetscQuadrature   quad;
1994   PetscSection      section, globalSection, sectionAux;
1995   PetscFECellGeom  *cgeom = NULL;
1996   PetscScalar      *cgeomScal;
1997   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
1998   PetscInt          dim, Nf, f, fieldI, fieldJ, numCells, c;
1999   PetscInt          totDim, totDimBd, totDimAux, numBd, bd;
2000   PetscBool         isShell, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2001   PetscErrorCode    ierr;
2002 
2003   PetscFunctionBegin;
2004   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2005   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2006   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2007   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2008   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2009   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2010   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2011   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2012   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2013   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2014   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2015   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2016   numCells = cEnd - cStart;
2017   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2018   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2019   if (dmAux) {
2020     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2021     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2022     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2023     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2024   }
2025   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2026   ierr = PetscMalloc5(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,hasJac ? numCells*totDim*totDim : 0,&elemMat,hasPrec ? numCells*totDim*totDim : 0, &elemMatP,hasDyn ? numCells*totDim*totDim : 0, &elemMatD);CHKERRQ(ierr);
2027   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2028   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2029   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2030   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2031     DM dmCell;
2032 
2033     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2034     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2035     for (c = 0; c < cEnd - cStart; c++) {
2036       PetscScalar *thisgeom;
2037 
2038       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2039       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2040     }
2041   } else {
2042     cgeom = (PetscFECellGeom *) cgeomScal;
2043   }
2044   for (c = cStart; c < cEnd; ++c) {
2045     PetscScalar *x = NULL,  *x_t = NULL;
2046     PetscInt     i;
2047 
2048     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2049     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2050     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2051     if (X_t) {
2052       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2053       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2054       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2055     }
2056     if (dmAux) {
2057       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2058       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2059       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2060     }
2061   }
2062   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2063   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2064   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2065   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2066     PetscClassId id;
2067     PetscFE  fe;
2068     PetscInt numQuadPoints, Nb;
2069     /* Conforming batches */
2070     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2071     /* Remainder */
2072     PetscInt Nr, offset;
2073 
2074     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2075     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2076     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2077     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2078     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2079     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2080     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2081     blockSize = Nb*numQuadPoints;
2082     batchSize = numBlocks * blockSize;
2083     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2084     numChunks = numCells / (numBatches*batchSize);
2085     Ne        = numChunks*numBatches*batchSize;
2086     Nr        = numCells % (numBatches*batchSize);
2087     offset    = numCells - Nr;
2088     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2089       if (hasJac) {
2090         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2091         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], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2092       }
2093       if (hasPrec) {
2094         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2095         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], t, X_tShift, &elemMatP[offset*totDim*totDim]);CHKERRQ(ierr);
2096       }
2097       if (hasDyn) {
2098         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2099         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], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2100       }
2101     }
2102   }
2103   if (hasDyn) {
2104     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2105   }
2106   if (hasFV) {
2107     PetscClassId id;
2108     PetscFV      fv;
2109     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2110 
2111     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2112       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2113       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2114       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2115       if (id != PETSCFV_CLASSID) continue;
2116       /* Put in the identity */
2117       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2118       for (c = cStart; c < cEnd; ++c) {
2119         const PetscInt eOffset = (c-cStart)*totDim*totDim;
2120         for (fc = 0; fc < NcI; ++fc) {
2121           for (f = 0; f < NbI; ++f) {
2122             const PetscInt i = offsetI + f*NcI+fc;
2123             if (hasPrec) {
2124               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2125               elemMatP[eOffset+i*totDim+i] = 1.0;
2126             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2127           }
2128         }
2129       }
2130     }
2131     /* No allocated space for FV stuff, so ignore the zero entries */
2132     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2133   }
2134   for (c = cStart; c < cEnd; ++c) {
2135     if (hasPrec) {
2136       if (hasJac) {
2137         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2138         ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2139       }
2140       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2141       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2142     } else {
2143       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2144       ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2145     }
2146   }
2147   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2148   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2149     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2150   } else {
2151     cgeom = NULL;
2152   }
2153   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2154   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2155   if (dmAux) {
2156     ierr = PetscFree(a);CHKERRQ(ierr);
2157     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2158   }
2159   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2160   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2161   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2162   ierr = DMGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
2163   for (bd = 0; bd < numBd; ++bd) {
2164     const char     *bdLabel;
2165     DMLabel         label;
2166     IS              pointIS;
2167     const PetscInt *points;
2168     const PetscInt *values;
2169     PetscInt        field, numValues, v, numPoints, p, dep, numFaces;
2170     PetscBool       isEssential;
2171     PetscObject     obj;
2172     PetscClassId    id;
2173 
2174     ierr = DMGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2175     ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
2176     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2177     if ((id != PETSCFE_CLASSID) || isEssential) continue;
2178     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2179     for (v = 0; v < numValues; ++v) {
2180       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
2181       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2182       if (!pointIS) continue; /* No points with that id on this process */
2183       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2184       for (p = 0, numFaces = 0; p < numPoints; ++p) {
2185         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2186         if (dep == dim-1) ++numFaces;
2187       }
2188       ierr = PetscMalloc3(numFaces*totDimBd,&u,numFaces,&cgeom,numFaces*totDimBd*totDimBd,&elemMat);CHKERRQ(ierr);
2189       if (X_t) {ierr = PetscMalloc1(numFaces*totDimBd,&u_t);CHKERRQ(ierr);}
2190       for (p = 0, f = 0; p < numPoints; ++p) {
2191         const PetscInt point = points[p];
2192         PetscScalar   *x     = NULL;
2193         PetscInt       i;
2194 
2195         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2196         if (dep != dim-1) continue;
2197         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, cgeom[f].v0, cgeom[f].J, cgeom[f].invJ, &cgeom[f].detJ);CHKERRQ(ierr);
2198         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, cgeom[f].n);CHKERRQ(ierr);
2199         if (cgeom[f].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", cgeom[f].detJ, point);
2200         ierr = DMPlexVecGetClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2201         for (i = 0; i < totDimBd; ++i) u[f*totDimBd+i] = x[i];
2202         ierr = DMPlexVecRestoreClosure(dm, section, X, point, NULL, &x);CHKERRQ(ierr);
2203         if (X_t) {
2204           ierr = DMPlexVecGetClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2205           for (i = 0; i < totDimBd; ++i) u_t[f*totDimBd+i] = x[i];
2206           ierr = DMPlexVecRestoreClosure(dm, section, X_t, point, NULL, &x);CHKERRQ(ierr);
2207         }
2208         ++f;
2209       }
2210       ierr = PetscMemzero(elemMat, numFaces*totDimBd*totDimBd * sizeof(PetscScalar));CHKERRQ(ierr);
2211       for (fieldI = 0; fieldI < Nf; ++fieldI) {
2212         PetscFE  fe;
2213         PetscInt numQuadPoints, Nb;
2214         /* Conforming batches */
2215         PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2216         /* Remainder */
2217         PetscInt Nr, offset;
2218 
2219         ierr = PetscDSGetBdDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2220         ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2221         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2222         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2223         ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2224         blockSize = Nb*numQuadPoints;
2225         batchSize = numBlocks * blockSize;
2226         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2227         numChunks = numFaces / (numBatches*batchSize);
2228         Ne        = numChunks*numBatches*batchSize;
2229         Nr        = numFaces % (numBatches*batchSize);
2230         offset    = numFaces - Nr;
2231         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2232           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, cgeom, u, u_t, NULL, NULL, t, X_tShift, elemMat);CHKERRQ(ierr);
2233           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &cgeom[offset], &u[offset*totDimBd], u_t ? &u_t[offset*totDimBd] : NULL, NULL, NULL, t, X_tShift, &elemMat[offset*totDimBd*totDimBd]);CHKERRQ(ierr);
2234         }
2235       }
2236       for (p = 0, f = 0; p < numPoints; ++p) {
2237         const PetscInt point = points[p];
2238 
2239         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2240         if (dep != dim-1) continue;
2241         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDimBd, totDimBd, &elemMat[f*totDimBd*totDimBd]);CHKERRQ(ierr);}
2242         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, point, &elemMat[f*totDimBd*totDimBd], ADD_VALUES);CHKERRQ(ierr);
2243         ++f;
2244       }
2245       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2246       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2247       ierr = PetscFree3(u,cgeom,elemMat);CHKERRQ(ierr);
2248       if (X_t) {ierr = PetscFree(u_t);CHKERRQ(ierr);}
2249     }
2250   }
2251   if (hasJac && hasPrec) {
2252     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2253     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2254   }
2255   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2256   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2257   if (mesh->printFEM) {
2258     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2259     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2260     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2261   }
2262   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2263   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2264   if (isShell) {
2265     JacActionCtx *jctx;
2266 
2267     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2268     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2269   }
2270   PetscFunctionReturn(0);
2271 }
2272 
2273 
2274 #undef __FUNCT__
2275 #define __FUNCT__ "DMPlexComputeJacobianAction_Internal"
2276 PetscErrorCode DMPlexComputeJacobianAction_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal t, PetscReal X_tShift, Vec X, Vec X_t, Vec Y, Vec Z, void *user)
2277 {
2278   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2279   const char       *name  = "Jacobian";
2280   DM                dmAux, plex;
2281   Vec               A, cellgeom;
2282   PetscDS           prob, probAux = NULL;
2283   PetscQuadrature   quad;
2284   PetscSection      section, globalSection, sectionAux;
2285   PetscFECellGeom  *cgeom = NULL;
2286   PetscScalar      *cgeomScal;
2287   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2288   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2289   PetscInt          totDim, totDimBd, totDimAux = 0;
2290   PetscBool         hasDyn;
2291   PetscErrorCode    ierr;
2292 
2293   PetscFunctionBegin;
2294   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2295   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2296   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2297   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2298   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2299   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2300   ierr = PetscDSGetTotalBdDimension(prob, &totDimBd);CHKERRQ(ierr);
2301   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2302   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2303   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2304   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2305   numCells = cEnd - cStart;
2306   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2307   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2308   if (dmAux) {
2309     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2310     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2311     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2312     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2313   }
2314   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2315   ierr = PetscMalloc6(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim*totDim,&elemMat,hasDyn ? numCells*totDim*totDim : 0, &elemMatD,numCells*totDim,&y,totDim,&z);CHKERRQ(ierr);
2316   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2317   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2318   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2319   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2320     DM dmCell;
2321 
2322     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2323     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2324     for (c = 0; c < cEnd - cStart; c++) {
2325       PetscScalar *thisgeom;
2326 
2327       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2328       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2329     }
2330   } else {
2331     cgeom = (PetscFECellGeom *) cgeomScal;
2332   }
2333   for (c = cStart; c < cEnd; ++c) {
2334     PetscScalar *x = NULL,  *x_t = NULL;
2335     PetscInt     i;
2336 
2337     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2338     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2339     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2340     if (X_t) {
2341       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2342       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2343       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2344     }
2345     if (dmAux) {
2346       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2347       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2348       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2349     }
2350     ierr = DMPlexVecGetClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2351     for (i = 0; i < totDim; ++i) y[(c-cStart)*totDim+i] = x[i];
2352     ierr = DMPlexVecRestoreClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2353   }
2354   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2355   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2356   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2357     PetscFE  fe;
2358     PetscInt numQuadPoints, Nb;
2359     /* Conforming batches */
2360     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2361     /* Remainder */
2362     PetscInt Nr, offset;
2363 
2364     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2365     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2366     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2367     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2368     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2369     blockSize = Nb*numQuadPoints;
2370     batchSize = numBlocks * blockSize;
2371     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2372     numChunks = numCells / (numBatches*batchSize);
2373     Ne        = numChunks*numBatches*batchSize;
2374     Nr        = numCells % (numBatches*batchSize);
2375     offset    = numCells - Nr;
2376     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2377       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2378       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], t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2379       if (hasDyn) {
2380         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2381         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], t, X_tShift, &elemMatD[offset*totDim*totDim]);CHKERRQ(ierr);
2382       }
2383     }
2384   }
2385   if (hasDyn) {
2386     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2387   }
2388   for (c = cStart; c < cEnd; ++c) {
2389     const PetscBLASInt M = totDim, one = 1;
2390     const PetscScalar  a = 1.0, b = 0.0;
2391 
2392     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[(c-cStart)*totDim*totDim], &M, &y[(c-cStart)*totDim], &one, &b, z, &one));
2393     if (mesh->printFEM > 1) {
2394       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);
2395       ierr = DMPrintCellVector(c, "Y",  totDim, &y[(c-cStart)*totDim]);CHKERRQ(ierr);
2396       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2397     }
2398     ierr = DMPlexVecSetClosure(dm, section, Z, c, z, ADD_VALUES);CHKERRQ(ierr);
2399   }
2400   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {ierr = PetscFree(cgeom);CHKERRQ(ierr);}
2401   else                                               {cgeom = NULL;}
2402   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2403   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2404   if (dmAux) {
2405     ierr = PetscFree(a);CHKERRQ(ierr);
2406     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2407   }
2408   if (mesh->printFEM) {
2409     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2410     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2411   }
2412   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2413   PetscFunctionReturn(0);
2414 }
2415 
2416 #undef __FUNCT__
2417 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2418 /*@
2419   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2420 
2421   Input Parameters:
2422 + dm - The mesh
2423 . X  - Local input vector
2424 - user - The user context
2425 
2426   Output Parameter:
2427 . Jac  - Jacobian matrix
2428 
2429   Note:
2430   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2431   like a GPU, or vectorize on a multicore machine.
2432 
2433   Level: developer
2434 
2435 .seealso: FormFunctionLocal()
2436 @*/
2437 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2438 {
2439   PetscInt       cStart, cEnd, cEndInterior;
2440   DM             plex;
2441   PetscErrorCode ierr;
2442 
2443   PetscFunctionBegin;
2444   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2445   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2446   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2447   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2448   ierr = DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2449   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2450   PetscFunctionReturn(0);
2451 }
2452 
2453 #undef __FUNCT__
2454 #define __FUNCT__ "DMPlexSNESComputeJacobianActionFEM"
2455 /*@
2456   DMPlexSNESComputeJacobianActionFEM - Form the local portion of the Jacobian action Z = J(X) Y at the local solution X using pointwise functions specified by the user.
2457 
2458   Input Parameters:
2459 + dm - The mesh
2460 . X  - Local solution vector
2461 . Y  - Local input vector
2462 - user - The user context
2463 
2464   Output Parameter:
2465 . Z - Local output vector
2466 
2467   Note:
2468   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2469   like a GPU, or vectorize on a multicore machine.
2470 
2471   Level: developer
2472 
2473 .seealso: FormFunctionLocal()
2474 @*/
2475 PetscErrorCode DMPlexSNESComputeJacobianActionFEM(DM dm, Vec X, Vec Y, Vec Z, void *user)
2476 {
2477   PetscInt       cStart, cEnd, cEndInterior;
2478   DM             plex;
2479   PetscErrorCode ierr;
2480 
2481   PetscFunctionBegin;
2482   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2483   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2484   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2485   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2486   ierr = DMPlexComputeJacobianAction_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Y, Z, user);CHKERRQ(ierr);
2487   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2488   PetscFunctionReturn(0);
2489 }
2490 
2491 #undef __FUNCT__
2492 #define __FUNCT__ "DMPlexSetSNESLocalFEM"
2493 /*@
2494   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2495 
2496   Input Parameters:
2497 + dm - The DM object
2498 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see DMAddBoundary())
2499 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2500 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2501 
2502   Level: developer
2503 @*/
2504 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2505 {
2506   PetscErrorCode ierr;
2507 
2508   PetscFunctionBegin;
2509   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2510   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2511   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2512   PetscFunctionReturn(0);
2513 }
2514 
2515 #undef __FUNCT__
2516 #define __FUNCT__ "DMSNESCheckFromOptions_Internal"
2517 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)
2518 {
2519   Mat            J, M;
2520   Vec            r, b;
2521   MatNullSpace   nullSpace;
2522   PetscReal     *error, res = 0.0;
2523   PetscInt       numFields;
2524   PetscErrorCode ierr;
2525 
2526   PetscFunctionBegin;
2527   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2528   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2529   M    = J;
2530   /* TODO Null space for J */
2531   /* Check discretization error */
2532   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2533   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2534   if (numFields > 1) {
2535     PetscInt f;
2536 
2537     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2538     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2539     for (f = 0; f < numFields; ++f) {
2540       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2541       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);CHKERRQ(ierr);}
2542       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2543     }
2544     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2545   } else {
2546     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2547     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);CHKERRQ(ierr);}
2548     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2549   }
2550   ierr = PetscFree(error);CHKERRQ(ierr);
2551   /* Check residual */
2552   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2553   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2554   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
2555   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2556   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2557   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2558   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2559   /* Check Jacobian */
2560   ierr = SNESComputeJacobian(snes, u, M, M);CHKERRQ(ierr);
2561   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2562   if (nullSpace) {
2563     PetscBool isNull;
2564     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2565     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2566   }
2567   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2568   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2569   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2570   ierr = MatMult(M, u, r);CHKERRQ(ierr);
2571   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2572   ierr = VecDestroy(&b);CHKERRQ(ierr);
2573   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2574   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
2575   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2576   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2577   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2578   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2579   ierr = VecDestroy(&r);CHKERRQ(ierr);
2580   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2581   ierr = MatDestroy(&J);CHKERRQ(ierr);
2582   PetscFunctionReturn(0);
2583 }
2584 
2585 #undef __FUNCT__
2586 #define __FUNCT__ "DMSNESCheckFromOptions"
2587 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2588 {
2589   DM             dm;
2590   Vec            sol;
2591   PetscBool      check;
2592   PetscErrorCode ierr;
2593 
2594   PetscFunctionBegin;
2595   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2596   if (!check) PetscFunctionReturn(0);
2597   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2598   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2599   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2600   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2601   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2602   PetscFunctionReturn(0);
2603 }
2604