xref: /petsc/src/snes/utils/dmplexsnes.c (revision e4160dc74dab80084503fe84ba2fe53b20773eaa)
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   for (p = 0; p < N; ++p) {foundProcs[p] = size;}
182   cellSF = NULL;
183   ierr = DMLocatePoints(dm, pointVec, DM_POINTLOCATION_REMOVE, &cellSF);CHKERRQ(ierr);
184   ierr = PetscSFGetGraph(cellSF,NULL,&numFound,&foundPoints,&foundCells);CHKERRQ(ierr);
185 #endif
186   for (p = 0; p < numFound; ++p) {
187     if (foundCells[p].index >= 0) foundProcs[foundPoints ? foundPoints[p] : p] = rank;
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   PetscFE        fem;
425   SNES           snes;
426   KSP            ksp;
427   PC             pc;
428   Vec            coordsLocal, r, ref, real;
429   Mat            J;
430   const PetscScalar *coords;
431   PetscScalar    *a;
432   PetscInt       p;
433   const PetscInt dof = ctx->dof;
434   PetscErrorCode ierr;
435 
436   PetscFunctionBegin;
437   ierr = DMGetField(dm, 0, (PetscObject *) &fem);CHKERRQ(ierr);
438   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
439   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
440   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
441   ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
442   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
443   ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
444   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
445   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
446   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
447   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
448   ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
449   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
450   ierr = MatSetUp(J);CHKERRQ(ierr);
451   ierr = SNESSetFunction(snes, r, QuadMap_Private, NULL);CHKERRQ(ierr);
452   ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, NULL);CHKERRQ(ierr);
453   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
454   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
455   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
456   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
457 
458   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
459   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
460   for (p = 0; p < ctx->n; ++p) {
461     PetscScalar *x = NULL, *vertices = NULL;
462     PetscScalar *xi;
463     PetscReal    xir[2];
464     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
465 
466     /* Can make this do all points at once */
467     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
468     if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
469     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
470     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
471     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
472     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
473     xi[0]  = coords[p*ctx->dim+0];
474     xi[1]  = coords[p*ctx->dim+1];
475     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
476     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
477     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
478     xir[0] = PetscRealPart(xi[0]);
479     xir[1] = PetscRealPart(xi[1]);
480     if (4*dof != xSize) {
481       PetscReal *B;
482       PetscInt   d;
483 
484       xir[0] = 2.0*xir[0] - 1.0; xir[1] = 2.0*xir[1] - 1.0;
485       ierr = PetscFEGetTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
486       for (comp = 0; comp < dof; ++comp) {
487         a[p*dof+comp] = 0.0;
488         for (d = 0; d < xSize/dof; ++d) {
489           a[p*dof+comp] += x[d*dof+comp]*B[d*dof+comp];
490         }
491       }
492       ierr = PetscFERestoreTabulation(fem, 1, xir, &B, NULL, NULL);CHKERRQ(ierr);
493     } else {
494       for (comp = 0; comp < dof; ++comp)
495         a[p*dof+comp] = x[0*dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*dof+comp]*xir[0]*(1 - xir[1]) + x[2*dof+comp]*xir[0]*xir[1] + x[3*dof+comp]*(1 - xir[0])*xir[1];
496     }
497     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
498     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
499     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
500   }
501   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
502   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
503 
504   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
505   ierr = VecDestroy(&r);CHKERRQ(ierr);
506   ierr = VecDestroy(&ref);CHKERRQ(ierr);
507   ierr = VecDestroy(&real);CHKERRQ(ierr);
508   ierr = MatDestroy(&J);CHKERRQ(ierr);
509   PetscFunctionReturn(0);
510 }
511 
512 #undef __FUNCT__
513 #define __FUNCT__ "HexMap_Private"
514 PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
515 {
516   const PetscScalar *vertices = (const PetscScalar*) ctx;
517   const PetscScalar x0        = vertices[0];
518   const PetscScalar y0        = vertices[1];
519   const PetscScalar z0        = vertices[2];
520   const PetscScalar x1        = vertices[9];
521   const PetscScalar y1        = vertices[10];
522   const PetscScalar z1        = vertices[11];
523   const PetscScalar x2        = vertices[6];
524   const PetscScalar y2        = vertices[7];
525   const PetscScalar z2        = vertices[8];
526   const PetscScalar x3        = vertices[3];
527   const PetscScalar y3        = vertices[4];
528   const PetscScalar z3        = vertices[5];
529   const PetscScalar x4        = vertices[12];
530   const PetscScalar y4        = vertices[13];
531   const PetscScalar z4        = vertices[14];
532   const PetscScalar x5        = vertices[15];
533   const PetscScalar y5        = vertices[16];
534   const PetscScalar z5        = vertices[17];
535   const PetscScalar x6        = vertices[18];
536   const PetscScalar y6        = vertices[19];
537   const PetscScalar z6        = vertices[20];
538   const PetscScalar x7        = vertices[21];
539   const PetscScalar y7        = vertices[22];
540   const PetscScalar z7        = vertices[23];
541   const PetscScalar f_1       = x1 - x0;
542   const PetscScalar g_1       = y1 - y0;
543   const PetscScalar h_1       = z1 - z0;
544   const PetscScalar f_3       = x3 - x0;
545   const PetscScalar g_3       = y3 - y0;
546   const PetscScalar h_3       = z3 - z0;
547   const PetscScalar f_4       = x4 - x0;
548   const PetscScalar g_4       = y4 - y0;
549   const PetscScalar h_4       = z4 - z0;
550   const PetscScalar f_01      = x2 - x1 - x3 + x0;
551   const PetscScalar g_01      = y2 - y1 - y3 + y0;
552   const PetscScalar h_01      = z2 - z1 - z3 + z0;
553   const PetscScalar f_12      = x7 - x3 - x4 + x0;
554   const PetscScalar g_12      = y7 - y3 - y4 + y0;
555   const PetscScalar h_12      = z7 - z3 - z4 + z0;
556   const PetscScalar f_02      = x5 - x1 - x4 + x0;
557   const PetscScalar g_02      = y5 - y1 - y4 + y0;
558   const PetscScalar h_02      = z5 - z1 - z4 + z0;
559   const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
560   const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
561   const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
562   const PetscScalar *ref;
563   PetscScalar       *real;
564   PetscErrorCode    ierr;
565 
566   PetscFunctionBegin;
567   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
568   ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
569   {
570     const PetscScalar p0 = ref[0];
571     const PetscScalar p1 = ref[1];
572     const PetscScalar p2 = ref[2];
573 
574     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;
575     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;
576     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;
577   }
578   ierr = PetscLogFlops(114);CHKERRQ(ierr);
579   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
580   ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
581   PetscFunctionReturn(0);
582 }
583 
584 #undef __FUNCT__
585 #define __FUNCT__ "HexJacobian_Private"
586 PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat J, Mat M, void *ctx)
587 {
588   const PetscScalar *vertices = (const PetscScalar*) ctx;
589   const PetscScalar x0        = vertices[0];
590   const PetscScalar y0        = vertices[1];
591   const PetscScalar z0        = vertices[2];
592   const PetscScalar x1        = vertices[9];
593   const PetscScalar y1        = vertices[10];
594   const PetscScalar z1        = vertices[11];
595   const PetscScalar x2        = vertices[6];
596   const PetscScalar y2        = vertices[7];
597   const PetscScalar z2        = vertices[8];
598   const PetscScalar x3        = vertices[3];
599   const PetscScalar y3        = vertices[4];
600   const PetscScalar z3        = vertices[5];
601   const PetscScalar x4        = vertices[12];
602   const PetscScalar y4        = vertices[13];
603   const PetscScalar z4        = vertices[14];
604   const PetscScalar x5        = vertices[15];
605   const PetscScalar y5        = vertices[16];
606   const PetscScalar z5        = vertices[17];
607   const PetscScalar x6        = vertices[18];
608   const PetscScalar y6        = vertices[19];
609   const PetscScalar z6        = vertices[20];
610   const PetscScalar x7        = vertices[21];
611   const PetscScalar y7        = vertices[22];
612   const PetscScalar z7        = vertices[23];
613   const PetscScalar f_xy      = x2 - x1 - x3 + x0;
614   const PetscScalar g_xy      = y2 - y1 - y3 + y0;
615   const PetscScalar h_xy      = z2 - z1 - z3 + z0;
616   const PetscScalar f_yz      = x7 - x3 - x4 + x0;
617   const PetscScalar g_yz      = y7 - y3 - y4 + y0;
618   const PetscScalar h_yz      = z7 - z3 - z4 + z0;
619   const PetscScalar f_xz      = x5 - x1 - x4 + x0;
620   const PetscScalar g_xz      = y5 - y1 - y4 + y0;
621   const PetscScalar h_xz      = z5 - z1 - z4 + z0;
622   const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
623   const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
624   const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
625   const PetscScalar *ref;
626   PetscErrorCode    ierr;
627 
628   PetscFunctionBegin;
629   ierr = VecGetArrayRead(Xref,  &ref);CHKERRQ(ierr);
630   {
631     const PetscScalar x       = ref[0];
632     const PetscScalar y       = ref[1];
633     const PetscScalar z       = ref[2];
634     const PetscInt    rows[3] = {0, 1, 2};
635     PetscScalar       values[9];
636 
637     values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
638     values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
639     values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
640     values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
641     values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
642     values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
643     values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
644     values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
645     values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;
646 
647     ierr = MatSetValues(J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
648   }
649   ierr = PetscLogFlops(152);CHKERRQ(ierr);
650   ierr = VecRestoreArrayRead(Xref,  &ref);CHKERRQ(ierr);
651   ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
652   ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
653   PetscFunctionReturn(0);
654 }
655 
656 #undef __FUNCT__
657 #define __FUNCT__ "DMInterpolate_Hex_Private"
658 PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
659 {
660   DM             dmCoord;
661   SNES           snes;
662   KSP            ksp;
663   PC             pc;
664   Vec            coordsLocal, r, ref, real;
665   Mat            J;
666   const PetscScalar *coords;
667   PetscScalar    *a;
668   PetscInt       p;
669   PetscErrorCode ierr;
670 
671   PetscFunctionBegin;
672   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
673   ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
674   ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
675   ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
676   ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
677   ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
678   ierr = VecSetType(r,dm->vectype);CHKERRQ(ierr);
679   ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
680   ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
681   ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
682   ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
683   ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
684   ierr = MatSetUp(J);CHKERRQ(ierr);
685   ierr = SNESSetFunction(snes, r, HexMap_Private, NULL);CHKERRQ(ierr);
686   ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, NULL);CHKERRQ(ierr);
687   ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
688   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
689   ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
690   ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
691 
692   ierr = VecGetArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
693   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
694   for (p = 0; p < ctx->n; ++p) {
695     PetscScalar *x = NULL, *vertices = NULL;
696     PetscScalar *xi;
697     PetscReal    xir[3];
698     PetscInt     c = ctx->cells[p], comp, coordSize, xSize;
699 
700     /* Can make this do all points at once */
701     ierr = DMPlexVecGetClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
702     if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
703     ierr = DMPlexVecGetClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
704     if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
705     ierr   = SNESSetFunction(snes, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
706     ierr   = SNESSetJacobian(snes, NULL, NULL, NULL, (void*) vertices);CHKERRQ(ierr);
707     ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
708     xi[0]  = coords[p*ctx->dim+0];
709     xi[1]  = coords[p*ctx->dim+1];
710     xi[2]  = coords[p*ctx->dim+2];
711     ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
712     ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
713     ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
714     xir[0] = PetscRealPart(xi[0]);
715     xir[1] = PetscRealPart(xi[1]);
716     xir[2] = PetscRealPart(xi[2]);
717     for (comp = 0; comp < ctx->dof; ++comp) {
718       a[p*ctx->dof+comp] =
719         x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
720         x[3*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
721         x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
722         x[1*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
723         x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
724         x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
725         x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
726         x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
727     }
728     ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
729     ierr = DMPlexVecRestoreClosure(dmCoord, NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
730     ierr = DMPlexVecRestoreClosure(dm, NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
731   }
732   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
733   ierr = VecRestoreArrayRead(ctx->coords, &coords);CHKERRQ(ierr);
734 
735   ierr = SNESDestroy(&snes);CHKERRQ(ierr);
736   ierr = VecDestroy(&r);CHKERRQ(ierr);
737   ierr = VecDestroy(&ref);CHKERRQ(ierr);
738   ierr = VecDestroy(&real);CHKERRQ(ierr);
739   ierr = MatDestroy(&J);CHKERRQ(ierr);
740   PetscFunctionReturn(0);
741 }
742 
743 #undef __FUNCT__
744 #define __FUNCT__ "DMInterpolationEvaluate"
745 /*
746   Input Parameters:
747 + ctx - The DMInterpolationInfo context
748 . dm  - The DM
749 - x   - The local vector containing the field to be interpolated
750 
751   Output Parameters:
752 . v   - The vector containing the interpolated values
753 */
754 PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
755 {
756   PetscInt       dim, coneSize, n;
757   PetscErrorCode ierr;
758 
759   PetscFunctionBegin;
760   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
761   PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
762   PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
763   ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
764   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);
765   if (n) {
766     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
767     ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
768     if (dim == 2) {
769       if (coneSize == 3) {
770         ierr = DMInterpolate_Triangle_Private(ctx, dm, x, v);CHKERRQ(ierr);
771       } else if (coneSize == 4) {
772         ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
773       } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
774     } else if (dim == 3) {
775       if (coneSize == 4) {
776         ierr = DMInterpolate_Tetrahedron_Private(ctx, dm, x, v);CHKERRQ(ierr);
777       } else {
778         ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
779       }
780     } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
781   }
782   PetscFunctionReturn(0);
783 }
784 
785 #undef __FUNCT__
786 #define __FUNCT__ "DMInterpolationDestroy"
787 PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
788 {
789   PetscErrorCode ierr;
790 
791   PetscFunctionBegin;
792   PetscValidPointer(ctx, 2);
793   ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
794   ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
795   ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
796   ierr = PetscFree(*ctx);CHKERRQ(ierr);
797   *ctx = NULL;
798   PetscFunctionReturn(0);
799 }
800 
801 #undef __FUNCT__
802 #define __FUNCT__ "SNESMonitorFields"
803 /*@C
804   SNESMonitorFields - Monitors the residual for each field separately
805 
806   Collective on SNES
807 
808   Input Parameters:
809 + snes   - the SNES context
810 . its    - iteration number
811 . fgnorm - 2-norm of residual
812 - vf  - PetscViewerAndFormat of type ASCII
813 
814   Notes:
815   This routine prints the residual norm at each iteration.
816 
817   Level: intermediate
818 
819 .keywords: SNES, nonlinear, default, monitor, norm
820 .seealso: SNESMonitorSet(), SNESMonitorDefault()
821 @*/
822 PetscErrorCode SNESMonitorFields(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
823 {
824   PetscViewer        viewer = vf->viewer;
825   Vec                res;
826   DM                 dm;
827   PetscSection       s;
828   const PetscScalar *r;
829   PetscReal         *lnorms, *norms;
830   PetscInt           numFields, f, pStart, pEnd, p;
831   PetscErrorCode     ierr;
832 
833   PetscFunctionBegin;
834   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
835   ierr = SNESGetFunction(snes, &res, 0, 0);CHKERRQ(ierr);
836   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
837   ierr = DMGetDefaultSection(dm, &s);CHKERRQ(ierr);
838   ierr = PetscSectionGetNumFields(s, &numFields);CHKERRQ(ierr);
839   ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
840   ierr = PetscCalloc2(numFields, &lnorms, numFields, &norms);CHKERRQ(ierr);
841   ierr = VecGetArrayRead(res, &r);CHKERRQ(ierr);
842   for (p = pStart; p < pEnd; ++p) {
843     for (f = 0; f < numFields; ++f) {
844       PetscInt fdof, foff, d;
845 
846       ierr = PetscSectionGetFieldDof(s, p, f, &fdof);CHKERRQ(ierr);
847       ierr = PetscSectionGetFieldOffset(s, p, f, &foff);CHKERRQ(ierr);
848       for (d = 0; d < fdof; ++d) lnorms[f] += PetscRealPart(PetscSqr(r[foff+d]));
849     }
850   }
851   ierr = VecRestoreArrayRead(res, &r);CHKERRQ(ierr);
852   ierr = MPIU_Allreduce(lnorms, norms, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
853   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
854   ierr = PetscViewerASCIIAddTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
855   ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
856   for (f = 0; f < numFields; ++f) {
857     if (f > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
858     ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", (double) PetscSqrtReal(norms[f]));CHKERRQ(ierr);
859   }
860   ierr = PetscViewerASCIIPrintf(viewer, "]\n");CHKERRQ(ierr);
861   ierr = PetscViewerASCIISubtractTab(viewer, ((PetscObject) snes)->tablevel);CHKERRQ(ierr);
862   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
863   ierr = PetscFree2(lnorms, norms);CHKERRQ(ierr);
864   PetscFunctionReturn(0);
865 }
866 
867 /********************* Residual Computation **************************/
868 
869 #undef __FUNCT__
870 #define __FUNCT__ "DMPlexSNESGetGeometryFEM"
871 /*@
872   DMPlexSNESGetGeometryFEM - Return precomputed geometric data
873 
874   Input Parameter:
875 . dm - The DM
876 
877   Output Parameters:
878 . cellgeom - The values precomputed from cell geometry
879 
880   Level: developer
881 
882 .seealso: DMPlexSNESSetFunctionLocal()
883 @*/
884 PetscErrorCode DMPlexSNESGetGeometryFEM(DM dm, Vec *cellgeom)
885 {
886   DMSNES         dmsnes;
887   PetscObject    obj;
888   PetscErrorCode ierr;
889 
890   PetscFunctionBegin;
891   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
892   ierr = DMGetDMSNES(dm, &dmsnes);CHKERRQ(ierr);
893   ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", &obj);CHKERRQ(ierr);
894   if (!obj) {
895     Vec cellgeom;
896 
897     ierr = DMPlexComputeGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
898     ierr = PetscObjectCompose((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject) cellgeom);CHKERRQ(ierr);
899     ierr = VecDestroy(&cellgeom);CHKERRQ(ierr);
900   }
901   if (cellgeom) {PetscValidPointer(cellgeom, 3); ierr = PetscObjectQuery((PetscObject) dmsnes, "DMPlexSNES_cellgeom_fem", (PetscObject *) cellgeom);CHKERRQ(ierr);}
902   PetscFunctionReturn(0);
903 }
904 
905 #undef __FUNCT__
906 #define __FUNCT__ "DMPlexSNESGetGeometryFVM"
907 /*@
908   DMPlexSNESGetGeometryFVM - Return precomputed geometric data
909 
910   Input Parameter:
911 . dm - The DM
912 
913   Output Parameters:
914 + facegeom - The values precomputed from face geometry
915 . cellgeom - The values precomputed from cell geometry
916 - minRadius - The minimum radius over the mesh of an inscribed sphere in a cell
917 
918   Level: developer
919 
920 .seealso: DMPlexTSSetRHSFunctionLocal()
921 @*/
922 PetscErrorCode DMPlexSNESGetGeometryFVM(DM dm, Vec *facegeom, Vec *cellgeom, PetscReal *minRadius)
923 {
924   DM             plex;
925   PetscErrorCode ierr;
926 
927   PetscFunctionBegin;
928   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
929   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
930   ierr = DMPlexGetDataFVM(plex, NULL, cellgeom, facegeom, NULL);CHKERRQ(ierr);
931   if (minRadius) {ierr = DMPlexGetMinRadius(plex, minRadius);CHKERRQ(ierr);}
932   ierr = DMDestroy(&plex);CHKERRQ(ierr);
933   PetscFunctionReturn(0);
934 }
935 
936 #undef __FUNCT__
937 #define __FUNCT__ "DMPlexSNESGetGradientDM"
938 /*@
939   DMPlexSNESGetGradientDM - Return gradient data layout
940 
941   Input Parameters:
942 + dm - The DM
943 - fv - The PetscFV
944 
945   Output Parameter:
946 . dmGrad - The layout for gradient values
947 
948   Level: developer
949 
950 .seealso: DMPlexSNESGetGeometryFVM()
951 @*/
952 PetscErrorCode DMPlexSNESGetGradientDM(DM dm, PetscFV fv, DM *dmGrad)
953 {
954   DM             plex;
955   PetscBool      computeGradients;
956   PetscErrorCode ierr;
957 
958   PetscFunctionBegin;
959   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
960   PetscValidHeaderSpecific(fv,PETSCFV_CLASSID,2);
961   PetscValidPointer(dmGrad,3);
962   ierr = PetscFVGetComputeGradients(fv, &computeGradients);CHKERRQ(ierr);
963   if (!computeGradients) {*dmGrad = NULL; PetscFunctionReturn(0);}
964   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
965   ierr = DMPlexGetDataFVM(plex, fv, NULL, NULL, dmGrad);CHKERRQ(ierr);
966   ierr = DMDestroy(&plex);CHKERRQ(ierr);
967   PetscFunctionReturn(0);
968 }
969 
970 #undef __FUNCT__
971 #define __FUNCT__ "DMPlexGetCellFields"
972 /*@C
973   DMPlexGetCellFields - Retrieve the field values values for a chunk of cells
974 
975   Input Parameters:
976 + dm     - The DM
977 . cStart - The first cell to include
978 . cEnd   - The first cell to exclude
979 . locX   - A local vector with the solution fields
980 . locX_t - A local vector with solution field time derivatives, or NULL
981 - locA   - A local vector with auxiliary fields, or NULL
982 
983   Output Parameters:
984 + u   - The field coefficients
985 . u_t - The fields derivative coefficients
986 - a   - The auxiliary field coefficients
987 
988   Level: developer
989 
990 .seealso: DMPlexGetFaceFields()
991 @*/
992 PetscErrorCode DMPlexGetCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
993 {
994   DM             dmAux;
995   PetscSection   section, sectionAux;
996   PetscDS        prob;
997   PetscInt       numCells = cEnd - cStart, totDim, totDimAux, c;
998   PetscErrorCode ierr;
999 
1000   PetscFunctionBegin;
1001   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1002   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1003   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1004   if (locA)   {PetscValidHeaderSpecific(locA, VEC_CLASSID, 6);}
1005   PetscValidPointer(u, 7);
1006   PetscValidPointer(u_t, 8);
1007   PetscValidPointer(a, 9);
1008   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1009   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1010   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1011   if (locA) {
1012     PetscDS probAux;
1013 
1014     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1015     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1016     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1017     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1018   }
1019   ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u);CHKERRQ(ierr);
1020   if (locX_t) {ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, u_t);CHKERRQ(ierr);} else {*u_t = NULL;}
1021   if (locA)   {ierr = DMGetWorkArray(dm, numCells*totDimAux, PETSC_SCALAR, a);CHKERRQ(ierr);} else {*a = NULL;}
1022   for (c = cStart; c < cEnd; ++c) {
1023     PetscScalar *x = NULL, *x_t = NULL, *ul = *u, *ul_t = *u_t, *al = *a;
1024     PetscInt     i;
1025 
1026     ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1027     for (i = 0; i < totDim; ++i) ul[(c-cStart)*totDim+i] = x[i];
1028     ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
1029     if (locX_t) {
1030       ierr = DMPlexVecGetClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1031       for (i = 0; i < totDim; ++i) ul_t[(c-cStart)*totDim+i] = x_t[i];
1032       ierr = DMPlexVecRestoreClosure(dm, section, locX_t, c, NULL, &x_t);CHKERRQ(ierr);
1033     }
1034     if (locA) {
1035       DM dmAuxPlex;
1036 
1037       ierr = DMSNESConvertPlex(dmAux, &dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1038       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1039       for (i = 0; i < totDimAux; ++i) al[(c-cStart)*totDimAux+i] = x[i];
1040       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
1041       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1042     }
1043   }
1044   PetscFunctionReturn(0);
1045 }
1046 
1047 #undef __FUNCT__
1048 #define __FUNCT__ "DMPlexRestoreCellFields"
1049 /*@C
1050   DMPlexRestoreCellFields - Restore the field values values for a chunk of cells
1051 
1052   Input Parameters:
1053 + dm     - The DM
1054 . cStart - The first cell to include
1055 . cEnd   - The first cell to exclude
1056 . locX   - A local vector with the solution fields
1057 . locX_t - A local vector with solution field time derivatives, or NULL
1058 - locA   - A local vector with auxiliary fields, or NULL
1059 
1060   Output Parameters:
1061 + u   - The field coefficients
1062 . u_t - The fields derivative coefficients
1063 - a   - The auxiliary field coefficients
1064 
1065   Level: developer
1066 
1067 .seealso: DMPlexGetFaceFields()
1068 @*/
1069 PetscErrorCode DMPlexRestoreCellFields(DM dm, PetscInt cStart, PetscInt cEnd, Vec locX, Vec locX_t, Vec locA, PetscScalar **u, PetscScalar **u_t, PetscScalar **a)
1070 {
1071   PetscErrorCode ierr;
1072 
1073   PetscFunctionBegin;
1074   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u);CHKERRQ(ierr);
1075   if (*u_t) {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, u_t);CHKERRQ(ierr);}
1076   if (*a)   {ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, a);CHKERRQ(ierr);}
1077   PetscFunctionReturn(0);
1078 }
1079 
1080 #undef __FUNCT__
1081 #define __FUNCT__ "DMPlexGetFaceFields"
1082 /*@C
1083   DMPlexGetFaceFields - Retrieve the field values values for a chunk of faces
1084 
1085   Input Parameters:
1086 + dm     - The DM
1087 . fStart - The first face to include
1088 . fEnd   - The first face to exclude
1089 . locX   - A local vector with the solution fields
1090 . locX_t - A local vector with solution field time derivatives, or NULL
1091 . faceGeometry - A local vector with face geometry
1092 . cellGeometry - A local vector with cell geometry
1093 - locaGrad - A local vector with field gradients, or NULL
1094 
1095   Output Parameters:
1096 + Nface - The number of faces with field values
1097 . uL - The field values at the left side of the face
1098 - uR - The field values at the right side of the face
1099 
1100   Level: developer
1101 
1102 .seealso: DMPlexGetCellFields()
1103 @*/
1104 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)
1105 {
1106   DM                 dmFace, dmCell, dmGrad = NULL;
1107   PetscSection       section;
1108   PetscDS            prob;
1109   DMLabel            ghostLabel;
1110   const PetscScalar *facegeom, *cellgeom, *x, *lgrad;
1111   PetscBool         *isFE;
1112   PetscInt           dim, Nf, f, Nc, numFaces = fEnd - fStart, iface, face;
1113   PetscErrorCode     ierr;
1114 
1115   PetscFunctionBegin;
1116   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1117   PetscValidHeaderSpecific(locX, VEC_CLASSID, 4);
1118   if (locX_t) {PetscValidHeaderSpecific(locX_t, VEC_CLASSID, 5);}
1119   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 6);
1120   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 7);
1121   if (locGrad) {PetscValidHeaderSpecific(locGrad, VEC_CLASSID, 8);}
1122   PetscValidPointer(uL, 9);
1123   PetscValidPointer(uR, 10);
1124   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1125   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1126   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1127   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1128   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1129   ierr = PetscMalloc1(Nf, &isFE);CHKERRQ(ierr);
1130   for (f = 0; f < Nf; ++f) {
1131     PetscObject  obj;
1132     PetscClassId id;
1133 
1134     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1135     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1136     if (id == PETSCFE_CLASSID)      {isFE[f] = PETSC_TRUE;}
1137     else if (id == PETSCFV_CLASSID) {isFE[f] = PETSC_FALSE;}
1138     else                            {isFE[f] = PETSC_FALSE;}
1139   }
1140   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1141   ierr = VecGetArrayRead(locX, &x);CHKERRQ(ierr);
1142   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1143   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1144   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1145   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1146   if (locGrad) {
1147     ierr = VecGetDM(locGrad, &dmGrad);CHKERRQ(ierr);
1148     ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1149   }
1150   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uL);CHKERRQ(ierr);
1151   ierr = DMGetWorkArray(dm, numFaces*Nc, PETSC_SCALAR, uR);CHKERRQ(ierr);
1152   /* Right now just eat the extra work for FE (could make a cell loop) */
1153   for (face = fStart, iface = 0; face < fEnd; ++face) {
1154     const PetscInt        *cells;
1155     PetscFVFaceGeom       *fg;
1156     PetscFVCellGeom       *cgL, *cgR;
1157     PetscScalar           *xL, *xR, *gL, *gR;
1158     PetscScalar           *uLl = *uL, *uRl = *uR;
1159     PetscInt               ghost, nsupp, nchild;
1160 
1161     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1162     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1163     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1164     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1165     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1166     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1167     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1168     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1169     for (f = 0; f < Nf; ++f) {
1170       PetscInt off;
1171 
1172       ierr = PetscDSGetComponentOffset(prob, f, &off);CHKERRQ(ierr);
1173       if (isFE[f]) {
1174         const PetscInt *cone;
1175         PetscInt        comp, coneSizeL, coneSizeR, faceLocL, faceLocR, ldof, rdof, d;
1176 
1177         xL = xR = NULL;
1178         ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1179         ierr = DMPlexVecGetClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1180         ierr = DMPlexVecGetClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1181         ierr = DMPlexGetCone(dm, cells[0], &cone);CHKERRQ(ierr);
1182         ierr = DMPlexGetConeSize(dm, cells[0], &coneSizeL);CHKERRQ(ierr);
1183         for (faceLocL = 0; faceLocL < coneSizeL; ++faceLocL) if (cone[faceLocL] == face) break;
1184         ierr = DMPlexGetCone(dm, cells[1], &cone);CHKERRQ(ierr);
1185         ierr = DMPlexGetConeSize(dm, cells[1], &coneSizeR);CHKERRQ(ierr);
1186         for (faceLocR = 0; faceLocR < coneSizeR; ++faceLocR) if (cone[faceLocR] == face) break;
1187         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]);
1188         /* Check that FEM field has values in the right cell (sometimes its an FV ghost cell) */
1189         /* TODO: this is a hack that might not be right for nonconforming */
1190         if (faceLocL < coneSizeL) {
1191           ierr = EvaluateFaceFields(prob, f, faceLocL, xL, &uLl[iface*Nc+off]);CHKERRQ(ierr);
1192           if (rdof == ldof && faceLocR < coneSizeR) {ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);}
1193           else              {for(d = 0; d < comp; ++d) uRl[iface*Nc+off+d] = uLl[iface*Nc+off+d];}
1194         }
1195         else {
1196           ierr = EvaluateFaceFields(prob, f, faceLocR, xR, &uRl[iface*Nc+off]);CHKERRQ(ierr);
1197           ierr = PetscSectionGetFieldComponents(section, f, &comp);CHKERRQ(ierr);
1198           for(d = 0; d < comp; ++d) uLl[iface*Nc+off+d] = uRl[iface*Nc+off+d];
1199         }
1200         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[0], &ldof, (PetscScalar **) &xL);CHKERRQ(ierr);
1201         ierr = DMPlexVecRestoreClosure(dm, section, locX, cells[1], &rdof, (PetscScalar **) &xR);CHKERRQ(ierr);
1202       } else {
1203         PetscFV  fv;
1204         PetscInt numComp, c;
1205 
1206         ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fv);CHKERRQ(ierr);
1207         ierr = PetscFVGetNumComponents(fv, &numComp);CHKERRQ(ierr);
1208         ierr = DMPlexPointLocalFieldRead(dm, cells[0], f, x, &xL);CHKERRQ(ierr);
1209         ierr = DMPlexPointLocalFieldRead(dm, cells[1], f, x, &xR);CHKERRQ(ierr);
1210         if (dmGrad) {
1211           PetscReal dxL[3], dxR[3];
1212 
1213           ierr = DMPlexPointLocalRead(dmGrad, cells[0], lgrad, &gL);CHKERRQ(ierr);
1214           ierr = DMPlexPointLocalRead(dmGrad, cells[1], lgrad, &gR);CHKERRQ(ierr);
1215           DMPlex_WaxpyD_Internal(dim, -1, cgL->centroid, fg->centroid, dxL);
1216           DMPlex_WaxpyD_Internal(dim, -1, cgR->centroid, fg->centroid, dxR);
1217           for (c = 0; c < numComp; ++c) {
1218             uLl[iface*Nc+off+c] = xL[c] + DMPlex_DotD_Internal(dim, &gL[c*dim], dxL);
1219             uRl[iface*Nc+off+c] = xR[c] + DMPlex_DotD_Internal(dim, &gR[c*dim], dxR);
1220           }
1221         } else {
1222           for (c = 0; c < numComp; ++c) {
1223             uLl[iface*Nc+off+c] = xL[c];
1224             uRl[iface*Nc+off+c] = xR[c];
1225           }
1226         }
1227       }
1228     }
1229     ++iface;
1230   }
1231   *Nface = iface;
1232   ierr = VecRestoreArrayRead(locX, &x);CHKERRQ(ierr);
1233   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1234   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1235   if (locGrad) {
1236     ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
1237   }
1238   ierr = PetscFree(isFE);CHKERRQ(ierr);
1239   PetscFunctionReturn(0);
1240 }
1241 
1242 #undef __FUNCT__
1243 #define __FUNCT__ "DMPlexRestoreFaceFields"
1244 /*@C
1245   DMPlexRestoreFaceFields - Restore the field values values for a chunk of faces
1246 
1247   Input Parameters:
1248 + dm     - The DM
1249 . fStart - The first face to include
1250 . fEnd   - The first face to exclude
1251 . locX   - A local vector with the solution fields
1252 . locX_t - A local vector with solution field time derivatives, or NULL
1253 . faceGeometry - A local vector with face geometry
1254 . cellGeometry - A local vector with cell geometry
1255 - locaGrad - A local vector with field gradients, or NULL
1256 
1257   Output Parameters:
1258 + Nface - The number of faces with field values
1259 . uL - The field values at the left side of the face
1260 - uR - The field values at the right side of the face
1261 
1262   Level: developer
1263 
1264 .seealso: DMPlexGetFaceFields()
1265 @*/
1266 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)
1267 {
1268   PetscErrorCode ierr;
1269 
1270   PetscFunctionBegin;
1271   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uL);CHKERRQ(ierr);
1272   ierr = DMRestoreWorkArray(dm, 0, PETSC_SCALAR, uR);CHKERRQ(ierr);
1273   PetscFunctionReturn(0);
1274 }
1275 
1276 #undef __FUNCT__
1277 #define __FUNCT__ "DMPlexGetFaceGeometry"
1278 /*@C
1279   DMPlexGetFaceGeometry - Retrieve the geometric values for a chunk of faces
1280 
1281   Input Parameters:
1282 + dm     - The DM
1283 . fStart - The first face to include
1284 . fEnd   - The first face to exclude
1285 . faceGeometry - A local vector with face geometry
1286 - cellGeometry - A local vector with cell geometry
1287 
1288   Output Parameters:
1289 + Nface - The number of faces with field values
1290 . fgeom - The extract the face centroid and normal
1291 - vol   - The cell volume
1292 
1293   Level: developer
1294 
1295 .seealso: DMPlexGetCellFields()
1296 @*/
1297 PetscErrorCode DMPlexGetFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1298 {
1299   DM                 dmFace, dmCell;
1300   DMLabel            ghostLabel;
1301   const PetscScalar *facegeom, *cellgeom;
1302   PetscInt           dim, numFaces = fEnd - fStart, iface, face;
1303   PetscErrorCode     ierr;
1304 
1305   PetscFunctionBegin;
1306   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1307   PetscValidHeaderSpecific(faceGeometry, VEC_CLASSID, 4);
1308   PetscValidHeaderSpecific(cellGeometry, VEC_CLASSID, 5);
1309   PetscValidPointer(fgeom, 6);
1310   PetscValidPointer(vol, 7);
1311   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1312   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1313   ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
1314   ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1315   ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
1316   ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1317   ierr = PetscMalloc1(numFaces, fgeom);CHKERRQ(ierr);
1318   ierr = DMGetWorkArray(dm, numFaces*2, PETSC_SCALAR, vol);CHKERRQ(ierr);
1319   for (face = fStart, iface = 0; face < fEnd; ++face) {
1320     const PetscInt        *cells;
1321     PetscFVFaceGeom       *fg;
1322     PetscFVCellGeom       *cgL, *cgR;
1323     PetscFVFaceGeom       *fgeoml = *fgeom;
1324     PetscReal             *voll   = *vol;
1325     PetscInt               ghost, d, nchild, nsupp;
1326 
1327     ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1328     ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1329     ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1330     if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1331     ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
1332     ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1333     ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cgL);CHKERRQ(ierr);
1334     ierr = DMPlexPointLocalRead(dmCell, cells[1], cellgeom, &cgR);CHKERRQ(ierr);
1335     for (d = 0; d < dim; ++d) {
1336       fgeoml[iface].centroid[d] = fg->centroid[d];
1337       fgeoml[iface].normal[d]   = fg->normal[d];
1338     }
1339     voll[iface*2+0] = cgL->volume;
1340     voll[iface*2+1] = cgR->volume;
1341     ++iface;
1342   }
1343   *Nface = iface;
1344   ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
1345   ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
1346   PetscFunctionReturn(0);
1347 }
1348 
1349 #undef __FUNCT__
1350 #define __FUNCT__ "DMPlexRestoreFaceGeometry"
1351 /*@C
1352   DMPlexRestoreFaceGeometry - Restore the field values values for a chunk of faces
1353 
1354   Input Parameters:
1355 + dm     - The DM
1356 . fStart - The first face to include
1357 . fEnd   - The first face to exclude
1358 . faceGeometry - A local vector with face geometry
1359 - cellGeometry - A local vector with cell geometry
1360 
1361   Output Parameters:
1362 + Nface - The number of faces with field values
1363 . fgeom - The extract the face centroid and normal
1364 - vol   - The cell volume
1365 
1366   Level: developer
1367 
1368 .seealso: DMPlexGetFaceFields()
1369 @*/
1370 PetscErrorCode DMPlexRestoreFaceGeometry(DM dm, PetscInt fStart, PetscInt fEnd, Vec faceGeometry, Vec cellGeometry, PetscInt *Nface, PetscFVFaceGeom **fgeom, PetscReal **vol)
1371 {
1372   PetscErrorCode ierr;
1373 
1374   PetscFunctionBegin;
1375   ierr = PetscFree(*fgeom);CHKERRQ(ierr);
1376   ierr = DMRestoreWorkArray(dm, 0, PETSC_REAL, vol);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 #undef __FUNCT__
1381 #define __FUNCT__ "DMPlexComputeBdResidual_Internal"
1382 PetscErrorCode DMPlexComputeBdResidual_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1383 {
1384   DM_Plex         *mesh = (DM_Plex *) dm->data;
1385   DM               dmAux = NULL, plex = NULL;
1386   PetscSection     section, sectionAux = NULL;
1387   PetscDS          prob, probAux = NULL;
1388   DMLabel          depth;
1389   Vec              locA = NULL;
1390   PetscFEFaceGeom *fgeom;
1391   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemVec = NULL;
1392   PetscInt         dim, totDim, totDimAux, numBd, bd;
1393   PetscErrorCode   ierr;
1394 
1395   PetscFunctionBegin;
1396   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1397   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1398   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
1399   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1400   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1401   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
1402   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1403   if (locA) {
1404     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1405     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
1406     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
1407     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1408     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1409   }
1410   for (bd = 0; bd < numBd; ++bd) {
1411     DMBoundaryConditionType type;
1412     const char             *bdLabel;
1413     DMLabel                 label;
1414     IS                      pointIS;
1415     const PetscInt         *points;
1416     const PetscInt         *values;
1417     PetscInt                field, numValues, v, numPoints, p, dep, numFaces, face;
1418     PetscObject             obj;
1419     PetscClassId            id;
1420 
1421     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &field, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
1422     ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
1423     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1424     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
1425     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
1426     for (v = 0; v < numValues; ++v) {
1427       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
1428       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
1429       if (!pointIS) continue; /* No points with that id on this process */
1430       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
1431       for (p = 0, numFaces = 0; p < numPoints; ++p) {
1432         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1433         if (dep == dim-1) ++numFaces;
1434       }
1435       ierr = PetscMalloc4(numFaces*totDim,&u,locX_t ? numFaces*totDim : 0, &u_t, numFaces,&fgeom, numFaces*totDim,&elemVec);CHKERRQ(ierr);
1436       if (locA) {ierr = PetscMalloc1(numFaces*totDimAux,&a);CHKERRQ(ierr);}
1437       for (p = 0, face = 0; p < numPoints; ++p) {
1438         const PetscInt point = points[p], *support, *cone;
1439         PetscScalar   *x     = NULL;
1440         PetscReal      dummyJ[9], dummyDetJ;
1441         PetscInt       i, coneSize, faceLoc;
1442 
1443         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
1444         if (dep != dim-1) continue;
1445         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1446         ierr = DMPlexComputeCellGeometryFEM(dm, support[0], NULL, NULL, dummyJ, fgeom[face].invJ[0], &dummyDetJ);CHKERRQ(ierr);
1447         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, fgeom[face].v0, fgeom[face].J, NULL, &fgeom[face].detJ);CHKERRQ(ierr);
1448         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, fgeom[face].n);CHKERRQ(ierr);
1449         if (fgeom[face].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", fgeom[face].detJ, point);
1450         ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
1451         ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
1452         for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
1453         if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of support[0] %d", point, support[0]);
1454         fgeom[face].face[0] = faceLoc;
1455         ierr = DMPlexVecGetClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1456         for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
1457         ierr = DMPlexVecRestoreClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
1458         if (locX_t) {
1459           ierr = DMPlexVecGetClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1460           for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
1461           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
1462         }
1463         if (locA) {
1464           ierr = DMPlexVecGetClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
1465           for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
1466           ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
1467         }
1468         ++face;
1469       }
1470       ierr = PetscMemzero(elemVec, numFaces* totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1471       {
1472         PetscFE         fe;
1473         PetscQuadrature q;
1474         PetscInt        numQuadPoints, Nb;
1475         /* Conforming batches */
1476         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1477         /* Remainder */
1478         PetscInt        Nr, offset;
1479 
1480         ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1481         ierr = PetscFEGetFaceQuadrature(fe, &q);CHKERRQ(ierr);
1482         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1483         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1484         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1485         blockSize = Nb*numQuadPoints;
1486         batchSize = numBlocks * blockSize;
1487         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1488         numChunks = numFaces / (numBatches*batchSize);
1489         Ne        = numChunks*numBatches*batchSize;
1490         Nr        = numFaces % (numBatches*batchSize);
1491         offset    = numFaces - Nr;
1492         ierr = PetscFEIntegrateBdResidual(fe, prob, field, Ne, fgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1493         ierr = PetscFEIntegrateBdResidual(fe, prob, field, Nr, &fgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, &elemVec[offset*totDim]);CHKERRQ(ierr);
1494       }
1495       for (p = 0, face = 0; p < numPoints; ++p) {
1496         const PetscInt point = points[p], *support;
1497 
1498         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
1499         if (dep != dim-1) continue;
1500         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(point, "BdResidual", totDim, &elemVec[face*totDim]);CHKERRQ(ierr);}
1501         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
1502         ierr = DMPlexVecSetClosure(dm, NULL, locF, support[0], &elemVec[face*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1503         ++face;
1504       }
1505       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
1506       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
1507       ierr = PetscFree4(u,u_t,fgeom,elemVec);CHKERRQ(ierr);
1508       if (locA) {ierr = PetscFree(a);CHKERRQ(ierr);}
1509     }
1510   }
1511   if (plex) {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
1512   PetscFunctionReturn(0);
1513 }
1514 
1515 #undef __FUNCT__
1516 #define __FUNCT__ "DMPlexComputeResidual_Internal"
1517 PetscErrorCode DMPlexComputeResidual_Internal(DM dm, PetscInt cStart, PetscInt cEnd, PetscReal time, Vec locX, Vec locX_t, PetscReal t, Vec locF, void *user)
1518 {
1519   DM_Plex          *mesh       = (DM_Plex *) dm->data;
1520   const char       *name       = "Residual";
1521   DM                dmAux      = NULL;
1522   DM                dmGrad     = NULL;
1523   DMLabel           ghostLabel = NULL;
1524   PetscDS           prob       = NULL;
1525   PetscDS           probAux    = NULL;
1526   PetscSection      section    = NULL;
1527   PetscBool         useFEM     = PETSC_FALSE;
1528   PetscBool         useFVM     = PETSC_FALSE;
1529   PetscBool         isImplicit = (locX_t || time == PETSC_MIN_REAL) ? PETSC_TRUE : PETSC_FALSE;
1530   PetscFV           fvm        = NULL;
1531   PetscFECellGeom  *cgeomFEM   = NULL;
1532   PetscScalar      *cgeomScal;
1533   PetscFVCellGeom  *cgeomFVM   = NULL;
1534   PetscFVFaceGeom  *fgeomFVM   = NULL;
1535   Vec               locA, cellGeometryFEM = NULL, cellGeometryFVM = NULL, faceGeometryFVM = NULL, grad, locGrad = NULL;
1536   PetscScalar      *u = NULL, *u_t, *a, *uL, *uR;
1537   PetscInt          Nf, f, totDim, totDimAux, numChunks, cellChunkSize, faceChunkSize, chunk, fStart, fEnd;
1538   PetscErrorCode    ierr;
1539 
1540   PetscFunctionBegin;
1541   ierr = PetscLogEventBegin(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1542   /* TODO The places where we have to use isFE are probably the member functions for the PetscDisc class */
1543   /* TODO The FVM geometry is over-manipulated. Make the precalc functions return exactly what we need */
1544   /* FEM+FVM */
1545   /* 1: Get sizes from dm and dmAux */
1546   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1547   ierr = DMGetLabel(dm, "ghost", &ghostLabel);CHKERRQ(ierr);
1548   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1549   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
1550   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1551   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
1552   if (locA) {
1553     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
1554     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1555     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1556   }
1557   /* 2: Get geometric data */
1558   for (f = 0; f < Nf; ++f) {
1559     PetscObject  obj;
1560     PetscClassId id;
1561     PetscBool    fimp;
1562 
1563     ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1564     if (isImplicit != fimp) continue;
1565     ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1566     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1567     if (id == PETSCFE_CLASSID) {useFEM = PETSC_TRUE;}
1568     if (id == PETSCFV_CLASSID) {useFVM = PETSC_TRUE; fvm = (PetscFV) obj;}
1569   }
1570   if (useFEM) {
1571     ierr = DMPlexSNESGetGeometryFEM(dm, &cellGeometryFEM);CHKERRQ(ierr);
1572     ierr = VecGetArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);
1573     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1574       DM dmCell;
1575       PetscInt c;
1576 
1577       ierr = VecGetDM(cellGeometryFEM,&dmCell);CHKERRQ(ierr);
1578       ierr = PetscMalloc1(cEnd-cStart,&cgeomFEM);CHKERRQ(ierr);
1579       for (c = 0; c < cEnd - cStart; c++) {
1580         PetscScalar *thisgeom;
1581 
1582         ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1583         cgeomFEM[c] = *((PetscFECellGeom *) thisgeom);
1584       }
1585     }
1586     else {
1587       cgeomFEM = (PetscFECellGeom *) cgeomScal;
1588     }
1589   }
1590   if (useFVM) {
1591     ierr = DMPlexSNESGetGeometryFVM(dm, &faceGeometryFVM, &cellGeometryFVM, NULL);CHKERRQ(ierr);
1592     ierr = VecGetArrayRead(faceGeometryFVM, (const PetscScalar **) &fgeomFVM);CHKERRQ(ierr);
1593     ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
1594     /* Reconstruct and limit cell gradients */
1595     ierr = DMPlexSNESGetGradientDM(dm, fvm, &dmGrad);CHKERRQ(ierr);
1596     if (dmGrad) {
1597       ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1598       ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1599       ierr = DMPlexReconstructGradients_Internal(dm, fvm, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
1600       /* Communicate gradient values */
1601       ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
1602       ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1603       ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
1604       ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
1605     }
1606     /* Handle non-essential (e.g. outflow) boundary values */
1607     ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, time, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
1608   }
1609   /* Loop over chunks */
1610   ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
1611   numChunks     = 1;
1612   cellChunkSize = (cEnd - cStart)/numChunks;
1613   faceChunkSize = (fEnd - fStart)/numChunks;
1614   for (chunk = 0; chunk < numChunks; ++chunk) {
1615     PetscScalar     *elemVec, *fluxL, *fluxR;
1616     PetscReal       *vol;
1617     PetscFVFaceGeom *fgeom;
1618     PetscInt         cS = cStart+chunk*cellChunkSize, cE = PetscMin(cS+cellChunkSize, cEnd), numCells = cE - cS, cell;
1619     PetscInt         fS = fStart+chunk*faceChunkSize, fE = PetscMin(fS+faceChunkSize, fEnd), numFaces = 0, face;
1620 
1621     /* Extract field coefficients */
1622     if (useFEM) {
1623       ierr = DMPlexGetCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1624       ierr = DMGetWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1625       ierr = PetscMemzero(elemVec, numCells*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1626     }
1627     if (useFVM) {
1628       ierr = DMPlexGetFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1629       ierr = DMPlexGetFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1630       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1631       ierr = DMGetWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1632       ierr = PetscMemzero(fluxL, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1633       ierr = PetscMemzero(fluxR, numFaces*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
1634     }
1635     /* TODO We will interlace both our field coefficients (u, u_t, uL, uR, etc.) and our output (elemVec, fL, fR). I think this works */
1636     /* Loop over fields */
1637     for (f = 0; f < Nf; ++f) {
1638       PetscObject  obj;
1639       PetscClassId id;
1640       PetscBool    fimp;
1641       PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;
1642 
1643       ierr = PetscDSGetImplicit(prob, f, &fimp);CHKERRQ(ierr);
1644       if (isImplicit != fimp) continue;
1645       ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1646       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1647       if (id == PETSCFE_CLASSID) {
1648         PetscFE         fe = (PetscFE) obj;
1649         PetscQuadrature q;
1650         PetscInt        Nq, Nb;
1651 
1652         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1653 
1654         ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1655         ierr = PetscQuadratureGetData(q, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
1656         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1657         blockSize = Nb*Nq;
1658         batchSize = numBlocks * blockSize;
1659         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1660         numChunks = numCells / (numBatches*batchSize);
1661         Ne        = numChunks*numBatches*batchSize;
1662         Nr        = numCells % (numBatches*batchSize);
1663         offset    = numCells - Nr;
1664         /* Integrate FE residual to get elemVec (need fields at quadrature points) */
1665         /*   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) */
1666         ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeomFEM, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1667         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);
1668       } else if (id == PETSCFV_CLASSID) {
1669         PetscFV fv = (PetscFV) obj;
1670 
1671         Ne = numFaces;
1672         /* Riemann solve over faces (need fields at face centroids) */
1673         /*   We need to evaluate FE fields at those coordinates */
1674         ierr = PetscFVIntegrateRHSFunction(fv, prob, f, Ne, fgeom, vol, uL, uR, fluxL, fluxR);CHKERRQ(ierr);
1675       } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
1676     }
1677     if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1678       ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);
1679     }
1680     else {
1681       cgeomFEM = NULL;
1682     }
1683     if (cellGeometryFEM) {ierr = VecRestoreArray(cellGeometryFEM, &cgeomScal);CHKERRQ(ierr);}
1684     /* Loop over domain */
1685     if (useFEM) {
1686       /* Add elemVec to locX */
1687       for (cell = cS; cell < cE; ++cell) {
1688         if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, name, totDim, &elemVec[cell*totDim]);CHKERRQ(ierr);}
1689         if (ghostLabel) {
1690           PetscInt ghostVal;
1691 
1692           ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1693           if (ghostVal > 0) continue;
1694         }
1695         ierr = DMPlexVecSetClosure(dm, section, locF, cell, &elemVec[cell*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1696       }
1697     }
1698     if (useFVM) {
1699       PetscScalar *fa;
1700       PetscInt     iface;
1701 
1702       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1703       for (f = 0; f < Nf; ++f) {
1704         PetscFV      fv;
1705         PetscObject  obj;
1706         PetscClassId id;
1707         PetscInt     foff, pdim;
1708 
1709         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1710         ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
1711         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1712         if (id != PETSCFV_CLASSID) continue;
1713         fv   = (PetscFV) obj;
1714         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1715         /* Accumulate fluxes to cells */
1716         for (face = fS, iface = 0; face < fE; ++face) {
1717           const PetscInt *cells;
1718           PetscScalar    *fL = NULL, *fR = NULL;
1719           PetscInt        ghost, d, nsupp, nchild;
1720 
1721           ierr = DMLabelGetValue(ghostLabel, face, &ghost);CHKERRQ(ierr);
1722           ierr = DMPlexGetSupportSize(dm, face, &nsupp);CHKERRQ(ierr);
1723           ierr = DMPlexGetTreeChildren(dm, face, &nchild, NULL);CHKERRQ(ierr);
1724           if (ghost >= 0 || nsupp > 2 || nchild > 0) continue;
1725           ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
1726           ierr = DMLabelGetValue(ghostLabel,cells[0],&ghost);CHKERRQ(ierr);
1727           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[0], f, fa, &fL);CHKERRQ(ierr);}
1728           ierr = DMLabelGetValue(ghostLabel,cells[1],&ghost);CHKERRQ(ierr);
1729           if (ghost <= 0) {ierr = DMPlexPointLocalFieldRef(dm, cells[1], f, fa, &fR);CHKERRQ(ierr);}
1730           for (d = 0; d < pdim; ++d) {
1731             if (fL) fL[d] -= fluxL[iface*totDim+foff+d];
1732             if (fR) fR[d] += fluxR[iface*totDim+foff+d];
1733           }
1734           ++iface;
1735         }
1736       }
1737       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1738     }
1739     /* Handle time derivative */
1740     if (locX_t) {
1741       PetscScalar *x_t, *fa;
1742 
1743       ierr = VecGetArray(locF, &fa);CHKERRQ(ierr);
1744       ierr = VecGetArray(locX_t, &x_t);CHKERRQ(ierr);
1745       for (f = 0; f < Nf; ++f) {
1746         PetscFV      fv;
1747         PetscObject  obj;
1748         PetscClassId id;
1749         PetscInt     pdim, d;
1750 
1751         ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
1752         ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
1753         if (id != PETSCFV_CLASSID) continue;
1754         fv   = (PetscFV) obj;
1755         ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
1756         for (cell = cS; cell < cE; ++cell) {
1757           PetscScalar *u_t, *r;
1758 
1759           if (ghostLabel) {
1760             PetscInt ghostVal;
1761 
1762             ierr = DMLabelGetValue(ghostLabel,cell,&ghostVal);CHKERRQ(ierr);
1763             if (ghostVal > 0) continue;
1764           }
1765           ierr = DMPlexPointLocalFieldRead(dm, cell, f, x_t, &u_t);CHKERRQ(ierr);
1766           ierr = DMPlexPointLocalFieldRef(dm, cell, f, fa, &r);CHKERRQ(ierr);
1767           for (d = 0; d < pdim; ++d) r[d] += u_t[d];
1768         }
1769       }
1770       ierr = VecRestoreArray(locX_t, &x_t);CHKERRQ(ierr);
1771       ierr = VecRestoreArray(locF, &fa);CHKERRQ(ierr);
1772     }
1773     if (useFEM) {
1774       ierr = DMPlexRestoreCellFields(dm, cS, cE, locX, locX_t, locA, &u, &u_t, &a);CHKERRQ(ierr);
1775       ierr = DMRestoreWorkArray(dm, numCells*totDim, PETSC_SCALAR, &elemVec);CHKERRQ(ierr);
1776     }
1777     if (useFVM) {
1778       ierr = DMPlexRestoreFaceFields(dm, fS, fE, locX, locX_t, faceGeometryFVM, cellGeometryFVM, locGrad, &numFaces, &uL, &uR);CHKERRQ(ierr);
1779       ierr = DMPlexRestoreFaceGeometry(dm, fS, fE, faceGeometryFVM, cellGeometryFVM, &numFaces, &fgeom, &vol);CHKERRQ(ierr);
1780       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxL);CHKERRQ(ierr);
1781       ierr = DMRestoreWorkArray(dm, numFaces*totDim, PETSC_SCALAR, &fluxR);CHKERRQ(ierr);
1782       if (dmGrad) {ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);}
1783     }
1784   }
1785 
1786   if (useFEM) {ierr = DMPlexComputeBdResidual_Internal(dm, locX, locX_t, t, locF, user);CHKERRQ(ierr);}
1787 
1788   /* FEM */
1789   /* 1: Get sizes from dm and dmAux */
1790   /* 2: Get geometric data */
1791   /* 3: Handle boundary values */
1792   /* 4: Loop over domain */
1793   /*   Extract coefficients */
1794   /* Loop over fields */
1795   /*   Set tiling for FE*/
1796   /*   Integrate FE residual to get elemVec */
1797   /*     Loop over subdomain */
1798   /*       Loop over quad points */
1799   /*         Transform coords to real space */
1800   /*         Evaluate field and aux fields at point */
1801   /*         Evaluate residual at point */
1802   /*         Transform residual to real space */
1803   /*       Add residual to elemVec */
1804   /* Loop over domain */
1805   /*   Add elemVec to locX */
1806 
1807   /* FVM */
1808   /* Get geometric data */
1809   /* If using gradients */
1810   /*   Compute gradient data */
1811   /*   Loop over domain faces */
1812   /*     Count computational faces */
1813   /*     Reconstruct cell gradient */
1814   /*   Loop over domain cells */
1815   /*     Limit cell gradients */
1816   /* Handle boundary values */
1817   /* Loop over domain faces */
1818   /*   Read out field, centroid, normal, volume for each side of face */
1819   /* Riemann solve over faces */
1820   /* Loop over domain faces */
1821   /*   Accumulate fluxes to cells */
1822   /* TODO Change printFEM to printDisc here */
1823   if (mesh->printFEM) {
1824     Vec         locFbc;
1825     PetscInt    pStart, pEnd, p, maxDof;
1826     PetscScalar *zeroes;
1827 
1828     ierr = VecDuplicate(locF,&locFbc);CHKERRQ(ierr);
1829     ierr = VecCopy(locF,locFbc);CHKERRQ(ierr);
1830     ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
1831     ierr = PetscSectionGetMaxDof(section,&maxDof);CHKERRQ(ierr);
1832     ierr = PetscCalloc1(maxDof,&zeroes);CHKERRQ(ierr);
1833     for (p = pStart; p < pEnd; p++) {
1834       ierr = VecSetValuesSection(locFbc,section,p,zeroes,INSERT_BC_VALUES);CHKERRQ(ierr);
1835     }
1836     ierr = PetscFree(zeroes);CHKERRQ(ierr);
1837     ierr = DMPrintLocalVec(dm, name, mesh->printTol, locFbc);CHKERRQ(ierr);
1838     ierr = VecDestroy(&locFbc);CHKERRQ(ierr);
1839   }
1840   ierr = PetscLogEventEnd(DMPLEX_ResidualFEM,dm,0,0,0);CHKERRQ(ierr);
1841   PetscFunctionReturn(0);
1842 }
1843 
1844 #undef __FUNCT__
1845 #define __FUNCT__ "DMPlexComputeResidualFEM_Check_Internal"
1846 static PetscErrorCode DMPlexComputeResidualFEM_Check_Internal(DM dm, Vec X, Vec X_t, PetscReal t, Vec F, void *user)
1847 {
1848   DM                dmCh, dmAux;
1849   Vec               A, cellgeom;
1850   PetscDS           prob, probCh, probAux = NULL;
1851   PetscQuadrature   q;
1852   PetscSection      section, sectionAux;
1853   PetscFECellGeom  *cgeom = NULL;
1854   PetscScalar      *cgeomScal;
1855   PetscScalar      *elemVec, *elemVecCh, *u, *u_t, *a = NULL;
1856   PetscInt          dim, Nf, f, numCells, cStart, cEnd, c;
1857   PetscInt          totDim, totDimAux = 0, diffCell = 0;
1858   PetscErrorCode    ierr;
1859 
1860   PetscFunctionBegin;
1861   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1862   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1863   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1864   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1865   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
1866   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1867   numCells = cEnd - cStart;
1868   ierr = PetscObjectQuery((PetscObject) dm, "dmCh", (PetscObject *) &dmCh);CHKERRQ(ierr);
1869   ierr = DMGetDS(dmCh, &probCh);CHKERRQ(ierr);
1870   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
1871   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
1872   if (dmAux) {
1873     ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
1874     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
1875     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
1876   }
1877   ierr = VecSet(F, 0.0);CHKERRQ(ierr);
1878   ierr = PetscMalloc3(numCells*totDim,&u,X_t ? numCells*totDim : 0,&u_t,numCells*totDim,&elemVec);CHKERRQ(ierr);
1879   ierr = PetscMalloc1(numCells*totDim,&elemVecCh);CHKERRQ(ierr);
1880   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
1881   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
1882   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1883   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1884     DM dmCell;
1885 
1886     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
1887     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
1888     for (c = 0; c < cEnd - cStart; c++) {
1889       PetscScalar *thisgeom;
1890 
1891       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
1892       cgeom[c] = *((PetscFECellGeom *) thisgeom);
1893     }
1894   }
1895   else {
1896     cgeom = (PetscFECellGeom *) cgeomScal;
1897   }
1898   for (c = cStart; c < cEnd; ++c) {
1899     PetscScalar *x = NULL, *x_t = NULL;
1900     PetscInt     i;
1901 
1902     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1903     for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
1904     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
1905     if (X_t) {
1906       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1907       for (i = 0; i < totDim; ++i) u_t[c*totDim+i] = x_t[i];
1908       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
1909     }
1910     if (dmAux) {
1911       DM dmAuxPlex;
1912 
1913       ierr = DMSNESConvertPlex(dmAux,&dmAuxPlex, PETSC_FALSE);CHKERRQ(ierr);
1914       ierr = DMPlexVecGetClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1915       for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
1916       ierr = DMPlexVecRestoreClosure(dmAuxPlex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
1917       ierr = DMDestroy(&dmAuxPlex);CHKERRQ(ierr);
1918     }
1919   }
1920   for (f = 0; f < Nf; ++f) {
1921     PetscFE  fe, feCh;
1922     PetscInt numQuadPoints, Nb;
1923     /* Conforming batches */
1924     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
1925     /* Remainder */
1926     PetscInt Nr, offset;
1927 
1928     ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1929     ierr = PetscDSGetDiscretization(probCh, f, (PetscObject *) &feCh);CHKERRQ(ierr);
1930     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1931     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1932     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
1933     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
1934     blockSize = Nb*numQuadPoints;
1935     batchSize = numBlocks * blockSize;
1936     ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
1937     numChunks = numCells / (numBatches*batchSize);
1938     Ne        = numChunks*numBatches*batchSize;
1939     Nr        = numCells % (numBatches*batchSize);
1940     offset    = numCells - Nr;
1941     ierr = PetscFEIntegrateResidual(fe, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVec);CHKERRQ(ierr);
1942     ierr = PetscFEIntegrateResidual(feCh, prob, f, Ne, cgeom, u, u_t, probAux, a, t, elemVecCh);CHKERRQ(ierr);
1943     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);
1944     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);
1945   }
1946   for (c = cStart; c < cEnd; ++c) {
1947     PetscBool diff = PETSC_FALSE;
1948     PetscInt  d;
1949 
1950     for (d = 0; d < totDim; ++d) if (PetscAbsScalar(elemVec[c*totDim+d] - elemVecCh[c*totDim+d]) > 1.0e-7) {diff = PETSC_TRUE;break;}
1951     if (diff) {
1952       ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Different cell %d\n", c);CHKERRQ(ierr);
1953       ierr = DMPrintCellVector(c, "Residual", totDim, &elemVec[c*totDim]);CHKERRQ(ierr);
1954       ierr = DMPrintCellVector(c, "Check Residual", totDim, &elemVecCh[c*totDim]);CHKERRQ(ierr);
1955       ++diffCell;
1956     }
1957     if (diffCell > 9) break;
1958     ierr = DMPlexVecSetClosure(dm, section, F, c, &elemVec[c*totDim], ADD_ALL_VALUES);CHKERRQ(ierr);
1959   }
1960   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
1961     ierr = PetscFree(cgeom);CHKERRQ(ierr);
1962   }
1963   else {
1964     cgeom = NULL;
1965   }
1966   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
1967   ierr = PetscFree3(u,u_t,elemVec);CHKERRQ(ierr);
1968   ierr = PetscFree(elemVecCh);CHKERRQ(ierr);
1969   if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
1970   PetscFunctionReturn(0);
1971 }
1972 
1973 #undef __FUNCT__
1974 #define __FUNCT__ "DMPlexSNESComputeResidualFEM"
1975 /*@
1976   DMPlexSNESComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user
1977 
1978   Input Parameters:
1979 + dm - The mesh
1980 . X  - Local solution
1981 - user - The user context
1982 
1983   Output Parameter:
1984 . F  - Local output vector
1985 
1986   Level: developer
1987 
1988 .seealso: DMPlexComputeJacobianActionFEM()
1989 @*/
1990 PetscErrorCode DMPlexSNESComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
1991 {
1992   PetscObject    check;
1993   PetscInt       cStart, cEnd, cEndInterior;
1994   DM             plex;
1995   PetscErrorCode ierr;
1996 
1997   PetscFunctionBegin;
1998   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
1999   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2000   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2001   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2002   /* The dmCh is used to check two mathematically equivalent discretizations for computational equivalence */
2003   ierr = PetscObjectQuery((PetscObject) plex, "dmCh", &check);CHKERRQ(ierr);
2004   if (check) {ierr = DMPlexComputeResidualFEM_Check_Internal(plex, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2005   else       {ierr = DMPlexComputeResidual_Internal(plex, cStart, cEnd, PETSC_MIN_REAL, X, NULL, 0.0, F, user);CHKERRQ(ierr);}
2006   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2007   PetscFunctionReturn(0);
2008 }
2009 
2010 #undef __FUNCT__
2011 #define __FUNCT__ "DMPlexSNESComputeBoundaryFEM"
2012 /*@
2013   DMPlexSNESComputeBoundaryFEM - Form the boundary values for the local input X
2014 
2015   Input Parameters:
2016 + dm - The mesh
2017 - user - The user context
2018 
2019   Output Parameter:
2020 . X  - Local solution
2021 
2022   Level: developer
2023 
2024 .seealso: DMPlexComputeJacobianActionFEM()
2025 @*/
2026 PetscErrorCode DMPlexSNESComputeBoundaryFEM(DM dm, Vec X, void *user)
2027 {
2028   DM             plex;
2029   PetscErrorCode ierr;
2030 
2031   PetscFunctionBegin;
2032   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2033   ierr = DMPlexInsertBoundaryValues(plex, PETSC_TRUE, X, PETSC_MIN_REAL, NULL, NULL, NULL);CHKERRQ(ierr);
2034   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2035   PetscFunctionReturn(0);
2036 }
2037 
2038 #undef __FUNCT__
2039 #define __FUNCT__ "DMPlexComputeBdJacobian_Internal"
2040 PetscErrorCode DMPlexComputeBdJacobian_Internal(DM dm, Vec locX, Vec locX_t, PetscReal t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
2041 {
2042   DM_Plex         *mesh = (DM_Plex *) dm->data;
2043   DM               dmAux = NULL, plex = NULL;
2044   PetscSection     section, globalSection, subSection, sectionAux = NULL;
2045   PetscDS          prob, probAux = NULL;
2046   DMLabel          depth;
2047   Vec              locA = NULL;
2048   PetscFEFaceGeom *fgeom;
2049   PetscScalar     *u = NULL, *u_t = NULL, *a = NULL, *elemMat = NULL;
2050   PetscInt         dim, totDim, totDimAux, numBd, bd, Nf;
2051   PetscBool        isMatISP;
2052   PetscErrorCode   ierr;
2053 
2054   PetscFunctionBegin;
2055   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2056   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2057   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2058   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2059   if (isMatISP) {
2060     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2061   }
2062   ierr = DMPlexGetDepthLabel(dm, &depth);CHKERRQ(ierr);
2063   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2064   ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
2065   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2066   ierr = PetscDSGetNumBoundary(prob, &numBd);CHKERRQ(ierr);
2067   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
2068   if (locA) {
2069     ierr = VecGetDM(locA, &dmAux);CHKERRQ(ierr);
2070     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2071     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2072     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2073     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2074   }
2075   for (bd = 0; bd < numBd; ++bd) {
2076     DMBoundaryConditionType type;
2077     const char             *bdLabel;
2078     DMLabel                 label;
2079     IS                      pointIS;
2080     const PetscInt         *points;
2081     const PetscInt         *values;
2082     PetscInt                fieldI, fieldJ, numValues, v, numPoints, p, dep, numFaces, face;
2083     PetscObject             obj;
2084     PetscClassId            id;
2085 
2086     ierr = PetscDSGetBoundary(prob, bd, &type, NULL, &bdLabel, &fieldI, NULL, NULL, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
2087     ierr = PetscDSGetDiscretization(prob, fieldI, &obj);CHKERRQ(ierr);
2088     ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2089     if ((id != PETSCFE_CLASSID) || (type & DM_BC_ESSENTIAL)) continue;
2090     ierr = DMGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
2091     for (v = 0; v < numValues; ++v) {
2092       ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
2093       ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
2094       if (!pointIS) continue; /* No points with that id on this process */
2095       ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
2096       for (p = 0, numFaces = 0; p < numPoints; ++p) {
2097         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2098         if (dep == dim-1) ++numFaces;
2099       }
2100       ierr = PetscMalloc4(numFaces*totDim,&u,locX_t ? numFaces*totDim : 0,&u_t,numFaces,&fgeom,numFaces*totDim*totDim,&elemMat);CHKERRQ(ierr);
2101       if (locA) {ierr = PetscMalloc1(numFaces*totDimAux,&a);CHKERRQ(ierr);}
2102       for (p = 0, face = 0; p < numPoints; ++p) {
2103         const PetscInt point = points[p], *support, *cone;
2104         PetscScalar   *x     = NULL;
2105         PetscReal      dummyJ[9], dummyDetJ;
2106         PetscInt       i, coneSize, faceLoc;
2107 
2108         ierr = DMLabelGetValue(depth, points[p], &dep);CHKERRQ(ierr);
2109         if (dep != dim-1) continue;
2110         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2111         ierr = DMPlexComputeCellGeometryFEM(dm, support[0], NULL, NULL, dummyJ, fgeom[face].invJ[0], &dummyDetJ);CHKERRQ(ierr);
2112         ierr = DMPlexComputeCellGeometryFEM(dm, point, NULL, fgeom[face].v0, fgeom[face].J, NULL, &fgeom[face].detJ);CHKERRQ(ierr);
2113         ierr = DMPlexComputeCellGeometryFVM(dm, point, NULL, NULL, fgeom[face].n);CHKERRQ(ierr);
2114         if (fgeom[face].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for face %d", fgeom[face].detJ, point);
2115         ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
2116         ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
2117         for (faceLoc = 0; faceLoc < coneSize; ++faceLoc) if (cone[faceLoc] == point) break;
2118         if (faceLoc == coneSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find face %d in cone of support[0] %d", point, support[0]);
2119         fgeom[face].face[0] = faceLoc;
2120         ierr = DMPlexVecGetClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2121         for (i = 0; i < totDim; ++i) u[face*totDim+i] = x[i];
2122         ierr = DMPlexVecRestoreClosure(dm, section, locX, support[0], NULL, &x);CHKERRQ(ierr);
2123         if (locX_t) {
2124           ierr = DMPlexVecGetClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2125           for (i = 0; i < totDim; ++i) u_t[face*totDim+i] = x[i];
2126           ierr = DMPlexVecRestoreClosure(dm, section, locX_t, support[0], NULL, &x);CHKERRQ(ierr);
2127         }
2128         if (locA) {
2129           ierr = DMPlexVecGetClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
2130           for (i = 0; i < totDimAux; ++i) a[face*totDimAux+i] = x[i];
2131           ierr = DMPlexVecRestoreClosure(plex, sectionAux, locA, support[0], NULL, &x);CHKERRQ(ierr);
2132         }
2133         ++face;
2134       }
2135       ierr = PetscMemzero(elemMat, numFaces*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2136       {
2137         PetscFE         fe;
2138         PetscQuadrature q;
2139         PetscInt        numQuadPoints, Nb;
2140         /* Conforming batches */
2141         PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2142         /* Remainder */
2143         PetscInt        Nr, offset;
2144 
2145         ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2146         ierr = PetscFEGetFaceQuadrature(fe, &q);CHKERRQ(ierr);
2147         ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2148         ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2149         ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2150         blockSize = Nb*numQuadPoints;
2151         batchSize = numBlocks * blockSize;
2152         ierr =  PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2153         numChunks = numFaces / (numBatches*batchSize);
2154         Ne        = numChunks*numBatches*batchSize;
2155         Nr        = numFaces % (numBatches*batchSize);
2156         offset    = numFaces - Nr;
2157         for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2158           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Ne, fgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2159           ierr = PetscFEIntegrateBdJacobian(fe, prob, fieldI, fieldJ, Nr, &fgeom[offset], &u[offset*totDim], u_t ? &u_t[offset*totDim] : NULL, probAux, a ? &a[offset*totDimAux] : NULL, t, X_tShift, &elemMat[offset*totDim*totDim]);CHKERRQ(ierr);
2160         }
2161       }
2162       for (p = 0, face = 0; p < numPoints; ++p) {
2163         const PetscInt point = points[p], *support;
2164 
2165         ierr = DMLabelGetValue(depth, point, &dep);CHKERRQ(ierr);
2166         if (dep != dim-1) continue;
2167         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(point, "BdJacobian", totDim, totDim, &elemMat[face*totDim*totDim]);CHKERRQ(ierr);}
2168         ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
2169         if (!isMatISP) {
2170           ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2171         } else {
2172           Mat lJ;
2173 
2174           ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2175           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, support[0], &elemMat[face*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2176         }
2177         ++face;
2178       }
2179       ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
2180       ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
2181       ierr = PetscFree4(u,u_t,fgeom,elemMat);CHKERRQ(ierr);
2182       if (locA) {ierr = PetscFree(a);CHKERRQ(ierr);}
2183     }
2184   }
2185   if (plex) {ierr = DMDestroy(&plex);CHKERRQ(ierr);}
2186   PetscFunctionReturn(0);
2187 }
2188 
2189 #undef __FUNCT__
2190 #define __FUNCT__ "DMPlexComputeJacobian_Internal"
2191 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)
2192 {
2193   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2194   const char       *name  = "Jacobian";
2195   DM                dmAux, plex;
2196   Vec               A, cellgeom;
2197   PetscDS           prob, probAux = NULL;
2198   PetscSection      section, globalSection, subSection, sectionAux;
2199   PetscFECellGeom  *cgeom = NULL;
2200   PetscScalar      *cgeomScal;
2201   PetscScalar      *elemMat, *elemMatP, *elemMatD, *u, *u_t, *a = NULL;
2202   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2203   PetscInt          totDim, totDimAux;
2204   PetscBool         isMatIS, isMatISP, isShell, hasJac, hasPrec, hasDyn, hasFV = PETSC_FALSE;
2205   PetscErrorCode    ierr;
2206 
2207   PetscFunctionBegin;
2208   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2209   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2210   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2211   ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatISP);CHKERRQ(ierr);
2212   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2213   if (isMatISP) {
2214     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2215   }
2216   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2217   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2218   ierr = PetscDSHasJacobian(prob, &hasJac);CHKERRQ(ierr);
2219   ierr = PetscDSHasJacobianPreconditioner(prob, &hasPrec);CHKERRQ(ierr);
2220   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2221   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2222   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2223   numCells = cEnd - cStart;
2224   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2225   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2226   if (dmAux) {
2227     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2228     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2229     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2230     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2231   }
2232   ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
2233   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);
2234   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2235   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2236   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2237   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2238     DM dmCell;
2239 
2240     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2241     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2242     for (c = 0; c < cEnd - cStart; c++) {
2243       PetscScalar *thisgeom;
2244 
2245       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2246       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2247     }
2248   } else {
2249     cgeom = (PetscFECellGeom *) cgeomScal;
2250   }
2251   for (c = cStart; c < cEnd; ++c) {
2252     PetscScalar *x = NULL,  *x_t = NULL;
2253     PetscInt     i;
2254 
2255     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2256     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2257     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2258     if (X_t) {
2259       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2260       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2261       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2262     }
2263     if (dmAux) {
2264       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2265       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2266       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2267     }
2268   }
2269   if (hasJac)  {ierr = PetscMemzero(elemMat,  numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2270   if (hasPrec) {ierr = PetscMemzero(elemMatP, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2271   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2272   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2273     PetscClassId    id;
2274     PetscFE         fe;
2275     PetscQuadrature q;
2276     PetscInt        numQuadPoints, Nb;
2277     /* Conforming batches */
2278     PetscInt        numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2279     /* Remainder */
2280     PetscInt        Nr, offset;
2281 
2282     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2283     ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
2284     if (id == PETSCFV_CLASSID) {hasFV = PETSC_TRUE; continue;}
2285     ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
2286     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2287     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2288     ierr = PetscQuadratureGetData(q, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2289     blockSize = Nb*numQuadPoints;
2290     batchSize = numBlocks * blockSize;
2291     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2292     numChunks = numCells / (numBatches*batchSize);
2293     Ne        = numChunks*numBatches*batchSize;
2294     Nr        = numCells % (numBatches*batchSize);
2295     offset    = numCells - Nr;
2296     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2297       if (hasJac) {
2298         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2299         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);
2300       }
2301       if (hasPrec) {
2302         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_PRE, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatP);CHKERRQ(ierr);
2303         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);
2304       }
2305       if (hasDyn) {
2306         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2307         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);
2308       }
2309     }
2310   }
2311   if (hasDyn) {
2312     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2313   }
2314   if (hasFV) {
2315     PetscClassId id;
2316     PetscFV      fv;
2317     PetscInt     offsetI, NcI, NbI = 1, fc, f;
2318 
2319     for (fieldI = 0; fieldI < Nf; ++fieldI) {
2320       ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fv);CHKERRQ(ierr);
2321       ierr = PetscDSGetFieldOffset(prob, fieldI, &offsetI);CHKERRQ(ierr);
2322       ierr = PetscObjectGetClassId((PetscObject) fv, &id);CHKERRQ(ierr);
2323       if (id != PETSCFV_CLASSID) continue;
2324       /* Put in the identity */
2325       ierr = PetscFVGetNumComponents(fv, &NcI);CHKERRQ(ierr);
2326       for (c = cStart; c < cEnd; ++c) {
2327         const PetscInt eOffset = (c-cStart)*totDim*totDim;
2328         for (fc = 0; fc < NcI; ++fc) {
2329           for (f = 0; f < NbI; ++f) {
2330             const PetscInt i = offsetI + f*NcI+fc;
2331             if (hasPrec) {
2332               if (hasJac) {elemMat[eOffset+i*totDim+i] = 1.0;}
2333               elemMatP[eOffset+i*totDim+i] = 1.0;
2334             } else {elemMat[eOffset+i*totDim+i] = 1.0;}
2335           }
2336         }
2337       }
2338     }
2339     /* No allocated space for FV stuff, so ignore the zero entries */
2340     ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE);CHKERRQ(ierr);
2341   }
2342   isMatIS = PETSC_FALSE;
2343   if (hasPrec && hasJac) {
2344     ierr = PetscObjectTypeCompare((PetscObject) JacP, MATIS, &isMatIS);CHKERRQ(ierr);
2345   }
2346   if (isMatIS && !subSection) {
2347     ierr = DMPlexGetSubdomainSection(dm, &subSection);CHKERRQ(ierr);
2348   }
2349   for (c = cStart; c < cEnd; ++c) {
2350     if (hasPrec) {
2351       if (hasJac) {
2352         if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2353         if (!isMatIS) {
2354           ierr = DMPlexMatSetClosure(dm, section, globalSection, Jac, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2355         } else {
2356           Mat lJ;
2357 
2358           ierr = MatISGetLocalMat(Jac,&lJ);CHKERRQ(ierr);
2359           ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2360         }
2361       }
2362       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMatP[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2363       if (!isMatISP) {
2364         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2365       } else {
2366         Mat lJ;
2367 
2368         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2369         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMatP[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2370       }
2371     } else {
2372       if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);}
2373       if (!isMatISP) {
2374         ierr = DMPlexMatSetClosure(dm, section, globalSection, JacP, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2375       } else {
2376         Mat lJ;
2377 
2378         ierr = MatISGetLocalMat(JacP,&lJ);CHKERRQ(ierr);
2379         ierr = DMPlexMatSetClosure(dm, section, subSection, lJ, c, &elemMat[(c-cStart)*totDim*totDim], ADD_VALUES);CHKERRQ(ierr);
2380       }
2381     }
2382   }
2383   if (hasFV) {ierr = MatSetOption(JacP, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);CHKERRQ(ierr);}
2384   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2385     ierr = PetscFree(cgeom);CHKERRQ(ierr);
2386   } else {
2387     cgeom = NULL;
2388   }
2389   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2390   ierr = PetscFree5(u,u_t,elemMat,elemMatP,elemMatD);CHKERRQ(ierr);
2391   if (dmAux) {
2392     ierr = PetscFree(a);CHKERRQ(ierr);
2393     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2394   }
2395   ierr = DMPlexComputeBdJacobian_Internal(dm, X, X_t, t, X_tShift, Jac, JacP, user);CHKERRQ(ierr);
2396   if (hasJac && hasPrec) {
2397     ierr = MatAssemblyBegin(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2398     ierr = MatAssemblyEnd(Jac, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2399   }
2400   ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2401   ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2402   if (mesh->printFEM) {
2403     ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
2404     ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
2405     ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2406   }
2407   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2408   ierr = PetscObjectTypeCompare((PetscObject) Jac, MATSHELL, &isShell);CHKERRQ(ierr);
2409   if (isShell) {
2410     JacActionCtx *jctx;
2411 
2412     ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
2413     ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
2414   }
2415   PetscFunctionReturn(0);
2416 }
2417 
2418 
2419 #undef __FUNCT__
2420 #define __FUNCT__ "DMPlexComputeJacobianAction_Internal"
2421 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)
2422 {
2423   DM_Plex          *mesh  = (DM_Plex *) dm->data;
2424   const char       *name  = "Jacobian";
2425   DM                dmAux, plex;
2426   Vec               A, cellgeom;
2427   PetscDS           prob, probAux = NULL;
2428   PetscQuadrature   quad;
2429   PetscSection      section, globalSection, sectionAux;
2430   PetscFECellGeom  *cgeom = NULL;
2431   PetscScalar      *cgeomScal;
2432   PetscScalar      *elemMat, *elemMatD, *u, *u_t, *a = NULL, *y, *z;
2433   PetscInt          dim, Nf, fieldI, fieldJ, numCells, c;
2434   PetscInt          totDim, totDimAux = 0;
2435   PetscBool         hasDyn;
2436   PetscErrorCode    ierr;
2437 
2438   PetscFunctionBegin;
2439   ierr = PetscLogEventBegin(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2440   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2441   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
2442   ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
2443   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
2444   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
2445   ierr = PetscDSHasDynamicJacobian(prob, &hasDyn);CHKERRQ(ierr);
2446   hasDyn = hasDyn && (X_tShift != 0.0) ? PETSC_TRUE : PETSC_FALSE;
2447   ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
2448   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
2449   numCells = cEnd - cStart;
2450   ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
2451   ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &A);CHKERRQ(ierr);
2452   if (dmAux) {
2453     ierr = DMConvert(dmAux, DMPLEX, &plex);CHKERRQ(ierr);
2454     ierr = DMGetDefaultSection(plex, &sectionAux);CHKERRQ(ierr);
2455     ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
2456     ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
2457   }
2458   ierr = VecSet(Z, 0.0);CHKERRQ(ierr);
2459   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);
2460   if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
2461   ierr = DMPlexSNESGetGeometryFEM(dm, &cellgeom);CHKERRQ(ierr);
2462   ierr = VecGetArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2463   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {
2464     DM dmCell;
2465 
2466     ierr = VecGetDM(cellgeom,&dmCell);CHKERRQ(ierr);
2467     ierr = PetscMalloc1(cEnd-cStart,&cgeom);CHKERRQ(ierr);
2468     for (c = 0; c < cEnd - cStart; c++) {
2469       PetscScalar *thisgeom;
2470 
2471       ierr = DMPlexPointLocalRef(dmCell, c + cStart, cgeomScal, &thisgeom);CHKERRQ(ierr);
2472       cgeom[c] = *((PetscFECellGeom *) thisgeom);
2473     }
2474   } else {
2475     cgeom = (PetscFECellGeom *) cgeomScal;
2476   }
2477   for (c = cStart; c < cEnd; ++c) {
2478     PetscScalar *x = NULL,  *x_t = NULL;
2479     PetscInt     i;
2480 
2481     ierr = DMPlexVecGetClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2482     for (i = 0; i < totDim; ++i) u[(c-cStart)*totDim+i] = x[i];
2483     ierr = DMPlexVecRestoreClosure(dm, section, X, c, NULL, &x);CHKERRQ(ierr);
2484     if (X_t) {
2485       ierr = DMPlexVecGetClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2486       for (i = 0; i < totDim; ++i) u_t[(c-cStart)*totDim+i] = x_t[i];
2487       ierr = DMPlexVecRestoreClosure(dm, section, X_t, c, NULL, &x_t);CHKERRQ(ierr);
2488     }
2489     if (dmAux) {
2490       ierr = DMPlexVecGetClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2491       for (i = 0; i < totDimAux; ++i) a[(c-cStart)*totDimAux+i] = x[i];
2492       ierr = DMPlexVecRestoreClosure(plex, sectionAux, A, c, NULL, &x);CHKERRQ(ierr);
2493     }
2494     ierr = DMPlexVecGetClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2495     for (i = 0; i < totDim; ++i) y[(c-cStart)*totDim+i] = x[i];
2496     ierr = DMPlexVecRestoreClosure(dm, section, Y, c, NULL, &x);CHKERRQ(ierr);
2497   }
2498   ierr = PetscMemzero(elemMat, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);
2499   if (hasDyn)  {ierr = PetscMemzero(elemMatD, numCells*totDim*totDim * sizeof(PetscScalar));CHKERRQ(ierr);}
2500   for (fieldI = 0; fieldI < Nf; ++fieldI) {
2501     PetscFE  fe;
2502     PetscInt numQuadPoints, Nb;
2503     /* Conforming batches */
2504     PetscInt numChunks, numBatches, numBlocks, Ne, blockSize, batchSize;
2505     /* Remainder */
2506     PetscInt Nr, offset;
2507 
2508     ierr = PetscDSGetDiscretization(prob, fieldI, (PetscObject *) &fe);CHKERRQ(ierr);
2509     ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
2510     ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
2511     ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
2512     ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, NULL, NULL);CHKERRQ(ierr);
2513     blockSize = Nb*numQuadPoints;
2514     batchSize = numBlocks * blockSize;
2515     ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
2516     numChunks = numCells / (numBatches*batchSize);
2517     Ne        = numChunks*numBatches*batchSize;
2518     Nr        = numCells % (numBatches*batchSize);
2519     offset    = numCells - Nr;
2520     for (fieldJ = 0; fieldJ < Nf; ++fieldJ) {
2521       ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMat);CHKERRQ(ierr);
2522       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);
2523       if (hasDyn) {
2524         ierr = PetscFEIntegrateJacobian(fe, prob, PETSCFE_JACOBIAN_DYN, fieldI, fieldJ, Ne, cgeom, u, u_t, probAux, a, t, X_tShift, elemMatD);CHKERRQ(ierr);
2525         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);
2526       }
2527     }
2528   }
2529   if (hasDyn) {
2530     for (c = 0; c < (cEnd - cStart)*totDim*totDim; ++c) elemMat[c] += X_tShift*elemMatD[c];
2531   }
2532   for (c = cStart; c < cEnd; ++c) {
2533     const PetscBLASInt M = totDim, one = 1;
2534     const PetscScalar  a = 1.0, b = 0.0;
2535 
2536     PetscStackCallBLAS("BLASgemv", BLASgemv_("N", &M, &M, &a, &elemMat[(c-cStart)*totDim*totDim], &M, &y[(c-cStart)*totDim], &one, &b, z, &one));
2537     if (mesh->printFEM > 1) {
2538       ierr = DMPrintCellMatrix(c, name, totDim, totDim, &elemMat[(c-cStart)*totDim*totDim]);CHKERRQ(ierr);
2539       ierr = DMPrintCellVector(c, "Y",  totDim, &y[(c-cStart)*totDim]);CHKERRQ(ierr);
2540       ierr = DMPrintCellVector(c, "Z",  totDim, z);CHKERRQ(ierr);
2541     }
2542     ierr = DMPlexVecSetClosure(dm, section, Z, c, z, ADD_VALUES);CHKERRQ(ierr);
2543   }
2544   if (sizeof(PetscFECellGeom) % sizeof(PetscScalar)) {ierr = PetscFree(cgeom);CHKERRQ(ierr);}
2545   else                                               {cgeom = NULL;}
2546   ierr = VecRestoreArray(cellgeom, &cgeomScal);CHKERRQ(ierr);
2547   ierr = PetscFree6(u,u_t,elemMat,elemMatD,y,z);CHKERRQ(ierr);
2548   if (dmAux) {
2549     ierr = PetscFree(a);CHKERRQ(ierr);
2550     ierr = DMDestroy(&plex);CHKERRQ(ierr);
2551   }
2552   if (mesh->printFEM) {
2553     ierr = PetscPrintf(PETSC_COMM_WORLD, "Z:\n");CHKERRQ(ierr);
2554     ierr = VecView(Z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2555   }
2556   ierr = PetscLogEventEnd(DMPLEX_JacobianFEM,dm,0,0,0);CHKERRQ(ierr);
2557   PetscFunctionReturn(0);
2558 }
2559 
2560 #undef __FUNCT__
2561 #define __FUNCT__ "DMPlexSNESComputeJacobianFEM"
2562 /*@
2563   DMPlexSNESComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.
2564 
2565   Input Parameters:
2566 + dm - The mesh
2567 . X  - Local input vector
2568 - user - The user context
2569 
2570   Output Parameter:
2571 . Jac  - Jacobian matrix
2572 
2573   Note:
2574   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2575   like a GPU, or vectorize on a multicore machine.
2576 
2577   Level: developer
2578 
2579 .seealso: FormFunctionLocal()
2580 @*/
2581 PetscErrorCode DMPlexSNESComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP,void *user)
2582 {
2583   PetscInt       cStart, cEnd, cEndInterior;
2584   DM             plex;
2585   PetscErrorCode ierr;
2586 
2587   PetscFunctionBegin;
2588   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2589   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2590   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2591   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2592   ierr = DMPlexComputeJacobian_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Jac, JacP, user);CHKERRQ(ierr);
2593   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2594   PetscFunctionReturn(0);
2595 }
2596 
2597 #undef __FUNCT__
2598 #define __FUNCT__ "DMPlexSNESComputeJacobianActionFEM"
2599 /*@
2600   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.
2601 
2602   Input Parameters:
2603 + dm - The mesh
2604 . X  - Local solution vector
2605 . Y  - Local input vector
2606 - user - The user context
2607 
2608   Output Parameter:
2609 . Z - Local output vector
2610 
2611   Note:
2612   We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
2613   like a GPU, or vectorize on a multicore machine.
2614 
2615   Level: developer
2616 
2617 .seealso: FormFunctionLocal()
2618 @*/
2619 PetscErrorCode DMPlexSNESComputeJacobianActionFEM(DM dm, Vec X, Vec Y, Vec Z, void *user)
2620 {
2621   PetscInt       cStart, cEnd, cEndInterior;
2622   DM             plex;
2623   PetscErrorCode ierr;
2624 
2625   PetscFunctionBegin;
2626   ierr = DMSNESConvertPlex(dm,&plex,PETSC_TRUE);CHKERRQ(ierr);
2627   ierr = DMPlexGetHeightStratum(plex, 0, &cStart, &cEnd);CHKERRQ(ierr);
2628   ierr = DMPlexGetHybridBounds(plex, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
2629   cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
2630   ierr = DMPlexComputeJacobianAction_Internal(plex, cStart, cEnd, 0.0, 0.0, X, NULL, Y, Z, user);CHKERRQ(ierr);
2631   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2632   PetscFunctionReturn(0);
2633 }
2634 
2635 #undef __FUNCT__
2636 #define __FUNCT__ "DMPlexSetSNESLocalFEM"
2637 /*@
2638   DMPlexSetSNESLocalFEM - Use DMPlex's internal FEM routines to compute SNES boundary values, residual, and Jacobian.
2639 
2640   Input Parameters:
2641 + dm - The DM object
2642 . boundaryctx - the user context that will be passed to pointwise evaluation of boundary values (see PetscDSAddBoundary())
2643 . residualctx - the user context that will be passed to pointwise evaluation of finite element residual computations (see PetscDSSetResidual())
2644 - jacobianctx - the user context that will be passed to pointwise evaluation of finite element Jacobian construction (see PetscDSSetJacobian())
2645 
2646   Level: developer
2647 @*/
2648 PetscErrorCode DMPlexSetSNESLocalFEM(DM dm, void *boundaryctx, void *residualctx, void *jacobianctx)
2649 {
2650   PetscErrorCode ierr;
2651 
2652   PetscFunctionBegin;
2653   ierr = DMSNESSetBoundaryLocal(dm,DMPlexSNESComputeBoundaryFEM,boundaryctx);CHKERRQ(ierr);
2654   ierr = DMSNESSetFunctionLocal(dm,DMPlexSNESComputeResidualFEM,residualctx);CHKERRQ(ierr);
2655   ierr = DMSNESSetJacobianLocal(dm,DMPlexSNESComputeJacobianFEM,jacobianctx);CHKERRQ(ierr);
2656   PetscFunctionReturn(0);
2657 }
2658 
2659 #undef __FUNCT__
2660 #define __FUNCT__ "DMSNESCheckFromOptions_Internal"
2661 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)
2662 {
2663   Mat            J, M;
2664   Vec            r, b;
2665   MatNullSpace   nullSpace;
2666   PetscReal     *error, res = 0.0;
2667   PetscInt       numFields;
2668   PetscErrorCode ierr;
2669 
2670   PetscFunctionBegin;
2671   ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
2672   ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
2673   M    = J;
2674   /* TODO Null space for J */
2675   /* Check discretization error */
2676   ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
2677   ierr = PetscMalloc1(PetscMax(1, numFields), &error);CHKERRQ(ierr);
2678   if (numFields > 1) {
2679     PetscInt f;
2680 
2681     ierr = DMComputeL2FieldDiff(dm, 0.0, exactFuncs, ctxs, u, error);CHKERRQ(ierr);
2682     ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: [");CHKERRQ(ierr);
2683     for (f = 0; f < numFields; ++f) {
2684       if (f) {ierr = PetscPrintf(PETSC_COMM_WORLD, ", ");CHKERRQ(ierr);}
2685       if (error[f] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "%g", error[f]);CHKERRQ(ierr);}
2686       else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "< 1.0e-11");CHKERRQ(ierr);}
2687     }
2688     ierr = PetscPrintf(PETSC_COMM_WORLD, "]\n");CHKERRQ(ierr);
2689   } else {
2690     ierr = DMComputeL2Diff(dm, 0.0, exactFuncs, ctxs, u, &error[0]);CHKERRQ(ierr);
2691     if (error[0] >= 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error[0]);CHKERRQ(ierr);}
2692     else                     {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
2693   }
2694   ierr = PetscFree(error);CHKERRQ(ierr);
2695   /* Check residual */
2696   ierr = SNESComputeFunction(snes, u, r);CHKERRQ(ierr);
2697   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2698   ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);CHKERRQ(ierr);
2699   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2700   ierr = PetscObjectSetName((PetscObject) r, "Initial Residual");CHKERRQ(ierr);
2701   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"res_");CHKERRQ(ierr);
2702   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2703   /* Check Jacobian */
2704   ierr = SNESComputeJacobian(snes, u, M, M);CHKERRQ(ierr);
2705   ierr = MatGetNullSpace(J, &nullSpace);CHKERRQ(ierr);
2706   if (nullSpace) {
2707     PetscBool isNull;
2708     ierr = MatNullSpaceTest(nullSpace, J, &isNull);CHKERRQ(ierr);
2709     if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
2710   }
2711   ierr = VecDuplicate(u, &b);CHKERRQ(ierr);
2712   ierr = VecSet(r, 0.0);CHKERRQ(ierr);
2713   ierr = SNESComputeFunction(snes, r, b);CHKERRQ(ierr);
2714   ierr = MatMult(M, u, r);CHKERRQ(ierr);
2715   ierr = VecAXPY(r, 1.0, b);CHKERRQ(ierr);
2716   ierr = VecDestroy(&b);CHKERRQ(ierr);
2717   ierr = VecNorm(r, NORM_2, &res);CHKERRQ(ierr);
2718   ierr = PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);CHKERRQ(ierr);
2719   ierr = VecChop(r, 1.0e-10);CHKERRQ(ierr);
2720   ierr = PetscObjectSetName((PetscObject) r, "Au - b = Au + F(0)");CHKERRQ(ierr);
2721   ierr = PetscObjectSetOptionsPrefix((PetscObject)r,"linear_res_");CHKERRQ(ierr);
2722   ierr = VecViewFromOptions(r, NULL, "-vec_view");CHKERRQ(ierr);
2723   ierr = VecDestroy(&r);CHKERRQ(ierr);
2724   ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
2725   ierr = MatDestroy(&J);CHKERRQ(ierr);
2726   PetscFunctionReturn(0);
2727 }
2728 
2729 #undef __FUNCT__
2730 #define __FUNCT__ "DMSNESCheckFromOptions"
2731 PetscErrorCode DMSNESCheckFromOptions(SNES snes, Vec u, PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx), void **ctxs)
2732 {
2733   DM             dm;
2734   Vec            sol;
2735   PetscBool      check;
2736   PetscErrorCode ierr;
2737 
2738   PetscFunctionBegin;
2739   ierr = PetscOptionsHasName(((PetscObject)snes)->options,((PetscObject)snes)->prefix, "-dmsnes_check", &check);CHKERRQ(ierr);
2740   if (!check) PetscFunctionReturn(0);
2741   ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
2742   ierr = VecDuplicate(u, &sol);CHKERRQ(ierr);
2743   ierr = SNESSetSolution(snes, sol);CHKERRQ(ierr);
2744   ierr = DMSNESCheckFromOptions_Internal(snes, dm, u, sol, exactFuncs, ctxs);CHKERRQ(ierr);
2745   ierr = VecDestroy(&sol);CHKERRQ(ierr);
2746   PetscFunctionReturn(0);
2747 }
2748