xref: /petsc/src/dm/impls/da/dalocal.c (revision f66eea085cceefc5191b4b3d61f096e7c3d8e689)
1 
2 /*
3   Code for manipulating distributed regular arrays in parallel.
4 */
5 
6 #include <petsc-private/dmdaimpl.h>    /*I   "petscdmda.h"   I*/
7 #include <petscbt.h>
8 #include <petscsf.h>
9 #include <petscds.h>
10 #include <petscfe.h>
11 
12 /*
13    This allows the DMDA vectors to properly tell MATLAB their dimensions
14 */
15 #if defined(PETSC_HAVE_MATLAB_ENGINE)
16 #include <engine.h>   /* MATLAB include file */
17 #include <mex.h>      /* MATLAB include file */
18 #undef __FUNCT__
19 #define __FUNCT__ "VecMatlabEnginePut_DA2d"
20 static PetscErrorCode  VecMatlabEnginePut_DA2d(PetscObject obj,void *mengine)
21 {
22   PetscErrorCode ierr;
23   PetscInt       n,m;
24   Vec            vec = (Vec)obj;
25   PetscScalar    *array;
26   mxArray        *mat;
27   DM             da;
28 
29   PetscFunctionBegin;
30   ierr = VecGetDM(vec, &da);CHKERRQ(ierr);
31   if (!da) SETERRQ(PetscObjectComm((PetscObject)vec),PETSC_ERR_ARG_WRONGSTATE,"Vector not associated with a DMDA");
32   ierr = DMDAGetGhostCorners(da,0,0,0,&m,&n,0);CHKERRQ(ierr);
33 
34   ierr = VecGetArray(vec,&array);CHKERRQ(ierr);
35 #if !defined(PETSC_USE_COMPLEX)
36   mat = mxCreateDoubleMatrix(m,n,mxREAL);
37 #else
38   mat = mxCreateDoubleMatrix(m,n,mxCOMPLEX);
39 #endif
40   ierr = PetscMemcpy(mxGetPr(mat),array,n*m*sizeof(PetscScalar));CHKERRQ(ierr);
41   ierr = PetscObjectName(obj);CHKERRQ(ierr);
42   engPutVariable((Engine*)mengine,obj->name,mat);
43 
44   ierr = VecRestoreArray(vec,&array);CHKERRQ(ierr);
45   PetscFunctionReturn(0);
46 }
47 #endif
48 
49 
50 #undef __FUNCT__
51 #define __FUNCT__ "DMCreateLocalVector_DA"
52 PetscErrorCode  DMCreateLocalVector_DA(DM da,Vec *g)
53 {
54   PetscErrorCode ierr;
55   DM_DA          *dd = (DM_DA*)da->data;
56 
57   PetscFunctionBegin;
58   PetscValidHeaderSpecific(da,DM_CLASSID,1);
59   PetscValidPointer(g,2);
60   if (da->defaultSection) {
61     ierr = DMCreateLocalVector_Section_Private(da,g);CHKERRQ(ierr);
62   } else {
63     ierr = VecCreate(PETSC_COMM_SELF,g);CHKERRQ(ierr);
64     ierr = VecSetSizes(*g,dd->nlocal,PETSC_DETERMINE);CHKERRQ(ierr);
65     ierr = VecSetBlockSize(*g,dd->w);CHKERRQ(ierr);
66     ierr = VecSetType(*g,da->vectype);CHKERRQ(ierr);
67     ierr = VecSetDM(*g, da);CHKERRQ(ierr);
68 #if defined(PETSC_HAVE_MATLAB_ENGINE)
69     if (dd->w == 1  && da->dim == 2) {
70       ierr = PetscObjectComposeFunction((PetscObject)*g,"PetscMatlabEnginePut_C",VecMatlabEnginePut_DA2d);CHKERRQ(ierr);
71     }
72 #endif
73   }
74   PetscFunctionReturn(0);
75 }
76 
77 #undef __FUNCT__
78 #define __FUNCT__ "DMDAGetNumCells"
79 /*@
80   DMDAGetNumCells - Get the number of cells in the local piece of the DMDA. This includes ghost cells.
81 
82   Input Parameter:
83 . dm - The DM object
84 
85   Output Parameters:
86 + numCellsX - The number of local cells in the x-direction
87 . numCellsY - The number of local cells in the y-direction
88 . numCellsZ - The number of local cells in the z-direction
89 - numCells - The number of local cells
90 
91   Level: developer
92 
93 .seealso: DMDAGetCellPoint()
94 @*/
95 PetscErrorCode DMDAGetNumCells(DM dm, PetscInt *numCellsX, PetscInt *numCellsY, PetscInt *numCellsZ, PetscInt *numCells)
96 {
97   DM_DA         *da  = (DM_DA*) dm->data;
98   const PetscInt dim = dm->dim;
99   const PetscInt mx  = (da->Xe - da->Xs)/da->w, my = da->Ye - da->Ys, mz = da->Ze - da->Zs;
100   const PetscInt nC  = (mx)*(dim > 1 ? (my)*(dim > 2 ? (mz) : 1) : 1);
101 
102   PetscFunctionBegin;
103   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
104   if (numCellsX) {
105     PetscValidIntPointer(numCellsX,2);
106     *numCellsX = mx;
107   }
108   if (numCellsY) {
109     PetscValidIntPointer(numCellsX,3);
110     *numCellsY = my;
111   }
112   if (numCellsZ) {
113     PetscValidIntPointer(numCellsX,4);
114     *numCellsZ = mz;
115   }
116   if (numCells) {
117     PetscValidIntPointer(numCells,5);
118     *numCells = nC;
119   }
120   PetscFunctionReturn(0);
121 }
122 
123 #undef __FUNCT__
124 #define __FUNCT__ "DMDAGetCellPoint"
125 /*@
126   DMDAGetCellPoint - Get the DM point corresponding to the tuple (i, j, k) in the DMDA
127 
128   Input Parameters:
129 + dm - The DM object
130 - i,j,k - The global indices for the cell
131 
132   Output Parameters:
133 . point - The local DM point
134 
135   Level: developer
136 
137 .seealso: DMDAGetNumCells()
138 @*/
139 PetscErrorCode DMDAGetCellPoint(DM dm, PetscInt i, PetscInt j, PetscInt k, PetscInt *point)
140 {
141   const PetscInt dim = dm->dim;
142   DMDALocalInfo  info;
143   PetscErrorCode ierr;
144 
145   PetscFunctionBegin;
146   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
147   PetscValidIntPointer(point,5);
148   ierr = DMDAGetLocalInfo(dm, &info);CHKERRQ(ierr);
149   if (dim > 0) {if ((i < info.gxs) || (i >= info.gxs+info.gxm)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "X index %d not in [%d, %d)", i, info.gxs, info.gxs+info.gxm);}
150   if (dim > 1) {if ((i < info.gys) || (i >= info.gys+info.gym)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Y index %d not in [%d, %d)", i, info.gys, info.gys+info.gym);}
151   if (dim > 2) {if ((i < info.gzs) || (i >= info.gzs+info.gzm)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Z index %d not in [%d, %d)", i, info.gzs, info.gzs+info.gzm);}
152   *point = i + (dim > 1 ? (j + (dim > 2 ? k*info.gym : 0))*info.gxm : 0);
153   PetscFunctionReturn(0);
154 }
155 
156 #undef __FUNCT__
157 #define __FUNCT__ "DMDAGetNumVertices"
158 PetscErrorCode DMDAGetNumVertices(DM dm, PetscInt *numVerticesX, PetscInt *numVerticesY, PetscInt *numVerticesZ, PetscInt *numVertices)
159 {
160   DM_DA          *da = (DM_DA*) dm->data;
161   const PetscInt dim = dm->dim;
162   const PetscInt mx  = (da->Xe - da->Xs)/da->w, my = da->Ye - da->Ys, mz = da->Ze - da->Zs;
163   const PetscInt nVx = mx+1;
164   const PetscInt nVy = dim > 1 ? (my+1) : 1;
165   const PetscInt nVz = dim > 2 ? (mz+1) : 1;
166   const PetscInt nV  = nVx*nVy*nVz;
167 
168   PetscFunctionBegin;
169   if (numVerticesX) {
170     PetscValidIntPointer(numVerticesX,2);
171     *numVerticesX = nVx;
172   }
173   if (numVerticesY) {
174     PetscValidIntPointer(numVerticesY,3);
175     *numVerticesY = nVy;
176   }
177   if (numVerticesZ) {
178     PetscValidIntPointer(numVerticesZ,4);
179     *numVerticesZ = nVz;
180   }
181   if (numVertices) {
182     PetscValidIntPointer(numVertices,5);
183     *numVertices = nV;
184   }
185   PetscFunctionReturn(0);
186 }
187 
188 #undef __FUNCT__
189 #define __FUNCT__ "DMDAGetNumFaces"
190 PetscErrorCode DMDAGetNumFaces(DM dm, PetscInt *numXFacesX, PetscInt *numXFaces, PetscInt *numYFacesY, PetscInt *numYFaces, PetscInt *numZFacesZ, PetscInt *numZFaces)
191 {
192   DM_DA          *da = (DM_DA*) dm->data;
193   const PetscInt dim = dm->dim;
194   const PetscInt mx  = (da->Xe - da->Xs)/da->w, my = da->Ye - da->Ys, mz = da->Ze - da->Zs;
195   const PetscInt nxF = (dim > 1 ? (my)*(dim > 2 ? (mz) : 1) : 1);
196   const PetscInt nXF = (mx+1)*nxF;
197   const PetscInt nyF = mx*(dim > 2 ? mz : 1);
198   const PetscInt nYF = dim > 1 ? (my+1)*nyF : 0;
199   const PetscInt nzF = mx*(dim > 1 ? my : 0);
200   const PetscInt nZF = dim > 2 ? (mz+1)*nzF : 0;
201 
202   PetscFunctionBegin;
203   if (numXFacesX) {
204     PetscValidIntPointer(numXFacesX,2);
205     *numXFacesX = nxF;
206   }
207   if (numXFaces) {
208     PetscValidIntPointer(numXFaces,3);
209     *numXFaces = nXF;
210   }
211   if (numYFacesY) {
212     PetscValidIntPointer(numYFacesY,4);
213     *numYFacesY = nyF;
214   }
215   if (numYFaces) {
216     PetscValidIntPointer(numYFaces,5);
217     *numYFaces = nYF;
218   }
219   if (numZFacesZ) {
220     PetscValidIntPointer(numZFacesZ,6);
221     *numZFacesZ = nzF;
222   }
223   if (numZFaces) {
224     PetscValidIntPointer(numZFaces,7);
225     *numZFaces = nZF;
226   }
227   PetscFunctionReturn(0);
228 }
229 
230 #undef __FUNCT__
231 #define __FUNCT__ "DMDAGetHeightStratum"
232 PetscErrorCode DMDAGetHeightStratum(DM dm, PetscInt height, PetscInt *pStart, PetscInt *pEnd)
233 {
234   const PetscInt dim = dm->dim;
235   PetscInt       nC, nV, nXF, nYF, nZF;
236   PetscErrorCode ierr;
237 
238   PetscFunctionBegin;
239   if (pStart) PetscValidIntPointer(pStart,3);
240   if (pEnd)   PetscValidIntPointer(pEnd,4);
241   ierr = DMDAGetNumCells(dm, NULL, NULL, NULL, &nC);CHKERRQ(ierr);
242   ierr = DMDAGetNumVertices(dm, NULL, NULL, NULL, &nV);CHKERRQ(ierr);
243   ierr = DMDAGetNumFaces(dm, NULL, &nXF, NULL, &nYF, NULL, &nZF);CHKERRQ(ierr);
244   if (height == 0) {
245     /* Cells */
246     if (pStart) *pStart = 0;
247     if (pEnd)   *pEnd   = nC;
248   } else if (height == 1) {
249     /* Faces */
250     if (pStart) *pStart = nC+nV;
251     if (pEnd)   *pEnd   = nC+nV+nXF+nYF+nZF;
252   } else if (height == dim) {
253     /* Vertices */
254     if (pStart) *pStart = nC;
255     if (pEnd)   *pEnd   = nC+nV;
256   } else if (height < 0) {
257     /* All points */
258     if (pStart) *pStart = 0;
259     if (pEnd)   *pEnd   = nC+nV+nXF+nYF+nZF;
260   } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No points of height %d in the DA", height);
261   PetscFunctionReturn(0);
262 }
263 
264 #undef __FUNCT__
265 #define __FUNCT__ "DMDAGetDepthStratum"
266 PetscErrorCode DMDAGetDepthStratum(DM dm, PetscInt depth, PetscInt *pStart, PetscInt *pEnd)
267 {
268   const PetscInt dim = dm->dim;
269   PetscInt       nC, nV, nXF, nYF, nZF;
270   PetscErrorCode ierr;
271 
272   PetscFunctionBegin;
273   if (pStart) PetscValidIntPointer(pStart,3);
274   if (pEnd)   PetscValidIntPointer(pEnd,4);
275   ierr = DMDAGetNumCells(dm, NULL, NULL, NULL, &nC);CHKERRQ(ierr);
276   ierr = DMDAGetNumVertices(dm, NULL, NULL, NULL, &nV);CHKERRQ(ierr);
277   ierr = DMDAGetNumFaces(dm, NULL, &nXF, NULL, &nYF, NULL, &nZF);CHKERRQ(ierr);
278   if (depth == dim) {
279     /* Cells */
280     if (pStart) *pStart = 0;
281     if (pEnd)   *pEnd   = nC;
282   } else if (depth == dim-1) {
283     /* Faces */
284     if (pStart) *pStart = nC+nV;
285     if (pEnd)   *pEnd   = nC+nV+nXF+nYF+nZF;
286   } else if (depth == 0) {
287     /* Vertices */
288     if (pStart) *pStart = nC;
289     if (pEnd)   *pEnd   = nC+nV;
290   } else if (depth < 0) {
291     /* All points */
292     if (pStart) *pStart = 0;
293     if (pEnd)   *pEnd   = nC+nV+nXF+nYF+nZF;
294   } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No points of depth %d in the DA", depth);
295   PetscFunctionReturn(0);
296 }
297 
298 #undef __FUNCT__
299 #define __FUNCT__ "DMDAGetConeSize"
300 PetscErrorCode DMDAGetConeSize(DM dm, PetscInt p, PetscInt *coneSize)
301 {
302   const PetscInt dim = dm->dim;
303   PetscInt       nC, nV, nXF, nYF, nZF;
304   PetscErrorCode ierr;
305 
306   PetscFunctionBegin;
307   *coneSize = 0;
308   ierr = DMDAGetNumCells(dm, NULL, NULL, NULL, &nC);CHKERRQ(ierr);
309   ierr = DMDAGetNumVertices(dm, NULL, NULL, NULL, &nV);CHKERRQ(ierr);
310   ierr = DMDAGetNumFaces(dm, NULL, &nXF, NULL, &nYF, NULL, &nZF);CHKERRQ(ierr);
311   switch (dim) {
312   case 2:
313     if (p >= 0) {
314       if (p < nC) {
315         *coneSize = 4;
316       } else if (p < nC+nV) {
317         *coneSize = 0;
318       } else if (p < nC+nV+nXF+nYF+nZF) {
319         *coneSize = 2;
320       } else SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Point %d should be in [0, %d)", p, nC+nV+nXF+nYF+nZF);
321     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative point %d is invalid", p);
322     break;
323   case 3:
324     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Too lazy to do 3D");
325     break;
326   }
327   PetscFunctionReturn(0);
328 }
329 
330 #undef __FUNCT__
331 #define __FUNCT__ "DMDAGetCone"
332 PetscErrorCode DMDAGetCone(DM dm, PetscInt p, PetscInt *cone[])
333 {
334   const PetscInt dim = dm->dim;
335   PetscInt       nCx, nCy, nCz, nC, nVx, nVy, nVz, nV, nxF, nyF, nzF, nXF, nYF, nZF;
336   PetscErrorCode ierr;
337 
338   PetscFunctionBegin;
339   if (!cone) {ierr = DMGetWorkArray(dm, 6, PETSC_INT, cone);CHKERRQ(ierr);}
340   ierr = DMDAGetNumCells(dm, &nCx, &nCy, &nCz, &nC);CHKERRQ(ierr);
341   ierr = DMDAGetNumVertices(dm, &nVx, &nVy, &nVz, &nV);CHKERRQ(ierr);
342   ierr = DMDAGetNumFaces(dm, &nxF, &nXF, &nyF, &nYF, &nzF, &nZF);CHKERRQ(ierr);
343   switch (dim) {
344   case 2:
345     if (p >= 0) {
346       if (p < nC) {
347         const PetscInt cy = p / nCx;
348         const PetscInt cx = p % nCx;
349 
350         (*cone)[0] = cy*nxF + cx + nC+nV;
351         (*cone)[1] = cx*nyF + cy + nyF + nC+nV+nXF;
352         (*cone)[2] = cy*nxF + cx + nxF + nC+nV;
353         (*cone)[3] = cx*nyF + cy + nC+nV+nXF;
354         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Too lazy to do cell cones");
355       } else if (p < nC+nV) {
356       } else if (p < nC+nV+nXF) {
357         const PetscInt fy = (p - nC+nV) / nxF;
358         const PetscInt fx = (p - nC+nV) % nxF;
359 
360         (*cone)[0] = fy*nVx + fx + nC;
361         (*cone)[1] = fy*nVx + fx + 1 + nC;
362       } else if (p < nC+nV+nXF+nYF) {
363         const PetscInt fx = (p - nC+nV+nXF) / nyF;
364         const PetscInt fy = (p - nC+nV+nXF) % nyF;
365 
366         (*cone)[0] = fy*nVx + fx + nC;
367         (*cone)[1] = fy*nVx + fx + nVx + nC;
368       } else SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Point %d should be in [0, %d)", p, nC+nV+nXF+nYF+nZF);
369     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative point %d is invalid", p);
370     break;
371   case 3:
372     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Too lazy to do 3D");
373     break;
374   }
375   PetscFunctionReturn(0);
376 }
377 
378 #undef __FUNCT__
379 #define __FUNCT__ "DMDARestoreCone"
380 PetscErrorCode DMDARestoreCone(DM dm, PetscInt p, PetscInt *cone[])
381 {
382   PetscErrorCode ierr;
383 
384   PetscFunctionBegin;
385   ierr = DMGetWorkArray(dm, 6, PETSC_INT, cone);CHKERRQ(ierr);
386   PetscFunctionReturn(0);
387 }
388 
389 #undef __FUNCT__
390 #define __FUNCT__ "DMDACreateSection"
391 /*@C
392   DMDACreateSection - Create a PetscSection inside the DMDA that describes data layout. This allows multiple fields with
393   different numbers of dofs on vertices, cells, and faces in each direction.
394 
395   Input Parameters:
396 + dm- The DMDA
397 . numFields - The number of fields
398 . numComp - The number of components in each field
399 . numDof - The number of dofs per dimension for each field
400 . numFaceDof - The number of dofs per face for each field and direction, or NULL
401 
402   Level: developer
403 
404   Note:
405   The default DMDA numbering is as follows:
406 
407     - Cells:    [0,             nC)
408     - Vertices: [nC,            nC+nV)
409     - X-Faces:  [nC+nV,         nC+nV+nXF)         normal is +- x-dir
410     - Y-Faces:  [nC+nV+nXF,     nC+nV+nXF+nYF)     normal is +- y-dir
411     - Z-Faces:  [nC+nV+nXF+nYF, nC+nV+nXF+nYF+nZF) normal is +- z-dir
412 
413   We interpret the default DMDA partition as a cell partition, and the data assignment as a cell assignment.
414 @*/
415 PetscErrorCode DMDACreateSection(DM dm, const PetscInt numComp[], const PetscInt numDof[], const PetscInt numFaceDof[], PetscSection *s)
416 {
417   PetscSection      section;
418   const PetscInt    dim = dm->dim;
419   PetscInt          numFields, numVertexTotDof = 0, numCellTotDof = 0, numFaceTotDof[3] = {0, 0, 0};
420   PetscBT           isLeaf;
421   PetscSF           sf;
422   PetscMPIInt       rank;
423   const PetscMPIInt *neighbors;
424   PetscInt          *localPoints;
425   PetscSFNode       *remotePoints;
426   PetscInt          nleaves = 0,  nleavesCheck = 0, nL = 0;
427   PetscInt          nC, nVx, nVy, nVz, nV, nxF, nXF, nyF, nYF, nzF, nZF;
428   PetscInt          pStart, pEnd, cStart, cEnd, vStart, vEnd, fStart, fEnd, xfStart, xfEnd, yfStart, yfEnd, zfStart, zfEnd;
429   PetscInt          f, v, c, xf, yf, zf, xn, yn, zn;
430   PetscErrorCode    ierr;
431 
432   PetscFunctionBegin;
433   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
434   PetscValidPointer(s, 4);
435   ierr    = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
436   ierr    = DMDAGetNumCells(dm, NULL, NULL, NULL, &nC);CHKERRQ(ierr);
437   ierr    = DMDAGetNumVertices(dm, &nVx, &nVy, &nVz, &nV);CHKERRQ(ierr);
438   ierr    = DMDAGetNumFaces(dm, &nxF, &nXF, &nyF, &nYF, &nzF, &nZF);CHKERRQ(ierr);
439   ierr    = DMDAGetHeightStratum(dm, -1,  &pStart, &pEnd);CHKERRQ(ierr);
440   ierr    = DMDAGetHeightStratum(dm, 0,   &cStart, &cEnd);CHKERRQ(ierr);
441   ierr    = DMDAGetHeightStratum(dm, 1,   &fStart, &fEnd);CHKERRQ(ierr);
442   ierr    = DMDAGetHeightStratum(dm, dim, &vStart, &vEnd);CHKERRQ(ierr);
443   xfStart = vEnd;  xfEnd = xfStart+nXF;
444   yfStart = xfEnd; yfEnd = yfStart+nYF;
445   zfStart = yfEnd; zfEnd = zfStart+nZF;
446   if (zfEnd != fEnd) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid face end %d, should be %d", zfEnd, fEnd);
447   /* Create local section */
448   ierr = DMDAGetInfo(dm, 0,0,0,0,0,0,0, &numFields, 0,0,0,0,0);CHKERRQ(ierr);
449   for (f = 0; f < numFields; ++f) {
450     numVertexTotDof  += numDof[f*(dim+1)+0];
451     numCellTotDof    += numDof[f*(dim+1)+dim];
452     numFaceTotDof[0] += dim > 0 ? (numFaceDof ? numFaceDof[f*dim+0] : numDof[f*(dim+1)+dim-1]) : 0;
453     numFaceTotDof[1] += dim > 1 ? (numFaceDof ? numFaceDof[f*dim+1] : numDof[f*(dim+1)+dim-1]) : 0;
454     numFaceTotDof[2] += dim > 2 ? (numFaceDof ? numFaceDof[f*dim+2] : numDof[f*(dim+1)+dim-1]) : 0;
455   }
456   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &section);CHKERRQ(ierr);
457   if (numFields > 0) {
458     ierr = PetscSectionSetNumFields(section, numFields);CHKERRQ(ierr);
459     for (f = 0; f < numFields; ++f) {
460       const char *name;
461 
462       ierr = DMDAGetFieldName(dm, f, &name);CHKERRQ(ierr);
463       ierr = PetscSectionSetFieldName(section, f, name ? name : "Field");CHKERRQ(ierr);
464       if (numComp) {
465         ierr = PetscSectionSetFieldComponents(section, f, numComp[f]);CHKERRQ(ierr);
466       }
467     }
468   }
469   ierr = PetscSectionSetChart(section, pStart, pEnd);CHKERRQ(ierr);
470   for (v = vStart; v < vEnd; ++v) {
471     for (f = 0; f < numFields; ++f) {
472       ierr = PetscSectionSetFieldDof(section, v, f, numDof[f*(dim+1)+0]);CHKERRQ(ierr);
473     }
474     ierr = PetscSectionSetDof(section, v, numVertexTotDof);CHKERRQ(ierr);
475   }
476   for (xf = xfStart; xf < xfEnd; ++xf) {
477     for (f = 0; f < numFields; ++f) {
478       ierr = PetscSectionSetFieldDof(section, xf, f, numFaceDof ? numFaceDof[f*dim+0] : numDof[f*(dim+1)+dim-1]);CHKERRQ(ierr);
479     }
480     ierr = PetscSectionSetDof(section, xf, numFaceTotDof[0]);CHKERRQ(ierr);
481   }
482   for (yf = yfStart; yf < yfEnd; ++yf) {
483     for (f = 0; f < numFields; ++f) {
484       ierr = PetscSectionSetFieldDof(section, yf, f, numFaceDof ? numFaceDof[f*dim+1] : numDof[f*(dim+1)+dim-1]);CHKERRQ(ierr);
485     }
486     ierr = PetscSectionSetDof(section, yf, numFaceTotDof[1]);CHKERRQ(ierr);
487   }
488   for (zf = zfStart; zf < zfEnd; ++zf) {
489     for (f = 0; f < numFields; ++f) {
490       ierr = PetscSectionSetFieldDof(section, zf, f, numFaceDof ? numFaceDof[f*dim+2] : numDof[f*(dim+1)+dim-1]);CHKERRQ(ierr);
491     }
492     ierr = PetscSectionSetDof(section, zf, numFaceTotDof[2]);CHKERRQ(ierr);
493   }
494   for (c = cStart; c < cEnd; ++c) {
495     for (f = 0; f < numFields; ++f) {
496       ierr = PetscSectionSetFieldDof(section, c, f, numDof[f*(dim+1)+dim]);CHKERRQ(ierr);
497     }
498     ierr = PetscSectionSetDof(section, c, numCellTotDof);CHKERRQ(ierr);
499   }
500   ierr = PetscSectionSetUp(section);CHKERRQ(ierr);
501   /* Create mesh point SF */
502   ierr = PetscBTCreate(pEnd-pStart, &isLeaf);CHKERRQ(ierr);
503   ierr = DMDAGetNeighbors(dm, &neighbors);CHKERRQ(ierr);
504   for (zn = 0; zn < (dim > 2 ? 3 : 1); ++zn) {
505     for (yn = 0; yn < (dim > 1 ? 3 : 1); ++yn) {
506       for (xn = 0; xn < 3; ++xn) {
507         const PetscInt xp       = xn-1, yp = dim > 1 ? yn-1 : 0, zp = dim > 2 ? zn-1 : 0;
508         const PetscInt neighbor = neighbors[(zn*3+yn)*3+xn];
509         PetscInt       xv, yv, zv;
510 
511         if (neighbor >= 0 && neighbor < rank) {
512           if (xp < 0) { /* left */
513             if (yp < 0) { /* bottom */
514               if (zp < 0) { /* back */
515                 const PetscInt localVertex  = (      0*nVy +     0)*nVx +     0 + nC; /* left bottom back vertex */
516                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
517               } else if (zp > 0) { /* front */
518                 const PetscInt localVertex  = ((nVz-1)*nVy +     0)*nVx +     0 + nC; /* left bottom front vertex */
519                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
520               } else {
521                 for (zv = 0; zv < nVz; ++zv) {
522                   const PetscInt localVertex  = (zv*nVy +     0)*nVx +     0 + nC; /* left bottom vertices */
523                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
524                 }
525               }
526             } else if (yp > 0) { /* top */
527               if (zp < 0) { /* back */
528                 const PetscInt localVertex  = (      0*nVy + nVy-1)*nVx +     0 + nC; /* left top back vertex */
529                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
530               } else if (zp > 0) { /* front */
531                 const PetscInt localVertex  = ((nVz-1)*nVy + nVy-1)*nVx +     0 + nC; /* left top front vertex */
532                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
533               } else {
534                 for (zv = 0; zv < nVz; ++zv) {
535                   const PetscInt localVertex  = (zv*nVy + nVy-1)*nVx +     0 + nC; /* left top vertices */
536                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
537                 }
538               }
539             } else {
540               if (zp < 0) { /* back */
541                 for (yv = 0; yv < nVy; ++yv) {
542                   const PetscInt localVertex  = (      0*nVy + yv)*nVx +     0 + nC; /* left back vertices */
543                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
544                 }
545               } else if (zp > 0) { /* front */
546                 for (yv = 0; yv < nVy; ++yv) {
547                   const PetscInt localVertex  = ((nVz-1)*nVy + yv)*nVx +     0 + nC; /* left front vertices */
548                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
549                 }
550               } else {
551                 for (zv = 0; zv < nVz; ++zv) {
552                   for (yv = 0; yv < nVy; ++yv) {
553                     const PetscInt localVertex  = (zv*nVy + yv)*nVx +     0 + nC; /* left vertices */
554                     if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
555                   }
556                 }
557 #if 0
558                 for (xf = 0; xf < nxF; ++xf) {
559                   /* THIS IS WRONG */
560                   const PetscInt localFace  = 0 + nC+nV; /* left faces */
561                   if (!PetscBTLookupSet(isLeaf, localFace)) ++nleaves;
562                 }
563 #endif
564               }
565             }
566           } else if (xp > 0) { /* right */
567             if (yp < 0) { /* bottom */
568               if (zp < 0) { /* back */
569                 const PetscInt localVertex  = (      0*nVy +     0)*nVx + nVx-1 + nC; /* right bottom back vertex */
570                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
571               } else if (zp > 0) { /* front */
572                 const PetscInt localVertex  = ((nVz-1)*nVy +     0)*nVx + nVx-1 + nC; /* right bottom front vertex */
573                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
574               } else {
575                 for (zv = 0; zv < nVz; ++zv) {
576                   const PetscInt localVertex  = (zv*nVy +     0)*nVx + nVx-1 + nC; /* right bottom vertices */
577                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
578                 }
579               }
580             } else if (yp > 0) { /* top */
581               if (zp < 0) { /* back */
582                 const PetscInt localVertex  = (      0*nVy + nVy-1)*nVx + nVx-1 + nC; /* right top back vertex */
583                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
584               } else if (zp > 0) { /* front */
585                 const PetscInt localVertex  = ((nVz-1)*nVy + nVy-1)*nVx + nVx-1 + nC; /* right top front vertex */
586                 if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
587               } else {
588                 for (zv = 0; zv < nVz; ++zv) {
589                   const PetscInt localVertex  = (zv*nVy + nVy-1)*nVx + nVx-1 + nC; /* right top vertices */
590                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
591                 }
592               }
593             } else {
594               if (zp < 0) { /* back */
595                 for (yv = 0; yv < nVy; ++yv) {
596                   const PetscInt localVertex  = (      0*nVy + yv)*nVx + nVx-1 + nC; /* right back vertices */
597                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
598                 }
599               } else if (zp > 0) { /* front */
600                 for (yv = 0; yv < nVy; ++yv) {
601                   const PetscInt localVertex  = ((nVz-1)*nVy + yv)*nVx + nVx-1 + nC; /* right front vertices */
602                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
603                 }
604               } else {
605                 for (zv = 0; zv < nVz; ++zv) {
606                   for (yv = 0; yv < nVy; ++yv) {
607                     const PetscInt localVertex  = (zv*nVy + yv)*nVx + nVx-1 + nC; /* right vertices */
608                     if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
609                   }
610                 }
611 #if 0
612                 for (xf = 0; xf < nxF; ++xf) {
613                   /* THIS IS WRONG */
614                   const PetscInt localFace  = 0 + nC+nV; /* right faces */
615                   if (!PetscBTLookupSet(isLeaf, localFace)) ++nleaves;
616                 }
617 #endif
618               }
619             }
620           } else {
621             if (yp < 0) { /* bottom */
622               if (zp < 0) { /* back */
623                 for (xv = 0; xv < nVx; ++xv) {
624                   const PetscInt localVertex  = (      0*nVy +     0)*nVx + xv + nC; /* bottom back vertices */
625                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
626                 }
627               } else if (zp > 0) { /* front */
628                 for (xv = 0; xv < nVx; ++xv) {
629                   const PetscInt localVertex  = ((nVz-1)*nVy +     0)*nVx + xv + nC; /* bottom front vertices */
630                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
631                 }
632               } else {
633                 for (zv = 0; zv < nVz; ++zv) {
634                   for (xv = 0; xv < nVx; ++xv) {
635                     const PetscInt localVertex  = (zv*nVy +     0)*nVx + xv + nC; /* bottom vertices */
636                     if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
637                   }
638                 }
639 #if 0
640                 for (yf = 0; yf < nyF; ++yf) {
641                   /* THIS IS WRONG */
642                   const PetscInt localFace  = 0 + nC+nV; /* bottom faces */
643                   if (!PetscBTLookupSet(isLeaf, localVFace)) ++nleaves;
644                 }
645 #endif
646               }
647             } else if (yp > 0) { /* top */
648               if (zp < 0) { /* back */
649                 for (xv = 0; xv < nVx; ++xv) {
650                   const PetscInt localVertex  = (      0*nVy + nVy-1)*nVx + xv + nC; /* top back vertices */
651                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
652                 }
653               } else if (zp > 0) { /* front */
654                 for (xv = 0; xv < nVx; ++xv) {
655                   const PetscInt localVertex  = ((nVz-1)*nVy + nVy-1)*nVx + xv + nC; /* top front vertices */
656                   if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
657                 }
658               } else {
659                 for (zv = 0; zv < nVz; ++zv) {
660                   for (xv = 0; xv < nVx; ++xv) {
661                     const PetscInt localVertex  = (zv*nVy + nVy-1)*nVx + xv + nC; /* top vertices */
662                     if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
663                   }
664                 }
665 #if 0
666                 for (yf = 0; yf < nyF; ++yf) {
667                   /* THIS IS WRONG */
668                   const PetscInt localFace  = 0 + nC+nV; /* top faces */
669                   if (!PetscBTLookupSet(isLeaf, localVFace)) ++nleaves;
670                 }
671 #endif
672               }
673             } else {
674               if (zp < 0) { /* back */
675                 for (yv = 0; yv < nVy; ++yv) {
676                   for (xv = 0; xv < nVx; ++xv) {
677                     const PetscInt localVertex  = (      0*nVy + yv)*nVx + xv + nC; /* back vertices */
678                     if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
679                   }
680                 }
681 #if 0
682                 for (zf = 0; zf < nzF; ++zf) {
683                   /* THIS IS WRONG */
684                   const PetscInt localFace  = 0 + nC+nV; /* back faces */
685                   if (!PetscBTLookupSet(isLeaf, localFace)) ++nleaves;
686                 }
687 #endif
688               } else if (zp > 0) { /* front */
689                 for (yv = 0; yv < nVy; ++yv) {
690                   for (xv = 0; xv < nVx; ++xv) {
691                     const PetscInt localVertex  = ((nVz-1)*nVy + yv)*nVx + xv + nC; /* front vertices */
692                     if (!PetscBTLookupSet(isLeaf, localVertex)) ++nleaves;
693                   }
694                 }
695 #if 0
696                 for (zf = 0; zf < nzF; ++zf) {
697                   /* THIS IS WRONG */
698                   const PetscInt localFace  = 0 + nC+nV; /* front faces */
699                   if (!PetscBTLookupSet(isLeaf, localFace)) ++nleaves;
700                 }
701 #endif
702               } else {
703                 /* Nothing is shared from the interior */
704               }
705             }
706           }
707         }
708       }
709     }
710   }
711   ierr = PetscBTMemzero(pEnd-pStart, isLeaf);CHKERRQ(ierr);
712   ierr = PetscMalloc2(nleaves,&localPoints,nleaves,&remotePoints);CHKERRQ(ierr);
713   for (zn = 0; zn < (dim > 2 ? 3 : 1); ++zn) {
714     for (yn = 0; yn < (dim > 1 ? 3 : 1); ++yn) {
715       for (xn = 0; xn < 3; ++xn) {
716         const PetscInt xp       = xn-1, yp = dim > 1 ? yn-1 : 0, zp = dim > 2 ? zn-1 : 0;
717         const PetscInt neighbor = neighbors[(zn*3+yn)*3+xn];
718         PetscInt       xv, yv, zv;
719 
720         if (neighbor >= 0 && neighbor < rank) {
721           if (xp < 0) { /* left */
722             if (yp < 0) { /* bottom */
723               if (zp < 0) { /* back */
724                 const PetscInt localVertex  = (      0*nVy +     0)*nVx +     0 + nC; /* left bottom back vertex */
725                 const PetscInt remoteVertex = ((nVz-1)*nVy + nVy-1)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
726 
727                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
728                   localPoints[nL]        = localVertex;
729                   remotePoints[nL].rank  = neighbor;
730                   remotePoints[nL].index = remoteVertex;
731                   ++nL;
732                 }
733               } else if (zp > 0) { /* front */
734                 const PetscInt localVertex  = ((nVz-1)*nVy +     0)*nVx +     0 + nC; /* left bottom front vertex */
735                 const PetscInt remoteVertex = (      0*nVy + nVy-1)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
736 
737                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
738                   localPoints[nL]        = localVertex;
739                   remotePoints[nL].rank  = neighbor;
740                   remotePoints[nL].index = remoteVertex;
741                   ++nL;
742                 }
743               } else {
744                 for (zv = 0; zv < nVz; ++zv) {
745                   const PetscInt localVertex  = (zv*nVy +     0)*nVx +     0 + nC; /* left bottom vertices */
746                   const PetscInt remoteVertex = (zv*nVy + nVy-1)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
747 
748                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
749                     localPoints[nL]        = localVertex;
750                     remotePoints[nL].rank  = neighbor;
751                     remotePoints[nL].index = remoteVertex;
752                     ++nL;
753                   }
754                 }
755               }
756             } else if (yp > 0) { /* top */
757               if (zp < 0) { /* back */
758                 const PetscInt localVertex  = (      0*nVy + nVy-1)*nVx +     0 + nC; /* left top back vertex */
759                 const PetscInt remoteVertex = ((nVz-1)*nVy +     0)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
760 
761                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
762                   localPoints[nL]        = localVertex;
763                   remotePoints[nL].rank  = neighbor;
764                   remotePoints[nL].index = remoteVertex;
765                   ++nL;
766                 }
767               } else if (zp > 0) { /* front */
768                 const PetscInt localVertex  = ((nVz-1)*nVy + nVy-1)*nVx +     0 + nC; /* left top front vertex */
769                 const PetscInt remoteVertex = (      0*nVy +     0)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
770 
771                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
772                   localPoints[nL]        = localVertex;
773                   remotePoints[nL].rank  = neighbor;
774                   remotePoints[nL].index = remoteVertex;
775                   ++nL;
776                 }
777               } else {
778                 for (zv = 0; zv < nVz; ++zv) {
779                   const PetscInt localVertex  = (zv*nVy + nVy-1)*nVx +     0 + nC; /* left top vertices */
780                   const PetscInt remoteVertex = (zv*nVy +     0)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
781 
782                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
783                     localPoints[nL]        = localVertex;
784                     remotePoints[nL].rank  = neighbor;
785                     remotePoints[nL].index = remoteVertex;
786                     ++nL;
787                   }
788                 }
789               }
790             } else {
791               if (zp < 0) { /* back */
792                 for (yv = 0; yv < nVy; ++yv) {
793                   const PetscInt localVertex  = (      0*nVy + yv)*nVx +     0 + nC; /* left back vertices */
794                   const PetscInt remoteVertex = ((nVz-1)*nVy + yv)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
795 
796                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
797                     localPoints[nL]        = localVertex;
798                     remotePoints[nL].rank  = neighbor;
799                     remotePoints[nL].index = remoteVertex;
800                     ++nL;
801                   }
802                 }
803               } else if (zp > 0) { /* front */
804                 for (yv = 0; yv < nVy; ++yv) {
805                   const PetscInt localVertex  = ((nVz-1)*nVy + yv)*nVx +     0 + nC; /* left front vertices */
806                   const PetscInt remoteVertex = (      0*nVy + yv)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
807 
808                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
809                     localPoints[nL]        = localVertex;
810                     remotePoints[nL].rank  = neighbor;
811                     remotePoints[nL].index = remoteVertex;
812                     ++nL;
813                   }
814                 }
815               } else {
816                 for (zv = 0; zv < nVz; ++zv) {
817                   for (yv = 0; yv < nVy; ++yv) {
818                     const PetscInt localVertex  = (zv*nVy + yv)*nVx +     0 + nC; /* left vertices */
819                     const PetscInt remoteVertex = (zv*nVy + yv)*nVx + nVx-1 + nC; /* TODO: Correct this for neighbor sizes */
820 
821                     if (!PetscBTLookupSet(isLeaf, localVertex)) {
822                       localPoints[nL]        = localVertex;
823                       remotePoints[nL].rank  = neighbor;
824                       remotePoints[nL].index = remoteVertex;
825                       ++nL;
826                     }
827                   }
828                 }
829 #if 0
830                 for (xf = 0; xf < nxF; ++xf) {
831                   /* THIS IS WRONG */
832                   const PetscInt localFace  = 0 + nC+nV; /* left faces */
833                   const PetscInt remoteFace = 0 + nC+nV;
834 
835                   if (!PetscBTLookupSet(isLeaf, localFace)) {
836                     localPoints[nL]        = localFace;
837                     remotePoints[nL].rank  = neighbor;
838                     remotePoints[nL].index = remoteFace;
839                   }
840                 }
841 #endif
842               }
843             }
844           } else if (xp > 0) { /* right */
845             if (yp < 0) { /* bottom */
846               if (zp < 0) { /* back */
847                 const PetscInt localVertex  = (      0*nVy +     0)*nVx + nVx-1 + nC; /* right bottom back vertex */
848                 const PetscInt remoteVertex = ((nVz-1)*nVy + nVy-1)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
849 
850                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
851                   localPoints[nL]        = localVertex;
852                   remotePoints[nL].rank  = neighbor;
853                   remotePoints[nL].index = remoteVertex;
854                   ++nL;
855                 }
856               } else if (zp > 0) { /* front */
857                 const PetscInt localVertex  = ((nVz-1)*nVy +     0)*nVx + nVx-1 + nC; /* right bottom front vertex */
858                 const PetscInt remoteVertex = (      0*nVy + nVy-1)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
859 
860                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
861                   localPoints[nL]        = localVertex;
862                   remotePoints[nL].rank  = neighbor;
863                   remotePoints[nL].index = remoteVertex;
864                   ++nL;
865                 }
866               } else {
867                 nleavesCheck += nVz;
868                 for (zv = 0; zv < nVz; ++zv) {
869                   const PetscInt localVertex  = (zv*nVy +     0)*nVx + nVx-1 + nC; /* right bottom vertices */
870                   const PetscInt remoteVertex = (zv*nVy + nVy-1)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
871 
872                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
873                     localPoints[nL]        = localVertex;
874                     remotePoints[nL].rank  = neighbor;
875                     remotePoints[nL].index = remoteVertex;
876                     ++nL;
877                   }
878                 }
879               }
880             } else if (yp > 0) { /* top */
881               if (zp < 0) { /* back */
882                 const PetscInt localVertex  = (      0*nVy + nVy-1)*nVx + nVx-1 + nC; /* right top back vertex */
883                 const PetscInt remoteVertex = ((nVz-1)*nVy +     0)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
884 
885                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
886                   localPoints[nL]        = localVertex;
887                   remotePoints[nL].rank  = neighbor;
888                   remotePoints[nL].index = remoteVertex;
889                   ++nL;
890                 }
891               } else if (zp > 0) { /* front */
892                 const PetscInt localVertex  = ((nVz-1)*nVy + nVy-1)*nVx + nVx-1 + nC; /* right top front vertex */
893                 const PetscInt remoteVertex = (      0*nVy +     0)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
894 
895                 if (!PetscBTLookupSet(isLeaf, localVertex)) {
896                   localPoints[nL]        = localVertex;
897                   remotePoints[nL].rank  = neighbor;
898                   remotePoints[nL].index = remoteVertex;
899                   ++nL;
900                 }
901               } else {
902                 for (zv = 0; zv < nVz; ++zv) {
903                   const PetscInt localVertex  = (zv*nVy + nVy-1)*nVx + nVx-1 + nC; /* right top vertices */
904                   const PetscInt remoteVertex = (zv*nVy +     0)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
905 
906                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
907                     localPoints[nL]        = localVertex;
908                     remotePoints[nL].rank  = neighbor;
909                     remotePoints[nL].index = remoteVertex;
910                     ++nL;
911                   }
912                 }
913               }
914             } else {
915               if (zp < 0) { /* back */
916                 for (yv = 0; yv < nVy; ++yv) {
917                   const PetscInt localVertex  = (      0*nVy + yv)*nVx + nVx-1 + nC; /* right back vertices */
918                   const PetscInt remoteVertex = ((nVz-1)*nVy + yv)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
919 
920                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
921                     localPoints[nL]        = localVertex;
922                     remotePoints[nL].rank  = neighbor;
923                     remotePoints[nL].index = remoteVertex;
924                     ++nL;
925                   }
926                 }
927               } else if (zp > 0) { /* front */
928                 for (yv = 0; yv < nVy; ++yv) {
929                   const PetscInt localVertex  = ((nVz-1)*nVy + yv)*nVx + nVx-1 + nC; /* right front vertices */
930                   const PetscInt remoteVertex = (      0*nVy + yv)*nVx +     0 + nC; /* TODO: Correct this for neighbor sizes */
931 
932                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
933                     localPoints[nL]        = localVertex;
934                     remotePoints[nL].rank  = neighbor;
935                     remotePoints[nL].index = remoteVertex;
936                     ++nL;
937                   }
938                 }
939               } else {
940                 for (zv = 0; zv < nVz; ++zv) {
941                   for (yv = 0; yv < nVy; ++yv) {
942                     const PetscInt localVertex  = (zv*nVy + yv)*nVx + nVx-1 + nC; /* right vertices */
943                     const PetscInt remoteVertex = (zv*nVy + yv)*nVx + 0     + nC; /* TODO: Correct this for neighbor sizes */
944 
945                     if (!PetscBTLookupSet(isLeaf, localVertex)) {
946                       localPoints[nL]        = localVertex;
947                       remotePoints[nL].rank  = neighbor;
948                       remotePoints[nL].index = remoteVertex;
949                       ++nL;
950                     }
951                   }
952                 }
953 #if 0
954                 for (xf = 0; xf < nxF; ++xf) {
955                   /* THIS IS WRONG */
956                   const PetscInt localFace  = 0 + nC+nV; /* right faces */
957                   const PetscInt remoteFace = 0 + nC+nV;
958 
959                   if (!PetscBTLookupSet(isLeaf, localFace)) {
960                     localPoints[nL]        = localFace;
961                     remotePoints[nL].rank  = neighbor;
962                     remotePoints[nL].index = remoteFace;
963                     ++nL;
964                   }
965                 }
966 #endif
967               }
968             }
969           } else {
970             if (yp < 0) { /* bottom */
971               if (zp < 0) { /* back */
972                 for (xv = 0; xv < nVx; ++xv) {
973                   const PetscInt localVertex  = (      0*nVy +     0)*nVx + xv + nC; /* bottom back vertices */
974                   const PetscInt remoteVertex = ((nVz-1)*nVy + nVy-1)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
975 
976                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
977                     localPoints[nL]        = localVertex;
978                     remotePoints[nL].rank  = neighbor;
979                     remotePoints[nL].index = remoteVertex;
980                     ++nL;
981                   }
982                 }
983               } else if (zp > 0) { /* front */
984                 for (xv = 0; xv < nVx; ++xv) {
985                   const PetscInt localVertex  = ((nVz-1)*nVy +     0)*nVx + xv + nC; /* bottom front vertices */
986                   const PetscInt remoteVertex = (      0*nVy + nVy-1)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
987 
988                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
989                     localPoints[nL]        = localVertex;
990                     remotePoints[nL].rank  = neighbor;
991                     remotePoints[nL].index = remoteVertex;
992                     ++nL;
993                   }
994                 }
995               } else {
996                 for (zv = 0; zv < nVz; ++zv) {
997                   for (xv = 0; xv < nVx; ++xv) {
998                     const PetscInt localVertex  = (zv*nVy +     0)*nVx + xv + nC; /* bottom vertices */
999                     const PetscInt remoteVertex = (zv*nVy + nVy-1)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
1000 
1001                     if (!PetscBTLookupSet(isLeaf, localVertex)) {
1002                       localPoints[nL]        = localVertex;
1003                       remotePoints[nL].rank  = neighbor;
1004                       remotePoints[nL].index = remoteVertex;
1005                       ++nL;
1006                     }
1007                   }
1008                 }
1009 #if 0
1010                 for (yf = 0; yf < nyF; ++yf) {
1011                   /* THIS IS WRONG */
1012                   const PetscInt localFace  = 0 + nC+nV; /* bottom faces */
1013                   const PetscInt remoteFace = 0 + nC+nV;
1014 
1015                   if (!PetscBTLookupSet(isLeaf, localFace)) {
1016                     localPoints[nL]        = localFace;
1017                     remotePoints[nL].rank  = neighbor;
1018                     remotePoints[nL].index = remoteFace;
1019                     ++nL;
1020                   }
1021                 }
1022 #endif
1023               }
1024             } else if (yp > 0) { /* top */
1025               if (zp < 0) { /* back */
1026                 for (xv = 0; xv < nVx; ++xv) {
1027                   const PetscInt localVertex  = (      0*nVy + nVy-1)*nVx + xv + nC; /* top back vertices */
1028                   const PetscInt remoteVertex = ((nVz-1)*nVy +     0)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
1029 
1030                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
1031                     localPoints[nL]        = localVertex;
1032                     remotePoints[nL].rank  = neighbor;
1033                     remotePoints[nL].index = remoteVertex;
1034                     ++nL;
1035                   }
1036                 }
1037               } else if (zp > 0) { /* front */
1038                 for (xv = 0; xv < nVx; ++xv) {
1039                   const PetscInt localVertex  = ((nVz-1)*nVy + nVy-1)*nVx + xv + nC; /* top front vertices */
1040                   const PetscInt remoteVertex = (      0*nVy +     0)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
1041 
1042                   if (!PetscBTLookupSet(isLeaf, localVertex)) {
1043                     localPoints[nL]        = localVertex;
1044                     remotePoints[nL].rank  = neighbor;
1045                     remotePoints[nL].index = remoteVertex;
1046                     ++nL;
1047                   }
1048                 }
1049               } else {
1050                 for (zv = 0; zv < nVz; ++zv) {
1051                   for (xv = 0; xv < nVx; ++xv) {
1052                     const PetscInt localVertex  = (zv*nVy + nVy-1)*nVx + xv + nC; /* top vertices */
1053                     const PetscInt remoteVertex = (zv*nVy +     0)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
1054 
1055                     if (!PetscBTLookupSet(isLeaf, localVertex)) {
1056                       localPoints[nL]        = localVertex;
1057                       remotePoints[nL].rank  = neighbor;
1058                       remotePoints[nL].index = remoteVertex;
1059                       ++nL;
1060                     }
1061                   }
1062                 }
1063 #if 0
1064                 for (yf = 0; yf < nyF; ++yf) {
1065                   /* THIS IS WRONG */
1066                   const PetscInt localFace  = 0 + nC+nV; /* top faces */
1067                   const PetscInt remoteFace = 0 + nC+nV;
1068 
1069                   if (!PetscBTLookupSet(isLeaf, localFace)) {
1070                     localPoints[nL]        = localFace;
1071                     remotePoints[nL].rank  = neighbor;
1072                     remotePoints[nL].index = remoteFace;
1073                     ++nL;
1074                   }
1075                 }
1076 #endif
1077               }
1078             } else {
1079               if (zp < 0) { /* back */
1080                 for (yv = 0; yv < nVy; ++yv) {
1081                   for (xv = 0; xv < nVx; ++xv) {
1082                     const PetscInt localVertex  = (      0*nVy + yv)*nVx + xv + nC; /* back vertices */
1083                     const PetscInt remoteVertex = ((nVz-1)*nVy + yv)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
1084 
1085                     if (!PetscBTLookupSet(isLeaf, localVertex)) {
1086                       localPoints[nL]        = localVertex;
1087                       remotePoints[nL].rank  = neighbor;
1088                       remotePoints[nL].index = remoteVertex;
1089                       ++nL;
1090                     }
1091                   }
1092                 }
1093 #if 0
1094                 for (zf = 0; zf < nzF; ++zf) {
1095                   /* THIS IS WRONG */
1096                   const PetscInt localFace  = 0 + nC+nV; /* back faces */
1097                   const PetscInt remoteFace = 0 + nC+nV;
1098 
1099                   if (!PetscBTLookupSet(isLeaf, localFace)) {
1100                     localPoints[nL]        = localFace;
1101                     remotePoints[nL].rank  = neighbor;
1102                     remotePoints[nL].index = remoteFace;
1103                     ++nL;
1104                   }
1105                 }
1106 #endif
1107               } else if (zp > 0) { /* front */
1108                 for (yv = 0; yv < nVy; ++yv) {
1109                   for (xv = 0; xv < nVx; ++xv) {
1110                     const PetscInt localVertex  = ((nVz-1)*nVy + yv)*nVx + xv + nC; /* front vertices */
1111                     const PetscInt remoteVertex = (      0*nVy + yv)*nVx + xv + nC; /* TODO: Correct this for neighbor sizes */
1112 
1113                     if (!PetscBTLookupSet(isLeaf, localVertex)) {
1114                       localPoints[nL]        = localVertex;
1115                       remotePoints[nL].rank  = neighbor;
1116                       remotePoints[nL].index = remoteVertex;
1117                       ++nL;
1118                     }
1119                   }
1120                 }
1121 #if 0
1122                 for (zf = 0; zf < nzF; ++zf) {
1123                   /* THIS IS WRONG */
1124                   const PetscInt localFace  = 0 + nC+nV; /* front faces */
1125                   const PetscInt remoteFace = 0 + nC+nV;
1126 
1127                   if (!PetscBTLookupSet(isLeaf, localFace)) {
1128                     localPoints[nL]        = localFace;
1129                     remotePoints[nL].rank  = neighbor;
1130                     remotePoints[nL].index = remoteFace;
1131                     ++nL;
1132                   }
1133                 }
1134 #endif
1135               } else {
1136                 /* Nothing is shared from the interior */
1137               }
1138             }
1139           }
1140         }
1141       }
1142     }
1143   }
1144   ierr = PetscBTDestroy(&isLeaf);CHKERRQ(ierr);
1145   /* Remove duplication in leaf determination */
1146   if (nleaves != nL) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "The number of leaves %d did not match the number of remote leaves %d", nleaves, nleavesCheck);
1147   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), &sf);CHKERRQ(ierr);
1148   ierr = PetscSFSetGraph(sf, pEnd, nleaves, localPoints, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
1149   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
1150   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1151   *s = section;
1152   PetscFunctionReturn(0);
1153 }
1154 
1155 #undef __FUNCT__
1156 #define __FUNCT__ "DMDASetVertexCoordinates"
1157 PetscErrorCode DMDASetVertexCoordinates(DM dm, PetscReal xl, PetscReal xu, PetscReal yl, PetscReal yu, PetscReal zl, PetscReal zu)
1158 {
1159   DM_DA         *da = (DM_DA *) dm->data;
1160   Vec            coordinates;
1161   PetscSection   section;
1162   PetscScalar   *coords;
1163   PetscReal      h[3];
1164   PetscInt       dim, size, M, N, P, nVx, nVy, nVz, nV, vStart, vEnd, v, i, j, k;
1165   PetscErrorCode ierr;
1166 
1167   PetscFunctionBegin;
1168   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1169   ierr = DMDAGetInfo(dm, &dim, &M, &N, &P, 0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
1170   h[0] = (xu - xl)/M;
1171   h[1] = (yu - yl)/N;
1172   h[2] = (zu - zl)/P;
1173   ierr = DMDAGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1174   ierr = DMDAGetNumVertices(dm, &nVx, &nVy, &nVz, &nV);CHKERRQ(ierr);
1175   ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &section);CHKERRQ(ierr);
1176   ierr = PetscSectionSetNumFields(section, 1);CHKERRQ(ierr);
1177   ierr = PetscSectionSetFieldComponents(section, 0, dim);CHKERRQ(ierr);
1178   ierr = PetscSectionSetChart(section, vStart, vEnd);CHKERRQ(ierr);
1179   for (v = vStart; v < vEnd; ++v) {
1180     ierr = PetscSectionSetDof(section, v, dim);CHKERRQ(ierr);
1181   }
1182   ierr = PetscSectionSetUp(section);CHKERRQ(ierr);
1183   ierr = PetscSectionGetStorageSize(section, &size);CHKERRQ(ierr);
1184   ierr = VecCreateSeq(PETSC_COMM_SELF, size, &coordinates);CHKERRQ(ierr);
1185   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1186   for (k = 0; k < nVz; ++k) {
1187     PetscInt ind[3], d, off;
1188 
1189     ind[0] = 0;
1190     ind[1] = 0;
1191     ind[2] = k + da->zs;
1192     for (j = 0; j < nVy; ++j) {
1193       ind[1] = j + da->ys;
1194       for (i = 0; i < nVx; ++i) {
1195         const PetscInt vertex = (k*nVy + j)*nVx + i + vStart;
1196 
1197         ierr = PetscSectionGetOffset(section, vertex, &off);CHKERRQ(ierr);
1198         ind[0] = i + da->xs;
1199         for (d = 0; d < dim; ++d) {
1200           coords[off+d] = h[d]*ind[d];
1201         }
1202       }
1203     }
1204   }
1205   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1206   ierr = DMSetCoordinateSection(dm, PETSC_DETERMINE, section);CHKERRQ(ierr);
1207   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1208   ierr = PetscSectionDestroy(&section);CHKERRQ(ierr);
1209   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1210   PetscFunctionReturn(0);
1211 }
1212 
1213 #undef __FUNCT__
1214 #define __FUNCT__ "DMDAProjectFunctionLocal"
1215 PetscErrorCode DMDAProjectFunctionLocal(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec localX)
1216 {
1217   PetscDS    prob;
1218   PetscFE         fe;
1219   PetscDualSpace  sp;
1220   PetscQuadrature q;
1221   PetscSection    section;
1222   PetscScalar    *values;
1223   PetscInt        numFields, numComp, numPoints, dim, dimEmbed, spDim, totDim, numValues, cStart, cEnd, f, c, v, d;
1224   PetscErrorCode  ierr;
1225 
1226   PetscFunctionBegin;
1227   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1228   ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
1229   ierr = PetscDSGetDiscretization(prob, 0, (PetscObject *) &fe);CHKERRQ(ierr);
1230   ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
1231   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1232   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1233   ierr = DMDAGetInfo(dm, &dim,0,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
1234   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
1235   ierr = DMDAGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1236   ierr = DMDAVecGetClosure(dm, section, localX, cStart, &numValues, NULL);CHKERRQ(ierr);
1237   if (numValues != totDim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The section cell closure size %d != dual space dimension %d", numValues, totDim);
1238   ierr = DMGetWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
1239   ierr = PetscQuadratureGetData(q, NULL, &numPoints, NULL, NULL);CHKERRQ(ierr);
1240   for (c = cStart; c < cEnd; ++c) {
1241     PetscFECellGeom geom;
1242 
1243     ierr          = DMDAComputeCellGeometryFEM(dm, c, q, geom.v0, geom.J, NULL, &geom.detJ);CHKERRQ(ierr);
1244     geom.dim      = dim;
1245     geom.dimEmbed = dimEmbed;
1246     for (f = 0, v = 0; f < numFields; ++f) {
1247       void * const ctx = ctxs ? ctxs[f] : NULL;
1248 
1249       ierr = PetscDSGetDiscretization(prob, f, (PetscObject *) &fe);CHKERRQ(ierr);
1250       ierr = PetscFEGetNumComponents(fe, &numComp);CHKERRQ(ierr);
1251       ierr = PetscFEGetDualSpace(fe, &sp);CHKERRQ(ierr);
1252       ierr = PetscDualSpaceGetDimension(sp, &spDim);CHKERRQ(ierr);
1253       for (d = 0; d < spDim; ++d) {
1254         ierr = PetscDualSpaceApply(sp, d, &geom, numComp, funcs[f], ctx, &values[v]);CHKERRQ(ierr);
1255         v += numComp;
1256       }
1257     }
1258     ierr = DMDAVecSetClosure(dm, section, localX, c, values, mode);CHKERRQ(ierr);
1259   }
1260   ierr = DMRestoreWorkArray(dm, numValues, PETSC_SCALAR, &values);CHKERRQ(ierr);
1261   PetscFunctionReturn(0);
1262 }
1263 
1264 #undef __FUNCT__
1265 #define __FUNCT__ "DMDAProjectFunction"
1266 /*@C
1267   DMDAProjectFunction - This projects the given function into the function space provided.
1268 
1269   Input Parameters:
1270 + dm      - The DM
1271 . funcs   - The coordinate functions to evaluate
1272 . ctxs    - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
1273 - mode    - The insertion mode for values
1274 
1275   Output Parameter:
1276 . X - vector
1277 
1278   Level: developer
1279 
1280 .seealso: DMDAComputeL2Diff()
1281 @*/
1282 PetscErrorCode DMDAProjectFunction(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, InsertMode mode, Vec X)
1283 {
1284   Vec            localX;
1285   PetscErrorCode ierr;
1286 
1287   PetscFunctionBegin;
1288   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1289   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
1290   ierr = DMDAProjectFunctionLocal(dm, funcs, ctxs, mode, localX);CHKERRQ(ierr);
1291   ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
1292   ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
1293   ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
1294   PetscFunctionReturn(0);
1295 }
1296 
1297 #undef __FUNCT__
1298 #define __FUNCT__ "DMDAComputeL2Diff"
1299 /*@C
1300   DMDAComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.
1301 
1302   Input Parameters:
1303 + dm    - The DM
1304 . funcs - The functions to evaluate for each field component
1305 . ctxs  - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
1306 - X     - The coefficient vector u_h
1307 
1308   Output Parameter:
1309 . diff - The diff ||u - u_h||_2
1310 
1311   Level: developer
1312 
1313 .seealso: DMDAProjectFunction(), DMDAComputeL2GradientDiff()
1314 @*/
1315 PetscErrorCode DMDAComputeL2Diff(DM dm, void (**funcs)(const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
1316 {
1317   const PetscInt  debug = 0;
1318   PetscDS    prob;
1319   PetscFE         fe;
1320   PetscQuadrature quad;
1321   PetscSection    section;
1322   Vec             localX;
1323   PetscScalar    *funcVal;
1324   PetscReal      *coords, *v0, *J, *invJ, detJ;
1325   PetscReal       localDiff = 0.0;
1326   PetscInt        dim, numFields, Nc, cStart, cEnd, c, field, fieldOffset, comp;
1327   PetscErrorCode  ierr;
1328 
1329   PetscFunctionBegin;
1330   ierr = DMDAGetInfo(dm, &dim,0,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
1331   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1332   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1333   ierr = PetscDSGetDiscretization(prob, 0, (PetscObject *) &fe);CHKERRQ(ierr);
1334   ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1335   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1336   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1337   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
1338   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
1339   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
1340   /* There are no BC values in DAs right now: ierr = DMDAProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
1341   ierr = PetscMalloc5(Nc,&funcVal,dim,&coords,dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
1342   ierr = DMDAGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1343   for (c = cStart; c < cEnd; ++c) {
1344     PetscScalar *x = NULL;
1345     PetscReal    elemDiff = 0.0;
1346 
1347     ierr = DMDAComputeCellGeometryFEM(dm, c, quad, v0, J, invJ, &detJ);CHKERRQ(ierr);
1348     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
1349     ierr = DMDAVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
1350 
1351     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
1352       void * const ctx = ctxs ? ctxs[field] : NULL;
1353       const PetscReal *quadPoints, *quadWeights;
1354       PetscReal       *basis;
1355       PetscInt         numQuadPoints, numBasisFuncs, numBasisComps, q, d, e, fc, f;
1356 
1357       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1358       ierr = PetscQuadratureGetData(quad, NULL, &numQuadPoints, &quadPoints, &quadWeights);CHKERRQ(ierr);
1359       ierr = PetscFEGetDimension(fe, &numBasisFuncs);CHKERRQ(ierr);
1360       ierr = PetscFEGetNumComponents(fe, &numBasisComps);CHKERRQ(ierr);
1361       ierr = PetscFEGetDefaultTabulation(fe, &basis, NULL, NULL);CHKERRQ(ierr);
1362       if (debug) {
1363         char title[1024];
1364         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
1365         ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
1366       }
1367       for (q = 0; q < numQuadPoints; ++q) {
1368         for (d = 0; d < dim; d++) {
1369           coords[d] = v0[d];
1370           for (e = 0; e < dim; e++) {
1371             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
1372           }
1373         }
1374         (*funcs[field])(coords, funcVal, ctx);
1375         for (fc = 0; fc < numBasisComps; ++fc) {
1376           PetscScalar interpolant = 0.0;
1377 
1378           for (f = 0; f < numBasisFuncs; ++f) {
1379             const PetscInt fidx = f*numBasisComps+fc;
1380             interpolant += x[fieldOffset+fidx]*basis[q*numBasisFuncs*numBasisComps+fidx];
1381           }
1382           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ);CHKERRQ(ierr);}
1383           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
1384         }
1385       }
1386       comp        += numBasisComps;
1387       fieldOffset += numBasisFuncs*numBasisComps;
1388     }
1389     ierr = DMDAVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
1390     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
1391     localDiff += elemDiff;
1392   }
1393   ierr  = PetscFree5(funcVal,coords,v0,J,invJ);CHKERRQ(ierr);
1394   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
1395   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
1396   *diff = PetscSqrtReal(*diff);
1397   PetscFunctionReturn(0);
1398 }
1399 
1400 #undef __FUNCT__
1401 #define __FUNCT__ "DMDAComputeL2GradientDiff"
1402 /*@C
1403   DMDAComputeL2GradientDiff - This function computes the L_2 difference between the gradient of a function u and an FEM interpolant solution grad u_h.
1404 
1405   Input Parameters:
1406 + dm    - The DM
1407 . funcs - The gradient functions to evaluate for each field component
1408 . ctxs  - Optional array of contexts to pass to each coordinate function.  ctxs itself may be null.
1409 . X     - The coefficient vector u_h
1410 - n     - The vector to project along
1411 
1412   Output Parameter:
1413 . diff - The diff ||(grad u - grad u_h) . n||_2
1414 
1415   Level: developer
1416 
1417 .seealso: DMDAProjectFunction(), DMPlexComputeL2Diff()
1418 @*/
1419 PetscErrorCode DMDAComputeL2GradientDiff(DM dm, void (**funcs)(const PetscReal [], const PetscReal [], PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
1420 {
1421   const PetscInt  debug = 0;
1422   PetscDS    prob;
1423   PetscFE         fe;
1424   PetscQuadrature quad;
1425   PetscSection    section;
1426   Vec             localX;
1427   PetscScalar    *funcVal, *interpolantVec;
1428   PetscReal      *coords, *realSpaceDer, *v0, *J, *invJ, detJ;
1429   PetscReal       localDiff = 0.0;
1430   PetscInt        dim, numFields, Nc, cStart, cEnd, c, field, fieldOffset, comp;
1431   PetscErrorCode  ierr;
1432 
1433   PetscFunctionBegin;
1434   ierr = DMDAGetInfo(dm, &dim,0,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
1435   ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
1436   ierr = PetscDSGetTotalComponents(prob, &Nc);CHKERRQ(ierr);
1437   ierr = PetscDSGetDiscretization(prob, 0, (PetscObject *) &fe);CHKERRQ(ierr);
1438   ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
1439   ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
1440   ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
1441   ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
1442   ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
1443   ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
1444   /* There are no BC values in DAs right now: ierr = DMDAProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
1445   ierr = PetscMalloc7(Nc,&funcVal,dim,&coords,dim,&realSpaceDer,dim,&v0,dim*dim,&J,dim*dim,&invJ,dim,&interpolantVec);CHKERRQ(ierr);
1446   ierr = DMDAGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1447   for (c = cStart; c < cEnd; ++c) {
1448     PetscScalar *x = NULL;
1449     PetscReal    elemDiff = 0.0;
1450 
1451     ierr = DMDAComputeCellGeometryFEM(dm, c, quad, v0, J, invJ, &detJ);CHKERRQ(ierr);
1452     if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
1453     ierr = DMDAVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
1454 
1455     for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
1456       void * const ctx = ctxs ? ctxs[field] : NULL;
1457       const PetscReal *quadPoints, *quadWeights;
1458       PetscReal       *basisDer;
1459       PetscInt         Nq, Nb, Nc, q, d, e, fc, f, g;
1460 
1461       ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fe);CHKERRQ(ierr);
1462       ierr = PetscQuadratureGetData(quad, NULL, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
1463       ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
1464       ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
1465       ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
1466       if (debug) {
1467         char title[1024];
1468         ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
1469         ierr = DMPrintCellVector(c, title, Nb*Nc, &x[fieldOffset]);CHKERRQ(ierr);
1470       }
1471       for (q = 0; q < Nq; ++q) {
1472         for (d = 0; d < dim; d++) {
1473           coords[d] = v0[d];
1474           for (e = 0; e < dim; e++) {
1475             coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
1476           }
1477         }
1478         (*funcs[field])(coords, n, funcVal, ctx);
1479         for (fc = 0; fc < Nc; ++fc) {
1480           PetscScalar interpolant = 0.0;
1481 
1482           for (d = 0; d < dim; ++d) interpolantVec[d] = 0.0;
1483           for (f = 0; f < Nb; ++f) {
1484             const PetscInt fidx = f*Nc+fc;
1485 
1486             for (d = 0; d < dim; ++d) {
1487               realSpaceDer[d] = 0.0;
1488               for (g = 0; g < dim; ++g) {
1489                 realSpaceDer[d] += invJ[g*dim+d]*basisDer[(q*Nb*Nc+fidx)*dim+g];
1490               }
1491               interpolantVec[d] += x[fieldOffset+fidx]*realSpaceDer[d];
1492             }
1493           }
1494           for (d = 0; d < dim; ++d) interpolant += interpolantVec[d]*n[d];
1495           if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d fieldDer %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ);CHKERRQ(ierr);}
1496           elemDiff += PetscSqr(PetscRealPart(interpolant - funcVal[fc]))*quadWeights[q]*detJ;
1497         }
1498       }
1499       comp        += Nc;
1500       fieldOffset += Nb*Nc;
1501     }
1502     ierr = DMDAVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
1503     if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
1504     localDiff += elemDiff;
1505   }
1506   ierr  = PetscFree7(funcVal,coords,realSpaceDer,v0,J,invJ,interpolantVec);CHKERRQ(ierr);
1507   ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
1508   ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
1509   *diff = PetscSqrtReal(*diff);
1510   PetscFunctionReturn(0);
1511 }
1512 
1513 /* ------------------------------------------------------------------- */
1514 
1515 #undef __FUNCT__
1516 #define __FUNCT__ "DMDAGetArray"
1517 /*@C
1518      DMDAGetArray - Gets a work array for a DMDA
1519 
1520     Input Parameter:
1521 +    da - information about my local patch
1522 -    ghosted - do you want arrays for the ghosted or nonghosted patch
1523 
1524     Output Parameters:
1525 .    vptr - array data structured
1526 
1527     Note:  The vector values are NOT initialized and may have garbage in them, so you may need
1528            to zero them.
1529 
1530   Level: advanced
1531 
1532 .seealso: DMDARestoreArray()
1533 
1534 @*/
1535 PetscErrorCode  DMDAGetArray(DM da,PetscBool ghosted,void *vptr)
1536 {
1537   PetscErrorCode ierr;
1538   PetscInt       j,i,xs,ys,xm,ym,zs,zm;
1539   char           *iarray_start;
1540   void           **iptr = (void**)vptr;
1541   DM_DA          *dd    = (DM_DA*)da->data;
1542 
1543   PetscFunctionBegin;
1544   PetscValidHeaderSpecific(da,DM_CLASSID,1);
1545   if (ghosted) {
1546     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1547       if (dd->arrayghostedin[i]) {
1548         *iptr                 = dd->arrayghostedin[i];
1549         iarray_start          = (char*)dd->startghostedin[i];
1550         dd->arrayghostedin[i] = NULL;
1551         dd->startghostedin[i] = NULL;
1552 
1553         goto done;
1554       }
1555     }
1556     xs = dd->Xs;
1557     ys = dd->Ys;
1558     zs = dd->Zs;
1559     xm = dd->Xe-dd->Xs;
1560     ym = dd->Ye-dd->Ys;
1561     zm = dd->Ze-dd->Zs;
1562   } else {
1563     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1564       if (dd->arrayin[i]) {
1565         *iptr          = dd->arrayin[i];
1566         iarray_start   = (char*)dd->startin[i];
1567         dd->arrayin[i] = NULL;
1568         dd->startin[i] = NULL;
1569 
1570         goto done;
1571       }
1572     }
1573     xs = dd->xs;
1574     ys = dd->ys;
1575     zs = dd->zs;
1576     xm = dd->xe-dd->xs;
1577     ym = dd->ye-dd->ys;
1578     zm = dd->ze-dd->zs;
1579   }
1580 
1581   switch (da->dim) {
1582   case 1: {
1583     void *ptr;
1584 
1585     ierr = PetscMalloc(xm*sizeof(PetscScalar),&iarray_start);CHKERRQ(ierr);
1586 
1587     ptr   = (void*)(iarray_start - xs*sizeof(PetscScalar));
1588     *iptr = (void*)ptr;
1589     break;
1590   }
1591   case 2: {
1592     void **ptr;
1593 
1594     ierr = PetscMalloc((ym+1)*sizeof(void*)+xm*ym*sizeof(PetscScalar),&iarray_start);CHKERRQ(ierr);
1595 
1596     ptr = (void**)(iarray_start + xm*ym*sizeof(PetscScalar) - ys*sizeof(void*));
1597     for (j=ys; j<ys+ym; j++) ptr[j] = iarray_start + sizeof(PetscScalar)*(xm*(j-ys) - xs);
1598     *iptr = (void*)ptr;
1599     break;
1600   }
1601   case 3: {
1602     void ***ptr,**bptr;
1603 
1604     ierr = PetscMalloc((zm+1)*sizeof(void**)+(ym*zm+1)*sizeof(void*)+xm*ym*zm*sizeof(PetscScalar),&iarray_start);CHKERRQ(ierr);
1605 
1606     ptr  = (void***)(iarray_start + xm*ym*zm*sizeof(PetscScalar) - zs*sizeof(void*));
1607     bptr = (void**)(iarray_start + xm*ym*zm*sizeof(PetscScalar) + zm*sizeof(void**));
1608     for (i=zs; i<zs+zm; i++) ptr[i] = bptr + ((i-zs)*ym - ys);
1609     for (i=zs; i<zs+zm; i++) {
1610       for (j=ys; j<ys+ym; j++) {
1611         ptr[i][j] = iarray_start + sizeof(PetscScalar)*(xm*ym*(i-zs) + xm*(j-ys) - xs);
1612       }
1613     }
1614     *iptr = (void*)ptr;
1615     break;
1616   }
1617   default:
1618     SETERRQ1(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Dimension %D not supported",da->dim);
1619   }
1620 
1621 done:
1622   /* add arrays to the checked out list */
1623   if (ghosted) {
1624     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1625       if (!dd->arrayghostedout[i]) {
1626         dd->arrayghostedout[i] = *iptr;
1627         dd->startghostedout[i] = iarray_start;
1628         break;
1629       }
1630     }
1631   } else {
1632     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1633       if (!dd->arrayout[i]) {
1634         dd->arrayout[i] = *iptr;
1635         dd->startout[i] = iarray_start;
1636         break;
1637       }
1638     }
1639   }
1640   PetscFunctionReturn(0);
1641 }
1642 
1643 #undef __FUNCT__
1644 #define __FUNCT__ "DMDARestoreArray"
1645 /*@C
1646      DMDARestoreArray - Restores an array of derivative types for a DMDA
1647 
1648     Input Parameter:
1649 +    da - information about my local patch
1650 .    ghosted - do you want arrays for the ghosted or nonghosted patch
1651 -    vptr - array data structured to be passed to ad_FormFunctionLocal()
1652 
1653      Level: advanced
1654 
1655 .seealso: DMDAGetArray()
1656 
1657 @*/
1658 PetscErrorCode  DMDARestoreArray(DM da,PetscBool ghosted,void *vptr)
1659 {
1660   PetscInt i;
1661   void     **iptr = (void**)vptr,*iarray_start = 0;
1662   DM_DA    *dd    = (DM_DA*)da->data;
1663 
1664   PetscFunctionBegin;
1665   PetscValidHeaderSpecific(da,DM_CLASSID,1);
1666   if (ghosted) {
1667     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1668       if (dd->arrayghostedout[i] == *iptr) {
1669         iarray_start           = dd->startghostedout[i];
1670         dd->arrayghostedout[i] = NULL;
1671         dd->startghostedout[i] = NULL;
1672         break;
1673       }
1674     }
1675     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1676       if (!dd->arrayghostedin[i]) {
1677         dd->arrayghostedin[i] = *iptr;
1678         dd->startghostedin[i] = iarray_start;
1679         break;
1680       }
1681     }
1682   } else {
1683     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1684       if (dd->arrayout[i] == *iptr) {
1685         iarray_start    = dd->startout[i];
1686         dd->arrayout[i] = NULL;
1687         dd->startout[i] = NULL;
1688         break;
1689       }
1690     }
1691     for (i=0; i<DMDA_MAX_WORK_ARRAYS; i++) {
1692       if (!dd->arrayin[i]) {
1693         dd->arrayin[i] = *iptr;
1694         dd->startin[i] = iarray_start;
1695         break;
1696       }
1697     }
1698   }
1699   PetscFunctionReturn(0);
1700 }
1701 
1702