xref: /petsc/src/dm/impls/plex/plextree.c (revision 4fc747eaadbeca11629f314a99edccbc2ed7b3d3)
1 #include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 #include <../src/sys/utils/hash.h>
3 #include <petsc/private/isimpl.h>
4 #include <petsc/private/petscfeimpl.h>
5 #include <petscsf.h>
6 #include <petscds.h>
7 
8 /** hierarchy routines */
9 
10 #undef __FUNCT__
11 #define __FUNCT__ "DMPlexSetReferenceTree"
12 /*@
13   DMPlexSetReferenceTree - set the reference tree for hierarchically non-conforming meshes.
14 
15   Not collective
16 
17   Input Parameters:
18 + dm - The DMPlex object
19 - ref - The reference tree DMPlex object
20 
21   Level: intermediate
22 
23 .seealso: DMPlexGetReferenceTree(), DMPlexCreateDefaultReferenceTree()
24 @*/
25 PetscErrorCode DMPlexSetReferenceTree(DM dm, DM ref)
26 {
27   DM_Plex        *mesh = (DM_Plex *)dm->data;
28   PetscErrorCode  ierr;
29 
30   PetscFunctionBegin;
31   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
32   if (ref) {PetscValidHeaderSpecific(ref, DM_CLASSID, 2);}
33   ierr = PetscObjectReference((PetscObject)ref);CHKERRQ(ierr);
34   ierr = DMDestroy(&mesh->referenceTree);CHKERRQ(ierr);
35   mesh->referenceTree = ref;
36   PetscFunctionReturn(0);
37 }
38 
39 #undef __FUNCT__
40 #define __FUNCT__ "DMPlexGetReferenceTree"
41 /*@
42   DMPlexGetReferenceTree - get the reference tree for hierarchically non-conforming meshes.
43 
44   Not collective
45 
46   Input Parameters:
47 . dm - The DMPlex object
48 
49   Output Parameters
50 . ref - The reference tree DMPlex object
51 
52   Level: intermediate
53 
54 .seealso: DMPlexSetReferenceTree(), DMPlexCreateDefaultReferenceTree()
55 @*/
56 PetscErrorCode DMPlexGetReferenceTree(DM dm, DM *ref)
57 {
58   DM_Plex        *mesh = (DM_Plex *)dm->data;
59 
60   PetscFunctionBegin;
61   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
62   PetscValidPointer(ref,2);
63   *ref = mesh->referenceTree;
64   PetscFunctionReturn(0);
65 }
66 
67 #undef __FUNCT__
68 #define __FUNCT__ "DMPlexReferenceTreeGetChildSymmetry_Default"
69 static PetscErrorCode DMPlexReferenceTreeGetChildSymmetry_Default(DM dm, PetscInt parent, PetscInt parentOrientA, PetscInt childOrientA, PetscInt childA, PetscInt parentOrientB, PetscInt *childOrientB, PetscInt *childB)
70 {
71   PetscInt       coneSize, dStart, dEnd, dim, ABswap, oAvert, oBvert, ABswapVert;
72   PetscErrorCode ierr;
73 
74   PetscFunctionBegin;
75   if (parentOrientA == parentOrientB) {
76     if (childOrientB) *childOrientB = childOrientA;
77     if (childB) *childB = childA;
78     PetscFunctionReturn(0);
79   }
80   for (dim = 0; dim < 3; dim++) {
81     ierr = DMPlexGetDepthStratum(dm,dim,&dStart,&dEnd);CHKERRQ(ierr);
82     if (parent >= dStart && parent <= dEnd) {
83       break;
84     }
85   }
86   if (dim > 2) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot perform child symmetry for %d-cells",dim);
87   if (!dim) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"A vertex has no children");
88   if (childA < dStart || childA >= dEnd) {
89     /* this is a lower-dimensional child: bootstrap */
90     PetscInt size, i, sA = -1, sB, sOrientB, sConeSize;
91     const PetscInt *supp, *coneA, *coneB, *oA, *oB;
92 
93     ierr = DMPlexGetSupportSize(dm,childA,&size);CHKERRQ(ierr);
94     ierr = DMPlexGetSupport(dm,childA,&supp);CHKERRQ(ierr);
95 
96     /* find a point sA in supp(childA) that has the same parent */
97     for (i = 0; i < size; i++) {
98       PetscInt sParent;
99 
100       sA   = supp[i];
101       if (sA == parent) continue;
102       ierr = DMPlexGetTreeParent(dm,sA,&sParent,NULL);CHKERRQ(ierr);
103       if (sParent == parent) {
104         break;
105       }
106     }
107     if (i == size) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"could not find support in children");
108     /* find out which point sB is in an equivalent position to sA under
109      * parentOrientB */
110     ierr = DMPlexReferenceTreeGetChildSymmetry_Default(dm,parent,parentOrientA,0,sA,parentOrientB,&sOrientB,&sB);CHKERRQ(ierr);
111     ierr = DMPlexGetConeSize(dm,sA,&sConeSize);CHKERRQ(ierr);
112     ierr = DMPlexGetCone(dm,sA,&coneA);CHKERRQ(ierr);
113     ierr = DMPlexGetCone(dm,sB,&coneB);CHKERRQ(ierr);
114     ierr = DMPlexGetConeOrientation(dm,sA,&oA);CHKERRQ(ierr);
115     ierr = DMPlexGetConeOrientation(dm,sB,&oB);CHKERRQ(ierr);
116     /* step through the cone of sA in natural order */
117     for (i = 0; i < sConeSize; i++) {
118       if (coneA[i] == childA) {
119         /* if childA is at position i in coneA,
120          * then we want the point that is at sOrientB*i in coneB */
121         PetscInt j = (sOrientB >= 0) ? ((sOrientB + i) % sConeSize) : ((sConeSize -(sOrientB+1) - i) % sConeSize);
122         if (childB) *childB = coneB[j];
123         if (childOrientB) {
124           PetscInt oBtrue;
125 
126           ierr          = DMPlexGetConeSize(dm,childA,&coneSize);CHKERRQ(ierr);
127           /* compose sOrientB and oB[j] */
128           if (coneSize != 0 && coneSize != 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expected a vertex or an edge");
129           /* we may have to flip an edge */
130           oBtrue        = coneSize ? ((sOrientB >= 0) ? oB[j] : -(oB[j] + 2)) : 0;
131           ABswap        = DihedralSwap(coneSize,oA[i],oBtrue);CHKERRQ(ierr);
132           *childOrientB = DihedralCompose(coneSize,childOrientA,ABswap);
133         }
134         break;
135       }
136     }
137     if (i == sConeSize) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"support cone mismatch");
138     PetscFunctionReturn(0);
139   }
140   /* get the cone size and symmetry swap */
141   ierr   = DMPlexGetConeSize(dm,parent,&coneSize);CHKERRQ(ierr);
142   ABswap = DihedralSwap(coneSize, parentOrientA, parentOrientB);
143   if (dim == 2) {
144     /* orientations refer to cones: we want them to refer to vertices:
145      * if it's a rotation, they are the same, but if the order is reversed, a
146      * permutation that puts side i first does *not* put vertex i first */
147     oAvert     = (parentOrientA >= 0) ? parentOrientA : -((-parentOrientA % coneSize) + 1);
148     oBvert     = (parentOrientB >= 0) ? parentOrientB : -((-parentOrientB % coneSize) + 1);
149     ABswapVert = DihedralSwap(coneSize, oAvert, oBvert);
150   } else {
151     ABswapVert = ABswap;
152   }
153   if (childB) {
154     /* assume that each child corresponds to a vertex, in the same order */
155     PetscInt p, posA = -1, numChildren, i;
156     const PetscInt *children;
157 
158     /* count which position the child is in */
159     ierr = DMPlexGetTreeChildren(dm,parent,&numChildren,&children);CHKERRQ(ierr);
160     for (i = 0; i < numChildren; i++) {
161       p = children[i];
162       if (p == childA) {
163         posA = i;
164         break;
165       }
166     }
167     if (posA >= coneSize) {
168       /* this is the triangle in the middle of a uniformly refined triangle: it
169        * is invariant */
170       if (dim != 2 || posA != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Expected a middle triangle, got something else");
171       *childB = childA;
172     }
173     else {
174       /* figure out position B by applying ABswapVert */
175       PetscInt posB;
176 
177       posB = (ABswapVert >= 0) ? ((ABswapVert + posA) % coneSize) : ((coneSize -(ABswapVert + 1) - posA) % coneSize);
178       if (childB) *childB = children[posB];
179     }
180   }
181   if (childOrientB) *childOrientB = DihedralCompose(coneSize,childOrientA,ABswap);
182   PetscFunctionReturn(0);
183 }
184 
185 #undef __FUNCT__
186 #define __FUNCT__ "DMPlexReferenceTreeGetChildSymmetry"
187 /*@
188   DMPlexReferenceTreeGetChildSymmetry - Given a reference tree, transform a childid and orientation from one parent frame to another
189 
190   Input Parameters:
191 + dm - the reference tree DMPlex object
192 . parent - the parent point
193 . parentOrientA - the reference orientation for describing the parent
194 . childOrientA - the reference orientation for describing the child
195 . childA - the reference childID for describing the child
196 - parentOrientB - the new orientation for describing the parent
197 
198   Output Parameters:
199 + childOrientB - if not NULL, set to the new oreintation for describing the child
200 . childB - if not NULL, the new childID for describing the child
201 
202   Level: developer
203 
204 .seealso: DMPlexGetReferenceTree(), DMPlexSetReferenceTree(), DMPlexSetTree()
205 @*/
206 PetscErrorCode DMPlexReferenceTreeGetChildSymmetry(DM dm, PetscInt parent, PetscInt parentOrientA, PetscInt childOrientA, PetscInt childA, PetscInt parentOrientB, PetscInt *childOrientB, PetscInt *childB)
207 {
208   DM_Plex        *mesh = (DM_Plex *)dm->data;
209   PetscErrorCode ierr;
210 
211   PetscFunctionBegin;
212   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
213   if (!mesh->getchildsymmetry) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DMPlexReferenceTreeGetChildSymmetry not implemented");
214   ierr = mesh->getchildsymmetry(dm,parent,parentOrientA,childOrientA,childA,parentOrientB,childOrientB,childB);CHKERRQ(ierr);
215   PetscFunctionReturn(0);
216 }
217 
218 static PetscErrorCode DMPlexSetTree_Internal(DM,PetscSection,PetscInt*,PetscInt*,PetscBool,PetscBool);
219 
220 #undef __FUNCT__
221 #define __FUNCT__ "DMPlexCreateReferenceTree_Union"
222 PetscErrorCode DMPlexCreateReferenceTree_Union(DM K, DM Kref, const char *labelName, DM *ref)
223 {
224   MPI_Comm       comm;
225   PetscInt       dim, p, pStart, pEnd, pRefStart, pRefEnd, d, offset, parentSize, *parents, *childIDs;
226   PetscInt      *permvals, *unionCones, *coneSizes, *unionOrientations, numUnionPoints, *numDimPoints, numCones, numVerts;
227   DMLabel        identity, identityRef;
228   PetscSection   unionSection, unionConeSection, parentSection;
229   PetscScalar   *unionCoords;
230   IS             perm;
231   PetscErrorCode ierr;
232 
233   PetscFunctionBegin;
234   comm = PetscObjectComm((PetscObject)K);
235   ierr = DMGetDimension(K, &dim);CHKERRQ(ierr);
236   ierr = DMPlexGetChart(K, &pStart, &pEnd);CHKERRQ(ierr);
237   ierr = DMGetLabel(K, labelName, &identity);CHKERRQ(ierr);
238   ierr = DMGetLabel(Kref, labelName, &identityRef);CHKERRQ(ierr);
239   ierr = DMPlexGetChart(Kref, &pRefStart, &pRefEnd);CHKERRQ(ierr);
240   ierr = PetscSectionCreate(comm, &unionSection);CHKERRQ(ierr);
241   ierr = PetscSectionSetChart(unionSection, 0, (pEnd - pStart) + (pRefEnd - pRefStart));CHKERRQ(ierr);
242   /* count points that will go in the union */
243   for (p = pStart; p < pEnd; p++) {
244     ierr = PetscSectionSetDof(unionSection, p - pStart, 1);CHKERRQ(ierr);
245   }
246   for (p = pRefStart; p < pRefEnd; p++) {
247     PetscInt q, qSize;
248     ierr = DMLabelGetValue(identityRef, p, &q);CHKERRQ(ierr);
249     ierr = DMLabelGetStratumSize(identityRef, q, &qSize);CHKERRQ(ierr);
250     if (qSize > 1) {
251       ierr = PetscSectionSetDof(unionSection, p - pRefStart + (pEnd - pStart), 1);CHKERRQ(ierr);
252     }
253   }
254   ierr = PetscMalloc1(pEnd - pStart + pRefEnd - pRefStart,&permvals);CHKERRQ(ierr);
255   offset = 0;
256   /* stratify points in the union by topological dimension */
257   for (d = 0; d <= dim; d++) {
258     PetscInt cStart, cEnd, c;
259 
260     ierr = DMPlexGetHeightStratum(K, d, &cStart, &cEnd);CHKERRQ(ierr);
261     for (c = cStart; c < cEnd; c++) {
262       permvals[offset++] = c;
263     }
264 
265     ierr = DMPlexGetHeightStratum(Kref, d, &cStart, &cEnd);CHKERRQ(ierr);
266     for (c = cStart; c < cEnd; c++) {
267       permvals[offset++] = c + (pEnd - pStart);
268     }
269   }
270   ierr = ISCreateGeneral(comm, (pEnd - pStart) + (pRefEnd - pRefStart), permvals, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
271   ierr = PetscSectionSetPermutation(unionSection,perm);CHKERRQ(ierr);
272   ierr = PetscSectionSetUp(unionSection);CHKERRQ(ierr);
273   ierr = PetscSectionGetStorageSize(unionSection,&numUnionPoints);CHKERRQ(ierr);
274   ierr = PetscMalloc2(numUnionPoints,&coneSizes,dim+1,&numDimPoints);CHKERRQ(ierr);
275   /* count dimension points */
276   for (d = 0; d <= dim; d++) {
277     PetscInt cStart, cOff, cOff2;
278     ierr = DMPlexGetHeightStratum(K,d,&cStart,NULL);CHKERRQ(ierr);
279     ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff);CHKERRQ(ierr);
280     if (d < dim) {
281       ierr = DMPlexGetHeightStratum(K,d+1,&cStart,NULL);CHKERRQ(ierr);
282       ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff2);CHKERRQ(ierr);
283     }
284     else {
285       cOff2 = numUnionPoints;
286     }
287     numDimPoints[dim - d] = cOff2 - cOff;
288   }
289   ierr = PetscSectionCreate(comm, &unionConeSection);CHKERRQ(ierr);
290   ierr = PetscSectionSetChart(unionConeSection, 0, numUnionPoints);CHKERRQ(ierr);
291   /* count the cones in the union */
292   for (p = pStart; p < pEnd; p++) {
293     PetscInt dof, uOff;
294 
295     ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
296     ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
297     ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
298     coneSizes[uOff] = dof;
299   }
300   for (p = pRefStart; p < pRefEnd; p++) {
301     PetscInt dof, uDof, uOff;
302 
303     ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
304     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
305     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
306     if (uDof) {
307       ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
308       coneSizes[uOff] = dof;
309     }
310   }
311   ierr = PetscSectionSetUp(unionConeSection);CHKERRQ(ierr);
312   ierr = PetscSectionGetStorageSize(unionConeSection,&numCones);CHKERRQ(ierr);
313   ierr = PetscMalloc2(numCones,&unionCones,numCones,&unionOrientations);CHKERRQ(ierr);
314   /* write the cones in the union */
315   for (p = pStart; p < pEnd; p++) {
316     PetscInt dof, uOff, c, cOff;
317     const PetscInt *cone, *orientation;
318 
319     ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
320     ierr = DMPlexGetCone(K, p, &cone);CHKERRQ(ierr);
321     ierr = DMPlexGetConeOrientation(K, p, &orientation);CHKERRQ(ierr);
322     ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
323     ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
324     for (c = 0; c < dof; c++) {
325       PetscInt e, eOff;
326       e                           = cone[c];
327       ierr                        = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
328       unionCones[cOff + c]        = eOff;
329       unionOrientations[cOff + c] = orientation[c];
330     }
331   }
332   for (p = pRefStart; p < pRefEnd; p++) {
333     PetscInt dof, uDof, uOff, c, cOff;
334     const PetscInt *cone, *orientation;
335 
336     ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
337     ierr = DMPlexGetCone(Kref, p, &cone);CHKERRQ(ierr);
338     ierr = DMPlexGetConeOrientation(Kref, p, &orientation);CHKERRQ(ierr);
339     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
340     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
341     if (uDof) {
342       ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
343       for (c = 0; c < dof; c++) {
344         PetscInt e, eOff, eDof;
345 
346         e    = cone[c];
347         ierr = PetscSectionGetDof(unionSection, e - pRefStart + (pEnd - pStart),&eDof);CHKERRQ(ierr);
348         if (eDof) {
349           ierr = PetscSectionGetOffset(unionSection, e - pRefStart + (pEnd - pStart), &eOff);CHKERRQ(ierr);
350         }
351         else {
352           ierr = DMLabelGetValue(identityRef, e, &e);CHKERRQ(ierr);
353           ierr = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
354         }
355         unionCones[cOff + c]        = eOff;
356         unionOrientations[cOff + c] = orientation[c];
357       }
358     }
359   }
360   /* get the coordinates */
361   {
362     PetscInt vStart, vEnd, vRefStart, vRefEnd, v, vDof, vOff;
363     PetscSection KcoordsSec, KrefCoordsSec;
364     Vec      KcoordsVec, KrefCoordsVec;
365     PetscScalar *Kcoords;
366 
367     DMGetCoordinateSection(K, &KcoordsSec);CHKERRQ(ierr);
368     DMGetCoordinatesLocal(K, &KcoordsVec);CHKERRQ(ierr);
369     DMGetCoordinateSection(Kref, &KrefCoordsSec);CHKERRQ(ierr);
370     DMGetCoordinatesLocal(Kref, &KrefCoordsVec);CHKERRQ(ierr);
371 
372     numVerts = numDimPoints[0];
373     ierr     = PetscMalloc1(numVerts * dim,&unionCoords);CHKERRQ(ierr);
374     ierr     = DMPlexGetDepthStratum(K,0,&vStart,&vEnd);CHKERRQ(ierr);
375 
376     offset = 0;
377     for (v = vStart; v < vEnd; v++) {
378       ierr = PetscSectionGetOffset(unionSection,v - pStart,&vOff);CHKERRQ(ierr);
379       ierr = VecGetValuesSection(KcoordsVec, KcoordsSec, v, &Kcoords);CHKERRQ(ierr);
380       for (d = 0; d < dim; d++) {
381         unionCoords[offset * dim + d] = Kcoords[d];
382       }
383       offset++;
384     }
385     ierr = DMPlexGetDepthStratum(Kref,0,&vRefStart,&vRefEnd);CHKERRQ(ierr);
386     for (v = vRefStart; v < vRefEnd; v++) {
387       ierr = PetscSectionGetDof(unionSection,v - pRefStart + (pEnd - pStart),&vDof);CHKERRQ(ierr);
388       ierr = PetscSectionGetOffset(unionSection,v - pRefStart + (pEnd - pStart),&vOff);CHKERRQ(ierr);
389       ierr = VecGetValuesSection(KrefCoordsVec, KrefCoordsSec, v, &Kcoords);CHKERRQ(ierr);
390       if (vDof) {
391         for (d = 0; d < dim; d++) {
392           unionCoords[offset * dim + d] = Kcoords[d];
393         }
394         offset++;
395       }
396     }
397   }
398   ierr = DMCreate(comm,ref);CHKERRQ(ierr);
399   ierr = DMSetType(*ref,DMPLEX);CHKERRQ(ierr);
400   ierr = DMSetDimension(*ref,dim);CHKERRQ(ierr);
401   ierr = DMPlexCreateFromDAG(*ref,dim,numDimPoints,coneSizes,unionCones,unionOrientations,unionCoords);CHKERRQ(ierr);
402   /* set the tree */
403   ierr = PetscSectionCreate(comm,&parentSection);CHKERRQ(ierr);
404   ierr = PetscSectionSetChart(parentSection,0,numUnionPoints);CHKERRQ(ierr);
405   for (p = pRefStart; p < pRefEnd; p++) {
406     PetscInt uDof, uOff;
407 
408     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
409     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
410     if (uDof) {
411       PetscSectionSetDof(parentSection,uOff,1);CHKERRQ(ierr);
412     }
413   }
414   ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
415   ierr = PetscSectionGetStorageSize(parentSection,&parentSize);CHKERRQ(ierr);
416   ierr = PetscMalloc2(parentSize,&parents,parentSize,&childIDs);CHKERRQ(ierr);
417   for (p = pRefStart; p < pRefEnd; p++) {
418     PetscInt uDof, uOff;
419 
420     ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
421     ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
422     if (uDof) {
423       PetscInt pOff, parent, parentU;
424       PetscSectionGetOffset(parentSection,uOff,&pOff);CHKERRQ(ierr);
425       DMLabelGetValue(identityRef,p,&parent);CHKERRQ(ierr);
426       ierr = PetscSectionGetOffset(unionSection, parent - pStart,&parentU);CHKERRQ(ierr);
427       parents[pOff] = parentU;
428       childIDs[pOff] = uOff;
429     }
430   }
431   ierr = DMPlexSetTree_Internal(*ref,parentSection,parents,childIDs,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
432   ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
433   ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
434 
435   /* clean up */
436   ierr = PetscSectionDestroy(&unionSection);CHKERRQ(ierr);
437   ierr = PetscSectionDestroy(&unionConeSection);CHKERRQ(ierr);
438   ierr = ISDestroy(&perm);CHKERRQ(ierr);
439   ierr = PetscFree(unionCoords);CHKERRQ(ierr);
440   ierr = PetscFree2(unionCones,unionOrientations);CHKERRQ(ierr);
441   ierr = PetscFree2(coneSizes,numDimPoints);CHKERRQ(ierr);
442   PetscFunctionReturn(0);
443 }
444 
445 #undef __FUNCT__
446 #define __FUNCT__ "DMPlexCreateDefaultReferenceTree"
447 /*@
448   DMPlexCreateDefaultReferenceTree - create a reference tree for isotropic hierarchical mesh refinement.
449 
450   Collective on comm
451 
452   Input Parameters:
453 + comm    - the MPI communicator
454 . dim     - the spatial dimension
455 - simplex - Flag for simplex, otherwise use a tensor-product cell
456 
457   Output Parameters:
458 . ref     - the reference tree DMPlex object
459 
460   Level: intermediate
461 
462 .keywords: reference cell
463 .seealso: DMPlexSetReferenceTree(), DMPlexGetReferenceTree()
464 @*/
465 PetscErrorCode DMPlexCreateDefaultReferenceTree(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *ref)
466 {
467   DM_Plex       *mesh;
468   DM             K, Kref;
469   PetscInt       p, pStart, pEnd;
470   DMLabel        identity;
471   PetscErrorCode ierr;
472 
473   PetscFunctionBegin;
474 #if 1
475   comm = PETSC_COMM_SELF;
476 #endif
477   /* create a reference element */
478   ierr = DMPlexCreateReferenceCell(comm, dim, simplex, &K);CHKERRQ(ierr);
479   ierr = DMCreateLabel(K, "identity");CHKERRQ(ierr);
480   ierr = DMGetLabel(K, "identity", &identity);CHKERRQ(ierr);
481   ierr = DMPlexGetChart(K, &pStart, &pEnd);CHKERRQ(ierr);
482   for (p = pStart; p < pEnd; p++) {
483     ierr = DMLabelSetValue(identity, p, p);CHKERRQ(ierr);
484   }
485   /* refine it */
486   ierr = DMRefine(K,comm,&Kref);CHKERRQ(ierr);
487 
488   /* the reference tree is the union of these two, without duplicating
489    * points that appear in both */
490   ierr = DMPlexCreateReferenceTree_Union(K, Kref, "identity", ref);CHKERRQ(ierr);
491   mesh = (DM_Plex *) (*ref)->data;
492   mesh->getchildsymmetry = DMPlexReferenceTreeGetChildSymmetry_Default;
493   ierr = DMDestroy(&K);CHKERRQ(ierr);
494   ierr = DMDestroy(&Kref);CHKERRQ(ierr);
495   PetscFunctionReturn(0);
496 }
497 
498 #undef __FUNCT__
499 #define __FUNCT__ "DMPlexTreeSymmetrize"
500 static PetscErrorCode DMPlexTreeSymmetrize(DM dm)
501 {
502   DM_Plex        *mesh = (DM_Plex *)dm->data;
503   PetscSection   childSec, pSec;
504   PetscInt       p, pSize, cSize, parMax = PETSC_MIN_INT, parMin = PETSC_MAX_INT;
505   PetscInt       *offsets, *children, pStart, pEnd;
506   PetscErrorCode ierr;
507 
508   PetscFunctionBegin;
509   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
510   ierr = PetscSectionDestroy(&mesh->childSection);CHKERRQ(ierr);
511   ierr = PetscFree(mesh->children);CHKERRQ(ierr);
512   pSec = mesh->parentSection;
513   if (!pSec) PetscFunctionReturn(0);
514   ierr = PetscSectionGetStorageSize(pSec,&pSize);CHKERRQ(ierr);
515   for (p = 0; p < pSize; p++) {
516     PetscInt par = mesh->parents[p];
517 
518     parMax = PetscMax(parMax,par+1);
519     parMin = PetscMin(parMin,par);
520   }
521   if (parMin > parMax) {
522     parMin = -1;
523     parMax = -1;
524   }
525   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)pSec),&childSec);CHKERRQ(ierr);
526   ierr = PetscSectionSetChart(childSec,parMin,parMax);CHKERRQ(ierr);
527   for (p = 0; p < pSize; p++) {
528     PetscInt par = mesh->parents[p];
529 
530     ierr = PetscSectionAddDof(childSec,par,1);CHKERRQ(ierr);
531   }
532   ierr = PetscSectionSetUp(childSec);CHKERRQ(ierr);
533   ierr = PetscSectionGetStorageSize(childSec,&cSize);CHKERRQ(ierr);
534   ierr = PetscMalloc1(cSize,&children);CHKERRQ(ierr);
535   ierr = PetscCalloc1(parMax-parMin,&offsets);CHKERRQ(ierr);
536   ierr = PetscSectionGetChart(pSec,&pStart,&pEnd);CHKERRQ(ierr);
537   for (p = pStart; p < pEnd; p++) {
538     PetscInt dof, off, i;
539 
540     ierr = PetscSectionGetDof(pSec,p,&dof);CHKERRQ(ierr);
541     ierr = PetscSectionGetOffset(pSec,p,&off);CHKERRQ(ierr);
542     for (i = 0; i < dof; i++) {
543       PetscInt par = mesh->parents[off + i], cOff;
544 
545       ierr = PetscSectionGetOffset(childSec,par,&cOff);CHKERRQ(ierr);
546       children[cOff + offsets[par-parMin]++] = p;
547     }
548   }
549   mesh->childSection = childSec;
550   mesh->children = children;
551   ierr = PetscFree(offsets);CHKERRQ(ierr);
552   PetscFunctionReturn(0);
553 }
554 
555 #undef __FUNCT__
556 #define __FUNCT__ "AnchorsFlatten"
557 static PetscErrorCode AnchorsFlatten (PetscSection section, IS is, PetscSection *sectionNew, IS *isNew)
558 {
559   PetscInt       pStart, pEnd, size, sizeNew, i, p, *valsNew = NULL;
560   const PetscInt *vals;
561   PetscSection   secNew;
562   PetscBool      anyNew, globalAnyNew;
563   PetscBool      compress;
564   PetscErrorCode ierr;
565 
566   PetscFunctionBegin;
567   ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
568   ierr = ISGetLocalSize(is,&size);CHKERRQ(ierr);
569   ierr = ISGetIndices(is,&vals);CHKERRQ(ierr);
570   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secNew);CHKERRQ(ierr);
571   ierr = PetscSectionSetChart(secNew,pStart,pEnd);CHKERRQ(ierr);
572   for (i = 0; i < size; i++) {
573     PetscInt dof;
574 
575     p = vals[i];
576     if (p < pStart || p >= pEnd) continue;
577     ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
578     if (dof) break;
579   }
580   if (i == size) {
581     ierr     = PetscSectionSetUp(secNew);CHKERRQ(ierr);
582     anyNew   = PETSC_FALSE;
583     compress = PETSC_FALSE;
584     sizeNew  = 0;
585   }
586   else {
587     anyNew = PETSC_TRUE;
588     for (p = pStart; p < pEnd; p++) {
589       PetscInt dof, off;
590 
591       ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
592       ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
593       for (i = 0; i < dof; i++) {
594         PetscInt q = vals[off + i], qDof = 0;
595 
596         if (q >= pStart && q < pEnd) {
597           ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
598         }
599         if (qDof) {
600           ierr = PetscSectionAddDof(secNew, p, qDof);CHKERRQ(ierr);
601         }
602         else {
603           ierr = PetscSectionAddDof(secNew, p, 1);CHKERRQ(ierr);
604         }
605       }
606     }
607     ierr = PetscSectionSetUp(secNew);CHKERRQ(ierr);
608     ierr = PetscSectionGetStorageSize(secNew,&sizeNew);CHKERRQ(ierr);
609     ierr = PetscMalloc1(sizeNew,&valsNew);CHKERRQ(ierr);
610     compress = PETSC_FALSE;
611     for (p = pStart; p < pEnd; p++) {
612       PetscInt dof, off, count, offNew, dofNew;
613 
614       ierr  = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
615       ierr  = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
616       ierr  = PetscSectionGetDof(secNew, p, &dofNew);CHKERRQ(ierr);
617       ierr  = PetscSectionGetOffset(secNew, p, &offNew);CHKERRQ(ierr);
618       count = 0;
619       for (i = 0; i < dof; i++) {
620         PetscInt q = vals[off + i], qDof = 0, qOff = 0, j;
621 
622         if (q >= pStart && q < pEnd) {
623           ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
624           ierr = PetscSectionGetOffset(section, q, &qOff);CHKERRQ(ierr);
625         }
626         if (qDof) {
627           PetscInt oldCount = count;
628 
629           for (j = 0; j < qDof; j++) {
630             PetscInt k, r = vals[qOff + j];
631 
632             for (k = 0; k < oldCount; k++) {
633               if (valsNew[offNew + k] == r) {
634                 break;
635               }
636             }
637             if (k == oldCount) {
638               valsNew[offNew + count++] = r;
639             }
640           }
641         }
642         else {
643           PetscInt k, oldCount = count;
644 
645           for (k = 0; k < oldCount; k++) {
646             if (valsNew[offNew + k] == q) {
647               break;
648             }
649           }
650           if (k == oldCount) {
651             valsNew[offNew + count++] = q;
652           }
653         }
654       }
655       if (count < dofNew) {
656         ierr = PetscSectionSetDof(secNew, p, count);CHKERRQ(ierr);
657         compress = PETSC_TRUE;
658       }
659     }
660   }
661   ierr = ISRestoreIndices(is,&vals);CHKERRQ(ierr);
662   ierr = MPIU_Allreduce(&anyNew,&globalAnyNew,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
663   if (!globalAnyNew) {
664     ierr = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
665     *sectionNew = NULL;
666     *isNew = NULL;
667   }
668   else {
669     PetscBool globalCompress;
670 
671     ierr = MPIU_Allreduce(&compress,&globalCompress,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
672     if (compress) {
673       PetscSection secComp;
674       PetscInt *valsComp = NULL;
675 
676       ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secComp);CHKERRQ(ierr);
677       ierr = PetscSectionSetChart(secComp,pStart,pEnd);CHKERRQ(ierr);
678       for (p = pStart; p < pEnd; p++) {
679         PetscInt dof;
680 
681         ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
682         ierr = PetscSectionSetDof(secComp, p, dof);CHKERRQ(ierr);
683       }
684       ierr = PetscSectionSetUp(secComp);CHKERRQ(ierr);
685       ierr = PetscSectionGetStorageSize(secComp,&sizeNew);CHKERRQ(ierr);
686       ierr = PetscMalloc1(sizeNew,&valsComp);CHKERRQ(ierr);
687       for (p = pStart; p < pEnd; p++) {
688         PetscInt dof, off, offNew, j;
689 
690         ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
691         ierr = PetscSectionGetOffset(secNew, p, &off);CHKERRQ(ierr);
692         ierr = PetscSectionGetOffset(secComp, p, &offNew);CHKERRQ(ierr);
693         for (j = 0; j < dof; j++) {
694           valsComp[offNew + j] = valsNew[off + j];
695         }
696       }
697       ierr    = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
698       secNew  = secComp;
699       ierr    = PetscFree(valsNew);CHKERRQ(ierr);
700       valsNew = valsComp;
701     }
702     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is),sizeNew,valsNew,PETSC_OWN_POINTER,isNew);CHKERRQ(ierr);
703   }
704   PetscFunctionReturn(0);
705 }
706 
707 #undef __FUNCT__
708 #define __FUNCT__ "DMPlexCreateAnchors_Tree"
709 static PetscErrorCode DMPlexCreateAnchors_Tree(DM dm)
710 {
711   PetscInt       p, pStart, pEnd, *anchors, size;
712   PetscInt       aMin = PETSC_MAX_INT, aMax = PETSC_MIN_INT;
713   PetscSection   aSec;
714   DMLabel        canonLabel;
715   IS             aIS;
716   PetscErrorCode ierr;
717 
718   PetscFunctionBegin;
719   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
720   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
721   ierr = DMGetLabel(dm,"canonical",&canonLabel);CHKERRQ(ierr);
722   for (p = pStart; p < pEnd; p++) {
723     PetscInt parent;
724 
725     if (canonLabel) {
726       PetscInt canon;
727 
728       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
729       if (p != canon) continue;
730     }
731     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
732     if (parent != p) {
733       aMin = PetscMin(aMin,p);
734       aMax = PetscMax(aMax,p+1);
735     }
736   }
737   if (aMin > aMax) {
738     aMin = -1;
739     aMax = -1;
740   }
741   ierr = PetscSectionCreate(PETSC_COMM_SELF,&aSec);CHKERRQ(ierr);
742   ierr = PetscSectionSetChart(aSec,aMin,aMax);CHKERRQ(ierr);
743   for (p = aMin; p < aMax; p++) {
744     PetscInt parent, ancestor = p;
745 
746     if (canonLabel) {
747       PetscInt canon;
748 
749       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
750       if (p != canon) continue;
751     }
752     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
753     while (parent != ancestor) {
754       ancestor = parent;
755       ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
756     }
757     if (ancestor != p) {
758       PetscInt closureSize, *closure = NULL;
759 
760       ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
761       ierr = PetscSectionSetDof(aSec,p,closureSize);CHKERRQ(ierr);
762       ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
763     }
764   }
765   ierr = PetscSectionSetUp(aSec);CHKERRQ(ierr);
766   ierr = PetscSectionGetStorageSize(aSec,&size);CHKERRQ(ierr);
767   ierr = PetscMalloc1(size,&anchors);CHKERRQ(ierr);
768   for (p = aMin; p < aMax; p++) {
769     PetscInt parent, ancestor = p;
770 
771     if (canonLabel) {
772       PetscInt canon;
773 
774       ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
775       if (p != canon) continue;
776     }
777     ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
778     while (parent != ancestor) {
779       ancestor = parent;
780       ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
781     }
782     if (ancestor != p) {
783       PetscInt j, closureSize, *closure = NULL, aOff;
784 
785       ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
786 
787       ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
788       for (j = 0; j < closureSize; j++) {
789         anchors[aOff + j] = closure[2*j];
790       }
791       ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
792     }
793   }
794   ierr = ISCreateGeneral(PETSC_COMM_SELF,size,anchors,PETSC_OWN_POINTER,&aIS);CHKERRQ(ierr);
795   {
796     PetscSection aSecNew = aSec;
797     IS           aISNew  = aIS;
798 
799     ierr = PetscObjectReference((PetscObject)aSec);CHKERRQ(ierr);
800     ierr = PetscObjectReference((PetscObject)aIS);CHKERRQ(ierr);
801     while (aSecNew) {
802       ierr    = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
803       ierr    = ISDestroy(&aIS);CHKERRQ(ierr);
804       aSec    = aSecNew;
805       aIS     = aISNew;
806       aSecNew = NULL;
807       aISNew  = NULL;
808       ierr    = AnchorsFlatten(aSec,aIS,&aSecNew,&aISNew);CHKERRQ(ierr);
809     }
810   }
811   ierr = DMPlexSetAnchors(dm,aSec,aIS);CHKERRQ(ierr);
812   ierr = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
813   ierr = ISDestroy(&aIS);CHKERRQ(ierr);
814   PetscFunctionReturn(0);
815 }
816 
817 #undef __FUNCT__
818 #define __FUNCT__ "DMPlexGetTrueSupportSize"
819 static PetscErrorCode DMPlexGetTrueSupportSize(DM dm,PetscInt p,PetscInt *dof,PetscInt *numTrueSupp)
820 {
821   PetscErrorCode ierr;
822 
823   PetscFunctionBegin;
824   if (numTrueSupp[p] == -1) {
825     PetscInt i, alldof;
826     const PetscInt *supp;
827     PetscInt count = 0;
828 
829     ierr = DMPlexGetSupportSize(dm,p,&alldof);CHKERRQ(ierr);
830     ierr = DMPlexGetSupport(dm,p,&supp);CHKERRQ(ierr);
831     for (i = 0; i < alldof; i++) {
832       PetscInt q = supp[i], numCones, j;
833       const PetscInt *cone;
834 
835       ierr = DMPlexGetConeSize(dm,q,&numCones);CHKERRQ(ierr);
836       ierr = DMPlexGetCone(dm,q,&cone);CHKERRQ(ierr);
837       for (j = 0; j < numCones; j++) {
838         if (cone[j] == p) break;
839       }
840       if (j < numCones) count++;
841     }
842     numTrueSupp[p] = count;
843   }
844   *dof = numTrueSupp[p];
845   PetscFunctionReturn(0);
846 }
847 
848 #undef __FUNCT__
849 #define __FUNCT__ "DMPlexTreeExchangeSupports"
850 static PetscErrorCode DMPlexTreeExchangeSupports(DM dm)
851 {
852   DM_Plex *mesh = (DM_Plex *)dm->data;
853   PetscSection newSupportSection;
854   PetscInt newSize, *newSupports, pStart, pEnd, p, d, depth;
855   PetscInt *numTrueSupp;
856   PetscInt *offsets;
857   PetscErrorCode ierr;
858 
859   PetscFunctionBegin;
860   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
861   /* symmetrize the hierarchy */
862   ierr = DMPlexGetDepth(dm,&depth);CHKERRQ(ierr);
863   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)(mesh->supportSection)),&newSupportSection);CHKERRQ(ierr);
864   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
865   ierr = PetscSectionSetChart(newSupportSection,pStart,pEnd);CHKERRQ(ierr);
866   ierr = PetscCalloc1(pEnd,&offsets);CHKERRQ(ierr);
867   ierr = PetscMalloc1(pEnd,&numTrueSupp);CHKERRQ(ierr);
868   for (p = 0; p < pEnd; p++) numTrueSupp[p] = -1;
869   /* if a point is in the (true) support of q, it should be in the support of
870    * parent(q) */
871   for (d = 0; d <= depth; d++) {
872     ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
873     for (p = pStart; p < pEnd; ++p) {
874       PetscInt dof, q, qdof, parent;
875 
876       ierr = DMPlexGetTrueSupportSize(dm,p,&dof,numTrueSupp);CHKERRQ(ierr);
877       ierr = PetscSectionAddDof(newSupportSection, p, dof);CHKERRQ(ierr);
878       q    = p;
879       ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
880       while (parent != q && parent >= pStart && parent < pEnd) {
881         q = parent;
882 
883         ierr = DMPlexGetTrueSupportSize(dm,q,&qdof,numTrueSupp);CHKERRQ(ierr);
884         ierr = PetscSectionAddDof(newSupportSection,p,qdof);CHKERRQ(ierr);
885         ierr = PetscSectionAddDof(newSupportSection,q,dof);CHKERRQ(ierr);
886         ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
887       }
888     }
889   }
890   ierr = PetscSectionSetUp(newSupportSection);CHKERRQ(ierr);
891   ierr = PetscSectionGetStorageSize(newSupportSection,&newSize);CHKERRQ(ierr);
892   ierr = PetscMalloc1(newSize,&newSupports);CHKERRQ(ierr);
893   for (d = 0; d <= depth; d++) {
894     ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
895     for (p = pStart; p < pEnd; p++) {
896       PetscInt dof, off, q, qdof, qoff, newDof, newOff, newqOff, i, parent;
897 
898       ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
899       ierr = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
900       ierr = PetscSectionGetDof(newSupportSection, p, &newDof);CHKERRQ(ierr);
901       ierr = PetscSectionGetOffset(newSupportSection, p, &newOff);CHKERRQ(ierr);
902       for (i = 0; i < dof; i++) {
903         PetscInt numCones, j;
904         const PetscInt *cone;
905         PetscInt q = mesh->supports[off + i];
906 
907         ierr = DMPlexGetConeSize(dm,q,&numCones);CHKERRQ(ierr);
908         ierr = DMPlexGetCone(dm,q,&cone);CHKERRQ(ierr);
909         for (j = 0; j < numCones; j++) {
910           if (cone[j] == p) break;
911         }
912         if (j < numCones) newSupports[newOff+offsets[p]++] = q;
913       }
914       mesh->maxSupportSize = PetscMax(mesh->maxSupportSize,newDof);
915 
916       q    = p;
917       ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
918       while (parent != q && parent >= pStart && parent < pEnd) {
919         q = parent;
920         ierr = PetscSectionGetDof(mesh->supportSection, q, &qdof);CHKERRQ(ierr);
921         ierr = PetscSectionGetOffset(mesh->supportSection, q, &qoff);CHKERRQ(ierr);
922         ierr = PetscSectionGetOffset(newSupportSection, q, &newqOff);CHKERRQ(ierr);
923         for (i = 0; i < qdof; i++) {
924           PetscInt numCones, j;
925           const PetscInt *cone;
926           PetscInt r = mesh->supports[qoff + i];
927 
928           ierr = DMPlexGetConeSize(dm,r,&numCones);CHKERRQ(ierr);
929           ierr = DMPlexGetCone(dm,r,&cone);CHKERRQ(ierr);
930           for (j = 0; j < numCones; j++) {
931             if (cone[j] == q) break;
932           }
933           if (j < numCones) newSupports[newOff+offsets[p]++] = r;
934         }
935         for (i = 0; i < dof; i++) {
936           PetscInt numCones, j;
937           const PetscInt *cone;
938           PetscInt r = mesh->supports[off + i];
939 
940           ierr = DMPlexGetConeSize(dm,r,&numCones);CHKERRQ(ierr);
941           ierr = DMPlexGetCone(dm,r,&cone);CHKERRQ(ierr);
942           for (j = 0; j < numCones; j++) {
943             if (cone[j] == p) break;
944           }
945           if (j < numCones) newSupports[newqOff+offsets[q]++] = r;
946         }
947         ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
948       }
949     }
950   }
951   ierr = PetscSectionDestroy(&mesh->supportSection);CHKERRQ(ierr);
952   mesh->supportSection = newSupportSection;
953   ierr = PetscFree(mesh->supports);CHKERRQ(ierr);
954   mesh->supports = newSupports;
955   ierr = PetscFree(offsets);CHKERRQ(ierr);
956   ierr = PetscFree(numTrueSupp);CHKERRQ(ierr);
957 
958   PetscFunctionReturn(0);
959 }
960 
961 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM,PetscSection,PetscSection,Mat);
962 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM,PetscSection,PetscSection,Mat);
963 
964 #undef __FUNCT__
965 #define __FUNCT__ "DMPlexSetTree_Internal"
966 static PetscErrorCode DMPlexSetTree_Internal(DM dm, PetscSection parentSection, PetscInt *parents, PetscInt *childIDs, PetscBool computeCanonical, PetscBool exchangeSupports)
967 {
968   DM_Plex       *mesh = (DM_Plex *)dm->data;
969   DM             refTree;
970   PetscInt       size;
971   PetscErrorCode ierr;
972 
973   PetscFunctionBegin;
974   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
975   PetscValidHeaderSpecific(parentSection, PETSC_SECTION_CLASSID, 2);
976   ierr = PetscObjectReference((PetscObject)parentSection);CHKERRQ(ierr);
977   ierr = PetscSectionDestroy(&mesh->parentSection);CHKERRQ(ierr);
978   mesh->parentSection = parentSection;
979   ierr = PetscSectionGetStorageSize(parentSection,&size);CHKERRQ(ierr);
980   if (parents != mesh->parents) {
981     ierr = PetscFree(mesh->parents);CHKERRQ(ierr);
982     ierr = PetscMalloc1(size,&mesh->parents);CHKERRQ(ierr);
983     ierr = PetscMemcpy(mesh->parents, parents, size * sizeof(*parents));CHKERRQ(ierr);
984   }
985   if (childIDs != mesh->childIDs) {
986     ierr = PetscFree(mesh->childIDs);CHKERRQ(ierr);
987     ierr = PetscMalloc1(size,&mesh->childIDs);CHKERRQ(ierr);
988     ierr = PetscMemcpy(mesh->childIDs, childIDs, size * sizeof(*childIDs));CHKERRQ(ierr);
989   }
990   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
991   if (refTree) {
992     DMLabel canonLabel;
993 
994     ierr = DMGetLabel(refTree,"canonical",&canonLabel);CHKERRQ(ierr);
995     if (canonLabel) {
996       PetscInt i;
997 
998       for (i = 0; i < size; i++) {
999         PetscInt canon;
1000         ierr = DMLabelGetValue(canonLabel, mesh->childIDs[i], &canon);CHKERRQ(ierr);
1001         if (canon >= 0) {
1002           mesh->childIDs[i] = canon;
1003         }
1004       }
1005     }
1006     mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_FromReference;
1007   }
1008   else {
1009     mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_Direct;
1010   }
1011   ierr = DMPlexTreeSymmetrize(dm);CHKERRQ(ierr);
1012   if (computeCanonical) {
1013     PetscInt d, dim;
1014 
1015     /* add the canonical label */
1016     ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
1017     ierr = DMCreateLabel(dm,"canonical");CHKERRQ(ierr);
1018     for (d = 0; d <= dim; d++) {
1019       PetscInt p, dStart, dEnd, canon = -1, cNumChildren;
1020       const PetscInt *cChildren;
1021 
1022       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
1023       for (p = dStart; p < dEnd; p++) {
1024         ierr = DMPlexGetTreeChildren(dm,p,&cNumChildren,&cChildren);CHKERRQ(ierr);
1025         if (cNumChildren) {
1026           canon = p;
1027           break;
1028         }
1029       }
1030       if (canon == -1) continue;
1031       for (p = dStart; p < dEnd; p++) {
1032         PetscInt numChildren, i;
1033         const PetscInt *children;
1034 
1035         ierr = DMPlexGetTreeChildren(dm,p,&numChildren,&children);CHKERRQ(ierr);
1036         if (numChildren) {
1037           if (numChildren != cNumChildren) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_PLIB,"All parent points in a stratum should have the same number of children: %d != %d", numChildren, cNumChildren);
1038           ierr = DMSetLabelValue(dm,"canonical",p,canon);CHKERRQ(ierr);
1039           for (i = 0; i < numChildren; i++) {
1040             ierr = DMSetLabelValue(dm,"canonical",children[i],cChildren[i]);CHKERRQ(ierr);
1041           }
1042         }
1043       }
1044     }
1045   }
1046   if (exchangeSupports) {
1047     ierr = DMPlexTreeExchangeSupports(dm);CHKERRQ(ierr);
1048   }
1049   mesh->createanchors = DMPlexCreateAnchors_Tree;
1050   /* reset anchors */
1051   ierr = DMPlexSetAnchors(dm,NULL,NULL);CHKERRQ(ierr);
1052   PetscFunctionReturn(0);
1053 }
1054 
1055 #undef __FUNCT__
1056 #define __FUNCT__ "DMPlexSetTree"
1057 /*@
1058   DMPlexSetTree - set the tree that describes the hierarchy of non-conforming mesh points.  This routine also creates
1059   the point-to-point constraints determined by the tree: a point is constained to the points in the closure of its
1060   tree root.
1061 
1062   Collective on dm
1063 
1064   Input Parameters:
1065 + dm - the DMPlex object
1066 . parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
1067                   offset indexes the parent and childID list; the reference count of parentSection is incremented
1068 . parents - a list of the point parents; copied, can be destroyed
1069 - childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
1070              the child corresponds to the point in the reference tree with index childIDs; copied, can be destroyed
1071 
1072   Level: intermediate
1073 
1074 .seealso: DMPlexGetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
1075 @*/
1076 PetscErrorCode DMPlexSetTree(DM dm, PetscSection parentSection, PetscInt parents[], PetscInt childIDs[])
1077 {
1078   PetscErrorCode ierr;
1079 
1080   PetscFunctionBegin;
1081   ierr = DMPlexSetTree_Internal(dm,parentSection,parents,childIDs,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
1082   PetscFunctionReturn(0);
1083 }
1084 
1085 #undef __FUNCT__
1086 #define __FUNCT__ "DMPlexGetTree"
1087 /*@
1088   DMPlexGetTree - get the tree that describes the hierarchy of non-conforming mesh points.
1089   Collective on dm
1090 
1091   Input Parameters:
1092 . dm - the DMPlex object
1093 
1094   Output Parameters:
1095 + parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
1096                   offset indexes the parent and childID list
1097 . parents - a list of the point parents
1098 . childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
1099              the child corresponds to the point in the reference tree with index childID
1100 . childSection - the inverse of the parent section
1101 - children - a list of the point children
1102 
1103   Level: intermediate
1104 
1105 .seealso: DMPlexSetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
1106 @*/
1107 PetscErrorCode DMPlexGetTree(DM dm, PetscSection *parentSection, PetscInt *parents[], PetscInt *childIDs[], PetscSection *childSection, PetscInt *children[])
1108 {
1109   DM_Plex        *mesh = (DM_Plex *)dm->data;
1110 
1111   PetscFunctionBegin;
1112   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1113   if (parentSection) *parentSection = mesh->parentSection;
1114   if (parents)       *parents       = mesh->parents;
1115   if (childIDs)      *childIDs      = mesh->childIDs;
1116   if (childSection)  *childSection  = mesh->childSection;
1117   if (children)      *children      = mesh->children;
1118   PetscFunctionReturn(0);
1119 }
1120 
1121 #undef __FUNCT__
1122 #define __FUNCT__ "DMPlexGetTreeParent"
1123 /*@
1124   DMPlexGetTreeParent - get the parent of a point in the tree describing the point hierarchy (not the Sieve DAG)
1125 
1126   Input Parameters:
1127 + dm - the DMPlex object
1128 - point - the query point
1129 
1130   Output Parameters:
1131 + parent - if not NULL, set to the parent of the point, or the point itself if the point does not have a parent
1132 - childID - if not NULL, set to the child ID of the point with respect to its parent, or 0 if the point
1133             does not have a parent
1134 
1135   Level: intermediate
1136 
1137 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeChildren()
1138 @*/
1139 PetscErrorCode DMPlexGetTreeParent(DM dm, PetscInt point, PetscInt *parent, PetscInt *childID)
1140 {
1141   DM_Plex       *mesh = (DM_Plex *)dm->data;
1142   PetscSection   pSec;
1143   PetscErrorCode ierr;
1144 
1145   PetscFunctionBegin;
1146   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1147   pSec = mesh->parentSection;
1148   if (pSec && point >= pSec->pStart && point < pSec->pEnd) {
1149     PetscInt dof;
1150 
1151     ierr = PetscSectionGetDof (pSec, point, &dof);CHKERRQ(ierr);
1152     if (dof) {
1153       PetscInt off;
1154 
1155       ierr = PetscSectionGetOffset (pSec, point, &off);CHKERRQ(ierr);
1156       if (parent)  *parent = mesh->parents[off];
1157       if (childID) *childID = mesh->childIDs[off];
1158       PetscFunctionReturn(0);
1159     }
1160   }
1161   if (parent) {
1162     *parent = point;
1163   }
1164   if (childID) {
1165     *childID = 0;
1166   }
1167   PetscFunctionReturn(0);
1168 }
1169 
1170 #undef __FUNCT__
1171 #define __FUNCT__ "DMPlexGetTreeChildren"
1172 /*@C
1173   DMPlexGetTreeChildren - get the children of a point in the tree describing the point hierarchy (not the Sieve DAG)
1174 
1175   Input Parameters:
1176 + dm - the DMPlex object
1177 - point - the query point
1178 
1179   Output Parameters:
1180 + numChildren - if not NULL, set to the number of children
1181 - children - if not NULL, set to a list children, or set to NULL if the point has no children
1182 
1183   Level: intermediate
1184 
1185   Fortran Notes:
1186   Since it returns an array, this routine is only available in Fortran 90, and you must
1187   include petsc.h90 in your code.
1188 
1189 .seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeParent()
1190 @*/
1191 PetscErrorCode DMPlexGetTreeChildren(DM dm, PetscInt point, PetscInt *numChildren, const PetscInt *children[])
1192 {
1193   DM_Plex       *mesh = (DM_Plex *)dm->data;
1194   PetscSection   childSec;
1195   PetscInt       dof = 0;
1196   PetscErrorCode ierr;
1197 
1198   PetscFunctionBegin;
1199   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1200   childSec = mesh->childSection;
1201   if (childSec && point >= childSec->pStart && point < childSec->pEnd) {
1202     ierr = PetscSectionGetDof (childSec, point, &dof);CHKERRQ(ierr);
1203   }
1204   if (numChildren) *numChildren = dof;
1205   if (children) {
1206     if (dof) {
1207       PetscInt off;
1208 
1209       ierr = PetscSectionGetOffset (childSec, point, &off);CHKERRQ(ierr);
1210       *children = &mesh->children[off];
1211     }
1212     else {
1213       *children = NULL;
1214     }
1215   }
1216   PetscFunctionReturn(0);
1217 }
1218 
1219 #undef __FUNCT__
1220 #define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_Direct"
1221 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM dm, PetscSection section, PetscSection cSec, Mat cMat)
1222 {
1223   PetscDS        ds;
1224   PetscInt       spdim;
1225   PetscInt       numFields, f, c, cStart, cEnd, pStart, pEnd, conStart, conEnd;
1226   const PetscInt *anchors;
1227   PetscSection   aSec;
1228   PetscReal      *v0, *v0parent, *vtmp, *J, *Jparent, *invJparent, detJ, detJparent;
1229   IS             aIS;
1230   PetscErrorCode ierr;
1231 
1232   PetscFunctionBegin;
1233   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1234   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1235   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1236   ierr = DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);CHKERRQ(ierr);
1237   ierr = DMPlexGetAnchors(dm,&aSec,&aIS);CHKERRQ(ierr);
1238   ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
1239   ierr = PetscSectionGetChart(cSec,&conStart,&conEnd);CHKERRQ(ierr);
1240   ierr = DMGetDimension(dm,&spdim);CHKERRQ(ierr);
1241   ierr = PetscMalloc6(spdim,&v0,spdim,&v0parent,spdim,&vtmp,spdim*spdim,&J,spdim*spdim,&Jparent,spdim*spdim,&invJparent);CHKERRQ(ierr);
1242 
1243   for (f = 0; f < numFields; f++) {
1244     PetscObject disc;
1245     PetscFE fe = NULL;
1246     PetscFV fv = NULL;
1247     PetscClassId id;
1248     PetscDualSpace space;
1249     PetscInt i, j, k, nPoints, offset;
1250     PetscInt fSize, fComp;
1251     PetscReal *B = NULL;
1252     PetscReal *weights, *pointsRef, *pointsReal;
1253     Mat Amat, Bmat, Xmat;
1254 
1255     ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
1256     ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
1257     if (id == PETSCFE_CLASSID) {
1258       fe = (PetscFE) disc;
1259       ierr = PetscFEGetDualSpace(fe,&space);CHKERRQ(ierr);
1260       ierr = PetscDualSpaceGetDimension(space,&fSize);CHKERRQ(ierr);
1261       ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1262     }
1263     else if (id == PETSCFV_CLASSID) {
1264       fv = (PetscFV) disc;
1265       ierr = PetscFVGetDualSpace(fv,&space);CHKERRQ(ierr);
1266       ierr = PetscDualSpaceGetDimension(space,&fSize);CHKERRQ(ierr);
1267       ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
1268     }
1269     else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);
1270 
1271     ierr = MatCreate(PETSC_COMM_SELF,&Amat);CHKERRQ(ierr);
1272     ierr = MatSetSizes(Amat,fSize,fSize,fSize,fSize);CHKERRQ(ierr);
1273     ierr = MatSetType(Amat,MATSEQDENSE);CHKERRQ(ierr);
1274     ierr = MatSetUp(Amat);CHKERRQ(ierr);
1275     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Bmat);CHKERRQ(ierr);
1276     ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Xmat);CHKERRQ(ierr);
1277     nPoints = 0;
1278     for (i = 0; i < fSize; i++) {
1279       PetscInt        qPoints;
1280       PetscQuadrature quad;
1281 
1282       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1283       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1284       nPoints += qPoints;
1285     }
1286     ierr = PetscMalloc3(nPoints,&weights,spdim*nPoints,&pointsRef,spdim*nPoints,&pointsReal);CHKERRQ(ierr);
1287     offset = 0;
1288     for (i = 0; i < fSize; i++) {
1289       PetscInt        qPoints;
1290       const PetscReal    *p, *w;
1291       PetscQuadrature quad;
1292 
1293       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1294       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,&p,&w);CHKERRQ(ierr);
1295       ierr = PetscMemcpy(weights+offset,w,qPoints*sizeof(*w));CHKERRQ(ierr);
1296       ierr = PetscMemcpy(pointsRef+spdim*offset,p,spdim*qPoints*sizeof(*p));CHKERRQ(ierr);
1297       offset += qPoints;
1298     }
1299     if (id == PETSCFE_CLASSID) {
1300       ierr = PetscFEGetTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1301     }
1302     else {
1303       ierr = PetscFVGetTabulation(fv,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1304     }
1305     offset = 0;
1306     for (i = 0; i < fSize; i++) {
1307       PetscInt        qPoints;
1308       PetscQuadrature quad;
1309 
1310       ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1311       ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1312       for (j = 0; j < fSize; j++) {
1313         PetscScalar val = 0.;
1314 
1315         for (k = 0; k < qPoints; k++) {
1316           val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1317         }
1318         ierr = MatSetValue(Amat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1319       }
1320       offset += qPoints;
1321     }
1322     if (id == PETSCFE_CLASSID) {
1323       ierr = PetscFERestoreTabulation(fe,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1324     }
1325     else {
1326       ierr = PetscFVRestoreTabulation(fv,nPoints,pointsRef,&B,NULL,NULL);CHKERRQ(ierr);
1327     }
1328     ierr = MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1329     ierr = MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1330     ierr = MatLUFactor(Amat,NULL,NULL,NULL);CHKERRQ(ierr);
1331     for (c = cStart; c < cEnd; c++) {
1332       PetscInt parent;
1333       PetscInt closureSize, closureSizeP, *closure = NULL, *closureP = NULL;
1334       PetscInt *childOffsets, *parentOffsets;
1335 
1336       ierr = DMPlexGetTreeParent(dm,c,&parent,NULL);CHKERRQ(ierr);
1337       if (parent == c) continue;
1338       ierr = DMPlexGetTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1339       for (i = 0; i < closureSize; i++) {
1340         PetscInt p = closure[2*i];
1341         PetscInt conDof;
1342 
1343         if (p < conStart || p >= conEnd) continue;
1344         if (numFields > 1) {
1345           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1346         }
1347         else {
1348           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1349         }
1350         if (conDof) break;
1351       }
1352       if (i == closureSize) {
1353         ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1354         continue;
1355       }
1356 
1357       ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
1358       ierr = DMPlexComputeCellGeometryFEM(dm, parent, NULL, v0parent, Jparent, invJparent, &detJparent);CHKERRQ(ierr);
1359       for (i = 0; i < nPoints; i++) {
1360         CoordinatesRefToReal(spdim, spdim, v0, J, &pointsRef[i*spdim],vtmp);CHKERRQ(ierr);
1361         CoordinatesRealToRef(spdim, spdim, v0parent, invJparent, vtmp, &pointsReal[i*spdim]);CHKERRQ(ierr);
1362       }
1363       if (id == PETSCFE_CLASSID) {
1364         ierr = PetscFEGetTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1365       }
1366       else {
1367         ierr = PetscFVGetTabulation(fv,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1368       }
1369       offset = 0;
1370       for (i = 0; i < fSize; i++) {
1371         PetscInt        qPoints;
1372         PetscQuadrature quad;
1373 
1374         ierr = PetscDualSpaceGetFunctional(space,i,&quad);CHKERRQ(ierr);
1375         ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
1376         for (j = 0; j < fSize; j++) {
1377           PetscScalar val = 0.;
1378 
1379           for (k = 0; k < qPoints; k++) {
1380             val += B[((offset + k) * fSize + j) * fComp] * weights[k];
1381           }
1382           MatSetValue(Bmat,i,j,val,INSERT_VALUES);CHKERRQ(ierr);
1383         }
1384         offset += qPoints;
1385       }
1386       if (id == PETSCFE_CLASSID) {
1387         ierr = PetscFERestoreTabulation(fe,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1388       }
1389       else {
1390         ierr = PetscFVRestoreTabulation(fv,nPoints,pointsReal,&B,NULL,NULL);CHKERRQ(ierr);
1391       }
1392       ierr = MatAssemblyBegin(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1393       ierr = MatAssemblyEnd(Bmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1394       ierr = MatMatSolve(Amat,Bmat,Xmat);CHKERRQ(ierr);
1395       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1396       ierr = PetscMalloc2(closureSize+1,&childOffsets,closureSizeP+1,&parentOffsets);CHKERRQ(ierr);
1397       childOffsets[0] = 0;
1398       for (i = 0; i < closureSize; i++) {
1399         PetscInt p = closure[2*i];
1400         PetscInt dof;
1401 
1402         if (numFields > 1) {
1403           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1404         }
1405         else {
1406           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1407         }
1408         childOffsets[i+1]=childOffsets[i]+dof / fComp;
1409       }
1410       parentOffsets[0] = 0;
1411       for (i = 0; i < closureSizeP; i++) {
1412         PetscInt p = closureP[2*i];
1413         PetscInt dof;
1414 
1415         if (numFields > 1) {
1416           ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
1417         }
1418         else {
1419           ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
1420         }
1421         parentOffsets[i+1]=parentOffsets[i]+dof / fComp;
1422       }
1423       for (i = 0; i < closureSize; i++) {
1424         PetscInt conDof, conOff, aDof, aOff;
1425         PetscInt p = closure[2*i];
1426         PetscInt o = closure[2*i+1];
1427 
1428         if (p < conStart || p >= conEnd) continue;
1429         if (numFields > 1) {
1430           ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
1431           ierr = PetscSectionGetFieldOffset(cSec,p,f,&conOff);CHKERRQ(ierr);
1432         }
1433         else {
1434           ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
1435           ierr = PetscSectionGetOffset(cSec,p,&conOff);CHKERRQ(ierr);
1436         }
1437         if (!conDof) continue;
1438         ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
1439         ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
1440         for (k = 0; k < aDof; k++) {
1441           PetscInt a = anchors[aOff + k];
1442           PetscInt aSecDof, aSecOff;
1443 
1444           if (numFields > 1) {
1445             ierr = PetscSectionGetFieldDof(section,a,f,&aSecDof);CHKERRQ(ierr);
1446             ierr = PetscSectionGetFieldOffset(section,a,f,&aSecOff);CHKERRQ(ierr);
1447           }
1448           else {
1449             ierr = PetscSectionGetDof(section,a,&aSecDof);CHKERRQ(ierr);
1450             ierr = PetscSectionGetOffset(section,a,&aSecOff);CHKERRQ(ierr);
1451           }
1452           if (!aSecDof) continue;
1453 
1454           for (j = 0; j < closureSizeP; j++) {
1455             PetscInt q = closureP[2*j];
1456             PetscInt oq = closureP[2*j+1];
1457 
1458             if (q == a) {
1459               PetscInt r, s, t;
1460 
1461               for (r = childOffsets[i]; r < childOffsets[i+1]; r++) {
1462                 for (s = parentOffsets[j]; s < parentOffsets[j+1]; s++) {
1463                   PetscScalar val;
1464                   PetscInt insertCol, insertRow;
1465 
1466                   ierr = MatGetValue(Xmat,r,s,&val);CHKERRQ(ierr);
1467                   if (o >= 0) {
1468                     insertRow = conOff + fComp * (r - childOffsets[i]);
1469                   }
1470                   else {
1471                     insertRow = conOff + fComp * (childOffsets[i + 1] - 1 - r);
1472                   }
1473                   if (oq >= 0) {
1474                     insertCol = aSecOff + fComp * (s - parentOffsets[j]);
1475                   }
1476                   else {
1477                     insertCol = aSecOff + fComp * (parentOffsets[j + 1] - 1 - s);
1478                   }
1479                   for (t = 0; t < fComp; t++) {
1480                     ierr = MatSetValue(cMat,insertRow + t,insertCol + t,val,INSERT_VALUES);CHKERRQ(ierr);
1481                   }
1482                 }
1483               }
1484             }
1485           }
1486         }
1487       }
1488       ierr = PetscFree2(childOffsets,parentOffsets);CHKERRQ(ierr);
1489       ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1490       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
1491     }
1492     ierr = MatDestroy(&Amat);CHKERRQ(ierr);
1493     ierr = MatDestroy(&Bmat);CHKERRQ(ierr);
1494     ierr = MatDestroy(&Xmat);CHKERRQ(ierr);
1495     ierr = PetscFree3(weights,pointsRef,pointsReal);CHKERRQ(ierr);
1496   }
1497   ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1498   ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1499   ierr = PetscFree6(v0,v0parent,vtmp,J,Jparent,invJparent);CHKERRQ(ierr);
1500   ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
1501 
1502   PetscFunctionReturn(0);
1503 }
1504 
1505 #undef __FUNCT__
1506 #define __FUNCT__ "DMPlexReferenceTreeGetChildrenMatrices"
1507 static PetscErrorCode DMPlexReferenceTreeGetChildrenMatrices(DM refTree, PetscScalar ****childrenMats, PetscInt ***childrenN)
1508 {
1509   Mat            refCmat;
1510   PetscDS        ds;
1511   PetscInt       numFields, f, pRefStart, pRefEnd, p, *rows, *cols, maxDof, maxAnDof, **refPointFieldN;
1512   PetscScalar    ***refPointFieldMats;
1513   PetscSection   refConSec, refAnSec, refSection;
1514   IS             refAnIS;
1515   const PetscInt *refAnchors;
1516   PetscErrorCode ierr;
1517 
1518   PetscFunctionBegin;
1519   ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
1520   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1521   ierr = DMGetDefaultConstraints(refTree,&refConSec,&refCmat);CHKERRQ(ierr);
1522   ierr = DMPlexGetAnchors(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
1523   ierr = ISGetIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
1524   ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
1525   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1526   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldMats);CHKERRQ(ierr);
1527   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldN);CHKERRQ(ierr);
1528   ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
1529   ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
1530   ierr = PetscMalloc1(maxDof,&rows);CHKERRQ(ierr);
1531   ierr = PetscMalloc1(maxDof*maxAnDof,&cols);CHKERRQ(ierr);
1532   for (p = pRefStart; p < pRefEnd; p++) {
1533     PetscInt parent, closureSize, *closure = NULL, pDof;
1534 
1535     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
1536     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
1537     if (!pDof || parent == p) continue;
1538 
1539     ierr = PetscMalloc1(numFields,&refPointFieldMats[p-pRefStart]);CHKERRQ(ierr);
1540     ierr = PetscCalloc1(numFields,&refPointFieldN[p-pRefStart]);CHKERRQ(ierr);
1541     ierr = DMPlexGetTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1542     for (f = 0; f < numFields; f++) {
1543       PetscInt cDof, cOff, numCols, r, i, fComp;
1544       PetscObject disc;
1545       PetscClassId id;
1546       PetscFE fe = NULL;
1547       PetscFV fv = NULL;
1548 
1549       ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
1550       ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
1551       if (id == PETSCFE_CLASSID) {
1552         fe = (PetscFE) disc;
1553         ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1554       }
1555       else if (id == PETSCFV_CLASSID) {
1556         fv = (PetscFV) disc;
1557         ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
1558       }
1559       else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);
1560 
1561       if (numFields > 1) {
1562         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
1563         ierr = PetscSectionGetFieldOffset(refConSec,p,f,&cOff);CHKERRQ(ierr);
1564       }
1565       else {
1566         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
1567         ierr = PetscSectionGetOffset(refConSec,p,&cOff);CHKERRQ(ierr);
1568       }
1569 
1570       for (r = 0; r < cDof; r++) {
1571         rows[r] = cOff + r;
1572       }
1573       numCols = 0;
1574       for (i = 0; i < closureSize; i++) {
1575         PetscInt q = closure[2*i];
1576         PetscInt o = closure[2*i+1];
1577         PetscInt aDof, aOff, j;
1578 
1579         if (numFields > 1) {
1580           ierr = PetscSectionGetFieldDof(refSection,q,f,&aDof);CHKERRQ(ierr);
1581           ierr = PetscSectionGetFieldOffset(refSection,q,f,&aOff);CHKERRQ(ierr);
1582         }
1583         else {
1584           ierr = PetscSectionGetDof(refSection,q,&aDof);CHKERRQ(ierr);
1585           ierr = PetscSectionGetOffset(refSection,q,&aOff);CHKERRQ(ierr);
1586         }
1587 
1588         for (j = 0; j < aDof; j++) {
1589           PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
1590           PetscInt comp = (j % fComp);
1591 
1592           cols[numCols++] = aOff + node * fComp + comp;
1593         }
1594       }
1595       refPointFieldN[p-pRefStart][f] = numCols;
1596       ierr = PetscMalloc1(cDof*numCols,&refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1597       ierr = MatGetValues(refCmat,cDof,rows,numCols,cols,refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
1598     }
1599     ierr = DMPlexRestoreTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1600   }
1601   *childrenMats = refPointFieldMats;
1602   *childrenN = refPointFieldN;
1603   ierr = ISRestoreIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
1604   ierr = PetscFree(rows);CHKERRQ(ierr);
1605   ierr = PetscFree(cols);CHKERRQ(ierr);
1606   PetscFunctionReturn(0);
1607 }
1608 
1609 #undef __FUNCT__
1610 #define __FUNCT__ "DMPlexReferenceTreeRestoreChildrenMatrices"
1611 static PetscErrorCode DMPlexReferenceTreeRestoreChildrenMatrices(DM refTree, PetscScalar ****childrenMats, PetscInt ***childrenN)
1612 {
1613   PetscDS        ds;
1614   PetscInt       **refPointFieldN;
1615   PetscScalar    ***refPointFieldMats;
1616   PetscInt       numFields, pRefStart, pRefEnd, p, f;
1617   PetscSection   refConSec;
1618   PetscErrorCode ierr;
1619 
1620   PetscFunctionBegin;
1621   refPointFieldN = *childrenN;
1622   *childrenN = NULL;
1623   refPointFieldMats = *childrenMats;
1624   *childrenMats = NULL;
1625   ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
1626   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1627   ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
1628   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1629   for (p = pRefStart; p < pRefEnd; p++) {
1630     PetscInt parent, pDof;
1631 
1632     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
1633     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
1634     if (!pDof || parent == p) continue;
1635 
1636     for (f = 0; f < numFields; f++) {
1637       PetscInt cDof;
1638 
1639       if (numFields > 1) {
1640         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
1641       }
1642       else {
1643         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
1644       }
1645 
1646       ierr = PetscFree(refPointFieldMats[p - pRefStart][f]);CHKERRQ(ierr);
1647     }
1648     ierr = PetscFree(refPointFieldMats[p - pRefStart]);CHKERRQ(ierr);
1649     ierr = PetscFree(refPointFieldN[p - pRefStart]);CHKERRQ(ierr);
1650   }
1651   ierr = PetscFree(refPointFieldMats);CHKERRQ(ierr);
1652   ierr = PetscFree(refPointFieldN);CHKERRQ(ierr);
1653   PetscFunctionReturn(0);
1654 }
1655 
1656 #undef __FUNCT__
1657 #define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_FromReference"
1658 static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM dm, PetscSection section, PetscSection conSec, Mat cMat)
1659 {
1660   DM             refTree;
1661   PetscDS        ds;
1662   Mat            refCmat;
1663   PetscInt       numFields, f, pRefStart, pRefEnd, p, maxDof, maxAnDof, *perm, *iperm, pStart, pEnd, conStart, conEnd, **refPointFieldN;
1664   PetscScalar ***refPointFieldMats, *pointWork;
1665   PetscSection   refConSec, refAnSec, anSec;
1666   IS             refAnIS, anIS;
1667   const PetscInt *anchors;
1668   PetscErrorCode ierr;
1669 
1670   PetscFunctionBegin;
1671   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1672   ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
1673   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
1674   ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
1675   ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
1676   ierr = DMGetDefaultConstraints(refTree,&refConSec,&refCmat);CHKERRQ(ierr);
1677   ierr = DMPlexGetAnchors(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
1678   ierr = DMPlexGetAnchors(dm,&anSec,&anIS);CHKERRQ(ierr);
1679   ierr = ISGetIndices(anIS,&anchors);CHKERRQ(ierr);
1680   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
1681   ierr = PetscSectionGetChart(conSec,&conStart,&conEnd);CHKERRQ(ierr);
1682   ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
1683   ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
1684   ierr = PetscMalloc1(maxDof*maxDof*maxAnDof,&pointWork);CHKERRQ(ierr);
1685 
1686   /* step 1: get submats for every constrained point in the reference tree */
1687   ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
1688 
1689   /* step 2: compute the preorder */
1690   ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
1691   ierr = PetscMalloc2(pEnd-pStart,&perm,pEnd-pStart,&iperm);CHKERRQ(ierr);
1692   for (p = pStart; p < pEnd; p++) {
1693     perm[p - pStart] = p;
1694     iperm[p - pStart] = p-pStart;
1695   }
1696   for (p = 0; p < pEnd - pStart;) {
1697     PetscInt point = perm[p];
1698     PetscInt parent;
1699 
1700     ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
1701     if (parent == point) {
1702       p++;
1703     }
1704     else {
1705       PetscInt size, closureSize, *closure = NULL, i;
1706 
1707       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1708       for (i = 0; i < closureSize; i++) {
1709         PetscInt q = closure[2*i];
1710         if (iperm[q-pStart] > iperm[point-pStart]) {
1711           /* swap */
1712           perm[p]               = q;
1713           perm[iperm[q-pStart]] = point;
1714           iperm[point-pStart]   = iperm[q-pStart];
1715           iperm[q-pStart]       = p;
1716           break;
1717         }
1718       }
1719       size = closureSize;
1720       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1721       if (i == size) {
1722         p++;
1723       }
1724     }
1725   }
1726 
1727   /* step 3: fill the constraint matrix */
1728   /* we are going to use a preorder progressive fill strategy.  Mat doesn't
1729    * allow progressive fill without assembly, so we are going to set up the
1730    * values outside of the Mat first.
1731    */
1732   {
1733     PetscInt nRows, row, nnz;
1734     PetscBool done;
1735     const PetscInt *ia, *ja;
1736     PetscScalar *vals;
1737 
1738     ierr = MatGetRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
1739     if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not get RowIJ of constraint matrix");
1740     nnz  = ia[nRows];
1741     /* malloc and then zero rows right before we fill them: this way valgrind
1742      * can tell if we are doing progressive fill in the wrong order */
1743     ierr = PetscMalloc1(nnz,&vals);CHKERRQ(ierr);
1744     for (p = 0; p < pEnd - pStart; p++) {
1745       PetscInt parent, childid, closureSize, *closure = NULL;
1746       PetscInt point = perm[p], pointDof;
1747 
1748       ierr = DMPlexGetTreeParent(dm,point,&parent,&childid);CHKERRQ(ierr);
1749       if ((point < conStart) || (point >= conEnd) || (parent == point)) continue;
1750       ierr = PetscSectionGetDof(conSec,point,&pointDof);CHKERRQ(ierr);
1751       if (!pointDof) continue;
1752       ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1753       for (f = 0; f < numFields; f++) {
1754         PetscInt cDof, cOff, numCols, numFillCols, i, r, fComp = -1, matOffset, offset;
1755         PetscScalar *pointMat;
1756         PetscObject disc;
1757         PetscClassId id;
1758         PetscFE fe = NULL;
1759         PetscFV fv = NULL;
1760 
1761         ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
1762         ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
1763         if (id == PETSCFE_CLASSID) {
1764           fe = (PetscFE) disc;
1765           ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
1766         }
1767         else if (id == PETSCFV_CLASSID) {
1768           fv = (PetscFV) disc;
1769           ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
1770         }
1771         else {
1772           SETERRQ(PetscObjectComm((PetscObject)disc),PETSC_ERR_SUP,"Unsupported discretization");
1773         }
1774 
1775         if (numFields > 1) {
1776           ierr = PetscSectionGetFieldDof(conSec,point,f,&cDof);CHKERRQ(ierr);
1777           ierr = PetscSectionGetFieldOffset(conSec,point,f,&cOff);CHKERRQ(ierr);
1778         }
1779         else {
1780           ierr = PetscSectionGetDof(conSec,point,&cDof);CHKERRQ(ierr);
1781           ierr = PetscSectionGetOffset(conSec,point,&cOff);CHKERRQ(ierr);
1782         }
1783         if (!cDof) continue;
1784 
1785         /* make sure that every row for this point is the same size */
1786 #if defined(PETSC_USE_DEBUG)
1787         for (r = 0; r < cDof; r++) {
1788           if (cDof > 1 && r) {
1789             if ((ia[cOff+r+1]-ia[cOff+r]) != (ia[cOff+r]-ia[cOff+r-1])) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Two point rows have different nnz: %D vs. %D", (ia[cOff+r+1]-ia[cOff+r]), (ia[cOff+r]-ia[cOff+r-1]));
1790           }
1791         }
1792 #endif
1793         /* zero rows */
1794         for (i = ia[cOff] ; i< ia[cOff+cDof];i++) {
1795           vals[i] = 0.;
1796         }
1797         matOffset = ia[cOff];
1798         numFillCols = ia[cOff+1] - matOffset;
1799         pointMat = refPointFieldMats[childid-pRefStart][f];
1800         numCols = refPointFieldN[childid-pRefStart][f];
1801         offset = 0;
1802         for (i = 0; i < closureSize; i++) {
1803           PetscInt q = closure[2*i];
1804           PetscInt o = closure[2*i+1];
1805           PetscInt aDof, aOff, j, k, qConDof, qConOff;
1806 
1807           qConDof = qConOff = 0;
1808           if (numFields > 1) {
1809             ierr = PetscSectionGetFieldDof(section,q,f,&aDof);CHKERRQ(ierr);
1810             ierr = PetscSectionGetFieldOffset(section,q,f,&aOff);CHKERRQ(ierr);
1811             if (q >= conStart && q < conEnd) {
1812               ierr = PetscSectionGetFieldDof(conSec,q,f,&qConDof);CHKERRQ(ierr);
1813               ierr = PetscSectionGetFieldOffset(conSec,q,f,&qConOff);CHKERRQ(ierr);
1814             }
1815           }
1816           else {
1817             ierr = PetscSectionGetDof(section,q,&aDof);CHKERRQ(ierr);
1818             ierr = PetscSectionGetOffset(section,q,&aOff);CHKERRQ(ierr);
1819             if (q >= conStart && q < conEnd) {
1820               ierr = PetscSectionGetDof(conSec,q,&qConDof);CHKERRQ(ierr);
1821               ierr = PetscSectionGetOffset(conSec,q,&qConOff);CHKERRQ(ierr);
1822             }
1823           }
1824           if (!aDof) continue;
1825           if (qConDof) {
1826             /* this point has anchors: its rows of the matrix should already
1827              * be filled, thanks to preordering */
1828             /* first multiply into pointWork, then set in matrix */
1829             PetscInt aMatOffset = ia[qConOff];
1830             PetscInt aNumFillCols = ia[qConOff + 1] - aMatOffset;
1831             for (r = 0; r < cDof; r++) {
1832               for (j = 0; j < aNumFillCols; j++) {
1833                 PetscScalar inVal = 0;
1834                 for (k = 0; k < aDof; k++) {
1835                   PetscInt node = (o >= 0) ? (k / fComp) : ((aDof - 1 - k) / fComp);
1836                   PetscInt comp = (k % fComp);
1837                   PetscInt col  = node * fComp + comp;
1838 
1839                   inVal += pointMat[r * numCols + offset + col] * vals[aMatOffset + aNumFillCols * k + j];
1840                 }
1841                 pointWork[r * aNumFillCols + j] = inVal;
1842               }
1843             }
1844             /* assume that the columns are sorted, spend less time searching */
1845             for (j = 0, k = 0; j < aNumFillCols; j++) {
1846               PetscInt col = ja[aMatOffset + j];
1847               for (;k < numFillCols; k++) {
1848                 if (ja[matOffset + k] == col) {
1849                   break;
1850                 }
1851               }
1852               if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, col);
1853               for (r = 0; r < cDof; r++) {
1854                 vals[matOffset + numFillCols * r + k] = pointWork[r * aNumFillCols + j];
1855               }
1856             }
1857           }
1858           else {
1859             /* find where to put this portion of pointMat into the matrix */
1860             for (k = 0; k < numFillCols; k++) {
1861               if (ja[matOffset + k] == aOff) {
1862                 break;
1863               }
1864             }
1865             if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, aOff);
1866             for (j = 0; j < aDof; j++) {
1867               PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
1868               PetscInt comp = (j % fComp);
1869               PetscInt col  = node * fComp + comp;
1870               for (r = 0; r < cDof; r++) {
1871                 vals[matOffset + numFillCols * r + k + col] += pointMat[r * numCols + offset + col];
1872               }
1873             }
1874           }
1875           offset += aDof;
1876         }
1877       }
1878       ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
1879     }
1880     for (row = 0; row < nRows; row++) {
1881       ierr = MatSetValues(cMat,1,&row,ia[row+1]-ia[row],&ja[ia[row]],&vals[ia[row]],INSERT_VALUES);CHKERRQ(ierr);
1882     }
1883     ierr = MatRestoreRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
1884     if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not restore RowIJ of constraint matrix");
1885     ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1886     ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1887     ierr = PetscFree(vals);CHKERRQ(ierr);
1888   }
1889 
1890   /* clean up */
1891   ierr = ISRestoreIndices(anIS,&anchors);CHKERRQ(ierr);
1892   ierr = PetscFree2(perm,iperm);CHKERRQ(ierr);
1893   ierr = PetscFree(pointWork);CHKERRQ(ierr);
1894   ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
1895   PetscFunctionReturn(0);
1896 }
1897 
1898 #undef __FUNCT__
1899 #define __FUNCT__ "DMPlexTreeRefineCell"
1900 /* refine a single cell on rank 0: this is not intended to provide good local refinement, only to create an example of
1901  * a non-conforming mesh.  Local refinement comes later */
1902 PetscErrorCode DMPlexTreeRefineCell (DM dm, PetscInt cell, DM *ncdm)
1903 {
1904   DM K;
1905   PetscMPIInt rank;
1906   PetscInt dim, *pNewStart, *pNewEnd, *pNewCount, *pOldStart, *pOldEnd, offset, d, pStart, pEnd;
1907   PetscInt numNewCones, *newConeSizes, *newCones, *newOrientations;
1908   PetscInt *Kembedding;
1909   PetscInt *cellClosure=NULL, nc;
1910   PetscScalar *newVertexCoords;
1911   PetscInt numPointsWithParents, *parents, *childIDs, *perm, *iperm, *preOrient, pOffset;
1912   PetscSection parentSection;
1913   PetscErrorCode ierr;
1914 
1915   PetscFunctionBegin;
1916   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm),&rank);CHKERRQ(ierr);
1917   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
1918   ierr = DMPlexCreate(PetscObjectComm((PetscObject)dm), ncdm);CHKERRQ(ierr);
1919   ierr = DMSetDimension(*ncdm,dim);CHKERRQ(ierr);
1920 
1921   ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
1922   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&parentSection);CHKERRQ(ierr);
1923   ierr = DMPlexGetReferenceTree(dm,&K);CHKERRQ(ierr);
1924   if (!rank) {
1925     /* compute the new charts */
1926     ierr = PetscMalloc5(dim+1,&pNewCount,dim+1,&pNewStart,dim+1,&pNewEnd,dim+1,&pOldStart,dim+1,&pOldEnd);CHKERRQ(ierr);
1927     offset = 0;
1928     for (d = 0; d <= dim; d++) {
1929       PetscInt pOldCount, kStart, kEnd, k;
1930 
1931       pNewStart[d] = offset;
1932       ierr = DMPlexGetHeightStratum(dm,d,&pOldStart[d],&pOldEnd[d]);CHKERRQ(ierr);
1933       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
1934       pOldCount = pOldEnd[d] - pOldStart[d];
1935       /* adding the new points */
1936       pNewCount[d] = pOldCount + kEnd - kStart;
1937       if (!d) {
1938         /* removing the cell */
1939         pNewCount[d]--;
1940       }
1941       for (k = kStart; k < kEnd; k++) {
1942         PetscInt parent;
1943         ierr = DMPlexGetTreeParent(K,k,&parent,NULL);CHKERRQ(ierr);
1944         if (parent == k) {
1945           /* avoid double counting points that won't actually be new */
1946           pNewCount[d]--;
1947         }
1948       }
1949       pNewEnd[d] = pNewStart[d] + pNewCount[d];
1950       offset = pNewEnd[d];
1951 
1952     }
1953     if (cell < pOldStart[0] || cell >= pOldEnd[0]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"%d not in cell range [%d, %d)", cell, pOldStart[0], pOldEnd[0]);
1954     /* get the current closure of the cell that we are removing */
1955     ierr = DMPlexGetTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
1956 
1957     ierr = PetscMalloc1(pNewEnd[dim],&newConeSizes);CHKERRQ(ierr);
1958     {
1959       PetscInt kStart, kEnd, k, closureSizeK, *closureK = NULL, j;
1960 
1961       ierr = DMPlexGetChart(K,&kStart,&kEnd);CHKERRQ(ierr);
1962       ierr = PetscMalloc4(kEnd-kStart,&Kembedding,kEnd-kStart,&perm,kEnd-kStart,&iperm,kEnd-kStart,&preOrient);CHKERRQ(ierr);
1963 
1964       for (k = kStart; k < kEnd; k++) {
1965         perm[k - kStart] = k;
1966         iperm [k - kStart] = k - kStart;
1967         preOrient[k - kStart] = 0;
1968       }
1969 
1970       ierr = DMPlexGetTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
1971       for (j = 1; j < closureSizeK; j++) {
1972         PetscInt parentOrientA = closureK[2*j+1];
1973         PetscInt parentOrientB = cellClosure[2*j+1];
1974         PetscInt p, q;
1975 
1976         p = closureK[2*j];
1977         q = cellClosure[2*j];
1978         for (d = 0; d <= dim; d++) {
1979           if (q >= pOldStart[d] && q < pOldEnd[d]) {
1980             Kembedding[p] = (q - pOldStart[d]) + pNewStart[d];
1981           }
1982         }
1983         if (parentOrientA != parentOrientB) {
1984           PetscInt numChildren, i;
1985           const PetscInt *children;
1986 
1987           ierr = DMPlexGetTreeChildren(K,p,&numChildren,&children);CHKERRQ(ierr);
1988           for (i = 0; i < numChildren; i++) {
1989             PetscInt kPerm, oPerm;
1990 
1991             k    = children[i];
1992             ierr = DMPlexReferenceTreeGetChildSymmetry(K,p,parentOrientA,0,k,parentOrientB,&oPerm,&kPerm);CHKERRQ(ierr);
1993             /* perm = what refTree position I'm in */
1994             perm[kPerm-kStart]      = k;
1995             /* iperm = who is at this position */
1996             iperm[k-kStart]         = kPerm-kStart;
1997             preOrient[kPerm-kStart] = oPerm;
1998           }
1999         }
2000       }
2001       ierr = DMPlexRestoreTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
2002     }
2003     ierr = PetscSectionSetChart(parentSection,0,pNewEnd[dim]);CHKERRQ(ierr);
2004     offset = 0;
2005     numNewCones = 0;
2006     for (d = 0; d <= dim; d++) {
2007       PetscInt kStart, kEnd, k;
2008       PetscInt p;
2009       PetscInt size;
2010 
2011       for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
2012         /* skip cell 0 */
2013         if (p == cell) continue;
2014         /* old cones to new cones */
2015         ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
2016         newConeSizes[offset++] = size;
2017         numNewCones += size;
2018       }
2019 
2020       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
2021       for (k = kStart; k < kEnd; k++) {
2022         PetscInt kParent;
2023 
2024         ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
2025         if (kParent != k) {
2026           Kembedding[k] = offset;
2027           ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
2028           newConeSizes[offset++] = size;
2029           numNewCones += size;
2030           if (kParent != 0) {
2031             ierr = PetscSectionSetDof(parentSection,Kembedding[k],1);CHKERRQ(ierr);
2032           }
2033         }
2034       }
2035     }
2036 
2037     ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
2038     ierr = PetscSectionGetStorageSize(parentSection,&numPointsWithParents);CHKERRQ(ierr);
2039     ierr = PetscMalloc2(numNewCones,&newCones,numNewCones,&newOrientations);CHKERRQ(ierr);
2040     ierr = PetscMalloc2(numPointsWithParents,&parents,numPointsWithParents,&childIDs);CHKERRQ(ierr);
2041 
2042     /* fill new cones */
2043     offset = 0;
2044     for (d = 0; d <= dim; d++) {
2045       PetscInt kStart, kEnd, k, l;
2046       PetscInt p;
2047       PetscInt size;
2048       const PetscInt *cone, *orientation;
2049 
2050       for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
2051         /* skip cell 0 */
2052         if (p == cell) continue;
2053         /* old cones to new cones */
2054         ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
2055         ierr = DMPlexGetCone(dm,p,&cone);CHKERRQ(ierr);
2056         ierr = DMPlexGetConeOrientation(dm,p,&orientation);CHKERRQ(ierr);
2057         for (l = 0; l < size; l++) {
2058           newCones[offset]          = (cone[l] - pOldStart[d + 1]) + pNewStart[d + 1];
2059           newOrientations[offset++] = orientation[l];
2060         }
2061       }
2062 
2063       ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
2064       for (k = kStart; k < kEnd; k++) {
2065         PetscInt kPerm = perm[k], kParent;
2066         PetscInt preO  = preOrient[k];
2067 
2068         ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
2069         if (kParent != k) {
2070           /* embed new cones */
2071           ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
2072           ierr = DMPlexGetCone(K,kPerm,&cone);CHKERRQ(ierr);
2073           ierr = DMPlexGetConeOrientation(K,kPerm,&orientation);CHKERRQ(ierr);
2074           for (l = 0; l < size; l++) {
2075             PetscInt q, m = (preO >= 0) ? ((preO + l) % size) : ((size -(preO + 1) - l) % size);
2076             PetscInt newO, lSize, oTrue;
2077 
2078             q                         = iperm[cone[m]];
2079             newCones[offset]          = Kembedding[q];
2080             ierr                      = DMPlexGetConeSize(K,q,&lSize);CHKERRQ(ierr);
2081             oTrue                     = orientation[m];
2082             oTrue                     = ((!lSize) || (preOrient[k] >= 0)) ? oTrue : -(oTrue + 2);
2083             newO                      = DihedralCompose(lSize,oTrue,preOrient[q]);
2084             newOrientations[offset++] = newO;
2085           }
2086           if (kParent != 0) {
2087             PetscInt newPoint = Kembedding[kParent];
2088             ierr              = PetscSectionGetOffset(parentSection,Kembedding[k],&pOffset);CHKERRQ(ierr);
2089             parents[pOffset]  = newPoint;
2090             childIDs[pOffset] = k;
2091           }
2092         }
2093       }
2094     }
2095 
2096     ierr = PetscMalloc1(dim*(pNewEnd[dim]-pNewStart[dim]),&newVertexCoords);CHKERRQ(ierr);
2097 
2098     /* fill coordinates */
2099     offset = 0;
2100     {
2101       PetscInt kStart, kEnd, l;
2102       PetscSection vSection;
2103       PetscInt v;
2104       Vec coords;
2105       PetscScalar *coordvals;
2106       PetscInt dof, off;
2107       PetscReal v0[3], J[9], detJ;
2108 
2109 #if defined(PETSC_USE_DEBUG)
2110       {
2111         PetscInt k;
2112         ierr = DMPlexGetHeightStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
2113         for (k = kStart; k < kEnd; k++) {
2114           ierr = DMPlexComputeCellGeometryFEM(K, k, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
2115           if (detJ <= 0.) SETERRQ1 (PETSC_COMM_SELF,PETSC_ERR_PLIB,"reference tree cell %d has bad determinant",k);
2116         }
2117       }
2118 #endif
2119       ierr = DMPlexComputeCellGeometryFEM(dm, cell, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
2120       ierr = DMGetCoordinateSection(dm,&vSection);CHKERRQ(ierr);
2121       ierr = DMGetCoordinatesLocal(dm,&coords);CHKERRQ(ierr);
2122       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
2123       for (v = pOldStart[dim]; v < pOldEnd[dim]; v++) {
2124 
2125         ierr = PetscSectionGetDof(vSection,v,&dof);CHKERRQ(ierr);
2126         ierr = PetscSectionGetOffset(vSection,v,&off);CHKERRQ(ierr);
2127         for (l = 0; l < dof; l++) {
2128           newVertexCoords[offset++] = coordvals[off + l];
2129         }
2130       }
2131       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
2132 
2133       ierr = DMGetCoordinateSection(K,&vSection);CHKERRQ(ierr);
2134       ierr = DMGetCoordinatesLocal(K,&coords);CHKERRQ(ierr);
2135       ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
2136       ierr = DMPlexGetDepthStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
2137       for (v = kStart; v < kEnd; v++) {
2138         PetscReal coord[3], newCoord[3];
2139         PetscInt  vPerm = perm[v];
2140         PetscInt  kParent;
2141 
2142         ierr = DMPlexGetTreeParent(K,v,&kParent,NULL);CHKERRQ(ierr);
2143         if (kParent != v) {
2144           /* this is a new vertex */
2145           ierr = PetscSectionGetOffset(vSection,vPerm,&off);CHKERRQ(ierr);
2146           for (l = 0; l < dim; ++l) coord[l] = PetscRealPart(coordvals[off+l]);
2147           CoordinatesRefToReal(dim, dim, v0, J, coord, newCoord);CHKERRQ(ierr);
2148           for (l = 0; l < dim; ++l) newVertexCoords[offset+l] = newCoord[l];
2149           offset += dim;
2150         }
2151       }
2152       ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
2153     }
2154 
2155     /* need to reverse the order of pNewCount: vertices first, cells last */
2156     for (d = 0; d < (dim + 1) / 2; d++) {
2157       PetscInt tmp;
2158 
2159       tmp = pNewCount[d];
2160       pNewCount[d] = pNewCount[dim - d];
2161       pNewCount[dim - d] = tmp;
2162     }
2163 
2164     ierr = DMPlexCreateFromDAG(*ncdm,dim,pNewCount,newConeSizes,newCones,newOrientations,newVertexCoords);CHKERRQ(ierr);
2165     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
2166     ierr = DMPlexSetTree(*ncdm,parentSection,parents,childIDs);CHKERRQ(ierr);
2167 
2168     /* clean up */
2169     ierr = DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
2170     ierr = PetscFree5(pNewCount,pNewStart,pNewEnd,pOldStart,pOldEnd);CHKERRQ(ierr);
2171     ierr = PetscFree(newConeSizes);CHKERRQ(ierr);
2172     ierr = PetscFree2(newCones,newOrientations);CHKERRQ(ierr);
2173     ierr = PetscFree(newVertexCoords);CHKERRQ(ierr);
2174     ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
2175     ierr = PetscFree4(Kembedding,perm,iperm,preOrient);CHKERRQ(ierr);
2176   }
2177   else {
2178     PetscInt    p, counts[4];
2179     PetscInt    *coneSizes, *cones, *orientations;
2180     Vec         coordVec;
2181     PetscScalar *coords;
2182 
2183     for (d = 0; d <= dim; d++) {
2184       PetscInt dStart, dEnd;
2185 
2186       ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
2187       counts[d] = dEnd - dStart;
2188     }
2189     ierr = PetscMalloc1(pEnd-pStart,&coneSizes);CHKERRQ(ierr);
2190     for (p = pStart; p < pEnd; p++) {
2191       ierr = DMPlexGetConeSize(dm,p,&coneSizes[p-pStart]);CHKERRQ(ierr);
2192     }
2193     ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
2194     ierr = DMPlexGetConeOrientations(dm, &orientations);CHKERRQ(ierr);
2195     ierr = DMGetCoordinatesLocal(dm,&coordVec);CHKERRQ(ierr);
2196     ierr = VecGetArray(coordVec,&coords);CHKERRQ(ierr);
2197 
2198     ierr = PetscSectionSetChart(parentSection,pStart,pEnd);CHKERRQ(ierr);
2199     ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
2200     ierr = DMPlexCreateFromDAG(*ncdm,dim,counts,coneSizes,cones,orientations,NULL);CHKERRQ(ierr);
2201     ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
2202     ierr = DMPlexSetTree(*ncdm,parentSection,NULL,NULL);CHKERRQ(ierr);
2203     ierr = VecRestoreArray(coordVec,&coords);CHKERRQ(ierr);
2204   }
2205   ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
2206 
2207   PetscFunctionReturn(0);
2208 }
2209 
2210 #undef __FUNCT__
2211 #define __FUNCT__ "DMPlexComputeInterpolatorTree"
2212 PetscErrorCode DMPlexComputeInterpolatorTree(DM coarse, DM fine, PetscSF coarseToFine, PetscInt *childIds, Mat mat)
2213 {
2214   PetscSF        coarseToFineEmbedded;
2215   PetscSection   globalCoarse, globalFine;
2216   PetscSection   localCoarse, localFine;
2217   PetscSection   aSec, cSec;
2218   PetscSection   rootIndicesSec, rootMatricesSec;
2219   PetscSection   leafIndicesSec, leafMatricesSec;
2220   PetscInt       *rootIndices, *leafIndices;
2221   PetscScalar    *rootMatrices, *leafMatrices;
2222   IS             aIS;
2223   const PetscInt *anchors;
2224   Mat            cMat;
2225   PetscInt       numFields;
2226   PetscInt       pStartC, pEndC, pStartF, pEndF, p;
2227   PetscInt       aStart, aEnd, cStart, cEnd;
2228   PetscInt       *maxChildIds;
2229   PetscInt       *offsets, *newOffsets, *offsetsCopy, *newOffsetsCopy, *rowOffsets, *numD, *numO;
2230   PetscErrorCode ierr;
2231 
2232   PetscFunctionBegin;
2233   ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
2234   ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
2235   ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
2236   { /* winnow fine points that don't have global dofs out of the sf */
2237     PetscInt dof, cdof, numPointsWithDofs, offset, *pointsWithDofs;
2238 
2239     for (p = pStartF, numPointsWithDofs = 0; p < pEndF; p++) {
2240       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
2241       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
2242       if ((dof - cdof) > 0) {
2243         numPointsWithDofs++;
2244       }
2245     }
2246     ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
2247     for (p = pStartF, offset = 0; p < pEndF; p++) {
2248       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
2249       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
2250       if ((dof - cdof) > 0) {
2251         pointsWithDofs[offset++] = p - pStartF;
2252       }
2253     }
2254     ierr = PetscSFCreateEmbeddedLeafSF(coarseToFine, numPointsWithDofs, pointsWithDofs, &coarseToFineEmbedded);CHKERRQ(ierr);
2255     ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
2256   }
2257   /* communicate back to the coarse mesh which coarse points have children (that may require interpolation) */
2258   ierr = PetscMalloc1(pEndC-pStartC,&maxChildIds);CHKERRQ(ierr);
2259   for (p = pStartC; p < pEndC; p++) {
2260     maxChildIds[p - pStartC] = -2;
2261   }
2262   ierr = PetscSFReduceBegin(coarseToFineEmbedded,MPIU_INT,childIds,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
2263   ierr = PetscSFReduceEnd(coarseToFineEmbedded,MPIU_INT,childIds,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
2264 
2265   ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
2266   ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
2267 
2268   ierr = DMPlexGetAnchors(coarse,&aSec,&aIS);CHKERRQ(ierr);
2269   ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
2270   ierr = PetscSectionGetChart(aSec,&aStart,&aEnd);CHKERRQ(ierr);
2271 
2272   ierr = DMGetDefaultConstraints(coarse,&cSec,&cMat);CHKERRQ(ierr);
2273   ierr = PetscSectionGetChart(cSec,&cStart,&cEnd);CHKERRQ(ierr);
2274 
2275   /* create sections that will send to children the indices and matrices they will need to construct the interpolator */
2276   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootIndicesSec);CHKERRQ(ierr);
2277   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootMatricesSec);CHKERRQ(ierr);
2278   ierr = PetscSectionSetChart(rootIndicesSec,pStartC,pEndC);CHKERRQ(ierr);
2279   ierr = PetscSectionSetChart(rootMatricesSec,pStartC,pEndC);CHKERRQ(ierr);
2280   ierr = PetscSectionGetNumFields(localCoarse,&numFields);CHKERRQ(ierr);
2281   {
2282     PetscInt maxFields = PetscMax(1,numFields) + 1;
2283     ierr = PetscMalloc7(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&newOffsets,maxFields,&newOffsetsCopy,maxFields,&rowOffsets,maxFields,&numD,maxFields,&numO);CHKERRQ(ierr);
2284   }
2285 
2286   for (p = pStartC; p < pEndC; p++) { /* count the sizes of the indices and matrices */
2287     PetscInt dof, matSize   = 0;
2288     PetscInt aDof           = 0;
2289     PetscInt cDof           = 0;
2290     PetscInt maxChildId     = maxChildIds[p - pStartC];
2291     PetscInt numRowIndices  = 0;
2292     PetscInt numColIndices  = 0;
2293     PetscInt f;
2294 
2295     ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
2296     if (dof < 0) {
2297       dof = -(dof + 1);
2298     }
2299     if (p >= aStart && p < aEnd) {
2300       ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
2301     }
2302     if (p >= cStart && p < cEnd) {
2303       ierr = PetscSectionGetDof(cSec,p,&cDof);CHKERRQ(ierr);
2304     }
2305     for (f = 0; f <= numFields; f++) offsets[f] = 0;
2306     for (f = 0; f <= numFields; f++) newOffsets[f] = 0;
2307     if (maxChildId >= 0) { /* this point has children (with dofs) that will need to be interpolated from the closure of p */
2308       PetscInt *closure = NULL, closureSize, cl;
2309 
2310       ierr = DMPlexGetTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2311       for (cl = 0; cl < closureSize; cl++) { /* get the closure */
2312         PetscInt c = closure[2 * cl], clDof;
2313 
2314         ierr = PetscSectionGetDof(localCoarse,c,&clDof);CHKERRQ(ierr);
2315         numRowIndices += clDof;
2316         for (f = 0; f < numFields; f++) {
2317           ierr = PetscSectionGetFieldDof(localCoarse,c,f,&clDof);CHKERRQ(ierr);
2318           offsets[f + 1] += clDof;
2319         }
2320       }
2321       for (f = 0; f < numFields; f++) {
2322         offsets[f + 1]   += offsets[f];
2323         newOffsets[f + 1] = offsets[f + 1];
2324       }
2325       /* get the number of indices needed and their field offsets */
2326       ierr = DMPlexAnchorsModifyMat(coarse,localCoarse,closureSize,numRowIndices,closure,NULL,NULL,&numColIndices,NULL,NULL,newOffsets,PETSC_FALSE);CHKERRQ(ierr);
2327       ierr = DMPlexRestoreTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
2328       if (!numColIndices) { /* there are no hanging constraint modifications, so the matrix is just the identity: do not send it */
2329         numColIndices = numRowIndices;
2330         matSize = 0;
2331       }
2332       else if (numFields) { /* we send one submat for each field: sum their sizes */
2333         matSize = 0;
2334         for (f = 0; f < numFields; f++) {
2335           PetscInt numRow, numCol;
2336 
2337           numRow = offsets[f + 1] - offsets[f];
2338           numCol = newOffsets[f + 1] - newOffsets[f];
2339           matSize += numRow * numCol;
2340         }
2341       }
2342       else {
2343         matSize = numRowIndices * numColIndices;
2344       }
2345     } else if (maxChildId == -1) {
2346       if (cDof > 0) { /* this point's dofs are interpolated via cMat: get the submatrix of cMat */
2347         PetscInt aOff, a;
2348 
2349         ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
2350         for (f = 0; f < numFields; f++) {
2351           PetscInt fDof;
2352 
2353           ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
2354           offsets[f+1] = fDof;
2355         }
2356         for (a = 0; a < aDof; a++) {
2357           PetscInt anchor = anchors[a + aOff], aLocalDof;
2358 
2359           ierr = PetscSectionGetDof(localCoarse,anchor,&aLocalDof);CHKERRQ(ierr);
2360           numColIndices += aLocalDof;
2361           for (f = 0; f < numFields; f++) {
2362             PetscInt fDof;
2363 
2364             ierr = PetscSectionGetFieldDof(localCoarse,anchor,f,&fDof);CHKERRQ(ierr);
2365             newOffsets[f+1] += fDof;
2366           }
2367         }
2368         if (numFields) {
2369           matSize = 0;
2370           for (f = 0; f < numFields; f++) {
2371             matSize += offsets[f+1] * newOffsets[f+1];
2372           }
2373         }
2374         else {
2375           matSize = numColIndices * dof;
2376         }
2377       }
2378       else { /* no children, and no constraints on dofs: just get the global indices */
2379         numColIndices = dof;
2380         matSize       = 0;
2381       }
2382     }
2383     /* we will pack the column indices with the field offsets */
2384     ierr = PetscSectionSetDof(rootIndicesSec,p,numColIndices ? numColIndices+2*numFields : 0);CHKERRQ(ierr);
2385     ierr = PetscSectionSetDof(rootMatricesSec,p,matSize);CHKERRQ(ierr);
2386   }
2387   ierr = PetscSectionSetUp(rootIndicesSec);CHKERRQ(ierr);
2388   ierr = PetscSectionSetUp(rootMatricesSec);CHKERRQ(ierr);
2389   {
2390     PetscInt numRootIndices, numRootMatrices;
2391 
2392     ierr = PetscSectionGetStorageSize(rootIndicesSec,&numRootIndices);CHKERRQ(ierr);
2393     ierr = PetscSectionGetStorageSize(rootMatricesSec,&numRootMatrices);CHKERRQ(ierr);
2394     ierr = PetscMalloc2(numRootIndices,&rootIndices,numRootMatrices,&rootMatrices);CHKERRQ(ierr);
2395     for (p = pStartC; p < pEndC; p++) {
2396       PetscInt    numRowIndices, numColIndices, matSize, dof;
2397       PetscInt    pIndOff, pMatOff, f;
2398       PetscInt    *pInd;
2399       PetscInt    maxChildId = maxChildIds[p - pStartC];
2400       PetscScalar *pMat = NULL;
2401 
2402       ierr = PetscSectionGetDof(rootIndicesSec,p,&numColIndices);CHKERRQ(ierr);
2403       if (!numColIndices) {
2404         continue;
2405       }
2406       for (f = 0; f <= numFields; f++) {
2407         offsets[f]        = 0;
2408         newOffsets[f]     = 0;
2409         offsetsCopy[f]    = 0;
2410         newOffsetsCopy[f] = 0;
2411       }
2412       numColIndices -= 2 * numFields;
2413       ierr = PetscSectionGetOffset(rootIndicesSec,p,&pIndOff);CHKERRQ(ierr);
2414       pInd = &(rootIndices[pIndOff]);
2415       ierr = PetscSectionGetDof(rootMatricesSec,p,&matSize);CHKERRQ(ierr);
2416       if (matSize) {
2417         ierr = PetscSectionGetOffset(rootMatricesSec,p,&pMatOff);CHKERRQ(ierr);
2418         pMat = &rootMatrices[pMatOff];
2419       }
2420       ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
2421       if (dof < 0) {
2422         dof = -(dof + 1);
2423       }
2424       if (maxChildId >= 0) { /* build an identity matrix, apply matrix constraints on the right */
2425         PetscInt i, j;
2426         PetscInt numRowIndices = matSize / numColIndices;
2427 
2428         if (!numRowIndices) { /* don't need to calculate the mat, just the indices */
2429           PetscInt numIndices, *indices;
2430           ierr = DMPlexGetClosureIndices(coarse,localCoarse,globalCoarse,p,&numIndices,&indices,offsets);CHKERRQ(ierr);
2431           if (numIndices != numColIndices) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"mismatching constraint indices calculations");
2432           for (i = 0; i < numColIndices; i++) {
2433             pInd[i] = indices[i];
2434           }
2435           for (i = 0; i < numFields; i++) {
2436             pInd[numColIndices + i]             = offsets[i+1];
2437             pInd[numColIndices + numFields + i] = offsets[i+1];
2438           }
2439           ierr = DMPlexRestoreClosureIndices(coarse,localCoarse,globalCoarse,p,&numIndices,&indices,offsets);CHKERRQ(ierr);
2440         }
2441         else {
2442           PetscInt closureSize, *closure = NULL, cl;
2443           PetscScalar *pMatIn, *pMatModified;
2444           PetscInt numPoints,*points;
2445 
2446           ierr = DMGetWorkArray(coarse,numRowIndices * numRowIndices,PETSC_SCALAR,&pMatIn);CHKERRQ(ierr);
2447           for (i = 0; i < numRowIndices; i++) { /* initialize to the identity */
2448             for (j = 0; j < numRowIndices; j++) {
2449               pMatIn[i * numRowIndices + j] = (i == j) ? 1. : 0.;
2450             }
2451           }
2452           ierr = DMPlexGetTransitiveClosure(coarse, p, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2453           if (numFields) {
2454             for (cl = 0; cl < closureSize; cl++) {
2455               PetscInt c = closure[2 * cl];
2456 
2457               for (f = 0; f < numFields; f++) {
2458                 PetscInt fDof;
2459 
2460                 ierr = PetscSectionGetFieldDof(localCoarse,c,f,&fDof);CHKERRQ(ierr);
2461                 offsets[f + 1] += fDof;
2462               }
2463             }
2464             for (f = 0; f < numFields; f++) {
2465               offsets[f + 1]   += offsets[f];
2466               newOffsets[f + 1] = offsets[f + 1];
2467             }
2468           }
2469           /* apply hanging node constraints on the right, get the new points and the new offsets */
2470           ierr = DMPlexAnchorsModifyMat(coarse,localCoarse,closureSize,numRowIndices,closure,pMatIn,&numPoints,NULL,&points,&pMatModified,newOffsets,PETSC_FALSE);CHKERRQ(ierr);
2471           if (!numFields) {
2472             for (i = 0; i < numRowIndices * numColIndices; i++) {
2473               pMat[i] = pMatModified[i];
2474             }
2475           }
2476           else {
2477             PetscInt i, j, count;
2478             for (f = 0, count = 0; f < numFields; f++) {
2479               for (i = offsets[f]; i < offsets[f+1]; i++) {
2480                 for (j = newOffsets[f]; j < newOffsets[f+1]; j++, count++) {
2481                   pMat[count] = pMatModified[i * numColIndices + j];
2482                 }
2483               }
2484             }
2485           }
2486           ierr = DMRestoreWorkArray(coarse,numRowIndices * numColIndices,PETSC_SCALAR,&pMatModified);CHKERRQ(ierr);
2487           ierr = DMPlexRestoreTransitiveClosure(coarse, p, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
2488           ierr = DMRestoreWorkArray(coarse,numRowIndices * numColIndices,PETSC_SCALAR,&pMatIn);CHKERRQ(ierr);
2489           if (numFields) {
2490             for (f = 0; f < numFields; f++) {
2491               pInd[numColIndices + f]             = offsets[f+1];
2492               pInd[numColIndices + numFields + f] = newOffsets[f+1];
2493             }
2494             for (cl = 0; cl < numPoints*2; cl += 2) {
2495               PetscInt o = points[cl+1], globalOff, c = points[cl];
2496               ierr = PetscSectionGetOffset(globalCoarse, c, &globalOff);CHKERRQ(ierr);
2497               DMPlexGetIndicesPointFields_Internal(localCoarse, c, globalOff < 0 ? -(globalOff+1) : globalOff, newOffsets, PETSC_FALSE, o, pInd);
2498             }
2499           } else {
2500             for (cl = 0; cl < numPoints*2; cl += 2) {
2501               PetscInt o = points[cl+1], c = points[cl], globalOff;
2502               ierr = PetscSectionGetOffset(globalCoarse, c, &globalOff);CHKERRQ(ierr);
2503               DMPlexGetIndicesPoint_Internal(localCoarse, c, globalOff < 0 ? -(globalOff+1) : globalOff, newOffsets, PETSC_FALSE, o, pInd);
2504             }
2505           }
2506           ierr = DMRestoreWorkArray(coarse,numPoints,PETSC_SCALAR,&points);CHKERRQ(ierr);
2507         }
2508       }
2509       else if (matSize) {
2510         PetscInt cOff;
2511         PetscInt *rowIndices, *colIndices, a, aDof, aOff;
2512 
2513         numRowIndices = matSize / numColIndices;
2514         if (numRowIndices != dof) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Miscounted dofs");
2515         ierr = DMGetWorkArray(coarse,numRowIndices,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2516         ierr = DMGetWorkArray(coarse,numColIndices,PETSC_INT,&colIndices);CHKERRQ(ierr);
2517         ierr = PetscSectionGetOffset(cSec,p,&cOff);CHKERRQ(ierr);
2518         ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
2519         ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
2520         if (numFields) {
2521           for (f = 0; f < numFields; f++) {
2522             PetscInt fDof;
2523 
2524             ierr = PetscSectionGetFieldDof(cSec,p,f,&fDof);CHKERRQ(ierr);
2525             offsets[f + 1] = fDof;
2526             for (a = 0; a < aDof; a++) {
2527               PetscInt anchor = anchors[a + aOff];
2528               ierr = PetscSectionGetFieldDof(localCoarse,anchor,f,&fDof);CHKERRQ(ierr);
2529               newOffsets[f + 1] += fDof;
2530             }
2531           }
2532           for (f = 0; f < numFields; f++) {
2533             offsets[f + 1]       += offsets[f];
2534             offsetsCopy[f + 1]    = offsets[f + 1];
2535             newOffsets[f + 1]    += newOffsets[f];
2536             newOffsetsCopy[f + 1] = newOffsets[f + 1];
2537           }
2538           DMPlexGetIndicesPointFields_Internal(cSec,p,cOff,offsetsCopy,PETSC_TRUE,0,rowIndices);CHKERRQ(ierr);
2539           for (a = 0; a < aDof; a++) {
2540             PetscInt anchor = anchors[a + aOff], lOff;
2541             ierr = PetscSectionGetOffset(localCoarse,anchor,&lOff);CHKERRQ(ierr);
2542             DMPlexGetIndicesPointFields_Internal(localCoarse,anchor,lOff,newOffsetsCopy,PETSC_TRUE,0,colIndices);CHKERRQ(ierr);
2543           }
2544         }
2545         else {
2546           DMPlexGetIndicesPoint_Internal(cSec,p,cOff,offsetsCopy,PETSC_TRUE,0,rowIndices);CHKERRQ(ierr);
2547           for (a = 0; a < aDof; a++) {
2548             PetscInt anchor = anchors[a + aOff], lOff;
2549             ierr = PetscSectionGetOffset(localCoarse,anchor,&lOff);CHKERRQ(ierr);
2550             DMPlexGetIndicesPoint_Internal(localCoarse,anchor,lOff,newOffsetsCopy,PETSC_TRUE,0,colIndices);CHKERRQ(ierr);
2551           }
2552         }
2553         if (numFields) {
2554           PetscInt count, a;
2555 
2556           for (f = 0, count = 0; f < numFields; f++) {
2557             PetscInt iSize = offsets[f + 1] - offsets[f];
2558             PetscInt jSize = newOffsets[f + 1] - newOffsets[f];
2559             ierr = MatGetValues(cMat,iSize,&rowIndices[offsets[f]],jSize,&colIndices[newOffsets[f]],&pMat[count]);CHKERRQ(ierr);
2560             count += iSize * jSize;
2561             pInd[numColIndices + f]             = offsets[f+1];
2562             pInd[numColIndices + numFields + f] = newOffsets[f+1];
2563           }
2564           for (a = 0; a < aDof; a++) {
2565             PetscInt anchor = anchors[a + aOff];
2566             PetscInt gOff;
2567             ierr = PetscSectionGetOffset(globalCoarse,anchor,&gOff);CHKERRQ(ierr);
2568             DMPlexGetIndicesPointFields_Internal(localCoarse,anchor,gOff < 0 ? -(gOff + 1) : gOff,newOffsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2569           }
2570         }
2571         else {
2572           PetscInt a;
2573           ierr = MatGetValues(cMat,numRowIndices,rowIndices,numColIndices,colIndices,pMat);CHKERRQ(ierr);
2574           for (a = 0; a < aDof; a++) {
2575             PetscInt anchor = anchors[a + aOff];
2576             PetscInt gOff;
2577             ierr = PetscSectionGetOffset(globalCoarse,anchor,&gOff);CHKERRQ(ierr);
2578             DMPlexGetIndicesPoint_Internal(localCoarse,anchor,gOff < 0 ? -(gOff + 1) : gOff,newOffsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2579           }
2580         }
2581         ierr = DMRestoreWorkArray(coarse,numColIndices,PETSC_INT,&colIndices);CHKERRQ(ierr);
2582         ierr = DMRestoreWorkArray(coarse,numRowIndices,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2583       }
2584       else {
2585         PetscInt gOff;
2586 
2587         ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);
2588         if (numFields) {
2589           for (f = 0; f < numFields; f++) {
2590             PetscInt fDof;
2591             ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
2592             offsets[f + 1] = fDof + offsets[f];
2593           }
2594           for (f = 0; f < numFields; f++) {
2595             pInd[numColIndices + f]             = offsets[f+1];
2596             pInd[numColIndices + numFields + f] = offsets[f+1];
2597           }
2598           DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2599         }
2600         else {
2601           DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
2602         }
2603       }
2604     }
2605     ierr = PetscFree(maxChildIds);CHKERRQ(ierr);
2606   }
2607   {
2608     PetscSF  indicesSF, matricesSF;
2609     PetscInt *remoteOffsetsIndices, *remoteOffsetsMatrices, numLeafIndices, numLeafMatrices;
2610 
2611     ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafIndicesSec);CHKERRQ(ierr);
2612     ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafMatricesSec);CHKERRQ(ierr);
2613     ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootIndicesSec,&remoteOffsetsIndices,leafIndicesSec);CHKERRQ(ierr);
2614     ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootMatricesSec,&remoteOffsetsMatrices,leafMatricesSec);CHKERRQ(ierr);
2615     ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootIndicesSec,remoteOffsetsIndices,leafIndicesSec,&indicesSF);CHKERRQ(ierr);
2616     ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootMatricesSec,remoteOffsetsMatrices,leafMatricesSec,&matricesSF);CHKERRQ(ierr);
2617     ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
2618     ierr = PetscFree(remoteOffsetsIndices);CHKERRQ(ierr);
2619     ierr = PetscFree(remoteOffsetsMatrices);CHKERRQ(ierr);
2620     ierr = PetscSectionGetStorageSize(leafIndicesSec,&numLeafIndices);CHKERRQ(ierr);
2621     ierr = PetscSectionGetStorageSize(leafMatricesSec,&numLeafMatrices);CHKERRQ(ierr);
2622     ierr = PetscMalloc2(numLeafIndices,&leafIndices,numLeafMatrices,&leafMatrices);CHKERRQ(ierr);
2623     ierr = PetscSFBcastBegin(indicesSF,MPIU_INT,rootIndices,leafIndices);CHKERRQ(ierr);
2624     ierr = PetscSFBcastBegin(matricesSF,MPIU_SCALAR,rootMatrices,leafMatrices);CHKERRQ(ierr);
2625     ierr = PetscSFBcastEnd(indicesSF,MPIU_INT,rootIndices,leafIndices);CHKERRQ(ierr);
2626     ierr = PetscSFBcastEnd(matricesSF,MPIU_SCALAR,rootMatrices,leafMatrices);CHKERRQ(ierr);
2627     ierr = PetscSFDestroy(&matricesSF);CHKERRQ(ierr);
2628     ierr = PetscSFDestroy(&indicesSF);CHKERRQ(ierr);
2629     ierr = PetscFree2(rootIndices,rootMatrices);CHKERRQ(ierr);
2630     ierr = PetscSectionDestroy(&rootIndicesSec);CHKERRQ(ierr);
2631     ierr = PetscSectionDestroy(&rootMatricesSec);CHKERRQ(ierr);
2632   }
2633   /* count to preallocate */
2634   ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
2635   {
2636     PetscInt    nGlobal;
2637     PetscInt    *dnnz, *onnz;
2638     PetscLayout rowMap, colMap;
2639     PetscInt    rowStart, rowEnd, colStart, colEnd;
2640     PetscInt    maxDof;
2641     PetscInt    *rowIndices;
2642     DM           refTree;
2643     PetscInt     **refPointFieldN;
2644     PetscScalar  ***refPointFieldMats;
2645     PetscSection refConSec, refAnSec;
2646     PetscInt     pRefStart,pRefEnd,maxConDof,maxColumns,leafStart,leafEnd;
2647     PetscScalar  *pointWork;
2648 
2649     ierr = PetscSectionGetConstrainedStorageSize(globalFine,&nGlobal);CHKERRQ(ierr);
2650     ierr = PetscCalloc2(nGlobal,&dnnz,nGlobal,&onnz);CHKERRQ(ierr);
2651     ierr = MatGetLayouts(mat,&rowMap,&colMap);CHKERRQ(ierr);
2652     ierr = PetscLayoutSetUp(rowMap);CHKERRQ(ierr);
2653     ierr = PetscLayoutSetUp(colMap);CHKERRQ(ierr);
2654     ierr = PetscLayoutGetRange(rowMap,&rowStart,&rowEnd);CHKERRQ(ierr);
2655     ierr = PetscLayoutGetRange(colMap,&colStart,&colEnd);CHKERRQ(ierr);
2656     ierr = PetscSectionGetMaxDof(globalFine,&maxDof);CHKERRQ(ierr);
2657     ierr = PetscSectionGetChart(leafIndicesSec,&leafStart,&leafEnd);CHKERRQ(ierr);
2658     ierr = DMGetWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2659     for (p = leafStart; p < leafEnd; p++) {
2660       PetscInt    gDof, gcDof, gOff;
2661       PetscInt    numColIndices, pIndOff, *pInd;
2662       PetscInt    matSize;
2663       PetscInt    i;
2664 
2665       ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
2666       ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
2667       if ((gDof - gcDof) <= 0) {
2668         continue;
2669       }
2670       ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
2671       if (gOff < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"I though having global dofs meant a non-negative offset");
2672       if ((gOff < rowStart) || ((gOff + gDof - gcDof) > rowEnd)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"I thought the row map would constrain the global dofs");
2673       ierr = PetscSectionGetDof(leafIndicesSec,p,&numColIndices);CHKERRQ(ierr);
2674       ierr = PetscSectionGetOffset(leafIndicesSec,p,&pIndOff);CHKERRQ(ierr);
2675       numColIndices -= 2 * numFields;
2676       if (numColIndices <= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"global fine dof with no dofs to interpolate from");
2677       pInd = &leafIndices[pIndOff];
2678       offsets[0]        = 0;
2679       offsetsCopy[0]    = 0;
2680       newOffsets[0]     = 0;
2681       newOffsetsCopy[0] = 0;
2682       if (numFields) {
2683         PetscInt f;
2684         for (f = 0; f < numFields; f++) {
2685           PetscInt rowDof;
2686 
2687           ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
2688           offsets[f + 1]        = offsets[f] + rowDof;
2689           offsetsCopy[f + 1]    = offsets[f + 1];
2690           newOffsets[f + 1]     = pInd[numColIndices + numFields + f];
2691           numD[f] = 0;
2692           numO[f] = 0;
2693         }
2694         ierr = DMPlexGetIndicesPointFields_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2695         for (f = 0; f < numFields; f++) {
2696           PetscInt colOffset    = newOffsets[f];
2697           PetscInt numFieldCols = newOffsets[f + 1] - newOffsets[f];
2698 
2699           for (i = 0; i < numFieldCols; i++) {
2700             PetscInt gInd = pInd[i + colOffset];
2701 
2702             if (gInd >= colStart && gInd < colEnd) {
2703               numD[f]++;
2704             }
2705             else if (gInd >= 0) { /* negative means non-entry */
2706               numO[f]++;
2707             }
2708           }
2709         }
2710       }
2711       else {
2712         ierr = DMPlexGetIndicesPoint_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2713         numD[0] = 0;
2714         numO[0] = 0;
2715         for (i = 0; i < numColIndices; i++) {
2716           PetscInt gInd = pInd[i];
2717 
2718           if (gInd >= colStart && gInd < colEnd) {
2719             numD[0]++;
2720           }
2721           else if (gInd >= 0) { /* negative means non-entry */
2722             numO[0]++;
2723           }
2724         }
2725       }
2726       ierr = PetscSectionGetDof(leafMatricesSec,p,&matSize);CHKERRQ(ierr);
2727       if (!matSize) { /* incoming matrix is identity */
2728         PetscInt childId;
2729 
2730         childId = childIds[p-pStartF];
2731         if (childId < 0) { /* no child interpolation: one nnz per */
2732           if (numFields) {
2733             PetscInt f;
2734             for (f = 0; f < numFields; f++) {
2735               PetscInt numRows = offsets[f+1] - offsets[f], row;
2736               for (row = 0; row < numRows; row++) {
2737                 PetscInt gIndCoarse = pInd[newOffsets[f] + row];
2738                 PetscInt gIndFine   = rowIndices[offsets[f] + row];
2739                 if (gIndCoarse >= colStart && gIndCoarse < colEnd) { /* local */
2740                   if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2741                   dnnz[gIndFine - rowStart] = 1;
2742                 }
2743                 else if (gIndCoarse >= 0) { /* remote */
2744                   if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2745                   onnz[gIndFine - rowStart] = 1;
2746                 }
2747                 else { /* constrained */
2748                   if (gIndFine >= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2749                 }
2750               }
2751             }
2752           }
2753           else {
2754             PetscInt i;
2755             for (i = 0; i < gDof; i++) {
2756               PetscInt gIndCoarse = pInd[i];
2757               PetscInt gIndFine   = rowIndices[i];
2758               if (gIndCoarse >= colStart && gIndCoarse < colEnd) { /* local */
2759                 if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2760                 dnnz[gIndFine - rowStart] = 1;
2761               }
2762               else if (gIndCoarse >= 0) { /* remote */
2763                 if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2764                 onnz[gIndFine - rowStart] = 1;
2765               }
2766               else { /* constrained */
2767                 if (gIndFine >= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2768               }
2769             }
2770           }
2771         }
2772         else { /* interpolate from all */
2773           if (numFields) {
2774             PetscInt f;
2775             for (f = 0; f < numFields; f++) {
2776               PetscInt numRows = offsets[f+1] - offsets[f], row;
2777               for (row = 0; row < numRows; row++) {
2778                 PetscInt gIndFine = rowIndices[offsets[f] + row];
2779                 if (gIndFine >= 0) {
2780                   if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2781                   dnnz[gIndFine - rowStart] = numD[f];
2782                   onnz[gIndFine - rowStart] = numO[f];
2783                 }
2784               }
2785             }
2786           }
2787           else {
2788             PetscInt i;
2789             for (i = 0; i < gDof; i++) {
2790               PetscInt gIndFine = rowIndices[i];
2791               if (gIndFine >= 0) {
2792                 if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2793                 dnnz[gIndFine - rowStart] = numD[0];
2794                 onnz[gIndFine - rowStart] = numO[0];
2795               }
2796             }
2797           }
2798         }
2799       }
2800       else { /* interpolate from all */
2801         if (numFields) {
2802           PetscInt f;
2803           for (f = 0; f < numFields; f++) {
2804             PetscInt numRows = offsets[f+1] - offsets[f], row;
2805             for (row = 0; row < numRows; row++) {
2806               PetscInt gIndFine = rowIndices[offsets[f] + row];
2807               if (gIndFine >= 0) {
2808                 if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2809                 dnnz[gIndFine - rowStart] = numD[f];
2810                 onnz[gIndFine - rowStart] = numO[f];
2811               }
2812             }
2813           }
2814         }
2815         else { /* every dof get a full row */
2816           PetscInt i;
2817           for (i = 0; i < gDof; i++) {
2818             PetscInt gIndFine = rowIndices[i];
2819             if (gIndFine >= 0) {
2820               if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
2821               dnnz[gIndFine - rowStart] = numD[0];
2822               onnz[gIndFine - rowStart] = numO[0];
2823             }
2824           }
2825         }
2826       }
2827     }
2828     ierr = MatXAIJSetPreallocation(mat,1,dnnz,onnz,NULL,NULL);CHKERRQ(ierr);
2829     ierr = PetscFree2(dnnz,onnz);CHKERRQ(ierr);
2830 
2831     ierr = DMPlexGetReferenceTree(fine,&refTree);CHKERRQ(ierr);
2832     ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
2833     ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
2834     ierr = DMPlexGetAnchors(refTree,&refAnSec,NULL);CHKERRQ(ierr);
2835     ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
2836     ierr = PetscSectionGetMaxDof(refConSec,&maxConDof);CHKERRQ(ierr);
2837     ierr = PetscSectionGetMaxDof(leafIndicesSec,&maxColumns);CHKERRQ(ierr);
2838     ierr = PetscMalloc1(maxConDof*maxColumns,&pointWork);CHKERRQ(ierr);
2839     for (p = leafStart; p < leafEnd; p++) {
2840       PetscInt    gDof, gcDof, gOff;
2841       PetscInt    numColIndices, pIndOff, *pInd;
2842       PetscInt    matSize;
2843       PetscInt    childId;
2844 
2845 
2846       ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
2847       ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
2848       if ((gDof - gcDof) <= 0) {
2849         continue;
2850       }
2851       childId = childIds[p-pStartF];
2852       ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
2853       ierr = PetscSectionGetDof(leafIndicesSec,p,&numColIndices);CHKERRQ(ierr);
2854       ierr = PetscSectionGetOffset(leafIndicesSec,p,&pIndOff);CHKERRQ(ierr);
2855       numColIndices -= 2 * numFields;
2856       pInd = &leafIndices[pIndOff];
2857       offsets[0]        = 0;
2858       offsetsCopy[0]    = 0;
2859       newOffsets[0]     = 0;
2860       newOffsetsCopy[0] = 0;
2861       rowOffsets[0]     = 0;
2862       if (numFields) {
2863         PetscInt f;
2864         for (f = 0; f < numFields; f++) {
2865           PetscInt rowDof;
2866 
2867           ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
2868           offsets[f + 1]     = offsets[f] + rowDof;
2869           offsetsCopy[f + 1] = offsets[f + 1];
2870           rowOffsets[f + 1]  = pInd[numColIndices + f];
2871           newOffsets[f + 1]  = pInd[numColIndices + numFields + f];
2872         }
2873         ierr = DMPlexGetIndicesPointFields_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2874       }
2875       else {
2876         ierr = DMPlexGetIndicesPoint_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
2877       }
2878       ierr = PetscSectionGetDof(leafMatricesSec,p,&matSize);CHKERRQ(ierr);
2879       if (!matSize) { /* incoming matrix is identity */
2880         if (childId < 0) { /* no child interpolation: scatter */
2881           if (numFields) {
2882             PetscInt f;
2883             for (f = 0; f < numFields; f++) {
2884               PetscInt numRows = offsets[f+1] - offsets[f], row;
2885               for (row = 0; row < numRows; row++) {
2886                 ierr = MatSetValue(mat,rowIndices[offsets[f]+row],pInd[newOffsets[f]+row],1.,INSERT_VALUES);CHKERRQ(ierr);
2887               }
2888             }
2889           }
2890           else {
2891             PetscInt numRows = gDof, row;
2892             for (row = 0; row < numRows; row++) {
2893               ierr = MatSetValue(mat,rowIndices[row],pInd[row],1.,INSERT_VALUES);CHKERRQ(ierr);
2894             }
2895           }
2896         }
2897         else { /* interpolate from all */
2898           if (numFields) {
2899             PetscInt f;
2900             for (f = 0; f < numFields; f++) {
2901               PetscInt numRows = offsets[f+1] - offsets[f];
2902               PetscInt numCols = newOffsets[f + 1] - newOffsets[f];
2903               ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],refPointFieldMats[childId - pRefStart][f],INSERT_VALUES);CHKERRQ(ierr);
2904             }
2905           }
2906           else {
2907             ierr = MatSetValues(mat,gDof,rowIndices,numColIndices,pInd,refPointFieldMats[childId - pRefStart][0],INSERT_VALUES);CHKERRQ(ierr);
2908           }
2909         }
2910       }
2911       else { /* interpolate from all */
2912         PetscInt    pMatOff;
2913         PetscScalar *pMat;
2914 
2915         ierr = PetscSectionGetOffset(leafMatricesSec,p,&pMatOff);CHKERRQ(ierr);
2916         pMat = &leafMatrices[pMatOff];
2917         if (childId < 0) { /* copy the incoming matrix */
2918           if (numFields) {
2919             PetscInt f, count;
2920             for (f = 0, count = 0; f < numFields; f++) {
2921               PetscInt numRows = offsets[f+1]-offsets[f];
2922               PetscInt numCols = newOffsets[f+1]-newOffsets[f];
2923               PetscInt numInRows = rowOffsets[f+1]-rowOffsets[f];
2924               PetscScalar *inMat = &pMat[count];
2925 
2926               ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],inMat,INSERT_VALUES);CHKERRQ(ierr);
2927               count += numCols * numInRows;
2928             }
2929           }
2930           else {
2931             ierr = MatSetValues(mat,gDof,rowIndices,numColIndices,pInd,pMat,INSERT_VALUES);CHKERRQ(ierr);
2932           }
2933         }
2934         else { /* multiply the incoming matrix by the child interpolation */
2935           if (numFields) {
2936             PetscInt f, count;
2937             for (f = 0, count = 0; f < numFields; f++) {
2938               PetscInt numRows = offsets[f+1]-offsets[f];
2939               PetscInt numCols = newOffsets[f+1]-newOffsets[f];
2940               PetscInt numInRows = rowOffsets[f+1]-rowOffsets[f];
2941               PetscScalar *inMat = &pMat[count];
2942               PetscInt i, j, k;
2943               if (refPointFieldN[childId - pRefStart][f] != numInRows) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Point constraint matrix multiply dimension mismatch");
2944               for (i = 0; i < numRows; i++) {
2945                 for (j = 0; j < numCols; j++) {
2946                   PetscScalar val = 0.;
2947                   for (k = 0; k < numInRows; k++) {
2948                     val += refPointFieldMats[childId - pRefStart][f][i * numInRows + k] * inMat[k * numCols + j];
2949                   }
2950                   pointWork[i * numCols + j] = val;
2951                 }
2952               }
2953               ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],pointWork,INSERT_VALUES);CHKERRQ(ierr);
2954               count += numCols * numInRows;
2955             }
2956           }
2957           else { /* every dof gets a full row */
2958             PetscInt numRows   = gDof;
2959             PetscInt numCols   = numColIndices;
2960             PetscInt numInRows = matSize / numColIndices;
2961             PetscInt i, j, k;
2962             if (refPointFieldN[childId - pRefStart][0] != numInRows) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Point constraint matrix multiply dimension mismatch");
2963             for (i = 0; i < numRows; i++) {
2964               for (j = 0; j < numCols; j++) {
2965                 PetscScalar val = 0.;
2966                 for (k = 0; k < numInRows; k++) {
2967                   val += refPointFieldMats[childId - pRefStart][0][i * numInRows + k] * pMat[k * numCols + j];
2968                 }
2969                 pointWork[i * numCols + j] = val;
2970               }
2971             }
2972             ierr = MatSetValues(mat,numRows,rowIndices,numCols,pInd,pointWork,INSERT_VALUES);CHKERRQ(ierr);
2973           }
2974         }
2975       }
2976     }
2977     ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
2978     ierr = DMRestoreWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
2979     ierr = PetscFree(pointWork);CHKERRQ(ierr);
2980   }
2981   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2982   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2983   ierr = PetscSectionDestroy(&leafIndicesSec);CHKERRQ(ierr);
2984   ierr = PetscSectionDestroy(&leafMatricesSec);CHKERRQ(ierr);
2985   ierr = PetscFree2(leafIndices,leafMatrices);CHKERRQ(ierr);
2986   ierr = PetscFree7(offsets,offsetsCopy,newOffsets,newOffsetsCopy,rowOffsets,numD,numO);CHKERRQ(ierr);
2987   ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
2988   PetscFunctionReturn(0);
2989 }
2990 
2991 #undef __FUNCT__
2992 #define __FUNCT__ "DMPlexComputeInjectorReferenceTree"
2993 /*
2994  * Assuming a nodal basis (w.r.t. the dual basis) basis:
2995  *
2996  * for each coarse dof \phi^c_i:
2997  *   for each quadrature point (w_l,x_l) in the dual basis definition of \phi^c_i:
2998  *     for each fine dof \phi^f_j;
2999  *       a_{i,j} = 0;
3000  *       for each fine dof \phi^f_k:
3001  *         a_{i,j} += interp_{i,k} * \phi^f_k(x_l) * \phi^f_j(x_l) * w_l
3002  *                    [^^^ this is = \phi^c_i ^^^]
3003  */
3004 PetscErrorCode DMPlexComputeInjectorReferenceTree(DM refTree, Mat *inj)
3005 {
3006   PetscDS        ds;
3007   PetscSection   section, cSection;
3008   DMLabel        canonical, depth;
3009   Mat            cMat, mat;
3010   PetscInt       *nnz;
3011   PetscInt       f, dim, numFields, numSecFields, p, pStart, pEnd, cStart, cEnd;
3012   PetscInt       m, n;
3013   PetscScalar    *pointScalar;
3014   PetscReal      *v0, *v0parent, *vtmp, *J, *Jparent, *invJ, *pointRef, detJ, detJparent;
3015   PetscErrorCode ierr;
3016 
3017   PetscFunctionBegin;
3018   ierr = DMGetDefaultSection(refTree,&section);CHKERRQ(ierr);
3019   ierr = DMGetDimension(refTree, &dim);CHKERRQ(ierr);
3020   ierr = PetscMalloc6(dim,&v0,dim,&v0parent,dim,&vtmp,dim*dim,&J,dim*dim,&Jparent,dim*dim,&invJ);CHKERRQ(ierr);
3021   ierr = PetscMalloc2(dim,&pointScalar,dim,&pointRef);CHKERRQ(ierr);
3022   ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
3023   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
3024   ierr = PetscSectionGetNumFields(section,&numSecFields);CHKERRQ(ierr);
3025   ierr = DMGetLabel(refTree,"canonical",&canonical);CHKERRQ(ierr);
3026   ierr = DMGetLabel(refTree,"depth",&depth);CHKERRQ(ierr);
3027   ierr = DMGetDefaultConstraints(refTree,&cSection,&cMat);CHKERRQ(ierr);
3028   ierr = DMPlexGetChart(refTree, &pStart, &pEnd);CHKERRQ(ierr);
3029   ierr = DMPlexGetHeightStratum(refTree, 0, &cStart, &cEnd);CHKERRQ(ierr);
3030   ierr = MatGetSize(cMat,&n,&m);CHKERRQ(ierr); /* the injector has transpose sizes from the constraint matrix */
3031   /* Step 1: compute non-zero pattern.  A proper subset of constraint matrix non-zero */
3032   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
3033   for (p = pStart; p < pEnd; p++) { /* a point will have non-zeros if it is canonical, it has dofs, and its children have dofs */
3034     const PetscInt *children;
3035     PetscInt numChildren;
3036     PetscInt i, numChildDof, numSelfDof;
3037 
3038     if (canonical) {
3039       PetscInt pCanonical;
3040       ierr = DMLabelGetValue(canonical,p,&pCanonical);CHKERRQ(ierr);
3041       if (p != pCanonical) continue;
3042     }
3043     ierr = DMPlexGetTreeChildren(refTree,p,&numChildren,&children);CHKERRQ(ierr);
3044     if (!numChildren) continue;
3045     for (i = 0, numChildDof = 0; i < numChildren; i++) {
3046       PetscInt child = children[i];
3047       PetscInt dof;
3048 
3049       ierr = PetscSectionGetDof(section,child,&dof);CHKERRQ(ierr);
3050       numChildDof += dof;
3051     }
3052     ierr = PetscSectionGetDof(section,p,&numSelfDof);CHKERRQ(ierr);
3053     if (!numChildDof || !numSelfDof) continue;
3054     for (f = 0; f < numFields; f++) {
3055       PetscInt selfOff;
3056 
3057       if (numSecFields) { /* count the dofs for just this field */
3058         for (i = 0, numChildDof = 0; i < numChildren; i++) {
3059           PetscInt child = children[i];
3060           PetscInt dof;
3061 
3062           ierr = PetscSectionGetFieldDof(section,child,f,&dof);CHKERRQ(ierr);
3063           numChildDof += dof;
3064         }
3065         ierr = PetscSectionGetFieldDof(section,p,f,&numSelfDof);CHKERRQ(ierr);
3066         ierr = PetscSectionGetFieldOffset(section,p,f,&selfOff);CHKERRQ(ierr);
3067       }
3068       else {
3069         ierr = PetscSectionGetOffset(section,p,&selfOff);CHKERRQ(ierr);
3070       }
3071       for (i = 0; i < numSelfDof; i++) {
3072         nnz[selfOff + i] = numChildDof;
3073       }
3074     }
3075   }
3076   ierr = MatCreateAIJ(PETSC_COMM_SELF,m,n,m,n,-1,nnz,-1,NULL,&mat);CHKERRQ(ierr);
3077   ierr = PetscFree(nnz);CHKERRQ(ierr);
3078   /* Setp 2: compute entries */
3079   for (p = pStart; p < pEnd; p++) {
3080     const PetscInt *children;
3081     PetscInt numChildren;
3082     PetscInt i, numChildDof, numSelfDof;
3083 
3084     /* same conditions about when entries occur */
3085     if (canonical) {
3086       PetscInt pCanonical;
3087       ierr = DMLabelGetValue(canonical,p,&pCanonical);CHKERRQ(ierr);
3088       if (p != pCanonical) continue;
3089     }
3090     ierr = DMPlexGetTreeChildren(refTree,p,&numChildren,&children);CHKERRQ(ierr);
3091     if (!numChildren) continue;
3092     for (i = 0, numChildDof = 0; i < numChildren; i++) {
3093       PetscInt child = children[i];
3094       PetscInt dof;
3095 
3096       ierr = PetscSectionGetDof(section,child,&dof);CHKERRQ(ierr);
3097       numChildDof += dof;
3098     }
3099     ierr = PetscSectionGetDof(section,p,&numSelfDof);CHKERRQ(ierr);
3100     if (!numChildDof || !numSelfDof) continue;
3101 
3102     for (f = 0; f < numFields; f++) {
3103       PetscInt       selfOff, fComp, numSelfShapes, numChildShapes, parentCell;
3104       PetscInt       cellShapeOff;
3105       PetscObject    disc;
3106       PetscDualSpace dsp;
3107       PetscClassId   classId;
3108       PetscScalar    *pointMat;
3109       PetscInt       *matRows, *matCols;
3110       PetscInt       pO = PETSC_MIN_INT;
3111       const PetscInt *depthNumDof;
3112 
3113       if (numSecFields) {
3114         for (i = 0, numChildDof = 0; i < numChildren; i++) {
3115           PetscInt child = children[i];
3116           PetscInt dof;
3117 
3118           ierr = PetscSectionGetFieldDof(section,child,f,&dof);CHKERRQ(ierr);
3119           numChildDof += dof;
3120         }
3121         ierr = PetscSectionGetFieldDof(section,p,f,&numSelfDof);CHKERRQ(ierr);
3122         ierr = PetscSectionGetFieldOffset(section,p,f,&selfOff);CHKERRQ(ierr);
3123         ierr = PetscSectionGetFieldComponents(section,f,&fComp);CHKERRQ(ierr);
3124       }
3125       else {
3126         ierr = PetscSectionGetOffset(section,p,&selfOff);CHKERRQ(ierr);
3127         fComp = 1;
3128       }
3129       numSelfShapes  = numSelfDof  / fComp;
3130       numChildShapes = numChildDof / fComp;
3131 
3132       /* find a cell whose closure contains p */
3133       if (p >= cStart && p < cEnd) {
3134         parentCell = p;
3135       }
3136       else {
3137         PetscInt *star = NULL;
3138         PetscInt numStar;
3139 
3140         parentCell = -1;
3141         ierr = DMPlexGetTransitiveClosure(refTree,p,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
3142         for (i = numStar - 1; i >= 0; i--) {
3143           PetscInt c = star[2 * i];
3144 
3145           if (c >= cStart && c < cEnd) {
3146             parentCell = c;
3147             break;
3148           }
3149         }
3150         ierr = DMPlexRestoreTransitiveClosure(refTree,p,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
3151       }
3152       /* determine the offset of p's shape functions withing parentCell's shape functions */
3153       ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
3154       ierr = PetscObjectGetClassId(disc,&classId);CHKERRQ(ierr);
3155       if (classId == PETSCFE_CLASSID) {
3156         ierr = PetscFEGetDualSpace((PetscFE)disc,&dsp);CHKERRQ(ierr);
3157       }
3158       else if (classId == PETSCFV_CLASSID) {
3159         ierr = PetscFVGetDualSpace((PetscFV)disc,&dsp);CHKERRQ(ierr);
3160       }
3161       else {
3162         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported discretization object");CHKERRQ(ierr);
3163       }
3164       ierr = PetscDualSpaceGetNumDof(dsp,&depthNumDof);CHKERRQ(ierr);
3165       {
3166         PetscInt *closure = NULL;
3167         PetscInt numClosure;
3168 
3169         ierr = DMPlexGetTransitiveClosure(refTree,parentCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
3170         for (i = 0, cellShapeOff = 0; i < numClosure; i++) {
3171           PetscInt point = closure[2 * i], pointDepth;
3172 
3173           pO = closure[2 * i + 1];
3174           if (point == p) break;
3175           ierr = DMLabelGetValue(depth,point,&pointDepth);CHKERRQ(ierr);
3176           cellShapeOff += depthNumDof[pointDepth];
3177         }
3178         ierr = DMPlexRestoreTransitiveClosure(refTree,parentCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
3179       }
3180 
3181       ierr = DMGetWorkArray(refTree, numSelfShapes * numChildShapes, PETSC_SCALAR,&pointMat);CHKERRQ(ierr);
3182       ierr = DMGetWorkArray(refTree, numSelfShapes + numChildShapes, PETSC_INT,&matRows);CHKERRQ(ierr);
3183       matCols = matRows + numSelfShapes;
3184       for (i = 0; i < numSelfShapes; i++) {
3185         matRows[i] = selfOff + i * fComp;
3186       }
3187       {
3188         PetscInt colOff = 0;
3189 
3190         for (i = 0; i < numChildren; i++) {
3191           PetscInt child = children[i];
3192           PetscInt dof, off, j;
3193 
3194           if (numSecFields) {
3195             ierr = PetscSectionGetFieldDof(cSection,child,f,&dof);CHKERRQ(ierr);
3196             ierr = PetscSectionGetFieldOffset(cSection,child,f,&off);CHKERRQ(ierr);
3197           }
3198           else {
3199             ierr = PetscSectionGetDof(cSection,child,&dof);CHKERRQ(ierr);
3200             ierr = PetscSectionGetOffset(cSection,child,&off);CHKERRQ(ierr);
3201           }
3202 
3203           for (j = 0; j < dof / fComp; j++) {
3204             matCols[colOff++] = off + j * fComp;
3205           }
3206         }
3207       }
3208       if (classId == PETSCFE_CLASSID) {
3209         PetscFE        fe = (PetscFE) disc;
3210         PetscInt       fSize;
3211 
3212         ierr = PetscFEGetDualSpace(fe,&dsp);CHKERRQ(ierr);
3213         ierr = PetscDualSpaceGetDimension(dsp,&fSize);CHKERRQ(ierr);
3214         for (i = 0; i < numSelfShapes; i++) { /* for every shape function */
3215           PetscQuadrature q;
3216           PetscInt        dim, numPoints, j, k;
3217           const PetscReal *points;
3218           const PetscReal *weights;
3219           PetscInt        *closure = NULL;
3220           PetscInt        numClosure;
3221           PetscInt        parentCellShapeDof = cellShapeOff + (pO < 0 ? (numSelfShapes - 1 - i) : i);
3222           PetscReal       *Bparent;
3223 
3224           ierr = PetscDualSpaceGetFunctional(dsp,parentCellShapeDof,&q);CHKERRQ(ierr);
3225           ierr = PetscQuadratureGetData(q,&dim,&numPoints,&points,&weights);CHKERRQ(ierr);
3226           ierr = PetscFEGetTabulation(fe,numPoints,points,&Bparent,NULL,NULL);CHKERRQ(ierr); /* I'm expecting a nodal basis: weights[:]' * Bparent[:,cellShapeDof] = 1. */
3227           for (k = 0; k < numChildShapes; k++) {
3228             pointMat[numChildShapes * i + k] = 0.;
3229           }
3230           for (j = 0; j < numPoints; j++) {
3231             PetscInt          childCell = -1;
3232             PetscReal         parentValAtPoint;
3233             const PetscReal   *pointReal = &points[dim * j];
3234             const PetscScalar *point;
3235             PetscReal         *Bchild;
3236             PetscInt          childCellShapeOff, pointMatOff;
3237 #if defined(PETSC_USE_COMPLEX)
3238             PetscInt          d;
3239 
3240             for (d = 0; d < dim; d++) {
3241               pointScalar[d] = points[dim * j + d];
3242             }
3243             point = pointScalar;
3244 #else
3245             point = pointReal;
3246 #endif
3247 
3248             parentValAtPoint = Bparent[(fSize * j + parentCellShapeDof) * fComp];
3249 
3250             for (k = 0; k < numChildren; k++) { /* locate the point in a child's star cell*/
3251               PetscInt child = children[k];
3252               PetscInt *star = NULL;
3253               PetscInt numStar, s;
3254 
3255               ierr = DMPlexGetTransitiveClosure(refTree,child,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
3256               for (s = numStar - 1; s >= 0; s--) {
3257                 PetscInt c = star[2 * s];
3258 
3259                 if (c < cStart || c >= cEnd) continue;
3260                 ierr = DMPlexLocatePoint_Internal(refTree,dim,point,c,&childCell);CHKERRQ(ierr);
3261                 if (childCell >= 0) break;
3262               }
3263               ierr = DMPlexRestoreTransitiveClosure(refTree,child,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
3264               if (childCell >= 0) break;
3265             }
3266             if (childCell < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Could not locate quadrature point");CHKERRQ(ierr);
3267             ierr = DMPlexComputeCellGeometryFEM(refTree, childCell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
3268             ierr = DMPlexComputeCellGeometryFEM(refTree, parentCell, NULL, v0parent, Jparent, NULL, &detJparent);CHKERRQ(ierr);
3269             CoordinatesRefToReal(dim, dim, v0parent, Jparent, pointReal, vtmp);
3270             CoordinatesRealToRef(dim, dim, v0, invJ, vtmp, pointRef);
3271 
3272             ierr = PetscFEGetTabulation(fe,1,pointRef,&Bchild,NULL,NULL);CHKERRQ(ierr);
3273             ierr = DMPlexGetTransitiveClosure(refTree,childCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
3274             for (k = 0, pointMatOff = 0; k < numChildren; k++) { /* point is located in cell => child dofs support at point are in closure of cell */
3275               PetscInt child = children[k], childDepth, childDof, childO = PETSC_MIN_INT;
3276               PetscInt l;
3277 
3278               ierr = DMLabelGetValue(depth,child,&childDepth);CHKERRQ(ierr);
3279               childDof = depthNumDof[childDepth];
3280               for (l = 0, childCellShapeOff = 0; l < numClosure; l++) {
3281                 PetscInt point = closure[2 * l];
3282                 PetscInt pointDepth;
3283 
3284                 childO = closure[2 * l + 1];
3285                 if (point == child) break;
3286                 ierr = DMLabelGetValue(depth,point,&pointDepth);CHKERRQ(ierr);
3287                 childCellShapeOff += depthNumDof[pointDepth];
3288               }
3289               if (l == numClosure) {
3290                 pointMatOff += childDof;
3291                 continue; /* child is not in the closure of the cell: has nothing to contribute to this point */
3292               }
3293               for (l = 0; l < childDof; l++) {
3294                 PetscInt    childCellDof    = childCellShapeOff + (childO ? (childDof - 1 - l) : l);
3295                 PetscReal   childValAtPoint = Bchild[childCellDof * fComp];
3296 
3297                 pointMat[i * numChildShapes + pointMatOff + l] += weights[j] * parentValAtPoint * childValAtPoint;
3298               }
3299               pointMatOff += childDof;
3300             }
3301             ierr = DMPlexRestoreTransitiveClosure(refTree,childCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
3302             ierr = PetscFERestoreTabulation(fe,1,pointRef,&Bchild,NULL,NULL);CHKERRQ(ierr);
3303           }
3304           ierr = PetscFERestoreTabulation(fe,numPoints,points,&Bparent,NULL,NULL);CHKERRQ(ierr);
3305         }
3306       }
3307       else { /* just the volume-weighted averages of the children */
3308         PetscInt  childShapeOff;
3309         PetscReal parentVol;
3310 
3311         ierr = DMPlexComputeCellGeometryFVM(refTree, p, &parentVol, NULL, NULL);CHKERRQ(ierr);
3312         for (i = 0, childShapeOff = 0; i < numChildren; i++) {
3313           PetscInt  child = children[i];
3314           PetscReal childVol;
3315 
3316           if (child < cStart || child >= cEnd) continue;
3317           ierr = DMPlexComputeCellGeometryFVM(refTree, child, &childVol, NULL, NULL);CHKERRQ(ierr);
3318           pointMat[childShapeOff] = childVol / parentVol;
3319           childShapeOff++;
3320         }
3321       }
3322       /* Insert pointMat into mat */
3323       for (i = 0; i < fComp; i++) {
3324         PetscInt j;
3325         ierr = MatSetValues(mat,numSelfShapes,matRows,numChildShapes,matCols,pointMat,INSERT_VALUES);CHKERRQ(ierr);
3326 
3327         for (j = 0; j < numSelfShapes; j++) {
3328           matRows[j]++;
3329         }
3330         for (j = 0; j < numChildShapes; j++) {
3331           matCols[j]++;
3332         }
3333       }
3334       ierr = DMRestoreWorkArray(refTree, numSelfShapes + numChildShapes, PETSC_INT,&matRows);CHKERRQ(ierr);
3335       ierr = DMRestoreWorkArray(refTree, numSelfShapes * numChildShapes, PETSC_SCALAR,&pointMat);CHKERRQ(ierr);
3336     }
3337   }
3338   ierr = PetscFree6(v0,v0parent,vtmp,J,Jparent,invJ);CHKERRQ(ierr);
3339   ierr = PetscFree2(pointScalar,pointRef);CHKERRQ(ierr);
3340   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3341   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3342   *inj = mat;
3343   PetscFunctionReturn(0);
3344 }
3345 
3346 #undef __FUNCT__
3347 #define __FUNCT__ "DMPlexReferenceTreeGetChildrenMatrices_Injection"
3348 static PetscErrorCode DMPlexReferenceTreeGetChildrenMatrices_Injection(DM refTree, Mat inj, PetscScalar ****childrenMats)
3349 {
3350   PetscDS        ds;
3351   PetscInt       numFields, f, pRefStart, pRefEnd, p, *rows, *cols, maxDof;
3352   PetscScalar    ***refPointFieldMats;
3353   PetscSection   refConSec, refSection;
3354   PetscErrorCode ierr;
3355 
3356   PetscFunctionBegin;
3357   ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
3358   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
3359   ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
3360   ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
3361   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
3362   ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldMats);CHKERRQ(ierr);
3363   ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
3364   ierr = PetscMalloc1(maxDof,&rows);CHKERRQ(ierr);
3365   ierr = PetscMalloc1(maxDof*maxDof,&cols);CHKERRQ(ierr);
3366   for (p = pRefStart; p < pRefEnd; p++) {
3367     PetscInt parent, pDof, parentDof;
3368 
3369     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
3370     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
3371     ierr = PetscSectionGetDof(refSection,parent,&parentDof);CHKERRQ(ierr);
3372     if (!pDof || !parentDof || parent == p) continue;
3373 
3374     ierr = PetscMalloc1(numFields,&refPointFieldMats[p-pRefStart]);CHKERRQ(ierr);
3375     for (f = 0; f < numFields; f++) {
3376       PetscInt cDof, cOff, numCols, r, fComp;
3377       PetscObject disc;
3378       PetscClassId id;
3379       PetscFE fe = NULL;
3380       PetscFV fv = NULL;
3381 
3382       ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
3383       ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
3384       if (id == PETSCFE_CLASSID) {
3385         fe = (PetscFE) disc;
3386         ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
3387       }
3388       else if (id == PETSCFV_CLASSID) {
3389         fv = (PetscFV) disc;
3390         ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
3391       }
3392       else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);
3393 
3394       if (numFields > 1) {
3395         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
3396         ierr = PetscSectionGetFieldOffset(refConSec,p,f,&cOff);CHKERRQ(ierr);
3397       }
3398       else {
3399         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
3400         ierr = PetscSectionGetOffset(refConSec,p,&cOff);CHKERRQ(ierr);
3401       }
3402 
3403       for (r = 0; r < cDof; r++) {
3404         rows[r] = cOff + r;
3405       }
3406       numCols = 0;
3407       {
3408         PetscInt aDof, aOff, j;
3409 
3410         if (numFields > 1) {
3411           ierr = PetscSectionGetFieldDof(refSection,parent,f,&aDof);CHKERRQ(ierr);
3412           ierr = PetscSectionGetFieldOffset(refSection,parent,f,&aOff);CHKERRQ(ierr);
3413         }
3414         else {
3415           ierr = PetscSectionGetDof(refSection,parent,&aDof);CHKERRQ(ierr);
3416           ierr = PetscSectionGetOffset(refSection,parent,&aOff);CHKERRQ(ierr);
3417         }
3418 
3419         for (j = 0; j < aDof; j++) {
3420           cols[numCols++] = aOff + j;
3421         }
3422       }
3423       ierr = PetscMalloc1(cDof*numCols,&refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
3424       /* transpose of constraint matrix */
3425       ierr = MatGetValues(inj,numCols,cols,cDof,rows,refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
3426     }
3427   }
3428   *childrenMats = refPointFieldMats;
3429   ierr = PetscFree(rows);CHKERRQ(ierr);
3430   ierr = PetscFree(cols);CHKERRQ(ierr);
3431   PetscFunctionReturn(0);
3432 }
3433 
3434 #undef __FUNCT__
3435 #define __FUNCT__ "DMPlexReferenceTreeRestoreChildrenMatrices_Injection"
3436 static PetscErrorCode DMPlexReferenceTreeRestoreChildrenMatrices_Injection(DM refTree, Mat inj, PetscScalar ****childrenMats)
3437 {
3438   PetscDS        ds;
3439   PetscScalar    ***refPointFieldMats;
3440   PetscInt       numFields, pRefStart, pRefEnd, p, f;
3441   PetscSection   refConSec, refSection;
3442   PetscErrorCode ierr;
3443 
3444   PetscFunctionBegin;
3445   refPointFieldMats = *childrenMats;
3446   *childrenMats = NULL;
3447   ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
3448   ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
3449   ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
3450   ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
3451   ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
3452   for (p = pRefStart; p < pRefEnd; p++) {
3453     PetscInt parent, pDof, parentDof;
3454 
3455     ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
3456     ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
3457     ierr = PetscSectionGetDof(refSection,parent,&parentDof);CHKERRQ(ierr);
3458     if (!pDof || !parentDof || parent == p) continue;
3459 
3460     for (f = 0; f < numFields; f++) {
3461       PetscInt cDof;
3462 
3463       if (numFields > 1) {
3464         ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
3465       }
3466       else {
3467         ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
3468       }
3469 
3470       ierr = PetscFree(refPointFieldMats[p - pRefStart][f]);CHKERRQ(ierr);
3471     }
3472     ierr = PetscFree(refPointFieldMats[p - pRefStart]);CHKERRQ(ierr);
3473   }
3474   ierr = PetscFree(refPointFieldMats);CHKERRQ(ierr);
3475   PetscFunctionReturn(0);
3476 }
3477 
3478 #undef __FUNCT__
3479 #define __FUNCT__ "DMPlexReferenceTreeGetInjector"
3480 static PetscErrorCode DMPlexReferenceTreeGetInjector(DM refTree,Mat *injRef)
3481 {
3482   Mat            cMatRef;
3483   PetscObject    injRefObj;
3484   PetscErrorCode ierr;
3485 
3486   PetscFunctionBegin;
3487   ierr = DMGetDefaultConstraints(refTree,NULL,&cMatRef);CHKERRQ(ierr);
3488   ierr = PetscObjectQuery((PetscObject)cMatRef,"DMPlexComputeInjectorTree_refTree",&injRefObj);CHKERRQ(ierr);
3489   *injRef = (Mat) injRefObj;
3490   if (!*injRef) {
3491     ierr = DMPlexComputeInjectorReferenceTree(refTree,injRef);CHKERRQ(ierr);
3492     ierr = PetscObjectCompose((PetscObject)cMatRef,"DMPlexComputeInjectorTree_refTree",(PetscObject)*injRef);CHKERRQ(ierr);
3493     /* there is now a reference in cMatRef, which should be the only one for symmetry with the above case */
3494     ierr = PetscObjectDereference((PetscObject)*injRef);CHKERRQ(ierr);
3495   }
3496   PetscFunctionReturn(0);
3497 }
3498 
3499 #undef __FUNCT__
3500 #define __FUNCT__ "DMPlexTransferInjectorTree"
3501 static PetscErrorCode DMPlexTransferInjectorTree(DM coarse, DM fine, PetscSF coarseToFine, const PetscInt *childIds, Vec fineVec, PetscInt numFields, PetscInt *offsets, PetscSection *rootMultiSec, PetscSection *multiLeafSec, PetscInt **gatheredIndices, PetscScalar **gatheredValues)
3502 {
3503   PetscInt       pStartF, pEndF, pStartC, pEndC, p, maxDof, numMulti;
3504   PetscSection   globalCoarse, globalFine;
3505   PetscSection   localCoarse, localFine, leafIndicesSec;
3506   PetscSection   multiRootSec, rootIndicesSec;
3507   PetscInt       *leafInds, *rootInds = NULL;
3508   const PetscInt *rootDegrees;
3509   PetscScalar    *leafVals = NULL, *rootVals = NULL;
3510   PetscSF        coarseToFineEmbedded;
3511   PetscErrorCode ierr;
3512 
3513   PetscFunctionBegin;
3514   ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
3515   ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
3516   ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
3517   ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
3518   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafIndicesSec);CHKERRQ(ierr);
3519   ierr = PetscSectionSetChart(leafIndicesSec,pStartF, pEndF);CHKERRQ(ierr);
3520   ierr = PetscSectionGetMaxDof(localFine,&maxDof);CHKERRQ(ierr);
3521   { /* winnow fine points that don't have global dofs out of the sf */
3522     PetscInt l, nleaves, dof, cdof, numPointsWithDofs, offset, *pointsWithDofs, numIndices;
3523     const PetscInt *leaves;
3524 
3525     ierr = PetscSFGetGraph(coarseToFine,NULL,&nleaves,&leaves,NULL);CHKERRQ(ierr);
3526     for (l = 0, numPointsWithDofs = 0; l < nleaves; l++) {
3527       p    = leaves ? leaves[l] : l;
3528       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
3529       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
3530       if ((dof - cdof) > 0) {
3531         numPointsWithDofs++;
3532 
3533         ierr = PetscSectionGetDof(localFine,p,&dof);CHKERRQ(ierr);
3534         ierr = PetscSectionSetDof(leafIndicesSec,p,dof + 1);CHKERRQ(ierr);
3535       }
3536     }
3537     ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
3538     ierr = PetscSectionSetUp(leafIndicesSec);CHKERRQ(ierr);
3539     ierr = PetscSectionGetStorageSize(leafIndicesSec,&numIndices);CHKERRQ(ierr);
3540     ierr = PetscMalloc1(gatheredIndices ? numIndices : (maxDof + 1),&leafInds);CHKERRQ(ierr);
3541     if (gatheredValues)  {ierr = PetscMalloc1(numIndices,&leafVals);CHKERRQ(ierr);}
3542     for (l = 0, offset = 0; l < nleaves; l++) {
3543       p    = leaves ? leaves[l] : l;
3544       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
3545       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
3546       if ((dof - cdof) > 0) {
3547         PetscInt    off, gOff;
3548         PetscInt    *pInd;
3549         PetscScalar *pVal = NULL;
3550 
3551         pointsWithDofs[offset++] = l;
3552 
3553         ierr = PetscSectionGetOffset(leafIndicesSec,p,&off);CHKERRQ(ierr);
3554 
3555         pInd = gatheredIndices ? (&leafInds[off + 1]) : leafInds;
3556         if (gatheredValues) {
3557           PetscInt i;
3558 
3559           pVal = &leafVals[off + 1];
3560           for (i = 0; i < dof; i++) pVal[i] = 0.;
3561         }
3562         ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
3563 
3564         offsets[0] = 0;
3565         if (numFields) {
3566           PetscInt f;
3567 
3568           for (f = 0; f < numFields; f++) {
3569             PetscInt fDof;
3570             ierr = PetscSectionGetFieldDof(localFine,p,f,&fDof);CHKERRQ(ierr);
3571             offsets[f + 1] = fDof + offsets[f];
3572           }
3573           DMPlexGetIndicesPointFields_Internal(localFine,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
3574         }
3575         else {
3576           DMPlexGetIndicesPoint_Internal(localFine,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
3577         }
3578         if (gatheredValues) {ierr = VecGetValues(fineVec,dof,pInd,pVal);CHKERRQ(ierr);}
3579       }
3580     }
3581     ierr = PetscSFCreateEmbeddedLeafSF(coarseToFine, numPointsWithDofs, pointsWithDofs, &coarseToFineEmbedded);CHKERRQ(ierr);
3582     ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
3583   }
3584 
3585   ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
3586   ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
3587   ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
3588 
3589   { /* there may be the case where an sf root has a parent: broadcast parents back to children */
3590     MPI_Datatype threeInt;
3591     PetscMPIInt  rank;
3592     PetscInt     (*parentNodeAndIdCoarse)[3];
3593     PetscInt     (*parentNodeAndIdFine)[3];
3594     PetscInt     p, nleaves, nleavesToParents;
3595     PetscSF      pointSF, sfToParents;
3596     const PetscInt *ilocal;
3597     const PetscSFNode *iremote;
3598     PetscSFNode  *iremoteToParents;
3599     PetscInt     *ilocalToParents;
3600 
3601     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)coarse),&rank);CHKERRQ(ierr);
3602     ierr = MPI_Type_contiguous(3,MPIU_INT,&threeInt);CHKERRQ(ierr);
3603     ierr = MPI_Type_commit(&threeInt);CHKERRQ(ierr);
3604     ierr = PetscMalloc2(pEndC-pStartC,&parentNodeAndIdCoarse,pEndF-pStartF,&parentNodeAndIdFine);CHKERRQ(ierr);
3605     ierr = DMGetPointSF(coarse,&pointSF);CHKERRQ(ierr);
3606     ierr = PetscSFGetGraph(pointSF,NULL,&nleaves,&ilocal,&iremote);CHKERRQ(ierr);
3607     for (p = pStartC; p < pEndC; p++) {
3608       PetscInt parent, childId;
3609       ierr = DMPlexGetTreeParent(coarse,p,&parent,&childId);CHKERRQ(ierr);
3610       parentNodeAndIdCoarse[p - pStartC][0] = rank;
3611       parentNodeAndIdCoarse[p - pStartC][1] = parent - pStartC;
3612       parentNodeAndIdCoarse[p - pStartC][2] = (p == parent) ? -1 : childId;
3613       if (nleaves > 0) {
3614         PetscInt leaf = -1;
3615 
3616         if (ilocal) {
3617           ierr  = PetscFindInt(parent,nleaves,ilocal,&leaf);CHKERRQ(ierr);
3618         }
3619         else {
3620           leaf = p - pStartC;
3621         }
3622         if (leaf >= 0) {
3623           parentNodeAndIdCoarse[p - pStartC][0] = iremote[leaf].rank;
3624           parentNodeAndIdCoarse[p - pStartC][1] = iremote[leaf].index;
3625         }
3626       }
3627     }
3628     for (p = pStartF; p < pEndF; p++) {
3629       parentNodeAndIdFine[p - pStartF][0] = -1;
3630       parentNodeAndIdFine[p - pStartF][1] = -1;
3631       parentNodeAndIdFine[p - pStartF][2] = -1;
3632     }
3633     ierr = PetscSFBcastBegin(coarseToFineEmbedded,threeInt,parentNodeAndIdCoarse,parentNodeAndIdFine);CHKERRQ(ierr);
3634     ierr = PetscSFBcastEnd(coarseToFineEmbedded,threeInt,parentNodeAndIdCoarse,parentNodeAndIdFine);CHKERRQ(ierr);
3635     for (p = pStartF, nleavesToParents = 0; p < pEndF; p++) {
3636       PetscInt dof;
3637 
3638       ierr = PetscSectionGetDof(leafIndicesSec,p,&dof);CHKERRQ(ierr);
3639       if (dof) {
3640         PetscInt off;
3641 
3642         ierr = PetscSectionGetOffset(leafIndicesSec,p,&off);CHKERRQ(ierr);
3643         if (gatheredIndices) {
3644           leafInds[off] = PetscMax(childIds[p-pStartF],parentNodeAndIdFine[p-pStartF][2]);
3645         } else if (gatheredValues) {
3646           leafVals[off] = (PetscScalar) PetscMax(childIds[p-pStartF],parentNodeAndIdFine[p-pStartF][2]);
3647         }
3648       }
3649       if (parentNodeAndIdFine[p-pStartF][0] >= 0) {
3650         nleavesToParents++;
3651       }
3652     }
3653     ierr = PetscMalloc1(nleavesToParents,&ilocalToParents);CHKERRQ(ierr);
3654     ierr = PetscMalloc1(nleavesToParents,&iremoteToParents);CHKERRQ(ierr);
3655     for (p = pStartF, nleavesToParents = 0; p < pEndF; p++) {
3656       if (parentNodeAndIdFine[p-pStartF][0] >= 0) {
3657         ilocalToParents[nleavesToParents] = p - pStartF;
3658         iremoteToParents[nleavesToParents].rank  = parentNodeAndIdFine[p-pStartF][0];
3659         iremoteToParents[nleavesToParents].index = parentNodeAndIdFine[p-pStartF][1];
3660         nleavesToParents++;
3661       }
3662     }
3663     ierr = PetscSFCreate(PetscObjectComm((PetscObject)coarse),&sfToParents);CHKERRQ(ierr);
3664     ierr = PetscSFSetGraph(sfToParents,pEndC-pStartC,nleavesToParents,ilocalToParents,PETSC_OWN_POINTER,iremoteToParents,PETSC_OWN_POINTER);CHKERRQ(ierr);
3665     ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
3666 
3667     coarseToFineEmbedded = sfToParents;
3668 
3669     ierr = PetscFree2(parentNodeAndIdCoarse,parentNodeAndIdFine);CHKERRQ(ierr);
3670     ierr = MPI_Type_free(&threeInt);CHKERRQ(ierr);
3671   }
3672 
3673   { /* winnow out coarse points that don't have dofs */
3674     PetscInt dof, cdof, numPointsWithDofs, offset, *pointsWithDofs;
3675     PetscSF  sfDofsOnly;
3676 
3677     for (p = pStartC, numPointsWithDofs = 0; p < pEndC; p++) {
3678       ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
3679       ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
3680       if ((dof - cdof) > 0) {
3681         numPointsWithDofs++;
3682       }
3683     }
3684     ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
3685     for (p = pStartC, offset = 0; p < pEndC; p++) {
3686       ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
3687       ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
3688       if ((dof - cdof) > 0) {
3689         pointsWithDofs[offset++] = p - pStartC;
3690       }
3691     }
3692     ierr = PetscSFCreateEmbeddedSF(coarseToFineEmbedded, numPointsWithDofs, pointsWithDofs, &sfDofsOnly);CHKERRQ(ierr);
3693     ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
3694     ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
3695     coarseToFineEmbedded = sfDofsOnly;
3696   }
3697 
3698   /* communicate back to the coarse mesh which coarse points have children (that may require injection) */
3699   ierr = PetscSFComputeDegreeBegin(coarseToFineEmbedded,&rootDegrees);CHKERRQ(ierr);
3700   ierr = PetscSFComputeDegreeEnd(coarseToFineEmbedded,&rootDegrees);CHKERRQ(ierr);
3701   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&multiRootSec);CHKERRQ(ierr);
3702   ierr = PetscSectionSetChart(multiRootSec,pStartC,pEndC);CHKERRQ(ierr);
3703   for (p = pStartC; p < pEndC; p++) {
3704     ierr = PetscSectionSetDof(multiRootSec,p,rootDegrees[p-pStartC]);CHKERRQ(ierr);
3705   }
3706   ierr = PetscSectionSetUp(multiRootSec);CHKERRQ(ierr);
3707   ierr = PetscSectionGetStorageSize(multiRootSec,&numMulti);CHKERRQ(ierr);
3708   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootIndicesSec);CHKERRQ(ierr);
3709   { /* distribute the leaf section */
3710     PetscSF multi, multiInv, indicesSF;
3711     PetscInt *remoteOffsets, numRootIndices;
3712 
3713     ierr = PetscSFGetMultiSF(coarseToFineEmbedded,&multi);CHKERRQ(ierr);
3714     ierr = PetscSFCreateInverseSF(multi,&multiInv);CHKERRQ(ierr);
3715     ierr = PetscSFDistributeSection(multiInv,leafIndicesSec,&remoteOffsets,rootIndicesSec);CHKERRQ(ierr);
3716     ierr = PetscSFCreateSectionSF(multiInv,leafIndicesSec,remoteOffsets,rootIndicesSec,&indicesSF);CHKERRQ(ierr);
3717     ierr = PetscFree(remoteOffsets);CHKERRQ(ierr);
3718     ierr = PetscSFDestroy(&multiInv);CHKERRQ(ierr);
3719     ierr = PetscSectionGetStorageSize(rootIndicesSec,&numRootIndices);CHKERRQ(ierr);
3720     if (gatheredIndices) {
3721       ierr = PetscMalloc1(numRootIndices,&rootInds);CHKERRQ(ierr);
3722       ierr = PetscSFBcastBegin(indicesSF,MPIU_INT,leafInds,rootInds);CHKERRQ(ierr);
3723       ierr = PetscSFBcastEnd(indicesSF,MPIU_INT,leafInds,rootInds);CHKERRQ(ierr);
3724     }
3725     if (gatheredValues) {
3726       ierr = PetscMalloc1(numRootIndices,&rootVals);CHKERRQ(ierr);
3727       ierr = PetscSFBcastBegin(indicesSF,MPIU_SCALAR,leafVals,rootVals);CHKERRQ(ierr);
3728       ierr = PetscSFBcastEnd(indicesSF,MPIU_SCALAR,leafVals,rootVals);CHKERRQ(ierr);
3729     }
3730     ierr = PetscSFDestroy(&indicesSF);CHKERRQ(ierr);
3731   }
3732   ierr = PetscSectionDestroy(&leafIndicesSec);CHKERRQ(ierr);
3733   ierr = PetscFree(leafInds);CHKERRQ(ierr);
3734   ierr = PetscFree(leafVals);CHKERRQ(ierr);
3735   ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
3736   *rootMultiSec = multiRootSec;
3737   *multiLeafSec = rootIndicesSec;
3738   if (gatheredIndices) *gatheredIndices = rootInds;
3739   if (gatheredValues)  *gatheredValues  = rootVals;
3740   PetscFunctionReturn(0);
3741 }
3742 
3743 #undef __FUNCT__
3744 #define __FUNCT__ "DMPlexComputeInjectorTree"
3745 PetscErrorCode DMPlexComputeInjectorTree(DM coarse, DM fine, PetscSF coarseToFine, PetscInt *childIds, Mat mat)
3746 {
3747   DM             refTree;
3748   PetscSection   multiRootSec, rootIndicesSec;
3749   PetscSection   globalCoarse, globalFine;
3750   PetscSection   localCoarse, localFine;
3751   PetscSection   cSecRef;
3752   PetscInt       *rootIndices, *parentIndices, pRefStart, pRefEnd;
3753   Mat            injRef;
3754   PetscInt       numFields, maxDof;
3755   PetscInt       pStartC, pEndC, pStartF, pEndF, p;
3756   PetscInt       *offsets, *offsetsCopy, *rowOffsets;
3757   PetscLayout    rowMap, colMap;
3758   PetscInt       rowStart, rowEnd, colStart, colEnd, *nnzD, *nnzO;
3759   PetscScalar    ***childrenMats=NULL ; /* gcc -O gives 'may be used uninitialized' warning'. Initializing to suppress this warning */
3760   PetscErrorCode ierr;
3761 
3762   PetscFunctionBegin;
3763 
3764   /* get the templates for the fine-to-coarse injection from the reference tree */
3765   ierr = DMPlexGetReferenceTree(coarse,&refTree);CHKERRQ(ierr);
3766   ierr = DMGetDefaultConstraints(refTree,&cSecRef,NULL);CHKERRQ(ierr);
3767   ierr = PetscSectionGetChart(cSecRef,&pRefStart,&pRefEnd);CHKERRQ(ierr);
3768   ierr = DMPlexReferenceTreeGetInjector(refTree,&injRef);CHKERRQ(ierr);
3769 
3770   ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
3771   ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
3772   ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
3773   ierr = PetscSectionGetNumFields(localFine,&numFields);CHKERRQ(ierr);
3774   ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
3775   ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
3776   ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
3777   ierr = PetscSectionGetMaxDof(localCoarse,&maxDof);CHKERRQ(ierr);
3778   {
3779     PetscInt maxFields = PetscMax(1,numFields) + 1;
3780     ierr = PetscMalloc3(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&rowOffsets);CHKERRQ(ierr);
3781   }
3782 
3783   ierr = DMPlexTransferInjectorTree(coarse,fine,coarseToFine,childIds,NULL,numFields,offsets,&multiRootSec,&rootIndicesSec,&rootIndices,NULL);CHKERRQ(ierr);
3784 
3785   ierr = PetscMalloc1(maxDof,&parentIndices);CHKERRQ(ierr);
3786 
3787   /* count indices */
3788   ierr = MatGetLayouts(mat,&rowMap,&colMap);CHKERRQ(ierr);
3789   ierr = PetscLayoutSetUp(rowMap);CHKERRQ(ierr);
3790   ierr = PetscLayoutSetUp(colMap);CHKERRQ(ierr);
3791   ierr = PetscLayoutGetRange(rowMap,&rowStart,&rowEnd);CHKERRQ(ierr);
3792   ierr = PetscLayoutGetRange(colMap,&colStart,&colEnd);CHKERRQ(ierr);
3793   ierr = PetscCalloc2(rowEnd-rowStart,&nnzD,rowEnd-rowStart,&nnzO);CHKERRQ(ierr);
3794   for (p = pStartC; p < pEndC; p++) {
3795     PetscInt numLeaves, leafStart, leafEnd, l, dof, cdof, gOff;
3796 
3797     ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
3798     ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
3799     if ((dof - cdof) <= 0) continue;
3800     ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);
3801 
3802     rowOffsets[0] = 0;
3803     offsetsCopy[0] = 0;
3804     if (numFields) {
3805       PetscInt f;
3806 
3807       for (f = 0; f < numFields; f++) {
3808         PetscInt fDof;
3809         ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
3810         rowOffsets[f + 1] = offsetsCopy[f + 1] = fDof + rowOffsets[f];
3811       }
3812       DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
3813     }
3814     else {
3815       DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
3816       rowOffsets[1] = offsetsCopy[0];
3817     }
3818 
3819     ierr = PetscSectionGetDof(multiRootSec,p,&numLeaves);CHKERRQ(ierr);
3820     ierr = PetscSectionGetOffset(multiRootSec,p,&leafStart);CHKERRQ(ierr);
3821     leafEnd = leafStart + numLeaves;
3822     for (l = leafStart; l < leafEnd; l++) {
3823       PetscInt numIndices, childId, offset;
3824       const PetscInt *childIndices;
3825 
3826       ierr = PetscSectionGetDof(rootIndicesSec,l,&numIndices);CHKERRQ(ierr);
3827       ierr = PetscSectionGetOffset(rootIndicesSec,l,&offset);CHKERRQ(ierr);
3828       childId = rootIndices[offset++];
3829       childIndices = &rootIndices[offset];
3830       numIndices--;
3831 
3832       if (childId == -1) { /* equivalent points: scatter */
3833         PetscInt i;
3834 
3835         for (i = 0; i < numIndices; i++) {
3836           PetscInt colIndex = childIndices[i];
3837           PetscInt rowIndex = parentIndices[i];
3838           if (rowIndex < 0) continue;
3839           if (colIndex < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unconstrained fine and constrained coarse");
3840           if (colIndex >= colStart && colIndex < colEnd) {
3841             nnzD[rowIndex - rowStart] = 1;
3842           }
3843           else {
3844             nnzO[rowIndex - rowStart] = 1;
3845           }
3846         }
3847       }
3848       else {
3849         PetscInt parentId, f, lim;
3850 
3851         ierr = DMPlexGetTreeParent(refTree,childId,&parentId,NULL);CHKERRQ(ierr);
3852 
3853         lim = PetscMax(1,numFields);
3854         offsets[0] = 0;
3855         if (numFields) {
3856           PetscInt f;
3857 
3858           for (f = 0; f < numFields; f++) {
3859             PetscInt fDof;
3860             ierr = PetscSectionGetFieldDof(cSecRef,childId,f,&fDof);CHKERRQ(ierr);
3861 
3862             offsets[f + 1] = fDof + offsets[f];
3863           }
3864         }
3865         else {
3866           PetscInt cDof;
3867 
3868           ierr = PetscSectionGetDof(cSecRef,childId,&cDof);CHKERRQ(ierr);
3869           offsets[1] = cDof;
3870         }
3871         for (f = 0; f < lim; f++) {
3872           PetscInt parentStart = rowOffsets[f], parentEnd = rowOffsets[f + 1];
3873           PetscInt childStart = offsets[f], childEnd = offsets[f + 1];
3874           PetscInt i, numD = 0, numO = 0;
3875 
3876           for (i = childStart; i < childEnd; i++) {
3877             PetscInt colIndex = childIndices[i];
3878 
3879             if (colIndex < 0) continue;
3880             if (colIndex >= colStart && colIndex < colEnd) {
3881               numD++;
3882             }
3883             else {
3884               numO++;
3885             }
3886           }
3887           for (i = parentStart; i < parentEnd; i++) {
3888             PetscInt rowIndex = parentIndices[i];
3889 
3890             if (rowIndex < 0) continue;
3891             nnzD[rowIndex - rowStart] += numD;
3892             nnzO[rowIndex - rowStart] += numO;
3893           }
3894         }
3895       }
3896     }
3897   }
3898   /* preallocate */
3899   ierr = MatXAIJSetPreallocation(mat,1,nnzD,nnzO,NULL,NULL);CHKERRQ(ierr);
3900   ierr = PetscFree2(nnzD,nnzO);CHKERRQ(ierr);
3901   /* insert values */
3902   ierr = DMPlexReferenceTreeGetChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
3903   for (p = pStartC; p < pEndC; p++) {
3904     PetscInt numLeaves, leafStart, leafEnd, l, dof, cdof, gOff;
3905 
3906     ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
3907     ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
3908     if ((dof - cdof) <= 0) continue;
3909     ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);
3910 
3911     rowOffsets[0] = 0;
3912     offsetsCopy[0] = 0;
3913     if (numFields) {
3914       PetscInt f;
3915 
3916       for (f = 0; f < numFields; f++) {
3917         PetscInt fDof;
3918         ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
3919         rowOffsets[f + 1] = offsetsCopy[f + 1] = fDof + rowOffsets[f];
3920       }
3921       DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
3922     }
3923     else {
3924       DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
3925       rowOffsets[1] = offsetsCopy[0];
3926     }
3927 
3928     ierr = PetscSectionGetDof(multiRootSec,p,&numLeaves);CHKERRQ(ierr);
3929     ierr = PetscSectionGetOffset(multiRootSec,p,&leafStart);CHKERRQ(ierr);
3930     leafEnd = leafStart + numLeaves;
3931     for (l = leafStart; l < leafEnd; l++) {
3932       PetscInt numIndices, childId, offset;
3933       const PetscInt *childIndices;
3934 
3935       ierr = PetscSectionGetDof(rootIndicesSec,l,&numIndices);CHKERRQ(ierr);
3936       ierr = PetscSectionGetOffset(rootIndicesSec,l,&offset);CHKERRQ(ierr);
3937       childId = rootIndices[offset++];
3938       childIndices = &rootIndices[offset];
3939       numIndices--;
3940 
3941       if (childId == -1) { /* equivalent points: scatter */
3942         PetscInt i;
3943 
3944         for (i = 0; i < numIndices; i++) {
3945           ierr = MatSetValue(mat,parentIndices[i],childIndices[i],1.,INSERT_VALUES);CHKERRQ(ierr);
3946         }
3947       }
3948       else {
3949         PetscInt parentId, f, lim;
3950 
3951         ierr = DMPlexGetTreeParent(refTree,childId,&parentId,NULL);CHKERRQ(ierr);
3952 
3953         lim = PetscMax(1,numFields);
3954         offsets[0] = 0;
3955         if (numFields) {
3956           PetscInt f;
3957 
3958           for (f = 0; f < numFields; f++) {
3959             PetscInt fDof;
3960             ierr = PetscSectionGetFieldDof(cSecRef,childId,f,&fDof);CHKERRQ(ierr);
3961 
3962             offsets[f + 1] = fDof + offsets[f];
3963           }
3964         }
3965         else {
3966           PetscInt cDof;
3967 
3968           ierr = PetscSectionGetDof(cSecRef,childId,&cDof);CHKERRQ(ierr);
3969           offsets[1] = cDof;
3970         }
3971         for (f = 0; f < lim; f++) {
3972           PetscScalar    *childMat   = &childrenMats[childId - pRefStart][f][0];
3973           PetscInt       *rowIndices = &parentIndices[rowOffsets[f]];
3974           const PetscInt *colIndices = &childIndices[offsets[f]];
3975 
3976           ierr = MatSetValues(mat,rowOffsets[f+1]-rowOffsets[f],rowIndices,offsets[f+1]-offsets[f],colIndices,childMat,INSERT_VALUES);CHKERRQ(ierr);
3977         }
3978       }
3979     }
3980   }
3981   ierr = PetscSectionDestroy(&multiRootSec);CHKERRQ(ierr);
3982   ierr = PetscSectionDestroy(&rootIndicesSec);CHKERRQ(ierr);
3983   ierr = PetscFree(parentIndices);CHKERRQ(ierr);
3984   ierr = DMPlexReferenceTreeRestoreChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
3985   ierr = PetscFree(rootIndices);CHKERRQ(ierr);
3986   ierr = PetscFree3(offsets,offsetsCopy,rowOffsets);CHKERRQ(ierr);
3987 
3988   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3989   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3990   PetscFunctionReturn(0);
3991 }
3992 
3993 #undef __FUNCT__
3994 #define __FUNCT__ "DMPlexTransferVecTree_Interpolate"
3995 static PetscErrorCode DMPlexTransferVecTree_Interpolate(DM coarse, Vec vecCoarseLocal, DM fine, Vec vecFine, PetscSF coarseToFine, PetscInt *cids, Vec grad, Vec cellGeom)
3996 {
3997   PetscDS           ds;
3998   PetscSF           coarseToFineEmbedded;
3999   PetscSection      globalCoarse, globalFine;
4000   PetscSection      localCoarse, localFine;
4001   PetscSection      aSec, cSec;
4002   PetscSection      rootValuesSec;
4003   PetscSection      leafValuesSec;
4004   PetscScalar       *rootValues, *leafValues;
4005   IS                aIS;
4006   const PetscInt    *anchors;
4007   Mat               cMat;
4008   PetscInt          numFields;
4009   PetscInt          pStartC, pEndC, pStartF, pEndF, p, cellStart, cellEnd;
4010   PetscInt          aStart, aEnd, cStart, cEnd;
4011   PetscInt          *maxChildIds;
4012   PetscInt          *offsets, *newOffsets, *offsetsCopy, *newOffsetsCopy, *rowOffsets, *numD, *numO;
4013   PetscFV           fv = NULL;
4014   PetscInt          dim, numFVcomps = -1, fvField = -1;
4015   DM                cellDM = NULL, gradDM = NULL;
4016   const PetscScalar *cellGeomArray = NULL;
4017   const PetscScalar *gradArray = NULL;
4018   PetscErrorCode    ierr;
4019 
4020   PetscFunctionBegin;
4021   ierr = VecSetOption(vecFine,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);CHKERRQ(ierr);
4022   ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
4023   ierr = DMPlexGetHeightStratum(coarse,0,&cellStart,&cellEnd);CHKERRQ(ierr);
4024   ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
4025   ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
4026   ierr = DMGetCoordinateDim(coarse,&dim);CHKERRQ(ierr);
4027   { /* winnow fine points that don't have global dofs out of the sf */
4028     PetscInt       nleaves, l;
4029     const PetscInt *leaves;
4030     PetscInt       dof, cdof, numPointsWithDofs, offset, *pointsWithDofs;
4031 
4032     ierr = PetscSFGetGraph(coarseToFine,NULL,&nleaves,&leaves,NULL);CHKERRQ(ierr);
4033 
4034     for (l = 0, numPointsWithDofs = 0; l < nleaves; l++) {
4035       PetscInt p = leaves ? leaves[l] : l;
4036 
4037       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
4038       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
4039       if ((dof - cdof) > 0) {
4040         numPointsWithDofs++;
4041       }
4042     }
4043     ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
4044     for (l = 0, offset = 0; l < nleaves; l++) {
4045       PetscInt p = leaves ? leaves[l] : l;
4046 
4047       ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
4048       ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
4049       if ((dof - cdof) > 0) {
4050         pointsWithDofs[offset++] = l;
4051       }
4052     }
4053     ierr = PetscSFCreateEmbeddedLeafSF(coarseToFine, numPointsWithDofs, pointsWithDofs, &coarseToFineEmbedded);CHKERRQ(ierr);
4054     ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
4055   }
4056   /* communicate back to the coarse mesh which coarse points have children (that may require interpolation) */
4057   ierr = PetscMalloc1(pEndC-pStartC,&maxChildIds);CHKERRQ(ierr);
4058   for (p = pStartC; p < pEndC; p++) {
4059     maxChildIds[p - pStartC] = -2;
4060   }
4061   ierr = PetscSFReduceBegin(coarseToFineEmbedded,MPIU_INT,cids,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
4062   ierr = PetscSFReduceEnd(coarseToFineEmbedded,MPIU_INT,cids,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
4063 
4064   ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
4065   ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
4066 
4067   ierr = DMPlexGetAnchors(coarse,&aSec,&aIS);CHKERRQ(ierr);
4068   ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
4069   ierr = PetscSectionGetChart(aSec,&aStart,&aEnd);CHKERRQ(ierr);
4070 
4071   ierr = DMGetDefaultConstraints(coarse,&cSec,&cMat);CHKERRQ(ierr);
4072   ierr = PetscSectionGetChart(cSec,&cStart,&cEnd);CHKERRQ(ierr);
4073 
4074   /* create sections that will send to children the indices and matrices they will need to construct the interpolator */
4075   ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootValuesSec);CHKERRQ(ierr);
4076   ierr = PetscSectionSetChart(rootValuesSec,pStartC,pEndC);CHKERRQ(ierr);
4077   ierr = PetscSectionGetNumFields(localCoarse,&numFields);CHKERRQ(ierr);
4078   {
4079     PetscInt maxFields = PetscMax(1,numFields) + 1;
4080     ierr = PetscMalloc7(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&newOffsets,maxFields,&newOffsetsCopy,maxFields,&rowOffsets,maxFields,&numD,maxFields,&numO);CHKERRQ(ierr);
4081   }
4082   if (grad) {
4083     PetscInt i;
4084 
4085     ierr = VecGetDM(cellGeom,&cellDM);CHKERRQ(ierr);
4086     ierr = VecGetArrayRead(cellGeom,&cellGeomArray);CHKERRQ(ierr);
4087     ierr = VecGetDM(grad,&gradDM);CHKERRQ(ierr);
4088     ierr = VecGetArrayRead(grad,&gradArray);CHKERRQ(ierr);
4089     for (i = 0; i < PetscMax(1,numFields); i++) {
4090       PetscObject  obj;
4091       PetscClassId id;
4092 
4093       ierr = DMGetField(coarse, i, &obj);CHKERRQ(ierr);
4094       ierr = PetscObjectGetClassId(obj,&id);CHKERRQ(ierr);
4095       if (id == PETSCFV_CLASSID) {
4096         fv      = (PetscFV) obj;
4097         ierr    = PetscFVGetNumComponents(fv,&numFVcomps);CHKERRQ(ierr);
4098         fvField = i;
4099         break;
4100       }
4101     }
4102   }
4103 
4104   for (p = pStartC; p < pEndC; p++) { /* count the sizes of the indices and matrices */
4105     PetscInt dof;
4106     PetscInt maxChildId     = maxChildIds[p - pStartC];
4107     PetscInt numValues      = 0;
4108 
4109     ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
4110     if (dof < 0) {
4111       dof = -(dof + 1);
4112     }
4113     offsets[0]    = 0;
4114     newOffsets[0] = 0;
4115     if (maxChildId >= 0) { /* this point has children (with dofs) that will need to be interpolated from the closure of p */
4116       PetscInt *closure = NULL, closureSize, cl;
4117 
4118       ierr = DMPlexGetTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
4119       for (cl = 0; cl < closureSize; cl++) { /* get the closure */
4120         PetscInt c = closure[2 * cl], clDof;
4121 
4122         ierr = PetscSectionGetDof(localCoarse,c,&clDof);CHKERRQ(ierr);
4123         numValues += clDof;
4124       }
4125       ierr = DMPlexRestoreTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
4126     }
4127     else if (maxChildId == -1) {
4128       ierr = PetscSectionGetDof(localCoarse,p,&numValues);CHKERRQ(ierr);
4129     }
4130     /* we will pack the column indices with the field offsets */
4131     if (maxChildId >= -1 && grad && p >= cellStart && p < cellEnd) {
4132       /* also send the centroid, and the gradient */
4133       numValues += dim * (1 + numFVcomps);
4134     }
4135     ierr = PetscSectionSetDof(rootValuesSec,p,numValues);CHKERRQ(ierr);
4136   }
4137   ierr = PetscSectionSetUp(rootValuesSec);CHKERRQ(ierr);
4138   {
4139     PetscInt          numRootValues;
4140     const PetscScalar *coarseArray;
4141 
4142     ierr = PetscSectionGetStorageSize(rootValuesSec,&numRootValues);CHKERRQ(ierr);
4143     ierr = PetscMalloc1(numRootValues,&rootValues);CHKERRQ(ierr);
4144     ierr = VecGetArrayRead(vecCoarseLocal,&coarseArray);CHKERRQ(ierr);
4145     for (p = pStartC; p < pEndC; p++) {
4146       PetscInt    numValues;
4147       PetscInt    pValOff;
4148       PetscScalar *pVal;
4149       PetscInt    maxChildId = maxChildIds[p - pStartC];
4150 
4151       ierr = PetscSectionGetDof(rootValuesSec,p,&numValues);CHKERRQ(ierr);
4152       if (!numValues) {
4153         continue;
4154       }
4155       ierr = PetscSectionGetOffset(rootValuesSec,p,&pValOff);CHKERRQ(ierr);
4156       pVal = &(rootValues[pValOff]);
4157       if (maxChildId >= 0) { /* build an identity matrix, apply matrix constraints on the right */
4158         PetscInt closureSize = numValues;
4159         ierr = DMPlexVecGetClosure(coarse,NULL,vecCoarseLocal,p,&closureSize,&pVal);CHKERRQ(ierr);
4160       }
4161       else if (maxChildId == -1) {
4162         PetscInt lDof, lOff, i;
4163 
4164         ierr = PetscSectionGetDof(localCoarse,p,&lDof);CHKERRQ(ierr);
4165         ierr = PetscSectionGetOffset(localCoarse,p,&lOff);CHKERRQ(ierr);
4166         for (i = 0; i < lDof; i++) pVal[i] = coarseArray[lOff + i];
4167       }
4168       if (grad && p >= cellStart && p < cellEnd) {
4169         PetscFVCellGeom *cg;
4170         PetscScalar     *gradVals = NULL;
4171         PetscInt        i;
4172 
4173         pVal += (numValues - dim * (1 + numFVcomps));
4174 
4175         ierr = DMPlexPointLocalRead(cellDM,p,cellGeomArray,(void *) &cg);CHKERRQ(ierr);
4176         for (i = 0; i < dim; i++) pVal[i] = cg->centroid[i];
4177         pVal += dim;
4178         ierr = DMPlexPointGlobalRead(gradDM,p,gradArray,(void *) &gradVals);CHKERRQ(ierr);
4179         for (i = 0; i < dim * numFVcomps; i++) pVal[i] = gradVals[i];
4180       }
4181     }
4182     ierr = VecRestoreArrayRead(vecCoarseLocal,&coarseArray);CHKERRQ(ierr);
4183     ierr = PetscFree(maxChildIds);CHKERRQ(ierr);
4184   }
4185   {
4186     PetscSF  valuesSF;
4187     PetscInt *remoteOffsetsValues, numLeafValues;
4188 
4189     ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafValuesSec);CHKERRQ(ierr);
4190     ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootValuesSec,&remoteOffsetsValues,leafValuesSec);CHKERRQ(ierr);
4191     ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootValuesSec,remoteOffsetsValues,leafValuesSec,&valuesSF);CHKERRQ(ierr);
4192     ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
4193     ierr = PetscFree(remoteOffsetsValues);CHKERRQ(ierr);
4194     ierr = PetscSectionGetStorageSize(leafValuesSec,&numLeafValues);CHKERRQ(ierr);
4195     ierr = PetscMalloc1(numLeafValues,&leafValues);CHKERRQ(ierr);
4196     ierr = PetscSFBcastBegin(valuesSF,MPIU_SCALAR,rootValues,leafValues);CHKERRQ(ierr);
4197     ierr = PetscSFBcastEnd(valuesSF,MPIU_SCALAR,rootValues,leafValues);CHKERRQ(ierr);
4198     ierr = PetscSFDestroy(&valuesSF);CHKERRQ(ierr);
4199     ierr = PetscFree(rootValues);CHKERRQ(ierr);
4200     ierr = PetscSectionDestroy(&rootValuesSec);CHKERRQ(ierr);
4201   }
4202   ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
4203   {
4204     PetscInt    maxDof;
4205     PetscInt    *rowIndices;
4206     DM           refTree;
4207     PetscInt     **refPointFieldN;
4208     PetscScalar  ***refPointFieldMats;
4209     PetscSection refConSec, refAnSec;
4210     PetscInt     pRefStart,pRefEnd,leafStart,leafEnd;
4211     PetscScalar  *pointWork;
4212 
4213     ierr = PetscSectionGetMaxDof(globalFine,&maxDof);CHKERRQ(ierr);
4214     ierr = DMGetWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
4215     ierr = DMGetWorkArray(fine,maxDof,PETSC_SCALAR,&pointWork);CHKERRQ(ierr);
4216     ierr = DMPlexGetReferenceTree(fine,&refTree);CHKERRQ(ierr);
4217     ierr = DMGetDS(fine,&ds);CHKERRQ(ierr);
4218     ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
4219     ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
4220     ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
4221     ierr = DMPlexGetAnchors(refTree,&refAnSec,NULL);CHKERRQ(ierr);
4222     ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
4223     ierr = PetscSectionGetChart(leafValuesSec,&leafStart,&leafEnd);CHKERRQ(ierr);
4224     ierr = DMPlexGetHeightStratum(fine,0,&cellStart,&cellEnd);CHKERRQ(ierr);
4225     for (p = leafStart; p < leafEnd; p++) {
4226       PetscInt          gDof, gcDof, gOff, lDof;
4227       PetscInt          numValues, pValOff;
4228       PetscInt          childId;
4229       const PetscScalar *pVal;
4230       const PetscScalar *fvGradData = NULL;
4231 
4232       ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
4233       ierr = PetscSectionGetDof(localFine,p,&lDof);CHKERRQ(ierr);
4234       ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
4235       if ((gDof - gcDof) <= 0) {
4236         continue;
4237       }
4238       ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
4239       ierr = PetscSectionGetDof(leafValuesSec,p,&numValues);CHKERRQ(ierr);
4240       if (!numValues) continue;
4241       ierr = PetscSectionGetOffset(leafValuesSec,p,&pValOff);CHKERRQ(ierr);
4242       pVal = &leafValues[pValOff];
4243       offsets[0]        = 0;
4244       offsetsCopy[0]    = 0;
4245       newOffsets[0]     = 0;
4246       newOffsetsCopy[0] = 0;
4247       childId           = cids[p - pStartF];
4248       if (grad && p >= cellStart && p < cellEnd) {
4249         numValues -= (dim * (1 + numFVcomps));
4250         fvGradData = &pVal[numValues];
4251       }
4252       if (numFields) {
4253         PetscInt f;
4254         for (f = 0; f < numFields; f++) {
4255           PetscInt rowDof;
4256 
4257           ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
4258           offsets[f + 1]        = offsets[f] + rowDof;
4259           offsetsCopy[f + 1]    = offsets[f + 1];
4260           /* TODO: closure indices */
4261           newOffsets[f + 1]     = newOffsets[f] + ((childId == -1) ? rowDof : refPointFieldN[childId - pRefStart][f]);
4262         }
4263         ierr = DMPlexGetIndicesPointFields_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
4264       }
4265       else {
4266         offsets[0]    = 0;
4267         offsets[1]    = lDof;
4268         newOffsets[0] = 0;
4269         newOffsets[1] = (childId == -1) ? lDof : refPointFieldN[childId - pRefStart][0];
4270         ierr = DMPlexGetIndicesPoint_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
4271       }
4272       if (childId == -1) { /* no child interpolation: one nnz per */
4273         ierr = VecSetValues(vecFine,numValues,rowIndices,pVal,ADD_VALUES);CHKERRQ(ierr);
4274       } else {
4275         PetscInt f;
4276 
4277         for (f = 0; f < PetscMax(1,numFields); f++) {
4278           const PetscScalar *childMat = refPointFieldMats[childId - pRefStart][f];
4279           PetscInt numRows = offsets[f+1] - offsets[f];
4280           PetscInt numCols = newOffsets[f + 1] - newOffsets[f];
4281           const PetscScalar *cVal = &pVal[newOffsets[f]];
4282           PetscScalar *rVal = &pointWork[offsets[f]];
4283           PetscInt i, j;
4284 
4285 #if 0
4286           ierr = PetscInfo6(coarse,"field %D, numFields %D, childId %D, numRows %D, numCols %D, refPointFieldN %D\n",f,numFields,childId,numRows,numCols,refPointFieldN[childId - pRefStart][f]);CHKERRQ(ierr);
4287 #endif
4288           for (i = 0; i < numRows; i++) {
4289             PetscScalar val = 0.;
4290             for (j = 0; j < numCols; j++) {
4291               val += childMat[i * numCols + j] * cVal[j];
4292             }
4293             rVal[i] = val;
4294           }
4295           if (f == fvField && p >= cellStart && p < cellEnd) {
4296             PetscReal   centroid[3];
4297             PetscScalar diff[3];
4298             const PetscScalar *parentCentroid = &fvGradData[0];
4299             const PetscScalar *gradient       = &fvGradData[dim];
4300 
4301             ierr = DMPlexComputeCellGeometryFVM(fine,p,NULL,centroid,NULL);CHKERRQ(ierr);
4302             for (i = 0; i < dim; i++) {
4303               diff[i] = centroid[i] - parentCentroid[i];
4304             }
4305             for (i = 0; i < numFVcomps; i++) {
4306               PetscScalar val = 0.;
4307 
4308               for (j = 0; j < 3; j++) {
4309                 val += gradient[dim * i + j] * diff[j];
4310               }
4311               rVal[i] += val;
4312             }
4313           }
4314           ierr = VecSetValues(vecFine,numRows,&rowIndices[offsets[f]],rVal,ADD_VALUES);CHKERRQ(ierr);
4315         }
4316       }
4317     }
4318     ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
4319     ierr = DMRestoreWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
4320     ierr = DMRestoreWorkArray(fine,maxDof,PETSC_SCALAR,&pointWork);CHKERRQ(ierr);
4321   }
4322   ierr = PetscFree(leafValues);CHKERRQ(ierr);
4323   ierr = PetscSectionDestroy(&leafValuesSec);CHKERRQ(ierr);
4324   ierr = PetscFree7(offsets,offsetsCopy,newOffsets,newOffsetsCopy,rowOffsets,numD,numO);CHKERRQ(ierr);
4325   ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
4326   PetscFunctionReturn(0);
4327 }
4328 
4329 #undef __FUNCT__
4330 #define __FUNCT__ "DMPlexTransferVecTree_Inject"
4331 static PetscErrorCode DMPlexTransferVecTree_Inject(DM fine, Vec vecFine, DM coarse, Vec vecCoarse, PetscSF coarseToFine, PetscInt *cids)
4332 {
4333   PetscDS        ds;
4334   DM             refTree;
4335   PetscSection   multiRootSec, rootIndicesSec;
4336   PetscSection   globalCoarse, globalFine;
4337   PetscSection   localCoarse, localFine;
4338   PetscSection   cSecRef;
4339   PetscInt       *parentIndices, pRefStart, pRefEnd;
4340   PetscScalar    *rootValues, *parentValues;
4341   Mat            injRef;
4342   PetscInt       numFields, maxDof;
4343   PetscInt       pStartC, pEndC, pStartF, pEndF, p;
4344   PetscInt       *offsets, *offsetsCopy, *rowOffsets;
4345   PetscLayout    rowMap, colMap;
4346   PetscInt       rowStart, rowEnd, colStart, colEnd;
4347   PetscScalar    ***childrenMats=NULL ; /* gcc -O gives 'may be used uninitialized' warning'. Initializing to suppress this warning */
4348   PetscErrorCode ierr;
4349 
4350   PetscFunctionBegin;
4351 
4352   /* get the templates for the fine-to-coarse injection from the reference tree */
4353   ierr = VecSetOption(vecFine,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);CHKERRQ(ierr);
4354   ierr = VecSetOption(vecCoarse,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);CHKERRQ(ierr);
4355   ierr = DMPlexGetReferenceTree(coarse,&refTree);CHKERRQ(ierr);
4356   ierr = DMGetDS(coarse,&ds);CHKERRQ(ierr);
4357   ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
4358   ierr = DMGetDefaultConstraints(refTree,&cSecRef,NULL);CHKERRQ(ierr);
4359   ierr = PetscSectionGetChart(cSecRef,&pRefStart,&pRefEnd);CHKERRQ(ierr);
4360   ierr = DMPlexReferenceTreeGetInjector(refTree,&injRef);CHKERRQ(ierr);
4361 
4362   ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
4363   ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
4364   ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
4365   ierr = PetscSectionGetNumFields(localFine,&numFields);CHKERRQ(ierr);
4366   ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
4367   ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
4368   ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
4369   ierr = PetscSectionGetMaxDof(localCoarse,&maxDof);CHKERRQ(ierr);
4370   {
4371     PetscInt maxFields = PetscMax(1,numFields) + 1;
4372     ierr = PetscMalloc3(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&rowOffsets);CHKERRQ(ierr);
4373   }
4374 
4375   ierr = DMPlexTransferInjectorTree(coarse,fine,coarseToFine,cids,vecFine,numFields,offsets,&multiRootSec,&rootIndicesSec,NULL,&rootValues);CHKERRQ(ierr);
4376 
4377   ierr = PetscMalloc2(maxDof,&parentIndices,maxDof,&parentValues);CHKERRQ(ierr);
4378 
4379   /* count indices */
4380   ierr = VecGetLayout(vecFine,&colMap);CHKERRQ(ierr);
4381   ierr = VecGetLayout(vecCoarse,&rowMap);CHKERRQ(ierr);
4382   ierr = PetscLayoutSetUp(rowMap);CHKERRQ(ierr);
4383   ierr = PetscLayoutSetUp(colMap);CHKERRQ(ierr);
4384   ierr = PetscLayoutGetRange(rowMap,&rowStart,&rowEnd);CHKERRQ(ierr);
4385   ierr = PetscLayoutGetRange(colMap,&colStart,&colEnd);CHKERRQ(ierr);
4386   /* insert values */
4387   ierr = DMPlexReferenceTreeGetChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
4388   for (p = pStartC; p < pEndC; p++) {
4389     PetscInt numLeaves, leafStart, leafEnd, l, dof, cdof, gOff;
4390 
4391     ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
4392     ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
4393     if ((dof - cdof) <= 0) continue;
4394     ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);
4395 
4396     rowOffsets[0] = 0;
4397     offsetsCopy[0] = 0;
4398     if (numFields) {
4399       PetscInt f;
4400 
4401       for (f = 0; f < numFields; f++) {
4402         PetscInt fDof;
4403         ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
4404         rowOffsets[f + 1] = offsetsCopy[f + 1] = fDof + rowOffsets[f];
4405       }
4406       DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
4407     }
4408     else {
4409       DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
4410       rowOffsets[1] = offsetsCopy[0];
4411     }
4412 
4413     ierr = PetscSectionGetDof(multiRootSec,p,&numLeaves);CHKERRQ(ierr);
4414     ierr = PetscSectionGetOffset(multiRootSec,p,&leafStart);CHKERRQ(ierr);
4415     leafEnd = leafStart + numLeaves;
4416     for (l = leafStart; l < leafEnd; l++) {
4417       PetscInt numIndices, childId, offset;
4418       const PetscScalar *childValues;
4419 
4420       ierr = PetscSectionGetDof(rootIndicesSec,l,&numIndices);CHKERRQ(ierr);
4421       ierr = PetscSectionGetOffset(rootIndicesSec,l,&offset);CHKERRQ(ierr);
4422       childId = (PetscInt) PetscRealPart(rootValues[offset++]);
4423       childValues = &rootValues[offset];
4424       numIndices--;
4425 
4426       if (childId == -2) { /* skip */
4427         continue;
4428       } else if (childId == -1) { /* equivalent points: scatter */
4429         ierr = VecSetValues(vecCoarse,numIndices,parentIndices,childValues,ADD_VALUES);CHKERRQ(ierr);
4430       } else {
4431         PetscInt parentId, f, lim;
4432 
4433         ierr = DMPlexGetTreeParent(refTree,childId,&parentId,NULL);CHKERRQ(ierr);
4434 
4435         lim = PetscMax(1,numFields);
4436         offsets[0] = 0;
4437         if (numFields) {
4438           PetscInt f;
4439 
4440           for (f = 0; f < numFields; f++) {
4441             PetscInt fDof;
4442             ierr = PetscSectionGetFieldDof(cSecRef,childId,f,&fDof);CHKERRQ(ierr);
4443 
4444             offsets[f + 1] = fDof + offsets[f];
4445           }
4446         }
4447         else {
4448           PetscInt cDof;
4449 
4450           ierr = PetscSectionGetDof(cSecRef,childId,&cDof);CHKERRQ(ierr);
4451           offsets[1] = cDof;
4452         }
4453         for (f = 0; f < lim; f++) {
4454           PetscScalar       *childMat   = &childrenMats[childId - pRefStart][f][0];
4455           PetscInt          *rowIndices = &parentIndices[rowOffsets[f]];
4456           PetscInt          m           = rowOffsets[f+1]-rowOffsets[f];
4457           PetscInt          n           = offsets[f+1]-offsets[f];
4458           PetscInt          i, j;
4459           const PetscScalar *colValues  = &childValues[offsets[f]];
4460 
4461           for (i = 0; i < m; i++) {
4462             PetscScalar val = 0.;
4463             for (j = 0; j < n; j++) {
4464               val += childMat[n * i + j] * colValues[j];
4465             }
4466             parentValues[i] = val;
4467           }
4468           ierr = VecSetValues(vecCoarse,m,rowIndices,parentValues,ADD_VALUES);CHKERRQ(ierr);
4469         }
4470       }
4471     }
4472   }
4473   ierr = PetscSectionDestroy(&multiRootSec);CHKERRQ(ierr);
4474   ierr = PetscSectionDestroy(&rootIndicesSec);CHKERRQ(ierr);
4475   ierr = PetscFree2(parentIndices,parentValues);CHKERRQ(ierr);
4476   ierr = DMPlexReferenceTreeRestoreChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
4477   ierr = PetscFree(rootValues);CHKERRQ(ierr);
4478   ierr = PetscFree3(offsets,offsetsCopy,rowOffsets);CHKERRQ(ierr);
4479   PetscFunctionReturn(0);
4480 }
4481 
4482 #undef __FUNCT__
4483 #define __FUNCT__ "DMPlexTransferVecTree"
4484 PetscErrorCode DMPlexTransferVecTree(DM dmIn, Vec vecIn, DM dmOut, Vec vecOut, PetscSF sfIn, PetscSF sfOut, PetscInt *cidsIn, PetscInt *cidsOut, PetscBool useBCs, PetscReal time)
4485 {
4486   PetscErrorCode ierr;
4487 
4488   PetscFunctionBegin;
4489   if (sfIn) {
4490     Vec vecInLocal;
4491     DM  dmGrad = NULL;
4492     Vec faceGeom = NULL, cellGeom = NULL, grad = NULL;
4493 
4494     ierr = DMGetLocalVector(dmIn,&vecInLocal);CHKERRQ(ierr);
4495     ierr = VecSet(vecInLocal,0.0);CHKERRQ(ierr);
4496     {
4497       PetscInt  numFields, i;
4498 
4499       ierr = DMGetNumFields(dmIn, &numFields);CHKERRQ(ierr);
4500       for (i = 0; i < numFields; i++) {
4501         PetscObject  obj;
4502         PetscClassId classid;
4503 
4504         ierr = DMGetField(dmIn, i, &obj);CHKERRQ(ierr);
4505         ierr = PetscObjectGetClassId(obj, &classid);CHKERRQ(ierr);
4506         if (classid == PETSCFV_CLASSID) {
4507           ierr = DMPlexGetDataFVM(dmIn,(PetscFV)obj,&cellGeom,&faceGeom,&dmGrad);CHKERRQ(ierr);
4508           break;
4509         }
4510       }
4511     }
4512     if (useBCs) {
4513       ierr = DMPlexInsertBoundaryValues(dmIn,PETSC_TRUE,vecInLocal,time,faceGeom,cellGeom,NULL);CHKERRQ(ierr);
4514     }
4515     ierr = DMGlobalToLocalBegin(dmIn,vecIn,INSERT_VALUES,vecInLocal);CHKERRQ(ierr);
4516     ierr = DMGlobalToLocalEnd(dmIn,vecIn,INSERT_VALUES,vecInLocal);CHKERRQ(ierr);
4517     if (dmGrad) {
4518       ierr = DMGetGlobalVector(dmGrad,&grad);CHKERRQ(ierr);
4519       ierr = DMPlexReconstructGradientsFVM(dmIn,vecInLocal,grad);CHKERRQ(ierr);
4520     }
4521     ierr = DMPlexTransferVecTree_Interpolate(dmIn,vecInLocal,dmOut,vecOut,sfIn,cidsIn,grad,cellGeom);CHKERRQ(ierr);
4522     ierr = DMRestoreLocalVector(dmIn,&vecInLocal);CHKERRQ(ierr);
4523     if (dmGrad) {
4524       ierr = DMRestoreGlobalVector(dmGrad,&grad);CHKERRQ(ierr);
4525     }
4526   }
4527   if (sfOut) {
4528     ierr = DMPlexTransferVecTree_Inject(dmIn,vecIn,dmOut,vecOut,sfOut,cidsOut);CHKERRQ(ierr);
4529   }
4530   PetscFunctionReturn(0);
4531 }
4532