xref: /petsc/src/dm/field/impls/ds/dmfieldds.c (revision 4ffacfe27a72f4cdf51b68a3bbb6aed96040fb2f)
1 #include <petsc/private/dmfieldimpl.h> /*I "petscdmfield.h" I*/
2 #include <petsc/private/petscfeimpl.h> /*I "petscdmfield.h" I*/
3 #include <petscfe.h>
4 #include <petscdmplex.h>
5 #include <petscds.h>
6 
7 typedef struct _n_DMField_DS
8 {
9   PetscBool    multifieldVec;
10   PetscInt     height;   /* Point height at which we want values and number of discretizations */
11   PetscInt     fieldNum; /* Number in DS of field which we evaluate */
12   PetscObject *disc;     /* Discretizations of this field at each height */
13   Vec          vec;      /* Field values */
14   DM           dmDG;     /* DM for the DG values */
15   PetscObject *discDG;   /* DG Discretizations of this field at each height */
16   Vec          vecDG;    /* DG Field values */
17 } DMField_DS;
18 
19 static PetscErrorCode DMFieldDestroy_DS(DMField field)
20 {
21   DMField_DS *dsfield = (DMField_DS *) field->data;
22   PetscInt    i;
23 
24   PetscFunctionBegin;
25   PetscCall(VecDestroy(&dsfield->vec));
26   for (i = 0; i < dsfield->height; i++) PetscCall(PetscObjectDereference(dsfield->disc[i]));
27   PetscCall(PetscFree(dsfield->disc));
28   PetscCall(VecDestroy(&dsfield->vecDG));
29   if (dsfield->discDG) for (i = 0; i < dsfield->height; i++) PetscCall(PetscObjectDereference(dsfield->discDG[i]));
30   PetscCall(PetscFree(dsfield->discDG));
31   PetscCall(PetscFree(dsfield));
32   PetscFunctionReturn(0);
33 }
34 
35 static PetscErrorCode DMFieldView_DS(DMField field,PetscViewer viewer)
36 {
37   DMField_DS *dsfield = (DMField_DS *) field->data;
38   PetscObject disc;
39   PetscBool   iascii;
40 
41   PetscFunctionBegin;
42   PetscCall(PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii));
43   disc = dsfield->disc[0];
44   if (iascii) {
45     PetscCall(PetscViewerASCIIPrintf(viewer, "PetscDS field %" PetscInt_FMT "\n", dsfield->fieldNum));
46     PetscCall(PetscViewerASCIIPushTab(viewer));
47     PetscCall(PetscObjectView(disc, viewer));
48     PetscCall(PetscViewerASCIIPopTab(viewer));
49   }
50   PetscCall(PetscViewerASCIIPushTab(viewer));
51   PetscCheck(!dsfield->multifieldVec, PetscObjectComm((PetscObject) field), PETSC_ERR_SUP, "View of subfield not implemented yet");
52   PetscCall(VecView(dsfield->vec, viewer));
53   PetscCall(PetscViewerASCIIPopTab(viewer));
54   PetscFunctionReturn(0);
55 }
56 
57 static PetscErrorCode DMFieldDSGetHeightDisc(DMField field, PetscInt height, PetscObject discList[], PetscObject *disc)
58 {
59   PetscFunctionBegin;
60   if (!discList[height]) {
61     PetscClassId id;
62 
63     PetscCall(PetscObjectGetClassId(discList[0], &id));
64     if (id == PETSCFE_CLASSID) PetscCall(PetscFECreateHeightTrace((PetscFE) discList[0], height, (PetscFE *) &discList[height]));
65   }
66   *disc = discList[height];
67   PetscFunctionReturn(0);
68 }
69 
70 /* y[m,c] = A[m,n,c] . b[n] */
71 #define DMFieldDSdot(y,A,b,m,n,c,cast)                                           \
72   do {                                                                           \
73     PetscInt _i, _j, _k;                                                         \
74     for (_i = 0; _i < (m); _i++) {                                               \
75       for (_k = 0; _k < (c); _k++) {                                             \
76         (y)[_i * (c) + _k] = 0.;                                                 \
77       }                                                                          \
78       for (_j = 0; _j < (n); _j++) {                                             \
79         for (_k = 0; _k < (c); _k++) {                                           \
80           (y)[_i * (c) + _k] += (A)[(_i * (n) + _j) * (c) + _k] * cast((b)[_j]); \
81         }                                                                        \
82       }                                                                          \
83     }                                                                            \
84   } while (0)
85 
86 /*
87   Since this is used for coordinates, we need to allow for the possibility that values come from multiple sections/Vecs, so that we can have DG version of the coordinates for periodicity. This reproduces DMPlexGetCellCoordinates_Internal().
88 */
89 PetscErrorCode DMFieldGetClosure_Internal(DMField field, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *values[])
90 {
91   DMField_DS        *dsfield = (DMField_DS *) field->data;
92   DM                 fdm     = dsfield->dmDG;
93   PetscSection       s       = NULL;
94   const PetscScalar *cvalues;
95   PetscInt           pStart, pEnd;
96 
97   PetscFunctionBeginHot;
98   *isDG   = PETSC_FALSE;
99   *Nc     = 0;
100   *array  = NULL;
101   *values = NULL;
102   /* Check for cellwise section */
103   if (fdm) PetscCall(DMGetLocalSection(fdm, &s));
104   if (!s) goto cg;
105   /* Check that the cell exists in the cellwise section */
106   PetscCall(PetscSectionGetChart(s, &pStart, &pEnd));
107   if (cell < pStart || cell >= pEnd) goto cg;
108   /* Check for cellwise coordinates for this cell */
109   PetscCall(PetscSectionGetDof(s, cell, Nc));
110   if (!*Nc) goto cg;
111   /* Check for cellwise coordinates */
112   if (!dsfield->vecDG) goto cg;
113   /* Get cellwise coordinates */
114   PetscCall(VecGetArrayRead(dsfield->vecDG, array));
115   PetscCall(DMPlexPointLocalRead(fdm, cell, *array, &cvalues));
116   PetscCall(DMGetWorkArray(fdm, *Nc, MPIU_SCALAR, values));
117   PetscCall(PetscArraycpy(*values, cvalues, *Nc));
118   PetscCall(VecRestoreArrayRead(dsfield->vecDG, array));
119   *isDG = PETSC_TRUE;
120   PetscFunctionReturn(0);
121 cg:
122   /* Use continuous values */
123   PetscCall(DMFieldGetDM(field, &fdm));
124   PetscCall(DMGetLocalSection(fdm, &s));
125   PetscCall(DMPlexVecGetClosure(fdm, s, dsfield->vec, cell, Nc, values));
126   PetscFunctionReturn(0);
127 }
128 
129 PetscErrorCode DMFieldRestoreClosure_Internal(DMField field, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *values[])
130 {
131   DMField_DS  *dsfield = (DMField_DS *) field->data;
132   DM           fdm;
133   PetscSection s;
134 
135   PetscFunctionBeginHot;
136   if (*isDG) {
137     PetscCall(DMRestoreWorkArray(dsfield->dmDG, *Nc, MPIU_SCALAR, values));
138   } else {
139     PetscCall(DMFieldGetDM(field, &fdm));
140     PetscCall(DMGetLocalSection(fdm, &s));
141     PetscCall(DMPlexVecRestoreClosure(fdm, s, dsfield->vec, cell, Nc, (PetscScalar **) values));
142   }
143   PetscFunctionReturn(0);
144 }
145 
146 /* TODO: Reorganize interface so that I can reuse a tabulation rather than mallocing each time */
147 static PetscErrorCode DMFieldEvaluateFE_DS(DMField field, IS pointIS, PetscQuadrature quad, PetscDataType type, void *B, void *D, void *H)
148 {
149   DMField_DS      *dsfield = (DMField_DS *) field->data;
150   DM              dm;
151   PetscObject     disc;
152   PetscClassId    classid;
153   PetscInt        nq, nc, dim, meshDim, numCells;
154   PetscSection    section;
155   const PetscReal *qpoints;
156   PetscBool       isStride;
157   const PetscInt  *points = NULL;
158   PetscInt        sfirst = -1, stride = -1;
159 
160   PetscFunctionBeginHot;
161   dm   = field->dm;
162   nc   = field->numComponents;
163   PetscCall(PetscQuadratureGetData(quad,&dim,NULL,&nq,&qpoints,NULL));
164   PetscCall(DMFieldDSGetHeightDisc(field, dsfield->height - 1 - dim, dsfield->disc, &disc));
165   PetscCall(DMGetDimension(dm,&meshDim));
166   PetscCall(DMGetLocalSection(dm,&section));
167   PetscCall(PetscSectionGetField(section,dsfield->fieldNum,&section));
168   PetscCall(PetscObjectGetClassId(disc,&classid));
169   /* TODO: batch */
170   PetscCall(PetscObjectTypeCompare((PetscObject)pointIS,ISSTRIDE,&isStride));
171   PetscCall(ISGetLocalSize(pointIS,&numCells));
172   if (isStride) PetscCall(ISStrideGetInfo(pointIS,&sfirst,&stride));
173   else PetscCall(ISGetIndices(pointIS,&points));
174   if (classid == PETSCFE_CLASSID) {
175     PetscFE      fe = (PetscFE) disc;
176     PetscInt     feDim, i;
177     PetscInt          K = H ? 2 : (D ? 1 : (B ? 0 : -1));
178     PetscTabulation   T;
179 
180     PetscCall(PetscFEGetDimension(fe,&feDim));
181     PetscCall(PetscFECreateTabulation(fe,1,nq,qpoints,K,&T));
182     for (i = 0; i < numCells; i++) {
183       PetscInt           c = isStride ? (sfirst + i * stride) : points[i];
184       PetscInt           closureSize;
185       const PetscScalar *array;
186       PetscScalar       *elem = NULL;
187       PetscBool          isDG;
188 
189       PetscCall(DMFieldGetClosure_Internal(field, c, &isDG, &closureSize, &array, &elem));
190       if (B) {
191         /* field[c] = T[q,b,c] . coef[b], so v[c] = T[q,b,c] . coords[b] */
192         if (type == PETSC_SCALAR) {
193           PetscScalar *cB = &((PetscScalar *) B)[nc * nq * i];
194 
195           DMFieldDSdot(cB,T->T[0],elem,nq,feDim,nc,(PetscScalar));
196         } else {
197           PetscReal *cB = &((PetscReal *) B)[nc * nq * i];
198 
199           DMFieldDSdot(cB,T->T[0],elem,nq,feDim,nc,PetscRealPart);
200         }
201       }
202       if (D) {
203         if (type == PETSC_SCALAR) {
204           PetscScalar *cD = &((PetscScalar *) D)[nc * nq * dim * i];
205 
206           DMFieldDSdot(cD,T->T[1],elem,nq,feDim,(nc * dim),(PetscScalar));
207         } else {
208           PetscReal *cD = &((PetscReal *) D)[nc * nq * dim * i];
209 
210           DMFieldDSdot(cD,T->T[1],elem,nq,feDim,(nc * dim),PetscRealPart);
211         }
212       }
213       if (H) {
214         if (type == PETSC_SCALAR) {
215           PetscScalar *cH = &((PetscScalar *) H)[nc * nq * dim * dim * i];
216 
217           DMFieldDSdot(cH,T->T[2],elem,nq,feDim,(nc * dim * dim),(PetscScalar));
218         } else {
219           PetscReal *cH = &((PetscReal *) H)[nc * nq * dim * dim * i];
220 
221           DMFieldDSdot(cH,T->T[2],elem,nq,feDim,(nc * dim * dim),PetscRealPart);
222         }
223       }
224       PetscCall(DMFieldRestoreClosure_Internal(field, c, &isDG, &closureSize, &array, &elem));
225     }
226     PetscCall(PetscTabulationDestroy(&T));
227   } else SETERRQ(PetscObjectComm((PetscObject)field),PETSC_ERR_SUP,"Not implemented");
228   if (!isStride) {
229     PetscCall(ISRestoreIndices(pointIS,&points));
230   }
231   PetscFunctionReturn(0);
232 }
233 
234 static PetscErrorCode DMFieldEvaluate_DS(DMField field, Vec points, PetscDataType datatype, void *B, void *D, void *H)
235 {
236   DMField_DS        *dsfield = (DMField_DS *) field->data;
237   PetscSF            cellSF = NULL;
238   const PetscSFNode *cells;
239   PetscInt           c, nFound, numCells, feDim, nc;
240   const PetscInt    *cellDegrees;
241   const PetscScalar *pointsArray;
242   PetscScalar       *cellPoints;
243   PetscInt           gatherSize, gatherMax;
244   PetscInt           dim, dimR, offset;
245   MPI_Datatype       pointType;
246   PetscObject        cellDisc;
247   PetscFE            cellFE;
248   PetscClassId       discID;
249   PetscReal         *coordsReal, *coordsRef;
250   PetscSection       section;
251   PetscScalar       *cellBs = NULL, *cellDs = NULL, *cellHs = NULL;
252   PetscReal         *cellBr = NULL, *cellDr = NULL, *cellHr = NULL;
253   PetscReal         *v, *J, *invJ, *detJ;
254 
255   PetscFunctionBegin;
256   nc   = field->numComponents;
257   PetscCall(DMGetLocalSection(field->dm,&section));
258   PetscCall(DMFieldDSGetHeightDisc(field, 0, dsfield->disc, &cellDisc));
259   PetscCall(PetscObjectGetClassId(cellDisc, &discID));
260   PetscCheck(discID == PETSCFE_CLASSID,PETSC_COMM_SELF,PETSC_ERR_PLIB, "Discretization type not supported");
261   cellFE = (PetscFE) cellDisc;
262   PetscCall(PetscFEGetDimension(cellFE,&feDim));
263   PetscCall(DMGetCoordinateDim(field->dm, &dim));
264   PetscCall(DMGetDimension(field->dm, &dimR));
265   PetscCall(DMLocatePoints(field->dm, points, DM_POINTLOCATION_NONE, &cellSF));
266   PetscCall(PetscSFGetGraph(cellSF, &numCells, &nFound, NULL, &cells));
267   for (c = 0; c < nFound; c++) {
268     PetscCheck(cells[c].index >= 0,PetscObjectComm((PetscObject)points),PETSC_ERR_ARG_WRONG, "Point %" PetscInt_FMT " could not be located", c);
269   }
270   PetscCall(PetscSFComputeDegreeBegin(cellSF,&cellDegrees));
271   PetscCall(PetscSFComputeDegreeEnd(cellSF,&cellDegrees));
272   for (c = 0, gatherSize = 0, gatherMax = 0; c < numCells; c++) {
273     gatherMax = PetscMax(gatherMax,cellDegrees[c]);
274     gatherSize += cellDegrees[c];
275   }
276   PetscCall(PetscMalloc3(gatherSize*dim,&cellPoints,gatherMax*dim,&coordsReal,gatherMax*dimR,&coordsRef));
277   PetscCall(PetscMalloc4(gatherMax*dimR,&v,gatherMax*dimR*dimR,&J,gatherMax*dimR*dimR,&invJ,gatherMax,&detJ));
278   if (datatype == PETSC_SCALAR) PetscCall(PetscMalloc3(B ? nc * gatherSize : 0, &cellBs, D ? nc * dim * gatherSize : 0, &cellDs, H ? nc * dim * dim * gatherSize : 0, &cellHs));
279   else PetscCall(PetscMalloc3(B ? nc * gatherSize : 0, &cellBr, D ? nc * dim * gatherSize : 0, &cellDr, H ? nc * dim * dim * gatherSize : 0, &cellHr));
280 
281   PetscCallMPI(MPI_Type_contiguous(dim,MPIU_SCALAR,&pointType));
282   PetscCallMPI(MPI_Type_commit(&pointType));
283   PetscCall(VecGetArrayRead(points,&pointsArray));
284   PetscCall(PetscSFGatherBegin(cellSF, pointType, pointsArray, cellPoints));
285   PetscCall(PetscSFGatherEnd(cellSF, pointType, pointsArray, cellPoints));
286   PetscCall(VecRestoreArrayRead(points,&pointsArray));
287   for (c = 0, offset = 0; c < numCells; c++) {
288     PetscInt nq = cellDegrees[c], p;
289 
290     if (nq) {
291       PetscInt           K = H ? 2 : (D ? 1 : (B ? 0 : -1));
292       PetscTabulation    T;
293       PetscQuadrature    quad;
294       const PetscScalar *array;
295       PetscScalar       *elem = NULL;
296       PetscReal         *quadPoints;
297       PetscBool          isDG;
298       PetscInt           closureSize, d, e, f, g;
299 
300       for (p = 0; p < dim * nq; p++) coordsReal[p] = PetscRealPart(cellPoints[dim * offset + p]);
301       PetscCall(DMPlexCoordinatesToReference(field->dm, c, nq, coordsReal, coordsRef));
302       PetscCall(PetscFECreateTabulation(cellFE,1,nq,coordsRef,K,&T));
303       PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &quad));
304       PetscCall(PetscMalloc1(dimR * nq, &quadPoints));
305       for (p = 0; p < dimR * nq; p++) quadPoints[p] = coordsRef[p];
306       PetscCall(PetscQuadratureSetData(quad, dimR, 0, nq, quadPoints, NULL));
307       PetscCall(DMPlexComputeCellGeometryFEM(field->dm, c, quad, v, J, invJ, detJ));
308       PetscCall(PetscQuadratureDestroy(&quad));
309       PetscCall(DMFieldGetClosure_Internal(field, c, &isDG, &closureSize, &array, &elem));
310       if (B) {
311         if (datatype == PETSC_SCALAR) {
312           PetscScalar *cB = &cellBs[nc * offset];
313 
314           DMFieldDSdot(cB,T->T[0],elem,nq,feDim,nc,(PetscScalar));
315         } else {
316           PetscReal *cB = &cellBr[nc * offset];
317 
318           DMFieldDSdot(cB,T->T[0],elem,nq,feDim,nc,PetscRealPart);
319         }
320       }
321       if (D) {
322         if (datatype == PETSC_SCALAR) {
323           PetscScalar *cD = &cellDs[nc * dim * offset];
324 
325           DMFieldDSdot(cD,T->T[1],elem,nq,feDim,(nc * dim),(PetscScalar));
326           for (p = 0; p < nq; p++) {
327             for (g = 0; g < nc; g++) {
328               PetscScalar vs[3];
329 
330               for (d = 0; d < dimR; d++) {
331                 vs[d] = 0.;
332                 for (e = 0; e < dimR; e++) {
333                   vs[d] += invJ[dimR * dimR * p + e * dimR + d] * cD[(nc * p + g) * dimR + e];
334                 }
335               }
336               for (d = 0; d < dimR; d++) {
337                 cD[(nc * p + g) * dimR + d] = vs[d];
338               }
339             }
340           }
341         } else {
342           PetscReal *cD = &cellDr[nc * dim * offset];
343 
344           DMFieldDSdot(cD,T->T[1],elem,nq,feDim,(nc * dim),PetscRealPart);
345           for (p = 0; p < nq; p++) {
346             for (g = 0; g < nc; g++) {
347               for (d = 0; d < dimR; d++) {
348                 v[d] = 0.;
349                 for (e = 0; e < dimR; e++) {
350                   v[d] += invJ[dimR * dimR * p + e * dimR + d] * cD[(nc * p + g) * dimR + e];
351                 }
352               }
353               for (d = 0; d < dimR; d++) {
354                 cD[(nc * p + g) * dimR + d] = v[d];
355               }
356             }
357           }
358         }
359       }
360       if (H) {
361         if (datatype == PETSC_SCALAR) {
362           PetscScalar *cH = &cellHs[nc * dim * dim * offset];
363 
364           DMFieldDSdot(cH,T->T[2],elem,nq,feDim,(nc * dim * dim),(PetscScalar));
365           for (p = 0; p < nq; p++) {
366             for (g = 0; g < nc * dimR; g++) {
367               PetscScalar vs[3];
368 
369               for (d = 0; d < dimR; d++) {
370                 vs[d] = 0.;
371                 for (e = 0; e < dimR; e++) {
372                   vs[d] += invJ[dimR * dimR * p + e * dimR + d] * cH[(nc * dimR * p + g) * dimR + e];
373                 }
374               }
375               for (d = 0; d < dimR; d++) {
376                 cH[(nc * dimR * p + g) * dimR + d] = vs[d];
377               }
378             }
379             for (g = 0; g < nc; g++) {
380               for (f = 0; f < dimR; f++) {
381                 PetscScalar vs[3];
382 
383                 for (d = 0; d < dimR; d++) {
384                   vs[d] = 0.;
385                   for (e = 0; e < dimR; e++) {
386                     vs[d] += invJ[dimR * dimR * p + e * dimR + d] * cH[((nc * p + g) * dimR + e) * dimR + f];
387                   }
388                 }
389                 for (d = 0; d < dimR; d++) {
390                   cH[((nc * p + g) * dimR + d) * dimR + f] = vs[d];
391                 }
392               }
393             }
394           }
395         } else {
396           PetscReal *cH = &cellHr[nc * dim * dim * offset];
397 
398           DMFieldDSdot(cH,T->T[2],elem,nq,feDim,(nc * dim * dim),PetscRealPart);
399           for (p = 0; p < nq; p++) {
400             for (g = 0; g < nc * dimR; g++) {
401               for (d = 0; d < dimR; d++) {
402                 v[d] = 0.;
403                 for (e = 0; e < dimR; e++) {
404                   v[d] += invJ[dimR * dimR * p + e * dimR + d] * cH[(nc * dimR * p + g) * dimR + e];
405                 }
406               }
407               for (d = 0; d < dimR; d++) {
408                 cH[(nc * dimR * p + g) * dimR + d] = v[d];
409               }
410             }
411             for (g = 0; g < nc; g++) {
412               for (f = 0; f < dimR; f++) {
413                 for (d = 0; d < dimR; d++) {
414                   v[d] = 0.;
415                   for (e = 0; e < dimR; e++) {
416                     v[d] += invJ[dimR * dimR * p + e * dimR + d] * cH[((nc * p + g) * dimR + e) * dimR + f];
417                   }
418                 }
419                 for (d = 0; d < dimR; d++) {
420                   cH[((nc * p + g) * dimR + d) * dimR + f] = v[d];
421                 }
422               }
423             }
424           }
425         }
426       }
427       PetscCall(DMFieldRestoreClosure_Internal(field, c, &isDG, &closureSize, &array, &elem));
428       PetscCall(PetscTabulationDestroy(&T));
429     }
430     offset += nq;
431   }
432   {
433     MPI_Datatype origtype;
434 
435     if (datatype == PETSC_SCALAR) {
436       origtype = MPIU_SCALAR;
437     } else {
438       origtype = MPIU_REAL;
439     }
440     if (B) {
441       MPI_Datatype Btype;
442 
443       PetscCallMPI(MPI_Type_contiguous(nc, origtype, &Btype));
444       PetscCallMPI(MPI_Type_commit(&Btype));
445       PetscCall(PetscSFScatterBegin(cellSF,Btype,(datatype == PETSC_SCALAR) ? (void *) cellBs : (void *) cellBr, B));
446       PetscCall(PetscSFScatterEnd(cellSF,Btype,(datatype == PETSC_SCALAR) ? (void *) cellBs : (void *) cellBr, B));
447       PetscCallMPI(MPI_Type_free(&Btype));
448     }
449     if (D) {
450       MPI_Datatype Dtype;
451 
452       PetscCallMPI(MPI_Type_contiguous(nc * dim, origtype, &Dtype));
453       PetscCallMPI(MPI_Type_commit(&Dtype));
454       PetscCall(PetscSFScatterBegin(cellSF,Dtype,(datatype == PETSC_SCALAR) ? (void *) cellDs : (void *) cellDr, D));
455       PetscCall(PetscSFScatterEnd(cellSF,Dtype,(datatype == PETSC_SCALAR) ? (void *) cellDs : (void *) cellDr, D));
456       PetscCallMPI(MPI_Type_free(&Dtype));
457     }
458     if (H) {
459       MPI_Datatype Htype;
460 
461       PetscCallMPI(MPI_Type_contiguous(nc * dim * dim, origtype, &Htype));
462       PetscCallMPI(MPI_Type_commit(&Htype));
463       PetscCall(PetscSFScatterBegin(cellSF,Htype,(datatype == PETSC_SCALAR) ? (void *) cellHs : (void *) cellHr, H));
464       PetscCall(PetscSFScatterEnd(cellSF,Htype,(datatype == PETSC_SCALAR) ? (void *) cellHs : (void *) cellHr, H));
465       PetscCallMPI(MPI_Type_free(&Htype));
466     }
467   }
468   PetscCall(PetscFree4(v,J,invJ,detJ));
469   PetscCall(PetscFree3(cellBr, cellDr, cellHr));
470   PetscCall(PetscFree3(cellBs, cellDs, cellHs));
471   PetscCall(PetscFree3(cellPoints,coordsReal,coordsRef));
472   PetscCallMPI(MPI_Type_free(&pointType));
473   PetscCall(PetscSFDestroy(&cellSF));
474   PetscFunctionReturn(0);
475 }
476 
477 static PetscErrorCode DMFieldEvaluateFV_DS(DMField field, IS pointIS, PetscDataType type, void *B, void *D, void *H)
478 {
479   DMField_DS      *dsfield = (DMField_DS *) field->data;
480   PetscInt         h, imin;
481   PetscInt         dim;
482   PetscClassId     id;
483   PetscQuadrature  quad = NULL;
484   PetscInt         maxDegree;
485   PetscFEGeom      *geom;
486   PetscInt         Nq, Nc, dimC, qNc, N;
487   PetscInt         numPoints;
488   void            *qB = NULL, *qD = NULL, *qH = NULL;
489   const PetscReal *weights;
490   MPI_Datatype     mpitype = type == PETSC_SCALAR ? MPIU_SCALAR : MPIU_REAL;
491   PetscObject      disc;
492   DMField          coordField;
493 
494   PetscFunctionBegin;
495   Nc = field->numComponents;
496   PetscCall(DMGetCoordinateDim(field->dm, &dimC));
497   PetscCall(DMGetDimension(field->dm, &dim));
498   PetscCall(ISGetLocalSize(pointIS, &numPoints));
499   PetscCall(ISGetMinMax(pointIS,&imin,NULL));
500   for (h = 0; h < dsfield->height; h++) {
501     PetscInt hEnd;
502 
503     PetscCall(DMPlexGetHeightStratum(field->dm,h,NULL,&hEnd));
504     if (imin < hEnd) break;
505   }
506   dim -= h;
507   PetscCall(DMFieldDSGetHeightDisc(field, h, dsfield->disc, &disc));
508   PetscCall(PetscObjectGetClassId(disc,&id));
509   PetscCheck(id == PETSCFE_CLASSID,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Discretization not supported");
510   PetscCall(DMGetCoordinateField(field->dm, &coordField));
511   PetscCall(DMFieldGetDegree(coordField, pointIS, NULL, &maxDegree));
512   if (maxDegree <= 1) {
513     PetscCall(DMFieldCreateDefaultQuadrature(coordField, pointIS, &quad));
514   }
515   if (!quad) PetscCall(DMFieldCreateDefaultQuadrature(field, pointIS, &quad));
516   PetscCheck(quad,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not determine quadrature for cell averages");
517   PetscCall(DMFieldCreateFEGeom(coordField,pointIS,quad,PETSC_FALSE,&geom));
518   PetscCall(PetscQuadratureGetData(quad, NULL, &qNc, &Nq, NULL, &weights));
519   PetscCheck(qNc == 1,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expected scalar quadrature components");
520   N = numPoints * Nq * Nc;
521   if (B) PetscCall(DMGetWorkArray(field->dm, N, mpitype, &qB));
522   if (D) PetscCall(DMGetWorkArray(field->dm, N * dimC, mpitype, &qD));
523   if (H) PetscCall(DMGetWorkArray(field->dm, N * dimC * dimC, mpitype, &qH));
524   PetscCall(DMFieldEvaluateFE(field,pointIS,quad,type,qB,qD,qH));
525   if (B) {
526     PetscInt i, j, k;
527 
528     if (type == PETSC_SCALAR) {
529       PetscScalar * sB  = (PetscScalar *) B;
530       PetscScalar * sqB = (PetscScalar *) qB;
531 
532       for (i = 0; i < numPoints; i++) {
533         PetscReal vol = 0.;
534 
535         for (j = 0; j < Nc; j++) {sB[i * Nc + j] = 0.;}
536         for (k = 0; k < Nq; k++) {
537           vol += geom->detJ[i * Nq + k] * weights[k];
538           for (j = 0; j < Nc; j++) {
539             sB[i * Nc + j] += geom->detJ[i * Nq + k] * weights[k] * sqB[ (i * Nq + k) * Nc + j];
540           }
541         }
542         for (k = 0; k < Nc; k++) sB[i * Nc + k] /= vol;
543       }
544     } else {
545       PetscReal * rB  = (PetscReal *) B;
546       PetscReal * rqB = (PetscReal *) qB;
547 
548       for (i = 0; i < numPoints; i++) {
549         PetscReal vol = 0.;
550 
551         for (j = 0; j < Nc; j++) {rB[i * Nc + j] = 0.;}
552         for (k = 0; k < Nq; k++) {
553           vol += geom->detJ[i * Nq + k] * weights[k];
554           for (j = 0; j < Nc; j++) {
555             rB[i * Nc + j] += weights[k] * rqB[ (i * Nq + k) * Nc + j];
556           }
557         }
558         for (k = 0; k < Nc; k++) rB[i * Nc + k] /= vol;
559       }
560     }
561   }
562   if (D) {
563     PetscInt i, j, k, l, m;
564 
565     if (type == PETSC_SCALAR) {
566       PetscScalar * sD  = (PetscScalar *) D;
567       PetscScalar * sqD = (PetscScalar *) qD;
568 
569       for (i = 0; i < numPoints; i++) {
570         PetscReal vol = 0.;
571 
572         for (j = 0; j < Nc * dimC; j++) {sD[i * Nc * dimC + j] = 0.;}
573         for (k = 0; k < Nq; k++) {
574           vol += geom->detJ[i * Nq + k] * weights[k];
575           for (j = 0; j < Nc; j++) {
576             PetscScalar pD[3] = {0.,0.,0.};
577 
578             for (l = 0; l < dimC; l++) {
579               for (m = 0; m < dim; m++) {
580                 pD[l] += geom->invJ[((i * Nq + k) * dimC + m) * dimC + l] * sqD[((i * Nq + k) * Nc + j) * dim + m];
581               }
582             }
583             for (l = 0; l < dimC; l++) {
584               sD[(i * Nc + j) * dimC + l] += geom->detJ[i * Nq + k] * weights[k] * pD[l];
585             }
586           }
587         }
588         for (k = 0; k < Nc * dimC; k++) sD[i * Nc * dimC + k] /= vol;
589       }
590     } else {
591       PetscReal * rD  = (PetscReal *) D;
592       PetscReal * rqD = (PetscReal *) qD;
593 
594       for (i = 0; i < numPoints; i++) {
595         PetscReal vol = 0.;
596 
597         for (j = 0; j < Nc * dimC; j++) {rD[i * Nc * dimC + j] = 0.;}
598         for (k = 0; k < Nq; k++) {
599           vol += geom->detJ[i * Nq + k] * weights[k];
600           for (j = 0; j < Nc; j++) {
601             PetscReal pD[3] = {0.,0.,0.};
602 
603             for (l = 0; l < dimC; l++) {
604               for (m = 0; m < dim; m++) {
605                 pD[l] += geom->invJ[((i * Nq + k) * dimC + m) * dimC + l] * rqD[((i * Nq + k) * Nc + j) * dim + m];
606               }
607             }
608             for (l = 0; l < dimC; l++) {
609               rD[(i * Nc + j) * dimC + l] += geom->detJ[i * Nq + k] * weights[k] * pD[l];
610             }
611           }
612         }
613         for (k = 0; k < Nc * dimC; k++) rD[i * Nc * dimC + k] /= vol;
614       }
615     }
616   }
617   if (H) {
618     PetscInt i, j, k, l, m, q, r;
619 
620     if (type == PETSC_SCALAR) {
621       PetscScalar * sH  = (PetscScalar *) H;
622       PetscScalar * sqH = (PetscScalar *) qH;
623 
624       for (i = 0; i < numPoints; i++) {
625         PetscReal vol = 0.;
626 
627         for (j = 0; j < Nc * dimC * dimC; j++) {sH[i * Nc * dimC * dimC + j] = 0.;}
628         for (k = 0; k < Nq; k++) {
629           const PetscReal *invJ = &geom->invJ[(i * Nq + k) * dimC * dimC];
630 
631           vol += geom->detJ[i * Nq + k] * weights[k];
632           for (j = 0; j < Nc; j++) {
633             PetscScalar pH[3][3] = {{0.,0.,0.},{0.,0.,0.},{0.,0.,0.}};
634             const PetscScalar *spH = &sqH[((i * Nq + k) * Nc + j) * dimC * dimC];
635 
636             for (l = 0; l < dimC; l++) {
637               for (m = 0; m < dimC; m++) {
638                 for (q = 0; q < dim; q++) {
639                   for (r = 0; r < dim; r++) {
640                     pH[l][m] += invJ[q * dimC + l] * invJ[r * dimC + m] * spH[q * dim + r];
641                   }
642                 }
643               }
644             }
645             for (l = 0; l < dimC; l++) {
646               for (m = 0; m < dimC; m++) {
647                 sH[(i * Nc + j) * dimC * dimC + l * dimC + m] += geom->detJ[i * Nq + k] * weights[k] * pH[l][m];
648               }
649             }
650           }
651         }
652         for (k = 0; k < Nc * dimC * dimC; k++) sH[i * Nc * dimC * dimC + k] /= vol;
653       }
654     } else {
655       PetscReal * rH  = (PetscReal *) H;
656       PetscReal * rqH = (PetscReal *) qH;
657 
658       for (i = 0; i < numPoints; i++) {
659         PetscReal vol = 0.;
660 
661         for (j = 0; j < Nc * dimC * dimC; j++) {rH[i * Nc * dimC * dimC + j] = 0.;}
662         for (k = 0; k < Nq; k++) {
663           const PetscReal *invJ = &geom->invJ[(i * Nq + k) * dimC * dimC];
664 
665           vol += geom->detJ[i * Nq + k] * weights[k];
666           for (j = 0; j < Nc; j++) {
667             PetscReal pH[3][3] = {{0.,0.,0.},{0.,0.,0.},{0.,0.,0.}};
668             const PetscReal *rpH = &rqH[((i * Nq + k) * Nc + j) * dimC * dimC];
669 
670             for (l = 0; l < dimC; l++) {
671               for (m = 0; m < dimC; m++) {
672                 for (q = 0; q < dim; q++) {
673                   for (r = 0; r < dim; r++) {
674                     pH[l][m] += invJ[q * dimC + l] * invJ[r * dimC + m] * rpH[q * dim + r];
675                   }
676                 }
677               }
678             }
679             for (l = 0; l < dimC; l++) {
680               for (m = 0; m < dimC; m++) {
681                 rH[(i * Nc + j) * dimC * dimC + l * dimC + m] += geom->detJ[i * Nq + k] * weights[k] * pH[l][m];
682               }
683             }
684           }
685         }
686         for (k = 0; k < Nc * dimC * dimC; k++) rH[i * Nc * dimC * dimC + k] /= vol;
687       }
688     }
689   }
690   if (B) PetscCall(DMRestoreWorkArray(field->dm, N, mpitype, &qB));
691   if (D) PetscCall(DMRestoreWorkArray(field->dm, N * dimC, mpitype, &qD));
692   if (H) PetscCall(DMRestoreWorkArray(field->dm, N * dimC * dimC, mpitype, &qH));
693   PetscCall(PetscFEGeomDestroy(&geom));
694   PetscCall(PetscQuadratureDestroy(&quad));
695   PetscFunctionReturn(0);
696 }
697 
698 static PetscErrorCode DMFieldGetDegree_DS(DMField field, IS pointIS, PetscInt *minDegree, PetscInt *maxDegree)
699 {
700   DMField_DS     *dsfield;
701   PetscObject    disc;
702   PetscInt       h, imin, imax;
703   PetscClassId   id;
704 
705   PetscFunctionBegin;
706   dsfield = (DMField_DS *) field->data;
707   PetscCall(ISGetMinMax(pointIS,&imin,&imax));
708   if (imin >= imax) {
709     h = 0;
710   } else {
711     for (h = 0; h < dsfield->height; h++) {
712       PetscInt hEnd;
713 
714       PetscCall(DMPlexGetHeightStratum(field->dm,h,NULL,&hEnd));
715       if (imin < hEnd) break;
716     }
717   }
718   PetscCall(DMFieldDSGetHeightDisc(field, h, dsfield->disc, &disc));
719   PetscCall(PetscObjectGetClassId(disc,&id));
720   if (id == PETSCFE_CLASSID) {
721     PetscFE    fe = (PetscFE) disc;
722     PetscSpace sp;
723 
724     PetscCall(PetscFEGetBasisSpace(fe, &sp));
725     PetscCall(PetscSpaceGetDegree(sp, minDegree, maxDegree));
726   }
727   PetscFunctionReturn(0);
728 }
729 
730 PetscErrorCode DMFieldGetFVQuadrature_Internal(DMField field, IS pointIS, PetscQuadrature *quad)
731 {
732   DM              dm = field->dm;
733   const PetscInt *points;
734   DMPolytopeType  ct;
735   PetscInt        dim, n;
736   PetscBool       isplex;
737 
738   PetscFunctionBegin;
739   PetscCall(PetscObjectTypeCompare((PetscObject) dm, DMPLEX, &isplex));
740   PetscCall(ISGetLocalSize(pointIS, &n));
741   if (isplex && n) {
742     PetscCall(DMGetDimension(dm, &dim));
743     PetscCall(ISGetIndices(pointIS, &points));
744     PetscCall(DMPlexGetCellType(dm, points[0], &ct));
745     switch (ct) {
746       case DM_POLYTOPE_TRIANGLE:
747       case DM_POLYTOPE_TETRAHEDRON:
748         PetscCall(PetscDTStroudConicalQuadrature(dim, 1, 1, -1.0, 1.0, quad));break;
749       default: PetscCall(PetscDTGaussTensorQuadrature(dim, 1, 1, -1.0, 1.0, quad));
750     }
751     PetscCall(ISRestoreIndices(pointIS, &points));
752   } else PetscCall(DMFieldCreateDefaultQuadrature(field, pointIS, quad));
753   PetscFunctionReturn(0);
754 }
755 
756 static PetscErrorCode DMFieldCreateDefaultQuadrature_DS(DMField field, IS pointIS, PetscQuadrature *quad)
757 {
758   PetscInt       h, dim, imax, imin, cellHeight;
759   DM             dm;
760   DMField_DS     *dsfield;
761   PetscObject    disc;
762   PetscFE        fe;
763   PetscClassId   id;
764 
765   PetscFunctionBegin;
766   dm = field->dm;
767   dsfield = (DMField_DS *) field->data;
768   PetscCall(ISGetMinMax(pointIS,&imin,&imax));
769   PetscCall(DMGetDimension(dm,&dim));
770   for (h = 0; h <= dim; h++) {
771     PetscInt hStart, hEnd;
772 
773     PetscCall(DMPlexGetHeightStratum(dm,h,&hStart,&hEnd));
774     if (imax >= hStart && imin < hEnd) break;
775   }
776   PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
777   h -= cellHeight;
778   *quad = NULL;
779   if (h < dsfield->height) {
780     PetscCall(DMFieldDSGetHeightDisc(field, h, dsfield->disc, &disc));
781     PetscCall(PetscObjectGetClassId(disc,&id));
782     if (id != PETSCFE_CLASSID) PetscFunctionReturn(0);
783     fe = (PetscFE) disc;
784     PetscCall(PetscFEGetQuadrature(fe,quad));
785     PetscCall(PetscObjectReference((PetscObject)*quad));
786   }
787   PetscFunctionReturn(0);
788 }
789 
790 static PetscErrorCode DMFieldComputeFaceData_DS(DMField field, IS pointIS, PetscQuadrature quad, PetscFEGeom *geom)
791 {
792   const PetscInt *points;
793   PetscInt        p, dim, dE, numFaces, Nq;
794   PetscInt        maxDegree;
795   DMLabel         depthLabel;
796   IS              cellIS;
797   DM              dm = field->dm;
798 
799   PetscFunctionBegin;
800   dim = geom->dim;
801   dE  = geom->dimEmbed;
802   PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
803   PetscCall(DMLabelGetStratumIS(depthLabel, dim + 1, &cellIS));
804   PetscCall(DMFieldGetDegree(field,cellIS,NULL,&maxDegree));
805   PetscCall(ISGetIndices(pointIS, &points));
806   numFaces = geom->numCells;
807   Nq = geom->numPoints;
808   /* First, set local faces and flip normals so that they are outward for the first supporting cell */
809   for (p = 0; p < numFaces; p++) {
810     PetscInt        point = points[p];
811     PetscInt        suppSize, s, coneSize, c, numChildren;
812     const PetscInt *supp, *cone, *ornt;
813 
814     PetscCall(DMPlexGetTreeChildren(dm, point, &numChildren, NULL));
815     PetscCheck(!numChildren,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Face data not valid for facets with children");
816     PetscCall(DMPlexGetSupportSize(dm, point, &suppSize));
817     PetscCheck(suppSize <= 2,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " has %" PetscInt_FMT " support, expected at most 2", point, suppSize);
818     if (!suppSize) continue;
819     PetscCall(DMPlexGetSupport(dm, point, &supp));
820     for (s = 0; s < suppSize; ++s) {
821       PetscCall(DMPlexGetConeSize(dm, supp[s], &coneSize));
822       PetscCall(DMPlexGetCone(dm, supp[s], &cone));
823       for (c = 0; c < coneSize; ++c) if (cone[c] == point) break;
824       PetscCheck(c != coneSize,PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid connectivity: point %" PetscInt_FMT " not found in cone of support point %" PetscInt_FMT, point, supp[s]);
825       geom->face[p][s] = c;
826     }
827     PetscCall(DMPlexGetConeOrientation(dm, supp[0], &ornt));
828     if (ornt[geom->face[p][0]] < 0) {
829       PetscInt Np = geom->numPoints, q, dE = geom->dimEmbed, d;
830 
831       for (q = 0; q < Np; ++q) for (d = 0; d < dE; ++d) geom->n[(p*Np + q)*dE + d] = -geom->n[(p*Np + q)*dE + d];
832     }
833   }
834   if (maxDegree <= 1) {
835     PetscInt        numCells, offset, *cells;
836     PetscFEGeom     *cellGeom;
837     IS              suppIS;
838 
839     for (p = 0, numCells = 0; p < numFaces; p++) {
840       PetscInt        point = points[p];
841       PetscInt        numSupp, numChildren;
842 
843       PetscCall(DMPlexGetTreeChildren(dm, point, &numChildren, NULL));
844       PetscCheck(!numChildren,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Face data not valid for facets with children");
845       PetscCall(DMPlexGetSupportSize(dm, point,&numSupp));
846       PetscCheck(numSupp <= 2,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " has %" PetscInt_FMT " support, expected at most 2", point, numSupp);
847       numCells += numSupp;
848     }
849     PetscCall(PetscMalloc1(numCells, &cells));
850     for (p = 0, offset = 0; p < numFaces; p++) {
851       PetscInt        point = points[p];
852       PetscInt        numSupp, s;
853       const PetscInt *supp;
854 
855       PetscCall(DMPlexGetSupportSize(dm, point,&numSupp));
856       PetscCall(DMPlexGetSupport(dm, point, &supp));
857       for (s = 0; s < numSupp; s++, offset++) {
858         cells[offset] = supp[s];
859       }
860     }
861     PetscCall(ISCreateGeneral(PETSC_COMM_SELF,numCells,cells,PETSC_USE_POINTER, &suppIS));
862     PetscCall(DMFieldCreateFEGeom(field,suppIS,quad,PETSC_FALSE,&cellGeom));
863     for (p = 0, offset = 0; p < numFaces; p++) {
864       PetscInt        point = points[p];
865       PetscInt        numSupp, s, q;
866       const PetscInt *supp;
867 
868       PetscCall(DMPlexGetSupportSize(dm, point,&numSupp));
869       PetscCall(DMPlexGetSupport(dm, point, &supp));
870       for (s = 0; s < numSupp; s++, offset++) {
871         for (q = 0; q < Nq * dE * dE; q++) {
872           geom->suppJ[s][p * Nq * dE * dE + q]    = cellGeom->J[offset * Nq * dE * dE + q];
873           geom->suppInvJ[s][p * Nq * dE * dE + q] = cellGeom->invJ[offset * Nq * dE * dE + q];
874         }
875         for (q = 0; q < Nq; q++) geom->suppDetJ[s][p * Nq + q] = cellGeom->detJ[offset * Nq + q];
876       }
877     }
878     PetscCall(PetscFEGeomDestroy(&cellGeom));
879     PetscCall(ISDestroy(&suppIS));
880     PetscCall(PetscFree(cells));
881   } else {
882     DMField_DS          *dsfield = (DMField_DS *) field->data;
883     PetscObject          faceDisc, cellDisc;
884     PetscClassId         faceId, cellId;
885     PetscDualSpace       dsp;
886     DM                   K;
887     DMPolytopeType       ct;
888     PetscInt           (*co)[2][3];
889     PetscInt             coneSize;
890     PetscInt           **counts;
891     PetscInt             f, i, o, q, s;
892     const PetscInt      *coneK;
893     PetscInt             eStart, minOrient, maxOrient, numOrient;
894     PetscInt            *orients;
895     PetscReal          **orientPoints;
896     PetscReal           *cellPoints;
897     PetscReal           *dummyWeights;
898     PetscQuadrature      cellQuad = NULL;
899 
900     PetscCall(DMFieldDSGetHeightDisc(field, 1, dsfield->disc, &faceDisc));
901     PetscCall(DMFieldDSGetHeightDisc(field, 0, dsfield->disc, &cellDisc));
902     PetscCall(PetscObjectGetClassId(faceDisc,&faceId));
903     PetscCall(PetscObjectGetClassId(cellDisc,&cellId));
904     PetscCheck(faceId == PETSCFE_CLASSID && cellId == PETSCFE_CLASSID,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Not supported");
905     PetscCall(PetscFEGetDualSpace((PetscFE)cellDisc, &dsp));
906     PetscCall(PetscDualSpaceGetDM(dsp, &K));
907     PetscCall(DMPlexGetHeightStratum(K, 1, &eStart, NULL));
908     PetscCall(DMPlexGetCellType(K, eStart, &ct));
909     PetscCall(DMPlexGetConeSize(K,0,&coneSize));
910     PetscCall(DMPlexGetCone(K,0,&coneK));
911     PetscCall(PetscMalloc2(numFaces, &co, coneSize, &counts));
912     PetscCall(PetscMalloc1(dE*Nq, &cellPoints));
913     PetscCall(PetscMalloc1(Nq, &dummyWeights));
914     PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &cellQuad));
915     PetscCall(PetscQuadratureSetData(cellQuad, dE, 1, Nq, cellPoints, dummyWeights));
916     minOrient = PETSC_MAX_INT;
917     maxOrient = PETSC_MIN_INT;
918     for (p = 0; p < numFaces; p++) { /* record the orientation of the facet wrt the support cells */
919       PetscInt        point = points[p];
920       PetscInt        numSupp, numChildren;
921       const PetscInt *supp;
922 
923       PetscCall(DMPlexGetTreeChildren(dm, point, &numChildren, NULL));
924       PetscCheck(!numChildren,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Face data not valid for facets with children");
925       PetscCall(DMPlexGetSupportSize(dm, point,&numSupp));
926       PetscCheck(numSupp <= 2,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " has %" PetscInt_FMT " support, expected at most 2", point, numSupp);
927       PetscCall(DMPlexGetSupport(dm, point, &supp));
928       for (s = 0; s < numSupp; s++) {
929         PetscInt        cell = supp[s];
930         PetscInt        numCone;
931         const PetscInt *cone, *orient;
932 
933         PetscCall(DMPlexGetConeSize(dm, cell, &numCone));
934         PetscCheck(numCone == coneSize,PETSC_COMM_SELF, PETSC_ERR_PLIB, "Support point does not match reference element");
935         PetscCall(DMPlexGetCone(dm, cell, &cone));
936         PetscCall(DMPlexGetConeOrientation(dm, cell, &orient));
937         for (f = 0; f < coneSize; f++) {
938           if (cone[f] == point) break;
939         }
940         co[p][s][0] = f;
941         co[p][s][1] = orient[f];
942         co[p][s][2] = cell;
943         minOrient = PetscMin(minOrient, orient[f]);
944         maxOrient = PetscMax(maxOrient, orient[f]);
945       }
946       for (; s < 2; s++) {
947         co[p][s][0] = -1;
948         co[p][s][1] = -1;
949         co[p][s][2] = -1;
950       }
951     }
952     numOrient = maxOrient + 1 - minOrient;
953     PetscCall(DMPlexGetCone(K,0,&coneK));
954     /* count all (face,orientation) doubles that appear */
955     PetscCall(PetscCalloc2(numOrient,&orients,numOrient,&orientPoints));
956     for (f = 0; f < coneSize; f++) PetscCall(PetscCalloc1(numOrient+1, &counts[f]));
957     for (p = 0; p < numFaces; p++) {
958       for (s = 0; s < 2; s++) {
959         if (co[p][s][0] >= 0) {
960           counts[co[p][s][0]][co[p][s][1] - minOrient]++;
961           orients[co[p][s][1] - minOrient]++;
962         }
963       }
964     }
965     for (o = 0; o < numOrient; o++) {
966       if (orients[o]) {
967         PetscInt orient = o + minOrient;
968         PetscInt q;
969 
970         PetscCall(PetscMalloc1(Nq * dim, &orientPoints[o]));
971         /* rotate the quadrature points appropriately */
972         switch (ct) {
973         case DM_POLYTOPE_POINT: break;
974         case DM_POLYTOPE_SEGMENT:
975           if (orient == -2 || orient == 1) {
976             for (q = 0; q < Nq; q++) {
977               orientPoints[o][q] = -geom->xi[q];
978             }
979           } else {
980             for (q = 0; q < Nq; q++) {
981               orientPoints[o][q] = geom->xi[q];
982             }
983           }
984           break;
985         case DM_POLYTOPE_TRIANGLE:
986           for (q = 0; q < Nq; q++) {
987             PetscReal lambda[3];
988             PetscReal lambdao[3];
989 
990             /* convert to barycentric */
991             lambda[0] = - (geom->xi[2 * q] + geom->xi[2 * q + 1]) / 2.;
992             lambda[1] = (geom->xi[2 * q] + 1.) / 2.;
993             lambda[2] = (geom->xi[2 * q + 1] + 1.) / 2.;
994             if (orient >= 0) {
995               for (i = 0; i < 3; i++) {
996                 lambdao[i] = lambda[(orient + i) % 3];
997               }
998             } else {
999               for (i = 0; i < 3; i++) {
1000                 lambdao[i] = lambda[(-(orient + i) + 3) % 3];
1001               }
1002             }
1003             /* convert to coordinates */
1004             orientPoints[o][2 * q + 0] = -(lambdao[0] + lambdao[2]) + lambdao[1];
1005             orientPoints[o][2 * q + 1] = -(lambdao[0] + lambdao[1]) + lambdao[2];
1006           }
1007           break;
1008         case DM_POLYTOPE_QUADRILATERAL:
1009           for (q = 0; q < Nq; q++) {
1010             PetscReal xi[2], xio[2];
1011             PetscInt oabs = (orient >= 0) ? orient : -(orient + 1);
1012 
1013             xi[0] = geom->xi[2 * q];
1014             xi[1] = geom->xi[2 * q + 1];
1015             switch (oabs) {
1016             case 1:
1017               xio[0] = xi[1];
1018               xio[1] = -xi[0];
1019               break;
1020             case 2:
1021               xio[0] = -xi[0];
1022               xio[1] = -xi[1];
1023             case 3:
1024               xio[0] = -xi[1];
1025               xio[1] = xi[0];
1026             case 0:
1027             default:
1028               xio[0] = xi[0];
1029               xio[1] = xi[1];
1030               break;
1031             }
1032             if (orient < 0) {
1033               xio[0] = -xio[0];
1034             }
1035             orientPoints[o][2 * q + 0] = xio[0];
1036             orientPoints[o][2 * q + 1] = xio[1];
1037           }
1038           break;
1039         default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cell type %s not yet supported", DMPolytopeTypes[ct]);
1040         }
1041       }
1042     }
1043     for (f = 0; f < coneSize; f++) {
1044       PetscInt face = coneK[f];
1045       PetscReal v0[3];
1046       PetscReal J[9], detJ;
1047       PetscInt numCells, offset;
1048       PetscInt *cells;
1049       IS suppIS;
1050 
1051       PetscCall(DMPlexComputeCellGeometryFEM(K, face, NULL, v0, J, NULL, &detJ));
1052       for (o = 0; o <= numOrient; o++) {
1053         PetscFEGeom *cellGeom;
1054 
1055         if (!counts[f][o]) continue;
1056         /* If this (face,orientation) double appears,
1057          * convert the face quadrature points into volume quadrature points */
1058         for (q = 0; q < Nq; q++) {
1059           PetscReal xi0[3] = {-1., -1., -1.};
1060 
1061           CoordinatesRefToReal(dE, dim, xi0, v0, J, &orientPoints[o][dim * q + 0], &cellPoints[dE * q + 0]);
1062         }
1063         for (p = 0, numCells = 0; p < numFaces; p++) {
1064           for (s = 0; s < 2; s++) {
1065             if (co[p][s][0] == f && co[p][s][1] == o + minOrient) numCells++;
1066           }
1067         }
1068         PetscCall(PetscMalloc1(numCells, &cells));
1069         for (p = 0, offset = 0; p < numFaces; p++) {
1070           for (s = 0; s < 2; s++) {
1071             if (co[p][s][0] == f && co[p][s][1] == o + minOrient) {
1072               cells[offset++] = co[p][s][2];
1073             }
1074           }
1075         }
1076         PetscCall(ISCreateGeneral(PETSC_COMM_SELF,numCells,cells,PETSC_USE_POINTER, &suppIS));
1077         PetscCall(DMFieldCreateFEGeom(field,suppIS,cellQuad,PETSC_FALSE,&cellGeom));
1078         for (p = 0, offset = 0; p < numFaces; p++) {
1079           for (s = 0; s < 2; s++) {
1080             if (co[p][s][0] == f && co[p][s][1] == o + minOrient) {
1081               for (q = 0; q < Nq * dE * dE; q++) {
1082                 geom->suppJ[s][p * Nq * dE * dE + q]    = cellGeom->J[offset * Nq * dE * dE + q];
1083                 geom->suppInvJ[s][p * Nq * dE * dE + q] = cellGeom->invJ[offset * Nq * dE * dE + q];
1084               }
1085               for (q = 0; q < Nq; q++) geom->suppDetJ[s][p * Nq + q] = cellGeom->detJ[offset * Nq + q];
1086               offset++;
1087             }
1088           }
1089         }
1090         PetscCall(PetscFEGeomDestroy(&cellGeom));
1091         PetscCall(ISDestroy(&suppIS));
1092         PetscCall(PetscFree(cells));
1093       }
1094     }
1095     for (o = 0; o < numOrient; o++) {
1096       if (orients[o]) {
1097         PetscCall(PetscFree(orientPoints[o]));
1098       }
1099     }
1100     PetscCall(PetscFree2(orients,orientPoints));
1101     PetscCall(PetscQuadratureDestroy(&cellQuad));
1102     for (f = 0; f < coneSize; f++) PetscCall(PetscFree(counts[f]));
1103     PetscCall(PetscFree2(co,counts));
1104   }
1105   PetscCall(ISRestoreIndices(pointIS, &points));
1106   PetscCall(ISDestroy(&cellIS));
1107   PetscFunctionReturn(0);
1108 }
1109 
1110 static PetscErrorCode DMFieldInitialize_DS(DMField field)
1111 {
1112   PetscFunctionBegin;
1113   field->ops->destroy                 = DMFieldDestroy_DS;
1114   field->ops->evaluate                = DMFieldEvaluate_DS;
1115   field->ops->evaluateFE              = DMFieldEvaluateFE_DS;
1116   field->ops->evaluateFV              = DMFieldEvaluateFV_DS;
1117   field->ops->getDegree               = DMFieldGetDegree_DS;
1118   field->ops->createDefaultQuadrature = DMFieldCreateDefaultQuadrature_DS;
1119   field->ops->view                    = DMFieldView_DS;
1120   field->ops->computeFaceData         = DMFieldComputeFaceData_DS;
1121   PetscFunctionReturn(0);
1122 }
1123 
1124 PETSC_INTERN PetscErrorCode DMFieldCreate_DS(DMField field)
1125 {
1126   DMField_DS     *dsfield;
1127 
1128   PetscFunctionBegin;
1129   PetscCall(PetscNewLog(field,&dsfield));
1130   field->data = dsfield;
1131   PetscCall(DMFieldInitialize_DS(field));
1132   PetscFunctionReturn(0);
1133 }
1134 
1135 PetscErrorCode DMFieldCreateDSWithDG(DM dm, DM dmDG, PetscInt fieldNum, Vec vec, Vec vecDG, DMField *field)
1136 {
1137   DMField      b;
1138   DMField_DS  *dsfield;
1139   PetscObject  disc = NULL, discDG = NULL;
1140   PetscSection section;
1141   PetscBool    isContainer = PETSC_FALSE;
1142   PetscClassId id = -1;
1143   PetscInt     numComponents = -1, dsNumFields;
1144 
1145   PetscFunctionBegin;
1146   PetscCall(DMGetLocalSection(dm, &section));
1147   PetscCall(PetscSectionGetFieldComponents(section, fieldNum, &numComponents));
1148   PetscCall(DMGetNumFields(dm, &dsNumFields));
1149   if (dsNumFields) PetscCall(DMGetField(dm, fieldNum, NULL, &disc));
1150   if (dsNumFields && dmDG) {
1151     PetscCall(DMGetField(dmDG, fieldNum, NULL, &discDG));
1152     PetscCall(PetscObjectReference(discDG));
1153   }
1154   if (disc) {
1155     PetscCall(PetscObjectGetClassId(disc, &id));
1156     isContainer = (id == PETSC_CONTAINER_CLASSID) ? PETSC_TRUE : PETSC_FALSE;
1157   }
1158   if (!disc || isContainer) {
1159     MPI_Comm       comm = PetscObjectComm((PetscObject) dm);
1160     PetscFE        fe;
1161     DMPolytopeType ct, locct = DM_POLYTOPE_UNKNOWN;
1162     PetscInt       dim, cStart, cEnd, cellHeight;
1163 
1164     PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
1165     PetscCall(DMGetDimension(dm, &dim));
1166     PetscCall(DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd));
1167     if (cEnd > cStart) PetscCall(DMPlexGetCellType(dm, cStart, &locct));
1168     PetscCallMPI(MPI_Allreduce(&locct, &ct, 1, MPI_INT, MPI_MIN, comm));
1169     PetscCall(PetscFECreateLagrangeByCell(PETSC_COMM_SELF, dim, numComponents, ct, 1, PETSC_DETERMINE, &fe));
1170     PetscCall(PetscFEViewFromOptions(fe, NULL, "-field_fe_view"));
1171     disc = (PetscObject) fe;
1172   } else PetscCall(PetscObjectReference(disc));
1173   PetscCall(PetscObjectGetClassId(disc, &id));
1174   if (id == PETSCFE_CLASSID) PetscCall(PetscFEGetNumComponents((PetscFE) disc, &numComponents));
1175   else                       SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Cannot determine number of discretization components");
1176   PetscCall(DMFieldCreate(dm, numComponents, DMFIELD_VERTEX, &b));
1177   PetscCall(DMFieldSetType(b, DMFIELDDS));
1178   dsfield = (DMField_DS *) b->data;
1179   dsfield->fieldNum = fieldNum;
1180   PetscCall(DMGetDimension(dm, &dsfield->height));
1181   dsfield->height++;
1182   PetscCall(PetscCalloc1(dsfield->height, &dsfield->disc));
1183   dsfield->disc[0] = disc;
1184   PetscCall(PetscObjectReference((PetscObject) vec));
1185   dsfield->vec = vec;
1186   if (dmDG) {
1187     dsfield->dmDG = dmDG;
1188     PetscCall(PetscCalloc1(dsfield->height, &dsfield->discDG));
1189     dsfield->discDG[0] = discDG;
1190     PetscCall(PetscObjectReference((PetscObject) vecDG));
1191     dsfield->vecDG = vecDG;
1192   }
1193   *field = b;
1194   PetscFunctionReturn(0);
1195 }
1196 
1197 PetscErrorCode DMFieldCreateDS(DM dm, PetscInt fieldNum, Vec vec, DMField *field)
1198 {
1199   PetscFunctionBegin;
1200   PetscCall(DMFieldCreateDSWithDG(dm, NULL, fieldNum, vec, NULL, field));
1201   PetscFunctionReturn(0);
1202 }
1203