xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision 40cbb1a031ea8f2be4fe2b92dc842b003ad37be3)
1 #include <petsc/private/petscimpl.h>
2 #include <petsc/private/pcbddcprivateimpl.h>
3 #include <petsc/private/pcbddcstructsimpl.h>
4 
5 PetscErrorCode PCBDDCDestroyGraphCandidatesIS(void *ctx)
6 {
7   PCBDDCGraphCandidates cand = (PCBDDCGraphCandidates)ctx;
8 
9   PetscFunctionBegin;
10   for (PetscInt i=0;i<cand->nfc;i++) PetscCall(ISDestroy(&cand->Faces[i]));
11   for (PetscInt i=0;i<cand->nec;i++) PetscCall(ISDestroy(&cand->Edges[i]));
12   PetscCall(PetscFree(cand->Faces));
13   PetscCall(PetscFree(cand->Edges));
14   PetscCall(ISDestroy(&cand->Vertices));
15   PetscCall(PetscFree(cand));
16   PetscFunctionReturn(0);
17 }
18 
19 PetscErrorCode PCBDDCGraphGetDirichletDofsB(PCBDDCGraph graph, IS* dirdofs)
20 {
21   PetscFunctionBegin;
22   if (graph->dirdofsB) {
23     PetscCall(PetscObjectReference((PetscObject)graph->dirdofsB));
24   } else if (graph->has_dirichlet) {
25     PetscInt i,size;
26     PetscInt *dirdofs_idxs;
27 
28     size = 0;
29     for (i=0;i<graph->nvtxs;i++) {
30       if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
31     }
32 
33     PetscCall(PetscMalloc1(size,&dirdofs_idxs));
34     size = 0;
35     for (i=0;i<graph->nvtxs;i++) {
36       if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
37     }
38     PetscCall(ISCreateGeneral(PETSC_COMM_SELF,size,dirdofs_idxs,PETSC_OWN_POINTER,&graph->dirdofsB));
39     PetscCall(PetscObjectReference((PetscObject)graph->dirdofsB));
40   }
41   *dirdofs = graph->dirdofsB;
42   PetscFunctionReturn(0);
43 }
44 
45 PetscErrorCode PCBDDCGraphGetDirichletDofs(PCBDDCGraph graph, IS* dirdofs)
46 {
47   PetscFunctionBegin;
48   if (graph->dirdofs) {
49     PetscCall(PetscObjectReference((PetscObject)graph->dirdofs));
50   } else if (graph->has_dirichlet) {
51     PetscInt i,size;
52     PetscInt *dirdofs_idxs;
53 
54     size = 0;
55     for (i=0;i<graph->nvtxs;i++) {
56       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
57     }
58 
59     PetscCall(PetscMalloc1(size,&dirdofs_idxs));
60     size = 0;
61     for (i=0;i<graph->nvtxs;i++) {
62       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
63     }
64     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)graph->l2gmap),size,dirdofs_idxs,PETSC_OWN_POINTER,&graph->dirdofs));
65     PetscCall(PetscObjectReference((PetscObject)graph->dirdofs));
66   }
67   *dirdofs = graph->dirdofs;
68   PetscFunctionReturn(0);
69 }
70 
71 PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer)
72 {
73   PetscInt       i,j,tabs;
74   PetscInt*      queue_in_global_numbering;
75 
76   PetscFunctionBegin;
77   PetscCall(PetscViewerASCIIPushSynchronized(viewer));
78   PetscCall(PetscViewerASCIIGetTab(viewer,&tabs));
79   PetscCall(PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n"));
80   PetscCall(PetscViewerFlush(viewer));
81   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"Local BDDC graph for subdomain %04d\n",PetscGlobalRank));
82   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"Number of vertices %" PetscInt_FMT "\n",graph->nvtxs));
83   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"Number of local subdomains %" PetscInt_FMT "\n",graph->n_local_subs ? graph->n_local_subs : 1));
84   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %" PetscInt_FMT "\n",graph->custom_minimal_size));
85   if (graph->maxcount != PETSC_MAX_INT) {
86     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"Max count %" PetscInt_FMT "\n",graph->maxcount));
87   }
88   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"Topological two dim? %s (set %s)\n",PetscBools[graph->twodim],PetscBools[graph->twodimset]));
89   if (verbosity_level > 2) {
90     for (i=0;i<graph->nvtxs;i++) {
91       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"%" PetscInt_FMT ":\n",i));
92       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %" PetscInt_FMT "\n",graph->which_dof[i]));
93       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %" PetscInt_FMT "\n",graph->special_dof[i]));
94       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %" PetscInt_FMT "\n",graph->count[i]));
95       PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
96       if (graph->count[i]) {
97         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:"));
98         for (j=0;j<graph->count[i];j++) {
99           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer," %" PetscInt_FMT,graph->neighbours_set[i][j]));
100         }
101         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"\n"));
102       }
103       PetscCall(PetscViewerASCIISetTab(viewer,tabs));
104       PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
105       if (graph->mirrors) {
106         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %" PetscInt_FMT "\n",graph->mirrors[i]));
107         if (graph->mirrors[i]) {
108           PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
109           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:"));
110           for (j=0;j<graph->mirrors[i];j++) {
111             PetscCall(PetscViewerASCIISynchronizedPrintf(viewer," %" PetscInt_FMT,graph->mirrors_set[i][j]));
112           }
113           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"\n"));
114           PetscCall(PetscViewerASCIISetTab(viewer,tabs));
115           PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
116         }
117       }
118       if (verbosity_level > 3) {
119         if (graph->xadj) {
120           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:"));
121           PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
122           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
123             PetscCall(PetscViewerASCIISynchronizedPrintf(viewer," %" PetscInt_FMT,graph->adjncy[j]));
124           }
125           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"\n"));
126           PetscCall(PetscViewerASCIISetTab(viewer,tabs));
127           PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
128         } else {
129           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   no adj info\n"));
130         }
131       }
132       if (graph->n_local_subs) {
133         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   local sub id: %" PetscInt_FMT "\n",graph->local_subs[i]));
134       }
135       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %" PetscInt_FMT "\n",graph->subset[i]));
136       if (graph->subset[i] && graph->subset_ncc) {
137         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %" PetscInt_FMT "\n",graph->subset_ncc[graph->subset[i]-1]));
138       }
139     }
140   }
141   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %" PetscInt_FMT "\n",graph->ncc));
142   PetscCall(PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering));
143   PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering));
144   for (i=0;i<graph->ncc;i++) {
145     PetscInt node_num=graph->queue[graph->cptr[i]];
146     PetscBool printcc = PETSC_FALSE;
147     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"  cc %" PetscInt_FMT " (size %" PetscInt_FMT ", fid %" PetscInt_FMT ", neighs:",i,graph->cptr[i+1]-graph->cptr[i],graph->which_dof[node_num]));
148     PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
149     for (j=0;j<graph->count[node_num];j++) {
150       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer," %" PetscInt_FMT,graph->neighbours_set[node_num][j]));
151     }
152     if (verbosity_level > 1) {
153       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"):"));
154       if (verbosity_level > 2 || graph->twodim || graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) {
155         printcc = PETSC_TRUE;
156       }
157       if (printcc) {
158         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
159           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer," %" PetscInt_FMT " (%" PetscInt_FMT ")",graph->queue[j],queue_in_global_numbering[j]));
160         }
161       }
162     } else {
163       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,")"));
164     }
165     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"\n"));
166     PetscCall(PetscViewerASCIISetTab(viewer,tabs));
167     PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
168   }
169   PetscCall(PetscFree(queue_in_global_numbering));
170   PetscCall(PetscViewerFlush(viewer));
171   PetscFunctionReturn(0);
172 }
173 
174 PetscErrorCode PCBDDCGraphRestoreCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
175 {
176   PetscInt       i;
177   PetscContainer gcand;
178 
179   PetscFunctionBegin;
180   PetscCall(PetscObjectQuery((PetscObject)graph->l2gmap,"_PCBDDCGraphCandidatesIS",(PetscObject*)&gcand));
181   if (gcand) {
182     if (n_faces)    *n_faces = 0;
183     if (n_edges)    *n_edges = 0;
184     if (FacesIS)    *FacesIS = NULL;
185     if (EdgesIS)    *EdgesIS = NULL;
186     if (VerticesIS) *VerticesIS = NULL;
187   }
188   if (n_faces) {
189     if (FacesIS) {
190       for (i=0;i<*n_faces;i++) {
191         PetscCall(ISDestroy(&((*FacesIS)[i])));
192       }
193       PetscCall(PetscFree(*FacesIS));
194     }
195     *n_faces = 0;
196   }
197   if (n_edges) {
198     if (EdgesIS) {
199       for (i=0;i<*n_edges;i++) {
200         PetscCall(ISDestroy(&((*EdgesIS)[i])));
201       }
202       PetscCall(PetscFree(*EdgesIS));
203     }
204     *n_edges = 0;
205   }
206   if (VerticesIS) {
207     PetscCall(ISDestroy(VerticesIS));
208   }
209   PetscFunctionReturn(0);
210 }
211 
212 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
213 {
214   IS             *ISForFaces,*ISForEdges,ISForVertices;
215   PetscInt       i,nfc,nec,nvc,*idx,*mark;
216   PetscContainer gcand;
217 
218   PetscFunctionBegin;
219   PetscCall(PetscObjectQuery((PetscObject)graph->l2gmap,"_PCBDDCGraphCandidatesIS",(PetscObject*)&gcand));
220   if (gcand) {
221     PCBDDCGraphCandidates cand;
222 
223     PetscCall(PetscContainerGetPointer(gcand,(void**)&cand));
224     if (n_faces)       *n_faces = cand->nfc;
225     if (FacesIS)       *FacesIS = cand->Faces;
226     if (n_edges)       *n_edges = cand->nec;
227     if (EdgesIS)       *EdgesIS = cand->Edges;
228     if (VerticesIS) *VerticesIS = cand->Vertices;
229     PetscFunctionReturn(0);
230   }
231   PetscCall(PetscCalloc1(graph->ncc,&mark));
232   /* loop on ccs to evalute number of faces, edges and vertices */
233   nfc = 0;
234   nec = 0;
235   nvc = 0;
236   for (i=0;i<graph->ncc;i++) {
237     PetscInt repdof = graph->queue[graph->cptr[i]];
238     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size && graph->count[repdof] < graph->maxcount) {
239       if (!graph->twodim && graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
240         nfc++;
241         mark[i] = 2;
242       } else {
243         nec++;
244         mark[i] = 1;
245       }
246     } else {
247       nvc += graph->cptr[i+1]-graph->cptr[i];
248     }
249   }
250 
251   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
252   if (FacesIS) {
253     PetscCall(PetscMalloc1(nfc,&ISForFaces));
254   }
255   if (EdgesIS) {
256     PetscCall(PetscMalloc1(nec,&ISForEdges));
257   }
258   if (VerticesIS) {
259     PetscCall(PetscMalloc1(nvc,&idx));
260   }
261 
262   /* loop on ccs to compute index sets for faces and edges */
263   if (!graph->queue_sorted) {
264     PetscInt *queue_global;
265 
266     PetscCall(PetscMalloc1(graph->cptr[graph->ncc],&queue_global));
267     PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global));
268     for (i=0;i<graph->ncc;i++) {
269       PetscCall(PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]));
270     }
271     PetscCall(PetscFree(queue_global));
272     graph->queue_sorted = PETSC_TRUE;
273   }
274   nfc = 0;
275   nec = 0;
276   for (i=0;i<graph->ncc;i++) {
277     if (mark[i] == 2) {
278       if (FacesIS) {
279         PetscCall(ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_USE_POINTER,&ISForFaces[nfc]));
280       }
281       nfc++;
282     } else if (mark[i] == 1) {
283       if (EdgesIS) {
284         PetscCall(ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_USE_POINTER,&ISForEdges[nec]));
285       }
286       nec++;
287     }
288   }
289 
290   /* index set for vertices */
291   if (VerticesIS) {
292     nvc = 0;
293     for (i=0;i<graph->ncc;i++) {
294       if (!mark[i]) {
295         PetscInt j;
296 
297         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
298           idx[nvc]=graph->queue[j];
299           nvc++;
300         }
301       }
302     }
303     /* sort vertex set (by local ordering) */
304     PetscCall(PetscSortInt(nvc,idx));
305     PetscCall(ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices));
306   }
307   PetscCall(PetscFree(mark));
308 
309   /* get back info */
310   if (n_faces)       *n_faces = nfc;
311   if (FacesIS)       *FacesIS = ISForFaces;
312   if (n_edges)       *n_edges = nec;
313   if (EdgesIS)       *EdgesIS = ISForEdges;
314   if (VerticesIS) *VerticesIS = ISForVertices;
315   PetscFunctionReturn(0);
316 }
317 
318 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
319 {
320   PetscBool      adapt_interface_reduced;
321   MPI_Comm       interface_comm;
322   PetscMPIInt    size;
323   PetscInt       i;
324   PetscBT        cornerp;
325 
326   PetscFunctionBegin;
327   /* compute connected components locally */
328   PetscCall(PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm));
329   PetscCall(PCBDDCGraphComputeConnectedComponentsLocal(graph));
330 
331   cornerp = NULL;
332   if (graph->active_coords) { /* face based corner selection */
333     PetscBT   excluded;
334     PetscReal *wdist;
335     PetscInt  n_neigh,*neigh,*n_shared,**shared;
336     PetscInt  maxc, ns;
337 
338     PetscCall(PetscBTCreate(graph->nvtxs,&cornerp));
339     PetscCall(ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared));
340     for (ns = 1, maxc = 0; ns < n_neigh; ns++) maxc = PetscMax(maxc,n_shared[ns]);
341     PetscCall(PetscMalloc1(maxc*graph->cdim,&wdist));
342     PetscCall(PetscBTCreate(maxc,&excluded));
343 
344     for (ns = 1; ns < n_neigh; ns++) { /* first proc is self */
345       PetscReal *anchor,mdist;
346       PetscInt  fst,j,k,d,cdim = graph->cdim,n = n_shared[ns];
347       PetscInt  point1,point2,point3,point4;
348 
349       /* import coordinates on shared interface */
350       PetscCall(PetscBTMemzero(n,excluded));
351       for (j=0,fst=-1,k=0;j<n;j++) {
352         PetscBool skip = PETSC_FALSE;
353         for (d=0;d<cdim;d++) {
354           PetscReal c = graph->coords[shared[ns][j]*cdim+d];
355           skip = (PetscBool)(skip || c == PETSC_MAX_REAL);
356           wdist[k++] = c;
357         }
358         if (skip) {
359           PetscCall(PetscBTSet(excluded,j));
360         } else if (fst == -1) fst = j;
361       }
362       if (fst == -1) continue;
363 
364       /* the dofs are sorted by global numbering, so each rank starts from the same id
365          and it will detect the same corners from the given set */
366 
367       /* find the farthest point from the starting one */
368       anchor = wdist + fst*cdim;
369       mdist  = -1.0;
370       point1 = fst;
371       for (j=fst;j<n;j++) {
372         PetscReal dist = 0.0;
373 
374         if (PetscUnlikely(PetscBTLookup(excluded,j))) continue;
375         for (d=0;d<cdim;d++) dist += (wdist[j*cdim+d]-anchor[d])*(wdist[j*cdim+d]-anchor[d]);
376         if (dist > mdist) { mdist = dist; point1 = j; }
377       }
378 
379       /* find the farthest point from point1 */
380       anchor = wdist + point1*cdim;
381       mdist  = -1.0;
382       point2 = point1;
383       for (j=fst;j<n;j++) {
384         PetscReal dist = 0.0;
385 
386         if (PetscUnlikely(PetscBTLookup(excluded,j))) continue;
387         for (d=0;d<cdim;d++) dist += (wdist[j*cdim+d]-anchor[d])*(wdist[j*cdim+d]-anchor[d]);
388         if (dist > mdist) { mdist = dist; point2 = j; }
389       }
390 
391       /* find the third point maximizing the triangle area */
392       point3 = point2;
393       if (cdim > 2) {
394         PetscReal a = 0.0;
395 
396         for (d=0;d<cdim;d++) a += (wdist[point1*cdim+d]-wdist[point2*cdim+d])*(wdist[point1*cdim+d]-wdist[point2*cdim+d]);
397         a = PetscSqrtReal(a);
398         mdist = -1.0;
399         for (j=fst;j<n;j++) {
400           PetscReal area,b = 0.0, c = 0.0,s;
401 
402           if (PetscUnlikely(PetscBTLookup(excluded,j))) continue;
403           for (d=0;d<cdim;d++) {
404             b += (wdist[point1*cdim+d]-wdist[j*cdim+d])*(wdist[point1*cdim+d]-wdist[j*cdim+d]);
405             c += (wdist[point2*cdim+d]-wdist[j*cdim+d])*(wdist[point2*cdim+d]-wdist[j*cdim+d]);
406           }
407           b = PetscSqrtReal(b);
408           c = PetscSqrtReal(c);
409           s = 0.5*(a+b+c);
410 
411           /* Heron's formula, area squared */
412           area = s*(s-a)*(s-b)*(s-c);
413           if (area > mdist) { mdist = area; point3 = j; }
414         }
415       }
416 
417       /* find the farthest point from point3 different from point1 and point2 */
418       anchor = wdist + point3*cdim;
419       mdist  = -1.0;
420       point4 = point3;
421       for (j=fst;j<n;j++) {
422         PetscReal dist = 0.0;
423 
424         if (PetscUnlikely(PetscBTLookup(excluded,j)) || j == point1 || j == point2 || j == point3) continue;
425         for (d=0;d<cdim;d++) dist += (wdist[j*cdim+d]-anchor[d])*(wdist[j*cdim+d]-anchor[d]);
426         if (dist > mdist) { mdist = dist; point4 = j; }
427       }
428 
429       PetscCall(PetscBTSet(cornerp,shared[ns][point1]));
430       PetscCall(PetscBTSet(cornerp,shared[ns][point2]));
431       PetscCall(PetscBTSet(cornerp,shared[ns][point3]));
432       PetscCall(PetscBTSet(cornerp,shared[ns][point4]));
433 
434       /* all dofs having the same coordinates will be primal */
435       for (j=fst;j<n;j++) {
436         PetscBool same[] = {PETSC_TRUE,PETSC_TRUE,PETSC_TRUE,PETSC_TRUE};
437 
438         if (PetscUnlikely(PetscBTLookup(excluded,j))) continue;
439         for (d=0;d<cdim;d++) {
440           same[0] = (PetscBool)(same[0] && (PetscAbsReal(wdist[j*cdim + d]-wdist[point1*cdim+d]) < PETSC_SMALL));
441           same[1] = (PetscBool)(same[1] && (PetscAbsReal(wdist[j*cdim + d]-wdist[point2*cdim+d]) < PETSC_SMALL));
442           same[2] = (PetscBool)(same[2] && (PetscAbsReal(wdist[j*cdim + d]-wdist[point3*cdim+d]) < PETSC_SMALL));
443           same[3] = (PetscBool)(same[3] && (PetscAbsReal(wdist[j*cdim + d]-wdist[point4*cdim+d]) < PETSC_SMALL));
444         }
445         if (same[0] || same[1] || same[2] || same[3]) {
446           PetscCall(PetscBTSet(cornerp,shared[ns][j]));
447         }
448       }
449     }
450     PetscCall(PetscBTDestroy(&excluded));
451     PetscCall(PetscFree(wdist));
452     PetscCall(ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared));
453   }
454 
455   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
456   PetscCallMPI(MPI_Comm_size(interface_comm,&size));
457   adapt_interface_reduced = PETSC_FALSE;
458   if (size > 1) {
459     PetscInt i;
460     PetscBool adapt_interface = cornerp ? PETSC_TRUE : PETSC_FALSE;
461     for (i=0;i<graph->n_subsets && !adapt_interface;i++) {
462       /* We are not sure that on a given subset of the local interface,
463          with two connected components, the latters be the same among sharing subdomains */
464       if (graph->subset_ncc[i] > 1) adapt_interface = PETSC_TRUE;
465     }
466     PetscCall(MPIU_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_BOOL,MPI_LOR,interface_comm));
467   }
468 
469   if (graph->n_subsets && adapt_interface_reduced) {
470     PetscBT     subset_cc_adapt;
471     MPI_Request *send_requests,*recv_requests;
472     PetscInt    *send_buffer,*recv_buffer;
473     PetscInt    sum_requests,start_of_recv,start_of_send;
474     PetscInt    *cum_recv_counts;
475     PetscInt    *labels;
476     PetscInt    ncc,cum_queue,mss,mns,j,k,s;
477     PetscInt    **refine_buffer=NULL,*private_labels = NULL;
478     PetscBool   *subset_has_corn,*recv_buffer_bool,*send_buffer_bool;
479 
480     PetscCall(PetscCalloc1(graph->n_subsets,&subset_has_corn));
481     if (cornerp) {
482       for (i=0;i<graph->n_subsets;i++) {
483         for (j=0;j<graph->subset_size[i];j++) {
484           if (PetscBTLookup(cornerp,graph->subset_idxs[i][j])) {
485             subset_has_corn[i] = PETSC_TRUE;
486             break;
487           }
488         }
489       }
490     }
491     PetscCall(PetscMalloc1(graph->nvtxs,&labels));
492     PetscCall(PetscArrayzero(labels,graph->nvtxs));
493     for (i=0,k=0;i<graph->ncc;i++) {
494       PetscInt s = 1;
495       for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
496         if (cornerp && PetscBTLookup(cornerp,graph->queue[j])) {
497           labels[graph->queue[j]] = k+s;
498           s += 1;
499         } else {
500           labels[graph->queue[j]] = k;
501         }
502       }
503       k += s;
504     }
505 
506     /* allocate some space */
507     PetscCall(PetscMalloc1(graph->n_subsets+1,&cum_recv_counts));
508     PetscCall(PetscArrayzero(cum_recv_counts,graph->n_subsets+1));
509 
510     /* first count how many neighbours per connected component I will receive from */
511     cum_recv_counts[0] = 0;
512     for (i=0;i<graph->n_subsets;i++) cum_recv_counts[i+1] = cum_recv_counts[i]+graph->count[graph->subset_idxs[i][0]];
513     PetscCall(PetscMalloc1(graph->n_subsets,&send_buffer_bool));
514     PetscCall(PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_buffer_bool));
515     PetscCall(PetscMalloc2(cum_recv_counts[graph->n_subsets],&send_requests,cum_recv_counts[graph->n_subsets],&recv_requests));
516     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
517       send_requests[i] = MPI_REQUEST_NULL;
518       recv_requests[i] = MPI_REQUEST_NULL;
519     }
520 
521     /* exchange with my neighbours the number of my connected components on the subset of interface */
522     sum_requests = 0;
523     for (i=0;i<graph->n_subsets;i++) {
524       send_buffer_bool[i] = (PetscBool)(graph->subset_ncc[i] > 1 || subset_has_corn[i]);
525     }
526     for (i=0;i<graph->n_subsets;i++) {
527       PetscMPIInt neigh,tag;
528       PetscInt    count,*neighs;
529 
530       count  = graph->count[graph->subset_idxs[i][0]];
531       neighs = graph->neighbours_set[graph->subset_idxs[i][0]];
532       PetscCall(PetscMPIIntCast(2*graph->subset_ref_node[i],&tag));
533       for (k=0;k<count;k++) {
534 
535         PetscCall(PetscMPIIntCast(neighs[k],&neigh));
536         PetscCallMPI(MPI_Isend(send_buffer_bool + i,           1,MPIU_BOOL,neigh,tag,interface_comm,&send_requests[sum_requests]));
537         PetscCallMPI(MPI_Irecv(recv_buffer_bool + sum_requests,1,MPIU_BOOL,neigh,tag,interface_comm,&recv_requests[sum_requests]));
538         sum_requests++;
539       }
540     }
541     PetscCallMPI(MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE));
542     PetscCallMPI(MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE));
543 
544     /* determine the subsets I have to adapt (those having more than 1 cc) */
545     PetscCall(PetscBTCreate(graph->n_subsets,&subset_cc_adapt));
546     PetscCall(PetscBTMemzero(graph->n_subsets,subset_cc_adapt));
547     for (i=0;i<graph->n_subsets;i++) {
548       if (graph->subset_ncc[i] > 1 || subset_has_corn[i]) {
549         PetscCall(PetscBTSet(subset_cc_adapt,i));
550         continue;
551       }
552       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++) {
553          if (recv_buffer_bool[j]) {
554           PetscCall(PetscBTSet(subset_cc_adapt,i));
555           break;
556         }
557       }
558     }
559     PetscCall(PetscFree(send_buffer_bool));
560     PetscCall(PetscFree(recv_buffer_bool));
561     PetscCall(PetscFree(subset_has_corn));
562 
563     /* determine send/recv buffers sizes */
564     j = 0;
565     mss = 0;
566     for (i=0;i<graph->n_subsets;i++) {
567       if (PetscBTLookup(subset_cc_adapt,i)) {
568         j  += graph->subset_size[i];
569         mss = PetscMax(graph->subset_size[i],mss);
570       }
571     }
572     k = 0;
573     mns = 0;
574     for (i=0;i<graph->n_subsets;i++) {
575       if (PetscBTLookup(subset_cc_adapt,i)) {
576         k  += (cum_recv_counts[i+1]-cum_recv_counts[i])*graph->subset_size[i];
577         mns = PetscMax(cum_recv_counts[i+1]-cum_recv_counts[i],mns);
578       }
579     }
580     PetscCall(PetscMalloc2(j,&send_buffer,k,&recv_buffer));
581 
582     /* fill send buffer (order matters: subset_idxs ordered by global ordering) */
583     j = 0;
584     for (i=0;i<graph->n_subsets;i++)
585       if (PetscBTLookup(subset_cc_adapt,i))
586         for (k=0;k<graph->subset_size[i];k++)
587           send_buffer[j++] = labels[graph->subset_idxs[i][k]];
588 
589     /* now exchange the data */
590     start_of_recv = 0;
591     start_of_send = 0;
592     sum_requests  = 0;
593     for (i=0;i<graph->n_subsets;i++) {
594       if (PetscBTLookup(subset_cc_adapt,i)) {
595         PetscMPIInt neigh,tag;
596         PetscInt    size_of_send = graph->subset_size[i];
597 
598         j    = graph->subset_idxs[i][0];
599         PetscCall(PetscMPIIntCast(2*graph->subset_ref_node[i]+1,&tag));
600         for (k=0;k<graph->count[j];k++) {
601           PetscCall(PetscMPIIntCast(graph->neighbours_set[j][k],&neigh));
602           PetscCallMPI(MPI_Isend(&send_buffer[start_of_send],size_of_send,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]));
603           PetscCallMPI(MPI_Irecv(&recv_buffer[start_of_recv],size_of_send,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]));
604           start_of_recv += size_of_send;
605           sum_requests++;
606         }
607         start_of_send += size_of_send;
608       }
609     }
610     PetscCallMPI(MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE));
611 
612     /* refine connected components */
613     start_of_recv = 0;
614     /* allocate some temporary space */
615     if (mss) {
616       PetscCall(PetscMalloc1(mss,&refine_buffer));
617       PetscCall(PetscMalloc2(mss*(mns+1),&refine_buffer[0],mss,&private_labels));
618     }
619     ncc = 0;
620     cum_queue = 0;
621     graph->cptr[0] = 0;
622     for (i=0;i<graph->n_subsets;i++) {
623       if (PetscBTLookup(subset_cc_adapt,i)) {
624         PetscInt subset_counter = 0;
625         PetscInt sharingprocs = cum_recv_counts[i+1]-cum_recv_counts[i]+1; /* count myself */
626         PetscInt buffer_size = graph->subset_size[i];
627 
628         /* compute pointers */
629         for (j=1;j<buffer_size;j++) refine_buffer[j] = refine_buffer[j-1] + sharingprocs;
630         /* analyze contributions from subdomains that share the i-th subset
631            The structure of refine_buffer is suitable to find intersections of ccs among sharingprocs.
632            supposing the current subset is shared by 3 processes and has dimension 5 with global dofs 0,1,2,3,4 (local 0,4,3,1,2)
633            sharing procs connected components:
634              neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
635              neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
636              neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
637            refine_buffer will be filled as:
638              [ 4, 3, 1;
639                4, 2, 1;
640                7, 2, 6;
641                4, 3, 5;
642                7, 2, 6; ];
643            The connected components in local ordering are [0], [1], [2 3], [4] */
644         /* fill temp_buffer */
645         for (k=0;k<buffer_size;k++) refine_buffer[k][0] = labels[graph->subset_idxs[i][k]];
646         for (j=0;j<sharingprocs-1;j++) {
647           for (k=0;k<buffer_size;k++) refine_buffer[k][j+1] = recv_buffer[start_of_recv+k];
648           start_of_recv += buffer_size;
649         }
650         PetscCall(PetscArrayzero(private_labels,buffer_size));
651         for (j=0;j<buffer_size;j++) {
652           if (!private_labels[j]) { /* found a new cc  */
653             PetscBool same_set;
654 
655             graph->cptr[ncc] = cum_queue;
656             ncc++;
657             subset_counter++;
658             private_labels[j] = subset_counter;
659             graph->queue[cum_queue++] = graph->subset_idxs[i][j];
660             for (k=j+1;k<buffer_size;k++) { /* check for other nodes in new cc */
661               same_set = PETSC_TRUE;
662               for (s=0;s<sharingprocs;s++) {
663                 if (refine_buffer[j][s] != refine_buffer[k][s]) {
664                   same_set = PETSC_FALSE;
665                   break;
666                 }
667               }
668               if (same_set) {
669                 private_labels[k] = subset_counter;
670                 graph->queue[cum_queue++] = graph->subset_idxs[i][k];
671               }
672             }
673           }
674         }
675         graph->cptr[ncc]     = cum_queue;
676         graph->subset_ncc[i] = subset_counter;
677         graph->queue_sorted  = PETSC_FALSE;
678       } else { /* this subset does not need to be adapted */
679         PetscCall(PetscArraycpy(graph->queue+cum_queue,graph->subset_idxs[i],graph->subset_size[i]));
680         ncc++;
681         cum_queue += graph->subset_size[i];
682         graph->cptr[ncc] = cum_queue;
683       }
684     }
685     graph->cptr[ncc] = cum_queue;
686     graph->ncc       = ncc;
687     if (mss) {
688       PetscCall(PetscFree2(refine_buffer[0],private_labels));
689       PetscCall(PetscFree(refine_buffer));
690     }
691     PetscCall(PetscFree(labels));
692     PetscCallMPI(MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE));
693     PetscCall(PetscFree2(send_requests,recv_requests));
694     PetscCall(PetscFree2(send_buffer,recv_buffer));
695     PetscCall(PetscFree(cum_recv_counts));
696     PetscCall(PetscBTDestroy(&subset_cc_adapt));
697   }
698   PetscCall(PetscBTDestroy(&cornerp));
699 
700   /* Determine if we are in 2D or 3D */
701   if (!graph->twodimset) {
702     PetscBool twodim = PETSC_TRUE;
703     for (i=0;i<graph->ncc;i++) {
704       PetscInt repdof = graph->queue[graph->cptr[i]];
705       PetscInt ccsize = graph->cptr[i+1]-graph->cptr[i];
706       if (graph->count[repdof] > 1 && ccsize > graph->custom_minimal_size) {
707         twodim = PETSC_FALSE;
708         break;
709       }
710     }
711     PetscCall(MPIU_Allreduce(&twodim,&graph->twodim,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)graph->l2gmap)));
712     graph->twodimset = PETSC_TRUE;
713   }
714   PetscFunctionReturn(0);
715 }
716 
717 static inline PetscErrorCode PCBDDCGraphComputeCC_Private(PCBDDCGraph graph,PetscInt pid,PetscInt* queue_tip,PetscInt n_prev,PetscInt* n_added)
718 {
719   PetscInt       i,j,n;
720   PetscInt       *xadj = graph->xadj,*adjncy = graph->adjncy;
721   PetscBT        touched = graph->touched;
722   PetscBool      havecsr = (PetscBool)(!!xadj);
723   PetscBool      havesubs = (PetscBool)(!!graph->n_local_subs);
724 
725   PetscFunctionBegin;
726   n = 0;
727   if (havecsr && !havesubs) {
728     for (i=-n_prev;i<0;i++) {
729       PetscInt start_dof = queue_tip[i];
730       /* we assume that if a dof has a size 1 adjacency list and the corresponding entry is negative, it is connected to all dofs */
731       if (xadj[start_dof+1]-xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
732         for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
733           PetscInt dof = graph->subset_idxs[pid-1][j];
734           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
735             PetscCall(PetscBTSet(touched,dof));
736             queue_tip[n] = dof;
737             n++;
738           }
739         }
740       } else {
741         for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
742           PetscInt dof = adjncy[j];
743           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
744             PetscCall(PetscBTSet(touched,dof));
745             queue_tip[n] = dof;
746             n++;
747           }
748         }
749       }
750     }
751   } else if (havecsr && havesubs) {
752     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
753     for (i=-n_prev;i<0;i++) {
754       PetscInt start_dof = queue_tip[i];
755       /* we assume that if a dof has a size 1 adjacency list and the corresponding entry is negative, it is connected to all dofs belonging to the local sub */
756       if (xadj[start_dof+1]-xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
757         for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
758           PetscInt dof = graph->subset_idxs[pid-1][j];
759           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
760             PetscCall(PetscBTSet(touched,dof));
761             queue_tip[n] = dof;
762             n++;
763           }
764         }
765       } else {
766         for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
767           PetscInt dof = adjncy[j];
768           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
769             PetscCall(PetscBTSet(touched,dof));
770             queue_tip[n] = dof;
771             n++;
772           }
773         }
774       }
775     }
776   } else if (havesubs) { /* sub info only */
777     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
778     for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
779       PetscInt dof = graph->subset_idxs[pid-1][j];
780       if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
781         PetscCall(PetscBTSet(touched,dof));
782         queue_tip[n] = dof;
783         n++;
784       }
785     }
786   } else {
787     for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
788       PetscInt dof = graph->subset_idxs[pid-1][j];
789       if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
790         PetscCall(PetscBTSet(touched,dof));
791         queue_tip[n] = dof;
792         n++;
793       }
794     }
795   }
796   *n_added = n;
797   PetscFunctionReturn(0);
798 }
799 
800 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
801 {
802   PetscInt       ncc,cum_queue,n;
803   PetscMPIInt    commsize;
804 
805   PetscFunctionBegin;
806   PetscCheck(graph->setupcalled,PetscObjectComm((PetscObject)graph->l2gmap),PETSC_ERR_ORDER,"PCBDDCGraphSetUp should be called first");
807   /* quiet return if there isn't any local info */
808   if (!graph->xadj && !graph->n_local_subs) {
809     PetscFunctionReturn(0);
810   }
811 
812   /* reset any previous search of connected components */
813   PetscCall(PetscBTMemzero(graph->nvtxs,graph->touched));
814   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&commsize));
815   if (commsize > graph->commsizelimit) {
816     PetscInt i;
817     for (i=0;i<graph->nvtxs;i++) {
818       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
819         PetscCall(PetscBTSet(graph->touched,i));
820       }
821     }
822   }
823 
824   /* begin search for connected components */
825   cum_queue = 0;
826   ncc = 0;
827   for (n=0;n<graph->n_subsets;n++) {
828     PetscInt pid = n+1;  /* partition labeled by 0 is discarded */
829     PetscInt found = 0,prev = 0,first = 0,ncc_pid = 0;
830     while (found != graph->subset_size[n]) {
831       PetscInt added = 0;
832       if (!prev) { /* search for new starting dof */
833         while (PetscBTLookup(graph->touched,graph->subset_idxs[n][first])) first++;
834         PetscCall(PetscBTSet(graph->touched,graph->subset_idxs[n][first]));
835         graph->queue[cum_queue] = graph->subset_idxs[n][first];
836         graph->cptr[ncc] = cum_queue;
837         prev = 1;
838         cum_queue++;
839         found++;
840         ncc_pid++;
841         ncc++;
842       }
843       PetscCall(PCBDDCGraphComputeCC_Private(graph,pid,graph->queue + cum_queue,prev,&added));
844       if (!added) {
845         graph->subset_ncc[n] = ncc_pid;
846         graph->cptr[ncc] = cum_queue;
847       }
848       prev = added;
849       found += added;
850       cum_queue += added;
851       if (added && found == graph->subset_size[n]) {
852         graph->subset_ncc[n] = ncc_pid;
853         graph->cptr[ncc] = cum_queue;
854       }
855     }
856   }
857   graph->ncc = ncc;
858   graph->queue_sorted = PETSC_FALSE;
859   PetscFunctionReturn(0);
860 }
861 
862 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
863 {
864   IS             subset,subset_n;
865   MPI_Comm       comm;
866   const PetscInt *is_indices;
867   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global;
868   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
869   PetscMPIInt    commsize;
870   PetscBool      same_set,mirrors_found;
871 
872   PetscFunctionBegin;
873   PetscValidLogicalCollectiveInt(graph->l2gmap,custom_minimal_size,2);
874   if (neumann_is) {
875     PetscValidHeaderSpecific(neumann_is,IS_CLASSID,3);
876     PetscCheckSameComm(graph->l2gmap,1,neumann_is,3);
877   }
878   graph->has_dirichlet = PETSC_FALSE;
879   if (dirichlet_is) {
880     PetscValidHeaderSpecific(dirichlet_is,IS_CLASSID,4);
881     PetscCheckSameComm(graph->l2gmap,1,dirichlet_is,4);
882     graph->has_dirichlet = PETSC_TRUE;
883   }
884   PetscValidLogicalCollectiveInt(graph->l2gmap,n_ISForDofs,5);
885   for (i=0;i<n_ISForDofs;i++) {
886     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,6);
887     PetscCheckSameComm(graph->l2gmap,1,ISForDofs[i],6);
888   }
889   if (custom_primal_vertices) {
890     PetscValidHeaderSpecific(custom_primal_vertices,IS_CLASSID,7);
891     PetscCheckSameComm(graph->l2gmap,1,custom_primal_vertices,7);
892   }
893   PetscCall(PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm));
894   PetscCallMPI(MPI_Comm_size(comm,&commsize));
895 
896   /* custom_minimal_size */
897   graph->custom_minimal_size = custom_minimal_size;
898   /* get info l2gmap and allocate work vectors  */
899   PetscCall(ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared));
900   /* check if we have any local periodic nodes (periodic BCs) */
901   mirrors_found = PETSC_FALSE;
902   if (graph->nvtxs && n_neigh) {
903     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
904     for (i=0; i<n_shared[0]; i++) {
905       if (graph->count[shared[0][i]] > 1) {
906         mirrors_found = PETSC_TRUE;
907         break;
908       }
909     }
910   }
911   /* compute local mirrors (if any) */
912   if (mirrors_found) {
913     IS       to,from;
914     PetscInt *local_indices,*global_indices;
915 
916     PetscCall(ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to));
917     PetscCall(ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from));
918     /* get arrays of local and global indices */
919     PetscCall(PetscMalloc1(graph->nvtxs,&local_indices));
920     PetscCall(ISGetIndices(to,(const PetscInt**)&is_indices));
921     PetscCall(PetscArraycpy(local_indices,is_indices,graph->nvtxs));
922     PetscCall(ISRestoreIndices(to,(const PetscInt**)&is_indices));
923     PetscCall(PetscMalloc1(graph->nvtxs,&global_indices));
924     PetscCall(ISGetIndices(from,(const PetscInt**)&is_indices));
925     PetscCall(PetscArraycpy(global_indices,is_indices,graph->nvtxs));
926     PetscCall(ISRestoreIndices(from,(const PetscInt**)&is_indices));
927     /* allocate space for mirrors */
928     PetscCall(PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set));
929     PetscCall(PetscArrayzero(graph->mirrors,graph->nvtxs));
930     graph->mirrors_set[0] = NULL;
931 
932     k=0;
933     for (i=0;i<n_shared[0];i++) {
934       j=shared[0][i];
935       if (graph->count[j] > 1) {
936         graph->mirrors[j]++;
937         k++;
938       }
939     }
940     /* allocate space for set of mirrors */
941     PetscCall(PetscMalloc1(k,&graph->mirrors_set[0]));
942     for (i=1;i<graph->nvtxs;i++)
943       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
944 
945     /* fill arrays */
946     PetscCall(PetscArrayzero(graph->mirrors,graph->nvtxs));
947     for (j=0;j<n_shared[0];j++) {
948       i=shared[0][j];
949       if (graph->count[i] > 1)
950         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
951     }
952     PetscCall(PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices));
953     for (i=0;i<graph->nvtxs;i++) {
954       if (graph->mirrors[i] > 0) {
955         PetscCall(PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k));
956         j = global_indices[k];
957         while (k > 0 && global_indices[k-1] == j) k--;
958         for (j=0;j<graph->mirrors[i];j++) {
959           graph->mirrors_set[i][j]=local_indices[k+j];
960         }
961         PetscCall(PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]));
962       }
963     }
964     PetscCall(PetscFree(local_indices));
965     PetscCall(PetscFree(global_indices));
966     PetscCall(ISDestroy(&to));
967     PetscCall(ISDestroy(&from));
968   }
969   PetscCall(PetscArrayzero(graph->count,graph->nvtxs));
970 
971   /* Count total number of neigh per node */
972   k = 0;
973   for (i=1;i<n_neigh;i++) {
974     k += n_shared[i];
975     for (j=0;j<n_shared[i];j++) {
976       graph->count[shared[i][j]] += 1;
977     }
978   }
979   /* Allocate space for storing the set of neighbours for each node */
980   if (graph->nvtxs) {
981     PetscCall(PetscMalloc1(k,&graph->neighbours_set[0]));
982   }
983   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
984     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
985   }
986   /* Get information for sharing subdomains */
987   PetscCall(PetscArrayzero(graph->count,graph->nvtxs));
988   for (i=1;i<n_neigh;i++) { /* dont count myself */
989     s = n_shared[i];
990     for (j=0;j<s;j++) {
991       k = shared[i][j];
992       graph->neighbours_set[k][graph->count[k]] = neigh[i];
993       graph->count[k] += 1;
994     }
995   }
996   /* sort set of sharing subdomains */
997   for (i=0;i<graph->nvtxs;i++) {
998     PetscCall(PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]));
999   }
1000   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
1001   PetscCall(ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared));
1002 
1003   /*
1004      Get info for dofs splitting
1005      User can specify just a subset; an additional field is considered as a complementary field
1006   */
1007   for (i=0,k=0;i<n_ISForDofs;i++) {
1008     PetscInt bs;
1009 
1010     PetscCall(ISGetBlockSize(ISForDofs[i],&bs));
1011     k   += bs;
1012   }
1013   for (i=0;i<graph->nvtxs;i++) graph->which_dof[i] = k; /* by default a dof belongs to the complement set */
1014   for (i=0,k=0;i<n_ISForDofs;i++) {
1015     PetscInt bs;
1016 
1017     PetscCall(ISGetLocalSize(ISForDofs[i],&is_size));
1018     PetscCall(ISGetBlockSize(ISForDofs[i],&bs));
1019     PetscCall(ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices));
1020     for (j=0;j<is_size/bs;j++) {
1021       PetscInt b;
1022 
1023       for (b=0;b<bs;b++) {
1024         PetscInt jj = bs*j + b;
1025 
1026         if (is_indices[jj] > -1 && is_indices[jj] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
1027           graph->which_dof[is_indices[jj]] = k+b;
1028         }
1029       }
1030     }
1031     PetscCall(ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices));
1032     k   += bs;
1033   }
1034 
1035   /* Take into account Neumann nodes */
1036   if (neumann_is) {
1037     PetscCall(ISGetLocalSize(neumann_is,&is_size));
1038     PetscCall(ISGetIndices(neumann_is,(const PetscInt**)&is_indices));
1039     for (i=0;i<is_size;i++) {
1040       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
1041         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_NEUMANN_MARK;
1042       }
1043     }
1044     PetscCall(ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices));
1045   }
1046   /* Take into account Dirichlet nodes (they overwrite any neumann boundary mark previously set) */
1047   if (dirichlet_is) {
1048     PetscCall(ISGetLocalSize(dirichlet_is,&is_size));
1049     PetscCall(ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices));
1050     for (i=0;i<is_size;i++) {
1051       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
1052         if (commsize > graph->commsizelimit) { /* dirichlet nodes treated as internal */
1053           PetscCall(PetscBTSet(graph->touched,is_indices[i]));
1054           graph->subset[is_indices[i]] = 0;
1055         }
1056         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_DIRICHLET_MARK;
1057       }
1058     }
1059     PetscCall(ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices));
1060   }
1061   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
1062   if (graph->mirrors) {
1063     for (i=0;i<graph->nvtxs;i++)
1064       if (graph->mirrors[i])
1065         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
1066 
1067     if (graph->xadj) {
1068       PetscInt *new_xadj,*new_adjncy;
1069       /* sort CSR graph */
1070       for (i=0;i<graph->nvtxs;i++) {
1071         PetscCall(PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]));
1072       }
1073       /* adapt local CSR graph in case of local periodicity */
1074       k = 0;
1075       for (i=0;i<graph->nvtxs;i++)
1076         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
1077           k += graph->mirrors[graph->adjncy[j]];
1078 
1079       PetscCall(PetscMalloc1(graph->nvtxs+1,&new_xadj));
1080       PetscCall(PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy));
1081       new_xadj[0] = 0;
1082       for (i=0;i<graph->nvtxs;i++) {
1083         k = graph->xadj[i+1]-graph->xadj[i];
1084         PetscCall(PetscArraycpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k));
1085         new_xadj[i+1] = new_xadj[i]+k;
1086         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
1087           k = graph->mirrors[graph->adjncy[j]];
1088           PetscCall(PetscArraycpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k));
1089           new_xadj[i+1] += k;
1090         }
1091         k = new_xadj[i+1]-new_xadj[i];
1092         PetscCall(PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]));
1093         new_xadj[i+1] = new_xadj[i]+k;
1094       }
1095       /* set new CSR into graph */
1096       PetscCall(PetscFree(graph->xadj));
1097       PetscCall(PetscFree(graph->adjncy));
1098       graph->xadj = new_xadj;
1099       graph->adjncy = new_adjncy;
1100     }
1101   }
1102 
1103   /* mark special nodes (if any) -> each will become a single node equivalence class */
1104   if (custom_primal_vertices) {
1105     PetscCall(ISGetLocalSize(custom_primal_vertices,&is_size));
1106     PetscCall(ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices));
1107     for (i=0,j=0;i<is_size;i++) {
1108       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs  && graph->special_dof[is_indices[i]] != PCBDDCGRAPH_DIRICHLET_MARK) { /* out of bounds indices (if any) are skipped */
1109         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_SPECIAL_MARK-j;
1110         j++;
1111       }
1112     }
1113     PetscCall(ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices));
1114   }
1115 
1116   /* mark interior nodes (if commsize > graph->commsizelimit) as touched and belonging to partition number 0 */
1117   if (commsize > graph->commsizelimit) {
1118     for (i=0;i<graph->nvtxs;i++) {
1119       if (!graph->count[i]) {
1120         PetscCall(PetscBTSet(graph->touched,i));
1121         graph->subset[i] = 0;
1122       }
1123     }
1124   }
1125 
1126   /* init graph structure and compute default subsets */
1127   nodes_touched = 0;
1128   for (i=0;i<graph->nvtxs;i++) {
1129     if (PetscBTLookup(graph->touched,i)) {
1130       nodes_touched++;
1131     }
1132   }
1133   i = 0;
1134   graph->ncc = 0;
1135   total_counts = 0;
1136 
1137   /* allocated space for queues */
1138   if (commsize == graph->commsizelimit) {
1139     PetscCall(PetscMalloc2(graph->nvtxs+1,&graph->cptr,graph->nvtxs,&graph->queue));
1140   } else {
1141     PetscInt nused = graph->nvtxs - nodes_touched;
1142     PetscCall(PetscMalloc2(nused+1,&graph->cptr,nused,&graph->queue));
1143   }
1144 
1145   while (nodes_touched<graph->nvtxs) {
1146     /*  find first untouched node in local ordering */
1147     while (PetscBTLookup(graph->touched,i)) i++;
1148     PetscCall(PetscBTSet(graph->touched,i));
1149     graph->subset[i] = graph->ncc+1;
1150     graph->cptr[graph->ncc] = total_counts;
1151     graph->queue[total_counts] = i;
1152     total_counts++;
1153     nodes_touched++;
1154     /* now find all other nodes having the same set of sharing subdomains */
1155     for (j=i+1;j<graph->nvtxs;j++) {
1156       /* check for same number of sharing subdomains, dof number and same special mark */
1157       if (!PetscBTLookup(graph->touched,j) && graph->count[i] == graph->count[j] && graph->which_dof[i] == graph->which_dof[j] && graph->special_dof[i] == graph->special_dof[j]) {
1158         /* check for same set of sharing subdomains */
1159         same_set = PETSC_TRUE;
1160         for (k=0;k<graph->count[j];k++) {
1161           if (graph->neighbours_set[i][k] != graph->neighbours_set[j][k]) {
1162             same_set = PETSC_FALSE;
1163           }
1164         }
1165         /* I have found a friend of mine */
1166         if (same_set) {
1167           PetscCall(PetscBTSet(graph->touched,j));
1168           graph->subset[j] = graph->ncc+1;
1169           nodes_touched++;
1170           graph->queue[total_counts] = j;
1171           total_counts++;
1172         }
1173       }
1174     }
1175     graph->ncc++;
1176   }
1177   /* set default number of subsets (at this point no info on csr and/or local_subs has been taken into account, so n_subsets = ncc */
1178   graph->n_subsets = graph->ncc;
1179   PetscCall(PetscMalloc1(graph->n_subsets,&graph->subset_ncc));
1180   for (i=0;i<graph->n_subsets;i++) {
1181     graph->subset_ncc[i] = 1;
1182   }
1183   /* final pointer */
1184   graph->cptr[graph->ncc] = total_counts;
1185 
1186   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each connected component */
1187   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
1188   PetscCall(PetscMalloc1(graph->ncc,&graph->subset_ref_node));
1189   PetscCall(PetscMalloc1(graph->cptr[graph->ncc],&queue_global));
1190   PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global));
1191   for (j=0;j<graph->ncc;j++) {
1192     PetscCall(PetscSortIntWithArray(graph->cptr[j+1]-graph->cptr[j],&queue_global[graph->cptr[j]],&graph->queue[graph->cptr[j]]));
1193     graph->subset_ref_node[j] = graph->queue[graph->cptr[j]];
1194   }
1195   PetscCall(PetscFree(queue_global));
1196   graph->queue_sorted = PETSC_TRUE;
1197 
1198   /* save information on subsets (needed when analyzing the connected components) */
1199   if (graph->ncc) {
1200     PetscCall(PetscMalloc2(graph->ncc,&graph->subset_size,graph->ncc,&graph->subset_idxs));
1201     PetscCall(PetscMalloc1(graph->cptr[graph->ncc],&graph->subset_idxs[0]));
1202     PetscCall(PetscArrayzero(graph->subset_idxs[0],graph->cptr[graph->ncc]));
1203     for (j=1;j<graph->ncc;j++) {
1204       graph->subset_size[j-1] = graph->cptr[j] - graph->cptr[j-1];
1205       graph->subset_idxs[j] = graph->subset_idxs[j-1] + graph->subset_size[j-1];
1206     }
1207     graph->subset_size[graph->ncc-1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc-1];
1208     PetscCall(PetscArraycpy(graph->subset_idxs[0],graph->queue,graph->cptr[graph->ncc]));
1209   }
1210 
1211   /* renumber reference nodes */
1212   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->ncc,graph->subset_ref_node,PETSC_COPY_VALUES,&subset_n));
1213   PetscCall(ISLocalToGlobalMappingApplyIS(graph->l2gmap,subset_n,&subset));
1214   PetscCall(ISDestroy(&subset_n));
1215   PetscCall(ISRenumber(subset,NULL,NULL,&subset_n));
1216   PetscCall(ISDestroy(&subset));
1217   PetscCall(ISGetLocalSize(subset_n,&k));
1218   PetscCheck(k == graph->ncc,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %" PetscInt_FMT " != %" PetscInt_FMT,k,graph->ncc);
1219   PetscCall(ISGetIndices(subset_n,&is_indices));
1220   PetscCall(PetscArraycpy(graph->subset_ref_node,is_indices,graph->ncc));
1221   PetscCall(ISRestoreIndices(subset_n,&is_indices));
1222   PetscCall(ISDestroy(&subset_n));
1223 
1224   /* free workspace */
1225   graph->setupcalled = PETSC_TRUE;
1226   PetscFunctionReturn(0);
1227 }
1228 
1229 PetscErrorCode PCBDDCGraphResetCoords(PCBDDCGraph graph)
1230 {
1231   PetscFunctionBegin;
1232   if (!graph) PetscFunctionReturn(0);
1233   PetscCall(PetscFree(graph->coords));
1234   graph->cdim  = 0;
1235   graph->cnloc = 0;
1236   graph->cloc  = PETSC_FALSE;
1237   PetscFunctionReturn(0);
1238 }
1239 
1240 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1241 {
1242   PetscFunctionBegin;
1243   if (!graph) PetscFunctionReturn(0);
1244   if (graph->freecsr) {
1245     PetscCall(PetscFree(graph->xadj));
1246     PetscCall(PetscFree(graph->adjncy));
1247   } else {
1248     graph->xadj = NULL;
1249     graph->adjncy = NULL;
1250   }
1251   graph->freecsr = PETSC_FALSE;
1252   graph->nvtxs_csr = 0;
1253   PetscFunctionReturn(0);
1254 }
1255 
1256 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1257 {
1258   PetscFunctionBegin;
1259   if (!graph) PetscFunctionReturn(0);
1260   PetscCall(ISLocalToGlobalMappingDestroy(&graph->l2gmap));
1261   PetscCall(PetscFree(graph->subset_ncc));
1262   PetscCall(PetscFree(graph->subset_ref_node));
1263   if (graph->nvtxs) {
1264     PetscCall(PetscFree(graph->neighbours_set[0]));
1265   }
1266   PetscCall(PetscBTDestroy(&graph->touched));
1267   PetscCall(PetscFree5(graph->count,graph->neighbours_set,graph->subset,graph->which_dof,graph->special_dof));
1268   PetscCall(PetscFree2(graph->cptr,graph->queue));
1269   if (graph->mirrors) {
1270     PetscCall(PetscFree(graph->mirrors_set[0]));
1271   }
1272   PetscCall(PetscFree2(graph->mirrors,graph->mirrors_set));
1273   if (graph->subset_idxs) {
1274     PetscCall(PetscFree(graph->subset_idxs[0]));
1275   }
1276   PetscCall(PetscFree2(graph->subset_size,graph->subset_idxs));
1277   PetscCall(ISDestroy(&graph->dirdofs));
1278   PetscCall(ISDestroy(&graph->dirdofsB));
1279   if (graph->n_local_subs) {
1280     PetscCall(PetscFree(graph->local_subs));
1281   }
1282   graph->has_dirichlet       = PETSC_FALSE;
1283   graph->twodimset           = PETSC_FALSE;
1284   graph->twodim              = PETSC_FALSE;
1285   graph->nvtxs               = 0;
1286   graph->nvtxs_global        = 0;
1287   graph->n_subsets           = 0;
1288   graph->custom_minimal_size = 1;
1289   graph->n_local_subs        = 0;
1290   graph->maxcount            = PETSC_MAX_INT;
1291   graph->setupcalled         = PETSC_FALSE;
1292   PetscFunctionReturn(0);
1293 }
1294 
1295 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N, PetscInt maxcount)
1296 {
1297   PetscInt       n;
1298 
1299   PetscFunctionBegin;
1300   PetscValidPointer(graph,1);
1301   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1302   PetscValidLogicalCollectiveInt(l2gmap,N,3);
1303   PetscValidLogicalCollectiveInt(l2gmap,maxcount,4);
1304   /* raise an error if already allocated */
1305   PetscCheck(!graph->nvtxs_global,PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1306   /* set number of vertices */
1307   PetscCall(PetscObjectReference((PetscObject)l2gmap));
1308   graph->l2gmap = l2gmap;
1309   PetscCall(ISLocalToGlobalMappingGetSize(l2gmap,&n));
1310   graph->nvtxs = n;
1311   graph->nvtxs_global = N;
1312   /* allocate used space */
1313   PetscCall(PetscBTCreate(graph->nvtxs,&graph->touched));
1314   PetscCall(PetscMalloc5(graph->nvtxs,&graph->count,graph->nvtxs,&graph->neighbours_set,graph->nvtxs,&graph->subset,graph->nvtxs,&graph->which_dof,graph->nvtxs,&graph->special_dof));
1315   /* zeroes memory */
1316   PetscCall(PetscArrayzero(graph->count,graph->nvtxs));
1317   PetscCall(PetscArrayzero(graph->subset,graph->nvtxs));
1318   /* use -1 as a default value for which_dof array */
1319   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1320   PetscCall(PetscArrayzero(graph->special_dof,graph->nvtxs));
1321   /* zeroes first pointer to neighbour set */
1322   if (graph->nvtxs) {
1323     graph->neighbours_set[0] = NULL;
1324   }
1325   /* zeroes workspace for values of ncc */
1326   graph->subset_ncc = NULL;
1327   graph->subset_ref_node = NULL;
1328   /* maxcount for cc */
1329   graph->maxcount = maxcount;
1330   PetscFunctionReturn(0);
1331 }
1332 
1333 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1334 {
1335   PetscFunctionBegin;
1336   PetscCall(PCBDDCGraphResetCSR(*graph));
1337   PetscCall(PCBDDCGraphResetCoords(*graph));
1338   PetscCall(PCBDDCGraphReset(*graph));
1339   PetscCall(PetscFree(*graph));
1340   PetscFunctionReturn(0);
1341 }
1342 
1343 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1344 {
1345   PCBDDCGraph    new_graph;
1346 
1347   PetscFunctionBegin;
1348   PetscCall(PetscNew(&new_graph));
1349   new_graph->custom_minimal_size = 1;
1350   new_graph->commsizelimit = 1;
1351   *graph = new_graph;
1352   PetscFunctionReturn(0);
1353 }
1354