xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision d5b43468fb8780a8feea140ccd6fa3e6a50411cc)
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) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Max count %" PetscInt_FMT "\n", graph->maxcount));
86   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Topological two dim? %s (set %s)\n", PetscBools[graph->twodim], PetscBools[graph->twodimset]));
87   if (verbosity_level > 2) {
88     for (i = 0; i < graph->nvtxs; i++) {
89       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%" PetscInt_FMT ":\n", i));
90       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   which_dof: %" PetscInt_FMT "\n", graph->which_dof[i]));
91       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   special_dof: %" PetscInt_FMT "\n", graph->special_dof[i]));
92       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   neighbours: %" PetscInt_FMT "\n", graph->count[i]));
93       PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
94       if (graph->count[i]) {
95         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "     set of neighbours:"));
96         for (j = 0; j < graph->count[i]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->neighbours_set[i][j]));
97         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
98       }
99       PetscCall(PetscViewerASCIISetTab(viewer, tabs));
100       PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
101       if (graph->mirrors) {
102         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   mirrors: %" PetscInt_FMT "\n", graph->mirrors[i]));
103         if (graph->mirrors[i]) {
104           PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
105           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "     set of mirrors:"));
106           for (j = 0; j < graph->mirrors[i]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->mirrors_set[i][j]));
107           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
108           PetscCall(PetscViewerASCIISetTab(viewer, tabs));
109           PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
110         }
111       }
112       if (verbosity_level > 3) {
113         if (graph->xadj) {
114           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   local adj list:"));
115           PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
116           for (j = graph->xadj[i]; j < graph->xadj[i + 1]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->adjncy[j]));
117           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
118           PetscCall(PetscViewerASCIISetTab(viewer, tabs));
119           PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
120         } else {
121           PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   no adj info\n"));
122         }
123       }
124       if (graph->n_local_subs) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   local sub id: %" PetscInt_FMT "\n", graph->local_subs[i]));
125       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   interface subset id: %" PetscInt_FMT "\n", graph->subset[i]));
126       if (graph->subset[i] && graph->subset_ncc) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   ncc for subset: %" PetscInt_FMT "\n", graph->subset_ncc[graph->subset[i] - 1]));
127     }
128   }
129   PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Total number of connected components %" PetscInt_FMT "\n", graph->ncc));
130   PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &queue_in_global_numbering));
131   PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap, graph->cptr[graph->ncc], graph->queue, queue_in_global_numbering));
132   for (i = 0; i < graph->ncc; i++) {
133     PetscInt  node_num = graph->queue[graph->cptr[i]];
134     PetscBool printcc  = PETSC_FALSE;
135     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]));
136     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
137     for (j = 0; j < graph->count[node_num]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->neighbours_set[node_num][j]));
138     if (verbosity_level > 1) {
139       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "):"));
140       if (verbosity_level > 2 || graph->twodim || graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) printcc = PETSC_TRUE;
141       if (printcc) {
142         for (j = graph->cptr[i]; j < graph->cptr[i + 1]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT " (%" PetscInt_FMT ")", graph->queue[j], queue_in_global_numbering[j]));
143       }
144     } else {
145       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ")"));
146     }
147     PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
148     PetscCall(PetscViewerASCIISetTab(viewer, tabs));
149     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
150   }
151   PetscCall(PetscFree(queue_in_global_numbering));
152   PetscCall(PetscViewerFlush(viewer));
153   PetscFunctionReturn(0);
154 }
155 
156 PetscErrorCode PCBDDCGraphRestoreCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
157 {
158   PetscInt       i;
159   PetscContainer gcand;
160 
161   PetscFunctionBegin;
162   PetscCall(PetscObjectQuery((PetscObject)graph->l2gmap, "_PCBDDCGraphCandidatesIS", (PetscObject *)&gcand));
163   if (gcand) {
164     if (n_faces) *n_faces = 0;
165     if (n_edges) *n_edges = 0;
166     if (FacesIS) *FacesIS = NULL;
167     if (EdgesIS) *EdgesIS = NULL;
168     if (VerticesIS) *VerticesIS = NULL;
169   }
170   if (n_faces) {
171     if (FacesIS) {
172       for (i = 0; i < *n_faces; i++) PetscCall(ISDestroy(&((*FacesIS)[i])));
173       PetscCall(PetscFree(*FacesIS));
174     }
175     *n_faces = 0;
176   }
177   if (n_edges) {
178     if (EdgesIS) {
179       for (i = 0; i < *n_edges; i++) PetscCall(ISDestroy(&((*EdgesIS)[i])));
180       PetscCall(PetscFree(*EdgesIS));
181     }
182     *n_edges = 0;
183   }
184   if (VerticesIS) PetscCall(ISDestroy(VerticesIS));
185   PetscFunctionReturn(0);
186 }
187 
188 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
189 {
190   IS            *ISForFaces, *ISForEdges, ISForVertices;
191   PetscInt       i, nfc, nec, nvc, *idx, *mark;
192   PetscContainer gcand;
193 
194   PetscFunctionBegin;
195   PetscCall(PetscObjectQuery((PetscObject)graph->l2gmap, "_PCBDDCGraphCandidatesIS", (PetscObject *)&gcand));
196   if (gcand) {
197     PCBDDCGraphCandidates cand;
198 
199     PetscCall(PetscContainerGetPointer(gcand, (void **)&cand));
200     if (n_faces) *n_faces = cand->nfc;
201     if (FacesIS) *FacesIS = cand->Faces;
202     if (n_edges) *n_edges = cand->nec;
203     if (EdgesIS) *EdgesIS = cand->Edges;
204     if (VerticesIS) *VerticesIS = cand->Vertices;
205     PetscFunctionReturn(0);
206   }
207   PetscCall(PetscCalloc1(graph->ncc, &mark));
208   /* loop on ccs to evalute number of faces, edges and vertices */
209   nfc = 0;
210   nec = 0;
211   nvc = 0;
212   for (i = 0; i < graph->ncc; i++) {
213     PetscInt repdof = graph->queue[graph->cptr[i]];
214     if (graph->cptr[i + 1] - graph->cptr[i] > graph->custom_minimal_size && graph->count[repdof] < graph->maxcount) {
215       if (!graph->twodim && graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
216         nfc++;
217         mark[i] = 2;
218       } else {
219         nec++;
220         mark[i] = 1;
221       }
222     } else {
223       nvc += graph->cptr[i + 1] - graph->cptr[i];
224     }
225   }
226 
227   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
228   if (FacesIS) PetscCall(PetscMalloc1(nfc, &ISForFaces));
229   if (EdgesIS) PetscCall(PetscMalloc1(nec, &ISForEdges));
230   if (VerticesIS) PetscCall(PetscMalloc1(nvc, &idx));
231 
232   /* loop on ccs to compute index sets for faces and edges */
233   if (!graph->queue_sorted) {
234     PetscInt *queue_global;
235 
236     PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &queue_global));
237     PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap, graph->cptr[graph->ncc], graph->queue, queue_global));
238     for (i = 0; i < graph->ncc; i++) PetscCall(PetscSortIntWithArray(graph->cptr[i + 1] - graph->cptr[i], &queue_global[graph->cptr[i]], &graph->queue[graph->cptr[i]]));
239     PetscCall(PetscFree(queue_global));
240     graph->queue_sorted = PETSC_TRUE;
241   }
242   nfc = 0;
243   nec = 0;
244   for (i = 0; i < graph->ncc; i++) {
245     if (mark[i] == 2) {
246       if (FacesIS) PetscCall(ISCreateGeneral(PETSC_COMM_SELF, graph->cptr[i + 1] - graph->cptr[i], &graph->queue[graph->cptr[i]], PETSC_USE_POINTER, &ISForFaces[nfc]));
247       nfc++;
248     } else if (mark[i] == 1) {
249       if (EdgesIS) PetscCall(ISCreateGeneral(PETSC_COMM_SELF, graph->cptr[i + 1] - graph->cptr[i], &graph->queue[graph->cptr[i]], PETSC_USE_POINTER, &ISForEdges[nec]));
250       nec++;
251     }
252   }
253 
254   /* index set for vertices */
255   if (VerticesIS) {
256     nvc = 0;
257     for (i = 0; i < graph->ncc; i++) {
258       if (!mark[i]) {
259         PetscInt j;
260 
261         for (j = graph->cptr[i]; j < graph->cptr[i + 1]; j++) {
262           idx[nvc] = graph->queue[j];
263           nvc++;
264         }
265       }
266     }
267     /* sort vertex set (by local ordering) */
268     PetscCall(PetscSortInt(nvc, idx));
269     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nvc, idx, PETSC_OWN_POINTER, &ISForVertices));
270   }
271   PetscCall(PetscFree(mark));
272 
273   /* get back info */
274   if (n_faces) *n_faces = nfc;
275   if (FacesIS) *FacesIS = ISForFaces;
276   if (n_edges) *n_edges = nec;
277   if (EdgesIS) *EdgesIS = ISForEdges;
278   if (VerticesIS) *VerticesIS = ISForVertices;
279   PetscFunctionReturn(0);
280 }
281 
282 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
283 {
284   PetscBool   adapt_interface_reduced;
285   MPI_Comm    interface_comm;
286   PetscMPIInt size;
287   PetscInt    i;
288   PetscBT     cornerp;
289 
290   PetscFunctionBegin;
291   /* compute connected components locally */
292   PetscCall(PetscObjectGetComm((PetscObject)(graph->l2gmap), &interface_comm));
293   PetscCall(PCBDDCGraphComputeConnectedComponentsLocal(graph));
294 
295   cornerp = NULL;
296   if (graph->active_coords) { /* face based corner selection */
297     PetscBT    excluded;
298     PetscReal *wdist;
299     PetscInt   n_neigh, *neigh, *n_shared, **shared;
300     PetscInt   maxc, ns;
301 
302     PetscCall(PetscBTCreate(graph->nvtxs, &cornerp));
303     PetscCall(ISLocalToGlobalMappingGetInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));
304     for (ns = 1, maxc = 0; ns < n_neigh; ns++) maxc = PetscMax(maxc, n_shared[ns]);
305     PetscCall(PetscMalloc1(maxc * graph->cdim, &wdist));
306     PetscCall(PetscBTCreate(maxc, &excluded));
307 
308     for (ns = 1; ns < n_neigh; ns++) { /* first proc is self */
309       PetscReal *anchor, mdist;
310       PetscInt   fst, j, k, d, cdim = graph->cdim, n = n_shared[ns];
311       PetscInt   point1, point2, point3, point4;
312 
313       /* import coordinates on shared interface */
314       PetscCall(PetscBTMemzero(n, excluded));
315       for (j = 0, fst = -1, k = 0; j < n; j++) {
316         PetscBool skip = PETSC_FALSE;
317         for (d = 0; d < cdim; d++) {
318           PetscReal c = graph->coords[shared[ns][j] * cdim + d];
319           skip        = (PetscBool)(skip || c == PETSC_MAX_REAL);
320           wdist[k++]  = c;
321         }
322         if (skip) {
323           PetscCall(PetscBTSet(excluded, j));
324         } else if (fst == -1) fst = j;
325       }
326       if (fst == -1) continue;
327 
328       /* the dofs are sorted by global numbering, so each rank starts from the same id
329          and it will detect the same corners from the given set */
330 
331       /* find the farthest point from the starting one */
332       anchor = wdist + fst * cdim;
333       mdist  = -1.0;
334       point1 = fst;
335       for (j = fst; j < n; j++) {
336         PetscReal dist = 0.0;
337 
338         if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
339         for (d = 0; d < cdim; d++) dist += (wdist[j * cdim + d] - anchor[d]) * (wdist[j * cdim + d] - anchor[d]);
340         if (dist > mdist) {
341           mdist  = dist;
342           point1 = j;
343         }
344       }
345 
346       /* find the farthest point from point1 */
347       anchor = wdist + point1 * cdim;
348       mdist  = -1.0;
349       point2 = point1;
350       for (j = fst; j < n; j++) {
351         PetscReal dist = 0.0;
352 
353         if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
354         for (d = 0; d < cdim; d++) dist += (wdist[j * cdim + d] - anchor[d]) * (wdist[j * cdim + d] - anchor[d]);
355         if (dist > mdist) {
356           mdist  = dist;
357           point2 = j;
358         }
359       }
360 
361       /* find the third point maximizing the triangle area */
362       point3 = point2;
363       if (cdim > 2) {
364         PetscReal a = 0.0;
365 
366         for (d = 0; d < cdim; d++) a += (wdist[point1 * cdim + d] - wdist[point2 * cdim + d]) * (wdist[point1 * cdim + d] - wdist[point2 * cdim + d]);
367         a     = PetscSqrtReal(a);
368         mdist = -1.0;
369         for (j = fst; j < n; j++) {
370           PetscReal area, b = 0.0, c = 0.0, s;
371 
372           if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
373           for (d = 0; d < cdim; d++) {
374             b += (wdist[point1 * cdim + d] - wdist[j * cdim + d]) * (wdist[point1 * cdim + d] - wdist[j * cdim + d]);
375             c += (wdist[point2 * cdim + d] - wdist[j * cdim + d]) * (wdist[point2 * cdim + d] - wdist[j * cdim + d]);
376           }
377           b = PetscSqrtReal(b);
378           c = PetscSqrtReal(c);
379           s = 0.5 * (a + b + c);
380 
381           /* Heron's formula, area squared */
382           area = s * (s - a) * (s - b) * (s - c);
383           if (area > mdist) {
384             mdist  = area;
385             point3 = j;
386           }
387         }
388       }
389 
390       /* find the farthest point from point3 different from point1 and point2 */
391       anchor = wdist + point3 * cdim;
392       mdist  = -1.0;
393       point4 = point3;
394       for (j = fst; j < n; j++) {
395         PetscReal dist = 0.0;
396 
397         if (PetscUnlikely(PetscBTLookup(excluded, j)) || j == point1 || j == point2 || j == point3) continue;
398         for (d = 0; d < cdim; d++) dist += (wdist[j * cdim + d] - anchor[d]) * (wdist[j * cdim + d] - anchor[d]);
399         if (dist > mdist) {
400           mdist  = dist;
401           point4 = j;
402         }
403       }
404 
405       PetscCall(PetscBTSet(cornerp, shared[ns][point1]));
406       PetscCall(PetscBTSet(cornerp, shared[ns][point2]));
407       PetscCall(PetscBTSet(cornerp, shared[ns][point3]));
408       PetscCall(PetscBTSet(cornerp, shared[ns][point4]));
409 
410       /* all dofs having the same coordinates will be primal */
411       for (j = fst; j < n; j++) {
412         PetscBool same[] = {PETSC_TRUE, PETSC_TRUE, PETSC_TRUE, PETSC_TRUE};
413 
414         if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
415         for (d = 0; d < cdim; d++) {
416           same[0] = (PetscBool)(same[0] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point1 * cdim + d]) < PETSC_SMALL));
417           same[1] = (PetscBool)(same[1] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point2 * cdim + d]) < PETSC_SMALL));
418           same[2] = (PetscBool)(same[2] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point3 * cdim + d]) < PETSC_SMALL));
419           same[3] = (PetscBool)(same[3] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point4 * cdim + d]) < PETSC_SMALL));
420         }
421         if (same[0] || same[1] || same[2] || same[3]) PetscCall(PetscBTSet(cornerp, shared[ns][j]));
422       }
423     }
424     PetscCall(PetscBTDestroy(&excluded));
425     PetscCall(PetscFree(wdist));
426     PetscCall(ISLocalToGlobalMappingRestoreInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));
427   }
428 
429   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
430   PetscCallMPI(MPI_Comm_size(interface_comm, &size));
431   adapt_interface_reduced = PETSC_FALSE;
432   if (size > 1) {
433     PetscInt  i;
434     PetscBool adapt_interface = cornerp ? PETSC_TRUE : PETSC_FALSE;
435     for (i = 0; i < graph->n_subsets && !adapt_interface; i++) {
436       /* We are not sure that on a given subset of the local interface,
437          with two connected components, the latters be the same among sharing subdomains */
438       if (graph->subset_ncc[i] > 1) adapt_interface = PETSC_TRUE;
439     }
440     PetscCall(MPIU_Allreduce(&adapt_interface, &adapt_interface_reduced, 1, MPIU_BOOL, MPI_LOR, interface_comm));
441   }
442 
443   if (graph->n_subsets && adapt_interface_reduced) {
444     PetscBT      subset_cc_adapt;
445     MPI_Request *send_requests, *recv_requests;
446     PetscInt    *send_buffer, *recv_buffer;
447     PetscInt     sum_requests, start_of_recv, start_of_send;
448     PetscInt    *cum_recv_counts;
449     PetscInt    *labels;
450     PetscInt     ncc, cum_queue, mss, mns, j, k, s;
451     PetscInt   **refine_buffer = NULL, *private_labels = NULL;
452     PetscBool   *subset_has_corn, *recv_buffer_bool, *send_buffer_bool;
453 
454     PetscCall(PetscCalloc1(graph->n_subsets, &subset_has_corn));
455     if (cornerp) {
456       for (i = 0; i < graph->n_subsets; i++) {
457         for (j = 0; j < graph->subset_size[i]; j++) {
458           if (PetscBTLookup(cornerp, graph->subset_idxs[i][j])) {
459             subset_has_corn[i] = PETSC_TRUE;
460             break;
461           }
462         }
463       }
464     }
465     PetscCall(PetscMalloc1(graph->nvtxs, &labels));
466     PetscCall(PetscArrayzero(labels, graph->nvtxs));
467     for (i = 0, k = 0; i < graph->ncc; i++) {
468       PetscInt s = 1;
469       for (j = graph->cptr[i]; j < graph->cptr[i + 1]; j++) {
470         if (cornerp && PetscBTLookup(cornerp, graph->queue[j])) {
471           labels[graph->queue[j]] = k + s;
472           s += 1;
473         } else {
474           labels[graph->queue[j]] = k;
475         }
476       }
477       k += s;
478     }
479 
480     /* allocate some space */
481     PetscCall(PetscMalloc1(graph->n_subsets + 1, &cum_recv_counts));
482     PetscCall(PetscArrayzero(cum_recv_counts, graph->n_subsets + 1));
483 
484     /* first count how many neighbours per connected component I will receive from */
485     cum_recv_counts[0] = 0;
486     for (i = 0; i < graph->n_subsets; i++) cum_recv_counts[i + 1] = cum_recv_counts[i] + graph->count[graph->subset_idxs[i][0]];
487     PetscCall(PetscMalloc1(graph->n_subsets, &send_buffer_bool));
488     PetscCall(PetscMalloc1(cum_recv_counts[graph->n_subsets], &recv_buffer_bool));
489     PetscCall(PetscMalloc2(cum_recv_counts[graph->n_subsets], &send_requests, cum_recv_counts[graph->n_subsets], &recv_requests));
490     for (i = 0; i < cum_recv_counts[graph->n_subsets]; i++) {
491       send_requests[i] = MPI_REQUEST_NULL;
492       recv_requests[i] = MPI_REQUEST_NULL;
493     }
494 
495     /* exchange with my neighbours the number of my connected components on the subset of interface */
496     sum_requests = 0;
497     for (i = 0; i < graph->n_subsets; i++) send_buffer_bool[i] = (PetscBool)(graph->subset_ncc[i] > 1 || subset_has_corn[i]);
498     for (i = 0; i < graph->n_subsets; i++) {
499       PetscMPIInt neigh, tag;
500       PetscInt    count, *neighs;
501 
502       count  = graph->count[graph->subset_idxs[i][0]];
503       neighs = graph->neighbours_set[graph->subset_idxs[i][0]];
504       PetscCall(PetscMPIIntCast(2 * graph->subset_ref_node[i], &tag));
505       for (k = 0; k < count; k++) {
506         PetscCall(PetscMPIIntCast(neighs[k], &neigh));
507         PetscCallMPI(MPI_Isend(send_buffer_bool + i, 1, MPIU_BOOL, neigh, tag, interface_comm, &send_requests[sum_requests]));
508         PetscCallMPI(MPI_Irecv(recv_buffer_bool + sum_requests, 1, MPIU_BOOL, neigh, tag, interface_comm, &recv_requests[sum_requests]));
509         sum_requests++;
510       }
511     }
512     PetscCallMPI(MPI_Waitall(sum_requests, recv_requests, MPI_STATUSES_IGNORE));
513     PetscCallMPI(MPI_Waitall(sum_requests, send_requests, MPI_STATUSES_IGNORE));
514 
515     /* determine the subsets I have to adapt (those having more than 1 cc) */
516     PetscCall(PetscBTCreate(graph->n_subsets, &subset_cc_adapt));
517     PetscCall(PetscBTMemzero(graph->n_subsets, subset_cc_adapt));
518     for (i = 0; i < graph->n_subsets; i++) {
519       if (graph->subset_ncc[i] > 1 || subset_has_corn[i]) {
520         PetscCall(PetscBTSet(subset_cc_adapt, i));
521         continue;
522       }
523       for (j = cum_recv_counts[i]; j < cum_recv_counts[i + 1]; j++) {
524         if (recv_buffer_bool[j]) {
525           PetscCall(PetscBTSet(subset_cc_adapt, i));
526           break;
527         }
528       }
529     }
530     PetscCall(PetscFree(send_buffer_bool));
531     PetscCall(PetscFree(recv_buffer_bool));
532     PetscCall(PetscFree(subset_has_corn));
533 
534     /* determine send/recv buffers sizes */
535     j   = 0;
536     mss = 0;
537     for (i = 0; i < graph->n_subsets; i++) {
538       if (PetscBTLookup(subset_cc_adapt, i)) {
539         j += graph->subset_size[i];
540         mss = PetscMax(graph->subset_size[i], mss);
541       }
542     }
543     k   = 0;
544     mns = 0;
545     for (i = 0; i < graph->n_subsets; i++) {
546       if (PetscBTLookup(subset_cc_adapt, i)) {
547         k += (cum_recv_counts[i + 1] - cum_recv_counts[i]) * graph->subset_size[i];
548         mns = PetscMax(cum_recv_counts[i + 1] - cum_recv_counts[i], mns);
549       }
550     }
551     PetscCall(PetscMalloc2(j, &send_buffer, k, &recv_buffer));
552 
553     /* fill send buffer (order matters: subset_idxs ordered by global ordering) */
554     j = 0;
555     for (i = 0; i < graph->n_subsets; i++)
556       if (PetscBTLookup(subset_cc_adapt, i))
557         for (k = 0; k < graph->subset_size[i]; k++) send_buffer[j++] = labels[graph->subset_idxs[i][k]];
558 
559     /* now exchange the data */
560     start_of_recv = 0;
561     start_of_send = 0;
562     sum_requests  = 0;
563     for (i = 0; i < graph->n_subsets; i++) {
564       if (PetscBTLookup(subset_cc_adapt, i)) {
565         PetscMPIInt neigh, tag;
566         PetscInt    size_of_send = graph->subset_size[i];
567 
568         j = graph->subset_idxs[i][0];
569         PetscCall(PetscMPIIntCast(2 * graph->subset_ref_node[i] + 1, &tag));
570         for (k = 0; k < graph->count[j]; k++) {
571           PetscCall(PetscMPIIntCast(graph->neighbours_set[j][k], &neigh));
572           PetscCallMPI(MPI_Isend(&send_buffer[start_of_send], size_of_send, MPIU_INT, neigh, tag, interface_comm, &send_requests[sum_requests]));
573           PetscCallMPI(MPI_Irecv(&recv_buffer[start_of_recv], size_of_send, MPIU_INT, neigh, tag, interface_comm, &recv_requests[sum_requests]));
574           start_of_recv += size_of_send;
575           sum_requests++;
576         }
577         start_of_send += size_of_send;
578       }
579     }
580     PetscCallMPI(MPI_Waitall(sum_requests, recv_requests, MPI_STATUSES_IGNORE));
581 
582     /* refine connected components */
583     start_of_recv = 0;
584     /* allocate some temporary space */
585     if (mss) {
586       PetscCall(PetscMalloc1(mss, &refine_buffer));
587       PetscCall(PetscMalloc2(mss * (mns + 1), &refine_buffer[0], mss, &private_labels));
588     }
589     ncc            = 0;
590     cum_queue      = 0;
591     graph->cptr[0] = 0;
592     for (i = 0; i < graph->n_subsets; i++) {
593       if (PetscBTLookup(subset_cc_adapt, i)) {
594         PetscInt subset_counter = 0;
595         PetscInt sharingprocs   = cum_recv_counts[i + 1] - cum_recv_counts[i] + 1; /* count myself */
596         PetscInt buffer_size    = graph->subset_size[i];
597 
598         /* compute pointers */
599         for (j = 1; j < buffer_size; j++) refine_buffer[j] = refine_buffer[j - 1] + sharingprocs;
600         /* analyze contributions from subdomains that share the i-th subset
601            The structure of refine_buffer is suitable to find intersections of ccs among sharingprocs.
602            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)
603            sharing procs connected components:
604              neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
605              neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
606              neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
607            refine_buffer will be filled as:
608              [ 4, 3, 1;
609                4, 2, 1;
610                7, 2, 6;
611                4, 3, 5;
612                7, 2, 6; ];
613            The connected components in local ordering are [0], [1], [2 3], [4] */
614         /* fill temp_buffer */
615         for (k = 0; k < buffer_size; k++) refine_buffer[k][0] = labels[graph->subset_idxs[i][k]];
616         for (j = 0; j < sharingprocs - 1; j++) {
617           for (k = 0; k < buffer_size; k++) refine_buffer[k][j + 1] = recv_buffer[start_of_recv + k];
618           start_of_recv += buffer_size;
619         }
620         PetscCall(PetscArrayzero(private_labels, buffer_size));
621         for (j = 0; j < buffer_size; j++) {
622           if (!private_labels[j]) { /* found a new cc  */
623             PetscBool same_set;
624 
625             graph->cptr[ncc] = cum_queue;
626             ncc++;
627             subset_counter++;
628             private_labels[j]         = subset_counter;
629             graph->queue[cum_queue++] = graph->subset_idxs[i][j];
630             for (k = j + 1; k < buffer_size; k++) { /* check for other nodes in new cc */
631               same_set = PETSC_TRUE;
632               for (s = 0; s < sharingprocs; s++) {
633                 if (refine_buffer[j][s] != refine_buffer[k][s]) {
634                   same_set = PETSC_FALSE;
635                   break;
636                 }
637               }
638               if (same_set) {
639                 private_labels[k]         = subset_counter;
640                 graph->queue[cum_queue++] = graph->subset_idxs[i][k];
641               }
642             }
643           }
644         }
645         graph->cptr[ncc]     = cum_queue;
646         graph->subset_ncc[i] = subset_counter;
647         graph->queue_sorted  = PETSC_FALSE;
648       } else { /* this subset does not need to be adapted */
649         PetscCall(PetscArraycpy(graph->queue + cum_queue, graph->subset_idxs[i], graph->subset_size[i]));
650         ncc++;
651         cum_queue += graph->subset_size[i];
652         graph->cptr[ncc] = cum_queue;
653       }
654     }
655     graph->cptr[ncc] = cum_queue;
656     graph->ncc       = ncc;
657     if (mss) {
658       PetscCall(PetscFree2(refine_buffer[0], private_labels));
659       PetscCall(PetscFree(refine_buffer));
660     }
661     PetscCall(PetscFree(labels));
662     PetscCallMPI(MPI_Waitall(sum_requests, send_requests, MPI_STATUSES_IGNORE));
663     PetscCall(PetscFree2(send_requests, recv_requests));
664     PetscCall(PetscFree2(send_buffer, recv_buffer));
665     PetscCall(PetscFree(cum_recv_counts));
666     PetscCall(PetscBTDestroy(&subset_cc_adapt));
667   }
668   PetscCall(PetscBTDestroy(&cornerp));
669 
670   /* Determine if we are in 2D or 3D */
671   if (!graph->twodimset) {
672     PetscBool twodim = PETSC_TRUE;
673     for (i = 0; i < graph->ncc; i++) {
674       PetscInt repdof = graph->queue[graph->cptr[i]];
675       PetscInt ccsize = graph->cptr[i + 1] - graph->cptr[i];
676       if (graph->count[repdof] > 1 && ccsize > graph->custom_minimal_size) {
677         twodim = PETSC_FALSE;
678         break;
679       }
680     }
681     PetscCall(MPIU_Allreduce(&twodim, &graph->twodim, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)graph->l2gmap)));
682     graph->twodimset = PETSC_TRUE;
683   }
684   PetscFunctionReturn(0);
685 }
686 
687 static inline PetscErrorCode PCBDDCGraphComputeCC_Private(PCBDDCGraph graph, PetscInt pid, PetscInt *queue_tip, PetscInt n_prev, PetscInt *n_added)
688 {
689   PetscInt  i, j, n;
690   PetscInt *xadj = graph->xadj, *adjncy = graph->adjncy;
691   PetscBT   touched  = graph->touched;
692   PetscBool havecsr  = (PetscBool)(!!xadj);
693   PetscBool havesubs = (PetscBool)(!!graph->n_local_subs);
694 
695   PetscFunctionBegin;
696   n = 0;
697   if (havecsr && !havesubs) {
698     for (i = -n_prev; i < 0; i++) {
699       PetscInt start_dof = queue_tip[i];
700       /* we assume that if a dof has a size 1 adjacency list and the corresponding entry is negative, it is connected to all dofs */
701       if (xadj[start_dof + 1] - xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
702         for (j = 0; j < graph->subset_size[pid - 1]; j++) { /* pid \in [1,graph->n_subsets] */
703           PetscInt dof = graph->subset_idxs[pid - 1][j];
704           if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid) {
705             PetscCall(PetscBTSet(touched, dof));
706             queue_tip[n] = dof;
707             n++;
708           }
709         }
710       } else {
711         for (j = xadj[start_dof]; j < xadj[start_dof + 1]; j++) {
712           PetscInt dof = adjncy[j];
713           if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid) {
714             PetscCall(PetscBTSet(touched, dof));
715             queue_tip[n] = dof;
716             n++;
717           }
718         }
719       }
720     }
721   } else if (havecsr && havesubs) {
722     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
723     for (i = -n_prev; i < 0; i++) {
724       PetscInt start_dof = queue_tip[i];
725       /* 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 */
726       if (xadj[start_dof + 1] - xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
727         for (j = 0; j < graph->subset_size[pid - 1]; j++) { /* pid \in [1,graph->n_subsets] */
728           PetscInt dof = graph->subset_idxs[pid - 1][j];
729           if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
730             PetscCall(PetscBTSet(touched, dof));
731             queue_tip[n] = dof;
732             n++;
733           }
734         }
735       } else {
736         for (j = xadj[start_dof]; j < xadj[start_dof + 1]; j++) {
737           PetscInt dof = adjncy[j];
738           if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
739             PetscCall(PetscBTSet(touched, dof));
740             queue_tip[n] = dof;
741             n++;
742           }
743         }
744       }
745     }
746   } else if (havesubs) { /* sub info only */
747     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
748     for (j = 0; j < graph->subset_size[pid - 1]; j++) { /* pid \in [1,graph->n_subsets] */
749       PetscInt dof = graph->subset_idxs[pid - 1][j];
750       if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
751         PetscCall(PetscBTSet(touched, dof));
752         queue_tip[n] = dof;
753         n++;
754       }
755     }
756   } else {
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) {
760         PetscCall(PetscBTSet(touched, dof));
761         queue_tip[n] = dof;
762         n++;
763       }
764     }
765   }
766   *n_added = n;
767   PetscFunctionReturn(0);
768 }
769 
770 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
771 {
772   PetscInt    ncc, cum_queue, n;
773   PetscMPIInt commsize;
774 
775   PetscFunctionBegin;
776   PetscCheck(graph->setupcalled, PetscObjectComm((PetscObject)graph->l2gmap), PETSC_ERR_ORDER, "PCBDDCGraphSetUp should be called first");
777   /* quiet return if there isn't any local info */
778   if (!graph->xadj && !graph->n_local_subs) PetscFunctionReturn(0);
779 
780   /* reset any previous search of connected components */
781   PetscCall(PetscBTMemzero(graph->nvtxs, graph->touched));
782   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap), &commsize));
783   if (commsize > graph->commsizelimit) {
784     PetscInt i;
785     for (i = 0; i < graph->nvtxs; i++) {
786       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) PetscCall(PetscBTSet(graph->touched, i));
787     }
788   }
789 
790   /* begin search for connected components */
791   cum_queue = 0;
792   ncc       = 0;
793   for (n = 0; n < graph->n_subsets; n++) {
794     PetscInt pid   = n + 1; /* partition labeled by 0 is discarded */
795     PetscInt found = 0, prev = 0, first = 0, ncc_pid = 0;
796     while (found != graph->subset_size[n]) {
797       PetscInt added = 0;
798       if (!prev) { /* search for new starting dof */
799         while (PetscBTLookup(graph->touched, graph->subset_idxs[n][first])) first++;
800         PetscCall(PetscBTSet(graph->touched, graph->subset_idxs[n][first]));
801         graph->queue[cum_queue] = graph->subset_idxs[n][first];
802         graph->cptr[ncc]        = cum_queue;
803         prev                    = 1;
804         cum_queue++;
805         found++;
806         ncc_pid++;
807         ncc++;
808       }
809       PetscCall(PCBDDCGraphComputeCC_Private(graph, pid, graph->queue + cum_queue, prev, &added));
810       if (!added) {
811         graph->subset_ncc[n] = ncc_pid;
812         graph->cptr[ncc]     = cum_queue;
813       }
814       prev = added;
815       found += added;
816       cum_queue += added;
817       if (added && found == graph->subset_size[n]) {
818         graph->subset_ncc[n] = ncc_pid;
819         graph->cptr[ncc]     = cum_queue;
820       }
821     }
822   }
823   graph->ncc          = ncc;
824   graph->queue_sorted = PETSC_FALSE;
825   PetscFunctionReturn(0);
826 }
827 
828 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
829 {
830   IS              subset, subset_n;
831   MPI_Comm        comm;
832   const PetscInt *is_indices;
833   PetscInt        n_neigh, *neigh, *n_shared, **shared, *queue_global;
834   PetscInt        i, j, k, s, total_counts, nodes_touched, is_size;
835   PetscMPIInt     commsize;
836   PetscBool       same_set, mirrors_found;
837 
838   PetscFunctionBegin;
839   PetscValidLogicalCollectiveInt(graph->l2gmap, custom_minimal_size, 2);
840   if (neumann_is) {
841     PetscValidHeaderSpecific(neumann_is, IS_CLASSID, 3);
842     PetscCheckSameComm(graph->l2gmap, 1, neumann_is, 3);
843   }
844   graph->has_dirichlet = PETSC_FALSE;
845   if (dirichlet_is) {
846     PetscValidHeaderSpecific(dirichlet_is, IS_CLASSID, 4);
847     PetscCheckSameComm(graph->l2gmap, 1, dirichlet_is, 4);
848     graph->has_dirichlet = PETSC_TRUE;
849   }
850   PetscValidLogicalCollectiveInt(graph->l2gmap, n_ISForDofs, 5);
851   for (i = 0; i < n_ISForDofs; i++) {
852     PetscValidHeaderSpecific(ISForDofs[i], IS_CLASSID, 6);
853     PetscCheckSameComm(graph->l2gmap, 1, ISForDofs[i], 6);
854   }
855   if (custom_primal_vertices) {
856     PetscValidHeaderSpecific(custom_primal_vertices, IS_CLASSID, 7);
857     PetscCheckSameComm(graph->l2gmap, 1, custom_primal_vertices, 7);
858   }
859   PetscCall(PetscObjectGetComm((PetscObject)(graph->l2gmap), &comm));
860   PetscCallMPI(MPI_Comm_size(comm, &commsize));
861 
862   /* custom_minimal_size */
863   graph->custom_minimal_size = custom_minimal_size;
864   /* get info l2gmap and allocate work vectors  */
865   PetscCall(ISLocalToGlobalMappingGetInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));
866   /* check if we have any local periodic nodes (periodic BCs) */
867   mirrors_found = PETSC_FALSE;
868   if (graph->nvtxs && n_neigh) {
869     for (i = 0; i < n_shared[0]; i++) graph->count[shared[0][i]] += 1;
870     for (i = 0; i < n_shared[0]; i++) {
871       if (graph->count[shared[0][i]] > 1) {
872         mirrors_found = PETSC_TRUE;
873         break;
874       }
875     }
876   }
877   /* compute local mirrors (if any) */
878   if (mirrors_found) {
879     IS        to, from;
880     PetscInt *local_indices, *global_indices;
881 
882     PetscCall(ISCreateStride(PETSC_COMM_SELF, graph->nvtxs, 0, 1, &to));
883     PetscCall(ISLocalToGlobalMappingApplyIS(graph->l2gmap, to, &from));
884     /* get arrays of local and global indices */
885     PetscCall(PetscMalloc1(graph->nvtxs, &local_indices));
886     PetscCall(ISGetIndices(to, (const PetscInt **)&is_indices));
887     PetscCall(PetscArraycpy(local_indices, is_indices, graph->nvtxs));
888     PetscCall(ISRestoreIndices(to, (const PetscInt **)&is_indices));
889     PetscCall(PetscMalloc1(graph->nvtxs, &global_indices));
890     PetscCall(ISGetIndices(from, (const PetscInt **)&is_indices));
891     PetscCall(PetscArraycpy(global_indices, is_indices, graph->nvtxs));
892     PetscCall(ISRestoreIndices(from, (const PetscInt **)&is_indices));
893     /* allocate space for mirrors */
894     PetscCall(PetscMalloc2(graph->nvtxs, &graph->mirrors, graph->nvtxs, &graph->mirrors_set));
895     PetscCall(PetscArrayzero(graph->mirrors, graph->nvtxs));
896     graph->mirrors_set[0] = NULL;
897 
898     k = 0;
899     for (i = 0; i < n_shared[0]; i++) {
900       j = shared[0][i];
901       if (graph->count[j] > 1) {
902         graph->mirrors[j]++;
903         k++;
904       }
905     }
906     /* allocate space for set of mirrors */
907     PetscCall(PetscMalloc1(k, &graph->mirrors_set[0]));
908     for (i = 1; i < graph->nvtxs; i++) graph->mirrors_set[i] = graph->mirrors_set[i - 1] + graph->mirrors[i - 1];
909 
910     /* fill arrays */
911     PetscCall(PetscArrayzero(graph->mirrors, graph->nvtxs));
912     for (j = 0; j < n_shared[0]; j++) {
913       i = shared[0][j];
914       if (graph->count[i] > 1) graph->mirrors_set[i][graph->mirrors[i]++] = global_indices[i];
915     }
916     PetscCall(PetscSortIntWithArray(graph->nvtxs, global_indices, local_indices));
917     for (i = 0; i < graph->nvtxs; i++) {
918       if (graph->mirrors[i] > 0) {
919         PetscCall(PetscFindInt(graph->mirrors_set[i][0], graph->nvtxs, global_indices, &k));
920         j = global_indices[k];
921         while (k > 0 && global_indices[k - 1] == j) k--;
922         for (j = 0; j < graph->mirrors[i]; j++) graph->mirrors_set[i][j] = local_indices[k + j];
923         PetscCall(PetscSortInt(graph->mirrors[i], graph->mirrors_set[i]));
924       }
925     }
926     PetscCall(PetscFree(local_indices));
927     PetscCall(PetscFree(global_indices));
928     PetscCall(ISDestroy(&to));
929     PetscCall(ISDestroy(&from));
930   }
931   PetscCall(PetscArrayzero(graph->count, graph->nvtxs));
932 
933   /* Count total number of neigh per node */
934   k = 0;
935   for (i = 1; i < n_neigh; i++) {
936     k += n_shared[i];
937     for (j = 0; j < n_shared[i]; j++) graph->count[shared[i][j]] += 1;
938   }
939   /* Allocate space for storing the set of neighbours for each node */
940   if (graph->nvtxs) PetscCall(PetscMalloc1(k, &graph->neighbours_set[0]));
941   for (i = 1; i < graph->nvtxs; i++) { /* dont count myself */
942     graph->neighbours_set[i] = graph->neighbours_set[i - 1] + graph->count[i - 1];
943   }
944   /* Get information for sharing subdomains */
945   PetscCall(PetscArrayzero(graph->count, graph->nvtxs));
946   for (i = 1; i < n_neigh; i++) { /* dont count myself */
947     s = n_shared[i];
948     for (j = 0; j < s; j++) {
949       k                                         = shared[i][j];
950       graph->neighbours_set[k][graph->count[k]] = neigh[i];
951       graph->count[k] += 1;
952     }
953   }
954   /* sort set of sharing subdomains */
955   for (i = 0; i < graph->nvtxs; i++) PetscCall(PetscSortRemoveDupsInt(&graph->count[i], graph->neighbours_set[i]));
956   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
957   PetscCall(ISLocalToGlobalMappingRestoreInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));
958 
959   /*
960      Get info for dofs splitting
961      User can specify just a subset; an additional field is considered as a complementary field
962   */
963   for (i = 0, k = 0; i < n_ISForDofs; i++) {
964     PetscInt bs;
965 
966     PetscCall(ISGetBlockSize(ISForDofs[i], &bs));
967     k += bs;
968   }
969   for (i = 0; i < graph->nvtxs; i++) graph->which_dof[i] = k; /* by default a dof belongs to the complement set */
970   for (i = 0, k = 0; i < n_ISForDofs; i++) {
971     PetscInt bs;
972 
973     PetscCall(ISGetLocalSize(ISForDofs[i], &is_size));
974     PetscCall(ISGetBlockSize(ISForDofs[i], &bs));
975     PetscCall(ISGetIndices(ISForDofs[i], (const PetscInt **)&is_indices));
976     for (j = 0; j < is_size / bs; j++) {
977       PetscInt b;
978 
979       for (b = 0; b < bs; b++) {
980         PetscInt jj = bs * j + b;
981 
982         if (is_indices[jj] > -1 && is_indices[jj] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
983           graph->which_dof[is_indices[jj]] = k + b;
984         }
985       }
986     }
987     PetscCall(ISRestoreIndices(ISForDofs[i], (const PetscInt **)&is_indices));
988     k += bs;
989   }
990 
991   /* Take into account Neumann nodes */
992   if (neumann_is) {
993     PetscCall(ISGetLocalSize(neumann_is, &is_size));
994     PetscCall(ISGetIndices(neumann_is, (const PetscInt **)&is_indices));
995     for (i = 0; i < is_size; i++) {
996       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
997         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_NEUMANN_MARK;
998       }
999     }
1000     PetscCall(ISRestoreIndices(neumann_is, (const PetscInt **)&is_indices));
1001   }
1002   /* Take into account Dirichlet nodes (they overwrite any neumann boundary mark previously set) */
1003   if (dirichlet_is) {
1004     PetscCall(ISGetLocalSize(dirichlet_is, &is_size));
1005     PetscCall(ISGetIndices(dirichlet_is, (const PetscInt **)&is_indices));
1006     for (i = 0; i < is_size; i++) {
1007       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
1008         if (commsize > graph->commsizelimit) {                  /* dirichlet nodes treated as internal */
1009           PetscCall(PetscBTSet(graph->touched, is_indices[i]));
1010           graph->subset[is_indices[i]] = 0;
1011         }
1012         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_DIRICHLET_MARK;
1013       }
1014     }
1015     PetscCall(ISRestoreIndices(dirichlet_is, (const PetscInt **)&is_indices));
1016   }
1017   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
1018   if (graph->mirrors) {
1019     for (i = 0; i < graph->nvtxs; i++)
1020       if (graph->mirrors[i]) graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
1021 
1022     if (graph->xadj) {
1023       PetscInt *new_xadj, *new_adjncy;
1024       /* sort CSR graph */
1025       for (i = 0; i < graph->nvtxs; i++) PetscCall(PetscSortInt(graph->xadj[i + 1] - graph->xadj[i], &graph->adjncy[graph->xadj[i]]));
1026       /* adapt local CSR graph in case of local periodicity */
1027       k = 0;
1028       for (i = 0; i < graph->nvtxs; i++)
1029         for (j = graph->xadj[i]; j < graph->xadj[i + 1]; j++) k += graph->mirrors[graph->adjncy[j]];
1030 
1031       PetscCall(PetscMalloc1(graph->nvtxs + 1, &new_xadj));
1032       PetscCall(PetscMalloc1(k + graph->xadj[graph->nvtxs], &new_adjncy));
1033       new_xadj[0] = 0;
1034       for (i = 0; i < graph->nvtxs; i++) {
1035         k = graph->xadj[i + 1] - graph->xadj[i];
1036         PetscCall(PetscArraycpy(&new_adjncy[new_xadj[i]], &graph->adjncy[graph->xadj[i]], k));
1037         new_xadj[i + 1] = new_xadj[i] + k;
1038         for (j = graph->xadj[i]; j < graph->xadj[i + 1]; j++) {
1039           k = graph->mirrors[graph->adjncy[j]];
1040           PetscCall(PetscArraycpy(&new_adjncy[new_xadj[i + 1]], graph->mirrors_set[graph->adjncy[j]], k));
1041           new_xadj[i + 1] += k;
1042         }
1043         k = new_xadj[i + 1] - new_xadj[i];
1044         PetscCall(PetscSortRemoveDupsInt(&k, &new_adjncy[new_xadj[i]]));
1045         new_xadj[i + 1] = new_xadj[i] + k;
1046       }
1047       /* set new CSR into graph */
1048       PetscCall(PetscFree(graph->xadj));
1049       PetscCall(PetscFree(graph->adjncy));
1050       graph->xadj   = new_xadj;
1051       graph->adjncy = new_adjncy;
1052     }
1053   }
1054 
1055   /* mark special nodes (if any) -> each will become a single node equivalence class */
1056   if (custom_primal_vertices) {
1057     PetscCall(ISGetLocalSize(custom_primal_vertices, &is_size));
1058     PetscCall(ISGetIndices(custom_primal_vertices, (const PetscInt **)&is_indices));
1059     for (i = 0, j = 0; i < is_size; i++) {
1060       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 */
1061         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_SPECIAL_MARK - j;
1062         j++;
1063       }
1064     }
1065     PetscCall(ISRestoreIndices(custom_primal_vertices, (const PetscInt **)&is_indices));
1066   }
1067 
1068   /* mark interior nodes (if commsize > graph->commsizelimit) as touched and belonging to partition number 0 */
1069   if (commsize > graph->commsizelimit) {
1070     for (i = 0; i < graph->nvtxs; i++) {
1071       if (!graph->count[i]) {
1072         PetscCall(PetscBTSet(graph->touched, i));
1073         graph->subset[i] = 0;
1074       }
1075     }
1076   }
1077 
1078   /* init graph structure and compute default subsets */
1079   nodes_touched = 0;
1080   for (i = 0; i < graph->nvtxs; i++) {
1081     if (PetscBTLookup(graph->touched, i)) nodes_touched++;
1082   }
1083   i            = 0;
1084   graph->ncc   = 0;
1085   total_counts = 0;
1086 
1087   /* allocated space for queues */
1088   if (commsize == graph->commsizelimit) {
1089     PetscCall(PetscMalloc2(graph->nvtxs + 1, &graph->cptr, graph->nvtxs, &graph->queue));
1090   } else {
1091     PetscInt nused = graph->nvtxs - nodes_touched;
1092     PetscCall(PetscMalloc2(nused + 1, &graph->cptr, nused, &graph->queue));
1093   }
1094 
1095   while (nodes_touched < graph->nvtxs) {
1096     /*  find first untouched node in local ordering */
1097     while (PetscBTLookup(graph->touched, i)) i++;
1098     PetscCall(PetscBTSet(graph->touched, i));
1099     graph->subset[i]           = graph->ncc + 1;
1100     graph->cptr[graph->ncc]    = total_counts;
1101     graph->queue[total_counts] = i;
1102     total_counts++;
1103     nodes_touched++;
1104     /* now find all other nodes having the same set of sharing subdomains */
1105     for (j = i + 1; j < graph->nvtxs; j++) {
1106       /* check for same number of sharing subdomains, dof number and same special mark */
1107       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]) {
1108         /* check for same set of sharing subdomains */
1109         same_set = PETSC_TRUE;
1110         for (k = 0; k < graph->count[j]; k++) {
1111           if (graph->neighbours_set[i][k] != graph->neighbours_set[j][k]) same_set = PETSC_FALSE;
1112         }
1113         /* I have found a friend of mine */
1114         if (same_set) {
1115           PetscCall(PetscBTSet(graph->touched, j));
1116           graph->subset[j] = graph->ncc + 1;
1117           nodes_touched++;
1118           graph->queue[total_counts] = j;
1119           total_counts++;
1120         }
1121       }
1122     }
1123     graph->ncc++;
1124   }
1125   /* 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 */
1126   graph->n_subsets = graph->ncc;
1127   PetscCall(PetscMalloc1(graph->n_subsets, &graph->subset_ncc));
1128   for (i = 0; i < graph->n_subsets; i++) graph->subset_ncc[i] = 1;
1129   /* final pointer */
1130   graph->cptr[graph->ncc] = total_counts;
1131 
1132   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each connected component */
1133   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
1134   PetscCall(PetscMalloc1(graph->ncc, &graph->subset_ref_node));
1135   PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &queue_global));
1136   PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap, graph->cptr[graph->ncc], graph->queue, queue_global));
1137   for (j = 0; j < graph->ncc; j++) {
1138     PetscCall(PetscSortIntWithArray(graph->cptr[j + 1] - graph->cptr[j], &queue_global[graph->cptr[j]], &graph->queue[graph->cptr[j]]));
1139     graph->subset_ref_node[j] = graph->queue[graph->cptr[j]];
1140   }
1141   PetscCall(PetscFree(queue_global));
1142   graph->queue_sorted = PETSC_TRUE;
1143 
1144   /* save information on subsets (needed when analyzing the connected components) */
1145   if (graph->ncc) {
1146     PetscCall(PetscMalloc2(graph->ncc, &graph->subset_size, graph->ncc, &graph->subset_idxs));
1147     PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &graph->subset_idxs[0]));
1148     PetscCall(PetscArrayzero(graph->subset_idxs[0], graph->cptr[graph->ncc]));
1149     for (j = 1; j < graph->ncc; j++) {
1150       graph->subset_size[j - 1] = graph->cptr[j] - graph->cptr[j - 1];
1151       graph->subset_idxs[j]     = graph->subset_idxs[j - 1] + graph->subset_size[j - 1];
1152     }
1153     graph->subset_size[graph->ncc - 1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc - 1];
1154     PetscCall(PetscArraycpy(graph->subset_idxs[0], graph->queue, graph->cptr[graph->ncc]));
1155   }
1156 
1157   /* renumber reference nodes */
1158   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)(graph->l2gmap)), graph->ncc, graph->subset_ref_node, PETSC_COPY_VALUES, &subset_n));
1159   PetscCall(ISLocalToGlobalMappingApplyIS(graph->l2gmap, subset_n, &subset));
1160   PetscCall(ISDestroy(&subset_n));
1161   PetscCall(ISRenumber(subset, NULL, NULL, &subset_n));
1162   PetscCall(ISDestroy(&subset));
1163   PetscCall(ISGetLocalSize(subset_n, &k));
1164   PetscCheck(k == graph->ncc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size of new subset! %" PetscInt_FMT " != %" PetscInt_FMT, k, graph->ncc);
1165   PetscCall(ISGetIndices(subset_n, &is_indices));
1166   PetscCall(PetscArraycpy(graph->subset_ref_node, is_indices, graph->ncc));
1167   PetscCall(ISRestoreIndices(subset_n, &is_indices));
1168   PetscCall(ISDestroy(&subset_n));
1169 
1170   /* free workspace */
1171   graph->setupcalled = PETSC_TRUE;
1172   PetscFunctionReturn(0);
1173 }
1174 
1175 PetscErrorCode PCBDDCGraphResetCoords(PCBDDCGraph graph)
1176 {
1177   PetscFunctionBegin;
1178   if (!graph) PetscFunctionReturn(0);
1179   PetscCall(PetscFree(graph->coords));
1180   graph->cdim  = 0;
1181   graph->cnloc = 0;
1182   graph->cloc  = PETSC_FALSE;
1183   PetscFunctionReturn(0);
1184 }
1185 
1186 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1187 {
1188   PetscFunctionBegin;
1189   if (!graph) PetscFunctionReturn(0);
1190   if (graph->freecsr) {
1191     PetscCall(PetscFree(graph->xadj));
1192     PetscCall(PetscFree(graph->adjncy));
1193   } else {
1194     graph->xadj   = NULL;
1195     graph->adjncy = NULL;
1196   }
1197   graph->freecsr   = PETSC_FALSE;
1198   graph->nvtxs_csr = 0;
1199   PetscFunctionReturn(0);
1200 }
1201 
1202 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1203 {
1204   PetscFunctionBegin;
1205   if (!graph) PetscFunctionReturn(0);
1206   PetscCall(ISLocalToGlobalMappingDestroy(&graph->l2gmap));
1207   PetscCall(PetscFree(graph->subset_ncc));
1208   PetscCall(PetscFree(graph->subset_ref_node));
1209   if (graph->nvtxs) PetscCall(PetscFree(graph->neighbours_set[0]));
1210   PetscCall(PetscBTDestroy(&graph->touched));
1211   PetscCall(PetscFree5(graph->count, graph->neighbours_set, graph->subset, graph->which_dof, graph->special_dof));
1212   PetscCall(PetscFree2(graph->cptr, graph->queue));
1213   if (graph->mirrors) PetscCall(PetscFree(graph->mirrors_set[0]));
1214   PetscCall(PetscFree2(graph->mirrors, graph->mirrors_set));
1215   if (graph->subset_idxs) PetscCall(PetscFree(graph->subset_idxs[0]));
1216   PetscCall(PetscFree2(graph->subset_size, graph->subset_idxs));
1217   PetscCall(ISDestroy(&graph->dirdofs));
1218   PetscCall(ISDestroy(&graph->dirdofsB));
1219   if (graph->n_local_subs) PetscCall(PetscFree(graph->local_subs));
1220   graph->has_dirichlet       = PETSC_FALSE;
1221   graph->twodimset           = PETSC_FALSE;
1222   graph->twodim              = PETSC_FALSE;
1223   graph->nvtxs               = 0;
1224   graph->nvtxs_global        = 0;
1225   graph->n_subsets           = 0;
1226   graph->custom_minimal_size = 1;
1227   graph->n_local_subs        = 0;
1228   graph->maxcount            = PETSC_MAX_INT;
1229   graph->setupcalled         = PETSC_FALSE;
1230   PetscFunctionReturn(0);
1231 }
1232 
1233 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N, PetscInt maxcount)
1234 {
1235   PetscInt n;
1236 
1237   PetscFunctionBegin;
1238   PetscValidPointer(graph, 1);
1239   PetscValidHeaderSpecific(l2gmap, IS_LTOGM_CLASSID, 2);
1240   PetscValidLogicalCollectiveInt(l2gmap, N, 3);
1241   PetscValidLogicalCollectiveInt(l2gmap, maxcount, 4);
1242   /* raise an error if already allocated */
1243   PetscCheck(!graph->nvtxs_global, PetscObjectComm((PetscObject)l2gmap), PETSC_ERR_PLIB, "BDDCGraph already initialized");
1244   /* set number of vertices */
1245   PetscCall(PetscObjectReference((PetscObject)l2gmap));
1246   graph->l2gmap = l2gmap;
1247   PetscCall(ISLocalToGlobalMappingGetSize(l2gmap, &n));
1248   graph->nvtxs        = n;
1249   graph->nvtxs_global = N;
1250   /* allocate used space */
1251   PetscCall(PetscBTCreate(graph->nvtxs, &graph->touched));
1252   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));
1253   /* zeroes memory */
1254   PetscCall(PetscArrayzero(graph->count, graph->nvtxs));
1255   PetscCall(PetscArrayzero(graph->subset, graph->nvtxs));
1256   /* use -1 as a default value for which_dof array */
1257   for (n = 0; n < graph->nvtxs; n++) graph->which_dof[n] = -1;
1258   PetscCall(PetscArrayzero(graph->special_dof, graph->nvtxs));
1259   /* zeroes first pointer to neighbour set */
1260   if (graph->nvtxs) graph->neighbours_set[0] = NULL;
1261   /* zeroes workspace for values of ncc */
1262   graph->subset_ncc      = NULL;
1263   graph->subset_ref_node = NULL;
1264   /* maxcount for cc */
1265   graph->maxcount = maxcount;
1266   PetscFunctionReturn(0);
1267 }
1268 
1269 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph *graph)
1270 {
1271   PetscFunctionBegin;
1272   PetscCall(PCBDDCGraphResetCSR(*graph));
1273   PetscCall(PCBDDCGraphResetCoords(*graph));
1274   PetscCall(PCBDDCGraphReset(*graph));
1275   PetscCall(PetscFree(*graph));
1276   PetscFunctionReturn(0);
1277 }
1278 
1279 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1280 {
1281   PCBDDCGraph new_graph;
1282 
1283   PetscFunctionBegin;
1284   PetscCall(PetscNew(&new_graph));
1285   new_graph->custom_minimal_size = 1;
1286   new_graph->commsizelimit       = 1;
1287   *graph                         = new_graph;
1288   PetscFunctionReturn(0);
1289 }
1290