xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision aed7e7d042b1e028e027f758acc1a77517c257bb)
1 #include <petsc/private/petscimpl.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <../src/ksp/pc/impls/bddc/bddcstructs.h>
4 
5 PetscErrorCode PCBDDCGraphGetDirichletDofsB(PCBDDCGraph graph, IS* dirdofs)
6 {
7   PetscErrorCode ierr;
8 
9   PetscFunctionBegin;
10   if (graph->dirdofsB) {
11     ierr = PetscObjectReference((PetscObject)graph->dirdofsB);CHKERRQ(ierr);
12   } else if (graph->has_dirichlet) {
13     PetscInt i,size;
14     PetscInt *dirdofs_idxs;
15 
16     size = 0;
17     for (i=0;i<graph->nvtxs;i++) {
18       if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
19     }
20 
21     ierr = PetscMalloc1(size,&dirdofs_idxs);CHKERRQ(ierr);
22     size = 0;
23     for (i=0;i<graph->nvtxs;i++) {
24       if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
25     }
26     ierr = ISCreateGeneral(PETSC_COMM_SELF,size,dirdofs_idxs,PETSC_OWN_POINTER,&graph->dirdofsB);CHKERRQ(ierr);
27     ierr = PetscObjectReference((PetscObject)graph->dirdofsB);CHKERRQ(ierr);
28   }
29   *dirdofs = graph->dirdofsB;
30   PetscFunctionReturn(0);
31 }
32 
33 PetscErrorCode PCBDDCGraphGetDirichletDofs(PCBDDCGraph graph, IS* dirdofs)
34 {
35   PetscErrorCode ierr;
36 
37   PetscFunctionBegin;
38   if (graph->dirdofs) {
39     ierr = PetscObjectReference((PetscObject)graph->dirdofs);CHKERRQ(ierr);
40   } else if (graph->has_dirichlet) {
41     PetscInt i,size;
42     PetscInt *dirdofs_idxs;
43 
44     size = 0;
45     for (i=0;i<graph->nvtxs;i++) {
46       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
47     }
48 
49     ierr = PetscMalloc1(size,&dirdofs_idxs);CHKERRQ(ierr);
50     size = 0;
51     for (i=0;i<graph->nvtxs;i++) {
52       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
53     }
54     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)graph->l2gmap),size,dirdofs_idxs,PETSC_OWN_POINTER,&graph->dirdofs);CHKERRQ(ierr);
55     ierr = PetscObjectReference((PetscObject)graph->dirdofs);CHKERRQ(ierr);
56   }
57   *dirdofs = graph->dirdofs;
58   PetscFunctionReturn(0);
59 }
60 
61 PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer)
62 {
63   PetscInt       i,j,tabs;
64   PetscInt*      queue_in_global_numbering;
65   PetscErrorCode ierr;
66 
67   PetscFunctionBegin;
68   ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
69   ierr = PetscViewerASCIIGetTab(viewer,&tabs);CHKERRQ(ierr);
70   ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
71   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
72   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Local BDDC graph for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
73   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Number of vertices %d\n",graph->nvtxs);CHKERRQ(ierr);
74   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %d\n",graph->custom_minimal_size);CHKERRQ(ierr);
75   if (graph->maxcount != PETSC_MAX_INT) {
76     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Max count %d\n",graph->maxcount);CHKERRQ(ierr);
77   }
78   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Topological two dim? %d (set %d)\n",graph->twodim,graph->twodimset);CHKERRQ(ierr);
79   if (verbosity_level > 2) {
80     for (i=0;i<graph->nvtxs;i++) {
81       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d:\n",i);CHKERRQ(ierr);
82       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %d\n",graph->which_dof[i]);CHKERRQ(ierr);
83       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %d\n",graph->special_dof[i]);CHKERRQ(ierr);
84       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %d\n",graph->count[i]);CHKERRQ(ierr);
85       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
86       if (graph->count[i]) {
87         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:");CHKERRQ(ierr);
88         for (j=0;j<graph->count[i];j++) {
89           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[i][j]);CHKERRQ(ierr);
90         }
91         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
92       }
93       ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
94       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
95       if (graph->mirrors) {
96         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %d\n",graph->mirrors[i]);CHKERRQ(ierr);
97         if (graph->mirrors[i]) {
98           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
99           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:");CHKERRQ(ierr);
100           for (j=0;j<graph->mirrors[i];j++) {
101             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->mirrors_set[i][j]);CHKERRQ(ierr);
102           }
103           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
104           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
105           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
106         }
107       }
108       if (verbosity_level > 3) {
109         if (graph->xadj) {
110           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:");CHKERRQ(ierr);
111           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
112           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
113             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->adjncy[j]);CHKERRQ(ierr);
114           }
115           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
116           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
117           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
118         } else {
119           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   no adj info\n");CHKERRQ(ierr);
120         }
121       }
122       if (graph->n_local_subs) {
123         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local sub id: %d\n",graph->local_subs[i]);CHKERRQ(ierr);
124       }
125       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
126       if (graph->subset[i] && graph->subset_ncc) {
127         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
128       }
129     }
130   }
131   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
132   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
133   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
134   for (i=0;i<graph->ncc;i++) {
135     PetscInt node_num=graph->queue[graph->cptr[i]];
136     PetscBool printcc = PETSC_FALSE;
137     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  cc %d (size %d, fid %d, neighs:",i,graph->cptr[i+1]-graph->cptr[i],graph->which_dof[node_num]);CHKERRQ(ierr);
138     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
139     for (j=0;j<graph->count[node_num];j++) {
140       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
141     }
142     if (verbosity_level > 1) {
143       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
144       if (verbosity_level > 2 || graph->twodim || graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) {
145         printcc = PETSC_TRUE;
146       }
147       if (printcc) {
148         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
149           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
150         }
151       }
152     } else {
153       ierr = PetscViewerASCIISynchronizedPrintf(viewer,")");CHKERRQ(ierr);
154     }
155     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
156     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
158   }
159   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
160   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
161   PetscFunctionReturn(0);
162 }
163 
164 PetscErrorCode PCBDDCGraphRestoreCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
165 {
166   PetscInt       i;
167   PetscErrorCode ierr;
168 
169   PetscFunctionBegin;
170   if (n_faces) {
171     if (FacesIS) {
172       for (i=0;i<*n_faces;i++) {
173         ierr = ISDestroy(&((*FacesIS)[i]));CHKERRQ(ierr);
174       }
175       ierr = PetscFree(*FacesIS);CHKERRQ(ierr);
176     }
177     *n_faces = 0;
178   }
179   if (n_edges) {
180     if (EdgesIS) {
181       for (i=0;i<*n_edges;i++) {
182         ierr = ISDestroy(&((*EdgesIS)[i]));CHKERRQ(ierr);
183       }
184       ierr = PetscFree(*EdgesIS);CHKERRQ(ierr);
185     }
186     *n_edges = 0;
187   }
188   if (VerticesIS) {
189     ierr = ISDestroy(VerticesIS);CHKERRQ(ierr);
190   }
191   PetscFunctionReturn(0);
192 }
193 
194 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
195 {
196   IS             *ISForFaces,*ISForEdges,ISForVertices;
197   PetscInt       i,nfc,nec,nvc,*idx,*mark;
198   PetscErrorCode ierr;
199 
200   PetscFunctionBegin;
201   ierr = PetscCalloc1(graph->ncc,&mark);CHKERRQ(ierr);
202   /* loop on ccs to evalute number of faces, edges and vertices */
203   nfc = 0;
204   nec = 0;
205   nvc = 0;
206   for (i=0;i<graph->ncc;i++) {
207     PetscInt repdof = graph->queue[graph->cptr[i]];
208     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size && graph->count[repdof] < graph->maxcount) {
209       if (!graph->twodim && graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
210         nfc++;
211         mark[i] = 2;
212       } else {
213         nec++;
214         mark[i] = 1;
215       }
216     } else {
217       nvc += graph->cptr[i+1]-graph->cptr[i];
218     }
219   }
220 
221   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
222   if (FacesIS) {
223     ierr = PetscMalloc1(nfc,&ISForFaces);CHKERRQ(ierr);
224   }
225   if (EdgesIS) {
226     ierr = PetscMalloc1(nec,&ISForEdges);CHKERRQ(ierr);
227   }
228   if (VerticesIS) {
229     ierr = PetscMalloc1(nvc,&idx);CHKERRQ(ierr);
230   }
231 
232   /* loop on ccs to compute index sets for faces and edges */
233   if (!graph->queue_sorted) {
234     PetscInt *queue_global;
235 
236     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
237     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
238     for (i=0;i<graph->ncc;i++) {
239       ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
240     }
241     ierr = PetscFree(queue_global);CHKERRQ(ierr);
242     graph->queue_sorted = PETSC_TRUE;
243   }
244   nfc = 0;
245   nec = 0;
246   for (i=0;i<graph->ncc;i++) {
247     if (mark[i] == 2) {
248       if (FacesIS) {
249         ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_USE_POINTER,&ISForFaces[nfc]);CHKERRQ(ierr);
250       }
251       nfc++;
252     } else if (mark[i] == 1) {
253       if (EdgesIS) {
254         ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_USE_POINTER,&ISForEdges[nec]);CHKERRQ(ierr);
255       }
256       nec++;
257     }
258   }
259 
260   /* index set for vertices */
261   if (VerticesIS) {
262     nvc = 0;
263     for (i=0;i<graph->ncc;i++) {
264       if (!mark[i]) {
265         PetscInt j;
266 
267         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
268           idx[nvc]=graph->queue[j];
269           nvc++;
270         }
271       }
272     }
273     /* sort vertex set (by local ordering) */
274     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
275     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
276   }
277   ierr = PetscFree(mark);CHKERRQ(ierr);
278 
279   /* get back info */
280   if (n_faces)       *n_faces = nfc;
281   if (FacesIS)       *FacesIS = ISForFaces;
282   if (n_edges)       *n_edges = nec;
283   if (EdgesIS)       *EdgesIS = ISForEdges;
284   if (VerticesIS) *VerticesIS = ISForVertices;
285   PetscFunctionReturn(0);
286 }
287 
288 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
289 {
290   PetscBool      adapt_interface_reduced;
291   MPI_Comm       interface_comm;
292   PetscMPIInt    size;
293   PetscInt       i;
294   PetscBT        cornerp;
295   PetscErrorCode ierr;
296 
297   PetscFunctionBegin;
298   /* compute connected components locally */
299   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
300   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
301 
302   cornerp = NULL;
303   if (graph->active_coords) { /* face based corner selection */
304     PetscReal      *wdist;
305     PetscInt       n_neigh,*neigh,*n_shared,**shared;
306     PetscInt       maxc, ns;
307 
308     ierr = PetscBTCreate(graph->nvtxs,&cornerp);CHKERRQ(ierr);
309     ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
310     for (ns = 1, maxc = 0; ns < n_neigh; ns++) maxc = PetscMax(maxc,n_shared[ns]);
311     ierr = PetscMalloc1(maxc*graph->cdim,&wdist);CHKERRQ(ierr);
312 
313     for (ns = 1; ns < n_neigh; ns++) { /* first proc is self */
314       PetscReal *anchor,mdist;
315       PetscInt  j,k,d,cdim = graph->cdim;
316       PetscInt  point1,point2,point3;
317 /*
318       PetscBool isface = PETSC_FALSE;
319 
320       for (i=0;i<n_shared[ns];i++) {
321         if (graph->count[shared[ns][i]] == 1) {
322           isface = PETSC_TRUE;
323           break;
324         }
325       }
326       if (!isface) continue;
327 */
328       /* import coordinates on shared interface */
329       for (j=0,k=0;j<n_shared[ns];j++)
330         for (d=0;d<cdim;d++)
331           wdist[k++] = graph->coords[shared[ns][j]*cdim+d];
332 
333       /* the dofs are sorted by global numbering, so each rank start from the same id and will detect the same corners */
334       anchor = wdist;
335 
336       /* find the farthest point from the starting one */
337       mdist = -1.0;
338       for (j=0,point1=0;j<n_shared[ns];j++) {
339         PetscReal dist = 0.0;
340 
341         for (d=0;d<cdim;d++) dist += (wdist[j*cdim+d]-anchor[d])*(wdist[j*cdim+d]-anchor[d]);
342         if (dist > mdist) { mdist = dist; point1 = j; }
343       }
344 
345       /* find the farthest point from point1 */
346       anchor = wdist + point1*cdim;
347       mdist  = -1.0;
348       for (j=0,point2=0;j<n_shared[ns];j++) {
349         PetscReal dist = 0.0;
350 
351         for (d=0;d<cdim;d++) dist += (wdist[j*cdim+d]-anchor[d])*(wdist[j*cdim+d]-anchor[d]);
352         if (dist > mdist) { mdist = dist; point2 = j; }
353       }
354 
355       /* find the third point maximizing the triangle area */
356       point3 = point2;
357       if (cdim > 2) {
358         PetscReal a = 0.0;
359 
360         for (d=0;d<cdim;d++) a += (wdist[point1*cdim+d]-wdist[point2*cdim+d])*(wdist[point1*cdim+d]-wdist[point2*cdim+d]);
361         mdist = -1.0;
362         for (j=0,point3=0;j<n_shared[ns];j++) {
363           PetscReal area,b = 0.0, c = 0.0;
364 
365           for (d=0;d<cdim;d++) {
366             b += (wdist[point1*cdim+d]-wdist[j*cdim+d])*(wdist[point1*cdim+d]-wdist[j*cdim+d]);
367             c += (wdist[point2*cdim+d]-wdist[j*cdim+d])*(wdist[point2*cdim+d]-wdist[j*cdim+d]);
368           }
369           area = (a+b+c)*(-a+b+c)*(a-b+c)*(a+b-c); /* Heron's formula without divisions by 2 */
370           if (area > mdist) { mdist = area; point3 = j; }
371         }
372       }
373 
374       /* all dofs having the same coordinates will be primal */
375       for (j=0;j<n_shared[ns];j++) {
376         PetscBool same[3] = {PETSC_TRUE,PETSC_TRUE,PETSC_TRUE};
377 
378         for (d=0;d<cdim;d++) {
379           same[0] = (PetscBool)(same[0] && (PetscAbsReal(wdist[j*cdim + d]-wdist[point1*cdim+d]) < PETSC_SMALL));
380           same[1] = (PetscBool)(same[1] && (PetscAbsReal(wdist[j*cdim + d]-wdist[point2*cdim+d]) < PETSC_SMALL));
381           same[2] = (PetscBool)(same[2] && (PetscAbsReal(wdist[j*cdim + d]-wdist[point3*cdim+d]) < PETSC_SMALL));
382         }
383         if (same[0] || same[1] || same[2]) {
384           ierr = PetscBTSet(cornerp,shared[ns][j]);CHKERRQ(ierr);
385         }
386       }
387     }
388     ierr = PetscFree(wdist);CHKERRQ(ierr);
389     ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
390   }
391 
392   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
393   ierr = MPI_Comm_size(interface_comm,&size);CHKERRQ(ierr);
394   adapt_interface_reduced = PETSC_FALSE;
395   if (size > 1) {
396     PetscInt i;
397     PetscBool adapt_interface = cornerp ? PETSC_TRUE : PETSC_FALSE;
398     for (i=0;i<graph->n_subsets && !adapt_interface;i++) {
399       /* We are not sure that on a given subset of the local interface,
400          with two connected components, the latters be the same among sharing subdomains */
401       if (graph->subset_ncc[i] > 1) adapt_interface = PETSC_TRUE;
402     }
403     ierr = MPIU_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_BOOL,MPI_LOR,interface_comm);CHKERRQ(ierr);
404   }
405 
406   if (graph->n_subsets && adapt_interface_reduced) {
407     PetscBT     subset_cc_adapt;
408     MPI_Request *send_requests,*recv_requests;
409     PetscInt    *send_buffer,*recv_buffer;
410     PetscInt    sum_requests,start_of_recv,start_of_send;
411     PetscInt    *cum_recv_counts;
412     PetscInt    *labels;
413     PetscInt    ncc,cum_queue,mss,mns,j,k,s;
414     PetscInt    **refine_buffer=NULL,*private_labels = NULL;
415     PetscBool   *subset_has_corn,*recv_buffer_bool;
416 
417     ierr = PetscCalloc1(graph->n_subsets,&subset_has_corn);CHKERRQ(ierr);
418     if (cornerp) {
419       for (i=0;i<graph->n_subsets;i++) {
420         for (j=0;j<graph->subset_size[i];j++) {
421           if (PetscBTLookup(cornerp,graph->subset_idxs[i][j])) {
422             subset_has_corn[i] = PETSC_TRUE;
423             break;
424           }
425         }
426       }
427     }
428     ierr = PetscMalloc1(graph->nvtxs,&labels);CHKERRQ(ierr);
429     ierr = PetscMemzero(labels,graph->nvtxs*sizeof(*labels));CHKERRQ(ierr);
430     for (i=0,k=0;i<graph->ncc;i++) {
431       PetscInt s = 1;
432       for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
433         if (cornerp && PetscBTLookup(cornerp,graph->queue[j])) {
434           labels[graph->queue[j]] = k+s;
435           s += 1;
436         } else {
437           labels[graph->queue[j]] = k;
438         }
439       }
440       k += s;
441     }
442 
443     /* allocate some space */
444     ierr = PetscMalloc1(graph->n_subsets+1,&cum_recv_counts);CHKERRQ(ierr);
445     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
446 
447     /* first count how many neighbours per connected component I will receive from */
448     cum_recv_counts[0] = 0;
449     for (i=0;i<graph->n_subsets;i++) cum_recv_counts[i+1] = cum_recv_counts[i]+graph->count[graph->subset_idxs[i][0]];
450     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_buffer_bool);CHKERRQ(ierr);
451     ierr = PetscMalloc2(cum_recv_counts[graph->n_subsets],&send_requests,cum_recv_counts[graph->n_subsets],&recv_requests);CHKERRQ(ierr);
452     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
453       send_requests[i] = MPI_REQUEST_NULL;
454       recv_requests[i] = MPI_REQUEST_NULL;
455     }
456 
457     /* exchange with my neighbours the number of my connected components on the subset of interface */
458     sum_requests = 0;
459     for (i=0;i<graph->n_subsets;i++) {
460       PetscMPIInt neigh,tag;
461       PetscInt    count,*neighs;
462 
463       count  = graph->count[graph->subset_idxs[i][0]];
464       neighs = graph->neighbours_set[graph->subset_idxs[i][0]];
465       ierr   = PetscMPIIntCast(2*graph->subset_ref_node[i],&tag);CHKERRQ(ierr);
466       for (k=0;k<count;k++) {
467         PetscBool ss = (PetscBool)(graph->subset_ncc[i] > 1 || subset_has_corn[i]);
468 
469         ierr = PetscMPIIntCast(neighs[k],&neigh);CHKERRQ(ierr);
470         ierr = MPI_Isend(&ss,1,MPIU_BOOL,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
471         ierr = MPI_Irecv(&recv_buffer_bool[sum_requests],1,MPIU_BOOL,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
472         sum_requests++;
473       }
474     }
475     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
476     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
477 
478     /* determine the subsets I have to adapt (those having more than 1 cc) */
479     ierr = PetscBTCreate(graph->n_subsets,&subset_cc_adapt);CHKERRQ(ierr);
480     ierr = PetscBTMemzero(graph->n_subsets,subset_cc_adapt);CHKERRQ(ierr);
481     for (i=0;i<graph->n_subsets;i++) {
482       if (graph->subset_ncc[i] > 1 || subset_has_corn[i]) {
483         ierr = PetscBTSet(subset_cc_adapt,i);CHKERRQ(ierr);
484         continue;
485       }
486       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
487          if (recv_buffer_bool[j]) {
488           ierr = PetscBTSet(subset_cc_adapt,i);CHKERRQ(ierr);
489           break;
490         }
491       }
492     }
493     ierr = PetscFree(recv_buffer_bool);CHKERRQ(ierr);
494     ierr = PetscFree(subset_has_corn);CHKERRQ(ierr);
495 
496     /* determine send/recv buffers sizes */
497     j = 0;
498     mss = 0;
499     for (i=0;i<graph->n_subsets;i++) {
500       if (PetscBTLookup(subset_cc_adapt,i)) {
501         j  += graph->subset_size[i];
502         mss = PetscMax(graph->subset_size[i],mss);
503       }
504     }
505     k = 0;
506     mns = 0;
507     for (i=0;i<graph->n_subsets;i++) {
508       if (PetscBTLookup(subset_cc_adapt,i)) {
509         k  += (cum_recv_counts[i+1]-cum_recv_counts[i])*graph->subset_size[i];
510         mns = PetscMax(cum_recv_counts[i+1]-cum_recv_counts[i],mns);
511       }
512     }
513     ierr = PetscMalloc2(j,&send_buffer,k,&recv_buffer);CHKERRQ(ierr);
514 
515     /* fill send buffer (order matters: subset_idxs ordered by global ordering) */
516     j = 0;
517     for (i=0;i<graph->n_subsets;i++)
518       if (PetscBTLookup(subset_cc_adapt,i))
519         for (k=0;k<graph->subset_size[i];k++)
520           send_buffer[j++] = labels[graph->subset_idxs[i][k]];
521 
522     /* now exchange the data */
523     start_of_recv = 0;
524     start_of_send = 0;
525     sum_requests  = 0;
526     for (i=0;i<graph->n_subsets;i++) {
527       if (PetscBTLookup(subset_cc_adapt,i)) {
528         PetscMPIInt neigh,tag;
529         PetscInt    size_of_send = graph->subset_size[i];
530 
531         j    = graph->subset_idxs[i][0];
532         ierr = PetscMPIIntCast(2*graph->subset_ref_node[i]+1,&tag);CHKERRQ(ierr);
533         for (k=0;k<graph->count[j];k++) {
534           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
535           ierr = MPI_Isend(&send_buffer[start_of_send],size_of_send,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
536           ierr = MPI_Irecv(&recv_buffer[start_of_recv],size_of_send,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
537           start_of_recv += size_of_send;
538           sum_requests++;
539         }
540         start_of_send += size_of_send;
541       }
542     }
543     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
544 
545     /* refine connected components */
546     start_of_recv = 0;
547     /* allocate some temporary space */
548     if (mss) {
549       ierr = PetscMalloc1(mss,&refine_buffer);CHKERRQ(ierr);
550       ierr = PetscMalloc2(mss*(mns+1),&refine_buffer[0],mss,&private_labels);CHKERRQ(ierr);
551     }
552     ncc = 0;
553     cum_queue = 0;
554     graph->cptr[0] = 0;
555     for (i=0;i<graph->n_subsets;i++) {
556       if (PetscBTLookup(subset_cc_adapt,i)) {
557         PetscInt subset_counter = 0;
558         PetscInt sharingprocs = cum_recv_counts[i+1]-cum_recv_counts[i]+1; /* count myself */
559         PetscInt buffer_size = graph->subset_size[i];
560 
561         /* compute pointers */
562         for (j=1;j<buffer_size;j++) refine_buffer[j] = refine_buffer[j-1] + sharingprocs;
563         /* analyze contributions from subdomains that share the i-th subset
564            The structure of refine_buffer is suitable to find intersections of ccs among sharingprocs.
565            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)
566            sharing procs connected components:
567              neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
568              neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
569              neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
570            refine_buffer will be filled as:
571              [ 4, 3, 1;
572                4, 2, 1;
573                7, 2, 6;
574                4, 3, 5;
575                7, 2, 6; ];
576            The connected components in local ordering are [0], [1], [2 3], [4] */
577         /* fill temp_buffer */
578         for (k=0;k<buffer_size;k++) refine_buffer[k][0] = labels[graph->subset_idxs[i][k]];
579         for (j=0;j<sharingprocs-1;j++) {
580           for (k=0;k<buffer_size;k++) refine_buffer[k][j+1] = recv_buffer[start_of_recv+k];
581           start_of_recv += buffer_size;
582         }
583         ierr = PetscMemzero(private_labels,buffer_size*sizeof(PetscInt));CHKERRQ(ierr);
584         for (j=0;j<buffer_size;j++) {
585           if (!private_labels[j]) { /* found a new cc  */
586             PetscBool same_set;
587 
588             graph->cptr[ncc] = cum_queue;
589             ncc++;
590             subset_counter++;
591             private_labels[j] = subset_counter;
592             graph->queue[cum_queue++] = graph->subset_idxs[i][j];
593             for (k=j+1;k<buffer_size;k++) { /* check for other nodes in new cc */
594               same_set = PETSC_TRUE;
595               for (s=0;s<sharingprocs;s++) {
596                 if (refine_buffer[j][s] != refine_buffer[k][s]) {
597                   same_set = PETSC_FALSE;
598                   break;
599                 }
600               }
601               if (same_set) {
602                 private_labels[k] = subset_counter;
603                 graph->queue[cum_queue++] = graph->subset_idxs[i][k];
604               }
605             }
606           }
607         }
608         graph->cptr[ncc]     = cum_queue;
609         graph->subset_ncc[i] = subset_counter;
610         graph->queue_sorted  = PETSC_FALSE;
611       } else { /* this subset does not need to be adapted */
612         ierr = PetscMemcpy(graph->queue+cum_queue,graph->subset_idxs[i],graph->subset_size[i]*sizeof(PetscInt));CHKERRQ(ierr);
613         ncc++;
614         cum_queue += graph->subset_size[i];
615         graph->cptr[ncc] = cum_queue;
616       }
617     }
618     graph->cptr[ncc] = cum_queue;
619     graph->ncc       = ncc;
620     if (mss) {
621       ierr = PetscFree2(refine_buffer[0],private_labels);CHKERRQ(ierr);
622       ierr = PetscFree(refine_buffer);CHKERRQ(ierr);
623     }
624     ierr = PetscFree(labels);CHKERRQ(ierr);
625     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
626     ierr = PetscFree2(send_requests,recv_requests);CHKERRQ(ierr);
627     ierr = PetscFree2(send_buffer,recv_buffer);CHKERRQ(ierr);
628     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
629     ierr = PetscBTDestroy(&subset_cc_adapt);CHKERRQ(ierr);
630   }
631   ierr = PetscBTDestroy(&cornerp);CHKERRQ(ierr);
632 
633   /* Determine if we are in 2D or 3D */
634   if (!graph->twodimset) {
635     PetscBool twodim = PETSC_TRUE;
636     for (i=0;i<graph->ncc;i++) {
637       PetscInt repdof = graph->queue[graph->cptr[i]];
638       PetscInt ccsize = graph->cptr[i+1]-graph->cptr[i];
639       if (graph->count[repdof] > 1 && ccsize > graph->custom_minimal_size) {
640         twodim = PETSC_FALSE;
641         break;
642       }
643     }
644     ierr = MPIU_Allreduce(&twodim,&graph->twodim,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
645     graph->twodimset = PETSC_TRUE;
646   }
647   PetscFunctionReturn(0);
648 }
649 
650 
651 PETSC_STATIC_INLINE PetscErrorCode PCBDDCGraphComputeCC_Private(PCBDDCGraph graph,PetscInt pid,PetscInt* queue_tip,PetscInt n_prev,PetscInt* n_added)
652 {
653   PetscInt       i,j,n;
654   PetscInt       *xadj = graph->xadj,*adjncy = graph->adjncy;
655   PetscBT        touched = graph->touched;
656   PetscBool      havecsr = (PetscBool)(!!xadj);
657   PetscBool      havesubs = (PetscBool)(!!graph->n_local_subs);
658   PetscErrorCode ierr;
659 
660   PetscFunctionBegin;
661   n = 0;
662   if (havecsr && !havesubs) {
663     for (i=-n_prev;i<0;i++) {
664       PetscInt start_dof = queue_tip[i];
665       /* we assume that if a dof has a size 1 adjacency list and the corresponding entry is negative, it is connected to all dofs */
666       if (xadj[start_dof+1]-xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
667         for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
668           PetscInt dof = graph->subset_idxs[pid-1][j];
669           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
670             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
671             queue_tip[n] = dof;
672             n++;
673           }
674         }
675       } else {
676         for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
677           PetscInt dof = adjncy[j];
678           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
679             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
680             queue_tip[n] = dof;
681             n++;
682           }
683         }
684       }
685     }
686   } else if (havecsr && havesubs) {
687     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
688     for (i=-n_prev;i<0;i++) {
689       PetscInt start_dof = queue_tip[i];
690       /* 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 */
691       if (xadj[start_dof+1]-xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
692         for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
693           PetscInt dof = graph->subset_idxs[pid-1][j];
694           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
695             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
696             queue_tip[n] = dof;
697             n++;
698           }
699         }
700       } else {
701         for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
702           PetscInt dof = adjncy[j];
703           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
704             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
705             queue_tip[n] = dof;
706             n++;
707           }
708         }
709       }
710     }
711   } else if (havesubs) { /* sub info only */
712     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
713     for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
714       PetscInt dof = graph->subset_idxs[pid-1][j];
715       if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
716         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
717         queue_tip[n] = dof;
718         n++;
719       }
720     }
721   } else {
722     for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
723       PetscInt dof = graph->subset_idxs[pid-1][j];
724       if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
725         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
726         queue_tip[n] = dof;
727         n++;
728       }
729     }
730   }
731   *n_added = n;
732   PetscFunctionReturn(0);
733 }
734 
735 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
736 {
737   PetscInt       ncc,cum_queue,n;
738   PetscMPIInt    commsize;
739   PetscErrorCode ierr;
740 
741   PetscFunctionBegin;
742   if (!graph->setupcalled) SETERRQ(PetscObjectComm((PetscObject)graph->l2gmap),PETSC_ERR_ORDER,"PCBDDCGraphSetUp should be called first");
743   /* quiet return if there isn't any local info */
744   if (!graph->xadj && !graph->n_local_subs) {
745     PetscFunctionReturn(0);
746   }
747 
748   /* reset any previous search of connected components */
749   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
750   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&commsize);CHKERRQ(ierr);
751   if (commsize > graph->commsizelimit) {
752     PetscInt i;
753     for (i=0;i<graph->nvtxs;i++) {
754       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
755         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
756       }
757     }
758   }
759 
760   /* begin search for connected components */
761   cum_queue = 0;
762   ncc = 0;
763   for (n=0;n<graph->n_subsets;n++) {
764     PetscInt pid = n+1;  /* partition labeled by 0 is discarded */
765     PetscInt found = 0,prev = 0,first = 0,ncc_pid = 0;
766     while (found != graph->subset_size[n]) {
767       PetscInt added = 0;
768       if (!prev) { /* search for new starting dof */
769         while (PetscBTLookup(graph->touched,graph->subset_idxs[n][first])) first++;
770         ierr = PetscBTSet(graph->touched,graph->subset_idxs[n][first]);CHKERRQ(ierr);
771         graph->queue[cum_queue] = graph->subset_idxs[n][first];
772         graph->cptr[ncc] = cum_queue;
773         prev = 1;
774         cum_queue++;
775         found++;
776         ncc_pid++;
777         ncc++;
778       }
779       ierr = PCBDDCGraphComputeCC_Private(graph,pid,graph->queue + cum_queue,prev,&added);CHKERRQ(ierr);
780       if (!added) {
781         graph->subset_ncc[n] = ncc_pid;
782         graph->cptr[ncc] = cum_queue;
783       }
784       prev = added;
785       found += added;
786       cum_queue += added;
787       if (added && found == graph->subset_size[n]) {
788         graph->subset_ncc[n] = ncc_pid;
789         graph->cptr[ncc] = cum_queue;
790       }
791     }
792   }
793   graph->ncc = ncc;
794   graph->queue_sorted = PETSC_FALSE;
795   PetscFunctionReturn(0);
796 }
797 
798 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
799 {
800   IS             subset,subset_n;
801   MPI_Comm       comm;
802   const PetscInt *is_indices;
803   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global;
804   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
805   PetscMPIInt    commsize;
806   PetscBool      same_set,mirrors_found;
807   PetscErrorCode ierr;
808 
809   PetscFunctionBegin;
810   PetscValidLogicalCollectiveInt(graph->l2gmap,custom_minimal_size,2);
811   if (neumann_is) {
812     PetscValidHeaderSpecific(neumann_is,IS_CLASSID,3);
813     PetscCheckSameComm(graph->l2gmap,1,neumann_is,3);
814   }
815   graph->has_dirichlet = PETSC_FALSE;
816   if (dirichlet_is) {
817     PetscValidHeaderSpecific(dirichlet_is,IS_CLASSID,4);
818     PetscCheckSameComm(graph->l2gmap,1,dirichlet_is,4);
819     graph->has_dirichlet = PETSC_TRUE;
820   }
821   PetscValidLogicalCollectiveInt(graph->l2gmap,n_ISForDofs,5);
822   for (i=0;i<n_ISForDofs;i++) {
823     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,6);
824     PetscCheckSameComm(graph->l2gmap,1,ISForDofs[i],6);
825   }
826   if (custom_primal_vertices) {
827     PetscValidHeaderSpecific(custom_primal_vertices,IS_CLASSID,7);
828     PetscCheckSameComm(graph->l2gmap,1,custom_primal_vertices,7);
829   }
830   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
831   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
832 
833   /* custom_minimal_size */
834   graph->custom_minimal_size = custom_minimal_size;
835   /* get info l2gmap and allocate work vectors  */
836   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
837   /* check if we have any local periodic nodes (periodic BCs) */
838   mirrors_found = PETSC_FALSE;
839   if (graph->nvtxs && n_neigh) {
840     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
841     for (i=0; i<n_shared[0]; i++) {
842       if (graph->count[shared[0][i]] > 1) {
843         mirrors_found = PETSC_TRUE;
844         break;
845       }
846     }
847   }
848   /* compute local mirrors (if any) */
849   if (mirrors_found) {
850     IS       to,from;
851     PetscInt *local_indices,*global_indices;
852 
853     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
854     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
855     /* get arrays of local and global indices */
856     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
857     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
858     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
859     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
860     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
861     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
862     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
863     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
864     /* allocate space for mirrors */
865     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
866     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
867     graph->mirrors_set[0] = 0;
868 
869     k=0;
870     for (i=0;i<n_shared[0];i++) {
871       j=shared[0][i];
872       if (graph->count[j] > 1) {
873         graph->mirrors[j]++;
874         k++;
875       }
876     }
877     /* allocate space for set of mirrors */
878     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
879     for (i=1;i<graph->nvtxs;i++)
880       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
881 
882     /* fill arrays */
883     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
884     for (j=0;j<n_shared[0];j++) {
885       i=shared[0][j];
886       if (graph->count[i] > 1)
887         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
888     }
889     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
890     for (i=0;i<graph->nvtxs;i++) {
891       if (graph->mirrors[i] > 0) {
892         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
893         j = global_indices[k];
894         while ( k > 0 && global_indices[k-1] == j) k--;
895         for (j=0;j<graph->mirrors[i];j++) {
896           graph->mirrors_set[i][j]=local_indices[k+j];
897         }
898         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
899       }
900     }
901     ierr = PetscFree(local_indices);CHKERRQ(ierr);
902     ierr = PetscFree(global_indices);CHKERRQ(ierr);
903     ierr = ISDestroy(&to);CHKERRQ(ierr);
904     ierr = ISDestroy(&from);CHKERRQ(ierr);
905   }
906   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
907 
908   /* Count total number of neigh per node */
909   k = 0;
910   for (i=1;i<n_neigh;i++) {
911     k += n_shared[i];
912     for (j=0;j<n_shared[i];j++) {
913       graph->count[shared[i][j]] += 1;
914     }
915   }
916   /* Allocate space for storing the set of neighbours for each node */
917   if (graph->nvtxs) {
918     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
919   }
920   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
921     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
922   }
923   /* Get information for sharing subdomains */
924   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
925   for (i=1;i<n_neigh;i++) { /* dont count myself */
926     s = n_shared[i];
927     for (j=0;j<s;j++) {
928       k = shared[i][j];
929       graph->neighbours_set[k][graph->count[k]] = neigh[i];
930       graph->count[k] += 1;
931     }
932   }
933   /* sort set of sharing subdomains */
934   for (i=0;i<graph->nvtxs;i++) {
935     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
936   }
937   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
938   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
939 
940   /*
941      Get info for dofs splitting
942      User can specify just a subset; an additional field is considered as a complementary field
943   */
944   for (i=0;i<graph->nvtxs;i++) graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
945   for (i=0;i<n_ISForDofs;i++) {
946     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
947     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
948     for (j=0;j<is_size;j++) {
949       if (is_indices[j] > -1 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
950         graph->which_dof[is_indices[j]] = i;
951       }
952     }
953     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
954   }
955 
956   /* Take into account Neumann nodes */
957   if (neumann_is) {
958     ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
959     ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
960     for (i=0;i<is_size;i++) {
961       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
962         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_NEUMANN_MARK;
963       }
964     }
965     ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
966   }
967   /* Take into account Dirichlet nodes (they overwrite any neumann boundary mark previously set) */
968   if (dirichlet_is) {
969     ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
970     ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
971     for (i=0;i<is_size;i++){
972       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
973         if (commsize > graph->commsizelimit) { /* dirichlet nodes treated as internal */
974           ierr = PetscBTSet(graph->touched,is_indices[i]);CHKERRQ(ierr);
975           graph->subset[is_indices[i]] = 0;
976         }
977         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_DIRICHLET_MARK;
978       }
979     }
980     ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
981   }
982   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
983   if (graph->mirrors) {
984     for (i=0;i<graph->nvtxs;i++)
985       if (graph->mirrors[i])
986         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
987 
988     if (graph->xadj) {
989       PetscInt *new_xadj,*new_adjncy;
990       /* sort CSR graph */
991       for (i=0;i<graph->nvtxs;i++)
992         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
993 
994       /* adapt local CSR graph in case of local periodicity */
995       k = 0;
996       for (i=0;i<graph->nvtxs;i++)
997         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
998           k += graph->mirrors[graph->adjncy[j]];
999 
1000       ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
1001       ierr = PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy);CHKERRQ(ierr);
1002       new_xadj[0] = 0;
1003       for (i=0;i<graph->nvtxs;i++) {
1004         k = graph->xadj[i+1]-graph->xadj[i];
1005         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
1006         new_xadj[i+1] = new_xadj[i]+k;
1007         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
1008           k = graph->mirrors[graph->adjncy[j]];
1009           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
1010           new_xadj[i+1] += k;
1011         }
1012         k = new_xadj[i+1]-new_xadj[i];
1013         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
1014         new_xadj[i+1] = new_xadj[i]+k;
1015       }
1016       /* set new CSR into graph */
1017       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1018       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1019       graph->xadj = new_xadj;
1020       graph->adjncy = new_adjncy;
1021     }
1022   }
1023 
1024   /* mark special nodes (if any) -> each will become a single node equivalence class */
1025   if (custom_primal_vertices) {
1026     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
1027     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1028     for (i=0,j=0;i<is_size;i++){
1029       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 */
1030         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_SPECIAL_MARK-j;
1031         j++;
1032       }
1033     }
1034     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1035   }
1036 
1037   /* mark interior nodes (if commsize > graph->commsizelimit) as touched and belonging to partition number 0 */
1038   if (commsize > graph->commsizelimit) {
1039     for (i=0;i<graph->nvtxs;i++) {
1040       if (!graph->count[i]) {
1041         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
1042         graph->subset[i] = 0;
1043       }
1044     }
1045   }
1046 
1047   /* init graph structure and compute default subsets */
1048   nodes_touched = 0;
1049   for (i=0;i<graph->nvtxs;i++) {
1050     if (PetscBTLookup(graph->touched,i)) {
1051       nodes_touched++;
1052     }
1053   }
1054   i = 0;
1055   graph->ncc = 0;
1056   total_counts = 0;
1057 
1058   /* allocated space for queues */
1059   if (commsize == graph->commsizelimit) {
1060     ierr = PetscMalloc2(graph->nvtxs+1,&graph->cptr,graph->nvtxs,&graph->queue);CHKERRQ(ierr);
1061   } else {
1062     PetscInt nused = graph->nvtxs - nodes_touched;
1063     ierr = PetscMalloc2(nused+1,&graph->cptr,nused,&graph->queue);CHKERRQ(ierr);
1064   }
1065 
1066   while (nodes_touched<graph->nvtxs) {
1067     /*  find first untouched node in local ordering */
1068     while (PetscBTLookup(graph->touched,i)) i++;
1069     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
1070     graph->subset[i] = graph->ncc+1;
1071     graph->cptr[graph->ncc] = total_counts;
1072     graph->queue[total_counts] = i;
1073     total_counts++;
1074     nodes_touched++;
1075     /* now find all other nodes having the same set of sharing subdomains */
1076     for (j=i+1;j<graph->nvtxs;j++) {
1077       /* check for same number of sharing subdomains, dof number and same special mark */
1078       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]) {
1079         /* check for same set of sharing subdomains */
1080         same_set = PETSC_TRUE;
1081         for (k=0;k<graph->count[j];k++){
1082           if (graph->neighbours_set[i][k] != graph->neighbours_set[j][k]) {
1083             same_set = PETSC_FALSE;
1084           }
1085         }
1086         /* I have found a friend of mine */
1087         if (same_set) {
1088           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
1089           graph->subset[j] = graph->ncc+1;
1090           nodes_touched++;
1091           graph->queue[total_counts] = j;
1092           total_counts++;
1093         }
1094       }
1095     }
1096     graph->ncc++;
1097   }
1098   /* 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 */
1099   graph->n_subsets = graph->ncc;
1100   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
1101   for (i=0;i<graph->n_subsets;i++) {
1102     graph->subset_ncc[i] = 1;
1103   }
1104   /* final pointer */
1105   graph->cptr[graph->ncc] = total_counts;
1106 
1107   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each connected component */
1108   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
1109   ierr = PetscMalloc1(graph->ncc,&graph->subset_ref_node);CHKERRQ(ierr);
1110   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
1111   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
1112   for (j=0;j<graph->ncc;j++) {
1113     ierr = PetscSortIntWithArray(graph->cptr[j+1]-graph->cptr[j],&queue_global[graph->cptr[j]],&graph->queue[graph->cptr[j]]);CHKERRQ(ierr);
1114     graph->subset_ref_node[j] = graph->queue[graph->cptr[j]];
1115   }
1116   ierr = PetscFree(queue_global);CHKERRQ(ierr);
1117   graph->queue_sorted = PETSC_TRUE;
1118 
1119   /* save information on subsets (needed when analyzing the connected components) */
1120   if (graph->ncc) {
1121     ierr = PetscMalloc2(graph->ncc,&graph->subset_size,graph->ncc,&graph->subset_idxs);CHKERRQ(ierr);
1122     ierr = PetscMalloc1(graph->cptr[graph->ncc],&graph->subset_idxs[0]);CHKERRQ(ierr);
1123     ierr = PetscMemzero(graph->subset_idxs[0],graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
1124     for (j=1;j<graph->ncc;j++) {
1125       graph->subset_size[j-1] = graph->cptr[j] - graph->cptr[j-1];
1126       graph->subset_idxs[j] = graph->subset_idxs[j-1] + graph->subset_size[j-1];
1127     }
1128     graph->subset_size[graph->ncc-1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc-1];
1129     ierr = PetscMemcpy(graph->subset_idxs[0],graph->queue,graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
1130   }
1131 
1132   /* renumber reference nodes */
1133   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->ncc,graph->subset_ref_node,PETSC_COPY_VALUES,&subset_n);CHKERRQ(ierr);
1134   ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,subset_n,&subset);CHKERRQ(ierr);
1135   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1136   ierr = ISRenumber(subset,NULL,NULL,&subset_n);CHKERRQ(ierr);
1137   ierr = ISDestroy(&subset);CHKERRQ(ierr);
1138   ierr = ISGetLocalSize(subset_n,&k);CHKERRQ(ierr);
1139   if (k != graph->ncc) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",k,graph->ncc);
1140   ierr = ISGetIndices(subset_n,&is_indices);CHKERRQ(ierr);
1141   ierr = PetscMemcpy(graph->subset_ref_node,is_indices,graph->ncc*sizeof(PetscInt));CHKERRQ(ierr);
1142   ierr = ISRestoreIndices(subset_n,&is_indices);CHKERRQ(ierr);
1143   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1144 
1145   /* free workspace */
1146   graph->setupcalled = PETSC_TRUE;
1147   PetscFunctionReturn(0);
1148 }
1149 
1150 PetscErrorCode PCBDDCGraphResetCoords(PCBDDCGraph graph)
1151 {
1152   PetscErrorCode ierr;
1153 
1154   PetscFunctionBegin;
1155   if (!graph) PetscFunctionReturn(0);
1156   ierr = PetscFree(graph->coords);CHKERRQ(ierr);
1157   graph->cdim  = 0;
1158   graph->cnloc = 0;
1159   graph->cloc  = PETSC_FALSE;
1160   PetscFunctionReturn(0);
1161 }
1162 
1163 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1164 {
1165   PetscErrorCode ierr;
1166 
1167   PetscFunctionBegin;
1168   if (!graph) PetscFunctionReturn(0);
1169   if (graph->freecsr) {
1170     ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1171     ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1172   } else {
1173     graph->xadj = NULL;
1174     graph->adjncy = NULL;
1175   }
1176   graph->freecsr = PETSC_FALSE;
1177   graph->nvtxs_csr = 0;
1178   PetscFunctionReturn(0);
1179 }
1180 
1181 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1182 {
1183   PetscErrorCode ierr;
1184 
1185   PetscFunctionBegin;
1186   if (!graph) PetscFunctionReturn(0);
1187   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
1188   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
1189   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1190   if (graph->nvtxs) {
1191     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1192   }
1193   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1194   ierr = PetscFree5(graph->count,
1195                     graph->neighbours_set,
1196                     graph->subset,
1197                     graph->which_dof,
1198                     graph->special_dof);CHKERRQ(ierr);
1199   ierr = PetscFree2(graph->cptr,graph->queue);CHKERRQ(ierr);
1200   if (graph->mirrors) {
1201     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1202   }
1203   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1204   if (graph->subset_idxs) {
1205     ierr = PetscFree(graph->subset_idxs[0]);CHKERRQ(ierr);
1206   }
1207   ierr = PetscFree2(graph->subset_size,graph->subset_idxs);CHKERRQ(ierr);
1208   ierr = ISDestroy(&graph->dirdofs);CHKERRQ(ierr);
1209   ierr = ISDestroy(&graph->dirdofsB);CHKERRQ(ierr);
1210   if (graph->n_local_subs) {
1211     ierr = PetscFree(graph->local_subs);CHKERRQ(ierr);
1212   }
1213   graph->has_dirichlet       = PETSC_FALSE;
1214   graph->twodimset           = PETSC_FALSE;
1215   graph->twodim              = PETSC_FALSE;
1216   graph->nvtxs               = 0;
1217   graph->nvtxs_global        = 0;
1218   graph->n_subsets           = 0;
1219   graph->custom_minimal_size = 1;
1220   graph->n_local_subs        = 0;
1221   graph->maxcount            = PETSC_MAX_INT;
1222   graph->setupcalled         = PETSC_FALSE;
1223   PetscFunctionReturn(0);
1224 }
1225 
1226 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N, PetscInt maxcount)
1227 {
1228   PetscInt       n;
1229   PetscErrorCode ierr;
1230 
1231   PetscFunctionBegin;
1232   PetscValidPointer(graph,1);
1233   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1234   PetscValidLogicalCollectiveInt(l2gmap,N,3);
1235   PetscValidLogicalCollectiveInt(l2gmap,maxcount,4);
1236   /* raise an error if already allocated */
1237   if (graph->nvtxs_global) SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1238   /* set number of vertices */
1239   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1240   graph->l2gmap = l2gmap;
1241   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1242   graph->nvtxs = n;
1243   graph->nvtxs_global = N;
1244   /* allocate used space */
1245   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1246   ierr = PetscMalloc5(graph->nvtxs,&graph->count,
1247                       graph->nvtxs,&graph->neighbours_set,
1248                       graph->nvtxs,&graph->subset,
1249                       graph->nvtxs,&graph->which_dof,
1250                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1251   /* zeroes memory */
1252   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1253   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1254   /* use -1 as a default value for which_dof array */
1255   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1256   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1257   /* zeroes first pointer to neighbour set */
1258   if (graph->nvtxs) {
1259     graph->neighbours_set[0] = 0;
1260   }
1261   /* zeroes workspace for values of ncc */
1262   graph->subset_ncc = 0;
1263   graph->subset_ref_node = 0;
1264   /* maxcount for cc */
1265   graph->maxcount = maxcount;
1266   PetscFunctionReturn(0);
1267 }
1268 
1269 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1270 {
1271   PetscErrorCode ierr;
1272 
1273   PetscFunctionBegin;
1274   ierr = PCBDDCGraphResetCSR(*graph);CHKERRQ(ierr);
1275   ierr = PCBDDCGraphResetCoords(*graph);CHKERRQ(ierr);
1276   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1277   ierr = PetscFree(*graph);CHKERRQ(ierr);
1278   PetscFunctionReturn(0);
1279 }
1280 
1281 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1282 {
1283   PCBDDCGraph    new_graph;
1284   PetscErrorCode ierr;
1285 
1286   PetscFunctionBegin;
1287   ierr = PetscNew(&new_graph);CHKERRQ(ierr);
1288   new_graph->custom_minimal_size = 1;
1289   new_graph->commsizelimit = 1;
1290   *graph = new_graph;
1291   PetscFunctionReturn(0);
1292 }
1293