xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision b41ce5d507ea9a58bfa83cf403107a702e77a67d)
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   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Max count %d\n",graph->maxcount);CHKERRQ(ierr);
76   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Topological two dim? %d (set %d)\n",graph->twodim,graph->twodimset);CHKERRQ(ierr);
77   if (verbosity_level > 2) {
78     for (i=0;i<graph->nvtxs;i++) {
79       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d:\n",i);CHKERRQ(ierr);
80       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %d\n",graph->which_dof[i]);CHKERRQ(ierr);
81       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %d\n",graph->special_dof[i]);CHKERRQ(ierr);
82       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %d\n",graph->count[i]);CHKERRQ(ierr);
83       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
84       if (graph->count[i]) {
85         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:");CHKERRQ(ierr);
86         for (j=0;j<graph->count[i];j++) {
87           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[i][j]);CHKERRQ(ierr);
88         }
89         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
90       }
91       ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
92       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
93       if (graph->mirrors) {
94         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %d\n",graph->mirrors[i]);CHKERRQ(ierr);
95         if (graph->mirrors[i]) {
96           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
97           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:");CHKERRQ(ierr);
98           for (j=0;j<graph->mirrors[i];j++) {
99             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->mirrors_set[i][j]);CHKERRQ(ierr);
100           }
101           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
102           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
103           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
104         }
105       }
106       if (verbosity_level > 3) {
107         if (graph->xadj) {
108           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:");CHKERRQ(ierr);
109           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
110           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
111             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->adjncy[j]);CHKERRQ(ierr);
112           }
113           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
114           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
115           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
116         } else {
117           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   no adj info\n");CHKERRQ(ierr);
118         }
119       }
120       if (graph->n_local_subs) {
121         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local sub id: %d\n",graph->local_subs[i]);CHKERRQ(ierr);
122       }
123       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
124       if (graph->subset[i] && graph->subset_ncc) {
125         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
126       }
127     }
128   }
129   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
130   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
131   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
132   for (i=0;i<graph->ncc;i++) {
133     PetscInt node_num=graph->queue[graph->cptr[i]];
134     PetscBool printcc = PETSC_FALSE;
135     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);
136     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
137     for (j=0;j<graph->count[node_num];j++) {
138       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
139     }
140     if (verbosity_level > 1) {
141       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
142       if (verbosity_level > 2 || graph->twodim || graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) {
143         printcc = PETSC_TRUE;
144       }
145       if (printcc) {
146         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
147           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
148         }
149       }
150     } else {
151       ierr = PetscViewerASCIISynchronizedPrintf(viewer,")");CHKERRQ(ierr);
152     }
153     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
154     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
155     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
156   }
157   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
158   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
159   PetscFunctionReturn(0);
160 }
161 
162 PetscErrorCode PCBDDCGraphRestoreCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
163 {
164   PetscInt       i;
165   PetscErrorCode ierr;
166 
167   PetscFunctionBegin;
168   if (n_faces) {
169     if (FacesIS) {
170       for (i=0;i<*n_faces;i++) {
171         ierr = ISDestroy(&((*FacesIS)[i]));CHKERRQ(ierr);
172       }
173       ierr = PetscFree(*FacesIS);CHKERRQ(ierr);
174     }
175     *n_faces = 0;
176   }
177   if (n_edges) {
178     if (EdgesIS) {
179       for (i=0;i<*n_edges;i++) {
180         ierr = ISDestroy(&((*EdgesIS)[i]));CHKERRQ(ierr);
181       }
182       ierr = PetscFree(*EdgesIS);CHKERRQ(ierr);
183     }
184     *n_edges = 0;
185   }
186   if (VerticesIS) {
187     ierr = ISDestroy(VerticesIS);CHKERRQ(ierr);
188   }
189   PetscFunctionReturn(0);
190 }
191 
192 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
193 {
194   IS             *ISForFaces,*ISForEdges,ISForVertices;
195   PetscInt       i,nfc,nec,nvc,*idx,*mark;
196   PetscErrorCode ierr;
197 
198   PetscFunctionBegin;
199   ierr = PetscCalloc1(graph->ncc,&mark);CHKERRQ(ierr);
200   /* loop on ccs to evalute number of faces, edges and vertices */
201   nfc = 0;
202   nec = 0;
203   nvc = 0;
204   for (i=0;i<graph->ncc;i++) {
205     PetscInt repdof = graph->queue[graph->cptr[i]];
206     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size && graph->count[repdof] < graph->maxcount) {
207       if (!graph->twodim && graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
208         nfc++;
209         mark[i] = 2;
210       } else {
211         nec++;
212         mark[i] = 1;
213       }
214     } else {
215       nvc += graph->cptr[i+1]-graph->cptr[i];
216     }
217   }
218 
219   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
220   if (FacesIS) {
221     ierr = PetscMalloc1(nfc,&ISForFaces);CHKERRQ(ierr);
222   }
223   if (EdgesIS) {
224     ierr = PetscMalloc1(nec,&ISForEdges);CHKERRQ(ierr);
225   }
226   if (VerticesIS) {
227     ierr = PetscMalloc1(nvc,&idx);CHKERRQ(ierr);
228   }
229 
230   /* loop on ccs to compute index sets for faces and edges */
231   if (!graph->queue_sorted) {
232     PetscInt *queue_global;
233 
234     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
235     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
236     for (i=0;i<graph->ncc;i++) {
237       ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
238     }
239     ierr = PetscFree(queue_global);CHKERRQ(ierr);
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) {
247         ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_USE_POINTER,&ISForFaces[nfc]);CHKERRQ(ierr);
248       }
249       nfc++;
250     } else if (mark[i] == 1) {
251       if (EdgesIS) {
252         ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_USE_POINTER,&ISForEdges[nec]);CHKERRQ(ierr);
253       }
254       nec++;
255     }
256   }
257 
258   /* index set for vertices */
259   if (VerticesIS) {
260     nvc = 0;
261     for (i=0;i<graph->ncc;i++) {
262       if (!mark[i]) {
263         PetscInt j;
264 
265         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
266           idx[nvc]=graph->queue[j];
267           nvc++;
268         }
269       }
270     }
271     /* sort vertex set (by local ordering) */
272     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
273     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
274   }
275   ierr = PetscFree(mark);CHKERRQ(ierr);
276 
277   /* get back info */
278   if (n_faces)       *n_faces = nfc;
279   if (FacesIS)       *FacesIS = ISForFaces;
280   if (n_edges)       *n_edges = nec;
281   if (EdgesIS)       *EdgesIS = ISForEdges;
282   if (VerticesIS) *VerticesIS = ISForVertices;
283   PetscFunctionReturn(0);
284 }
285 
286 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
287 {
288   PetscBool      adapt_interface_reduced;
289   MPI_Comm       interface_comm;
290   PetscMPIInt    size;
291   PetscInt       i;
292   PetscErrorCode ierr;
293 
294   PetscFunctionBegin;
295   /* compute connected components locally */
296   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
297   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
298   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
299   ierr = MPI_Comm_size(interface_comm,&size);CHKERRQ(ierr);
300   adapt_interface_reduced = PETSC_FALSE;
301   if (size > 1) {
302     PetscInt i;
303     PetscBool adapt_interface = PETSC_FALSE;
304     for (i=0;i<graph->n_subsets;i++) {
305       /* We are not sure that on a given subset of the local interface,
306          with two connected components, the latters be the same among sharing subdomains */
307       if (graph->subset_ncc[i] > 1) {
308         adapt_interface = PETSC_TRUE;
309         break;
310       }
311     }
312     ierr = MPIU_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_BOOL,MPI_LOR,interface_comm);CHKERRQ(ierr);
313   }
314 
315   if (graph->n_subsets && adapt_interface_reduced) {
316     PetscBT     subset_cc_adapt;
317     MPI_Request *send_requests,*recv_requests;
318     PetscInt    *send_buffer,*recv_buffer;
319     PetscInt    sum_requests,start_of_recv,start_of_send;
320     PetscInt    *cum_recv_counts;
321     PetscInt    *labels;
322     PetscInt    ncc,cum_queue,mss,mns,j,k,s;
323     PetscInt    **refine_buffer=NULL,*private_labels = NULL;
324 
325     ierr = PetscMalloc1(graph->nvtxs,&labels);CHKERRQ(ierr);
326     ierr = PetscMemzero(labels,graph->nvtxs*sizeof(*labels));CHKERRQ(ierr);
327     for (i=0;i<graph->ncc;i++)
328       for (j=graph->cptr[i];j<graph->cptr[i+1];j++)
329         labels[graph->queue[j]] = i;
330 
331     /* allocate some space */
332     ierr = PetscMalloc1(graph->n_subsets+1,&cum_recv_counts);CHKERRQ(ierr);
333     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
334 
335     /* first count how many neighbours per connected component I will receive from */
336     cum_recv_counts[0] = 0;
337     for (i=0;i<graph->n_subsets;i++) cum_recv_counts[i+1] = cum_recv_counts[i]+graph->count[graph->subset_idxs[i][0]];
338     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_buffer);CHKERRQ(ierr);
339     ierr = PetscMalloc2(cum_recv_counts[graph->n_subsets],&send_requests,cum_recv_counts[graph->n_subsets],&recv_requests);CHKERRQ(ierr);
340     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
341       send_requests[i] = MPI_REQUEST_NULL;
342       recv_requests[i] = MPI_REQUEST_NULL;
343     }
344 
345     /* exchange with my neighbours the number of my connected components on the subset of interface */
346     sum_requests = 0;
347     for (i=0;i<graph->n_subsets;i++) {
348       PetscMPIInt neigh,tag;
349       PetscInt    count,*neighs;
350 
351       count = graph->count[graph->subset_idxs[i][0]];
352       neighs = graph->neighbours_set[graph->subset_idxs[i][0]];
353       ierr = PetscMPIIntCast(2*graph->subset_ref_node[i],&tag);CHKERRQ(ierr);
354       for (k=0;k<count;k++) {
355         ierr = PetscMPIIntCast(neighs[k],&neigh);CHKERRQ(ierr);
356         ierr = MPI_Isend(&graph->subset_ncc[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
357         ierr = MPI_Irecv(&recv_buffer[sum_requests],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
358         sum_requests++;
359       }
360     }
361     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
362     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
363 
364     /* determine the subsets I have to adapt (those having more than 1 cc) */
365     ierr = PetscBTCreate(graph->n_subsets,&subset_cc_adapt);CHKERRQ(ierr);
366     ierr = PetscBTMemzero(graph->n_subsets,subset_cc_adapt);CHKERRQ(ierr);
367     for (i=0;i<graph->n_subsets;i++) {
368       if (graph->subset_ncc[i] > 1) {
369         ierr = PetscBTSet(subset_cc_adapt,i);CHKERRQ(ierr);
370         continue;
371       }
372       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
373          if (recv_buffer[j] > 1) {
374           ierr = PetscBTSet(subset_cc_adapt,i);CHKERRQ(ierr);
375           break;
376         }
377       }
378     }
379     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
380 
381     /* determine send/recv buffers sizes */
382     j = 0;
383     mss = 0;
384     for (i=0;i<graph->n_subsets;i++) {
385       if (PetscBTLookup(subset_cc_adapt,i)) {
386         j += graph->subset_size[i];
387         mss = PetscMax(graph->subset_size[i],mss);
388       }
389     }
390     k = 0;
391     mns = 0;
392     for (i=0;i<graph->n_subsets;i++) {
393       if (PetscBTLookup(subset_cc_adapt,i)) {
394         k += (cum_recv_counts[i+1]-cum_recv_counts[i])*graph->subset_size[i];
395         mns = PetscMax(cum_recv_counts[i+1]-cum_recv_counts[i],mns);
396       }
397     }
398     ierr = PetscMalloc2(j,&send_buffer,k,&recv_buffer);CHKERRQ(ierr);
399 
400     /* fill send buffer (order matters: subset_idxs ordered by global ordering) */
401     j = 0;
402     for (i=0;i<graph->n_subsets;i++)
403       if (PetscBTLookup(subset_cc_adapt,i))
404         for (k=0;k<graph->subset_size[i];k++)
405           send_buffer[j++] = labels[graph->subset_idxs[i][k]];
406 
407     /* now exchange the data */
408     start_of_recv = 0;
409     start_of_send = 0;
410     sum_requests = 0;
411     for (i=0;i<graph->n_subsets;i++) {
412       if (PetscBTLookup(subset_cc_adapt,i)) {
413         PetscMPIInt neigh,tag;
414         PetscInt    size_of_send = graph->subset_size[i];
415 
416         j = graph->subset_idxs[i][0];
417         ierr = PetscMPIIntCast(2*graph->subset_ref_node[i]+1,&tag);CHKERRQ(ierr);
418         for (k=0;k<graph->count[j];k++) {
419           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
420           ierr = MPI_Isend(&send_buffer[start_of_send],size_of_send,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
421           ierr = MPI_Irecv(&recv_buffer[start_of_recv],size_of_send,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
422           start_of_recv += size_of_send;
423           sum_requests++;
424         }
425         start_of_send += size_of_send;
426       }
427     }
428     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
429 
430     /* refine connected components */
431     start_of_recv = 0;
432     /* allocate some temporary space */
433     if (mss) {
434       ierr = PetscMalloc1(mss,&refine_buffer);CHKERRQ(ierr);
435       ierr = PetscMalloc2(mss*(mns+1),&refine_buffer[0],mss,&private_labels);CHKERRQ(ierr);
436     }
437     ncc = 0;
438     cum_queue = 0;
439     graph->cptr[0] = 0;
440     for (i=0;i<graph->n_subsets;i++) {
441       if (PetscBTLookup(subset_cc_adapt,i)) {
442         PetscInt subset_counter = 0;
443         PetscInt sharingprocs = cum_recv_counts[i+1]-cum_recv_counts[i]+1; /* count myself */
444         PetscInt buffer_size = graph->subset_size[i];
445 
446         /* compute pointers */
447         for (j=1;j<buffer_size;j++) refine_buffer[j] = refine_buffer[j-1] + sharingprocs;
448         /* analyze contributions from subdomains that share the i-th subset
449            The stricture of refine_buffer is suitable to find intersections of ccs among sharingprocs.
450            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)
451            sharing procs connected components:
452              neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
453              neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
454              neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
455            refine_buffer will be filled as:
456              [ 4, 3, 1;
457                4, 2, 1;
458                7, 2, 6;
459                4, 3, 5;
460                7, 2, 6; ];
461            The connected components in local ordering are [0], [1], [2 3], [4] */
462         /* fill temp_buffer */
463         for (k=0;k<buffer_size;k++) refine_buffer[k][0] = labels[graph->subset_idxs[i][k]];
464         for (j=0;j<sharingprocs-1;j++) {
465           for (k=0;k<buffer_size;k++) refine_buffer[k][j+1] = recv_buffer[start_of_recv+k];
466           start_of_recv += buffer_size;
467         }
468         ierr = PetscMemzero(private_labels,buffer_size*sizeof(PetscInt));CHKERRQ(ierr);
469         for (j=0;j<buffer_size;j++) {
470           if (!private_labels[j]) { /* found a new cc  */
471             PetscBool same_set;
472 
473             graph->cptr[ncc] = cum_queue;
474             ncc++;
475             subset_counter++;
476             private_labels[j] = subset_counter;
477             graph->queue[cum_queue++] = graph->subset_idxs[i][j];
478             for (k=j+1;k<buffer_size;k++) { /* check for other nodes in new cc */
479               same_set = PETSC_TRUE;
480               for (s=0;s<sharingprocs;s++) {
481                 if (refine_buffer[j][s] != refine_buffer[k][s]) {
482                   same_set = PETSC_FALSE;
483                   break;
484                 }
485               }
486               if (same_set) {
487                 private_labels[k] = subset_counter;
488                 graph->queue[cum_queue++] = graph->subset_idxs[i][k];
489               }
490             }
491           }
492         }
493         graph->cptr[ncc] = cum_queue;
494         graph->subset_ncc[i] = subset_counter;
495         graph->queue_sorted = PETSC_FALSE;
496       } else { /* this subset does not need to be adapted */
497         ierr = PetscMemcpy(graph->queue+cum_queue,graph->subset_idxs[i],graph->subset_size[i]*sizeof(PetscInt));CHKERRQ(ierr);
498         ncc++;
499         cum_queue += graph->subset_size[i];
500         graph->cptr[ncc] = cum_queue;
501       }
502     }
503     graph->cptr[ncc] = cum_queue;
504     graph->ncc = ncc;
505     if (mss) {
506       ierr = PetscFree2(refine_buffer[0],private_labels);CHKERRQ(ierr);
507       ierr = PetscFree(refine_buffer);CHKERRQ(ierr);
508     }
509     ierr = PetscFree(labels);CHKERRQ(ierr);
510     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
511     ierr = PetscFree2(send_requests,recv_requests);CHKERRQ(ierr);
512     ierr = PetscFree2(send_buffer,recv_buffer);CHKERRQ(ierr);
513     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
514     ierr = PetscBTDestroy(&subset_cc_adapt);CHKERRQ(ierr);
515   }
516 
517   /* Determine if we are in 2D or 3D */
518   if (!graph->twodimset) {
519     PetscBool twodim = PETSC_TRUE;
520     for (i=0;i<graph->ncc;i++) {
521       PetscInt repdof = graph->queue[graph->cptr[i]];
522       PetscInt ccsize = graph->cptr[i+1]-graph->cptr[i];
523       if (graph->count[repdof] > 1 && ccsize > graph->custom_minimal_size) {
524         twodim = PETSC_FALSE;
525         break;
526       }
527     }
528     ierr = MPIU_Allreduce(&twodim,&graph->twodim,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
529     graph->twodimset = PETSC_TRUE;
530   }
531   PetscFunctionReturn(0);
532 }
533 
534 
535 PETSC_STATIC_INLINE PetscErrorCode PCBDDCGraphComputeCC_Private(PCBDDCGraph graph,PetscInt pid,PetscInt* queue_tip,PetscInt n_prev,PetscInt* n_added)
536 {
537   PetscInt       i,j,n;
538   PetscInt       *xadj = graph->xadj,*adjncy = graph->adjncy;
539   PetscBT        touched = graph->touched;
540   PetscBool      havecsr = (PetscBool)(!!xadj);
541   PetscBool      havesubs = (PetscBool)(!!graph->n_local_subs);
542   PetscErrorCode ierr;
543 
544   PetscFunctionBegin;
545   n = 0;
546   if (havecsr && !havesubs) {
547     for (i=-n_prev;i<0;i++) {
548       PetscInt start_dof = queue_tip[i];
549       /* we assume that if a dof has a size 1 adjacency list and the corresponding entry is negative, it is connected to all dofs */
550       if (xadj[start_dof+1]-xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
551         for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
552           PetscInt dof = graph->subset_idxs[pid-1][j];
553           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
554             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
555             queue_tip[n] = dof;
556             n++;
557           }
558         }
559       } else {
560         for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
561           PetscInt dof = adjncy[j];
562           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid) {
563             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
564             queue_tip[n] = dof;
565             n++;
566           }
567         }
568       }
569     }
570   } else if (havecsr && havesubs) {
571     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
572     for (i=-n_prev;i<0;i++) {
573       PetscInt start_dof = queue_tip[i];
574       /* 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 */
575       if (xadj[start_dof+1]-xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
576         for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
577           PetscInt dof = graph->subset_idxs[pid-1][j];
578           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
579             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
580             queue_tip[n] = dof;
581             n++;
582           }
583         }
584       } else {
585         for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
586           PetscInt dof = adjncy[j];
587           if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
588             ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
589             queue_tip[n] = dof;
590             n++;
591           }
592         }
593       }
594     }
595   } else { /* sub info only */
596     PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
597     for (j=0;j<graph->subset_size[pid-1];j++) { /* pid \in [1,graph->n_subsets] */
598       PetscInt dof = graph->subset_idxs[pid-1][j];
599       if (!PetscBTLookup(touched,dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
600         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
601         queue_tip[n] = dof;
602         n++;
603       }
604     }
605   }
606   *n_added = n;
607   PetscFunctionReturn(0);
608 }
609 
610 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
611 {
612   PetscInt       ncc,cum_queue,n;
613   PetscMPIInt    commsize;
614   PetscErrorCode ierr;
615 
616   PetscFunctionBegin;
617   if (!graph->setupcalled) SETERRQ(PetscObjectComm((PetscObject)graph->l2gmap),PETSC_ERR_ORDER,"PCBDDCGraphSetUp should be called first");
618   /* quiet return if there isn't any local info */
619   if (!graph->xadj && !graph->n_local_subs) {
620     PetscFunctionReturn(0);
621   }
622 
623   /* reset any previous search of connected components */
624   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
625   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&commsize);CHKERRQ(ierr);
626   if (commsize > graph->commsizelimit) {
627     PetscInt i;
628     for (i=0;i<graph->nvtxs;i++) {
629       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
630         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
631       }
632     }
633   }
634 
635   /* begin search for connected components */
636   cum_queue = 0;
637   ncc = 0;
638   for (n=0;n<graph->n_subsets;n++) {
639     PetscInt pid = n+1;  /* partition labeled by 0 is discarded */
640     PetscInt found = 0,prev = 0,first = 0,ncc_pid = 0;
641     while (found != graph->subset_size[n]) {
642       PetscInt added = 0;
643       if (!prev) { /* search for new starting dof */
644         while (PetscBTLookup(graph->touched,graph->subset_idxs[n][first])) first++;
645         ierr = PetscBTSet(graph->touched,graph->subset_idxs[n][first]);CHKERRQ(ierr);
646         graph->queue[cum_queue] = graph->subset_idxs[n][first];
647         graph->cptr[ncc] = cum_queue;
648         prev = 1;
649         cum_queue++;
650         found++;
651         ncc_pid++;
652         ncc++;
653       }
654       ierr = PCBDDCGraphComputeCC_Private(graph,pid,graph->queue + cum_queue,prev,&added);CHKERRQ(ierr);
655       if (!added) {
656         graph->subset_ncc[n] = ncc_pid;
657         graph->cptr[ncc] = cum_queue;
658       }
659       prev = added;
660       found += added;
661       cum_queue += added;
662       if (added && found == graph->subset_size[n]) {
663         graph->subset_ncc[n] = ncc_pid;
664         graph->cptr[ncc] = cum_queue;
665       }
666     }
667   }
668   graph->ncc = ncc;
669   graph->queue_sorted = PETSC_FALSE;
670   PetscFunctionReturn(0);
671 }
672 
673 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
674 {
675   IS             subset,subset_n;
676   MPI_Comm       comm;
677   const PetscInt *is_indices;
678   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global;
679   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
680   PetscMPIInt    commsize;
681   PetscBool      same_set,mirrors_found;
682   PetscErrorCode ierr;
683 
684   PetscFunctionBegin;
685   PetscValidLogicalCollectiveInt(graph->l2gmap,custom_minimal_size,2);
686   if (neumann_is) {
687     PetscValidHeaderSpecific(neumann_is,IS_CLASSID,3);
688     PetscCheckSameComm(graph->l2gmap,1,neumann_is,3);
689   }
690   graph->has_dirichlet = PETSC_FALSE;
691   if (dirichlet_is) {
692     PetscValidHeaderSpecific(dirichlet_is,IS_CLASSID,4);
693     PetscCheckSameComm(graph->l2gmap,1,dirichlet_is,4);
694     graph->has_dirichlet = PETSC_TRUE;
695   }
696   PetscValidLogicalCollectiveInt(graph->l2gmap,n_ISForDofs,5);
697   for (i=0;i<n_ISForDofs;i++) {
698     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,6);
699     PetscCheckSameComm(graph->l2gmap,1,ISForDofs[i],6);
700   }
701   if (custom_primal_vertices) {
702     PetscValidHeaderSpecific(custom_primal_vertices,IS_CLASSID,6);
703     PetscCheckSameComm(graph->l2gmap,1,custom_primal_vertices,7);
704   }
705   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
706   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
707 
708   /* custom_minimal_size */
709   graph->custom_minimal_size = custom_minimal_size;
710   /* get info l2gmap and allocate work vectors  */
711   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
712   /* check if we have any local periodic nodes (periodic BCs) */
713   mirrors_found = PETSC_FALSE;
714   if (graph->nvtxs && n_neigh) {
715     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
716     for (i=0; i<n_shared[0]; i++) {
717       if (graph->count[shared[0][i]] > 1) {
718         mirrors_found = PETSC_TRUE;
719         break;
720       }
721     }
722   }
723   /* compute local mirrors (if any) */
724   if (mirrors_found) {
725     IS       to,from;
726     PetscInt *local_indices,*global_indices;
727 
728     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
729     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
730     /* get arrays of local and global indices */
731     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
732     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
733     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
734     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
735     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
736     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
737     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
738     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
739     /* allocate space for mirrors */
740     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
741     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
742     graph->mirrors_set[0] = 0;
743 
744     k=0;
745     for (i=0;i<n_shared[0];i++) {
746       j=shared[0][i];
747       if (graph->count[j] > 1) {
748         graph->mirrors[j]++;
749         k++;
750       }
751     }
752     /* allocate space for set of mirrors */
753     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
754     for (i=1;i<graph->nvtxs;i++)
755       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
756 
757     /* fill arrays */
758     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
759     for (j=0;j<n_shared[0];j++) {
760       i=shared[0][j];
761       if (graph->count[i] > 1)
762         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
763     }
764     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
765     for (i=0;i<graph->nvtxs;i++) {
766       if (graph->mirrors[i] > 0) {
767         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
768         j = global_indices[k];
769         while ( k > 0 && global_indices[k-1] == j) k--;
770         for (j=0;j<graph->mirrors[i];j++) {
771           graph->mirrors_set[i][j]=local_indices[k+j];
772         }
773         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
774       }
775     }
776     ierr = PetscFree(local_indices);CHKERRQ(ierr);
777     ierr = PetscFree(global_indices);CHKERRQ(ierr);
778     ierr = ISDestroy(&to);CHKERRQ(ierr);
779     ierr = ISDestroy(&from);CHKERRQ(ierr);
780   }
781   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
782 
783   /* Count total number of neigh per node */
784   k = 0;
785   for (i=1;i<n_neigh;i++) {
786     k += n_shared[i];
787     for (j=0;j<n_shared[i];j++) {
788       graph->count[shared[i][j]] += 1;
789     }
790   }
791   /* Allocate space for storing the set of neighbours for each node */
792   if (graph->nvtxs) {
793     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
794   }
795   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
796     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
797   }
798   /* Get information for sharing subdomains */
799   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
800   for (i=1;i<n_neigh;i++) { /* dont count myself */
801     s = n_shared[i];
802     for (j=0;j<s;j++) {
803       k = shared[i][j];
804       graph->neighbours_set[k][graph->count[k]] = neigh[i];
805       graph->count[k] += 1;
806     }
807   }
808   /* sort set of sharing subdomains */
809   for (i=0;i<graph->nvtxs;i++) {
810     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
811   }
812   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
813   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
814 
815   /*
816      Get info for dofs splitting
817      User can specify just a subset; an additional field is considered as a complementary field
818   */
819   for (i=0;i<graph->nvtxs;i++) graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
820   for (i=0;i<n_ISForDofs;i++) {
821     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
822     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
823     for (j=0;j<is_size;j++) {
824       if (is_indices[j] > -1 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
825         graph->which_dof[is_indices[j]] = i;
826       }
827     }
828     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
829   }
830 
831   /* Take into account Neumann nodes */
832   if (neumann_is) {
833     ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
834     ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
835     for (i=0;i<is_size;i++) {
836       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
837         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_NEUMANN_MARK;
838       }
839     }
840     ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
841   }
842   /* Take into account Dirichlet nodes (they overwrite any neumann boundary mark previously set) */
843   if (dirichlet_is) {
844     ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
845     ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
846     for (i=0;i<is_size;i++){
847       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
848         if (commsize > graph->commsizelimit) { /* dirichlet nodes treated as internal */
849           ierr = PetscBTSet(graph->touched,is_indices[i]);CHKERRQ(ierr);
850           graph->subset[is_indices[i]] = 0;
851         }
852         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_DIRICHLET_MARK;
853       }
854     }
855     ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
856   }
857   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
858   if (graph->mirrors) {
859     for (i=0;i<graph->nvtxs;i++)
860       if (graph->mirrors[i])
861         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
862 
863     if (graph->xadj) {
864       PetscInt *new_xadj,*new_adjncy;
865       /* sort CSR graph */
866       for (i=0;i<graph->nvtxs;i++)
867         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
868 
869       /* adapt local CSR graph in case of local periodicity */
870       k = 0;
871       for (i=0;i<graph->nvtxs;i++)
872         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
873           k += graph->mirrors[graph->adjncy[j]];
874 
875       ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
876       ierr = PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy);CHKERRQ(ierr);
877       new_xadj[0] = 0;
878       for (i=0;i<graph->nvtxs;i++) {
879         k = graph->xadj[i+1]-graph->xadj[i];
880         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
881         new_xadj[i+1] = new_xadj[i]+k;
882         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
883           k = graph->mirrors[graph->adjncy[j]];
884           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
885           new_xadj[i+1] += k;
886         }
887         k = new_xadj[i+1]-new_xadj[i];
888         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
889         new_xadj[i+1] = new_xadj[i]+k;
890       }
891       /* set new CSR into graph */
892       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
893       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
894       graph->xadj = new_xadj;
895       graph->adjncy = new_adjncy;
896     }
897   }
898 
899   /* mark special nodes (if any) -> each will become a single node equivalence class */
900   if (custom_primal_vertices) {
901     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
902     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
903     for (i=0,j=0;i<is_size;i++){
904       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 */
905         graph->special_dof[is_indices[i]] = PCBDDCGRAPH_SPECIAL_MARK-j;
906         j++;
907       }
908     }
909     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
910   }
911 
912   /* mark interior nodes (if commsize > graph->commsizelimit) as touched and belonging to partition number 0 */
913   if (commsize > graph->commsizelimit) {
914     for (i=0;i<graph->nvtxs;i++) {
915       if (!graph->count[i]) {
916         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
917         graph->subset[i] = 0;
918       }
919     }
920   }
921 
922   /* init graph structure and compute default subsets */
923   nodes_touched = 0;
924   for (i=0;i<graph->nvtxs;i++) {
925     if (PetscBTLookup(graph->touched,i)) {
926       nodes_touched++;
927     }
928   }
929   i = 0;
930   graph->ncc = 0;
931   total_counts = 0;
932 
933   /* allocated space for queues */
934   if (commsize == graph->commsizelimit) {
935     ierr = PetscMalloc2(graph->nvtxs+1,&graph->cptr,graph->nvtxs,&graph->queue);CHKERRQ(ierr);
936   } else {
937     PetscInt nused = graph->nvtxs - nodes_touched;
938     ierr = PetscMalloc2(nused+1,&graph->cptr,nused,&graph->queue);CHKERRQ(ierr);
939   }
940 
941   while (nodes_touched<graph->nvtxs) {
942     /*  find first untouched node in local ordering */
943     while (PetscBTLookup(graph->touched,i)) i++;
944     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
945     graph->subset[i] = graph->ncc+1;
946     graph->cptr[graph->ncc] = total_counts;
947     graph->queue[total_counts] = i;
948     total_counts++;
949     nodes_touched++;
950     /* now find all other nodes having the same set of sharing subdomains */
951     for (j=i+1;j<graph->nvtxs;j++) {
952       /* check for same number of sharing subdomains, dof number and same special mark */
953       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]) {
954         /* check for same set of sharing subdomains */
955         same_set = PETSC_TRUE;
956         for (k=0;k<graph->count[j];k++){
957           if (graph->neighbours_set[i][k] != graph->neighbours_set[j][k]) {
958             same_set = PETSC_FALSE;
959           }
960         }
961         /* I found a friend of mine */
962         if (same_set) {
963           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
964           graph->subset[j] = graph->ncc+1;
965           nodes_touched++;
966           graph->queue[total_counts] = j;
967           total_counts++;
968         }
969       }
970     }
971     graph->ncc++;
972   }
973   /* 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 */
974   graph->n_subsets = graph->ncc;
975   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
976   for (i=0;i<graph->n_subsets;i++) {
977     graph->subset_ncc[i] = 1;
978   }
979   /* final pointer */
980   graph->cptr[graph->ncc] = total_counts;
981 
982   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each connected component */
983   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
984   ierr = PetscMalloc1(graph->ncc,&graph->subset_ref_node);CHKERRQ(ierr);
985   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
986   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
987   for (j=0;j<graph->ncc;j++) {
988     ierr = PetscSortIntWithArray(graph->cptr[j+1]-graph->cptr[j],&queue_global[graph->cptr[j]],&graph->queue[graph->cptr[j]]);CHKERRQ(ierr);
989     graph->subset_ref_node[j] = graph->queue[graph->cptr[j]];
990   }
991   ierr = PetscFree(queue_global);CHKERRQ(ierr);
992   graph->queue_sorted = PETSC_TRUE;
993 
994   /* save information on subsets (needed when analyzing the connected components) */
995   if (graph->ncc) {
996     ierr = PetscMalloc2(graph->ncc,&graph->subset_size,graph->ncc,&graph->subset_idxs);CHKERRQ(ierr);
997     ierr = PetscMalloc1(graph->cptr[graph->ncc],&graph->subset_idxs[0]);CHKERRQ(ierr);
998     ierr = PetscMemzero(graph->subset_idxs[0],graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
999     for (j=1;j<graph->ncc;j++) {
1000       graph->subset_size[j-1] = graph->cptr[j] - graph->cptr[j-1];
1001       graph->subset_idxs[j] = graph->subset_idxs[j-1] + graph->subset_size[j-1];
1002     }
1003     graph->subset_size[graph->ncc-1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc-1];
1004     ierr = PetscMemcpy(graph->subset_idxs[0],graph->queue,graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
1005   }
1006 
1007   /* renumber reference nodes */
1008   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->ncc,graph->subset_ref_node,PETSC_COPY_VALUES,&subset_n);CHKERRQ(ierr);
1009   ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,subset_n,&subset);CHKERRQ(ierr);
1010   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1011   ierr = ISRenumber(subset,NULL,NULL,&subset_n);CHKERRQ(ierr);
1012   ierr = ISDestroy(&subset);CHKERRQ(ierr);
1013   ierr = ISGetLocalSize(subset_n,&k);CHKERRQ(ierr);
1014   if (k != graph->ncc) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",k,graph->ncc);
1015   ierr = ISGetIndices(subset_n,&is_indices);CHKERRQ(ierr);
1016   ierr = PetscMemcpy(graph->subset_ref_node,is_indices,graph->ncc*sizeof(PetscInt));CHKERRQ(ierr);
1017   ierr = ISRestoreIndices(subset_n,&is_indices);CHKERRQ(ierr);
1018   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1019 
1020   /* free workspace */
1021   graph->setupcalled = PETSC_TRUE;
1022   PetscFunctionReturn(0);
1023 }
1024 
1025 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1026 {
1027   PetscErrorCode ierr;
1028 
1029   PetscFunctionBegin;
1030   if (!graph) PetscFunctionReturn(0);
1031   if (graph->freecsr) {
1032     ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1033     ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1034   } else {
1035     graph->xadj = NULL;
1036     graph->adjncy = NULL;
1037   }
1038   graph->freecsr = PETSC_FALSE;
1039   graph->nvtxs_csr = 0;
1040   PetscFunctionReturn(0);
1041 }
1042 
1043 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1044 {
1045   PetscErrorCode ierr;
1046 
1047   PetscFunctionBegin;
1048   if (!graph) PetscFunctionReturn(0);
1049   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
1050   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
1051   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1052   if (graph->nvtxs) {
1053     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1054   }
1055   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1056   ierr = PetscFree5(graph->count,
1057                     graph->neighbours_set,
1058                     graph->subset,
1059                     graph->which_dof,
1060                     graph->special_dof);CHKERRQ(ierr);
1061   ierr = PetscFree2(graph->cptr,graph->queue);CHKERRQ(ierr);
1062   if (graph->mirrors) {
1063     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1064   }
1065   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1066   if (graph->subset_idxs) {
1067     ierr = PetscFree(graph->subset_idxs[0]);CHKERRQ(ierr);
1068   }
1069   ierr = PetscFree2(graph->subset_size,graph->subset_idxs);CHKERRQ(ierr);
1070   ierr = ISDestroy(&graph->dirdofs);CHKERRQ(ierr);
1071   ierr = ISDestroy(&graph->dirdofsB);CHKERRQ(ierr);
1072   if (graph->n_local_subs) {
1073     ierr = PetscFree(graph->local_subs);CHKERRQ(ierr);
1074   }
1075   graph->has_dirichlet       = PETSC_FALSE;
1076   graph->twodimset           = PETSC_FALSE;
1077   graph->twodim              = PETSC_FALSE;
1078   graph->nvtxs               = 0;
1079   graph->nvtxs_global        = 0;
1080   graph->n_subsets           = 0;
1081   graph->custom_minimal_size = 1;
1082   graph->n_local_subs        = 0;
1083   graph->maxcount            = PETSC_MAX_INT;
1084   graph->setupcalled         = PETSC_FALSE;
1085   PetscFunctionReturn(0);
1086 }
1087 
1088 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N, PetscInt maxcount)
1089 {
1090   PetscInt       n;
1091   PetscErrorCode ierr;
1092 
1093   PetscFunctionBegin;
1094   PetscValidPointer(graph,1);
1095   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1096   PetscValidLogicalCollectiveInt(l2gmap,N,3);
1097   PetscValidLogicalCollectiveInt(l2gmap,maxcount,4);
1098   /* raise an error if already allocated */
1099   if (graph->nvtxs_global) SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1100   /* set number of vertices */
1101   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1102   graph->l2gmap = l2gmap;
1103   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1104   graph->nvtxs = n;
1105   graph->nvtxs_global = N;
1106   /* allocate used space */
1107   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1108   ierr = PetscMalloc5(graph->nvtxs,&graph->count,
1109                       graph->nvtxs,&graph->neighbours_set,
1110                       graph->nvtxs,&graph->subset,
1111                       graph->nvtxs,&graph->which_dof,
1112                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1113   /* zeroes memory */
1114   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1115   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1116   /* use -1 as a default value for which_dof array */
1117   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1118   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1119   /* zeroes first pointer to neighbour set */
1120   if (graph->nvtxs) {
1121     graph->neighbours_set[0] = 0;
1122   }
1123   /* zeroes workspace for values of ncc */
1124   graph->subset_ncc = 0;
1125   graph->subset_ref_node = 0;
1126   /* maxcount for cc */
1127   graph->maxcount = maxcount;
1128   PetscFunctionReturn(0);
1129 }
1130 
1131 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1132 {
1133   PetscErrorCode ierr;
1134 
1135   PetscFunctionBegin;
1136   ierr = PCBDDCGraphResetCSR(*graph);CHKERRQ(ierr);
1137   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1138   ierr = PetscFree(*graph);CHKERRQ(ierr);
1139   PetscFunctionReturn(0);
1140 }
1141 
1142 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1143 {
1144   PCBDDCGraph    new_graph;
1145   PetscErrorCode ierr;
1146 
1147   PetscFunctionBegin;
1148   ierr = PetscNew(&new_graph);CHKERRQ(ierr);
1149   new_graph->custom_minimal_size = 1;
1150   new_graph->commsizelimit = 1;
1151   *graph = new_graph;
1152   PetscFunctionReturn(0);
1153 }
1154