xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision 7babac9bb9641478c5e21ab936f161f7768d083d)
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 #undef __FUNCT__
6 #define __FUNCT__ "PCBDDCGraphGetDirichletDofs"
7 PetscErrorCode PCBDDCGraphGetDirichletDofs(PCBDDCGraph graph,IS* dirdofs)
8 {
9   PetscInt       i,size,sizer;
10   PetscErrorCode ierr;
11 
12   PetscFunctionBegin;
13   size = 0;
14   for (i=0;i<graph->nvtxs;i++) {
15     if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
16   }
17   ierr = MPI_Allreduce(&size,&sizer,1,MPIU_INT,MPI_LOR,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
18   if (sizer) {
19     PetscInt *dirdofs_idxs;
20 
21     ierr = PetscMalloc1(size,&dirdofs_idxs);CHKERRQ(ierr);
22     size = 0;
23     for (i=0;i<graph->nvtxs;i++) {
24       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
25     }
26     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)graph->l2gmap),size,dirdofs_idxs,PETSC_OWN_POINTER,dirdofs);CHKERRQ(ierr);
27   } else {
28     *dirdofs = NULL;
29   }
30   PetscFunctionReturn(0);
31 }
32 
33 #undef __FUNCT__
34 #define __FUNCT__ "PCBDDCGraphASCIIView"
35 PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer)
36 {
37   PetscInt       i,j,tabs;
38   PetscInt*      queue_in_global_numbering;
39   PetscErrorCode ierr;
40 
41   PetscFunctionBegin;
42   ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
43   ierr = PetscViewerASCIIGetTab(viewer,&tabs);CHKERRQ(ierr);
44   ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
45   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
46   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Local BDDC graph for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
47   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Number of vertices %d\n",graph->nvtxs);CHKERRQ(ierr);
48   if (verbosity_level > 1) {
49     for (i=0;i<graph->nvtxs;i++) {
50       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d:\n",i);CHKERRQ(ierr);
51       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %d\n",graph->which_dof[i]);CHKERRQ(ierr);
52       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %d\n",graph->special_dof[i]);CHKERRQ(ierr);
53       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %d\n",graph->count[i]);CHKERRQ(ierr);
54       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
55       if (graph->count[i]) {
56         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:");CHKERRQ(ierr);
57         for (j=0;j<graph->count[i];j++) {
58           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[i][j]);CHKERRQ(ierr);
59         }
60         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
61       }
62       ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
63       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
64       if (graph->mirrors) {
65         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %d\n",graph->mirrors[i]);CHKERRQ(ierr);
66         if (graph->mirrors[i]) {
67           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
68           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:");CHKERRQ(ierr);
69           for (j=0;j<graph->mirrors[i];j++) {
70             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->mirrors_set[i][j]);CHKERRQ(ierr);
71           }
72           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
73           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
74           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
75         }
76       }
77       if (verbosity_level > 2) {
78         if (graph->xadj && graph->adjncy) {
79           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:");CHKERRQ(ierr);
80           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
81           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
82             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->adjncy[j]);CHKERRQ(ierr);
83           }
84           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
85           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
86           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
87         } else {
88           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   no adj info\n");CHKERRQ(ierr);
89         }
90       }
91       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
92       if (graph->subset[i] && graph->subset_ncc) {
93         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
94       }
95     }
96   }
97   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
98   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
99   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
100   for (i=0;i<graph->ncc;i++) {
101     PetscInt node_num=graph->queue[graph->cptr[i]];
102     PetscBool printcc = PETSC_FALSE;
103     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  %d (neighs:",i);CHKERRQ(ierr);
104     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
105     for (j=0;j<graph->count[node_num];j++) {
106       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
107     }
108     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
109     if (verbosity_level > 1) {
110       printcc = PETSC_TRUE;
111     } else if (graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) {
112       printcc = PETSC_TRUE;
113     }
114     if (printcc) {
115       for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
116         ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
117       }
118     }
119     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
120     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
121     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
122   }
123   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
124   if (graph->custom_minimal_size > 1 && verbosity_level > 1) {
125     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %d\n",graph->custom_minimal_size);CHKERRQ(ierr);
126   }
127   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
128   PetscFunctionReturn(0);
129 }
130 
131 #undef __FUNCT__
132 #define __FUNCT__ "PCBDDCGraphGetCandidatesIS"
133 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
134 {
135   IS             *ISForFaces,*ISForEdges,ISForVertices;
136   PetscInt       i,nfc,nec,nvc,*idx;
137   PetscErrorCode ierr;
138 
139   PetscFunctionBegin;
140   /* loop on ccs to evalute number of faces, edges and vertices */
141   nfc = 0;
142   nec = 0;
143   nvc = 0;
144   for (i=0;i<graph->ncc;i++) {
145     PetscInt repdof = graph->queue[graph->cptr[i]];
146     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
147       if (graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
148         nfc++;
149       } else { /* note that nec will be zero in 2d */
150         nec++;
151       }
152     } else {
153       nvc += graph->cptr[i+1]-graph->cptr[i];
154     }
155   }
156 
157   /* check if we are in 2D or 3D */
158   if (graph->twodim) { /* we are in a 2D case -> edges are shared by 2 subregions and faces don't exist */
159     nec = nfc;
160     nfc = 0;
161   }
162 
163   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
164   if (FacesIS) {
165     ierr = PetscMalloc1(nfc,&ISForFaces);CHKERRQ(ierr);
166   }
167   if (EdgesIS) {
168     ierr = PetscMalloc1(nec,&ISForEdges);CHKERRQ(ierr);
169   }
170   if (VerticesIS) {
171     ierr = PetscMalloc1(nvc,&idx);CHKERRQ(ierr);
172   }
173 
174   /* loop on ccs to compute index sets for faces and edges */
175   nfc = 0;
176   nec = 0;
177   for (i=0;i<graph->ncc;i++) {
178     PetscInt repdof = graph->queue[graph->cptr[i]];
179     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
180       if (graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
181         if (graph->twodim) {
182           if (EdgesIS) {
183             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
184           }
185           nec++;
186         } else {
187           if (FacesIS) {
188             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForFaces[nfc]);CHKERRQ(ierr);
189           }
190           nfc++;
191         }
192       } else {
193         if (EdgesIS) {
194           ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
195         }
196         nec++;
197       }
198     }
199   }
200   /* index set for vertices */
201   if (VerticesIS) {
202     nvc = 0;
203     for (i=0;i<graph->ncc;i++) {
204       if (graph->cptr[i+1]-graph->cptr[i] <= graph->custom_minimal_size) {
205         PetscInt j;
206 
207         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
208           idx[nvc]=graph->queue[j];
209           nvc++;
210         }
211       }
212     }
213     /* sort vertex set (by local ordering) */
214     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
215     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
216   }
217   /* get back info */
218   if (n_faces) *n_faces = nfc;
219   if (FacesIS) {
220     *FacesIS = ISForFaces;
221   }
222   if (n_edges) *n_edges = nec;
223   if (EdgesIS) {
224     *EdgesIS = ISForEdges;
225   }
226   if (VerticesIS) {
227     *VerticesIS = ISForVertices;
228   }
229   PetscFunctionReturn(0);
230 }
231 
232 #undef __FUNCT__
233 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponents"
234 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
235 {
236   PetscBool      adapt_interface_reduced;
237   MPI_Comm       interface_comm;
238   PetscMPIInt    size;
239   PetscInt       i;
240   PetscBool      twodim;
241   PetscErrorCode ierr;
242 
243   PetscFunctionBegin;
244   /* compute connected components locally */
245   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
246   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
247   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
248   ierr = MPI_Comm_size(interface_comm,&size);CHKERRQ(ierr);
249   adapt_interface_reduced = PETSC_FALSE;
250   if (size > 1) {
251     PetscInt i;
252     PetscBool adapt_interface = PETSC_FALSE;
253     for (i=0;i<graph->n_subsets;i++) {
254       /* We are not sure that on a given subset of the local interface,
255          with two connected components, the latters be the same among sharing subdomains */
256       if (graph->subset_ncc[i] > 1) {
257         adapt_interface = PETSC_TRUE;
258         break;
259       }
260     }
261     ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_BOOL,MPI_LOR,interface_comm);CHKERRQ(ierr);
262   }
263 
264   if (graph->n_subsets && adapt_interface_reduced) {
265     /* old csr stuff */
266     PetscInt    *aux_new_xadj,*new_xadj,*new_adjncy;
267     PetscInt    *old_xadj,*old_adjncy;
268     PetscBT     subset_cc_adapt;
269     /* MPI */
270     MPI_Request *send_requests,*recv_requests;
271     PetscInt    *send_buffer,*recv_buffer;
272     PetscInt    sum_requests,start_of_recv,start_of_send;
273     PetscInt    *cum_recv_counts;
274     /* others */
275     PetscInt    *labels;
276     PetscInt    global_subset_counter;
277     PetscInt    j,k,s;
278 
279     /* Retrict adjacency graph using information from previously computed connected components */
280     ierr = PetscMalloc1(graph->nvtxs,&aux_new_xadj);CHKERRQ(ierr);
281     for (i=0;i<graph->nvtxs;i++) {
282       aux_new_xadj[i]=1;
283     }
284     for (i=0;i<graph->ncc;i++) {
285       k = graph->cptr[i+1]-graph->cptr[i];
286       for (j=0;j<k;j++) {
287         aux_new_xadj[graph->queue[graph->cptr[i]+j]]=k;
288       }
289     }
290     j = 0;
291     for (i=0;i<graph->nvtxs;i++) {
292       j += aux_new_xadj[i];
293     }
294     ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
295     ierr = PetscMalloc1(j,&new_adjncy);CHKERRQ(ierr);
296     new_xadj[0]=0;
297     for (i=0;i<graph->nvtxs;i++) {
298       new_xadj[i+1]=new_xadj[i]+aux_new_xadj[i];
299       if (aux_new_xadj[i]==1) {
300         new_adjncy[new_xadj[i]]=i;
301       }
302     }
303     ierr = PetscFree(aux_new_xadj);CHKERRQ(ierr);
304     ierr = PetscMalloc1(graph->nvtxs,&labels);CHKERRQ(ierr);
305     ierr = PetscMemzero(labels,graph->nvtxs*sizeof(*labels));CHKERRQ(ierr);
306     for (i=0;i<graph->ncc;i++) {
307       k = graph->cptr[i+1]-graph->cptr[i];
308       for (j=0;j<k;j++) {
309         ierr = PetscMemcpy(&new_adjncy[new_xadj[graph->queue[graph->cptr[i]+j]]],&graph->queue[graph->cptr[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
310         labels[graph->queue[graph->cptr[i]+j]] = i;
311       }
312     }
313     /* set temporarly new CSR into graph */
314     old_xadj = graph->xadj;
315     old_adjncy = graph->adjncy;
316     graph->xadj = new_xadj;
317     graph->adjncy = new_adjncy;
318     /* allocate some space */
319     ierr = PetscMalloc1(graph->n_subsets+1,&cum_recv_counts);CHKERRQ(ierr);
320     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
321     /* first count how many neighbours per connected component I will receive from */
322     cum_recv_counts[0]=0;
323     for (i=0;i<graph->n_subsets;i++) {
324       cum_recv_counts[i+1]=cum_recv_counts[i]+graph->count[graph->subsets[i][0]];
325     }
326     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_buffer);CHKERRQ(ierr);
327     ierr = PetscMalloc2(cum_recv_counts[graph->n_subsets],&send_requests,cum_recv_counts[graph->n_subsets],&recv_requests);CHKERRQ(ierr);
328     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
329       send_requests[i]=MPI_REQUEST_NULL;
330       recv_requests[i]=MPI_REQUEST_NULL;
331     }
332     /* exchange with my neighbours the number of my connected components on the subset of interface */
333     sum_requests = 0;
334     for (i=0;i<graph->n_subsets;i++) {
335       PetscMPIInt neigh,tag;
336 
337       j = graph->subsets[i][0];
338       ierr = PetscMPIIntCast(2*graph->subset_ref_node[i],&tag);CHKERRQ(ierr);
339       for (k=0;k<graph->count[j];k++) {
340         ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
341         ierr = MPI_Isend(&graph->subset_ncc[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
342         ierr = MPI_Irecv(&recv_buffer[sum_requests],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
343         sum_requests++;
344       }
345     }
346     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
347     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
348     /* determine the subsets I have to adapt */
349     ierr = PetscBTCreate(graph->n_subsets,&subset_cc_adapt);CHKERRQ(ierr);
350     ierr = PetscBTMemzero(graph->n_subsets,subset_cc_adapt);CHKERRQ(ierr);
351     for (i=0;i<graph->n_subsets;i++) {
352       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
353         /* adapt if more than one cc is present */
354          if (graph->subset_ncc[i] > 1 || recv_buffer[j] > 1) {
355           ierr = PetscBTSet(subset_cc_adapt,i);
356           break;
357         }
358       }
359     }
360     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
361     /* determine send/recv buffers sizes */
362     j = 0;
363     for (i=0;i<graph->n_subsets;i++) {
364       if (PetscBTLookup(subset_cc_adapt,i)) {
365         j += graph->subsets_size[i];
366       }
367     }
368     k = 0;
369     for (i=0;i<graph->n_subsets;i++) {
370       if (PetscBTLookup(subset_cc_adapt,i)) {
371         k += (cum_recv_counts[i+1]-cum_recv_counts[i])*graph->subsets_size[i];
372       }
373     }
374     ierr = PetscMalloc2(j,&send_buffer,k,&recv_buffer);CHKERRQ(ierr);
375 
376     /* fill send buffer */
377     j = 0;
378     for (i=0;i<graph->n_subsets;i++) {
379       if (PetscBTLookup(subset_cc_adapt,i)) {
380         for (k=0;k<graph->subsets_size[i];k++) {
381           send_buffer[j++] = labels[graph->subsets[i][k]];
382         }
383       }
384     }
385     ierr = PetscFree(labels);CHKERRQ(ierr);
386 
387     /* now exchange the data */
388     start_of_recv = 0;
389     start_of_send = 0;
390     sum_requests = 0;
391     for (i=0;i<graph->n_subsets;i++) {
392       if (PetscBTLookup(subset_cc_adapt,i)) {
393         PetscMPIInt neigh,tag;
394         PetscInt    size_of_send = graph->subsets_size[i];
395 
396         j = graph->subsets[i][0];
397         ierr = PetscMPIIntCast(2*graph->subset_ref_node[i]+1,&tag);CHKERRQ(ierr);
398         for (k=0;k<graph->count[j];k++) {
399           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
400           ierr = MPI_Isend(&send_buffer[start_of_send],size_of_send,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
401           ierr = MPI_Irecv(&recv_buffer[start_of_recv],size_of_send,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
402           start_of_recv += size_of_send;
403           sum_requests++;
404         }
405         start_of_send += size_of_send;
406       }
407     }
408     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
409     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
410     ierr = PetscFree2(send_requests,recv_requests);CHKERRQ(ierr);
411     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
412 
413     start_of_recv = 0;
414     global_subset_counter = 0;
415     for (i=0;i<graph->n_subsets;i++) {
416       if (PetscBTLookup(subset_cc_adapt,i)) {
417         PetscInt **temp_buffer,temp_buffer_size,*private_label;
418 
419         /* allocate some temporary space */
420         temp_buffer_size = graph->subsets_size[i];
421         ierr = PetscMalloc1(temp_buffer_size,&temp_buffer);CHKERRQ(ierr);
422         ierr = PetscMalloc1(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i]),&temp_buffer[0]);CHKERRQ(ierr);
423         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
424         for (j=1;j<temp_buffer_size;j++) {
425           temp_buffer[j] = temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
426         }
427         /* analyze contributions from neighbouring subdomains for i-th subset
428            temp buffer structure:
429            supposing part of the interface has dimension 5
430            e.g with global dofs 0,1,2,3,4, locally ordered on the current process as 0,4,3,1,2
431            3 neighs procs having connected components:
432              neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
433              neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
434              neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
435            tempbuffer (row-oriented) will be filled as:
436              [ 4, 3, 1;
437                4, 2, 1;
438                7, 2, 6;
439                4, 3, 5;
440                7, 2, 6; ];
441            This way we can simply find intersections of ccs among neighs.
442            The graph->subset array will need to be modified. The output for the example is [0], [1], [2 3], [4];
443                                                                                                                                    */
444         for (j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
445           for (k=0;k<temp_buffer_size;k++) {
446             temp_buffer[k][j] = recv_buffer[start_of_recv+k];
447           }
448           start_of_recv += temp_buffer_size;
449         }
450         ierr = PetscMalloc1(temp_buffer_size,&private_label);CHKERRQ(ierr);
451         ierr = PetscMemzero(private_label,temp_buffer_size*sizeof(*private_label));CHKERRQ(ierr);
452         for (j=0;j<temp_buffer_size;j++) {
453           if (!private_label[j]) { /* found a new cc  */
454             PetscBool same_set;
455 
456             global_subset_counter++;
457             private_label[j] = global_subset_counter;
458             for (k=j+1;k<temp_buffer_size;k++) { /* check for other nodes in new cc */
459               same_set = PETSC_TRUE;
460               for (s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++) {
461                 if (temp_buffer[j][s] != temp_buffer[k][s]) {
462                   same_set = PETSC_FALSE;
463                   break;
464                 }
465               }
466               if (same_set) {
467                 private_label[k] = global_subset_counter;
468               }
469             }
470           }
471         }
472         /* insert private labels in graph structure */
473         for (j=0;j<graph->subsets_size[i];j++) {
474           graph->subset[graph->subsets[i][j]] = graph->n_subsets+private_label[j];
475         }
476         ierr = PetscFree(private_label);CHKERRQ(ierr);
477         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
478         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
479       }
480     }
481     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
482     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
483     ierr = PetscBTDestroy(&subset_cc_adapt);CHKERRQ(ierr);
484     /* We are ready to find for connected components which are consistent among neighbouring subdomains */
485     if (global_subset_counter) {
486       ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
487       global_subset_counter = 0;
488       for (i=0;i<graph->nvtxs;i++) {
489         if (graph->subset[i] && !PetscBTLookup(graph->touched,i)) {
490           global_subset_counter++;
491           for (j=i+1;j<graph->nvtxs;j++) {
492             if (!PetscBTLookup(graph->touched,j) && graph->subset[j]==graph->subset[i]) {
493               graph->subset[j] = global_subset_counter;
494               ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
495             }
496           }
497           graph->subset[i] = global_subset_counter;
498           ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
499         }
500       }
501       /* refine connected components locally */
502       ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
503     }
504     /* restore original CSR graph of dofs */
505     ierr = PetscFree(new_xadj);CHKERRQ(ierr);
506     ierr = PetscFree(new_adjncy);CHKERRQ(ierr);
507     graph->xadj = old_xadj;
508     graph->adjncy = old_adjncy;
509   }
510 
511   /* Determine if we are in 2D or 3D */
512   twodim  = PETSC_TRUE;
513   for (i=0;i<graph->ncc;i++) {
514     PetscInt repdof = graph->queue[graph->cptr[i]];
515     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
516       if (graph->count[repdof] > 1 || graph->special_dof[repdof] == PCBDDCGRAPH_NEUMANN_MARK) {
517         twodim = PETSC_FALSE;
518         break;
519       }
520     }
521   }
522   ierr = MPI_Allreduce(&twodim,&graph->twodim,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
523   PetscFunctionReturn(0);
524 }
525 
526 /* The following code has been adapted from function IsConnectedSubdomain contained
527    in source file contig.c of METIS library (version 5.0.1)
528    It finds connected components for each subset  */
529 #undef __FUNCT__
530 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponentsLocal"
531 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
532 {
533   PetscInt       i,j,k,first,last,nleft,ncc,pid,cum_queue,n,ncc_pid;
534   PetscInt       *queue_global;
535   PetscMPIInt    size;
536   PetscErrorCode ierr;
537 
538   PetscFunctionBegin;
539   /* quiet return if no csr info is available */
540   if (!graph->xadj || !graph->adjncy) {
541     PetscFunctionReturn(0);
542   }
543 
544   /* reset any previous search of connected components */
545   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
546   graph->n_subsets = 0;
547   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&size);CHKERRQ(ierr);
548   if (size == 1) {
549     if (graph->nvtxs) {
550       graph->n_subsets = 1;
551       for (i=0;i<graph->nvtxs;i++) {
552         graph->subset[i] = 1;
553       }
554     }
555   } else {
556     for (i=0;i<graph->nvtxs;i++) {
557       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
558         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
559         graph->subset[i] = 0;
560       }
561       graph->n_subsets = PetscMax(graph->n_subsets,graph->subset[i]);
562     }
563   }
564   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
565   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
566 
567   /* begin search for connected components */
568   cum_queue = 0;
569   ncc = 0;
570   for (n=0;n<graph->n_subsets;n++) {
571     pid = n+1;  /* partition labeled by 0 is discarded */
572     nleft = 0;
573     for (i=0;i<graph->nvtxs;i++) {
574       if (graph->subset[i] == pid) {
575         nleft++;
576       }
577     }
578     for (i=0; i<graph->nvtxs; i++) {
579       if (graph->subset[i] == pid) {
580         break;
581       }
582     }
583     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
584     graph->queue[cum_queue] = i;
585     first = 0;
586     last = 1;
587     graph->cptr[ncc] = cum_queue;
588     ncc_pid = 0;
589     while (first != nleft) {
590       if (first == last) {
591         graph->cptr[++ncc] = first+cum_queue;
592         ncc_pid++;
593         for (i=0; i<graph->nvtxs; i++) { /* TODO-> use a while! */
594           if (graph->subset[i] == pid && !PetscBTLookup(graph->touched,i)) {
595             break;
596           }
597         }
598         graph->queue[cum_queue+last] = i;
599         last++;
600         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
601       }
602       i = graph->queue[cum_queue+first];
603       first++;
604       for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
605         k = graph->adjncy[j];
606         if (graph->subset[k] == pid && !PetscBTLookup(graph->touched,k)) {
607           graph->queue[cum_queue+last] = k;
608           last++;
609           ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
610         }
611       }
612     }
613     graph->cptr[++ncc] = first+cum_queue;
614     ncc_pid++;
615     cum_queue = graph->cptr[ncc];
616     graph->subset_ncc[n] = ncc_pid;
617   }
618   graph->ncc = ncc;
619   /* For consistency among neighbours, I need to sort (by global ordering) each connected component */
620   if (size > 1) {
621     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
622     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
623     for (i=0;i<graph->ncc;i++) {
624       ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
625     }
626     ierr = PetscFree(queue_global);CHKERRQ(ierr);
627   }
628   PetscFunctionReturn(0);
629 }
630 
631 #undef __FUNCT__
632 #define __FUNCT__ "PCBDDCGraphSetUp"
633 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
634 {
635   VecScatter     scatter_ctx;
636   Vec            local_vec,local_vec2,global_vec;
637   IS             to,from;
638   MPI_Comm       comm;
639   PetscScalar    *array,*array2;
640   const PetscInt *is_indices;
641   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global,*subset_ref_node_global;
642   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
643   PetscMPIInt    size;
644   PetscBool      same_set,mirrors_found;
645   PetscErrorCode ierr;
646 
647   PetscFunctionBegin;
648   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
649   /* custom_minimal_size */
650   graph->custom_minimal_size = PetscMax(graph->custom_minimal_size,custom_minimal_size);
651   /* get info l2gmap and allocate work vectors  */
652   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
653   /* check if we have any local periodic nodes (periodic BCs) */
654   mirrors_found = PETSC_FALSE;
655   if (graph->nvtxs && n_neigh) {
656     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
657     for (i=0; i<n_shared[0]; i++) {
658       if (graph->count[shared[0][i]] > 1) {
659         mirrors_found = PETSC_TRUE;
660         break;
661       }
662     }
663   }
664   /* create some workspace objects */
665   local_vec = NULL;
666   local_vec2 = NULL;
667   global_vec = NULL;
668   to = NULL;
669   from = NULL;
670   scatter_ctx = NULL;
671   if (n_ISForDofs || dirichlet_is || neumann_is || custom_primal_vertices) {
672     ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
673     ierr = VecSetSizes(local_vec,PETSC_DECIDE,graph->nvtxs);CHKERRQ(ierr);
674     ierr = VecSetType(local_vec,VECSTANDARD);CHKERRQ(ierr);
675     ierr = VecDuplicate(local_vec,&local_vec2);CHKERRQ(ierr);
676     ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
677     ierr = VecSetSizes(global_vec,PETSC_DECIDE,graph->nvtxs_global);CHKERRQ(ierr);
678     ierr = VecSetType(global_vec,VECSTANDARD);CHKERRQ(ierr);
679     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
680     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
681     ierr = VecScatterCreate(global_vec,from,local_vec,to,&scatter_ctx);CHKERRQ(ierr);
682   } else if (mirrors_found) {
683     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
684     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
685   }
686   /* compute local mirrors (if any) */
687   if (mirrors_found) {
688     PetscInt *local_indices,*global_indices;
689     /* get arrays of local and global indices */
690     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
691     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
692     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
693     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
694     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
695     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
696     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
697     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
698     /* allocate space for mirrors */
699     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
700     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
701     graph->mirrors_set[0] = 0;
702 
703     k=0;
704     for (i=0;i<n_shared[0];i++) {
705       j=shared[0][i];
706       if (graph->count[j] > 1) {
707         graph->mirrors[j]++;
708         k++;
709       }
710     }
711     /* allocate space for set of mirrors */
712     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
713     for (i=1;i<graph->nvtxs;i++)
714       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
715 
716     /* fill arrays */
717     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
718     for (j=0;j<n_shared[0];j++) {
719       i=shared[0][j];
720       if (graph->count[i] > 1)
721         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
722     }
723     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
724     for (i=0;i<graph->nvtxs;i++) {
725       if (graph->mirrors[i] > 0) {
726         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
727         j = global_indices[k];
728         while ( k > 0 && global_indices[k-1] == j) k--;
729         for (j=0;j<graph->mirrors[i];j++) {
730           graph->mirrors_set[i][j]=local_indices[k+j];
731         }
732         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
733       }
734     }
735     ierr = PetscFree(local_indices);CHKERRQ(ierr);
736     ierr = PetscFree(global_indices);CHKERRQ(ierr);
737   }
738   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
739   ierr = ISDestroy(&to);CHKERRQ(ierr);
740   ierr = ISDestroy(&from);CHKERRQ(ierr);
741 
742   /* Count total number of neigh per node */
743   k=0;
744   for (i=1;i<n_neigh;i++) {
745     k += n_shared[i];
746     for (j=0;j<n_shared[i];j++) {
747       graph->count[shared[i][j]] += 1;
748     }
749   }
750   /* Allocate space for storing the set of neighbours for each node */
751   if (graph->nvtxs) {
752     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
753   }
754   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
755     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
756   }
757   /* Get information for sharing subdomains */
758   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
759   for (i=1;i<n_neigh;i++) { /* dont count myself */
760     s = n_shared[i];
761     for (j=0;j<s;j++) {
762       k = shared[i][j];
763       graph->neighbours_set[k][graph->count[k]] = neigh[i];
764       graph->count[k] += 1;
765     }
766   }
767   /* sort set of sharing subdomains */
768   for (i=0;i<graph->nvtxs;i++) {
769     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
770   }
771   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
772   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
773 
774   /*
775      Get info for dofs splitting
776      User can specify just a subset; an additional field is considered as a complementary field
777   */
778   for (i=0;i<graph->nvtxs;i++) {
779     graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
780   }
781   if (n_ISForDofs) {
782     ierr = VecSet(local_vec,-1.0);CHKERRQ(ierr);
783   }
784   for (i=0;i<n_ISForDofs;i++) {
785     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
786     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
787     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
788     for (j=0;j<is_size;j++) {
789       if (is_indices[j] > -1 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
790         graph->which_dof[is_indices[j]] = i;
791         array[is_indices[j]] = 1.*i;
792       }
793     }
794     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
795     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
796   }
797   /* Check consistency among neighbours */
798   if (n_ISForDofs) {
799     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
800     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
801     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
802     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
803     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
804     ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
805     for (i=0;i<graph->nvtxs;i++){
806       PetscInt field1,field2;
807 
808       field1 = (PetscInt)PetscRealPart(array[i]);
809       field2 = (PetscInt)PetscRealPart(array2[i]);
810       if (field1 != field2) {
811         SETERRQ3(comm,PETSC_ERR_USER,"Local node %d have been assigned two different field ids %d and %d at the same time\n",i,field1,field2);
812       }
813     }
814     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
815     ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
816   }
817   if (neumann_is || dirichlet_is) {
818     /* Take into account Neumann nodes */
819     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
820     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
821     if (neumann_is) {
822       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
823       ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
824       ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
825       for (i=0;i<is_size;i++) {
826         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
827           array[is_indices[i]] = 1.0;
828         }
829       }
830       ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
831       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
832     }
833     /* Neumann nodes: impose consistency among neighbours */
834     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
835     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
836     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
837     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
838     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
839     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
840     for (i=0;i<graph->nvtxs;i++) {
841       if (PetscRealPart(array[i]) > 0.1) {
842         graph->special_dof[i] = PCBDDCGRAPH_NEUMANN_MARK;
843       }
844     }
845     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
846     /* Take into account Dirichlet nodes */
847     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
848     if (dirichlet_is) {
849       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
850       ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
851       ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
852       ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
853       for (i=0;i<is_size;i++){
854         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
855           k = is_indices[i];
856           if (graph->count[k] && !PetscBTLookup(graph->touched,k)) {
857             if (PetscRealPart(array[k]) > 0.1) {
858               SETERRQ1(comm,PETSC_ERR_USER,"BDDC cannot have boundary nodes which are marked Neumann and Dirichlet at the same time! Local node %d is wrong\n",k);
859             }
860             array2[k] = 1.0;
861           }
862         }
863       }
864       ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
865       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
866       ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
867     }
868     /* Dirichlet nodes: impose consistency among neighbours */
869     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
870     ierr = VecScatterBegin(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
871     ierr = VecScatterEnd(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
872     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
873     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
874     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
875     for (i=0;i<graph->nvtxs;i++) {
876       if (PetscRealPart(array[i]) > 0.1) {
877         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
878         graph->subset[i] = 0; /* dirichlet nodes treated as internal -> is it ok? */
879         graph->special_dof[i] = PCBDDCGRAPH_DIRICHLET_MARK;
880       }
881     }
882     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
883   }
884   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
885   if (graph->mirrors) {
886     for (i=0;i<graph->nvtxs;i++)
887       if (graph->mirrors[i])
888         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
889 
890     if (graph->xadj && graph->adjncy) {
891       PetscInt *new_xadj,*new_adjncy;
892       /* sort CSR graph */
893       for (i=0;i<graph->nvtxs;i++)
894         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
895 
896       /* adapt local CSR graph in case of local periodicity */
897       k=0;
898       for (i=0;i<graph->nvtxs;i++)
899         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
900           k += graph->mirrors[graph->adjncy[j]];
901 
902       ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
903       ierr = PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy);CHKERRQ(ierr);
904       new_xadj[0]=0;
905       for (i=0;i<graph->nvtxs;i++) {
906         k = graph->xadj[i+1]-graph->xadj[i];
907         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
908         new_xadj[i+1]=new_xadj[i]+k;
909         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
910           k = graph->mirrors[graph->adjncy[j]];
911           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
912           new_xadj[i+1]+=k;
913         }
914         k = new_xadj[i+1]-new_xadj[i];
915         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
916         new_xadj[i+1]=new_xadj[i]+k;
917       }
918       /* set new CSR into graph */
919       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
920       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
921       graph->xadj = new_xadj;
922       graph->adjncy = new_adjncy;
923     }
924   }
925 
926   /* mark special nodes (if any) -> each will become a single node equivalence class */
927   if (custom_primal_vertices) {
928     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
929     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
930     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
931     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
932     for (i=0;i<is_size;i++){
933       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
934         array[is_indices[i]] = 1.0;
935       }
936     }
937     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
938     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
939     /* special nodes: impose consistency among neighbours */
940     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
941     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
942     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
943     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
944     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
945     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
946     j = 0;
947     for (i=0;i<graph->nvtxs;i++) {
948       if (PetscRealPart(array[i]) > 0.1 && graph->special_dof[i] != PCBDDCGRAPH_DIRICHLET_MARK) {
949         graph->special_dof[i] = PCBDDCGRAPH_SPECIAL_MARK-j;
950         j++;
951       }
952     }
953     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
954   }
955 
956   /* mark interior nodes as touched and belonging to partition number 0 */
957   for (i=0;i<graph->nvtxs;i++) {
958     if (!graph->count[i]) {
959       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
960       graph->subset[i] = 0;
961     }
962   }
963   /* init graph structure and compute default subsets */
964   nodes_touched=0;
965   for (i=0;i<graph->nvtxs;i++) {
966     if (PetscBTLookup(graph->touched,i)) {
967       nodes_touched++;
968     }
969   }
970   i = 0;
971   graph->ncc = 0;
972   total_counts = 0;
973 
974   /* allocated space for queues */
975   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
976   if (size == 1) {
977     ierr = PetscMalloc2(graph->nvtxs+1,&graph->cptr,graph->nvtxs,&graph->queue);CHKERRQ(ierr);
978   } else {
979     PetscInt nused = graph->nvtxs - nodes_touched;
980     ierr = PetscMalloc2(nused+1,&graph->cptr,nused,&graph->queue);CHKERRQ(ierr);
981   }
982 
983   while (nodes_touched<graph->nvtxs) {
984     /*  find first untouched node in local ordering */
985     while (PetscBTLookup(graph->touched,i)) {
986       i++;
987     }
988     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
989     graph->subset[i] = graph->ncc+1;
990     graph->cptr[graph->ncc] = total_counts;
991     graph->queue[total_counts] = i;
992     total_counts++;
993     nodes_touched++;
994     /* now find all other nodes having the same set of sharing subdomains */
995     for (j=i+1;j<graph->nvtxs;j++) {
996       /* check for same number of sharing subdomains, dof number and same special mark */
997       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]) {
998         /* check for same set of sharing subdomains */
999         same_set=PETSC_TRUE;
1000         for (k=0;k<graph->count[j];k++){
1001           if (graph->neighbours_set[i][k]!=graph->neighbours_set[j][k]) {
1002             same_set=PETSC_FALSE;
1003           }
1004         }
1005         /* I found a friend of mine */
1006         if (same_set) {
1007           graph->subset[j]=graph->ncc+1;
1008           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
1009           nodes_touched++;
1010           graph->queue[total_counts] = j;
1011           total_counts++;
1012         }
1013       }
1014     }
1015     graph->ncc++;
1016   }
1017   /* set default number of subsets (at this point no info on csr graph has been taken into account, so n_subsets = ncc */
1018   graph->n_subsets = graph->ncc;
1019   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
1020   for (i=0;i<graph->n_subsets;i++) {
1021     graph->subset_ncc[i] = 1;
1022   }
1023   /* final pointer */
1024   graph->cptr[graph->ncc] = total_counts;
1025 
1026   /* save information on subsets (needed if we have to adapt the connected components later) */
1027   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each subset */
1028   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
1029   ierr = PetscMalloc2(graph->ncc,&subset_ref_node_global,graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
1030   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
1031   for (j=0;j<graph->ncc;j++) {
1032     ierr = PetscSortIntWithArray(graph->cptr[j+1]-graph->cptr[j],&queue_global[graph->cptr[j]],&graph->queue[graph->cptr[j]]);CHKERRQ(ierr);
1033     subset_ref_node_global[j] = graph->queue[graph->cptr[j]];
1034   }
1035   if (graph->ncc) {
1036     ierr = PetscMalloc2(graph->ncc,&graph->subsets_size,graph->ncc,&graph->subsets);CHKERRQ(ierr);
1037     ierr = PetscMalloc1(graph->cptr[graph->ncc],&graph->subsets[0]);CHKERRQ(ierr);
1038     ierr = PetscMemzero(graph->subsets[0],graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
1039     for (j=1;j<graph->ncc;j++) {
1040       graph->subsets_size[j-1] = graph->cptr[j] - graph->cptr[j-1];
1041       graph->subsets[j] = graph->subsets[j-1] + graph->subsets_size[j-1];
1042     }
1043     graph->subsets_size[graph->ncc-1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc-1];
1044     for (j=0;j<graph->ncc;j++) {
1045       ierr = PetscMemcpy(graph->subsets[j],&graph->queue[graph->cptr[j]],graph->subsets_size[j]*sizeof(PetscInt));CHKERRQ(ierr);
1046     }
1047   }
1048   /* renumber reference nodes */
1049   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->l2gmap,graph->ncc,subset_ref_node_global,NULL,&k,&graph->subset_ref_node);CHKERRQ(ierr);
1050 
1051   /* free workspace */
1052   ierr = PetscFree2(subset_ref_node_global,queue_global);CHKERRQ(ierr);
1053   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1054   ierr = VecDestroy(&local_vec2);CHKERRQ(ierr);
1055   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1056   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 #undef __FUNCT__
1061 #define __FUNCT__ "PCBDDCGraphResetCSR"
1062 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1063 {
1064   PetscErrorCode ierr;
1065 
1066   PetscFunctionBegin;
1067   ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1068   ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1069   graph->nvtxs_csr = 0;
1070   PetscFunctionReturn(0);
1071 }
1072 
1073 #undef __FUNCT__
1074 #define __FUNCT__ "PCBDDCGraphReset"
1075 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1076 {
1077   PetscErrorCode ierr;
1078 
1079   PetscFunctionBegin;
1080   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
1081   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
1082   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1083   if (graph->nvtxs) {
1084     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1085   }
1086   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1087   ierr = PetscFree5(graph->count,
1088                     graph->neighbours_set,
1089                     graph->subset,
1090                     graph->which_dof,
1091                     graph->special_dof);CHKERRQ(ierr);
1092   ierr = PetscFree2(graph->cptr,graph->queue);CHKERRQ(ierr);
1093   if (graph->mirrors) {
1094     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1095   }
1096   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1097   if (graph->subsets) {
1098     ierr = PetscFree(graph->subsets[0]);CHKERRQ(ierr);
1099   }
1100   ierr = PetscFree2(graph->subsets_size,graph->subsets);CHKERRQ(ierr);
1101   graph->nvtxs = 0;
1102   graph->nvtxs_global = 0;
1103   graph->n_subsets = 0;
1104   graph->custom_minimal_size = 1;
1105   PetscFunctionReturn(0);
1106 }
1107 
1108 #undef __FUNCT__
1109 #define __FUNCT__ "PCBDDCGraphInit"
1110 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N)
1111 {
1112   PetscInt       n;
1113   PetscErrorCode ierr;
1114 
1115   PetscFunctionBegin;
1116   PetscValidPointer(graph,1);
1117   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1118   PetscValidLogicalCollectiveInt(l2gmap,N,3);
1119   /* raise an error if already allocated */
1120   if (graph->nvtxs_global) {
1121     SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1122   }
1123   /* set number of vertices */
1124   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1125   graph->l2gmap = l2gmap;
1126   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1127   graph->nvtxs = n;
1128   graph->nvtxs_global = N;
1129   /* allocate used space */
1130   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1131   ierr = PetscMalloc5(graph->nvtxs,&graph->count,
1132                       graph->nvtxs,&graph->neighbours_set,
1133                       graph->nvtxs,&graph->subset,
1134                       graph->nvtxs,&graph->which_dof,
1135                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1136   /* zeroes memory */
1137   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1138   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1139   /* use -1 as a default value for which_dof array */
1140   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1141   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1142   /* zeroes first pointer to neighbour set */
1143   if (graph->nvtxs) {
1144     graph->neighbours_set[0] = 0;
1145   }
1146   /* zeroes workspace for values of ncc */
1147   graph->subset_ncc = 0;
1148   graph->subset_ref_node = 0;
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 #undef __FUNCT__
1153 #define __FUNCT__ "PCBDDCGraphDestroy"
1154 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1155 {
1156   PetscErrorCode ierr;
1157 
1158   PetscFunctionBegin;
1159   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1160   ierr = PetscFree(*graph);CHKERRQ(ierr);
1161   PetscFunctionReturn(0);
1162 }
1163 
1164 #undef __FUNCT__
1165 #define __FUNCT__ "PCBDDCGraphCreate"
1166 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1167 {
1168   PCBDDCGraph    new_graph;
1169   PetscErrorCode ierr;
1170 
1171   PetscFunctionBegin;
1172   ierr = PetscNew(&new_graph);CHKERRQ(ierr);
1173   new_graph->custom_minimal_size = 1;
1174   *graph = new_graph;
1175   PetscFunctionReturn(0);
1176 }
1177