xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision 67c9da694bc355307fef111169dbc0aca808e1d6)
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__ "PCBDDCGraphASCIIView"
7 PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer)
8 {
9   PetscInt       i,j,tabs;
10   PetscInt*      queue_in_global_numbering;
11   PetscErrorCode ierr;
12 
13   PetscFunctionBegin;
14   ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
15   ierr = PetscViewerASCIIGetTab(viewer,&tabs);CHKERRQ(ierr);
16   ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
17   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
18   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Local BDDC graph for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
19   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Number of vertices %d\n",graph->nvtxs);CHKERRQ(ierr);
20   if (verbosity_level > 1) {
21     for (i=0;i<graph->nvtxs;i++) {
22       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d:\n",i);CHKERRQ(ierr);
23       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %d\n",graph->which_dof[i]);CHKERRQ(ierr);
24       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %d\n",graph->special_dof[i]);CHKERRQ(ierr);
25       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %d\n",graph->count[i]);CHKERRQ(ierr);
26       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
27       if (graph->count[i]) {
28         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:");CHKERRQ(ierr);
29         for (j=0;j<graph->count[i];j++) {
30           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[i][j]);CHKERRQ(ierr);
31         }
32         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
33       }
34       ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
35       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
36       if (graph->mirrors) {
37         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %d\n",graph->mirrors[i]);CHKERRQ(ierr);
38         if (graph->mirrors[i]) {
39           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
40           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:");CHKERRQ(ierr);
41           for (j=0;j<graph->mirrors[i];j++) {
42             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->mirrors_set[i][j]);CHKERRQ(ierr);
43           }
44           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
45           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
46           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
47         }
48       }
49       if (verbosity_level > 2) {
50         if (graph->xadj && graph->adjncy) {
51           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:");CHKERRQ(ierr);
52           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
53           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
54             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->adjncy[j]);CHKERRQ(ierr);
55           }
56           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
57           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
58           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
59         }
60       }
61       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
62       if (graph->subset[i] && graph->subset_ncc) {
63         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
64       }
65     }
66   }
67   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
68   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
69   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
70   for (i=0;i<graph->ncc;i++) {
71     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  %d (neighs:",i);CHKERRQ(ierr);
72     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
73     PetscInt node_num=graph->queue[graph->cptr[i]];
74     for (j=0;j<graph->count[node_num];j++) {
75       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
76     }
77     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
78     for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
79       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
80     }
81     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
82     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
83     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
84   }
85   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
86   if (graph->custom_minimal_size > 1 && verbosity_level > 1) {
87     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %d\n",graph->custom_minimal_size);CHKERRQ(ierr);
88   }
89   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
90   PetscFunctionReturn(0);
91 }
92 
93 #undef __FUNCT__
94 #define __FUNCT__ "PCBDDCGraphGetCandidatesIS"
95 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscBool use_faces, PetscBool use_edges, PetscBool use_vertices, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
96 {
97   IS             *ISForFaces,*ISForEdges,ISForVertices;
98   PetscInt       i,j,nfc,nec,nvc,*idx;
99   PetscBool      twodim_flag;
100   PetscErrorCode ierr;
101 
102   PetscFunctionBegin;
103   /* loop on ccs to evalute number of faces, edges and vertices */
104   nfc = 0;
105   nec = 0;
106   nvc = 0;
107   twodim_flag = PETSC_FALSE;
108   for (i=0;i<graph->ncc;i++) {
109     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
110       if (graph->count[graph->queue[graph->cptr[i]]] == 1 && graph->special_dof[graph->queue[graph->cptr[i]]] != PCBDDCGRAPH_NEUMANN_MARK) {
111         nfc++;
112       } else { /* note that nec will be zero in 2d */
113         nec++;
114       }
115     } else {
116       nvc += graph->cptr[i+1]-graph->cptr[i];
117     }
118   }
119   j=0;
120   ierr = MPI_Allreduce(&nec,&j,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
121   if (!j) { /* we are in a 2D case -> no faces, only edges */
122     nec = nfc;
123     nfc = 0;
124     twodim_flag = PETSC_TRUE;
125   }
126   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
127   ISForFaces = 0;
128   ISForEdges = 0;
129   ISForVertices = 0;
130   if (use_faces && nfc) {
131     ierr = PetscMalloc1(nfc,&ISForFaces);CHKERRQ(ierr);
132   }
133   if (use_edges && nec) {
134     ierr = PetscMalloc1(nec,&ISForEdges);CHKERRQ(ierr);
135   }
136   if (use_vertices && nvc) {
137     ierr = PetscMalloc1(nvc,&idx);CHKERRQ(ierr);
138   }
139   /* loop on ccs to compute index sets for faces and edges */
140   nfc = 0;
141   nec = 0;
142   for (i=0;i<graph->ncc;i++) {
143     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
144       if (graph->count[graph->queue[graph->cptr[i]]] == 1 && graph->special_dof[graph->queue[graph->cptr[i]]] != PCBDDCGRAPH_NEUMANN_MARK) {
145         if (twodim_flag) {
146           if (use_edges) {
147             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
148             nec++;
149           }
150         } else {
151           if (use_faces) {
152             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForFaces[nfc]);CHKERRQ(ierr);
153             nfc++;
154           }
155         }
156       } else {
157         if (use_edges) {
158           ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
159           nec++;
160         }
161       }
162     }
163   }
164   /* index set for vertices */
165   if (use_vertices && nvc) {
166     nvc = 0;
167     for (i=0;i<graph->ncc;i++) {
168       if (graph->cptr[i+1]-graph->cptr[i] <= graph->custom_minimal_size) {
169         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
170           idx[nvc]=graph->queue[j];
171           nvc++;
172         }
173       }
174     }
175     /* sort vertex set (by local ordering) */
176     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
177     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
178   }
179   /* get back info */
180   *n_faces = nfc;
181   *FacesIS = ISForFaces;
182   *n_edges = nec;
183   *EdgesIS = ISForEdges;
184   *VerticesIS = ISForVertices;
185   PetscFunctionReturn(0);
186 }
187 
188 #undef __FUNCT__
189 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponents"
190 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
191 {
192   PetscInt       i,adapt_interface,adapt_interface_reduced;
193   MPI_Comm       interface_comm;
194   PetscErrorCode ierr;
195 
196   PetscFunctionBegin;
197   /* compute connected components locally */
198   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
199   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
200   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
201   adapt_interface = 0;
202   adapt_interface_reduced = 0;
203   for (i=0;i<graph->n_subsets;i++) {
204     /* We are not sure that on a given subset of the local interface,
205        with two connected components, the latters be the same among sharing subdomains */
206     if (graph->subset_ncc[i] > 1) {
207       adapt_interface=1;
208       break;
209     }
210   }
211   ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_INT,MPI_LOR,interface_comm);CHKERRQ(ierr);
212 
213   if (graph->n_subsets && adapt_interface_reduced) {
214     MPI_Request *send_requests;
215     MPI_Request *recv_requests;
216     PetscInt    *aux_new_xadj,*new_xadj,*new_adjncy,**temp_buffer;
217     PetscInt    *old_xadj,*old_adjncy;
218     PetscInt    j,k,s,sum_requests,buffer_size,size_of_recv,temp_buffer_size;
219     PetscMPIInt rank,neigh,tag,mpi_buffer_size;
220     PetscInt    *cum_recv_counts,*subset_to_nodes_indices,*recv_buffer_subset,*nodes_to_temp_buffer_indices;
221     PetscInt    *send_buffer,*recv_buffer,*queue_in_global_numbering,*sizes_of_sends,*add_to_subset;
222     PetscInt    start_of_recv,start_of_send,size_of_send,global_subset_counter,ins_val;
223     PetscBool   *subset_cc_adapt,same_set;
224 
225     /* Retrict adjacency graph using information from previously computed connected components */
226     ierr = PetscMalloc1(graph->nvtxs,&aux_new_xadj);CHKERRQ(ierr);
227     for (i=0;i<graph->nvtxs;i++) {
228       aux_new_xadj[i]=1;
229     }
230     for (i=0;i<graph->ncc;i++) {
231       k = graph->cptr[i+1]-graph->cptr[i];
232       for (j=0;j<k;j++) {
233         aux_new_xadj[graph->queue[graph->cptr[i]+j]]=k;
234       }
235     }
236     j = 0;
237     for (i=0;i<graph->nvtxs;i++) {
238       j += aux_new_xadj[i];
239     }
240     ierr = PetscMalloc1((graph->nvtxs+1),&new_xadj);CHKERRQ(ierr);
241     ierr = PetscMalloc1(j,&new_adjncy);CHKERRQ(ierr);
242     new_xadj[0]=0;
243     for (i=0;i<graph->nvtxs;i++) {
244       new_xadj[i+1]=new_xadj[i]+aux_new_xadj[i];
245       if (aux_new_xadj[i]==1) {
246         new_adjncy[new_xadj[i]]=i;
247       }
248     }
249     ierr = PetscFree(aux_new_xadj);CHKERRQ(ierr);
250     for (i=0;i<graph->ncc;i++) {
251       k = graph->cptr[i+1]-graph->cptr[i];
252       for (j=0;j<k;j++) {
253         ierr = PetscMemcpy(&new_adjncy[new_xadj[graph->queue[graph->cptr[i]+j]]],&graph->queue[graph->cptr[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
254       }
255     }
256     /* set temporarly new CSR into graph */
257     old_xadj = graph->xadj;
258     old_adjncy = graph->adjncy;
259     graph->xadj = new_xadj;
260     graph->adjncy = new_adjncy;
261     /* allocate some space */
262     ierr = MPI_Comm_rank(interface_comm,&rank);CHKERRQ(ierr);
263     ierr = PetscMalloc1((graph->n_subsets+1),&cum_recv_counts);CHKERRQ(ierr);
264     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
265     ierr = PetscMalloc1(graph->n_subsets,&subset_to_nodes_indices);CHKERRQ(ierr);
266     /* first count how many neighbours per connected component I will receive from */
267     cum_recv_counts[0]=0;
268     for (i=1;i<graph->n_subsets+1;i++) {
269       j = 0;
270       while (graph->subset[j] != i) {
271         j++;
272       }
273       subset_to_nodes_indices[i-1]=j;
274       /* We don't want sends/recvs_to/from_self -> here I don't count myself  */
275       cum_recv_counts[i]=cum_recv_counts[i-1]+graph->count[j];
276     }
277     ierr = PetscMalloc1(2*cum_recv_counts[graph->n_subsets],&recv_buffer_subset);CHKERRQ(ierr);
278     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&send_requests);CHKERRQ(ierr);
279     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_requests);CHKERRQ(ierr);
280     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
281       send_requests[i]=MPI_REQUEST_NULL;
282       recv_requests[i]=MPI_REQUEST_NULL;
283     }
284     /* exchange with my neighbours the number of my connected components on the shared interface */
285     sum_requests = 0;
286     for (i=0;i<graph->n_subsets;i++) {
287       j = subset_to_nodes_indices[i];
288       ierr = PetscMPIIntCast(graph->subset_ref_node[i],&tag);CHKERRQ(ierr);
289       for (k=0;k<graph->count[j];k++) {
290         ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
291         ierr = MPI_Isend(&graph->subset_ncc[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
292         ierr = MPI_Irecv(&recv_buffer_subset[sum_requests],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
293         sum_requests++;
294       }
295     }
296     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
297     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
298     /* determine the connected component I need to adapt */
299     ierr = PetscMalloc1(graph->n_subsets,&subset_cc_adapt);CHKERRQ(ierr);
300     ierr = PetscMemzero(subset_cc_adapt,graph->n_subsets*sizeof(*subset_cc_adapt));CHKERRQ(ierr);
301     for (i=0;i<graph->n_subsets;i++) {
302       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
303         /* The first condition is natural (someone has a different number of ccs than me), the second one is just to be safe */
304         if (graph->subset_ncc[i] != recv_buffer_subset[j] || graph->subset_ncc[i] > 1) {
305           subset_cc_adapt[i] = PETSC_TRUE;
306           break;
307         }
308       }
309     }
310     buffer_size = 0;
311     for (i=0;i<graph->n_subsets;i++) {
312       if (subset_cc_adapt[i]) {
313         for (j=i;j<graph->ncc;j++) {
314           if (graph->subset[graph->queue[graph->cptr[j]]] == i+1) { /* WARNING -> subset values goes from 1 to graph->n_subsets included */
315             buffer_size += 1 + graph->cptr[j+1]-graph->cptr[j];
316           }
317         }
318       }
319     }
320     ierr = PetscMalloc1(buffer_size,&send_buffer);CHKERRQ(ierr);
321     /* now get from neighbours their ccs (in global numbering) and adapt them (in case it is needed) */
322     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
323     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
324     /* determine how much data to send (size of each queue plus the global indices) and communicate it to neighbours */
325     ierr = PetscMalloc1(graph->n_subsets,&sizes_of_sends);CHKERRQ(ierr);
326     ierr = PetscMemzero(sizes_of_sends,graph->n_subsets*sizeof(*sizes_of_sends));CHKERRQ(ierr);
327     sum_requests = 0;
328     start_of_send = 0;
329     start_of_recv = cum_recv_counts[graph->n_subsets];
330     for (i=0;i<graph->n_subsets;i++) {
331       if (subset_cc_adapt[i]) {
332         size_of_send = 0;
333         for (j=i;j<graph->ncc;j++) {
334           if (graph->subset[graph->queue[graph->cptr[j]]] == i+1) { /* WARNING -> subset values goes from 1 to graph->n_subsets included */
335             send_buffer[start_of_send+size_of_send]=graph->cptr[j+1]-graph->cptr[j];
336             size_of_send += 1;
337             ierr = PetscMemcpy(&send_buffer[start_of_send+size_of_send],
338                                &queue_in_global_numbering[graph->cptr[j]],
339                                (graph->cptr[j+1]-graph->cptr[j])*sizeof(*send_buffer));CHKERRQ(ierr);
340             size_of_send = size_of_send+graph->cptr[j+1]-graph->cptr[j];
341           }
342         }
343         j = subset_to_nodes_indices[i];
344         sizes_of_sends[i] = size_of_send;
345         ierr = PetscMPIIntCast(graph->subset_ref_node[i]+1,&tag);CHKERRQ(ierr);
346         for (k=0;k<graph->count[j];k++) {
347           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
348           ierr = MPI_Isend(&sizes_of_sends[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
349           ierr = MPI_Irecv(&recv_buffer_subset[sum_requests+start_of_recv],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
350           sum_requests++;
351         }
352         start_of_send += size_of_send;
353       }
354     }
355     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
356     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
357     buffer_size = 0;
358     for (k=0;k<sum_requests;k++) {
359       buffer_size += recv_buffer_subset[start_of_recv+k];
360     }
361     ierr = PetscMalloc1(buffer_size,&recv_buffer);CHKERRQ(ierr);
362     /* now exchange the data */
363     start_of_recv = 0;
364     start_of_send = 0;
365     sum_requests = 0;
366     for (i=0;i<graph->n_subsets;i++) {
367       if (subset_cc_adapt[i]) {
368         size_of_send = sizes_of_sends[i];
369         j = subset_to_nodes_indices[i];
370         ierr = PetscMPIIntCast(graph->subset_ref_node[i]+2,&tag);CHKERRQ(ierr);
371         for (k=0;k<graph->count[j];k++) {
372           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
373           ierr = PetscMPIIntCast(size_of_send,&mpi_buffer_size);CHKERRQ(ierr);
374           ierr = MPI_Isend(&send_buffer[start_of_send],mpi_buffer_size,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
375           size_of_recv = recv_buffer_subset[cum_recv_counts[graph->n_subsets]+sum_requests];
376           ierr = PetscMPIIntCast(size_of_recv,&mpi_buffer_size);CHKERRQ(ierr);
377           ierr = MPI_Irecv(&recv_buffer[start_of_recv],mpi_buffer_size,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
378           start_of_recv += size_of_recv;
379           sum_requests++;
380         }
381         start_of_send += size_of_send;
382       }
383     }
384     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
385     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
386     for (j=0;j<buffer_size;) {
387        ierr = ISGlobalToLocalMappingApply(graph->l2gmap,IS_GTOLM_MASK,recv_buffer[j],&recv_buffer[j+1],&recv_buffer[j],&recv_buffer[j+1]);CHKERRQ(ierr);
388        /* we need to adapt the output of GlobalToLocal mapping if there are mirrored nodes */
389        if (graph->mirrors) {
390          PetscBool mirrored_found=PETSC_FALSE;
391          for (k=0;k<recv_buffer[j];k++) {
392            if (graph->mirrors[recv_buffer[j+k+1]]) {
393              mirrored_found=PETSC_TRUE;
394              recv_buffer[j+k+1]=graph->mirrors_set[recv_buffer[j+k+1]][0];
395            }
396          }
397          if (mirrored_found) {
398            ierr = PetscSortInt(recv_buffer[j],&recv_buffer[j+1]);CHKERRQ(ierr);
399            k=0;
400            while (k<recv_buffer[j]) {
401              for (s=1;s<graph->mirrors[recv_buffer[j+1+k]];s++) {
402                recv_buffer[j+1+k+s] = graph->mirrors_set[recv_buffer[j+1+k]][s];
403              }
404              k+=graph->mirrors[recv_buffer[j+1+k]]+s;
405            }
406          }
407        }
408        k = recv_buffer[j]+1;
409        j += k;
410     }
411     sum_requests = cum_recv_counts[graph->n_subsets];
412     start_of_recv = 0;
413     ierr = PetscMalloc1(graph->nvtxs,&nodes_to_temp_buffer_indices);CHKERRQ(ierr);
414     global_subset_counter = 0;
415     for (i=0;i<graph->n_subsets;i++) {
416       if (subset_cc_adapt[i]) {
417         temp_buffer_size = 0;
418         /* find nodes on the shared interface we need to adapt */
419         for (j=0;j<graph->nvtxs;j++) {
420           if (graph->subset[j]==i+1) {
421             nodes_to_temp_buffer_indices[j] = temp_buffer_size;
422             temp_buffer_size++;
423           } else {
424             nodes_to_temp_buffer_indices[j] = -1;
425           }
426         }
427         /* allocate some temporary space */
428         ierr = PetscMalloc1(temp_buffer_size,&temp_buffer);CHKERRQ(ierr);
429         ierr = PetscMalloc1(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i]),&temp_buffer[0]);CHKERRQ(ierr);
430         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
431         for (j=1;j<temp_buffer_size;j++) {
432           temp_buffer[j] = temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
433         }
434         /* analyze contributions from neighbouring subdomains for i-th conn comp
435            temp buffer structure:
436            supposing part of the interface has dimension 5 (for example with global dofs 0,1,2,3,4)
437            3 neighs procs with structured connected components:
438              neigh 0: [0 1 4], [2 3];  (2 connected components)
439              neigh 1: [0 1], [2 3 4];  (2 connected components)
440              neigh 2: [0 4], [1], [2 3]; (3 connected components)
441            tempbuffer (row-oriented) will be filled as:
442              [ 0, 0, 0;
443                0, 0, 1;
444                1, 1, 2;
445                1, 1, 2;
446                0, 1, 0; ];
447            This way we can simply find intersections of ccs among neighs.
448            For the example above, the graph->subset array will be modified to reproduce the following 4 connected components [0], [1], [2 3], [4];
449                                                                                                                                    */
450         for (j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
451           ins_val = 0;
452           size_of_recv = recv_buffer_subset[sum_requests];  /* total size of recv from neighs */
453           for (buffer_size=0;buffer_size<size_of_recv;) {  /* loop until all data from neighs has been taken into account */
454             for (k=1;k<recv_buffer[buffer_size+start_of_recv]+1;k++) { /* filling properly temp_buffer using data from a single recv */
455               temp_buffer[nodes_to_temp_buffer_indices[recv_buffer[start_of_recv+buffer_size+k]]][j] = ins_val;
456             }
457             buffer_size += k;
458             ins_val++;
459           }
460           start_of_recv += size_of_recv;
461           sum_requests++;
462         }
463         ierr = PetscMalloc1(temp_buffer_size,&add_to_subset);CHKERRQ(ierr);
464         ierr = PetscMemzero(add_to_subset,temp_buffer_size*sizeof(*add_to_subset));CHKERRQ(ierr);
465         for (j=0;j<temp_buffer_size;j++) {
466           if (!add_to_subset[j]) { /* found a new cc  */
467             global_subset_counter++;
468             add_to_subset[j] = global_subset_counter;
469             for (k=j+1;k<temp_buffer_size;k++) { /* check for other nodes in new cc */
470               same_set = PETSC_TRUE;
471               for (s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++) {
472                 if (temp_buffer[j][s]!=temp_buffer[k][s]) {
473                   same_set = PETSC_FALSE;
474                   break;
475                 }
476               }
477               if (same_set) {
478                 add_to_subset[k] = global_subset_counter;
479               }
480             }
481           }
482         }
483         /* insert new data in subset array */
484         temp_buffer_size = 0;
485         for (j=0;j<graph->nvtxs;j++) {
486           if (graph->subset[j]==i+1) {
487             graph->subset[j] = graph->n_subsets+add_to_subset[temp_buffer_size];
488             temp_buffer_size++;
489           }
490         }
491         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
492         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
493         ierr = PetscFree(add_to_subset);CHKERRQ(ierr);
494       }
495     }
496     ierr = PetscFree(nodes_to_temp_buffer_indices);CHKERRQ(ierr);
497     ierr = PetscFree(sizes_of_sends);CHKERRQ(ierr);
498     ierr = PetscFree(send_requests);CHKERRQ(ierr);
499     ierr = PetscFree(recv_requests);CHKERRQ(ierr);
500     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
501     ierr = PetscFree(recv_buffer_subset);CHKERRQ(ierr);
502     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
503     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
504     ierr = PetscFree(subset_to_nodes_indices);CHKERRQ(ierr);
505     ierr = PetscFree(subset_cc_adapt);CHKERRQ(ierr);
506     /* We are ready to find for connected components consistent among neighbouring subdomains */
507     if (global_subset_counter) {
508       ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
509       global_subset_counter = 0;
510       for (i=0;i<graph->nvtxs;i++) {
511         if (graph->subset[i] && !PetscBTLookup(graph->touched,i)) {
512           global_subset_counter++;
513           for (j=i+1;j<graph->nvtxs;j++) {
514             if (!PetscBTLookup(graph->touched,j) && graph->subset[j]==graph->subset[i]) {
515               graph->subset[j] = global_subset_counter;
516               ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
517             }
518           }
519           graph->subset[i] = global_subset_counter;
520           ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
521         }
522       }
523       /* refine connected components locally */
524       ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
525     }
526     /* restore original CSR graph of dofs */
527     ierr = PetscFree(new_xadj);CHKERRQ(ierr);
528     ierr = PetscFree(new_adjncy);CHKERRQ(ierr);
529     graph->xadj = old_xadj;
530     graph->adjncy = old_adjncy;
531     ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
532   }
533   PetscFunctionReturn(0);
534 }
535 
536 /* The following code has been adapted from function IsConnectedSubdomain contained
537    in source file contig.c of METIS library (version 5.0.1)
538    It finds connected components for each subset  */
539 #undef __FUNCT__
540 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponentsLocal"
541 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
542 {
543   PetscInt       i,j,k,first,last,nleft,ncc,pid,cum_queue,n,ncc_pid;
544   PetscInt       *queue_global;
545   PetscErrorCode ierr;
546 
547   PetscFunctionBegin;
548   /* quiet return if no csr info is available */
549   if (!graph->xadj || !graph->adjncy) {
550     PetscFunctionReturn(0);
551   }
552 
553   /* reset any previous search of connected components */
554   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
555   graph->n_subsets = 0;
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   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
564   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
565   ierr = PetscMemzero(graph->subset_ncc,graph->n_subsets*sizeof(*graph->subset_ncc));CHKERRQ(ierr);
566   ierr = PetscMemzero(graph->cptr,(graph->nvtxs+1)*sizeof(*graph->cptr));CHKERRQ(ierr);
567   ierr = PetscMemzero(graph->queue,graph->nvtxs*sizeof(*graph->queue));CHKERRQ(ierr);
568 
569   /* begin search for connected components */
570   cum_queue = 0;
571   ncc = 0;
572   for (n=0;n<graph->n_subsets;n++) {
573     pid = n+1;  /* partition labeled by 0 is discarded */
574     nleft = 0;
575     for (i=0;i<graph->nvtxs;i++) {
576       if (graph->subset[i] == pid) {
577         nleft++;
578       }
579     }
580     for (i=0; i<graph->nvtxs; i++) {
581       if (graph->subset[i] == pid) {
582         break;
583       }
584     }
585     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
586     graph->queue[cum_queue] = i;
587     first = 0;
588     last = 1;
589     graph->cptr[ncc] = cum_queue;
590     ncc_pid = 0;
591     while (first != nleft) {
592       if (first == last) {
593         graph->cptr[++ncc] = first+cum_queue;
594         ncc_pid++;
595         for (i=0; i<graph->nvtxs; i++) { /* TODO-> use a while! */
596           if (graph->subset[i] == pid && !PetscBTLookup(graph->touched,i)) {
597             break;
598           }
599         }
600         graph->queue[cum_queue+last] = i;
601         last++;
602         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
603       }
604       i = graph->queue[cum_queue+first];
605       first++;
606       for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
607         k = graph->adjncy[j];
608         if (graph->subset[k] == pid && !PetscBTLookup(graph->touched,k)) {
609           graph->queue[cum_queue+last] = k;
610           last++;
611           ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
612         }
613       }
614     }
615     graph->cptr[++ncc] = first+cum_queue;
616     ncc_pid++;
617     cum_queue = graph->cptr[ncc];
618     graph->subset_ncc[n] = ncc_pid;
619   }
620   graph->ncc = ncc;
621   /* For consistency among neighbours, I need to sort (by global ordering) each connected component */
622   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
623   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
624   for (i=0;i<graph->ncc;i++) {
625     ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
626   }
627   ierr = PetscFree(queue_global);CHKERRQ(ierr);
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;
642   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
643   PetscErrorCode ierr;
644   PetscBool      same_set,mirrors_found;
645 
646   PetscFunctionBegin;
647   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
648   /* custom_minimal_size */
649   graph->custom_minimal_size = PetscMax(graph->custom_minimal_size,custom_minimal_size);
650   /* get info l2gmap and allocate work vectors  */
651   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
652   ierr = ISLocalToGlobalMappingGetIndices(graph->l2gmap,&is_indices);CHKERRQ(ierr);
653   j = 0;
654   for (i=0;i<graph->nvtxs;i++) {
655     j = PetscMax(j,is_indices[i]);
656   }
657   ierr = MPI_Allreduce(&j,&i,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
658   i++;
659   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
660   ierr = VecSetSizes(local_vec,PETSC_DECIDE,graph->nvtxs);CHKERRQ(ierr);
661   ierr = VecSetType(local_vec,VECSTANDARD);CHKERRQ(ierr);
662   ierr = VecDuplicate(local_vec,&local_vec2);CHKERRQ(ierr);
663   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
664   ierr = VecSetSizes(global_vec,PETSC_DECIDE,i);CHKERRQ(ierr);
665   ierr = VecSetType(global_vec,VECSTANDARD);CHKERRQ(ierr);
666   ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
667   ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
668   ierr = VecScatterCreate(global_vec,from,local_vec,to,&scatter_ctx);CHKERRQ(ierr);
669 
670   /* get local periodic nodes */
671   mirrors_found = PETSC_FALSE;
672   if (graph->nvtxs && n_neigh) {
673     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
674     for (i=0; i<n_shared[0]; i++) {
675       if (graph->count[shared[0][i]] > 1) {
676         mirrors_found = PETSC_TRUE;
677         break;
678       }
679     }
680   }
681   /* compute local mirrors (if any) */
682   if (mirrors_found) {
683     PetscInt *local_indices,*global_indices;
684     /* get arrays of local and global indices */
685     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
686     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
687     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
688     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
689     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
690     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
691     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
692     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
693     /* allocate space for mirrors */
694     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
695     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
696     graph->mirrors_set[0] = 0;
697 
698     k=0;
699     for (i=0;i<n_shared[0];i++) {
700       j=shared[0][i];
701       if (graph->count[j] > 1) {
702         graph->mirrors[j]++;
703         k++;
704       }
705     }
706     /* allocate space for set of mirrors */
707     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
708     for (i=1;i<graph->nvtxs;i++)
709       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
710 
711     /* fill arrays */
712     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
713     for (j=0;j<n_shared[0];j++) {
714       i=shared[0][j];
715       if (graph->count[i] > 1)
716         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
717     }
718     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
719     for (i=0;i<graph->nvtxs;i++) {
720       if (graph->mirrors[i] > 0) {
721         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
722         j = global_indices[k];
723         while ( k > 0 && global_indices[k-1] == j) k--;
724         for (j=0;j<graph->mirrors[i];j++) {
725           graph->mirrors_set[i][j]=local_indices[k+j];
726         }
727         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
728       }
729     }
730     ierr = PetscFree(local_indices);CHKERRQ(ierr);
731     ierr = PetscFree(global_indices);CHKERRQ(ierr);
732   }
733   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
734   ierr = ISDestroy(&to);CHKERRQ(ierr);
735   ierr = ISDestroy(&from);CHKERRQ(ierr);
736 
737   /* Count total number of neigh per node */
738   k=0;
739   for (i=1;i<n_neigh;i++) {
740     k += n_shared[i];
741     for (j=0;j<n_shared[i];j++) {
742       graph->count[shared[i][j]] += 1;
743     }
744   }
745   /* Allocate space for storing the set of neighbours for each node */
746   if (graph->nvtxs) {
747     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
748   }
749   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
750     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
751   }
752   /* Get information for sharing subdomains */
753   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
754   for (i=1;i<n_neigh;i++) { /* dont count myself */
755     s = n_shared[i];
756     for (j=0;j<s;j++) {
757       k = shared[i][j];
758       graph->neighbours_set[k][graph->count[k]] = neigh[i];
759       graph->count[k] += 1;
760     }
761   }
762   /* sort set of sharing subdomains */
763   for (i=0;i<graph->nvtxs;i++) {
764     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
765   }
766   /*
767      Get info for dofs splitting
768      User can specify only a subset; an additional field is considered as a complementary set
769   */
770   for (i=0;i<graph->nvtxs;i++) {
771     graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
772   }
773   for (i=0;i<n_ISForDofs;i++) {
774     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
775     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
776     for (j=0;j<is_size;j++) {
777       if (is_indices[j] > 0 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
778         graph->which_dof[is_indices[j]] = i;
779       }
780     }
781     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
782   }
783   /* Take into account Neumann nodes */
784   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
785   ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
786   if (neumann_is) {
787     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
788     ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
789     ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
790     for (i=0;i<is_size;i++) {
791       array[is_indices[i]] = 1.0;
792     }
793     ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
794     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
795   }
796   /* Neumann nodes: impose consistency among neighbours */
797   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
798   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
799   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
800   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
801   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
802   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
803   for (i=0;i<graph->nvtxs;i++) {
804     if (PetscRealPart(array[i]) > 0.0) {
805       graph->special_dof[i] = PCBDDCGRAPH_NEUMANN_MARK;
806     }
807   }
808   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
809   /* Take into account Dirichlet nodes */
810   ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
811   if (dirichlet_is) {
812     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
813     ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
814     ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
815     ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
816     for (i=0;i<is_size;i++){
817       k = is_indices[i];
818       if (graph->count[k] && !PetscBTLookup(graph->touched,k)) {
819         if (PetscRealPart(array[k]) > 0.0) {
820           SETERRQ1(PETSC_COMM_SELF,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);
821         }
822         array2[k] = 1.0;
823       }
824     }
825     ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
826     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
827     ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
828   }
829   /* Dirichlet nodes: impose consistency among neighbours */
830   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
831   ierr = VecScatterBegin(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
832   ierr = VecScatterEnd(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
833   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
834   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
835   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
836   for (i=0;i<graph->nvtxs;i++) {
837     if (PetscRealPart(array[i]) > 0.0) {
838       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
839       graph->subset[i] = 0; /* dirichlet nodes treated as internal -> is it ok? */
840       graph->special_dof[i] = PCBDDCGRAPH_DIRICHLET_MARK;
841     }
842   }
843   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
844 
845   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
846   if (graph->mirrors) {
847     for (i=0;i<graph->nvtxs;i++)
848       if (graph->mirrors[i])
849         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
850 
851     if (graph->xadj && graph->adjncy) {
852       PetscInt *new_xadj,*new_adjncy;
853       /* sort CSR graph */
854       for (i=0;i<graph->nvtxs;i++)
855         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
856 
857       /* adapt local CSR graph in case of local periodicity */
858       k=0;
859       for (i=0;i<graph->nvtxs;i++)
860         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
861           k += graph->mirrors[graph->adjncy[j]];
862 
863       ierr = PetscMalloc1((graph->nvtxs+1),&new_xadj);CHKERRQ(ierr);
864       ierr = PetscMalloc1((k+graph->xadj[graph->nvtxs]),&new_adjncy);CHKERRQ(ierr);
865       new_xadj[0]=0;
866       for (i=0;i<graph->nvtxs;i++) {
867         k = graph->xadj[i+1]-graph->xadj[i];
868         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
869         new_xadj[i+1]=new_xadj[i]+k;
870         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
871           k = graph->mirrors[graph->adjncy[j]];
872           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
873           new_xadj[i+1]+=k;
874         }
875         k = new_xadj[i+1]-new_xadj[i];
876         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
877         new_xadj[i+1]=new_xadj[i]+k;
878       }
879       /* set new CSR into graph */
880       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
881       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
882       graph->xadj = new_xadj;
883       graph->adjncy = new_adjncy;
884     }
885   }
886 
887   /* mark special nodes -> each will become a single node equivalence class */
888   if (custom_primal_vertices) {
889     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
890     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
891     for (i=0;i<is_size;i++) {
892       graph->special_dof[is_indices[i]] = PCBDDCGRAPH_SPECIAL_MARK-i;
893     }
894     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
895   }
896   /* mark interior nodes as touched and belonging to partition number 0 */
897   for (i=0;i<graph->nvtxs;i++) {
898     if (!graph->count[i]) {
899       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
900       graph->subset[i] = 0;
901     }
902   }
903   /* init graph structure and compute default subsets */
904   nodes_touched=0;
905   for (i=0;i<graph->nvtxs;i++) {
906     if (PetscBTLookup(graph->touched,i)) {
907       nodes_touched++;
908     }
909   }
910   i = 0;
911   graph->ncc = 0;
912   total_counts = 0;
913   while (nodes_touched<graph->nvtxs) {
914     /*  find first untouched node in local ordering */
915     while (PetscBTLookup(graph->touched,i)) {
916       i++;
917     }
918     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
919     graph->subset[i] = graph->ncc+1;
920     graph->cptr[graph->ncc] = total_counts;
921     graph->queue[total_counts] = i;
922     total_counts++;
923     nodes_touched++;
924     /* now find all other nodes having the same set of sharing subdomains */
925     for (j=i+1;j<graph->nvtxs;j++) {
926       /* check for same number of sharing subdomains, dof number and same special mark */
927       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]) {
928         /* check for same set of sharing subdomains */
929         same_set=PETSC_TRUE;
930         for (k=0;k<graph->count[j];k++){
931           if (graph->neighbours_set[i][k]!=graph->neighbours_set[j][k]) {
932             same_set=PETSC_FALSE;
933           }
934         }
935         /* I found a friend of mine */
936         if (same_set) {
937           graph->subset[j]=graph->ncc+1;
938           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
939           nodes_touched++;
940           graph->queue[total_counts] = j;
941           total_counts++;
942         }
943       }
944     }
945     graph->ncc++;
946   }
947   /* set default number of subsets (at this point no info on csr graph has been taken into account, so n_subsets = ncc */
948   graph->n_subsets = graph->ncc;
949   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
950   for (i=0;i<graph->n_subsets;i++) {
951     graph->subset_ncc[i] = 1;
952   }
953   /* final pointer */
954   graph->cptr[graph->ncc] = total_counts;
955   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
956   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
957   /* get a reference node (min index in global ordering) for each subset */
958   ierr = PetscMalloc1(graph->ncc,&graph->subset_ref_node);CHKERRQ(ierr);
959   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
960   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
961   for (i=0;i<graph->ncc;i++) {
962     PetscInt minval = queue_global[graph->cptr[i]];
963     for (j=graph->cptr[i]+1;j<graph->cptr[i+1];j++) {
964       minval = PetscMin(minval,queue_global[j]);
965     }
966     graph->subset_ref_node[i] = minval;
967   }
968   ierr = PetscFree(queue_global);CHKERRQ(ierr);
969   /* free objects */
970   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
971   ierr = VecDestroy(&local_vec2);CHKERRQ(ierr);
972   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
973   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
974   PetscFunctionReturn(0);
975 }
976 
977 #undef __FUNCT__
978 #define __FUNCT__ "PCBDDCGraphResetCSR"
979 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
980 {
981   PetscErrorCode ierr;
982 
983   PetscFunctionBegin;
984   ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
985   ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
986   graph->nvtxs_csr = 0;
987   PetscFunctionReturn(0);
988 }
989 
990 #undef __FUNCT__
991 #define __FUNCT__ "PCBDDCGraphReset"
992 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
993 {
994   PetscErrorCode ierr;
995 
996   PetscFunctionBegin;
997   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
998   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
999   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1000   if (graph->nvtxs) {
1001     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1002   }
1003   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1004   ierr = PetscFree7(graph->count,
1005                     graph->neighbours_set,
1006                     graph->subset,
1007                     graph->which_dof,
1008                     graph->cptr,
1009                     graph->queue,
1010                     graph->special_dof);CHKERRQ(ierr);
1011   if (graph->mirrors) {
1012     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1013   }
1014   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1015   graph->nvtxs = 0;
1016   graph->n_subsets = 0;
1017   graph->custom_minimal_size = 1;
1018   PetscFunctionReturn(0);
1019 }
1020 
1021 #undef __FUNCT__
1022 #define __FUNCT__ "PCBDDCGraphInit"
1023 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap)
1024 {
1025   PetscInt       n;
1026   PetscErrorCode ierr;
1027 
1028   PetscFunctionBegin;
1029   PetscValidPointer(graph,1);
1030   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1031   /* raise an error if already allocated */
1032   if (graph->nvtxs) {
1033     SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1034   }
1035   /* set number of vertices */
1036   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1037   graph->l2gmap = l2gmap;
1038   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1039   graph->nvtxs = n;
1040   /* allocate used space */
1041   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1042   ierr = PetscMalloc7(graph->nvtxs,&graph->count,
1043                       graph->nvtxs,&graph->neighbours_set,
1044                       graph->nvtxs,&graph->subset,
1045                       graph->nvtxs,&graph->which_dof,
1046                       graph->nvtxs+1,&graph->cptr,
1047                       graph->nvtxs,&graph->queue,
1048                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1049   /* zeroes memory */
1050   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1051   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1052   /* use -1 as a default value for which_dof array */
1053   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1054   ierr = PetscMemzero(graph->cptr,(graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
1055   ierr = PetscMemzero(graph->queue,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1056   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1057   /* zeroes first pointer to neighbour set */
1058   if (graph->nvtxs) {
1059     graph->neighbours_set[0] = 0;
1060   }
1061   /* zeroes workspace for values of ncc */
1062   graph->subset_ncc = 0;
1063   graph->subset_ref_node = 0;
1064   PetscFunctionReturn(0);
1065 }
1066 
1067 #undef __FUNCT__
1068 #define __FUNCT__ "PCBDDCGraphDestroy"
1069 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1070 {
1071   PetscErrorCode ierr;
1072 
1073   PetscFunctionBegin;
1074   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1075   ierr = PetscFree(*graph);CHKERRQ(ierr);
1076   PetscFunctionReturn(0);
1077 }
1078 
1079 #undef __FUNCT__
1080 #define __FUNCT__ "PCBDDCGraphCreate"
1081 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1082 {
1083   PCBDDCGraph    new_graph;
1084   PetscErrorCode ierr;
1085 
1086   PetscFunctionBegin;
1087   ierr = PetscMalloc(sizeof(*new_graph),&new_graph);CHKERRQ(ierr);
1088   /* local to global mapping of dofs */
1089   new_graph->l2gmap = 0;
1090   /* vertex size */
1091   new_graph->nvtxs = 0;
1092   new_graph->n_subsets = 0;
1093   new_graph->custom_minimal_size = 1;
1094   /* zeroes ponters */
1095   new_graph->mirrors = 0;
1096   new_graph->mirrors_set = 0;
1097   new_graph->neighbours_set = 0;
1098   new_graph->subset = 0;
1099   new_graph->which_dof = 0;
1100   new_graph->special_dof = 0;
1101   new_graph->cptr = 0;
1102   new_graph->queue = 0;
1103   new_graph->count = 0;
1104   new_graph->subset_ncc = 0;
1105   new_graph->subset_ref_node = 0;
1106   new_graph->touched = 0;
1107   /* zeroes pointers to csr graph of local nodes connectivity (optional data) */
1108   new_graph->nvtxs_csr = 0;
1109   new_graph->xadj = 0;
1110   new_graph->adjncy = 0;
1111   *graph = new_graph;
1112   PetscFunctionReturn(0);
1113 }
1114