xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision cf5a6209970185a07c62c3d51231f232aaad6491)
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         }
88       }
89       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
90       if (graph->subset[i] && graph->subset_ncc) {
91         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
92       }
93     }
94   }
95   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
96   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
97   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
98   for (i=0;i<graph->ncc;i++) {
99     PetscInt node_num=graph->queue[graph->cptr[i]];
100     PetscBool printcc = PETSC_FALSE;
101     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  %d (neighs:",i);CHKERRQ(ierr);
102     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
103     for (j=0;j<graph->count[node_num];j++) {
104       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
105     }
106     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
107     if (verbosity_level > 1) {
108       printcc = PETSC_TRUE;
109     } else if (graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) {
110       printcc = PETSC_TRUE;
111     }
112     if (printcc) {
113       for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
114         ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
115       }
116     }
117     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
118     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
119     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
120   }
121   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
122   if (graph->custom_minimal_size > 1 && verbosity_level > 1) {
123     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %d\n",graph->custom_minimal_size);CHKERRQ(ierr);
124   }
125   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
126   PetscFunctionReturn(0);
127 }
128 
129 #undef __FUNCT__
130 #define __FUNCT__ "PCBDDCGraphGetCandidatesIS"
131 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
132 {
133   IS             *ISForFaces,*ISForEdges,ISForVertices;
134   PetscInt       i,j,nfc,nec,nvc,*idx;
135   PetscBool      twodim_flag;
136   PetscErrorCode ierr;
137 
138   PetscFunctionBegin;
139   /* loop on ccs to evalute number of faces, edges and vertices */
140   nfc = 0;
141   nec = 0;
142   nvc = 0;
143   twodim_flag = PETSC_FALSE;
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   j=0;
157   ierr = MPI_Allreduce(&nec,&j,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
158   if (!j) { /* we are in a 2D case -> no faces, only edges */
159     nec = nfc;
160     nfc = 0;
161     twodim_flag = PETSC_TRUE;
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 (twodim_flag) {
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         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
206           idx[nvc]=graph->queue[j];
207           nvc++;
208         }
209       }
210     }
211     /* sort vertex set (by local ordering) */
212     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
213     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
214   }
215   /* get back info */
216   if (n_faces) *n_faces = nfc;
217   if (FacesIS) {
218     *FacesIS = ISForFaces;
219   }
220   if (n_edges) *n_edges = nec;
221   if (EdgesIS) {
222     *EdgesIS = ISForEdges;
223   }
224   if (VerticesIS) {
225     *VerticesIS = ISForVertices;
226   }
227   PetscFunctionReturn(0);
228 }
229 
230 #undef __FUNCT__
231 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponents"
232 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
233 {
234   PetscBool      adapt_interface_reduced;
235   MPI_Comm       interface_comm;
236   PetscMPIInt    size;
237   PetscErrorCode ierr;
238 
239   PetscFunctionBegin;
240   /* compute connected components locally */
241   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
242   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
243   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
244   ierr = MPI_Comm_size(interface_comm,&size);CHKERRQ(ierr);
245   adapt_interface_reduced = PETSC_FALSE;
246   if (size > 1) {
247     PetscInt i;
248     PetscBool adapt_interface = PETSC_FALSE;
249     for (i=0;i<graph->n_subsets;i++) {
250       /* We are not sure that on a given subset of the local interface,
251          with two connected components, the latters be the same among sharing subdomains */
252       if (graph->subset_ncc[i] > 1) {
253         adapt_interface = PETSC_TRUE;
254         break;
255       }
256     }
257     ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_BOOL,MPI_LOR,interface_comm);CHKERRQ(ierr);
258   }
259 
260   if (graph->n_subsets && adapt_interface_reduced) {
261     MPI_Request *send_requests;
262     MPI_Request *recv_requests;
263     PetscInt    *aux_new_xadj,*new_xadj,*new_adjncy,**temp_buffer;
264     PetscInt    *old_xadj,*old_adjncy;
265     PetscInt    i,j,k,s,sum_requests,buffer_size,size_of_recv,temp_buffer_size;
266     PetscMPIInt rank,neigh,tag,mpi_buffer_size;
267     PetscInt    *cum_recv_counts,*subset_to_nodes_indices,*recv_buffer_subset,*nodes_to_temp_buffer_indices;
268     PetscInt    *send_buffer,*recv_buffer,*queue_in_global_numbering,*sizes_of_sends,*add_to_subset;
269     PetscInt    start_of_recv,start_of_send,size_of_send,global_subset_counter,ins_val;
270     PetscBool   *subset_cc_adapt,same_set;
271 
272     /* Retrict adjacency graph using information from previously computed connected components */
273     ierr = PetscMalloc1(graph->nvtxs,&aux_new_xadj);CHKERRQ(ierr);
274     for (i=0;i<graph->nvtxs;i++) {
275       aux_new_xadj[i]=1;
276     }
277     for (i=0;i<graph->ncc;i++) {
278       k = graph->cptr[i+1]-graph->cptr[i];
279       for (j=0;j<k;j++) {
280         aux_new_xadj[graph->queue[graph->cptr[i]+j]]=k;
281       }
282     }
283     j = 0;
284     for (i=0;i<graph->nvtxs;i++) {
285       j += aux_new_xadj[i];
286     }
287     ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
288     ierr = PetscMalloc1(j,&new_adjncy);CHKERRQ(ierr);
289     new_xadj[0]=0;
290     for (i=0;i<graph->nvtxs;i++) {
291       new_xadj[i+1]=new_xadj[i]+aux_new_xadj[i];
292       if (aux_new_xadj[i]==1) {
293         new_adjncy[new_xadj[i]]=i;
294       }
295     }
296     ierr = PetscFree(aux_new_xadj);CHKERRQ(ierr);
297     for (i=0;i<graph->ncc;i++) {
298       k = graph->cptr[i+1]-graph->cptr[i];
299       for (j=0;j<k;j++) {
300         ierr = PetscMemcpy(&new_adjncy[new_xadj[graph->queue[graph->cptr[i]+j]]],&graph->queue[graph->cptr[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
301       }
302     }
303     /* set temporarly new CSR into graph */
304     old_xadj = graph->xadj;
305     old_adjncy = graph->adjncy;
306     graph->xadj = new_xadj;
307     graph->adjncy = new_adjncy;
308     /* allocate some space */
309     ierr = MPI_Comm_rank(interface_comm,&rank);CHKERRQ(ierr);
310     ierr = PetscMalloc1(graph->n_subsets+1,&cum_recv_counts);CHKERRQ(ierr);
311     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
312     ierr = PetscMalloc1(graph->n_subsets,&subset_to_nodes_indices);CHKERRQ(ierr);
313     /* first count how many neighbours per connected component I will receive from */
314     cum_recv_counts[0]=0;
315     for (i=1;i<graph->n_subsets+1;i++) {
316       j = 0;
317       while (graph->subset[j] != i) {
318         j++;
319       }
320       subset_to_nodes_indices[i-1]=j;
321       /* We don't want sends/recvs_to/from_self -> here I don't count myself  */
322       cum_recv_counts[i]=cum_recv_counts[i-1]+graph->count[j];
323     }
324     ierr = PetscMalloc1(2*cum_recv_counts[graph->n_subsets],&recv_buffer_subset);CHKERRQ(ierr);
325     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&send_requests);CHKERRQ(ierr);
326     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_requests);CHKERRQ(ierr);
327     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
328       send_requests[i]=MPI_REQUEST_NULL;
329       recv_requests[i]=MPI_REQUEST_NULL;
330     }
331     /* exchange with my neighbours the number of my connected components on the shared interface */
332     sum_requests = 0;
333     for (i=0;i<graph->n_subsets;i++) {
334       j = subset_to_nodes_indices[i];
335       ierr = PetscMPIIntCast(3*graph->subset_ref_node[i],&tag);CHKERRQ(ierr);
336       for (k=0;k<graph->count[j];k++) {
337         ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
338         ierr = MPI_Isend(&graph->subset_ncc[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
339         ierr = MPI_Irecv(&recv_buffer_subset[sum_requests],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
340         sum_requests++;
341       }
342     }
343     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
344     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
345     /* determine the connected component I need to adapt */
346     ierr = PetscMalloc1(graph->n_subsets,&subset_cc_adapt);CHKERRQ(ierr);
347     ierr = PetscMemzero(subset_cc_adapt,graph->n_subsets*sizeof(*subset_cc_adapt));CHKERRQ(ierr);
348     for (i=0;i<graph->n_subsets;i++) {
349       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
350         /* The first condition is natural (someone has a different number of ccs than me), the second one is just to be safe */
351         if (graph->subset_ncc[i] != recv_buffer_subset[j] || graph->subset_ncc[i] > 1) {
352           subset_cc_adapt[i] = PETSC_TRUE;
353           break;
354         }
355       }
356     }
357     buffer_size = 0;
358     for (i=0;i<graph->n_subsets;i++) {
359       if (subset_cc_adapt[i]) {
360         for (j=i;j<graph->ncc;j++) {
361           if (graph->subset[graph->queue[graph->cptr[j]]] == i+1) { /* WARNING -> subset values goes from 1 to graph->n_subsets included */
362             buffer_size += 1 + graph->cptr[j+1]-graph->cptr[j];
363           }
364         }
365       }
366     }
367     ierr = PetscMalloc1(buffer_size,&send_buffer);CHKERRQ(ierr);
368     /* now get from neighbours their ccs (in global numbering) and adapt them (in case it is needed) */
369     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
370     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
371     /* determine how much data to send (size of each queue plus the global indices) and communicate it to neighbours */
372     ierr = PetscMalloc1(graph->n_subsets,&sizes_of_sends);CHKERRQ(ierr);
373     ierr = PetscMemzero(sizes_of_sends,graph->n_subsets*sizeof(*sizes_of_sends));CHKERRQ(ierr);
374     sum_requests = 0;
375     start_of_send = 0;
376     start_of_recv = cum_recv_counts[graph->n_subsets];
377     for (i=0;i<graph->n_subsets;i++) {
378       if (subset_cc_adapt[i]) {
379         size_of_send = 0;
380         for (j=i;j<graph->ncc;j++) {
381           if (graph->subset[graph->queue[graph->cptr[j]]] == i+1) { /* WARNING -> subset values goes from 1 to graph->n_subsets included */
382             send_buffer[start_of_send+size_of_send]=graph->cptr[j+1]-graph->cptr[j];
383             size_of_send += 1;
384             ierr = PetscMemcpy(&send_buffer[start_of_send+size_of_send],
385                                &queue_in_global_numbering[graph->cptr[j]],
386                                (graph->cptr[j+1]-graph->cptr[j])*sizeof(*send_buffer));CHKERRQ(ierr);
387             size_of_send = size_of_send+graph->cptr[j+1]-graph->cptr[j];
388           }
389         }
390         j = subset_to_nodes_indices[i];
391         sizes_of_sends[i] = size_of_send;
392         ierr = PetscMPIIntCast(3*graph->subset_ref_node[i]+1,&tag);CHKERRQ(ierr);
393         for (k=0;k<graph->count[j];k++) {
394           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
395           ierr = MPI_Isend(&sizes_of_sends[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
396           ierr = MPI_Irecv(&recv_buffer_subset[sum_requests+start_of_recv],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
397           sum_requests++;
398         }
399         start_of_send += size_of_send;
400       }
401     }
402     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
403     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
404     buffer_size = 0;
405     for (k=0;k<sum_requests;k++) {
406       buffer_size += recv_buffer_subset[start_of_recv+k];
407     }
408     ierr = PetscMalloc1(buffer_size,&recv_buffer);CHKERRQ(ierr);
409     /* now exchange the data */
410     start_of_recv = 0;
411     start_of_send = 0;
412     sum_requests = 0;
413     for (i=0;i<graph->n_subsets;i++) {
414       if (subset_cc_adapt[i]) {
415         size_of_send = sizes_of_sends[i];
416         j = subset_to_nodes_indices[i];
417         ierr = PetscMPIIntCast(3*graph->subset_ref_node[i]+2,&tag);CHKERRQ(ierr);
418         for (k=0;k<graph->count[j];k++) {
419           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
420           ierr = PetscMPIIntCast(size_of_send,&mpi_buffer_size);CHKERRQ(ierr);
421           ierr = MPI_Isend(&send_buffer[start_of_send],mpi_buffer_size,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
422           size_of_recv = recv_buffer_subset[cum_recv_counts[graph->n_subsets]+sum_requests];
423           ierr = PetscMPIIntCast(size_of_recv,&mpi_buffer_size);CHKERRQ(ierr);
424           ierr = MPI_Irecv(&recv_buffer[start_of_recv],mpi_buffer_size,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
425           start_of_recv += size_of_recv;
426           sum_requests++;
427         }
428         start_of_send += size_of_send;
429       }
430     }
431     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
432     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
433     for (j=0;j<buffer_size;) {
434       PetscInt rbs = recv_buffer[j];
435 
436       ierr = ISGlobalToLocalMappingApply(graph->l2gmap,IS_GTOLM_DROP,rbs,&recv_buffer[j+1],&recv_buffer[j],&recv_buffer[j+1]);CHKERRQ(ierr);
437       if (rbs != recv_buffer[j]) {
438         SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mapped received buffer size %d differs from input size %d\n",rbs,recv_buffer[j]);
439       }
440       /* we need to adapt the output of GlobalToLocal mapping if there are mirrored nodes */
441       if (graph->mirrors) {
442         PetscBool mirrored_found=PETSC_FALSE;
443         for (k=0;k<recv_buffer[j];k++) {
444           if (graph->mirrors[recv_buffer[j+k+1]]) {
445             mirrored_found=PETSC_TRUE;
446             recv_buffer[j+k+1]=graph->mirrors_set[recv_buffer[j+k+1]][0];
447           }
448         }
449         if (mirrored_found) {
450           ierr = PetscSortInt(recv_buffer[j],&recv_buffer[j+1]);CHKERRQ(ierr);
451           k=0;
452           while (k<recv_buffer[j]) {
453             PetscInt nmir = graph->mirrors[recv_buffer[j+1+k]];
454             for (s=1;s<nmir;s++) {
455               recv_buffer[j+1+k+s] = graph->mirrors_set[recv_buffer[j+1+k]][s];
456             }
457             k += nmir;
458           }
459         }
460       }
461       k = recv_buffer[j]+1;
462       j += k;
463     }
464     sum_requests = cum_recv_counts[graph->n_subsets];
465     start_of_recv = 0;
466     ierr = PetscMalloc1(graph->nvtxs,&nodes_to_temp_buffer_indices);CHKERRQ(ierr);
467     global_subset_counter = 0;
468     for (i=0;i<graph->n_subsets;i++) {
469       if (subset_cc_adapt[i]) {
470         temp_buffer_size = 0;
471         /* find nodes on the shared interface we need to adapt */
472         for (j=0;j<graph->nvtxs;j++) {
473           if (graph->subset[j]==i+1) {
474             nodes_to_temp_buffer_indices[j] = temp_buffer_size;
475             temp_buffer_size++;
476           } else {
477             nodes_to_temp_buffer_indices[j] = -1;
478           }
479         }
480         /* allocate some temporary space */
481         ierr = PetscMalloc1(temp_buffer_size,&temp_buffer);CHKERRQ(ierr);
482         ierr = PetscMalloc1(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i]),&temp_buffer[0]);CHKERRQ(ierr);
483         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
484         for (j=1;j<temp_buffer_size;j++) {
485           temp_buffer[j] = temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
486         }
487         /* analyze contributions from neighbouring subdomains for i-th conn comp
488            temp buffer structure:
489            supposing part of the interface has dimension 5 (for example with global dofs 0,1,2,3,4)
490            3 neighs procs with structured connected components:
491              neigh 0: [0 1 4], [2 3];  (2 connected components)
492              neigh 1: [0 1], [2 3 4];  (2 connected components)
493              neigh 2: [0 4], [1], [2 3]; (3 connected components)
494            tempbuffer (row-oriented) will be filled as:
495              [ 0, 0, 0;
496                0, 0, 1;
497                1, 1, 2;
498                1, 1, 2;
499                0, 1, 0; ];
500            This way we can simply find intersections of ccs among neighs.
501            For the example above, the graph->subset array will be modified to reproduce the following 4 connected components [0], [1], [2 3], [4];
502                                                                                                                                    */
503         for (j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
504           ins_val = 0;
505           size_of_recv = recv_buffer_subset[sum_requests];  /* total size of recv from neighs */
506           for (buffer_size=0;buffer_size<size_of_recv;) {  /* loop until all data from neighs has been taken into account */
507             for (k=1;k<recv_buffer[buffer_size+start_of_recv]+1;k++) { /* filling properly temp_buffer using data from a single recv */
508               temp_buffer[nodes_to_temp_buffer_indices[recv_buffer[start_of_recv+buffer_size+k]]][j] = ins_val;
509             }
510             buffer_size += k;
511             ins_val++;
512           }
513           start_of_recv += size_of_recv;
514           sum_requests++;
515         }
516         ierr = PetscMalloc1(temp_buffer_size,&add_to_subset);CHKERRQ(ierr);
517         ierr = PetscMemzero(add_to_subset,temp_buffer_size*sizeof(*add_to_subset));CHKERRQ(ierr);
518         for (j=0;j<temp_buffer_size;j++) {
519           if (!add_to_subset[j]) { /* found a new cc  */
520             global_subset_counter++;
521             add_to_subset[j] = global_subset_counter;
522             for (k=j+1;k<temp_buffer_size;k++) { /* check for other nodes in new cc */
523               same_set = PETSC_TRUE;
524               for (s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++) {
525                 if (temp_buffer[j][s]!=temp_buffer[k][s]) {
526                   same_set = PETSC_FALSE;
527                   break;
528                 }
529               }
530               if (same_set) {
531                 add_to_subset[k] = global_subset_counter;
532               }
533             }
534           }
535         }
536         /* insert new data in subset array */
537         temp_buffer_size = 0;
538         for (j=0;j<graph->nvtxs;j++) {
539           if (graph->subset[j]==i+1) {
540             graph->subset[j] = graph->n_subsets+add_to_subset[temp_buffer_size];
541             temp_buffer_size++;
542           }
543         }
544         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
545         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
546         ierr = PetscFree(add_to_subset);CHKERRQ(ierr);
547       }
548     }
549     ierr = PetscFree(nodes_to_temp_buffer_indices);CHKERRQ(ierr);
550     ierr = PetscFree(sizes_of_sends);CHKERRQ(ierr);
551     ierr = PetscFree(send_requests);CHKERRQ(ierr);
552     ierr = PetscFree(recv_requests);CHKERRQ(ierr);
553     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
554     ierr = PetscFree(recv_buffer_subset);CHKERRQ(ierr);
555     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
556     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
557     ierr = PetscFree(subset_to_nodes_indices);CHKERRQ(ierr);
558     ierr = PetscFree(subset_cc_adapt);CHKERRQ(ierr);
559     /* We are ready to find for connected components consistent among neighbouring subdomains */
560     if (global_subset_counter) {
561       ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
562       global_subset_counter = 0;
563       for (i=0;i<graph->nvtxs;i++) {
564         if (graph->subset[i] && !PetscBTLookup(graph->touched,i)) {
565           global_subset_counter++;
566           for (j=i+1;j<graph->nvtxs;j++) {
567             if (!PetscBTLookup(graph->touched,j) && graph->subset[j]==graph->subset[i]) {
568               graph->subset[j] = global_subset_counter;
569               ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
570             }
571           }
572           graph->subset[i] = global_subset_counter;
573           ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
574         }
575       }
576       /* refine connected components locally */
577       ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
578     }
579     /* restore original CSR graph of dofs */
580     ierr = PetscFree(new_xadj);CHKERRQ(ierr);
581     ierr = PetscFree(new_adjncy);CHKERRQ(ierr);
582     graph->xadj = old_xadj;
583     graph->adjncy = old_adjncy;
584     ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
585   }
586   PetscFunctionReturn(0);
587 }
588 
589 /* The following code has been adapted from function IsConnectedSubdomain contained
590    in source file contig.c of METIS library (version 5.0.1)
591    It finds connected components for each subset  */
592 #undef __FUNCT__
593 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponentsLocal"
594 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
595 {
596   PetscInt       i,j,k,first,last,nleft,ncc,pid,cum_queue,n,ncc_pid;
597   PetscInt       *queue_global;
598   PetscMPIInt    size;
599   PetscErrorCode ierr;
600 
601   PetscFunctionBegin;
602   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&size);CHKERRQ(ierr);
603   /* quiet return if no csr info is available */
604   if (!graph->xadj || !graph->adjncy) {
605     PetscFunctionReturn(0);
606   }
607 
608   /* reset any previous search of connected components */
609   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
610   graph->n_subsets = 0;
611   if (size == 1) {
612     if (graph->nvtxs) {
613       graph->n_subsets = 1;
614       for (i=0;i<graph->nvtxs;i++) {
615         graph->subset[i] = 1;
616       }
617     }
618   } else {
619     for (i=0;i<graph->nvtxs;i++) {
620       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
621         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
622         graph->subset[i] = 0;
623       }
624       graph->n_subsets = PetscMax(graph->n_subsets,graph->subset[i]);
625     }
626   }
627   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
628   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
629   ierr = PetscMemzero(graph->subset_ncc,graph->n_subsets*sizeof(*graph->subset_ncc));CHKERRQ(ierr);
630   ierr = PetscMemzero(graph->cptr,(graph->nvtxs+1)*sizeof(*graph->cptr));CHKERRQ(ierr);
631   ierr = PetscMemzero(graph->queue,graph->nvtxs*sizeof(*graph->queue));CHKERRQ(ierr);
632 
633   /* begin search for connected components */
634   cum_queue = 0;
635   ncc = 0;
636   for (n=0;n<graph->n_subsets;n++) {
637     pid = n+1;  /* partition labeled by 0 is discarded */
638     nleft = 0;
639     for (i=0;i<graph->nvtxs;i++) {
640       if (graph->subset[i] == pid) {
641         nleft++;
642       }
643     }
644     for (i=0; i<graph->nvtxs; i++) {
645       if (graph->subset[i] == pid) {
646         break;
647       }
648     }
649     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
650     graph->queue[cum_queue] = i;
651     first = 0;
652     last = 1;
653     graph->cptr[ncc] = cum_queue;
654     ncc_pid = 0;
655     while (first != nleft) {
656       if (first == last) {
657         graph->cptr[++ncc] = first+cum_queue;
658         ncc_pid++;
659         for (i=0; i<graph->nvtxs; i++) { /* TODO-> use a while! */
660           if (graph->subset[i] == pid && !PetscBTLookup(graph->touched,i)) {
661             break;
662           }
663         }
664         graph->queue[cum_queue+last] = i;
665         last++;
666         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
667       }
668       i = graph->queue[cum_queue+first];
669       first++;
670       for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
671         k = graph->adjncy[j];
672         if (graph->subset[k] == pid && !PetscBTLookup(graph->touched,k)) {
673           graph->queue[cum_queue+last] = k;
674           last++;
675           ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
676         }
677       }
678     }
679     graph->cptr[++ncc] = first+cum_queue;
680     ncc_pid++;
681     cum_queue = graph->cptr[ncc];
682     graph->subset_ncc[n] = ncc_pid;
683   }
684   graph->ncc = ncc;
685   /* For consistency among neighbours, I need to sort (by global ordering) each connected component */
686   if (size > 1) {
687     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
688     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
689     for (i=0;i<graph->ncc;i++) {
690       ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
691     }
692     ierr = PetscFree(queue_global);CHKERRQ(ierr);
693   }
694   PetscFunctionReturn(0);
695 }
696 
697 #undef __FUNCT__
698 #define __FUNCT__ "PCBDDCGraphSetUp"
699 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
700 {
701   VecScatter     scatter_ctx;
702   Vec            local_vec,local_vec2,global_vec;
703   IS             to,from;
704   MPI_Comm       comm;
705   PetscScalar    *array,*array2;
706   const PetscInt *is_indices;
707   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global,*subset_ref_node_global;
708   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
709   PetscErrorCode ierr;
710   PetscBool      same_set,mirrors_found;
711 
712   PetscFunctionBegin;
713   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
714   /* custom_minimal_size */
715   graph->custom_minimal_size = PetscMax(graph->custom_minimal_size,custom_minimal_size);
716   /* get info l2gmap and allocate work vectors  */
717   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
718   ierr = ISLocalToGlobalMappingGetIndices(graph->l2gmap,&is_indices);CHKERRQ(ierr);
719   j = 0;
720   for (i=0;i<graph->nvtxs;i++) {
721     j = PetscMax(j,is_indices[i]);
722   }
723   ierr = ISLocalToGlobalMappingRestoreIndices(graph->l2gmap,&is_indices);CHKERRQ(ierr);
724   ierr = MPI_Allreduce(&j,&i,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
725   i++;
726   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
727   ierr = VecSetSizes(local_vec,PETSC_DECIDE,graph->nvtxs);CHKERRQ(ierr);
728   ierr = VecSetType(local_vec,VECSTANDARD);CHKERRQ(ierr);
729   ierr = VecDuplicate(local_vec,&local_vec2);CHKERRQ(ierr);
730   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
731   ierr = VecSetSizes(global_vec,PETSC_DECIDE,i);CHKERRQ(ierr);
732   ierr = VecSetType(global_vec,VECSTANDARD);CHKERRQ(ierr);
733   ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
734   ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
735   ierr = VecScatterCreate(global_vec,from,local_vec,to,&scatter_ctx);CHKERRQ(ierr);
736 
737   /* get local periodic nodes */
738   mirrors_found = PETSC_FALSE;
739   if (graph->nvtxs && n_neigh) {
740     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
741     for (i=0; i<n_shared[0]; i++) {
742       if (graph->count[shared[0][i]] > 1) {
743         mirrors_found = PETSC_TRUE;
744         break;
745       }
746     }
747   }
748   /* compute local mirrors (if any) */
749   if (mirrors_found) {
750     PetscInt *local_indices,*global_indices;
751     /* get arrays of local and global indices */
752     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
753     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
754     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
755     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
756     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
757     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
758     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
759     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
760     /* allocate space for mirrors */
761     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
762     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
763     graph->mirrors_set[0] = 0;
764 
765     k=0;
766     for (i=0;i<n_shared[0];i++) {
767       j=shared[0][i];
768       if (graph->count[j] > 1) {
769         graph->mirrors[j]++;
770         k++;
771       }
772     }
773     /* allocate space for set of mirrors */
774     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
775     for (i=1;i<graph->nvtxs;i++)
776       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
777 
778     /* fill arrays */
779     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
780     for (j=0;j<n_shared[0];j++) {
781       i=shared[0][j];
782       if (graph->count[i] > 1)
783         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
784     }
785     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
786     for (i=0;i<graph->nvtxs;i++) {
787       if (graph->mirrors[i] > 0) {
788         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
789         j = global_indices[k];
790         while ( k > 0 && global_indices[k-1] == j) k--;
791         for (j=0;j<graph->mirrors[i];j++) {
792           graph->mirrors_set[i][j]=local_indices[k+j];
793         }
794         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
795       }
796     }
797     ierr = PetscFree(local_indices);CHKERRQ(ierr);
798     ierr = PetscFree(global_indices);CHKERRQ(ierr);
799   }
800   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
801   ierr = ISDestroy(&to);CHKERRQ(ierr);
802   ierr = ISDestroy(&from);CHKERRQ(ierr);
803 
804   /* Count total number of neigh per node */
805   k=0;
806   for (i=1;i<n_neigh;i++) {
807     k += n_shared[i];
808     for (j=0;j<n_shared[i];j++) {
809       graph->count[shared[i][j]] += 1;
810     }
811   }
812   /* Allocate space for storing the set of neighbours for each node */
813   if (graph->nvtxs) {
814     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
815   }
816   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
817     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
818   }
819   /* Get information for sharing subdomains */
820   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
821   for (i=1;i<n_neigh;i++) { /* dont count myself */
822     s = n_shared[i];
823     for (j=0;j<s;j++) {
824       k = shared[i][j];
825       graph->neighbours_set[k][graph->count[k]] = neigh[i];
826       graph->count[k] += 1;
827     }
828   }
829   /* sort set of sharing subdomains */
830   for (i=0;i<graph->nvtxs;i++) {
831     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
832   }
833   /*
834      Get info for dofs splitting
835      User can specify only a subset; an additional field is considered as a complementary set
836   */
837   for (i=0;i<graph->nvtxs;i++) {
838     graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
839   }
840   for (i=0;i<n_ISForDofs;i++) {
841     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
842     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
843     for (j=0;j<is_size;j++) {
844       if (is_indices[j] > -1 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
845         graph->which_dof[is_indices[j]] = i;
846       }
847     }
848     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
849   }
850   /* Take into account Neumann nodes */
851   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
852   ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
853   if (neumann_is) {
854     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
855     ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
856     ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
857     for (i=0;i<is_size;i++) {
858       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
859         array[is_indices[i]] = 1.0;
860       }
861     }
862     ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
863     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
864   }
865   /* Neumann nodes: impose consistency among neighbours */
866   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
867   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
868   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
869   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
870   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
871   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
872   for (i=0;i<graph->nvtxs;i++) {
873     if (PetscRealPart(array[i]) > 0.1) {
874       graph->special_dof[i] = PCBDDCGRAPH_NEUMANN_MARK;
875     }
876   }
877   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
878   /* Take into account Dirichlet nodes */
879   ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
880   if (dirichlet_is) {
881     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
882     ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
883     ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
884     ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
885     for (i=0;i<is_size;i++){
886       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
887         k = is_indices[i];
888         if (graph->count[k] && !PetscBTLookup(graph->touched,k)) {
889           if (PetscRealPart(array[k]) > 0.1) {
890             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);
891           }
892           array2[k] = 1.0;
893         }
894       }
895     }
896     ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
897     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
898     ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
899   }
900   /* Dirichlet nodes: impose consistency among neighbours */
901   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
902   ierr = VecScatterBegin(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
903   ierr = VecScatterEnd(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
904   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
905   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
906   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
907   for (i=0;i<graph->nvtxs;i++) {
908     if (PetscRealPart(array[i]) > 0.1) {
909       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
910       graph->subset[i] = 0; /* dirichlet nodes treated as internal -> is it ok? */
911       graph->special_dof[i] = PCBDDCGRAPH_DIRICHLET_MARK;
912     }
913   }
914   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
915 
916   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
917   if (graph->mirrors) {
918     for (i=0;i<graph->nvtxs;i++)
919       if (graph->mirrors[i])
920         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
921 
922     if (graph->xadj && graph->adjncy) {
923       PetscInt *new_xadj,*new_adjncy;
924       /* sort CSR graph */
925       for (i=0;i<graph->nvtxs;i++)
926         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
927 
928       /* adapt local CSR graph in case of local periodicity */
929       k=0;
930       for (i=0;i<graph->nvtxs;i++)
931         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
932           k += graph->mirrors[graph->adjncy[j]];
933 
934       ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
935       ierr = PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy);CHKERRQ(ierr);
936       new_xadj[0]=0;
937       for (i=0;i<graph->nvtxs;i++) {
938         k = graph->xadj[i+1]-graph->xadj[i];
939         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
940         new_xadj[i+1]=new_xadj[i]+k;
941         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
942           k = graph->mirrors[graph->adjncy[j]];
943           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
944           new_xadj[i+1]+=k;
945         }
946         k = new_xadj[i+1]-new_xadj[i];
947         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
948         new_xadj[i+1]=new_xadj[i]+k;
949       }
950       /* set new CSR into graph */
951       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
952       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
953       graph->xadj = new_xadj;
954       graph->adjncy = new_adjncy;
955     }
956   }
957 
958   /* mark special nodes -> each will become a single node equivalence class */
959   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
960   if (custom_primal_vertices) {
961     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
962     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
963     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
964     for (i=0;i<is_size;i++){
965       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
966         array[is_indices[i]] = 1.0;
967       }
968     }
969     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
970     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
971   }
972   /* special nodes: impose consistency among neighbours */
973   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
974   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
975   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
976   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
977   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
978   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
979   j = 0;
980   for (i=0;i<graph->nvtxs;i++) {
981     if (PetscRealPart(array[i]) > 0.1 && graph->special_dof[i] != PCBDDCGRAPH_DIRICHLET_MARK) {
982       graph->special_dof[i] = PCBDDCGRAPH_SPECIAL_MARK-j;
983       j++;
984     }
985   }
986   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
987 
988   /* mark interior nodes as touched and belonging to partition number 0 */
989   for (i=0;i<graph->nvtxs;i++) {
990     if (!graph->count[i]) {
991       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
992       graph->subset[i] = 0;
993     }
994   }
995   /* init graph structure and compute default subsets */
996   nodes_touched=0;
997   for (i=0;i<graph->nvtxs;i++) {
998     if (PetscBTLookup(graph->touched,i)) {
999       nodes_touched++;
1000     }
1001   }
1002   i = 0;
1003   graph->ncc = 0;
1004   total_counts = 0;
1005   while (nodes_touched<graph->nvtxs) {
1006     /*  find first untouched node in local ordering */
1007     while (PetscBTLookup(graph->touched,i)) {
1008       i++;
1009     }
1010     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
1011     graph->subset[i] = graph->ncc+1;
1012     graph->cptr[graph->ncc] = total_counts;
1013     graph->queue[total_counts] = i;
1014     total_counts++;
1015     nodes_touched++;
1016     /* now find all other nodes having the same set of sharing subdomains */
1017     for (j=i+1;j<graph->nvtxs;j++) {
1018       /* check for same number of sharing subdomains, dof number and same special mark */
1019       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]) {
1020         /* check for same set of sharing subdomains */
1021         same_set=PETSC_TRUE;
1022         for (k=0;k<graph->count[j];k++){
1023           if (graph->neighbours_set[i][k]!=graph->neighbours_set[j][k]) {
1024             same_set=PETSC_FALSE;
1025           }
1026         }
1027         /* I found a friend of mine */
1028         if (same_set) {
1029           graph->subset[j]=graph->ncc+1;
1030           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
1031           nodes_touched++;
1032           graph->queue[total_counts] = j;
1033           total_counts++;
1034         }
1035       }
1036     }
1037     graph->ncc++;
1038   }
1039   /* set default number of subsets (at this point no info on csr graph has been taken into account, so n_subsets = ncc */
1040   graph->n_subsets = graph->ncc;
1041   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
1042   for (i=0;i<graph->n_subsets;i++) {
1043     graph->subset_ncc[i] = 1;
1044   }
1045   /* final pointer */
1046   graph->cptr[graph->ncc] = total_counts;
1047   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
1048   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
1049   /* get a reference node (min index in global ordering) for each subset */
1050   ierr = PetscMalloc1(graph->ncc,&subset_ref_node_global);CHKERRQ(ierr);
1051   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
1052   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
1053   for (i=0;i<graph->ncc;i++) {
1054     PetscInt minval = queue_global[graph->cptr[i]];
1055     PetscInt minloc = graph->queue[graph->cptr[i]];
1056     for (j=graph->cptr[i]+1;j<graph->cptr[i+1];j++) {
1057       if (minval > queue_global[j]) {
1058         minval = queue_global[j];
1059         minloc = graph->queue[j];
1060       }
1061     }
1062     subset_ref_node_global[i] = minloc;
1063     /* For consistency among neighbours, I need to sort (by global ordering) each connected component */
1064     ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
1065   }
1066   /* renumber reference nodes */
1067   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->l2gmap,graph->ncc,subset_ref_node_global,NULL,&k,&graph->subset_ref_node);CHKERRQ(ierr);
1068   ierr = PetscFree(subset_ref_node_global);CHKERRQ(ierr);
1069   ierr = PetscFree(queue_global);CHKERRQ(ierr);
1070   /* free objects */
1071   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1072   ierr = VecDestroy(&local_vec2);CHKERRQ(ierr);
1073   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1074   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1075   PetscFunctionReturn(0);
1076 }
1077 
1078 #undef __FUNCT__
1079 #define __FUNCT__ "PCBDDCGraphResetCSR"
1080 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1081 {
1082   PetscErrorCode ierr;
1083 
1084   PetscFunctionBegin;
1085   ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1086   ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1087   graph->nvtxs_csr = 0;
1088   PetscFunctionReturn(0);
1089 }
1090 
1091 #undef __FUNCT__
1092 #define __FUNCT__ "PCBDDCGraphReset"
1093 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1094 {
1095   PetscErrorCode ierr;
1096 
1097   PetscFunctionBegin;
1098   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
1099   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
1100   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1101   if (graph->nvtxs) {
1102     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1103   }
1104   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1105   ierr = PetscFree7(graph->count,
1106                     graph->neighbours_set,
1107                     graph->subset,
1108                     graph->which_dof,
1109                     graph->cptr,
1110                     graph->queue,
1111                     graph->special_dof);CHKERRQ(ierr);
1112   if (graph->mirrors) {
1113     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1114   }
1115   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1116   graph->nvtxs = 0;
1117   graph->n_subsets = 0;
1118   graph->custom_minimal_size = 1;
1119   PetscFunctionReturn(0);
1120 }
1121 
1122 #undef __FUNCT__
1123 #define __FUNCT__ "PCBDDCGraphInit"
1124 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap)
1125 {
1126   PetscInt       n;
1127   PetscErrorCode ierr;
1128 
1129   PetscFunctionBegin;
1130   PetscValidPointer(graph,1);
1131   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1132   /* raise an error if already allocated */
1133   if (graph->nvtxs) {
1134     SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1135   }
1136   /* set number of vertices */
1137   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1138   graph->l2gmap = l2gmap;
1139   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1140   graph->nvtxs = n;
1141   /* allocate used space */
1142   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1143   ierr = PetscMalloc7(graph->nvtxs,&graph->count,
1144                       graph->nvtxs,&graph->neighbours_set,
1145                       graph->nvtxs,&graph->subset,
1146                       graph->nvtxs,&graph->which_dof,
1147                       graph->nvtxs+1,&graph->cptr,
1148                       graph->nvtxs,&graph->queue,
1149                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1150   /* zeroes memory */
1151   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1152   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1153   /* use -1 as a default value for which_dof array */
1154   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1155   ierr = PetscMemzero(graph->cptr,(graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
1156   ierr = PetscMemzero(graph->queue,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1157   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1158   /* zeroes first pointer to neighbour set */
1159   if (graph->nvtxs) {
1160     graph->neighbours_set[0] = 0;
1161   }
1162   /* zeroes workspace for values of ncc */
1163   graph->subset_ncc = 0;
1164   graph->subset_ref_node = 0;
1165   PetscFunctionReturn(0);
1166 }
1167 
1168 #undef __FUNCT__
1169 #define __FUNCT__ "PCBDDCGraphDestroy"
1170 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1171 {
1172   PetscErrorCode ierr;
1173 
1174   PetscFunctionBegin;
1175   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1176   ierr = PetscFree(*graph);CHKERRQ(ierr);
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 #undef __FUNCT__
1181 #define __FUNCT__ "PCBDDCGraphCreate"
1182 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1183 {
1184   PCBDDCGraph    new_graph;
1185   PetscErrorCode ierr;
1186 
1187   PetscFunctionBegin;
1188   ierr = PetscNew(&new_graph);CHKERRQ(ierr);
1189   /* local to global mapping of dofs */
1190   new_graph->l2gmap = 0;
1191   /* vertex size */
1192   new_graph->nvtxs = 0;
1193   new_graph->n_subsets = 0;
1194   new_graph->custom_minimal_size = 1;
1195   /* zeroes ponters */
1196   new_graph->mirrors = 0;
1197   new_graph->mirrors_set = 0;
1198   new_graph->neighbours_set = 0;
1199   new_graph->subset = 0;
1200   new_graph->which_dof = 0;
1201   new_graph->special_dof = 0;
1202   new_graph->cptr = 0;
1203   new_graph->queue = 0;
1204   new_graph->count = 0;
1205   new_graph->subset_ncc = 0;
1206   new_graph->subset_ref_node = 0;
1207   new_graph->touched = 0;
1208   /* zeroes pointers to csr graph of local nodes connectivity (optional data) */
1209   new_graph->nvtxs_csr = 0;
1210   new_graph->xadj = 0;
1211   new_graph->adjncy = 0;
1212   *graph = new_graph;
1213   PetscFunctionReturn(0);
1214 }
1215