xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision f9426fe092dba0ba2fdf65dfec8d938c4b10a31c)
1 #include <petsc-private/petscimpl.h>
2 #include "bddcprivate.h"
3 #include "bddcstructs.h"
4 
5 /* special marks: they cannot be enums, since special marks should in principle range from -4 to -max_int */
6 #define NEUMANN_MARK -1
7 #define DIRICHLET_MARK -2
8 #define LOCAL_PERIODIC_MARK -3
9 #define SPECIAL_MARK -4
10 
11 #undef __FUNCT__
12 #define __FUNCT__ "PCBDDCGraphASCIIView"
13 PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer)
14 {
15   PetscInt       i,j,tabs;
16   PetscInt*      queue_in_global_numbering;
17   PetscErrorCode ierr;
18 
19   PetscFunctionBegin;
20   ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
21   ierr = PetscViewerASCIIGetTab(viewer,&tabs);CHKERRQ(ierr);
22   ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
23   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
24   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Local BDDC graph for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
25   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Number of vertices %d\n",graph->nvtxs);CHKERRQ(ierr);
26   if (verbosity_level > 1) {
27     for (i=0;i<graph->nvtxs;i++) {
28       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d:\n",i);CHKERRQ(ierr);
29       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %d\n",graph->which_dof[i]);CHKERRQ(ierr);
30       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %d\n",graph->special_dof[i]);CHKERRQ(ierr);
31       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %d\n",graph->count[i]);CHKERRQ(ierr);
32       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
33       if (graph->count[i]) {
34         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:");CHKERRQ(ierr);
35         for (j=0;j<graph->count[i];j++) {
36           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[i][j]);CHKERRQ(ierr);
37         }
38         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
39       }
40       ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
41       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
42       if (graph->mirrors) {
43         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %d\n",graph->mirrors[i]);CHKERRQ(ierr);
44         if (graph->mirrors[i]) {
45           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
46           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:");CHKERRQ(ierr);
47           for (j=0;j<graph->mirrors[i];j++) {
48             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->mirrors_set[i][j]);CHKERRQ(ierr);
49           }
50           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
51           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
52           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
53         }
54       }
55       if (verbosity_level > 2) {
56         if (graph->xadj && graph->adjncy) {
57           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:");CHKERRQ(ierr);
58           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
59           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
60             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->adjncy[j]);CHKERRQ(ierr);
61           }
62           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
63           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
64           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
65         }
66       }
67       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
68       if (graph->subset[i] && graph->subset_ncc) {
69         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
70       }
71     }
72   }
73   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
74   ierr = PetscMalloc(graph->cptr[graph->ncc]*sizeof(*queue_in_global_numbering),&queue_in_global_numbering);CHKERRQ(ierr);
75   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
76   for (i=0;i<graph->ncc;i++) {
77     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  %d (neighs:",i);CHKERRQ(ierr);
78     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
79     PetscInt node_num=graph->queue[graph->cptr[i]];
80     for (j=0;j<graph->count[node_num];j++) {
81       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
82     }
83     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
84     for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
85       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
86     }
87     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
88     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
89     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
90   }
91   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
92   if (graph->custom_minimal_size > 1 && verbosity_level > 1) {
93     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %d\n",graph->custom_minimal_size);CHKERRQ(ierr);
94   }
95   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
96   PetscFunctionReturn(0);
97 }
98 
99 #undef __FUNCT__
100 #define __FUNCT__ "PCBDDCGraphGetCandidatesIS"
101 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)
102 {
103   IS             *ISForFaces,*ISForEdges,ISForVertices;
104   PetscInt       i,j,nfc,nec,nvc,*idx;
105   PetscBool      twodim_flag;
106   PetscErrorCode ierr;
107 
108   PetscFunctionBegin;
109   /* loop on ccs to evalute number of faces, edges and vertices */
110   nfc = 0;
111   nec = 0;
112   nvc = 0;
113   twodim_flag = PETSC_FALSE;
114   for (i=0;i<graph->ncc;i++) {
115     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
116       if (graph->count[graph->queue[graph->cptr[i]]] == 1 && graph->special_dof[graph->queue[graph->cptr[i]]] != NEUMANN_MARK) {
117         nfc++;
118       } else { /* note that nec will be zero in 2d */
119         nec++;
120       }
121     } else {
122       nvc += graph->cptr[i+1]-graph->cptr[i];
123     }
124   }
125   if (!nec) { /* we are in a 2d case -> no faces, only edges */
126     nec = nfc;
127     nfc = 0;
128     twodim_flag = PETSC_TRUE;
129   }
130   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
131   ISForFaces = 0;
132   ISForEdges = 0;
133   ISForVertices = 0;
134   if (use_faces && nfc) {
135     ierr = PetscMalloc(nfc*sizeof(IS),&ISForFaces);CHKERRQ(ierr);
136   }
137   if (use_edges && nec) {
138     ierr = PetscMalloc(nec*sizeof(IS),&ISForEdges);CHKERRQ(ierr);
139   }
140   if (use_vertices && nvc) {
141     ierr = PetscMalloc(nvc*sizeof(PetscInt),&idx);CHKERRQ(ierr);
142   }
143   /* loop on ccs to compute index sets for faces and edges */
144   nfc = 0;
145   nec = 0;
146   for (i=0;i<graph->ncc;i++) {
147     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
148       if (graph->count[graph->queue[graph->cptr[i]]] == 1 && graph->special_dof[graph->queue[graph->cptr[i]]] != NEUMANN_MARK) {
149         if (twodim_flag) {
150           if (use_edges) {
151             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
152             nec++;
153           }
154         } else {
155           if (use_faces) {
156             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForFaces[nfc]);CHKERRQ(ierr);
157             nfc++;
158           }
159         }
160       } else {
161         if (use_edges) {
162           ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
163           nec++;
164         }
165       }
166     }
167   }
168   /* index set for vertices */
169   if (use_vertices && nvc) {
170     nvc = 0;
171     for (i=0;i<graph->ncc;i++) {
172       if (graph->cptr[i+1]-graph->cptr[i] <= graph->custom_minimal_size) {
173         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
174           idx[nvc]=graph->queue[j];
175           nvc++;
176         }
177       }
178     }
179     /* sort vertex set (by local ordering) */
180     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
181     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
182   }
183   /* get back info */
184   *n_faces = nfc;
185   *FacesIS = ISForFaces;
186   *n_edges = nec;
187   *EdgesIS = ISForEdges;
188   *VerticesIS = ISForVertices;
189   PetscFunctionReturn(0);
190 }
191 
192 #undef __FUNCT__
193 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponents"
194 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
195 {
196   PetscInt    adapt_interface,adapt_interface_reduced;
197   MPI_Comm    interface_comm;
198   MPI_Request *send_requests;
199   MPI_Request *recv_requests;
200   PetscInt    *aux_new_xadj,*new_xadj,*new_adjncy,**temp_buffer;
201   PetscInt    i,j,k,s,sum_requests,buffer_size,size_of_recv,temp_buffer_size;
202   PetscMPIInt rank,neigh,tag,mpi_buffer_size;
203   PetscInt    *cum_recv_counts,*subset_to_nodes_indices,*recv_buffer_subset,*nodes_to_temp_buffer_indices;
204   PetscInt    *send_buffer,*recv_buffer,*queue_in_global_numbering,*sizes_of_sends,*add_to_subset;
205   PetscInt    start_of_recv,start_of_send,size_of_send,global_subset_counter,ins_val;
206   PetscBool   *subset_cc_adapt,same_set;
207   PetscErrorCode ierr;
208 
209   PetscFunctionBegin;
210   /* compute connected components locally */
211   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
212   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
213   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
214   adapt_interface = 0;
215   adapt_interface_reduced = 0;
216   for (i=0;i<graph->n_subsets;i++) {
217     /* We are not sure that on a given subset of the local interface,
218        with two connected components, the latters be the same among sharing subdomains */
219     if (graph->subset_ncc[i] > 1) {
220       adapt_interface=1;
221       break;
222     }
223   }
224   ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_INT,MPI_LOR,interface_comm);CHKERRQ(ierr);
225 
226   if (graph->n_subsets && adapt_interface_reduced) {
227     /* Retrict adjacency graph using information from previously computed connected components */
228     ierr = PetscMalloc(graph->nvtxs*sizeof(PetscInt),&aux_new_xadj);CHKERRQ(ierr);
229     for (i=0;i<graph->nvtxs;i++) {
230       aux_new_xadj[i]=1;
231     }
232     for (i=0;i<graph->ncc;i++) {
233       k = graph->cptr[i+1]-graph->cptr[i];
234       for (j=0;j<k;j++) {
235         aux_new_xadj[graph->queue[graph->cptr[i]+j]]=k;
236       }
237     }
238     j = 0;
239     for (i=0;i<graph->nvtxs;i++) {
240       j += aux_new_xadj[i];
241     }
242     ierr = PetscMalloc((graph->nvtxs+1)*sizeof(PetscInt),&new_xadj);CHKERRQ(ierr);
243     ierr = PetscMalloc(j*sizeof(PetscInt),&new_adjncy);CHKERRQ(ierr);
244     new_xadj[0]=0;
245     for (i=0;i<graph->nvtxs;i++) {
246       new_xadj[i+1]=new_xadj[i]+aux_new_xadj[i];
247       if (aux_new_xadj[i]==1) {
248         new_adjncy[new_xadj[i]]=i;
249       }
250     }
251     ierr = PetscFree(aux_new_xadj);CHKERRQ(ierr);
252     for (i=0;i<graph->ncc;i++) {
253       k = graph->cptr[i+1]-graph->cptr[i];
254       for (j=0;j<k;j++) {
255         ierr = PetscMemcpy(&new_adjncy[new_xadj[graph->queue[graph->cptr[i]+j]]],&graph->queue[graph->cptr[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
256       }
257     }
258     /* set new CSR into graph */
259     ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
260     ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
261     graph->xadj = new_xadj;
262     graph->adjncy = new_adjncy;
263     /* allocate some space */
264     ierr = MPI_Comm_rank(interface_comm,&rank);CHKERRQ(ierr);
265     ierr = PetscMalloc((graph->n_subsets+1)*sizeof(*cum_recv_counts),&cum_recv_counts);CHKERRQ(ierr);
266     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
267     ierr = PetscMalloc(graph->n_subsets*sizeof(*subset_to_nodes_indices),&subset_to_nodes_indices);CHKERRQ(ierr);
268     /* first count how many neighbours per connected component I will receive from */
269     cum_recv_counts[0]=0;
270     for (i=1;i<graph->n_subsets+1;i++) {
271       j = 0;
272       while (graph->subset[j] != i) {
273         j++;
274       }
275       subset_to_nodes_indices[i-1]=j;
276       /* We don't want sends/recvs_to/from_self -> here I don't count myself  */
277       cum_recv_counts[i]=cum_recv_counts[i-1]+graph->count[j];
278     }
279     ierr = PetscMalloc(2*cum_recv_counts[graph->n_subsets]*sizeof(*recv_buffer_subset),&recv_buffer_subset);CHKERRQ(ierr);
280     ierr = PetscMalloc(cum_recv_counts[graph->n_subsets]*sizeof(MPI_Request),&send_requests);CHKERRQ(ierr);
281     ierr = PetscMalloc(cum_recv_counts[graph->n_subsets]*sizeof(MPI_Request),&recv_requests);CHKERRQ(ierr);
282     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
283       send_requests[i]=MPI_REQUEST_NULL;
284       recv_requests[i]=MPI_REQUEST_NULL;
285     }
286     /* exchange with my neighbours the number of my connected components on the shared interface */
287     sum_requests = 0;
288     for (i=0;i<graph->n_subsets;i++) {
289       j = subset_to_nodes_indices[i];
290       for (k=0;k<graph->count[j];k++) {
291         ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
292         ierr = PetscMPIIntCast((PetscInt)(rank+1)*graph->count[j],&tag);CHKERRQ(ierr);
293         ierr = MPI_Isend(&graph->subset_ncc[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
294         ierr = PetscMPIIntCast((PetscInt)(neigh+1)*graph->count[j],&tag);CHKERRQ(ierr);
295         ierr = MPI_Irecv(&recv_buffer_subset[sum_requests],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
296         sum_requests++;
297       }
298     }
299     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
300     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
301     /* determine the connected component I need to adapt */
302     ierr = PetscMalloc(graph->n_subsets*sizeof(*subset_cc_adapt),&subset_cc_adapt);CHKERRQ(ierr);
303     ierr = PetscMemzero(subset_cc_adapt,graph->n_subsets*sizeof(*subset_cc_adapt));CHKERRQ(ierr);
304     for (i=0;i<graph->n_subsets;i++) {
305       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
306         /* The first condition is natural (someone has a different number of ccs than me), the second one is just to be safe */
307         if ( graph->subset_ncc[i] != recv_buffer_subset[j] || graph->subset_ncc[i] > 1 ) {
308           subset_cc_adapt[i] = PETSC_TRUE;
309           break;
310         }
311       }
312     }
313     buffer_size = 0;
314     for (i=0;i<graph->n_subsets;i++) {
315       if (subset_cc_adapt[i]) {
316         for (j=i;j<graph->ncc;j++) {
317           if (graph->subset[graph->queue[graph->cptr[j]]] == i+1) { /* WARNING -> subset values goes from 1 to graph->n_subsets included */
318             buffer_size += 1 + graph->cptr[j+1]-graph->cptr[j];
319           }
320         }
321       }
322     }
323     ierr = PetscMalloc(buffer_size*sizeof(*send_buffer),&send_buffer);CHKERRQ(ierr);
324     /* now get from neighbours their ccs (in global numbering) and adapt them (in case it is needed) */
325     ierr = PetscMalloc(graph->cptr[graph->ncc]*sizeof(*queue_in_global_numbering),&queue_in_global_numbering);CHKERRQ(ierr);
326     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
327     /* determine how much data to send (size of each queue plus the global indices) and communicate it to neighbours */
328     ierr = PetscMalloc(graph->n_subsets*sizeof(*sizes_of_sends),&sizes_of_sends);CHKERRQ(ierr);
329     ierr = PetscMemzero(sizes_of_sends,graph->n_subsets*sizeof(*sizes_of_sends));CHKERRQ(ierr);
330     sum_requests = 0;
331     start_of_send = 0;
332     start_of_recv = cum_recv_counts[graph->n_subsets];
333     for (i=0;i<graph->n_subsets;i++) {
334       if (subset_cc_adapt[i]) {
335         size_of_send = 0;
336         for (j=i;j<graph->ncc;j++) {
337           if (graph->subset[graph->queue[graph->cptr[j]]] == i+1) { /* WARNING -> subset values goes from 1 to graph->n_subsets included */
338             send_buffer[start_of_send+size_of_send]=graph->cptr[j+1]-graph->cptr[j];
339             size_of_send += 1;
340             ierr = PetscMemcpy(&send_buffer[start_of_send+size_of_send],
341                                &queue_in_global_numbering[graph->cptr[j]],
342                                (graph->cptr[j+1]-graph->cptr[j])*sizeof(*send_buffer));CHKERRQ(ierr);
343             size_of_send = size_of_send+graph->cptr[j+1]-graph->cptr[j];
344           }
345         }
346         j = subset_to_nodes_indices[i];
347         sizes_of_sends[i] = size_of_send;
348         for (k=0;k<graph->count[j];k++) {
349           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
350           ierr = PetscMPIIntCast((PetscInt)(rank+1)*graph->count[j],&tag);CHKERRQ(ierr);
351           ierr = MPI_Isend(&sizes_of_sends[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
352           ierr = PetscMPIIntCast((PetscInt)(neigh+1)*graph->count[j],&tag);CHKERRQ(ierr);
353           ierr = MPI_Irecv(&recv_buffer_subset[sum_requests+start_of_recv],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
354           sum_requests++;
355         }
356         start_of_send += size_of_send;
357       }
358     }
359     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
360     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
361     buffer_size = 0;
362     for (k=0;k<sum_requests;k++) {
363       buffer_size += recv_buffer_subset[start_of_recv+k];
364     }
365     ierr = PetscMalloc(buffer_size*sizeof(*recv_buffer),&recv_buffer);CHKERRQ(ierr);
366     /* now exchange the data */
367     start_of_recv = 0;
368     start_of_send = 0;
369     sum_requests = 0;
370     for (i=0;i<graph->n_subsets;i++) {
371       if (subset_cc_adapt[i]) {
372         size_of_send = sizes_of_sends[i];
373         j = subset_to_nodes_indices[i];
374         for (k=0;k<graph->count[j];k++) {
375           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
376           ierr = PetscMPIIntCast((PetscInt)(rank+1)*graph->count[j],&tag);CHKERRQ(ierr);
377           ierr = PetscMPIIntCast(size_of_send,&mpi_buffer_size);CHKERRQ(ierr);
378           ierr = MPI_Isend(&send_buffer[start_of_send],mpi_buffer_size,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
379           size_of_recv = recv_buffer_subset[cum_recv_counts[graph->n_subsets]+sum_requests];
380           ierr = PetscMPIIntCast((PetscInt)(neigh+1)*graph->count[j],&tag);CHKERRQ(ierr);
381           ierr = PetscMPIIntCast(size_of_recv,&mpi_buffer_size);CHKERRQ(ierr);
382           ierr = MPI_Irecv(&recv_buffer[start_of_recv],mpi_buffer_size,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
383           start_of_recv += size_of_recv;
384           sum_requests++;
385         }
386         start_of_send += size_of_send;
387       }
388     }
389     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
390     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
391     for (j=0;j<buffer_size;) {
392        ierr = ISGlobalToLocalMappingApply(graph->l2gmap,IS_GTOLM_MASK,recv_buffer[j],&recv_buffer[j+1],&recv_buffer[j],&recv_buffer[j+1]);CHKERRQ(ierr);
393        /* we need to adapt the output of GlobalToLocal mapping if there are mirrored nodes */
394        if (graph->mirrors) {
395          PetscBool mirrored_found=PETSC_FALSE;
396          for (k=0;k<recv_buffer[j];k++) {
397            if (graph->mirrors[recv_buffer[j+k+1]]) {
398              mirrored_found=PETSC_TRUE;
399              recv_buffer[j+k+1]=graph->mirrors_set[recv_buffer[j+k+1]][0];
400            }
401          }
402          if (mirrored_found) {
403            ierr = PetscSortInt(recv_buffer[j],&recv_buffer[j+1]);CHKERRQ(ierr);
404            k=0;
405            while (k<recv_buffer[j]) {
406              for (s=1;s<graph->mirrors[recv_buffer[j+1+k]];s++) {
407                recv_buffer[j+1+k+s] = graph->mirrors_set[recv_buffer[j+1+k]][s];
408              }
409              k+=graph->mirrors[recv_buffer[j+1+k]]+s;
410            }
411          }
412        }
413        k = recv_buffer[j]+1;
414        j += k;
415     }
416     sum_requests = cum_recv_counts[graph->n_subsets];
417     start_of_recv = 0;
418     ierr = PetscMalloc(graph->nvtxs*sizeof(*nodes_to_temp_buffer_indices),&nodes_to_temp_buffer_indices);CHKERRQ(ierr);
419     global_subset_counter = 0;
420     for (i=0;i<graph->n_subsets;i++) {
421       if (subset_cc_adapt[i]) {
422         temp_buffer_size = 0;
423         /* find nodes on the shared interface we need to adapt */
424         for (j=0;j<graph->nvtxs;j++) {
425           if (graph->subset[j]==i+1) {
426             nodes_to_temp_buffer_indices[j] = temp_buffer_size;
427             temp_buffer_size++;
428           } else {
429             nodes_to_temp_buffer_indices[j] = -1;
430           }
431         }
432         /* allocate some temporary space */
433         ierr = PetscMalloc(temp_buffer_size*sizeof(PetscInt*),&temp_buffer);CHKERRQ(ierr);
434         ierr = PetscMalloc(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt),&temp_buffer[0]);CHKERRQ(ierr);
435         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
436         for (j=1;j<temp_buffer_size;j++) {
437           temp_buffer[j] = temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
438         }
439         /* analyze contributions from neighbouring subdomains for i-th conn comp
440            temp buffer structure:
441            supposing part of the interface has dimension 5 (for example with global dofs 0,1,2,3,4)
442            3 neighs procs with structured connected components:
443              neigh 0: [0 1 4], [2 3];  (2 connected components)
444              neigh 1: [0 1], [2 3 4];  (2 connected components)
445              neigh 2: [0 4], [1], [2 3]; (3 connected components)
446            tempbuffer (row-oriented) will be filled as:
447              [ 0, 0, 0;
448                0, 0, 1;
449                1, 1, 2;
450                1, 1, 2;
451                0, 1, 0; ];
452            This way we can simply find intersections of ccs among neighs.
453            For the example above, the graph->subset array will be modified to reproduce the following 4 connected components [0], [1], [2 3], [4];
454                                                                                                                                    */
455         for (j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
456           ins_val = 0;
457           size_of_recv = recv_buffer_subset[sum_requests];  /* total size of recv from neighs */
458           for (buffer_size=0;buffer_size<size_of_recv;) {  /* loop until all data from neighs has been taken into account */
459             for (k=1;k<recv_buffer[buffer_size+start_of_recv]+1;k++) { /* filling properly temp_buffer using data from a single recv */
460               temp_buffer[nodes_to_temp_buffer_indices[recv_buffer[start_of_recv+buffer_size+k]]][j] = ins_val;
461             }
462             buffer_size += k;
463             ins_val++;
464           }
465           start_of_recv += size_of_recv;
466           sum_requests++;
467         }
468         ierr = PetscMalloc(temp_buffer_size*sizeof(*add_to_subset),&add_to_subset);CHKERRQ(ierr);
469         ierr = PetscMemzero(add_to_subset,temp_buffer_size*sizeof(*add_to_subset));CHKERRQ(ierr);
470         for (j=0;j<temp_buffer_size;j++) {
471           if (!add_to_subset[j]) { /* found a new cc  */
472             global_subset_counter++;
473             add_to_subset[j] = global_subset_counter;
474             for (k=j+1;k<temp_buffer_size;k++) { /* check for other nodes in new cc */
475               same_set = PETSC_TRUE;
476               for (s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++) {
477                 if (temp_buffer[j][s]!=temp_buffer[k][s]) {
478                   same_set = PETSC_FALSE;
479                   break;
480                 }
481               }
482               if (same_set) {
483                 add_to_subset[k] = global_subset_counter;
484               }
485             }
486           }
487         }
488         /* insert new data in subset array */
489         temp_buffer_size = 0;
490         for (j=0;j<graph->nvtxs;j++) {
491           if (graph->subset[j]==i+1) {
492             graph->subset[j] = graph->n_subsets+add_to_subset[temp_buffer_size];
493             temp_buffer_size++;
494           }
495         }
496         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
497         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
498         ierr = PetscFree(add_to_subset);CHKERRQ(ierr);
499       }
500     }
501     ierr = PetscFree(nodes_to_temp_buffer_indices);CHKERRQ(ierr);
502     ierr = PetscFree(sizes_of_sends);CHKERRQ(ierr);
503     ierr = PetscFree(send_requests);CHKERRQ(ierr);
504     ierr = PetscFree(recv_requests);CHKERRQ(ierr);
505     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
506     ierr = PetscFree(recv_buffer_subset);CHKERRQ(ierr);
507     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
508     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
509     ierr = PetscFree(subset_to_nodes_indices);CHKERRQ(ierr);
510     ierr = PetscFree(subset_cc_adapt);CHKERRQ(ierr);
511     /* We are ready to find for connected components consistent among neighbouring subdomains */
512     if (global_subset_counter) {
513       ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
514       global_subset_counter = 0;
515       for (i=0;i<graph->nvtxs;i++) {
516         if (graph->subset[i] && !PetscBTLookup(graph->touched,i)) {
517           global_subset_counter++;
518           for (j=i+1;j<graph->nvtxs;j++) {
519             if (!PetscBTLookup(graph->touched,j) && graph->subset[j]==graph->subset[i]) {
520               graph->subset[j] = global_subset_counter;
521               ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
522             }
523           }
524           graph->subset[i] = global_subset_counter;
525           ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
526         }
527       }
528       /* refine connected components locally */
529       ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
530     }
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] == 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 = PetscMalloc(graph->n_subsets*sizeof(*graph->subset_ncc),&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 = PetscMalloc(graph->cptr[graph->ncc]*sizeof(*queue_global),&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;
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 = PetscMalloc(graph->nvtxs*sizeof(PetscInt),&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 = PetscMalloc(graph->nvtxs*sizeof(PetscInt),&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,PetscInt,&graph->mirrors,
695                         graph->nvtxs,PetscInt*,&graph->mirrors_set);CHKERRQ(ierr);
696     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
697     graph->mirrors_set[0] = 0;
698 
699     k=0;
700     for (i=0;i<n_shared[0];i++) {
701       j=shared[0][i];
702       if (graph->count[j] > 1) {
703         graph->mirrors[j]++;
704         k++;
705       }
706     }
707     /* allocate space for set of mirrors */
708     ierr = PetscMalloc(k*sizeof(PetscInt*),&graph->mirrors_set[0]);CHKERRQ(ierr);
709     for (i=1;i<graph->nvtxs;i++)
710       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
711 
712     /* fill arrays */
713     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
714     for (j=0;j<n_shared[0];j++) {
715       i=shared[0][j];
716       if (graph->count[i] > 1)
717         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
718     }
719     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
720     for (i=0;i<graph->nvtxs;i++) {
721       if (graph->mirrors[i] > 0) {
722         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
723         j = global_indices[k];
724         while ( k > 0 && global_indices[k-1] == j) k--;
725         for (j=0;j<graph->mirrors[i];j++) {
726           graph->mirrors_set[i][j]=local_indices[k+j];
727         }
728         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
729       }
730     }
731     ierr = PetscFree(local_indices);CHKERRQ(ierr);
732     ierr = PetscFree(global_indices);CHKERRQ(ierr);
733   }
734   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
735   ierr = ISDestroy(&to);CHKERRQ(ierr);
736   ierr = ISDestroy(&from);CHKERRQ(ierr);
737 
738   /* Count total number of neigh per node */
739   k=0;
740   for (i=1;i<n_neigh;i++) {
741     k += n_shared[i];
742     for (j=0;j<n_shared[i];j++) {
743       graph->count[shared[i][j]] += 1;
744     }
745   }
746   /* Allocate space for storing the set of neighbours for each node */
747   if (graph->nvtxs) {
748     ierr = PetscMalloc(k*sizeof(PetscInt),&graph->neighbours_set[0]);CHKERRQ(ierr);
749   }
750   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
751     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
752   }
753   /* Get information for sharing subdomains */
754   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
755   for (i=1;i<n_neigh;i++) { /* dont count myself */
756     s = n_shared[i];
757     for (j=0;j<s;j++) {
758       k = shared[i][j];
759       graph->neighbours_set[k][graph->count[k]] = neigh[i];
760       graph->count[k] += 1;
761     }
762   }
763   /* sort set of sharing subdomains */
764   for (i=0;i<graph->nvtxs;i++) {
765     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
766   }
767   /* Get info for dofs splitting */
768   for (i=0;i<n_ISForDofs;i++) {
769     ierr = ISGetSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
770     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
771     for (j=0;j<is_size;j++) {
772       graph->which_dof[is_indices[j]]=i;
773     }
774     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
775   }
776   /* Take into account Neumann nodes */
777   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
778   ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
779   if (neumann_is) {
780     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
781     ierr = ISGetSize(neumann_is,&is_size);CHKERRQ(ierr);
782     ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
783     for (i=0;i<is_size;i++) {
784       array[is_indices[i]] = 1.0;
785     }
786     ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
787     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
788   }
789   /* Neumann nodes: impose consistency among neighbours */
790   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
791   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
792   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
793   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
794   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
795   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
796   for (i=0;i<graph->nvtxs;i++) {
797     if (PetscRealPart(array[i]) > 0.0) {
798       graph->special_dof[i] = NEUMANN_MARK;
799     }
800   }
801   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
802   /* Take into account Dirichlet nodes */
803   ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
804   if (dirichlet_is) {
805     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
806     ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
807     ierr = ISGetSize(dirichlet_is,&is_size);CHKERRQ(ierr);
808     ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
809     for (i=0;i<is_size;i++){
810       k = is_indices[i];
811       if (graph->count[k] && !PetscBTLookup(graph->touched,k)) {
812         if (PetscRealPart(array[k]) > 0.0) {
813           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);
814         }
815         array2[k] = 1.0;
816       }
817     }
818     ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
819     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
820     ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
821   }
822   /* Dirichlet nodes: impose consistency among neighbours */
823   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
824   ierr = VecScatterBegin(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
825   ierr = VecScatterEnd(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
826   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
827   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
828   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
829   for (i=0;i<graph->nvtxs;i++) {
830     if (PetscRealPart(array[i]) > 0.0) {
831       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
832       graph->subset[i] = 0; /* dirichlet nodes treated as internal -> is it ok? */
833       graph->special_dof[i] = DIRICHLET_MARK;
834     }
835   }
836   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
837 
838   /* mark local periodic nodes (if any) and adapt CSR graph */
839   if (graph->mirrors) {
840     PetscInt *new_xadj,*new_adjncy;
841 
842     for (i=0;i<graph->nvtxs;i++)
843       if (graph->mirrors[i])
844         graph->special_dof[i] = LOCAL_PERIODIC_MARK;
845 
846     /* sort CSR graph */
847     for (i=0;i<graph->nvtxs;i++)
848       ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
849 
850     /* adapt local CSR graph in case of local periodicity */
851     k=0;
852     for (i=0;i<graph->nvtxs;i++)
853       for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
854         k += graph->mirrors[graph->adjncy[j]];
855 
856     ierr = PetscMalloc((graph->nvtxs+1)*sizeof(PetscInt),&new_xadj);CHKERRQ(ierr);
857     ierr = PetscMalloc((k+graph->xadj[graph->nvtxs])*sizeof(PetscInt),&new_adjncy);CHKERRQ(ierr);
858     new_xadj[0]=0;
859     for (i=0;i<graph->nvtxs;i++) {
860       k = graph->xadj[i+1]-graph->xadj[i];
861       ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
862       new_xadj[i+1]=new_xadj[i]+k;
863       for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
864         k = graph->mirrors[graph->adjncy[j]];
865         ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
866         new_xadj[i+1]+=k;
867       }
868       k = new_xadj[i+1]-new_xadj[i];
869       ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
870       new_xadj[i+1]=new_xadj[i]+k;
871     }
872     /* set new CSR into graph */
873     ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
874     ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
875     graph->xadj = new_xadj;
876     graph->adjncy = new_adjncy;
877   }
878 
879   /* mark special nodes -> each will become a single node equivalence class */
880   if (custom_primal_vertices) {
881     ierr = ISGetSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
882     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
883     for (i=0;i<is_size;i++) {
884       graph->special_dof[is_indices[i]] = SPECIAL_MARK-i;
885     }
886     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
887   }
888   /* mark interior nodes as touched and belonging to partition number 0 */
889   for (i=0;i<graph->nvtxs;i++) {
890     if (!graph->count[i]) {
891       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
892       graph->subset[i] = 0;
893     }
894   }
895   /* init graph structure and compute default subsets */
896   nodes_touched=0;
897   for (i=0;i<graph->nvtxs;i++) {
898     if (PetscBTLookup(graph->touched,i)) {
899       nodes_touched++;
900     }
901   }
902   i = 0;
903   graph->ncc = 0;
904   total_counts = 0;
905   while (nodes_touched<graph->nvtxs) {
906     /*  find first untouched node in local ordering */
907     while (PetscBTLookup(graph->touched,i)) {
908       i++;
909     }
910     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
911     graph->subset[i] = graph->ncc+1;
912     graph->cptr[graph->ncc] = total_counts;
913     graph->queue[total_counts] = i;
914     total_counts++;
915     nodes_touched++;
916     /* now find all other nodes having the same set of sharing subdomains */
917     for (j=i+1;j<graph->nvtxs;j++) {
918       /* check for same number of sharing subdomains, dof number and same special mark */
919       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]) {
920         /* check for same set of sharing subdomains */
921         same_set=PETSC_TRUE;
922         for (k=0;k<graph->count[j];k++){
923           if (graph->neighbours_set[i][k]!=graph->neighbours_set[j][k]) {
924             same_set=PETSC_FALSE;
925           }
926         }
927         /* I found a friend of mine */
928         if (same_set) {
929           graph->subset[j]=graph->ncc+1;
930           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
931           nodes_touched++;
932           graph->queue[total_counts] = j;
933           total_counts++;
934         }
935       }
936     }
937     graph->ncc++;
938   }
939   /* set default number of subsets (at this point no info on csr graph has been taken into account, so n_subsets = ncc */
940   graph->n_subsets = graph->ncc;
941   ierr = PetscMalloc(graph->n_subsets*sizeof(*graph->subset_ncc),&graph->subset_ncc);CHKERRQ(ierr);
942   for (i=0;i<graph->n_subsets;i++) {
943     graph->subset_ncc[i] = 1;
944   }
945   /* final pointer */
946   graph->cptr[graph->ncc] = total_counts;
947   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
948   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
949   /* free objects */
950   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
951   ierr = VecDestroy(&local_vec2);CHKERRQ(ierr);
952   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
953   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
954   PetscFunctionReturn(0);
955 }
956 
957 #undef __FUNCT__
958 #define __FUNCT__ "PCBDDCGraphResetCSR"
959 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
960 {
961   PetscErrorCode ierr;
962 
963   PetscFunctionBegin;
964   ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
965   ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
966   graph->nvtxs_csr = 0;
967   PetscFunctionReturn(0);
968 }
969 
970 #undef __FUNCT__
971 #define __FUNCT__ "PCBDDCGraphReset"
972 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
973 {
974   PetscErrorCode ierr;
975 
976   PetscFunctionBegin;
977   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
978   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
979   if (graph->nvtxs) {
980     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
981   }
982   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
983   ierr = PetscFree7(graph->count,
984                     graph->neighbours_set,
985                     graph->subset,
986                     graph->which_dof,
987                     graph->cptr,
988                     graph->queue,
989                     graph->special_dof);CHKERRQ(ierr);
990   if (graph->mirrors) {
991     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
992   }
993   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
994   graph->nvtxs = 0;
995   graph->n_subsets = 0;
996   graph->custom_minimal_size = 1;
997   PetscFunctionReturn(0);
998 }
999 
1000 #undef __FUNCT__
1001 #define __FUNCT__ "PCBDDCGraphInit"
1002 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap)
1003 {
1004   PetscInt       n;
1005   PetscErrorCode ierr;
1006 
1007   PetscFunctionBegin;
1008   PetscValidPointer(graph,1);
1009   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1010   /* reset graph if already allocated */
1011   if (graph->nvtxs) {
1012     ierr = PCBDDCGraphReset(graph);CHKERRQ(ierr);
1013   }
1014   /* set number of vertices */
1015   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1016   graph->l2gmap = l2gmap;
1017   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1018   graph->nvtxs = n;
1019   /* allocate used space */
1020   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1021   ierr = PetscMalloc7(graph->nvtxs,PetscInt,&graph->count,
1022                       graph->nvtxs,PetscInt*,&graph->neighbours_set,
1023                       graph->nvtxs,PetscInt,&graph->subset,
1024                       graph->nvtxs,PetscInt,&graph->which_dof,
1025                       graph->nvtxs+1,PetscInt,&graph->cptr,
1026                       graph->nvtxs,PetscInt,&graph->queue,
1027                       graph->nvtxs,PetscInt,&graph->special_dof);CHKERRQ(ierr);
1028   /* zeroes memory */
1029   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1030   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1031   ierr = PetscMemzero(graph->which_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1032   ierr = PetscMemzero(graph->cptr,(graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
1033   ierr = PetscMemzero(graph->queue,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1034   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1035   /* zeroes first pointer to neighbour set */
1036   if (graph->nvtxs) {
1037     graph->neighbours_set[0] = 0;
1038   }
1039   /* zeroes workspace for values of ncc */
1040   graph->subset_ncc = 0;
1041   PetscFunctionReturn(0);
1042 }
1043 
1044 #undef __FUNCT__
1045 #define __FUNCT__ "PCBDDCGraphDestroy"
1046 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1047 {
1048   PetscErrorCode ierr;
1049 
1050   PetscFunctionBegin;
1051   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1052   ierr = PetscFree(*graph);CHKERRQ(ierr);
1053   PetscFunctionReturn(0);
1054 }
1055 
1056 #undef __FUNCT__
1057 #define __FUNCT__ "PCBDDCGraphCreate"
1058 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1059 {
1060   PCBDDCGraph    new_graph;
1061   PetscErrorCode ierr;
1062 
1063   PetscFunctionBegin;
1064   ierr = PetscMalloc(sizeof(*new_graph),&new_graph);CHKERRQ(ierr);
1065   /* local to global mapping of dofs */
1066   new_graph->l2gmap = 0;
1067   /* vertex size */
1068   new_graph->nvtxs = 0;
1069   new_graph->n_subsets = 0;
1070   new_graph->custom_minimal_size = 1;
1071   /* zeroes ponters */
1072   new_graph->mirrors = 0;
1073   new_graph->mirrors_set = 0;
1074   new_graph->neighbours_set = 0;
1075   new_graph->subset = 0;
1076   new_graph->which_dof = 0;
1077   new_graph->special_dof = 0;
1078   new_graph->cptr = 0;
1079   new_graph->queue = 0;
1080   new_graph->count = 0;
1081   new_graph->subset_ncc = 0;
1082   new_graph->touched = 0;
1083   /* zeroes pointers to csr graph of local nodes connectivity (optional data) */
1084   new_graph->nvtxs_csr = 0;
1085   new_graph->xadj = 0;
1086   new_graph->adjncy = 0;
1087   *graph = new_graph;
1088   PetscFunctionReturn(0);
1089 }
1090