xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision acc113db8e0560a6e36834f59af9dd9073b2176d)
1 #include <petsc/private/petscimpl.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <../src/ksp/pc/impls/bddc/bddcstructs.h>
4 
5 #undef __FUNCT__
6 #define __FUNCT__ "PCBDDCGraphGetDirichletDofs"
7 PetscErrorCode PCBDDCGraphGetDirichletDofs(PCBDDCGraph graph,IS* dirdofs)
8 {
9   PetscInt       i,size,sizer;
10   PetscErrorCode ierr;
11 
12   PetscFunctionBegin;
13   size = 0;
14   for (i=0;i<graph->nvtxs;i++) {
15     if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
16   }
17   ierr = MPI_Allreduce(&size,&sizer,1,MPIU_INT,MPI_LOR,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
18   if (sizer) {
19     PetscInt *dirdofs_idxs;
20 
21     ierr = PetscMalloc1(size,&dirdofs_idxs);CHKERRQ(ierr);
22     size = 0;
23     for (i=0;i<graph->nvtxs;i++) {
24       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
25     }
26     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)graph->l2gmap),size,dirdofs_idxs,PETSC_OWN_POINTER,dirdofs);CHKERRQ(ierr);
27   } else {
28     *dirdofs = NULL;
29   }
30   PetscFunctionReturn(0);
31 }
32 
33 #undef __FUNCT__
34 #define __FUNCT__ "PCBDDCGraphASCIIView"
35 PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer)
36 {
37   PetscInt       i,j,tabs;
38   PetscInt*      queue_in_global_numbering;
39   PetscErrorCode ierr;
40 
41   PetscFunctionBegin;
42   ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
43   ierr = PetscViewerASCIIGetTab(viewer,&tabs);CHKERRQ(ierr);
44   ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
45   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
46   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Local BDDC graph for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
47   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Number of vertices %d\n",graph->nvtxs);CHKERRQ(ierr);
48   if (verbosity_level > 1) {
49     for (i=0;i<graph->nvtxs;i++) {
50       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d:\n",i);CHKERRQ(ierr);
51       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %d\n",graph->which_dof[i]);CHKERRQ(ierr);
52       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %d\n",graph->special_dof[i]);CHKERRQ(ierr);
53       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %d\n",graph->count[i]);CHKERRQ(ierr);
54       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
55       if (graph->count[i]) {
56         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:");CHKERRQ(ierr);
57         for (j=0;j<graph->count[i];j++) {
58           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[i][j]);CHKERRQ(ierr);
59         }
60         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
61       }
62       ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
63       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
64       if (graph->mirrors) {
65         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %d\n",graph->mirrors[i]);CHKERRQ(ierr);
66         if (graph->mirrors[i]) {
67           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
68           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:");CHKERRQ(ierr);
69           for (j=0;j<graph->mirrors[i];j++) {
70             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->mirrors_set[i][j]);CHKERRQ(ierr);
71           }
72           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
73           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
74           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
75         }
76       }
77       if (verbosity_level > 2) {
78         if (graph->xadj && graph->adjncy) {
79           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:");CHKERRQ(ierr);
80           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
81           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
82             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->adjncy[j]);CHKERRQ(ierr);
83           }
84           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
85           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
86           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
87         } else {
88           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   no adj info\n");CHKERRQ(ierr);
89         }
90       }
91       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
92       if (graph->subset[i] && graph->subset_ncc) {
93         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
94       }
95     }
96   }
97   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
98   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
99   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
100   for (i=0;i<graph->ncc;i++) {
101     PetscInt node_num=graph->queue[graph->cptr[i]];
102     PetscBool printcc = PETSC_FALSE;
103     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  %d (neighs:",i);CHKERRQ(ierr);
104     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
105     for (j=0;j<graph->count[node_num];j++) {
106       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
107     }
108     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
109     if (verbosity_level > 1) {
110       printcc = PETSC_TRUE;
111     } else if (graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) {
112       printcc = PETSC_TRUE;
113     }
114     if (printcc) {
115       for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
116         ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
117       }
118     }
119     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
120     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
121     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
122   }
123   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
124   if (graph->custom_minimal_size > 1 && verbosity_level > 1) {
125     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %d\n",graph->custom_minimal_size);CHKERRQ(ierr);
126   }
127   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
128   PetscFunctionReturn(0);
129 }
130 
131 #undef __FUNCT__
132 #define __FUNCT__ "PCBDDCGraphGetCandidatesIS"
133 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
134 {
135   IS             *ISForFaces,*ISForEdges,ISForVertices;
136   PetscInt       i,nfc,nec,nvc,*idx;
137   PetscErrorCode ierr;
138 
139   PetscFunctionBegin;
140   /* loop on ccs to evalute number of faces, edges and vertices */
141   nfc = 0;
142   nec = 0;
143   nvc = 0;
144   for (i=0;i<graph->ncc;i++) {
145     PetscInt repdof = graph->queue[graph->cptr[i]];
146     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
147       if (graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
148         nfc++;
149       } else { /* note that nec will be zero in 2d */
150         nec++;
151       }
152     } else {
153       nvc += graph->cptr[i+1]-graph->cptr[i];
154     }
155   }
156 
157   /* check if we are in 2D or 3D */
158   if (graph->twodim) { /* we are in a 2D case -> edges are shared by 2 subregions and faces don't exist */
159     nec = nfc;
160     nfc = 0;
161   }
162 
163   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
164   if (FacesIS) {
165     ierr = PetscMalloc1(nfc,&ISForFaces);CHKERRQ(ierr);
166   }
167   if (EdgesIS) {
168     ierr = PetscMalloc1(nec,&ISForEdges);CHKERRQ(ierr);
169   }
170   if (VerticesIS) {
171     ierr = PetscMalloc1(nvc,&idx);CHKERRQ(ierr);
172   }
173 
174   /* loop on ccs to compute index sets for faces and edges */
175   if (!graph->queue_sorted) {
176     PetscInt *queue_global;
177 
178     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
179     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
180     for (i=0;i<graph->ncc;i++) {
181       ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
182     }
183     ierr = PetscFree(queue_global);CHKERRQ(ierr);
184     graph->queue_sorted = PETSC_TRUE;
185   }
186   nfc = 0;
187   nec = 0;
188   for (i=0;i<graph->ncc;i++) {
189     PetscInt repdof = graph->queue[graph->cptr[i]];
190     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
191       if (graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
192         if (graph->twodim) {
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         } else {
198           if (FacesIS) {
199             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForFaces[nfc]);CHKERRQ(ierr);
200           }
201           nfc++;
202         }
203       } else {
204         if (EdgesIS) {
205           ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
206         }
207         nec++;
208       }
209     }
210   }
211   /* index set for vertices */
212   if (VerticesIS) {
213     nvc = 0;
214     for (i=0;i<graph->ncc;i++) {
215       if (graph->cptr[i+1]-graph->cptr[i] <= graph->custom_minimal_size) {
216         PetscInt j;
217 
218         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
219           idx[nvc]=graph->queue[j];
220           nvc++;
221         }
222       }
223     }
224     /* sort vertex set (by local ordering) */
225     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
226     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
227   }
228   /* get back info */
229   if (n_faces) *n_faces = nfc;
230   if (FacesIS) {
231     *FacesIS = ISForFaces;
232   }
233   if (n_edges) *n_edges = nec;
234   if (EdgesIS) {
235     *EdgesIS = ISForEdges;
236   }
237   if (VerticesIS) {
238     *VerticesIS = ISForVertices;
239   }
240   PetscFunctionReturn(0);
241 }
242 
243 #undef __FUNCT__
244 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponents"
245 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
246 {
247   PetscBool      adapt_interface_reduced;
248   MPI_Comm       interface_comm;
249   PetscMPIInt    size;
250   PetscInt       i;
251   PetscBool      twodim;
252   PetscErrorCode ierr;
253 
254   PetscFunctionBegin;
255   /* compute connected components locally */
256   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
257   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
258   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
259   ierr = MPI_Comm_size(interface_comm,&size);CHKERRQ(ierr);
260   adapt_interface_reduced = PETSC_FALSE;
261   if (size > 1) {
262     PetscInt i;
263     PetscBool adapt_interface = PETSC_FALSE;
264     for (i=0;i<graph->n_subsets;i++) {
265       /* We are not sure that on a given subset of the local interface,
266          with two connected components, the latters be the same among sharing subdomains */
267       if (graph->subset_ncc[i] > 1) {
268         adapt_interface = PETSC_TRUE;
269         break;
270       }
271     }
272     ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_BOOL,MPI_LOR,interface_comm);CHKERRQ(ierr);
273   }
274 
275   if (graph->n_subsets && adapt_interface_reduced) {
276     /* old csr stuff */
277     PetscInt    *aux_new_xadj,*new_xadj,*new_adjncy;
278     PetscInt    *old_xadj,*old_adjncy;
279     PetscBT     subset_cc_adapt;
280     /* MPI */
281     MPI_Request *send_requests,*recv_requests;
282     PetscInt    *send_buffer,*recv_buffer;
283     PetscInt    sum_requests,start_of_recv,start_of_send;
284     PetscInt    *cum_recv_counts;
285     /* others */
286     PetscInt    *labels;
287     PetscInt    global_subset_counter;
288     PetscInt    j,k,s;
289 
290     /* Retrict adjacency graph using information from previously computed connected components */
291     ierr = PetscMalloc1(graph->nvtxs,&aux_new_xadj);CHKERRQ(ierr);
292     for (i=0;i<graph->nvtxs;i++) {
293       aux_new_xadj[i]=1;
294     }
295     for (i=0;i<graph->ncc;i++) {
296       k = graph->cptr[i+1]-graph->cptr[i];
297       for (j=0;j<k;j++) {
298         aux_new_xadj[graph->queue[graph->cptr[i]+j]]=k;
299       }
300     }
301     j = 0;
302     for (i=0;i<graph->nvtxs;i++) {
303       j += aux_new_xadj[i];
304     }
305     ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
306     ierr = PetscMalloc1(j,&new_adjncy);CHKERRQ(ierr);
307     new_xadj[0]=0;
308     for (i=0;i<graph->nvtxs;i++) {
309       new_xadj[i+1]=new_xadj[i]+aux_new_xadj[i];
310       if (aux_new_xadj[i]==1) {
311         new_adjncy[new_xadj[i]]=i;
312       }
313     }
314     ierr = PetscFree(aux_new_xadj);CHKERRQ(ierr);
315     ierr = PetscMalloc1(graph->nvtxs,&labels);CHKERRQ(ierr);
316     ierr = PetscMemzero(labels,graph->nvtxs*sizeof(*labels));CHKERRQ(ierr);
317     for (i=0;i<graph->ncc;i++) {
318       k = graph->cptr[i+1]-graph->cptr[i];
319       for (j=0;j<k;j++) {
320         ierr = PetscMemcpy(&new_adjncy[new_xadj[graph->queue[graph->cptr[i]+j]]],&graph->queue[graph->cptr[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
321         labels[graph->queue[graph->cptr[i]+j]] = i;
322       }
323     }
324     /* set temporarly new CSR into graph */
325     old_xadj = graph->xadj;
326     old_adjncy = graph->adjncy;
327     graph->xadj = new_xadj;
328     graph->adjncy = new_adjncy;
329     /* allocate some space */
330     ierr = PetscMalloc1(graph->n_subsets+1,&cum_recv_counts);CHKERRQ(ierr);
331     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
332     /* first count how many neighbours per connected component I will receive from */
333     cum_recv_counts[0]=0;
334     for (i=0;i<graph->n_subsets;i++) {
335       cum_recv_counts[i+1]=cum_recv_counts[i]+graph->count[graph->subsets[i][0]];
336     }
337     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_buffer);CHKERRQ(ierr);
338     ierr = PetscMalloc2(cum_recv_counts[graph->n_subsets],&send_requests,cum_recv_counts[graph->n_subsets],&recv_requests);CHKERRQ(ierr);
339     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
340       send_requests[i]=MPI_REQUEST_NULL;
341       recv_requests[i]=MPI_REQUEST_NULL;
342     }
343     /* exchange with my neighbours the number of my connected components on the subset of interface */
344     sum_requests = 0;
345     for (i=0;i<graph->n_subsets;i++) {
346       PetscMPIInt neigh,tag;
347 
348       j = graph->subsets[i][0];
349       ierr = PetscMPIIntCast(2*graph->subset_ref_node[i],&tag);CHKERRQ(ierr);
350       for (k=0;k<graph->count[j];k++) {
351         ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
352         ierr = MPI_Isend(&graph->subset_ncc[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
353         ierr = MPI_Irecv(&recv_buffer[sum_requests],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
354         sum_requests++;
355       }
356     }
357     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
358     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
359     /* determine the subsets I have to adapt */
360     ierr = PetscBTCreate(graph->n_subsets,&subset_cc_adapt);CHKERRQ(ierr);
361     ierr = PetscBTMemzero(graph->n_subsets,subset_cc_adapt);CHKERRQ(ierr);
362     for (i=0;i<graph->n_subsets;i++) {
363       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
364         /* adapt if more than one cc is present */
365          if (graph->subset_ncc[i] > 1 || recv_buffer[j] > 1) {
366           ierr = PetscBTSet(subset_cc_adapt,i);
367           break;
368         }
369       }
370     }
371     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
372     /* determine send/recv buffers sizes */
373     j = 0;
374     for (i=0;i<graph->n_subsets;i++) {
375       if (PetscBTLookup(subset_cc_adapt,i)) {
376         j += graph->subsets_size[i];
377       }
378     }
379     k = 0;
380     for (i=0;i<graph->n_subsets;i++) {
381       if (PetscBTLookup(subset_cc_adapt,i)) {
382         k += (cum_recv_counts[i+1]-cum_recv_counts[i])*graph->subsets_size[i];
383       }
384     }
385     ierr = PetscMalloc2(j,&send_buffer,k,&recv_buffer);CHKERRQ(ierr);
386 
387     /* fill send buffer */
388     j = 0;
389     for (i=0;i<graph->n_subsets;i++) {
390       if (PetscBTLookup(subset_cc_adapt,i)) {
391         for (k=0;k<graph->subsets_size[i];k++) {
392           send_buffer[j++] = labels[graph->subsets[i][k]];
393         }
394       }
395     }
396     ierr = PetscFree(labels);CHKERRQ(ierr);
397 
398     /* now exchange the data */
399     start_of_recv = 0;
400     start_of_send = 0;
401     sum_requests = 0;
402     for (i=0;i<graph->n_subsets;i++) {
403       if (PetscBTLookup(subset_cc_adapt,i)) {
404         PetscMPIInt neigh,tag;
405         PetscInt    size_of_send = graph->subsets_size[i];
406 
407         j = graph->subsets[i][0];
408         ierr = PetscMPIIntCast(2*graph->subset_ref_node[i]+1,&tag);CHKERRQ(ierr);
409         for (k=0;k<graph->count[j];k++) {
410           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
411           ierr = MPI_Isend(&send_buffer[start_of_send],size_of_send,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
412           ierr = MPI_Irecv(&recv_buffer[start_of_recv],size_of_send,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
413           start_of_recv += size_of_send;
414           sum_requests++;
415         }
416         start_of_send += size_of_send;
417       }
418     }
419     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
420     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
421     ierr = PetscFree2(send_requests,recv_requests);CHKERRQ(ierr);
422     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
423 
424     start_of_recv = 0;
425     global_subset_counter = 0;
426     for (i=0;i<graph->n_subsets;i++) {
427       if (PetscBTLookup(subset_cc_adapt,i)) {
428         PetscInt **temp_buffer,temp_buffer_size,*private_label;
429 
430         /* allocate some temporary space */
431         temp_buffer_size = graph->subsets_size[i];
432         ierr = PetscMalloc1(temp_buffer_size,&temp_buffer);CHKERRQ(ierr);
433         ierr = PetscMalloc1(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i]),&temp_buffer[0]);CHKERRQ(ierr);
434         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
435         for (j=1;j<temp_buffer_size;j++) {
436           temp_buffer[j] = temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
437         }
438         /* analyze contributions from neighbouring subdomains for i-th subset
439            temp buffer structure:
440            supposing part of the interface has dimension 5
441            e.g with global dofs 0,1,2,3,4, locally ordered on the current process as 0,4,3,1,2
442            3 neighs procs having connected components:
443              neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
444              neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
445              neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
446            tempbuffer (row-oriented) will be filled as:
447              [ 4, 3, 1;
448                4, 2, 1;
449                7, 2, 6;
450                4, 3, 5;
451                7, 2, 6; ];
452            This way we can simply find intersections of ccs among neighs.
453            The graph->subset array will need to be modified. The output for the example is [0], [1], [2 3], [4];
454                                                                                                                                    */
455         for (j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
456           for (k=0;k<temp_buffer_size;k++) {
457             temp_buffer[k][j] = recv_buffer[start_of_recv+k];
458           }
459           start_of_recv += temp_buffer_size;
460         }
461         ierr = PetscMalloc1(temp_buffer_size,&private_label);CHKERRQ(ierr);
462         ierr = PetscMemzero(private_label,temp_buffer_size*sizeof(*private_label));CHKERRQ(ierr);
463         for (j=0;j<temp_buffer_size;j++) {
464           if (!private_label[j]) { /* found a new cc  */
465             PetscBool same_set;
466 
467             global_subset_counter++;
468             private_label[j] = global_subset_counter;
469             for (k=j+1;k<temp_buffer_size;k++) { /* check for other nodes in new cc */
470               same_set = PETSC_TRUE;
471               for (s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++) {
472                 if (temp_buffer[j][s] != temp_buffer[k][s]) {
473                   same_set = PETSC_FALSE;
474                   break;
475                 }
476               }
477               if (same_set) {
478                 private_label[k] = global_subset_counter;
479               }
480             }
481           }
482         }
483         /* insert private labels in graph structure */
484         for (j=0;j<graph->subsets_size[i];j++) {
485           graph->subset[graph->subsets[i][j]] = graph->n_subsets+private_label[j];
486         }
487         ierr = PetscFree(private_label);CHKERRQ(ierr);
488         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
489         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
490       }
491     }
492     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
493     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
494     ierr = PetscBTDestroy(&subset_cc_adapt);CHKERRQ(ierr);
495     /* We are ready to find for connected components which are consistent among neighbouring subdomains */
496     if (global_subset_counter) {
497       ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
498       global_subset_counter = 0;
499       for (i=0;i<graph->nvtxs;i++) {
500         if (graph->subset[i] && !PetscBTLookup(graph->touched,i)) {
501           global_subset_counter++;
502           for (j=i+1;j<graph->nvtxs;j++) {
503             if (!PetscBTLookup(graph->touched,j) && graph->subset[j]==graph->subset[i]) {
504               graph->subset[j] = global_subset_counter;
505               ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
506             }
507           }
508           graph->subset[i] = global_subset_counter;
509           ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
510         }
511       }
512       /* refine connected components locally */
513       ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
514     }
515     /* restore original CSR graph of dofs */
516     ierr = PetscFree(new_xadj);CHKERRQ(ierr);
517     ierr = PetscFree(new_adjncy);CHKERRQ(ierr);
518     graph->xadj = old_xadj;
519     graph->adjncy = old_adjncy;
520   }
521 
522   /* Determine if we are in 2D or 3D */
523   twodim  = PETSC_TRUE;
524   for (i=0;i<graph->ncc;i++) {
525     PetscInt repdof = graph->queue[graph->cptr[i]];
526     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
527       if (graph->count[repdof] > 1 || graph->special_dof[repdof] == PCBDDCGRAPH_NEUMANN_MARK) {
528         twodim = PETSC_FALSE;
529         break;
530       }
531     }
532   }
533   ierr = MPI_Allreduce(&twodim,&graph->twodim,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
534   PetscFunctionReturn(0);
535 }
536 
537 /* The following code has been adapted from function IsConnectedSubdomain contained
538    in source file contig.c of METIS library (version 5.0.1)
539    It finds connected components for each subset  */
540 #undef __FUNCT__
541 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponentsLocal"
542 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
543 {
544   PetscInt       i,j,k,first,last,nleft,ncc,pid,cum_queue,n,ncc_pid;
545   PetscMPIInt    size;
546   PetscErrorCode ierr;
547 
548   PetscFunctionBegin;
549   /* quiet return if no csr info is available */
550   if (!graph->xadj || !graph->adjncy) {
551     PetscFunctionReturn(0);
552   }
553 
554   /* reset any previous search of connected components */
555   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
556   graph->n_subsets = 0;
557   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&size);CHKERRQ(ierr);
558   if (size == 1) {
559     if (graph->nvtxs) {
560       graph->n_subsets = 1;
561       for (i=0;i<graph->nvtxs;i++) {
562         graph->subset[i] = 1;
563       }
564     }
565   } else {
566     for (i=0;i<graph->nvtxs;i++) {
567       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
568         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
569         graph->subset[i] = 0;
570       }
571       graph->n_subsets = PetscMax(graph->n_subsets,graph->subset[i]);
572     }
573   }
574   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
575   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
576 
577   /* begin search for connected components */
578   cum_queue = 0;
579   ncc = 0;
580   for (n=0;n<graph->n_subsets;n++) {
581     pid = n+1;  /* partition labeled by 0 is discarded */
582     nleft = 0;
583     for (i=0;i<graph->nvtxs;i++) {
584       if (graph->subset[i] == pid) {
585         nleft++;
586       }
587     }
588     for (i=0; i<graph->nvtxs; i++) {
589       if (graph->subset[i] == pid) {
590         break;
591       }
592     }
593     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
594     graph->queue[cum_queue] = i;
595     first = 0;
596     last = 1;
597     graph->cptr[ncc] = cum_queue;
598     ncc_pid = 0;
599     while (first != nleft) {
600       if (first == last) {
601         graph->cptr[++ncc] = first+cum_queue;
602         ncc_pid++;
603         for (i=0; i<graph->nvtxs; i++) { /* TODO-> use a while! */
604           if (graph->subset[i] == pid && !PetscBTLookup(graph->touched,i)) {
605             break;
606           }
607         }
608         graph->queue[cum_queue+last] = i;
609         last++;
610         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
611       }
612       i = graph->queue[cum_queue+first];
613       first++;
614       for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
615         k = graph->adjncy[j];
616         if (graph->subset[k] == pid && !PetscBTLookup(graph->touched,k)) {
617           graph->queue[cum_queue+last] = k;
618           last++;
619           ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
620         }
621       }
622     }
623     graph->cptr[++ncc] = first+cum_queue;
624     ncc_pid++;
625     cum_queue = graph->cptr[ncc];
626     graph->subset_ncc[n] = ncc_pid;
627   }
628   graph->ncc = ncc;
629   graph->queue_sorted = PETSC_FALSE;
630   PetscFunctionReturn(0);
631 }
632 
633 #undef __FUNCT__
634 #define __FUNCT__ "PCBDDCGraphSetUp"
635 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
636 {
637   VecScatter     scatter_ctx;
638   Vec            local_vec,local_vec2,global_vec;
639   IS             to,from;
640   MPI_Comm       comm;
641   PetscScalar    *array,*array2;
642   const PetscInt *is_indices;
643   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global,*subset_ref_node_global;
644   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
645   PetscMPIInt    size;
646   PetscBool      same_set,mirrors_found;
647   PetscErrorCode ierr;
648 
649   PetscFunctionBegin;
650   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
651   /* custom_minimal_size */
652   graph->custom_minimal_size = PetscMax(graph->custom_minimal_size,custom_minimal_size);
653   /* get info l2gmap and allocate work vectors  */
654   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
655   /* check if we have any local periodic nodes (periodic BCs) */
656   mirrors_found = PETSC_FALSE;
657   if (graph->nvtxs && n_neigh) {
658     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
659     for (i=0; i<n_shared[0]; i++) {
660       if (graph->count[shared[0][i]] > 1) {
661         mirrors_found = PETSC_TRUE;
662         break;
663       }
664     }
665   }
666   /* create some workspace objects */
667   local_vec = NULL;
668   local_vec2 = NULL;
669   global_vec = NULL;
670   to = NULL;
671   from = NULL;
672   scatter_ctx = NULL;
673   if (n_ISForDofs || dirichlet_is || neumann_is || custom_primal_vertices) {
674     ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
675     ierr = VecSetSizes(local_vec,PETSC_DECIDE,graph->nvtxs);CHKERRQ(ierr);
676     ierr = VecSetType(local_vec,VECSTANDARD);CHKERRQ(ierr);
677     ierr = VecDuplicate(local_vec,&local_vec2);CHKERRQ(ierr);
678     ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
679     ierr = VecSetSizes(global_vec,PETSC_DECIDE,graph->nvtxs_global);CHKERRQ(ierr);
680     ierr = VecSetType(global_vec,VECSTANDARD);CHKERRQ(ierr);
681     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
682     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
683     ierr = VecScatterCreate(global_vec,from,local_vec,to,&scatter_ctx);CHKERRQ(ierr);
684   } else if (mirrors_found) {
685     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
686     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
687   }
688   /* compute local mirrors (if any) */
689   if (mirrors_found) {
690     PetscInt *local_indices,*global_indices;
691     /* get arrays of local and global indices */
692     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
693     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
694     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
695     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
696     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
697     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
698     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
699     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
700     /* allocate space for mirrors */
701     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
702     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
703     graph->mirrors_set[0] = 0;
704 
705     k=0;
706     for (i=0;i<n_shared[0];i++) {
707       j=shared[0][i];
708       if (graph->count[j] > 1) {
709         graph->mirrors[j]++;
710         k++;
711       }
712     }
713     /* allocate space for set of mirrors */
714     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
715     for (i=1;i<graph->nvtxs;i++)
716       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
717 
718     /* fill arrays */
719     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
720     for (j=0;j<n_shared[0];j++) {
721       i=shared[0][j];
722       if (graph->count[i] > 1)
723         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
724     }
725     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
726     for (i=0;i<graph->nvtxs;i++) {
727       if (graph->mirrors[i] > 0) {
728         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
729         j = global_indices[k];
730         while ( k > 0 && global_indices[k-1] == j) k--;
731         for (j=0;j<graph->mirrors[i];j++) {
732           graph->mirrors_set[i][j]=local_indices[k+j];
733         }
734         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
735       }
736     }
737     ierr = PetscFree(local_indices);CHKERRQ(ierr);
738     ierr = PetscFree(global_indices);CHKERRQ(ierr);
739   }
740   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
741   ierr = ISDestroy(&to);CHKERRQ(ierr);
742   ierr = ISDestroy(&from);CHKERRQ(ierr);
743 
744   /* Count total number of neigh per node */
745   k=0;
746   for (i=1;i<n_neigh;i++) {
747     k += n_shared[i];
748     for (j=0;j<n_shared[i];j++) {
749       graph->count[shared[i][j]] += 1;
750     }
751   }
752   /* Allocate space for storing the set of neighbours for each node */
753   if (graph->nvtxs) {
754     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
755   }
756   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
757     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
758   }
759   /* Get information for sharing subdomains */
760   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
761   for (i=1;i<n_neigh;i++) { /* dont count myself */
762     s = n_shared[i];
763     for (j=0;j<s;j++) {
764       k = shared[i][j];
765       graph->neighbours_set[k][graph->count[k]] = neigh[i];
766       graph->count[k] += 1;
767     }
768   }
769   /* sort set of sharing subdomains */
770   for (i=0;i<graph->nvtxs;i++) {
771     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
772   }
773   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
774   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
775 
776   /*
777      Get info for dofs splitting
778      User can specify just a subset; an additional field is considered as a complementary field
779   */
780   for (i=0;i<graph->nvtxs;i++) {
781     graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
782   }
783   if (n_ISForDofs) {
784     ierr = VecSet(local_vec,-1.0);CHKERRQ(ierr);
785   }
786   for (i=0;i<n_ISForDofs;i++) {
787     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
788     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
789     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
790     for (j=0;j<is_size;j++) {
791       if (is_indices[j] > -1 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
792         graph->which_dof[is_indices[j]] = i;
793         array[is_indices[j]] = 1.*i;
794       }
795     }
796     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
797     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
798   }
799   /* Check consistency among neighbours */
800   if (n_ISForDofs) {
801     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
802     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
803     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
804     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
805     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
806     ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
807     for (i=0;i<graph->nvtxs;i++){
808       PetscInt field1,field2;
809 
810       field1 = (PetscInt)PetscRealPart(array[i]);
811       field2 = (PetscInt)PetscRealPart(array2[i]);
812       if (field1 != field2) {
813         SETERRQ3(comm,PETSC_ERR_USER,"Local node %d have been assigned two different field ids %d and %d at the same time\n",i,field1,field2);
814       }
815     }
816     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
817     ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
818   }
819   if (neumann_is || dirichlet_is) {
820     /* Take into account Neumann nodes */
821     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
822     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
823     if (neumann_is) {
824       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
825       ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
826       ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
827       for (i=0;i<is_size;i++) {
828         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
829           array[is_indices[i]] = 1.0;
830         }
831       }
832       ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
833       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
834     }
835     /* Neumann nodes: impose consistency among neighbours */
836     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
837     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
838     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
839     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
840     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
841     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
842     for (i=0;i<graph->nvtxs;i++) {
843       if (PetscRealPart(array[i]) > 0.1) {
844         graph->special_dof[i] = PCBDDCGRAPH_NEUMANN_MARK;
845       }
846     }
847     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
848     /* Take into account Dirichlet nodes */
849     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
850     if (dirichlet_is) {
851       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
852       ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
853       ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
854       ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
855       for (i=0;i<is_size;i++){
856         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
857           k = is_indices[i];
858           if (graph->count[k] && !PetscBTLookup(graph->touched,k)) {
859             if (PetscRealPart(array[k]) > 0.1) {
860               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);
861             }
862             array2[k] = 1.0;
863           }
864         }
865       }
866       ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
867       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
868       ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
869     }
870     /* Dirichlet nodes: impose consistency among neighbours */
871     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
872     ierr = VecScatterBegin(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
873     ierr = VecScatterEnd(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
874     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
875     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
876     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
877     for (i=0;i<graph->nvtxs;i++) {
878       if (PetscRealPart(array[i]) > 0.1) {
879         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
880         graph->subset[i] = 0; /* dirichlet nodes treated as internal -> is it ok? */
881         graph->special_dof[i] = PCBDDCGRAPH_DIRICHLET_MARK;
882       }
883     }
884     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
885   }
886   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
887   if (graph->mirrors) {
888     for (i=0;i<graph->nvtxs;i++)
889       if (graph->mirrors[i])
890         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
891 
892     if (graph->xadj && graph->adjncy) {
893       PetscInt *new_xadj,*new_adjncy;
894       /* sort CSR graph */
895       for (i=0;i<graph->nvtxs;i++)
896         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
897 
898       /* adapt local CSR graph in case of local periodicity */
899       k=0;
900       for (i=0;i<graph->nvtxs;i++)
901         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
902           k += graph->mirrors[graph->adjncy[j]];
903 
904       ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
905       ierr = PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy);CHKERRQ(ierr);
906       new_xadj[0]=0;
907       for (i=0;i<graph->nvtxs;i++) {
908         k = graph->xadj[i+1]-graph->xadj[i];
909         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
910         new_xadj[i+1]=new_xadj[i]+k;
911         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
912           k = graph->mirrors[graph->adjncy[j]];
913           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
914           new_xadj[i+1]+=k;
915         }
916         k = new_xadj[i+1]-new_xadj[i];
917         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
918         new_xadj[i+1]=new_xadj[i]+k;
919       }
920       /* set new CSR into graph */
921       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
922       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
923       graph->xadj = new_xadj;
924       graph->adjncy = new_adjncy;
925     }
926   }
927 
928   /* mark special nodes (if any) -> each will become a single node equivalence class */
929   if (custom_primal_vertices) {
930     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
931     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
932     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
933     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
934     for (i=0;i<is_size;i++){
935       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
936         array[is_indices[i]] = 1.0;
937       }
938     }
939     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
940     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
941     /* special nodes: impose consistency among neighbours */
942     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
943     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
944     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
945     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
946     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
947     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
948     j = 0;
949     for (i=0;i<graph->nvtxs;i++) {
950       if (PetscRealPart(array[i]) > 0.1 && graph->special_dof[i] != PCBDDCGRAPH_DIRICHLET_MARK) {
951         graph->special_dof[i] = PCBDDCGRAPH_SPECIAL_MARK-j;
952         j++;
953       }
954     }
955     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
956   }
957 
958   /* mark interior nodes as touched and belonging to partition number 0 */
959   for (i=0;i<graph->nvtxs;i++) {
960     if (!graph->count[i]) {
961       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
962       graph->subset[i] = 0;
963     }
964   }
965   /* init graph structure and compute default subsets */
966   nodes_touched=0;
967   for (i=0;i<graph->nvtxs;i++) {
968     if (PetscBTLookup(graph->touched,i)) {
969       nodes_touched++;
970     }
971   }
972   i = 0;
973   graph->ncc = 0;
974   total_counts = 0;
975 
976   /* allocated space for queues */
977   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
978   if (size == 1) {
979     ierr = PetscMalloc2(graph->nvtxs+1,&graph->cptr,graph->nvtxs,&graph->queue);CHKERRQ(ierr);
980   } else {
981     PetscInt nused = graph->nvtxs - nodes_touched;
982     ierr = PetscMalloc2(nused+1,&graph->cptr,nused,&graph->queue);CHKERRQ(ierr);
983   }
984 
985   while (nodes_touched<graph->nvtxs) {
986     /*  find first untouched node in local ordering */
987     while (PetscBTLookup(graph->touched,i)) {
988       i++;
989     }
990     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
991     graph->subset[i] = graph->ncc+1;
992     graph->cptr[graph->ncc] = total_counts;
993     graph->queue[total_counts] = i;
994     total_counts++;
995     nodes_touched++;
996     /* now find all other nodes having the same set of sharing subdomains */
997     for (j=i+1;j<graph->nvtxs;j++) {
998       /* check for same number of sharing subdomains, dof number and same special mark */
999       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]) {
1000         /* check for same set of sharing subdomains */
1001         same_set=PETSC_TRUE;
1002         for (k=0;k<graph->count[j];k++){
1003           if (graph->neighbours_set[i][k]!=graph->neighbours_set[j][k]) {
1004             same_set=PETSC_FALSE;
1005           }
1006         }
1007         /* I found a friend of mine */
1008         if (same_set) {
1009           graph->subset[j]=graph->ncc+1;
1010           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
1011           nodes_touched++;
1012           graph->queue[total_counts] = j;
1013           total_counts++;
1014         }
1015       }
1016     }
1017     graph->ncc++;
1018   }
1019   /* set default number of subsets (at this point no info on csr graph has been taken into account, so n_subsets = ncc */
1020   graph->n_subsets = graph->ncc;
1021   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
1022   for (i=0;i<graph->n_subsets;i++) {
1023     graph->subset_ncc[i] = 1;
1024   }
1025   /* final pointer */
1026   graph->cptr[graph->ncc] = total_counts;
1027 
1028   /* save information on subsets (needed if we have to adapt the connected components later) */
1029   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each subset */
1030   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
1031   ierr = PetscMalloc2(graph->ncc,&subset_ref_node_global,graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
1032   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
1033   for (j=0;j<graph->ncc;j++) {
1034     ierr = PetscSortIntWithArray(graph->cptr[j+1]-graph->cptr[j],&queue_global[graph->cptr[j]],&graph->queue[graph->cptr[j]]);CHKERRQ(ierr);
1035     subset_ref_node_global[j] = graph->queue[graph->cptr[j]];
1036   }
1037   graph->queue_sorted = PETSC_TRUE;
1038   if (graph->ncc) {
1039     ierr = PetscMalloc2(graph->ncc,&graph->subsets_size,graph->ncc,&graph->subsets);CHKERRQ(ierr);
1040     ierr = PetscMalloc1(graph->cptr[graph->ncc],&graph->subsets[0]);CHKERRQ(ierr);
1041     ierr = PetscMemzero(graph->subsets[0],graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
1042     for (j=1;j<graph->ncc;j++) {
1043       graph->subsets_size[j-1] = graph->cptr[j] - graph->cptr[j-1];
1044       graph->subsets[j] = graph->subsets[j-1] + graph->subsets_size[j-1];
1045     }
1046     graph->subsets_size[graph->ncc-1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc-1];
1047     for (j=0;j<graph->ncc;j++) {
1048       ierr = PetscMemcpy(graph->subsets[j],&graph->queue[graph->cptr[j]],graph->subsets_size[j]*sizeof(PetscInt));CHKERRQ(ierr);
1049     }
1050   }
1051   /* renumber reference nodes */
1052   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->l2gmap,graph->ncc,subset_ref_node_global,NULL,&k,&graph->subset_ref_node);CHKERRQ(ierr);
1053 
1054   /* free workspace */
1055   ierr = PetscFree2(subset_ref_node_global,queue_global);CHKERRQ(ierr);
1056   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1057   ierr = VecDestroy(&local_vec2);CHKERRQ(ierr);
1058   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1059   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1060   PetscFunctionReturn(0);
1061 }
1062 
1063 #undef __FUNCT__
1064 #define __FUNCT__ "PCBDDCGraphResetCSR"
1065 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1066 {
1067   PetscErrorCode ierr;
1068 
1069   PetscFunctionBegin;
1070   ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1071   ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1072   graph->nvtxs_csr = 0;
1073   PetscFunctionReturn(0);
1074 }
1075 
1076 #undef __FUNCT__
1077 #define __FUNCT__ "PCBDDCGraphReset"
1078 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1079 {
1080   PetscErrorCode ierr;
1081 
1082   PetscFunctionBegin;
1083   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
1084   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
1085   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1086   if (graph->nvtxs) {
1087     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1088   }
1089   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1090   ierr = PetscFree5(graph->count,
1091                     graph->neighbours_set,
1092                     graph->subset,
1093                     graph->which_dof,
1094                     graph->special_dof);CHKERRQ(ierr);
1095   ierr = PetscFree2(graph->cptr,graph->queue);CHKERRQ(ierr);
1096   if (graph->mirrors) {
1097     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1098   }
1099   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1100   if (graph->subsets) {
1101     ierr = PetscFree(graph->subsets[0]);CHKERRQ(ierr);
1102   }
1103   ierr = PetscFree2(graph->subsets_size,graph->subsets);CHKERRQ(ierr);
1104   graph->nvtxs = 0;
1105   graph->nvtxs_global = 0;
1106   graph->n_subsets = 0;
1107   graph->custom_minimal_size = 1;
1108   PetscFunctionReturn(0);
1109 }
1110 
1111 #undef __FUNCT__
1112 #define __FUNCT__ "PCBDDCGraphInit"
1113 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N)
1114 {
1115   PetscInt       n;
1116   PetscErrorCode ierr;
1117 
1118   PetscFunctionBegin;
1119   PetscValidPointer(graph,1);
1120   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1121   PetscValidLogicalCollectiveInt(l2gmap,N,3);
1122   /* raise an error if already allocated */
1123   if (graph->nvtxs_global) {
1124     SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1125   }
1126   /* set number of vertices */
1127   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1128   graph->l2gmap = l2gmap;
1129   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1130   graph->nvtxs = n;
1131   graph->nvtxs_global = N;
1132   /* allocate used space */
1133   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1134   ierr = PetscMalloc5(graph->nvtxs,&graph->count,
1135                       graph->nvtxs,&graph->neighbours_set,
1136                       graph->nvtxs,&graph->subset,
1137                       graph->nvtxs,&graph->which_dof,
1138                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1139   /* zeroes memory */
1140   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1141   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1142   /* use -1 as a default value for which_dof array */
1143   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1144   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1145   /* zeroes first pointer to neighbour set */
1146   if (graph->nvtxs) {
1147     graph->neighbours_set[0] = 0;
1148   }
1149   /* zeroes workspace for values of ncc */
1150   graph->subset_ncc = 0;
1151   graph->subset_ref_node = 0;
1152   PetscFunctionReturn(0);
1153 }
1154 
1155 #undef __FUNCT__
1156 #define __FUNCT__ "PCBDDCGraphDestroy"
1157 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1158 {
1159   PetscErrorCode ierr;
1160 
1161   PetscFunctionBegin;
1162   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1163   ierr = PetscFree(*graph);CHKERRQ(ierr);
1164   PetscFunctionReturn(0);
1165 }
1166 
1167 #undef __FUNCT__
1168 #define __FUNCT__ "PCBDDCGraphCreate"
1169 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1170 {
1171   PCBDDCGraph    new_graph;
1172   PetscErrorCode ierr;
1173 
1174   PetscFunctionBegin;
1175   ierr = PetscNew(&new_graph);CHKERRQ(ierr);
1176   new_graph->custom_minimal_size = 1;
1177   *graph = new_graph;
1178   PetscFunctionReturn(0);
1179 }
1180