xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision 84cbee23719c0fdecf4c07de44cb1c7015e82944)
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__ "PCBDDCGraphGetDirichletDofsB"
7 PetscErrorCode PCBDDCGraphGetDirichletDofsB(PCBDDCGraph graph, IS* dirdofs)
8 {
9   PetscErrorCode ierr;
10 
11   PetscFunctionBegin;
12   if (graph->dirdofsB) {
13     ierr = PetscObjectReference((PetscObject)graph->dirdofsB);CHKERRQ(ierr);
14   } else if (graph->has_dirichlet) {
15     PetscInt i,size;
16     PetscInt *dirdofs_idxs;
17 
18     size = 0;
19     for (i=0;i<graph->nvtxs;i++) {
20       if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
21     }
22 
23     ierr = PetscMalloc1(size,&dirdofs_idxs);CHKERRQ(ierr);
24     size = 0;
25     for (i=0;i<graph->nvtxs;i++) {
26       if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
27     }
28     ierr = ISCreateGeneral(PETSC_COMM_SELF,size,dirdofs_idxs,PETSC_OWN_POINTER,&graph->dirdofsB);CHKERRQ(ierr);
29     ierr = PetscObjectReference((PetscObject)graph->dirdofsB);CHKERRQ(ierr);
30   }
31   *dirdofs = graph->dirdofsB;
32   PetscFunctionReturn(0);
33 }
34 
35 #undef __FUNCT__
36 #define __FUNCT__ "PCBDDCGraphGetDirichletDofs"
37 PetscErrorCode PCBDDCGraphGetDirichletDofs(PCBDDCGraph graph, IS* dirdofs)
38 {
39   PetscErrorCode ierr;
40 
41   PetscFunctionBegin;
42   if (graph->dirdofs) {
43     ierr = PetscObjectReference((PetscObject)graph->dirdofs);CHKERRQ(ierr);
44   } else if (graph->has_dirichlet) {
45     PetscInt i,size;
46     PetscInt *dirdofs_idxs;
47 
48     size = 0;
49     for (i=0;i<graph->nvtxs;i++) {
50       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
51     }
52 
53     ierr = PetscMalloc1(size,&dirdofs_idxs);CHKERRQ(ierr);
54     size = 0;
55     for (i=0;i<graph->nvtxs;i++) {
56       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
57     }
58     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)graph->l2gmap),size,dirdofs_idxs,PETSC_OWN_POINTER,&graph->dirdofs);CHKERRQ(ierr);
59     ierr = PetscObjectReference((PetscObject)graph->dirdofs);CHKERRQ(ierr);
60   }
61   *dirdofs = graph->dirdofs;
62   PetscFunctionReturn(0);
63 }
64 
65 #undef __FUNCT__
66 #define __FUNCT__ "PCBDDCGraphASCIIView"
67 PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer)
68 {
69   PetscInt       i,j,tabs;
70   PetscInt*      queue_in_global_numbering;
71   PetscErrorCode ierr;
72 
73   PetscFunctionBegin;
74   ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
75   ierr = PetscViewerASCIIGetTab(viewer,&tabs);CHKERRQ(ierr);
76   ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
77   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
78   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Local BDDC graph for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
79   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Number of vertices %d\n",graph->nvtxs);CHKERRQ(ierr);
80   if (verbosity_level > 1) {
81     for (i=0;i<graph->nvtxs;i++) {
82       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d:\n",i);CHKERRQ(ierr);
83       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   which_dof: %d\n",graph->which_dof[i]);CHKERRQ(ierr);
84       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   special_dof: %d\n",graph->special_dof[i]);CHKERRQ(ierr);
85       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   neighbours: %d\n",graph->count[i]);CHKERRQ(ierr);
86       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
87       if (graph->count[i]) {
88         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of neighbours:");CHKERRQ(ierr);
89         for (j=0;j<graph->count[i];j++) {
90           ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[i][j]);CHKERRQ(ierr);
91         }
92         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
93       }
94       ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
95       ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
96       if (graph->mirrors) {
97         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   mirrors: %d\n",graph->mirrors[i]);CHKERRQ(ierr);
98         if (graph->mirrors[i]) {
99           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
100           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"     set of mirrors:");CHKERRQ(ierr);
101           for (j=0;j<graph->mirrors[i];j++) {
102             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->mirrors_set[i][j]);CHKERRQ(ierr);
103           }
104           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
105           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
106           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
107         }
108       }
109       if (verbosity_level > 2) {
110         if (graph->xadj && graph->adjncy) {
111           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   local adj list:");CHKERRQ(ierr);
112           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
113           for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
114             ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->adjncy[j]);CHKERRQ(ierr);
115           }
116           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
117           ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
118           ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
119         } else {
120           ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   no adj info\n");CHKERRQ(ierr);
121         }
122       }
123       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   interface subset id: %d\n",graph->subset[i]);CHKERRQ(ierr);
124       if (graph->subset[i] && graph->subset_ncc) {
125         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"   ncc for subset: %d\n",graph->subset_ncc[graph->subset[i]-1]);CHKERRQ(ierr);
126       }
127     }
128   }
129   ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Total number of connected components %d\n",graph->ncc);CHKERRQ(ierr);
130   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_in_global_numbering);CHKERRQ(ierr);
131   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_in_global_numbering);CHKERRQ(ierr);
132   for (i=0;i<graph->ncc;i++) {
133     PetscInt node_num=graph->queue[graph->cptr[i]];
134     PetscBool printcc = PETSC_FALSE;
135     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  %d (neighs:",i);CHKERRQ(ierr);
136     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
137     for (j=0;j<graph->count[node_num];j++) {
138       ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d",graph->neighbours_set[node_num][j]);CHKERRQ(ierr);
139     }
140     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"):");CHKERRQ(ierr);
141     if (verbosity_level > 1 || graph->twodim) {
142       printcc = PETSC_TRUE;
143     } else if (graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) {
144       printcc = PETSC_TRUE;
145     }
146     if (printcc) {
147       for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
148         ierr = PetscViewerASCIISynchronizedPrintf(viewer," %d (%d)",graph->queue[j],queue_in_global_numbering[j]);CHKERRQ(ierr);
149       }
150     }
151     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");CHKERRQ(ierr);
152     ierr = PetscViewerASCIISetTab(viewer,tabs);CHKERRQ(ierr);
153     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
154   }
155   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
156   if (graph->custom_minimal_size > 1 && verbosity_level > 1) {
157     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Custom minimal size %d\n",graph->custom_minimal_size);CHKERRQ(ierr);
158   }
159   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
160   PetscFunctionReturn(0);
161 }
162 
163 #undef __FUNCT__
164 #define __FUNCT__ "PCBDDCGraphGetCandidatesIS"
165 PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS)
166 {
167   IS             *ISForFaces,*ISForEdges,ISForVertices;
168   PetscInt       i,nfc,nec,nvc,*idx;
169   PetscErrorCode ierr;
170 
171   PetscFunctionBegin;
172   /* loop on ccs to evalute number of faces, edges and vertices */
173   nfc = 0;
174   nec = 0;
175   nvc = 0;
176   for (i=0;i<graph->ncc;i++) {
177     PetscInt repdof = graph->queue[graph->cptr[i]];
178     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
179       if (graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
180         nfc++;
181       } else { /* note that nec will be zero in 2d */
182         nec++;
183       }
184     } else {
185       nvc += graph->cptr[i+1]-graph->cptr[i];
186     }
187   }
188 
189   /* check if we are in 2D or 3D */
190   if (graph->twodim) { /* we are in a 2D case -> edges are shared by 2 subregions and faces don't exist */
191     nec = nfc;
192     nfc = 0;
193   }
194 
195   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
196   if (FacesIS) {
197     ierr = PetscMalloc1(nfc,&ISForFaces);CHKERRQ(ierr);
198   }
199   if (EdgesIS) {
200     ierr = PetscMalloc1(nec,&ISForEdges);CHKERRQ(ierr);
201   }
202   if (VerticesIS) {
203     ierr = PetscMalloc1(nvc,&idx);CHKERRQ(ierr);
204   }
205 
206   /* loop on ccs to compute index sets for faces and edges */
207   if (!graph->queue_sorted) {
208     PetscInt *queue_global;
209 
210     ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
211     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
212     for (i=0;i<graph->ncc;i++) {
213       ierr = PetscSortIntWithArray(graph->cptr[i+1]-graph->cptr[i],&queue_global[graph->cptr[i]],&graph->queue[graph->cptr[i]]);CHKERRQ(ierr);
214     }
215     ierr = PetscFree(queue_global);CHKERRQ(ierr);
216     graph->queue_sorted = PETSC_TRUE;
217   }
218   nfc = 0;
219   nec = 0;
220   for (i=0;i<graph->ncc;i++) {
221     PetscInt repdof = graph->queue[graph->cptr[i]];
222     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
223       if (graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
224         if (graph->twodim) {
225           if (EdgesIS) {
226             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
227           }
228           nec++;
229         } else {
230           if (FacesIS) {
231             ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForFaces[nfc]);CHKERRQ(ierr);
232           }
233           nfc++;
234         }
235       } else {
236         if (EdgesIS) {
237           ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],&graph->queue[graph->cptr[i]],PETSC_COPY_VALUES,&ISForEdges[nec]);CHKERRQ(ierr);
238         }
239         nec++;
240       }
241     }
242   }
243   /* index set for vertices */
244   if (VerticesIS) {
245     nvc = 0;
246     for (i=0;i<graph->ncc;i++) {
247       if (graph->cptr[i+1]-graph->cptr[i] <= graph->custom_minimal_size) {
248         PetscInt j;
249 
250         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
251           idx[nvc]=graph->queue[j];
252           nvc++;
253         }
254       }
255     }
256     /* sort vertex set (by local ordering) */
257     ierr = PetscSortInt(nvc,idx);CHKERRQ(ierr);
258     ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,idx,PETSC_OWN_POINTER,&ISForVertices);CHKERRQ(ierr);
259   }
260   /* get back info */
261   if (n_faces) *n_faces = nfc;
262   if (FacesIS) {
263     *FacesIS = ISForFaces;
264   }
265   if (n_edges) *n_edges = nec;
266   if (EdgesIS) {
267     *EdgesIS = ISForEdges;
268   }
269   if (VerticesIS) {
270     *VerticesIS = ISForVertices;
271   }
272   PetscFunctionReturn(0);
273 }
274 
275 #undef __FUNCT__
276 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponents"
277 PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph)
278 {
279   PetscBool      adapt_interface_reduced;
280   MPI_Comm       interface_comm;
281   PetscMPIInt    size;
282   PetscInt       i;
283   PetscBool      twodim;
284   PetscErrorCode ierr;
285 
286   PetscFunctionBegin;
287   /* compute connected components locally */
288   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&interface_comm);CHKERRQ(ierr);
289   ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
290   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
291   ierr = MPI_Comm_size(interface_comm,&size);CHKERRQ(ierr);
292   adapt_interface_reduced = PETSC_FALSE;
293   if (size > 1) {
294     PetscInt i;
295     PetscBool adapt_interface = PETSC_FALSE;
296     for (i=0;i<graph->n_subsets;i++) {
297       /* We are not sure that on a given subset of the local interface,
298          with two connected components, the latters be the same among sharing subdomains */
299       if (graph->subset_ncc[i] > 1) {
300         adapt_interface = PETSC_TRUE;
301         break;
302       }
303     }
304     ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_BOOL,MPI_LOR,interface_comm);CHKERRQ(ierr);
305   }
306 
307   if (graph->n_subsets && adapt_interface_reduced) {
308     /* old csr stuff */
309     PetscInt    *aux_new_xadj,*new_xadj,*new_adjncy;
310     PetscInt    *old_xadj,*old_adjncy;
311     PetscBT     subset_cc_adapt;
312     /* MPI */
313     MPI_Request *send_requests,*recv_requests;
314     PetscInt    *send_buffer,*recv_buffer;
315     PetscInt    sum_requests,start_of_recv,start_of_send;
316     PetscInt    *cum_recv_counts;
317     /* others */
318     PetscInt    *labels;
319     PetscInt    global_subset_counter;
320     PetscInt    j,k,s;
321 
322     /* Retrict adjacency graph using information from previously computed connected components */
323     ierr = PetscMalloc1(graph->nvtxs,&aux_new_xadj);CHKERRQ(ierr);
324     for (i=0;i<graph->nvtxs;i++) {
325       aux_new_xadj[i]=1;
326     }
327     for (i=0;i<graph->ncc;i++) {
328       k = graph->cptr[i+1]-graph->cptr[i];
329       for (j=0;j<k;j++) {
330         aux_new_xadj[graph->queue[graph->cptr[i]+j]]=k;
331       }
332     }
333     j = 0;
334     for (i=0;i<graph->nvtxs;i++) {
335       j += aux_new_xadj[i];
336     }
337     ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
338     ierr = PetscMalloc1(j,&new_adjncy);CHKERRQ(ierr);
339     new_xadj[0]=0;
340     for (i=0;i<graph->nvtxs;i++) {
341       new_xadj[i+1]=new_xadj[i]+aux_new_xadj[i];
342       if (aux_new_xadj[i]==1) {
343         new_adjncy[new_xadj[i]]=i;
344       }
345     }
346     ierr = PetscFree(aux_new_xadj);CHKERRQ(ierr);
347     ierr = PetscMalloc1(graph->nvtxs,&labels);CHKERRQ(ierr);
348     ierr = PetscMemzero(labels,graph->nvtxs*sizeof(*labels));CHKERRQ(ierr);
349     for (i=0;i<graph->ncc;i++) {
350       k = graph->cptr[i+1]-graph->cptr[i];
351       for (j=0;j<k;j++) {
352         ierr = PetscMemcpy(&new_adjncy[new_xadj[graph->queue[graph->cptr[i]+j]]],&graph->queue[graph->cptr[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
353         labels[graph->queue[graph->cptr[i]+j]] = i;
354       }
355     }
356     /* set temporarly new CSR into graph */
357     old_xadj = graph->xadj;
358     old_adjncy = graph->adjncy;
359     graph->xadj = new_xadj;
360     graph->adjncy = new_adjncy;
361     /* allocate some space */
362     ierr = PetscMalloc1(graph->n_subsets+1,&cum_recv_counts);CHKERRQ(ierr);
363     ierr = PetscMemzero(cum_recv_counts,(graph->n_subsets+1)*sizeof(*cum_recv_counts));CHKERRQ(ierr);
364     /* first count how many neighbours per connected component I will receive from */
365     cum_recv_counts[0]=0;
366     for (i=0;i<graph->n_subsets;i++) {
367       cum_recv_counts[i+1]=cum_recv_counts[i]+graph->count[graph->subsets[i][0]];
368     }
369     ierr = PetscMalloc1(cum_recv_counts[graph->n_subsets],&recv_buffer);CHKERRQ(ierr);
370     ierr = PetscMalloc2(cum_recv_counts[graph->n_subsets],&send_requests,cum_recv_counts[graph->n_subsets],&recv_requests);CHKERRQ(ierr);
371     for (i=0;i<cum_recv_counts[graph->n_subsets];i++) {
372       send_requests[i]=MPI_REQUEST_NULL;
373       recv_requests[i]=MPI_REQUEST_NULL;
374     }
375     /* exchange with my neighbours the number of my connected components on the subset of interface */
376     sum_requests = 0;
377     for (i=0;i<graph->n_subsets;i++) {
378       PetscMPIInt neigh,tag;
379 
380       j = graph->subsets[i][0];
381       ierr = PetscMPIIntCast(2*graph->subset_ref_node[i],&tag);CHKERRQ(ierr);
382       for (k=0;k<graph->count[j];k++) {
383         ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
384         ierr = MPI_Isend(&graph->subset_ncc[i],1,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
385         ierr = MPI_Irecv(&recv_buffer[sum_requests],1,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
386         sum_requests++;
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     /* determine the subsets I have to adapt */
392     ierr = PetscBTCreate(graph->n_subsets,&subset_cc_adapt);CHKERRQ(ierr);
393     ierr = PetscBTMemzero(graph->n_subsets,subset_cc_adapt);CHKERRQ(ierr);
394     for (i=0;i<graph->n_subsets;i++) {
395       for (j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
396         /* adapt if more than one cc is present */
397          if (graph->subset_ncc[i] > 1 || recv_buffer[j] > 1) {
398           ierr = PetscBTSet(subset_cc_adapt,i);
399           break;
400         }
401       }
402     }
403     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
404     /* determine send/recv buffers sizes */
405     j = 0;
406     for (i=0;i<graph->n_subsets;i++) {
407       if (PetscBTLookup(subset_cc_adapt,i)) {
408         j += graph->subsets_size[i];
409       }
410     }
411     k = 0;
412     for (i=0;i<graph->n_subsets;i++) {
413       if (PetscBTLookup(subset_cc_adapt,i)) {
414         k += (cum_recv_counts[i+1]-cum_recv_counts[i])*graph->subsets_size[i];
415       }
416     }
417     ierr = PetscMalloc2(j,&send_buffer,k,&recv_buffer);CHKERRQ(ierr);
418 
419     /* fill send buffer */
420     j = 0;
421     for (i=0;i<graph->n_subsets;i++) {
422       if (PetscBTLookup(subset_cc_adapt,i)) {
423         for (k=0;k<graph->subsets_size[i];k++) {
424           send_buffer[j++] = labels[graph->subsets[i][k]];
425         }
426       }
427     }
428     ierr = PetscFree(labels);CHKERRQ(ierr);
429 
430     /* now exchange the data */
431     start_of_recv = 0;
432     start_of_send = 0;
433     sum_requests = 0;
434     for (i=0;i<graph->n_subsets;i++) {
435       if (PetscBTLookup(subset_cc_adapt,i)) {
436         PetscMPIInt neigh,tag;
437         PetscInt    size_of_send = graph->subsets_size[i];
438 
439         j = graph->subsets[i][0];
440         ierr = PetscMPIIntCast(2*graph->subset_ref_node[i]+1,&tag);CHKERRQ(ierr);
441         for (k=0;k<graph->count[j];k++) {
442           ierr = PetscMPIIntCast(graph->neighbours_set[j][k],&neigh);CHKERRQ(ierr);
443           ierr = MPI_Isend(&send_buffer[start_of_send],size_of_send,MPIU_INT,neigh,tag,interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
444           ierr = MPI_Irecv(&recv_buffer[start_of_recv],size_of_send,MPIU_INT,neigh,tag,interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
445           start_of_recv += size_of_send;
446           sum_requests++;
447         }
448         start_of_send += size_of_send;
449       }
450     }
451     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
452     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
453     ierr = PetscFree2(send_requests,recv_requests);CHKERRQ(ierr);
454 
455     start_of_recv = 0;
456     global_subset_counter = 0;
457     for (i=0;i<graph->n_subsets;i++) {
458       if (PetscBTLookup(subset_cc_adapt,i)) {
459         PetscInt **temp_buffer,temp_buffer_size,*private_label;
460 
461         /* allocate some temporary space */
462         temp_buffer_size = graph->subsets_size[i];
463         ierr = PetscMalloc1(temp_buffer_size,&temp_buffer);CHKERRQ(ierr);
464         ierr = PetscMalloc1(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i]),&temp_buffer[0]);CHKERRQ(ierr);
465         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
466         for (j=1;j<temp_buffer_size;j++) {
467           temp_buffer[j] = temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
468         }
469         /* analyze contributions from neighbouring subdomains for i-th subset
470            temp buffer structure:
471            supposing part of the interface has dimension 5
472            e.g with global dofs 0,1,2,3,4, locally ordered on the current process as 0,4,3,1,2
473            3 neighs procs having connected components:
474              neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
475              neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
476              neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
477            tempbuffer (row-oriented) will be filled as:
478              [ 4, 3, 1;
479                4, 2, 1;
480                7, 2, 6;
481                4, 3, 5;
482                7, 2, 6; ];
483            This way we can simply find intersections of ccs among neighs.
484            The graph->subset array will need to be modified. The output for the example is [0], [1], [2 3], [4];
485                                                                                                                                    */
486         for (j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
487           for (k=0;k<temp_buffer_size;k++) {
488             temp_buffer[k][j] = recv_buffer[start_of_recv+k];
489           }
490           start_of_recv += temp_buffer_size;
491         }
492         ierr = PetscMalloc1(temp_buffer_size,&private_label);CHKERRQ(ierr);
493         ierr = PetscMemzero(private_label,temp_buffer_size*sizeof(*private_label));CHKERRQ(ierr);
494         for (j=0;j<temp_buffer_size;j++) {
495           if (!private_label[j]) { /* found a new cc  */
496             PetscBool same_set;
497 
498             global_subset_counter++;
499             private_label[j] = global_subset_counter;
500             for (k=j+1;k<temp_buffer_size;k++) { /* check for other nodes in new cc */
501               same_set = PETSC_TRUE;
502               for (s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++) {
503                 if (temp_buffer[j][s] != temp_buffer[k][s]) {
504                   same_set = PETSC_FALSE;
505                   break;
506                 }
507               }
508               if (same_set) {
509                 private_label[k] = global_subset_counter;
510               }
511             }
512           }
513         }
514         /* insert private labels in graph structure */
515         for (j=0;j<graph->subsets_size[i];j++) {
516           graph->subset[graph->subsets[i][j]] = graph->n_subsets+private_label[j];
517         }
518         ierr = PetscFree(private_label);CHKERRQ(ierr);
519         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
520         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
521       }
522     }
523     ierr = PetscFree2(send_buffer,recv_buffer);CHKERRQ(ierr);
524     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
525     ierr = PetscBTDestroy(&subset_cc_adapt);CHKERRQ(ierr);
526     /* We are ready to find for connected components which are consistent among neighbouring subdomains */
527     if (global_subset_counter) {
528       PetscInt o_nsubs;
529 
530       ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
531       global_subset_counter = 0;
532       for (i=0;i<graph->nvtxs;i++) {
533         if (graph->subset[i] && !PetscBTLookup(graph->touched,i)) {
534           global_subset_counter++;
535           for (j=i+1;j<graph->nvtxs;j++) {
536             if (!PetscBTLookup(graph->touched,j) && graph->subset[j]==graph->subset[i]) {
537               graph->subset[j] = global_subset_counter;
538               ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
539             }
540           }
541           graph->subset[i] = global_subset_counter;
542           ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
543         }
544       }
545       /* disable subdomains info since it is local (info contained in CSR) */
546       o_nsubs = graph->n_local_subs;
547       graph->n_local_subs = 0;
548       /* refine connected components locally */
549       ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
550       /* restore subdomains info */
551       graph->n_local_subs = o_nsubs;
552     }
553     /* restore original CSR graph of dofs */
554     ierr = PetscFree(new_xadj);CHKERRQ(ierr);
555     ierr = PetscFree(new_adjncy);CHKERRQ(ierr);
556     graph->xadj = old_xadj;
557     graph->adjncy = old_adjncy;
558   }
559 
560   /* Determine if we are in 2D or 3D */
561   twodim  = PETSC_TRUE;
562   for (i=0;i<graph->ncc;i++) {
563     PetscInt repdof = graph->queue[graph->cptr[i]];
564     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
565       if (graph->count[repdof] > 1 || graph->special_dof[repdof] == PCBDDCGRAPH_NEUMANN_MARK) {
566         twodim = PETSC_FALSE;
567         break;
568       }
569     }
570   }
571   ierr = MPI_Allreduce(&twodim,&graph->twodim,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
572   PetscFunctionReturn(0);
573 }
574 
575 /* The following code has been adapted from function IsConnectedSubdomain contained
576    in source file contig.c of METIS library (version 5.0.1)
577    It finds connected components for each subset  */
578 #undef __FUNCT__
579 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponentsLocal"
580 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
581 {
582   PetscInt       i,j,k,first,last,nleft,ncc,pid,cum_queue,n,ncc_pid;
583   PetscMPIInt    size;
584   PetscErrorCode ierr;
585 
586   PetscFunctionBegin;
587   /* quiet return if no csr info is available */
588   if ((!graph->xadj || !graph->adjncy) && !graph->n_local_subs) {
589     PetscFunctionReturn(0);
590   }
591 
592   /* reset any previous search of connected components */
593   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
594   graph->n_subsets = 0;
595   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&size);CHKERRQ(ierr);
596   if (size == 1) {
597     if (graph->nvtxs) {
598       graph->n_subsets = 1;
599       for (i=0;i<graph->nvtxs;i++) {
600         graph->subset[i] = 1;
601       }
602     }
603   } else {
604     for (i=0;i<graph->nvtxs;i++) {
605       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
606         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
607         graph->subset[i] = 0;
608       }
609       graph->n_subsets = PetscMax(graph->n_subsets,graph->subset[i]);
610     }
611   }
612   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
613   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
614 
615   /* begin search for connected components */
616   cum_queue = 0;
617   ncc = 0;
618   for (n=0;n<graph->n_subsets;n++) {
619     pid = n+1;  /* partition labeled by 0 is discarded */
620     nleft = 0;
621     for (i=0;i<graph->nvtxs;i++) {
622       if (graph->subset[i] == pid) {
623         nleft++;
624       }
625     }
626     for (i=0; i<graph->nvtxs; i++) {
627       if (graph->subset[i] == pid) {
628         break;
629       }
630     }
631     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
632     graph->queue[cum_queue] = i;
633     first = 0;
634     last = 1;
635     graph->cptr[ncc] = cum_queue;
636     ncc_pid = 0;
637     while (first != nleft) {
638       if (first == last) {
639         graph->cptr[++ncc] = first+cum_queue;
640         ncc_pid++;
641         for (i=0; i<graph->nvtxs; i++) {
642           if (graph->subset[i] == pid && !PetscBTLookup(graph->touched,i)) {
643             break;
644           }
645         }
646         graph->queue[cum_queue+last] = i;
647         last++;
648         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
649       }
650       i = graph->queue[cum_queue+first];
651       first++;
652       if (!graph->xadj || !graph->adjncy) { /* sub info only, loop over all remaining vertices */
653         for (k=i+1;k<graph->nvtxs;k++) {
654           if (!PetscBTLookup(graph->touched,k) && graph->subset[k] == pid && graph->local_subs[i] == graph->local_subs[k]) {
655             graph->queue[cum_queue+last] = k;
656             last++;
657             ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
658           }
659         }
660       } else {
661         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
662           PetscBool same_sub;
663 
664           k = graph->adjncy[j];
665           /* get local subdomain id if needed */
666           if (graph->n_local_subs) {
667             same_sub = (PetscBool)(graph->local_subs[i] == graph->local_subs[j]);
668           } else {
669             same_sub = PETSC_TRUE;
670           }
671           if (!PetscBTLookup(graph->touched,k) && graph->subset[k] == pid && same_sub) {
672             graph->queue[cum_queue+last] = k;
673             last++;
674             ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
675           }
676         }
677       }
678     }
679     graph->cptr[++ncc] = first+cum_queue;
680     ncc_pid++;
681     cum_queue = graph->cptr[ncc];
682     graph->subset_ncc[n] = ncc_pid;
683   }
684   graph->ncc = ncc;
685   graph->queue_sorted = PETSC_FALSE;
686   PetscFunctionReturn(0);
687 }
688 
689 #undef __FUNCT__
690 #define __FUNCT__ "PCBDDCGraphSetUp"
691 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
692 {
693   VecScatter     scatter_ctx;
694   Vec            local_vec,local_vec2,global_vec;
695   IS             to,from,subset,subset_n;
696   MPI_Comm       comm;
697   PetscScalar    *array,*array2;
698   const PetscInt *is_indices;
699   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global;
700   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
701   PetscMPIInt    size;
702   PetscBool      same_set,mirrors_found;
703   PetscErrorCode ierr;
704 
705   PetscFunctionBegin;
706   graph->has_dirichlet = PETSC_FALSE;
707   if (dirichlet_is) {
708     PetscCheckSameComm(graph->l2gmap,1,dirichlet_is,4);
709     graph->has_dirichlet = PETSC_TRUE;
710   }
711   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
712   /* custom_minimal_size */
713   graph->custom_minimal_size = PetscMax(graph->custom_minimal_size,custom_minimal_size);
714   /* get info l2gmap and allocate work vectors  */
715   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
716   /* check if we have any local periodic nodes (periodic BCs) */
717   mirrors_found = PETSC_FALSE;
718   if (graph->nvtxs && n_neigh) {
719     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
720     for (i=0; i<n_shared[0]; i++) {
721       if (graph->count[shared[0][i]] > 1) {
722         mirrors_found = PETSC_TRUE;
723         break;
724       }
725     }
726   }
727   /* create some workspace objects */
728   local_vec = NULL;
729   local_vec2 = NULL;
730   global_vec = NULL;
731   to = NULL;
732   from = NULL;
733   scatter_ctx = NULL;
734   if (n_ISForDofs || dirichlet_is || neumann_is || custom_primal_vertices) {
735     ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
736     ierr = VecSetSizes(local_vec,PETSC_DECIDE,graph->nvtxs);CHKERRQ(ierr);
737     ierr = VecSetType(local_vec,VECSTANDARD);CHKERRQ(ierr);
738     ierr = VecDuplicate(local_vec,&local_vec2);CHKERRQ(ierr);
739     ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
740     ierr = VecSetSizes(global_vec,PETSC_DECIDE,graph->nvtxs_global);CHKERRQ(ierr);
741     ierr = VecSetType(global_vec,VECSTANDARD);CHKERRQ(ierr);
742     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
743     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
744     ierr = VecScatterCreate(global_vec,from,local_vec,to,&scatter_ctx);CHKERRQ(ierr);
745   } else if (mirrors_found) {
746     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
747     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
748   }
749   /* compute local mirrors (if any) */
750   if (mirrors_found) {
751     PetscInt *local_indices,*global_indices;
752     /* get arrays of local and global indices */
753     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
754     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
755     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
756     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
757     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
758     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
759     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
760     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
761     /* allocate space for mirrors */
762     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
763     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
764     graph->mirrors_set[0] = 0;
765 
766     k=0;
767     for (i=0;i<n_shared[0];i++) {
768       j=shared[0][i];
769       if (graph->count[j] > 1) {
770         graph->mirrors[j]++;
771         k++;
772       }
773     }
774     /* allocate space for set of mirrors */
775     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
776     for (i=1;i<graph->nvtxs;i++)
777       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
778 
779     /* fill arrays */
780     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
781     for (j=0;j<n_shared[0];j++) {
782       i=shared[0][j];
783       if (graph->count[i] > 1)
784         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
785     }
786     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
787     for (i=0;i<graph->nvtxs;i++) {
788       if (graph->mirrors[i] > 0) {
789         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
790         j = global_indices[k];
791         while ( k > 0 && global_indices[k-1] == j) k--;
792         for (j=0;j<graph->mirrors[i];j++) {
793           graph->mirrors_set[i][j]=local_indices[k+j];
794         }
795         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
796       }
797     }
798     ierr = PetscFree(local_indices);CHKERRQ(ierr);
799     ierr = PetscFree(global_indices);CHKERRQ(ierr);
800   }
801   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
802   ierr = ISDestroy(&to);CHKERRQ(ierr);
803   ierr = ISDestroy(&from);CHKERRQ(ierr);
804 
805   /* Count total number of neigh per node */
806   k=0;
807   for (i=1;i<n_neigh;i++) {
808     k += n_shared[i];
809     for (j=0;j<n_shared[i];j++) {
810       graph->count[shared[i][j]] += 1;
811     }
812   }
813   /* Allocate space for storing the set of neighbours for each node */
814   if (graph->nvtxs) {
815     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
816   }
817   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
818     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
819   }
820   /* Get information for sharing subdomains */
821   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
822   for (i=1;i<n_neigh;i++) { /* dont count myself */
823     s = n_shared[i];
824     for (j=0;j<s;j++) {
825       k = shared[i][j];
826       graph->neighbours_set[k][graph->count[k]] = neigh[i];
827       graph->count[k] += 1;
828     }
829   }
830   /* sort set of sharing subdomains */
831   for (i=0;i<graph->nvtxs;i++) {
832     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
833   }
834   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
835   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
836 
837   /*
838      Get info for dofs splitting
839      User can specify just a subset; an additional field is considered as a complementary field
840   */
841   for (i=0;i<graph->nvtxs;i++) {
842     graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
843   }
844   if (n_ISForDofs) {
845     ierr = VecSet(local_vec,-1.0);CHKERRQ(ierr);
846   }
847   for (i=0;i<n_ISForDofs;i++) {
848     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
849     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
850     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
851     for (j=0;j<is_size;j++) {
852       if (is_indices[j] > -1 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
853         graph->which_dof[is_indices[j]] = i;
854         array[is_indices[j]] = 1.*i;
855       }
856     }
857     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
858     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
859   }
860   /* Check consistency among neighbours */
861   if (n_ISForDofs) {
862     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
863     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
864     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
865     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
866     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
867     ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
868     for (i=0;i<graph->nvtxs;i++){
869       PetscInt field1,field2;
870 
871       field1 = (PetscInt)PetscRealPart(array[i]);
872       field2 = (PetscInt)PetscRealPart(array2[i]);
873       if (field1 != field2) {
874         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);
875       }
876     }
877     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
878     ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
879   }
880   if (neumann_is || dirichlet_is) {
881     /* Take into account Neumann nodes */
882     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
883     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
884     if (neumann_is) {
885       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
886       ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
887       ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
888       for (i=0;i<is_size;i++) {
889         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
890           array[is_indices[i]] = 1.0;
891         }
892       }
893       ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
894       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
895     }
896     /* Neumann nodes: impose consistency among neighbours */
897     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
898     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
899     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
900     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
901     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
902     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
903     for (i=0;i<graph->nvtxs;i++) {
904       if (PetscRealPart(array[i]) > 0.1) {
905         graph->special_dof[i] = PCBDDCGRAPH_NEUMANN_MARK;
906       }
907     }
908     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
909     /* Take into account Dirichlet nodes */
910     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
911     if (dirichlet_is) {
912       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
913       ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
914       ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
915       ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
916       for (i=0;i<is_size;i++){
917         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
918           k = is_indices[i];
919           if (!PetscBTLookup(graph->touched,k)) {
920             if (PetscRealPart(array[k]) > 0.1) {
921               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);
922             }
923             array2[k] = 1.0;
924           }
925         }
926       }
927       ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
928       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
929       ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
930     }
931     /* Dirichlet nodes: impose consistency among neighbours */
932     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
933     ierr = VecScatterBegin(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
934     ierr = VecScatterEnd(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
935     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
936     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
937     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
938     for (i=0;i<graph->nvtxs;i++) {
939       if (PetscRealPart(array[i]) > 0.1) {
940         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
941         graph->subset[i] = 0; /* dirichlet nodes treated as internal -> is it ok? */
942         graph->special_dof[i] = PCBDDCGRAPH_DIRICHLET_MARK;
943       }
944     }
945     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
946   }
947   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
948   if (graph->mirrors) {
949     for (i=0;i<graph->nvtxs;i++)
950       if (graph->mirrors[i])
951         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
952 
953     if (graph->xadj && graph->adjncy) {
954       PetscInt *new_xadj,*new_adjncy;
955       /* sort CSR graph */
956       for (i=0;i<graph->nvtxs;i++)
957         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
958 
959       /* adapt local CSR graph in case of local periodicity */
960       k=0;
961       for (i=0;i<graph->nvtxs;i++)
962         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
963           k += graph->mirrors[graph->adjncy[j]];
964 
965       ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
966       ierr = PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy);CHKERRQ(ierr);
967       new_xadj[0]=0;
968       for (i=0;i<graph->nvtxs;i++) {
969         k = graph->xadj[i+1]-graph->xadj[i];
970         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
971         new_xadj[i+1]=new_xadj[i]+k;
972         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
973           k = graph->mirrors[graph->adjncy[j]];
974           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
975           new_xadj[i+1]+=k;
976         }
977         k = new_xadj[i+1]-new_xadj[i];
978         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
979         new_xadj[i+1]=new_xadj[i]+k;
980       }
981       /* set new CSR into graph */
982       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
983       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
984       graph->xadj = new_xadj;
985       graph->adjncy = new_adjncy;
986     }
987   }
988 
989   /* mark special nodes (if any) -> each will become a single node equivalence class */
990   if (custom_primal_vertices) {
991     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
992     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
993     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
994     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
995     for (i=0;i<is_size;i++){
996       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
997         array[is_indices[i]] = 1.0;
998       }
999     }
1000     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1001     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1002     /* special nodes: impose consistency among neighbours */
1003     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1004     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1005     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1006     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1007     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1008     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1009     j = 0;
1010     for (i=0;i<graph->nvtxs;i++) {
1011       if (PetscRealPart(array[i]) > 0.1 && graph->special_dof[i] != PCBDDCGRAPH_DIRICHLET_MARK) {
1012         graph->special_dof[i] = PCBDDCGRAPH_SPECIAL_MARK-j;
1013         j++;
1014       }
1015     }
1016     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1017   }
1018 
1019   /* mark interior nodes as touched and belonging to partition number 0 */
1020   for (i=0;i<graph->nvtxs;i++) {
1021     if (!graph->count[i]) {
1022       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
1023       graph->subset[i] = 0;
1024     }
1025   }
1026   /* init graph structure and compute default subsets */
1027   nodes_touched=0;
1028   for (i=0;i<graph->nvtxs;i++) {
1029     if (PetscBTLookup(graph->touched,i)) {
1030       nodes_touched++;
1031     }
1032   }
1033   i = 0;
1034   graph->ncc = 0;
1035   total_counts = 0;
1036 
1037   /* allocated space for queues */
1038   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1039   if (size == 1) {
1040     ierr = PetscMalloc2(graph->nvtxs+1,&graph->cptr,graph->nvtxs,&graph->queue);CHKERRQ(ierr);
1041   } else {
1042     PetscInt nused = graph->nvtxs - nodes_touched;
1043     ierr = PetscMalloc2(nused+1,&graph->cptr,nused,&graph->queue);CHKERRQ(ierr);
1044   }
1045 
1046   while (nodes_touched<graph->nvtxs) {
1047     /*  find first untouched node in local ordering */
1048     while (PetscBTLookup(graph->touched,i)) {
1049       i++;
1050     }
1051     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
1052     graph->subset[i] = graph->ncc+1;
1053     graph->cptr[graph->ncc] = total_counts;
1054     graph->queue[total_counts] = i;
1055     total_counts++;
1056     nodes_touched++;
1057     /* now find all other nodes having the same set of sharing subdomains */
1058     for (j=i+1;j<graph->nvtxs;j++) {
1059       /* check for same number of sharing subdomains, dof number and same special mark */
1060       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]) {
1061         /* check for same set of sharing subdomains */
1062         same_set=PETSC_TRUE;
1063         for (k=0;k<graph->count[j];k++){
1064           if (graph->neighbours_set[i][k]!=graph->neighbours_set[j][k]) {
1065             same_set=PETSC_FALSE;
1066           }
1067         }
1068         /* I found a friend of mine */
1069         if (same_set) {
1070           graph->subset[j]=graph->ncc+1;
1071           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
1072           nodes_touched++;
1073           graph->queue[total_counts] = j;
1074           total_counts++;
1075         }
1076       }
1077     }
1078     graph->ncc++;
1079   }
1080   /* set default number of subsets (at this point no info on csr graph has been taken into account, so n_subsets = ncc */
1081   graph->n_subsets = graph->ncc;
1082   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
1083   for (i=0;i<graph->n_subsets;i++) {
1084     graph->subset_ncc[i] = 1;
1085   }
1086   /* final pointer */
1087   graph->cptr[graph->ncc] = total_counts;
1088 
1089   /* save information on subsets (needed if we have to adapt the connected components later) */
1090   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each subset */
1091   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
1092   ierr = PetscMalloc1(graph->ncc,&graph->subset_ref_node);CHKERRQ(ierr);
1093   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
1094   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
1095   for (j=0;j<graph->ncc;j++) {
1096     ierr = PetscSortIntWithArray(graph->cptr[j+1]-graph->cptr[j],&queue_global[graph->cptr[j]],&graph->queue[graph->cptr[j]]);CHKERRQ(ierr);
1097     graph->subset_ref_node[j] = graph->queue[graph->cptr[j]];
1098   }
1099   ierr = PetscFree(queue_global);CHKERRQ(ierr);
1100   graph->queue_sorted = PETSC_TRUE;
1101   if (graph->ncc) {
1102     ierr = PetscMalloc2(graph->ncc,&graph->subsets_size,graph->ncc,&graph->subsets);CHKERRQ(ierr);
1103     ierr = PetscMalloc1(graph->cptr[graph->ncc],&graph->subsets[0]);CHKERRQ(ierr);
1104     ierr = PetscMemzero(graph->subsets[0],graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
1105     for (j=1;j<graph->ncc;j++) {
1106       graph->subsets_size[j-1] = graph->cptr[j] - graph->cptr[j-1];
1107       graph->subsets[j] = graph->subsets[j-1] + graph->subsets_size[j-1];
1108     }
1109     graph->subsets_size[graph->ncc-1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc-1];
1110     for (j=0;j<graph->ncc;j++) {
1111       ierr = PetscMemcpy(graph->subsets[j],&graph->queue[graph->cptr[j]],graph->subsets_size[j]*sizeof(PetscInt));CHKERRQ(ierr);
1112     }
1113   }
1114   /* renumber reference nodes */
1115   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->ncc,graph->subset_ref_node,PETSC_COPY_VALUES,&subset_n);CHKERRQ(ierr);
1116   ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,subset_n,&subset);CHKERRQ(ierr);
1117   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1118   ierr = PCBDDCSubsetNumbering(subset,NULL,NULL,&subset_n);CHKERRQ(ierr);
1119   ierr = ISDestroy(&subset);CHKERRQ(ierr);
1120   ierr = ISGetLocalSize(subset_n,&k);CHKERRQ(ierr);
1121   if (k != graph->ncc) {
1122     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %d != %d",k,graph->ncc);
1123   }
1124   ierr = ISGetIndices(subset_n,&is_indices);CHKERRQ(ierr);
1125   ierr = PetscMemcpy(graph->subset_ref_node,is_indices,graph->ncc*sizeof(PetscInt));CHKERRQ(ierr);
1126   ierr = ISRestoreIndices(subset_n,&is_indices);CHKERRQ(ierr);
1127   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1128 
1129   /* free workspace */
1130   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1131   ierr = VecDestroy(&local_vec2);CHKERRQ(ierr);
1132   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1133   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1134   PetscFunctionReturn(0);
1135 }
1136 
1137 #undef __FUNCT__
1138 #define __FUNCT__ "PCBDDCGraphResetCSR"
1139 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1140 {
1141   PetscErrorCode ierr;
1142 
1143   PetscFunctionBegin;
1144   ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1145   ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1146   graph->nvtxs_csr = 0;
1147   PetscFunctionReturn(0);
1148 }
1149 
1150 #undef __FUNCT__
1151 #define __FUNCT__ "PCBDDCGraphReset"
1152 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1153 {
1154   PetscErrorCode ierr;
1155 
1156   PetscFunctionBegin;
1157   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
1158   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
1159   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1160   if (graph->nvtxs) {
1161     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1162   }
1163   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1164   ierr = PetscFree5(graph->count,
1165                     graph->neighbours_set,
1166                     graph->subset,
1167                     graph->which_dof,
1168                     graph->special_dof);CHKERRQ(ierr);
1169   ierr = PetscFree2(graph->cptr,graph->queue);CHKERRQ(ierr);
1170   if (graph->mirrors) {
1171     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1172   }
1173   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1174   if (graph->subsets) {
1175     ierr = PetscFree(graph->subsets[0]);CHKERRQ(ierr);
1176   }
1177   ierr = PetscFree2(graph->subsets_size,graph->subsets);CHKERRQ(ierr);
1178   ierr = ISDestroy(&graph->dirdofs);CHKERRQ(ierr);
1179   ierr = ISDestroy(&graph->dirdofsB);CHKERRQ(ierr);
1180   if (graph->n_local_subs) {
1181     ierr = PetscFree(graph->local_subs);CHKERRQ(ierr);
1182   }
1183   ierr = PCBDDCGraphResetCSR(graph);CHKERRQ(ierr);
1184   graph->has_dirichlet = PETSC_FALSE;
1185   graph->nvtxs = 0;
1186   graph->nvtxs_global = 0;
1187   graph->n_subsets = 0;
1188   graph->custom_minimal_size = 1;
1189   graph->n_local_subs = 0;
1190   PetscFunctionReturn(0);
1191 }
1192 
1193 #undef __FUNCT__
1194 #define __FUNCT__ "PCBDDCGraphInit"
1195 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N)
1196 {
1197   PetscInt       n;
1198   PetscErrorCode ierr;
1199 
1200   PetscFunctionBegin;
1201   PetscValidPointer(graph,1);
1202   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1203   PetscValidLogicalCollectiveInt(l2gmap,N,3);
1204   /* raise an error if already allocated */
1205   if (graph->nvtxs_global) {
1206     SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1207   }
1208   /* set number of vertices */
1209   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1210   graph->l2gmap = l2gmap;
1211   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1212   graph->nvtxs = n;
1213   graph->nvtxs_global = N;
1214   /* allocate used space */
1215   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1216   ierr = PetscMalloc5(graph->nvtxs,&graph->count,
1217                       graph->nvtxs,&graph->neighbours_set,
1218                       graph->nvtxs,&graph->subset,
1219                       graph->nvtxs,&graph->which_dof,
1220                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1221   /* zeroes memory */
1222   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1223   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1224   /* use -1 as a default value for which_dof array */
1225   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1226   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1227   /* zeroes first pointer to neighbour set */
1228   if (graph->nvtxs) {
1229     graph->neighbours_set[0] = 0;
1230   }
1231   /* zeroes workspace for values of ncc */
1232   graph->subset_ncc = 0;
1233   graph->subset_ref_node = 0;
1234   PetscFunctionReturn(0);
1235 }
1236 
1237 #undef __FUNCT__
1238 #define __FUNCT__ "PCBDDCGraphDestroy"
1239 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1240 {
1241   PetscErrorCode ierr;
1242 
1243   PetscFunctionBegin;
1244   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1245   ierr = PetscFree(*graph);CHKERRQ(ierr);
1246   PetscFunctionReturn(0);
1247 }
1248 
1249 #undef __FUNCT__
1250 #define __FUNCT__ "PCBDDCGraphCreate"
1251 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1252 {
1253   PCBDDCGraph    new_graph;
1254   PetscErrorCode ierr;
1255 
1256   PetscFunctionBegin;
1257   ierr = PetscNew(&new_graph);CHKERRQ(ierr);
1258   new_graph->custom_minimal_size = 1;
1259   *graph = new_graph;
1260   PetscFunctionReturn(0);
1261 }
1262