xref: /petsc/src/ksp/pc/impls/bddc/bddcgraph.c (revision 4f1b2e486e300201af44616c8751d8bf1ae87a02)
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       ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
529       global_subset_counter = 0;
530       for (i=0;i<graph->nvtxs;i++) {
531         if (graph->subset[i] && !PetscBTLookup(graph->touched,i)) {
532           global_subset_counter++;
533           for (j=i+1;j<graph->nvtxs;j++) {
534             if (!PetscBTLookup(graph->touched,j) && graph->subset[j]==graph->subset[i]) {
535               graph->subset[j] = global_subset_counter;
536               ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
537             }
538           }
539           graph->subset[i] = global_subset_counter;
540           ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
541         }
542       }
543       /* refine connected components locally */
544       ierr = PCBDDCGraphComputeConnectedComponentsLocal(graph);CHKERRQ(ierr);
545     }
546     /* restore original CSR graph of dofs */
547     ierr = PetscFree(new_xadj);CHKERRQ(ierr);
548     ierr = PetscFree(new_adjncy);CHKERRQ(ierr);
549     graph->xadj = old_xadj;
550     graph->adjncy = old_adjncy;
551   }
552 
553   /* Determine if we are in 2D or 3D */
554   twodim  = PETSC_TRUE;
555   for (i=0;i<graph->ncc;i++) {
556     PetscInt repdof = graph->queue[graph->cptr[i]];
557     if (graph->cptr[i+1]-graph->cptr[i] > graph->custom_minimal_size) {
558       if (graph->count[repdof] > 1 || graph->special_dof[repdof] == PCBDDCGRAPH_NEUMANN_MARK) {
559         twodim = PETSC_FALSE;
560         break;
561       }
562     }
563   }
564   ierr = MPI_Allreduce(&twodim,&graph->twodim,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)graph->l2gmap));CHKERRQ(ierr);
565   PetscFunctionReturn(0);
566 }
567 
568 /* The following code has been adapted from function IsConnectedSubdomain contained
569    in source file contig.c of METIS library (version 5.0.1)
570    It finds connected components for each subset  */
571 #undef __FUNCT__
572 #define __FUNCT__ "PCBDDCGraphComputeConnectedComponentsLocal"
573 PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph)
574 {
575   PetscInt       i,j,k,first,last,nleft,ncc,pid,cum_queue,n,ncc_pid;
576   PetscMPIInt    size;
577   PetscErrorCode ierr;
578 
579   PetscFunctionBegin;
580   /* quiet return if no csr info is available */
581   if ((!graph->xadj || !graph->adjncy) && !graph->n_local_subs) {
582     PetscFunctionReturn(0);
583   }
584 
585   /* reset any previous search of connected components */
586   ierr = PetscBTMemzero(graph->nvtxs,graph->touched);CHKERRQ(ierr);
587   graph->n_subsets = 0;
588   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap),&size);CHKERRQ(ierr);
589   if (size == 1) {
590     if (graph->nvtxs) {
591       graph->n_subsets = 1;
592       for (i=0;i<graph->nvtxs;i++) {
593         graph->subset[i] = 1;
594       }
595     }
596   } else {
597     for (i=0;i<graph->nvtxs;i++) {
598       if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) {
599         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
600         graph->subset[i] = 0;
601       }
602       graph->n_subsets = PetscMax(graph->n_subsets,graph->subset[i]);
603     }
604   }
605   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
606   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
607 
608   /* begin search for connected components */
609   cum_queue = 0;
610   ncc = 0;
611   for (n=0;n<graph->n_subsets;n++) {
612     pid = n+1;  /* partition labeled by 0 is discarded */
613     nleft = 0;
614     for (i=0;i<graph->nvtxs;i++) {
615       if (graph->subset[i] == pid) {
616         nleft++;
617       }
618     }
619     for (i=0; i<graph->nvtxs; i++) {
620       if (graph->subset[i] == pid) {
621         break;
622       }
623     }
624     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
625     graph->queue[cum_queue] = i;
626     first = 0;
627     last = 1;
628     graph->cptr[ncc] = cum_queue;
629     ncc_pid = 0;
630     while (first != nleft) {
631       if (first == last) {
632         graph->cptr[++ncc] = first+cum_queue;
633         ncc_pid++;
634         for (i=0; i<graph->nvtxs; i++) {
635           if (graph->subset[i] == pid && !PetscBTLookup(graph->touched,i)) {
636             break;
637           }
638         }
639         graph->queue[cum_queue+last] = i;
640         last++;
641         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
642       }
643       i = graph->queue[cum_queue+first];
644       first++;
645       if (!graph->xadj || !graph->adjncy) { /* sub info only, loop over all remaining vertices */
646         for (k=i+1;k<graph->nvtxs;k++) {
647           if (!PetscBTLookup(graph->touched,k) && graph->subset[k] == pid && graph->local_subs[i] == graph->local_subs[k]) {
648             graph->queue[cum_queue+last] = k;
649             last++;
650             ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
651           }
652         }
653       } else {
654         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
655           PetscBool same_sub;
656 
657           k = graph->adjncy[j];
658           /* get local subdomain id if needed */
659           if (graph->n_local_subs) {
660             same_sub = (PetscBool)(graph->local_subs[i] == graph->local_subs[j]);
661           } else {
662             same_sub = PETSC_TRUE;
663           }
664           if (!PetscBTLookup(graph->touched,k) && graph->subset[k] == pid && same_sub) {
665             graph->queue[cum_queue+last] = k;
666             last++;
667             ierr = PetscBTSet(graph->touched,k);CHKERRQ(ierr);
668           }
669         }
670       }
671     }
672     graph->cptr[++ncc] = first+cum_queue;
673     ncc_pid++;
674     cum_queue = graph->cptr[ncc];
675     graph->subset_ncc[n] = ncc_pid;
676   }
677   graph->ncc = ncc;
678   graph->queue_sorted = PETSC_FALSE;
679   PetscFunctionReturn(0);
680 }
681 
682 #undef __FUNCT__
683 #define __FUNCT__ "PCBDDCGraphSetUp"
684 PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices)
685 {
686   VecScatter     scatter_ctx;
687   Vec            local_vec,local_vec2,global_vec;
688   IS             to,from,subset,subset_n;
689   MPI_Comm       comm;
690   PetscScalar    *array,*array2;
691   const PetscInt *is_indices;
692   PetscInt       n_neigh,*neigh,*n_shared,**shared,*queue_global;
693   PetscInt       i,j,k,s,total_counts,nodes_touched,is_size;
694   PetscMPIInt    size;
695   PetscBool      same_set,mirrors_found;
696   PetscErrorCode ierr;
697 
698   PetscFunctionBegin;
699   graph->has_dirichlet = PETSC_FALSE;
700   if (dirichlet_is) {
701     PetscCheckSameComm(graph->l2gmap,1,dirichlet_is,4);
702     graph->has_dirichlet = PETSC_TRUE;
703   }
704   ierr = PetscObjectGetComm((PetscObject)(graph->l2gmap),&comm);CHKERRQ(ierr);
705   /* custom_minimal_size */
706   graph->custom_minimal_size = PetscMax(graph->custom_minimal_size,custom_minimal_size);
707   /* get info l2gmap and allocate work vectors  */
708   ierr = ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
709   /* check if we have any local periodic nodes (periodic BCs) */
710   mirrors_found = PETSC_FALSE;
711   if (graph->nvtxs && n_neigh) {
712     for (i=0; i<n_shared[0]; i++) graph->count[shared[0][i]] += 1;
713     for (i=0; i<n_shared[0]; i++) {
714       if (graph->count[shared[0][i]] > 1) {
715         mirrors_found = PETSC_TRUE;
716         break;
717       }
718     }
719   }
720   /* create some workspace objects */
721   local_vec = NULL;
722   local_vec2 = NULL;
723   global_vec = NULL;
724   to = NULL;
725   from = NULL;
726   scatter_ctx = NULL;
727   if (n_ISForDofs || dirichlet_is || neumann_is || custom_primal_vertices) {
728     ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
729     ierr = VecSetSizes(local_vec,PETSC_DECIDE,graph->nvtxs);CHKERRQ(ierr);
730     ierr = VecSetType(local_vec,VECSTANDARD);CHKERRQ(ierr);
731     ierr = VecDuplicate(local_vec,&local_vec2);CHKERRQ(ierr);
732     ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
733     ierr = VecSetSizes(global_vec,PETSC_DECIDE,graph->nvtxs_global);CHKERRQ(ierr);
734     ierr = VecSetType(global_vec,VECSTANDARD);CHKERRQ(ierr);
735     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
736     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
737     ierr = VecScatterCreate(global_vec,from,local_vec,to,&scatter_ctx);CHKERRQ(ierr);
738   } else if (mirrors_found) {
739     ierr = ISCreateStride(PETSC_COMM_SELF,graph->nvtxs,0,1,&to);CHKERRQ(ierr);
740     ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,to,&from);CHKERRQ(ierr);
741   }
742   /* compute local mirrors (if any) */
743   if (mirrors_found) {
744     PetscInt *local_indices,*global_indices;
745     /* get arrays of local and global indices */
746     ierr = PetscMalloc1(graph->nvtxs,&local_indices);CHKERRQ(ierr);
747     ierr = ISGetIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
748     ierr = PetscMemcpy(local_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
749     ierr = ISRestoreIndices(to,(const PetscInt**)&is_indices);CHKERRQ(ierr);
750     ierr = PetscMalloc1(graph->nvtxs,&global_indices);CHKERRQ(ierr);
751     ierr = ISGetIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
752     ierr = PetscMemcpy(global_indices,is_indices,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
753     ierr = ISRestoreIndices(from,(const PetscInt**)&is_indices);CHKERRQ(ierr);
754     /* allocate space for mirrors */
755     ierr = PetscMalloc2(graph->nvtxs,&graph->mirrors,graph->nvtxs,&graph->mirrors_set);CHKERRQ(ierr);
756     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
757     graph->mirrors_set[0] = 0;
758 
759     k=0;
760     for (i=0;i<n_shared[0];i++) {
761       j=shared[0][i];
762       if (graph->count[j] > 1) {
763         graph->mirrors[j]++;
764         k++;
765       }
766     }
767     /* allocate space for set of mirrors */
768     ierr = PetscMalloc1(k,&graph->mirrors_set[0]);CHKERRQ(ierr);
769     for (i=1;i<graph->nvtxs;i++)
770       graph->mirrors_set[i]=graph->mirrors_set[i-1]+graph->mirrors[i-1];
771 
772     /* fill arrays */
773     ierr = PetscMemzero(graph->mirrors,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
774     for (j=0;j<n_shared[0];j++) {
775       i=shared[0][j];
776       if (graph->count[i] > 1)
777         graph->mirrors_set[i][graph->mirrors[i]++]=global_indices[i];
778     }
779     ierr = PetscSortIntWithArray(graph->nvtxs,global_indices,local_indices);CHKERRQ(ierr);
780     for (i=0;i<graph->nvtxs;i++) {
781       if (graph->mirrors[i] > 0) {
782         ierr = PetscFindInt(graph->mirrors_set[i][0],graph->nvtxs,global_indices,&k);CHKERRQ(ierr);
783         j = global_indices[k];
784         while ( k > 0 && global_indices[k-1] == j) k--;
785         for (j=0;j<graph->mirrors[i];j++) {
786           graph->mirrors_set[i][j]=local_indices[k+j];
787         }
788         ierr = PetscSortInt(graph->mirrors[i],graph->mirrors_set[i]);CHKERRQ(ierr);
789       }
790     }
791     ierr = PetscFree(local_indices);CHKERRQ(ierr);
792     ierr = PetscFree(global_indices);CHKERRQ(ierr);
793   }
794   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
795   ierr = ISDestroy(&to);CHKERRQ(ierr);
796   ierr = ISDestroy(&from);CHKERRQ(ierr);
797 
798   /* Count total number of neigh per node */
799   k=0;
800   for (i=1;i<n_neigh;i++) {
801     k += n_shared[i];
802     for (j=0;j<n_shared[i];j++) {
803       graph->count[shared[i][j]] += 1;
804     }
805   }
806   /* Allocate space for storing the set of neighbours for each node */
807   if (graph->nvtxs) {
808     ierr = PetscMalloc1(k,&graph->neighbours_set[0]);CHKERRQ(ierr);
809   }
810   for (i=1;i<graph->nvtxs;i++) { /* dont count myself */
811     graph->neighbours_set[i]=graph->neighbours_set[i-1]+graph->count[i-1];
812   }
813   /* Get information for sharing subdomains */
814   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(*graph->count));CHKERRQ(ierr);
815   for (i=1;i<n_neigh;i++) { /* dont count myself */
816     s = n_shared[i];
817     for (j=0;j<s;j++) {
818       k = shared[i][j];
819       graph->neighbours_set[k][graph->count[k]] = neigh[i];
820       graph->count[k] += 1;
821     }
822   }
823   /* sort set of sharing subdomains */
824   for (i=0;i<graph->nvtxs;i++) {
825     ierr = PetscSortRemoveDupsInt(&graph->count[i],graph->neighbours_set[i]);CHKERRQ(ierr);
826   }
827   /* free memory allocated by ISLocalToGlobalMappingGetInfo */
828   ierr = ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);CHKERRQ(ierr);
829 
830   /*
831      Get info for dofs splitting
832      User can specify just a subset; an additional field is considered as a complementary field
833   */
834   for (i=0;i<graph->nvtxs;i++) {
835     graph->which_dof[i] = n_ISForDofs; /* by default a dof belongs to the complement set */
836   }
837   if (n_ISForDofs) {
838     ierr = VecSet(local_vec,-1.0);CHKERRQ(ierr);
839   }
840   for (i=0;i<n_ISForDofs;i++) {
841     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
842     ierr = ISGetLocalSize(ISForDofs[i],&is_size);CHKERRQ(ierr);
843     ierr = ISGetIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
844     for (j=0;j<is_size;j++) {
845       if (is_indices[j] > -1 && is_indices[j] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
846         graph->which_dof[is_indices[j]] = i;
847         array[is_indices[j]] = 1.*i;
848       }
849     }
850     ierr = ISRestoreIndices(ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
851     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
852   }
853   /* Check consistency among neighbours */
854   if (n_ISForDofs) {
855     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
856     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
857     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
858     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
859     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
860     ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
861     for (i=0;i<graph->nvtxs;i++){
862       PetscInt field1,field2;
863 
864       field1 = (PetscInt)PetscRealPart(array[i]);
865       field2 = (PetscInt)PetscRealPart(array2[i]);
866       if (field1 != field2) {
867         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);
868       }
869     }
870     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
871     ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
872   }
873   if (neumann_is || dirichlet_is) {
874     /* Take into account Neumann nodes */
875     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
876     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
877     if (neumann_is) {
878       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
879       ierr = ISGetLocalSize(neumann_is,&is_size);CHKERRQ(ierr);
880       ierr = ISGetIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
881       for (i=0;i<is_size;i++) {
882         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
883           array[is_indices[i]] = 1.0;
884         }
885       }
886       ierr = ISRestoreIndices(neumann_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
887       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
888     }
889     /* Neumann nodes: impose consistency among neighbours */
890     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
891     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
892     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
893     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
894     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
895     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
896     for (i=0;i<graph->nvtxs;i++) {
897       if (PetscRealPart(array[i]) > 0.1) {
898         graph->special_dof[i] = PCBDDCGRAPH_NEUMANN_MARK;
899       }
900     }
901     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
902     /* Take into account Dirichlet nodes */
903     ierr = VecSet(local_vec2,0.0);CHKERRQ(ierr);
904     if (dirichlet_is) {
905       ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
906       ierr = VecGetArray(local_vec2,&array2);CHKERRQ(ierr);
907       ierr = ISGetLocalSize(dirichlet_is,&is_size);CHKERRQ(ierr);
908       ierr = ISGetIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
909       for (i=0;i<is_size;i++){
910         if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
911           k = is_indices[i];
912           if (!PetscBTLookup(graph->touched,k)) {
913             if (PetscRealPart(array[k]) > 0.1) {
914               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);
915             }
916             array2[k] = 1.0;
917           }
918         }
919       }
920       ierr = ISRestoreIndices(dirichlet_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
921       ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
922       ierr = VecRestoreArray(local_vec2,&array2);CHKERRQ(ierr);
923     }
924     /* Dirichlet nodes: impose consistency among neighbours */
925     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
926     ierr = VecScatterBegin(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
927     ierr = VecScatterEnd(scatter_ctx,local_vec2,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
928     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
929     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
930     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
931     for (i=0;i<graph->nvtxs;i++) {
932       if (PetscRealPart(array[i]) > 0.1) {
933         ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
934         graph->subset[i] = 0; /* dirichlet nodes treated as internal -> is it ok? */
935         graph->special_dof[i] = PCBDDCGRAPH_DIRICHLET_MARK;
936       }
937     }
938     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
939   }
940   /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
941   if (graph->mirrors) {
942     for (i=0;i<graph->nvtxs;i++)
943       if (graph->mirrors[i])
944         graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;
945 
946     if (graph->xadj && graph->adjncy) {
947       PetscInt *new_xadj,*new_adjncy;
948       /* sort CSR graph */
949       for (i=0;i<graph->nvtxs;i++)
950         ierr = PetscSortInt(graph->xadj[i+1]-graph->xadj[i],&graph->adjncy[graph->xadj[i]]);CHKERRQ(ierr);
951 
952       /* adapt local CSR graph in case of local periodicity */
953       k=0;
954       for (i=0;i<graph->nvtxs;i++)
955         for (j=graph->xadj[i];j<graph->xadj[i+1];j++)
956           k += graph->mirrors[graph->adjncy[j]];
957 
958       ierr = PetscMalloc1(graph->nvtxs+1,&new_xadj);CHKERRQ(ierr);
959       ierr = PetscMalloc1(k+graph->xadj[graph->nvtxs],&new_adjncy);CHKERRQ(ierr);
960       new_xadj[0]=0;
961       for (i=0;i<graph->nvtxs;i++) {
962         k = graph->xadj[i+1]-graph->xadj[i];
963         ierr = PetscMemcpy(&new_adjncy[new_xadj[i]],&graph->adjncy[graph->xadj[i]],k*sizeof(PetscInt));CHKERRQ(ierr);
964         new_xadj[i+1]=new_xadj[i]+k;
965         for (j=graph->xadj[i];j<graph->xadj[i+1];j++) {
966           k = graph->mirrors[graph->adjncy[j]];
967           ierr = PetscMemcpy(&new_adjncy[new_xadj[i+1]],graph->mirrors_set[graph->adjncy[j]],k*sizeof(PetscInt));CHKERRQ(ierr);
968           new_xadj[i+1]+=k;
969         }
970         k = new_xadj[i+1]-new_xadj[i];
971         ierr = PetscSortRemoveDupsInt(&k,&new_adjncy[new_xadj[i]]);CHKERRQ(ierr);
972         new_xadj[i+1]=new_xadj[i]+k;
973       }
974       /* set new CSR into graph */
975       ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
976       ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
977       graph->xadj = new_xadj;
978       graph->adjncy = new_adjncy;
979     }
980   }
981 
982   /* mark special nodes (if any) -> each will become a single node equivalence class */
983   if (custom_primal_vertices) {
984     ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
985     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
986     ierr = ISGetLocalSize(custom_primal_vertices,&is_size);CHKERRQ(ierr);
987     ierr = ISGetIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
988     for (i=0;i<is_size;i++){
989       if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
990         array[is_indices[i]] = 1.0;
991       }
992     }
993     ierr = ISRestoreIndices(custom_primal_vertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
994     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
995     /* special nodes: impose consistency among neighbours */
996     ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
997     ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
998     ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
999     ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1000     ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1001     ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1002     j = 0;
1003     for (i=0;i<graph->nvtxs;i++) {
1004       if (PetscRealPart(array[i]) > 0.1 && graph->special_dof[i] != PCBDDCGRAPH_DIRICHLET_MARK) {
1005         graph->special_dof[i] = PCBDDCGRAPH_SPECIAL_MARK-j;
1006         j++;
1007       }
1008     }
1009     ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1010   }
1011 
1012   /* mark interior nodes as touched and belonging to partition number 0 */
1013   for (i=0;i<graph->nvtxs;i++) {
1014     if (!graph->count[i]) {
1015       ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
1016       graph->subset[i] = 0;
1017     }
1018   }
1019   /* init graph structure and compute default subsets */
1020   nodes_touched=0;
1021   for (i=0;i<graph->nvtxs;i++) {
1022     if (PetscBTLookup(graph->touched,i)) {
1023       nodes_touched++;
1024     }
1025   }
1026   i = 0;
1027   graph->ncc = 0;
1028   total_counts = 0;
1029 
1030   /* allocated space for queues */
1031   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1032   if (size == 1) {
1033     ierr = PetscMalloc2(graph->nvtxs+1,&graph->cptr,graph->nvtxs,&graph->queue);CHKERRQ(ierr);
1034   } else {
1035     PetscInt nused = graph->nvtxs - nodes_touched;
1036     ierr = PetscMalloc2(nused+1,&graph->cptr,nused,&graph->queue);CHKERRQ(ierr);
1037   }
1038 
1039   while (nodes_touched<graph->nvtxs) {
1040     /*  find first untouched node in local ordering */
1041     while (PetscBTLookup(graph->touched,i)) {
1042       i++;
1043     }
1044     ierr = PetscBTSet(graph->touched,i);CHKERRQ(ierr);
1045     graph->subset[i] = graph->ncc+1;
1046     graph->cptr[graph->ncc] = total_counts;
1047     graph->queue[total_counts] = i;
1048     total_counts++;
1049     nodes_touched++;
1050     /* now find all other nodes having the same set of sharing subdomains */
1051     for (j=i+1;j<graph->nvtxs;j++) {
1052       /* check for same number of sharing subdomains, dof number and same special mark */
1053       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]) {
1054         /* check for same set of sharing subdomains */
1055         same_set=PETSC_TRUE;
1056         for (k=0;k<graph->count[j];k++){
1057           if (graph->neighbours_set[i][k]!=graph->neighbours_set[j][k]) {
1058             same_set=PETSC_FALSE;
1059           }
1060         }
1061         /* I found a friend of mine */
1062         if (same_set) {
1063           graph->subset[j]=graph->ncc+1;
1064           ierr = PetscBTSet(graph->touched,j);CHKERRQ(ierr);
1065           nodes_touched++;
1066           graph->queue[total_counts] = j;
1067           total_counts++;
1068         }
1069       }
1070     }
1071     graph->ncc++;
1072   }
1073   /* set default number of subsets (at this point no info on csr graph has been taken into account, so n_subsets = ncc */
1074   graph->n_subsets = graph->ncc;
1075   ierr = PetscMalloc1(graph->n_subsets,&graph->subset_ncc);CHKERRQ(ierr);
1076   for (i=0;i<graph->n_subsets;i++) {
1077     graph->subset_ncc[i] = 1;
1078   }
1079   /* final pointer */
1080   graph->cptr[graph->ncc] = total_counts;
1081 
1082   /* save information on subsets (needed if we have to adapt the connected components later) */
1083   /* For consistency reasons (among neighbours), I need to sort (by global ordering) each subset */
1084   /* Get a reference node (min index in global ordering) for each subset for tagging messages */
1085   ierr = PetscMalloc1(graph->ncc,&graph->subset_ref_node);CHKERRQ(ierr);
1086   ierr = PetscMalloc1(graph->cptr[graph->ncc],&queue_global);CHKERRQ(ierr);
1087   ierr = ISLocalToGlobalMappingApply(graph->l2gmap,graph->cptr[graph->ncc],graph->queue,queue_global);CHKERRQ(ierr);
1088   for (j=0;j<graph->ncc;j++) {
1089     ierr = PetscSortIntWithArray(graph->cptr[j+1]-graph->cptr[j],&queue_global[graph->cptr[j]],&graph->queue[graph->cptr[j]]);CHKERRQ(ierr);
1090     graph->subset_ref_node[j] = graph->queue[graph->cptr[j]];
1091   }
1092   ierr = PetscFree(queue_global);CHKERRQ(ierr);
1093   graph->queue_sorted = PETSC_TRUE;
1094   if (graph->ncc) {
1095     ierr = PetscMalloc2(graph->ncc,&graph->subsets_size,graph->ncc,&graph->subsets);CHKERRQ(ierr);
1096     ierr = PetscMalloc1(graph->cptr[graph->ncc],&graph->subsets[0]);CHKERRQ(ierr);
1097     ierr = PetscMemzero(graph->subsets[0],graph->cptr[graph->ncc]*sizeof(PetscInt));CHKERRQ(ierr);
1098     for (j=1;j<graph->ncc;j++) {
1099       graph->subsets_size[j-1] = graph->cptr[j] - graph->cptr[j-1];
1100       graph->subsets[j] = graph->subsets[j-1] + graph->subsets_size[j-1];
1101     }
1102     graph->subsets_size[graph->ncc-1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc-1];
1103     for (j=0;j<graph->ncc;j++) {
1104       ierr = PetscMemcpy(graph->subsets[j],&graph->queue[graph->cptr[j]],graph->subsets_size[j]*sizeof(PetscInt));CHKERRQ(ierr);
1105     }
1106   }
1107   /* renumber reference nodes */
1108   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)(graph->l2gmap)),graph->ncc,graph->subset_ref_node,PETSC_COPY_VALUES,&subset_n);CHKERRQ(ierr);
1109   ierr = ISLocalToGlobalMappingApplyIS(graph->l2gmap,subset_n,&subset);CHKERRQ(ierr);
1110   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1111   ierr = PCBDDCSubsetNumbering(subset,NULL,NULL,&subset_n);CHKERRQ(ierr);
1112   ierr = ISDestroy(&subset);CHKERRQ(ierr);
1113   ierr = ISGetLocalSize(subset_n,&k);CHKERRQ(ierr);
1114   if (k != graph->ncc) {
1115     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %d != %d",k,graph->ncc);
1116   }
1117   ierr = ISGetIndices(subset_n,&is_indices);CHKERRQ(ierr);
1118   ierr = PetscMemcpy(graph->subset_ref_node,is_indices,graph->ncc*sizeof(PetscInt));CHKERRQ(ierr);
1119   ierr = ISRestoreIndices(subset_n,&is_indices);CHKERRQ(ierr);
1120   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
1121 
1122   /* free workspace */
1123   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1124   ierr = VecDestroy(&local_vec2);CHKERRQ(ierr);
1125   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1126   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 #undef __FUNCT__
1131 #define __FUNCT__ "PCBDDCGraphResetCSR"
1132 PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph)
1133 {
1134   PetscErrorCode ierr;
1135 
1136   PetscFunctionBegin;
1137   ierr = PetscFree(graph->xadj);CHKERRQ(ierr);
1138   ierr = PetscFree(graph->adjncy);CHKERRQ(ierr);
1139   graph->nvtxs_csr = 0;
1140   PetscFunctionReturn(0);
1141 }
1142 
1143 #undef __FUNCT__
1144 #define __FUNCT__ "PCBDDCGraphReset"
1145 PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph)
1146 {
1147   PetscErrorCode ierr;
1148 
1149   PetscFunctionBegin;
1150   ierr = ISLocalToGlobalMappingDestroy(&graph->l2gmap);CHKERRQ(ierr);
1151   ierr = PetscFree(graph->subset_ncc);CHKERRQ(ierr);
1152   ierr = PetscFree(graph->subset_ref_node);CHKERRQ(ierr);
1153   if (graph->nvtxs) {
1154     ierr = PetscFree(graph->neighbours_set[0]);CHKERRQ(ierr);
1155   }
1156   ierr = PetscBTDestroy(&graph->touched);CHKERRQ(ierr);
1157   ierr = PetscFree5(graph->count,
1158                     graph->neighbours_set,
1159                     graph->subset,
1160                     graph->which_dof,
1161                     graph->special_dof);CHKERRQ(ierr);
1162   ierr = PetscFree2(graph->cptr,graph->queue);CHKERRQ(ierr);
1163   if (graph->mirrors) {
1164     ierr = PetscFree(graph->mirrors_set[0]);CHKERRQ(ierr);
1165   }
1166   ierr = PetscFree2(graph->mirrors,graph->mirrors_set);CHKERRQ(ierr);
1167   if (graph->subsets) {
1168     ierr = PetscFree(graph->subsets[0]);CHKERRQ(ierr);
1169   }
1170   ierr = PetscFree2(graph->subsets_size,graph->subsets);CHKERRQ(ierr);
1171   ierr = ISDestroy(&graph->dirdofs);CHKERRQ(ierr);
1172   ierr = ISDestroy(&graph->dirdofsB);CHKERRQ(ierr);
1173   if (graph->n_local_subs) {
1174     ierr = PetscFree(graph->local_subs);CHKERRQ(ierr);
1175   }
1176   ierr = PCBDDCGraphResetCSR(graph);CHKERRQ(ierr);
1177   graph->has_dirichlet = PETSC_FALSE;
1178   graph->nvtxs = 0;
1179   graph->nvtxs_global = 0;
1180   graph->n_subsets = 0;
1181   graph->custom_minimal_size = 1;
1182   graph->n_local_subs = 0;
1183   PetscFunctionReturn(0);
1184 }
1185 
1186 #undef __FUNCT__
1187 #define __FUNCT__ "PCBDDCGraphInit"
1188 PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N)
1189 {
1190   PetscInt       n;
1191   PetscErrorCode ierr;
1192 
1193   PetscFunctionBegin;
1194   PetscValidPointer(graph,1);
1195   PetscValidHeaderSpecific(l2gmap,IS_LTOGM_CLASSID,2);
1196   PetscValidLogicalCollectiveInt(l2gmap,N,3);
1197   /* raise an error if already allocated */
1198   if (graph->nvtxs_global) {
1199     SETERRQ(PetscObjectComm((PetscObject)l2gmap),PETSC_ERR_PLIB,"BDDCGraph already initialized");
1200   }
1201   /* set number of vertices */
1202   ierr = PetscObjectReference((PetscObject)l2gmap);CHKERRQ(ierr);
1203   graph->l2gmap = l2gmap;
1204   ierr = ISLocalToGlobalMappingGetSize(l2gmap,&n);CHKERRQ(ierr);
1205   graph->nvtxs = n;
1206   graph->nvtxs_global = N;
1207   /* allocate used space */
1208   ierr = PetscBTCreate(graph->nvtxs,&graph->touched);CHKERRQ(ierr);
1209   ierr = PetscMalloc5(graph->nvtxs,&graph->count,
1210                       graph->nvtxs,&graph->neighbours_set,
1211                       graph->nvtxs,&graph->subset,
1212                       graph->nvtxs,&graph->which_dof,
1213                       graph->nvtxs,&graph->special_dof);CHKERRQ(ierr);
1214   /* zeroes memory */
1215   ierr = PetscMemzero(graph->count,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1216   ierr = PetscMemzero(graph->subset,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1217   /* use -1 as a default value for which_dof array */
1218   for (n=0;n<graph->nvtxs;n++) graph->which_dof[n] = -1;
1219   ierr = PetscMemzero(graph->special_dof,graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
1220   /* zeroes first pointer to neighbour set */
1221   if (graph->nvtxs) {
1222     graph->neighbours_set[0] = 0;
1223   }
1224   /* zeroes workspace for values of ncc */
1225   graph->subset_ncc = 0;
1226   graph->subset_ref_node = 0;
1227   PetscFunctionReturn(0);
1228 }
1229 
1230 #undef __FUNCT__
1231 #define __FUNCT__ "PCBDDCGraphDestroy"
1232 PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph* graph)
1233 {
1234   PetscErrorCode ierr;
1235 
1236   PetscFunctionBegin;
1237   ierr = PCBDDCGraphReset(*graph);CHKERRQ(ierr);
1238   ierr = PetscFree(*graph);CHKERRQ(ierr);
1239   PetscFunctionReturn(0);
1240 }
1241 
1242 #undef __FUNCT__
1243 #define __FUNCT__ "PCBDDCGraphCreate"
1244 PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph)
1245 {
1246   PCBDDCGraph    new_graph;
1247   PetscErrorCode ierr;
1248 
1249   PetscFunctionBegin;
1250   ierr = PetscNew(&new_graph);CHKERRQ(ierr);
1251   new_graph->custom_minimal_size = 1;
1252   *graph = new_graph;
1253   PetscFunctionReturn(0);
1254 }
1255