xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 68270318ecc5c404e2b4dcece0dfbfca1a83be3a)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 
4 static PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt*,PetscInt,PetscBT,PetscInt*,PetscInt*,PetscInt*);
5 
6 #undef __FUNCT__
7 #define __FUNCT__ "PCBDDCSubSchursSetUpNew"
8 PetscErrorCode PCBDDCSubSchursSetUpNew(PCBDDCSubSchurs sub_schurs, PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers)
9 {
10   Mat                    A_II,A_IB,A_BI,A_BB;
11   Mat                    AE_II,*AE_IE,*AE_EI,*AE_EE;
12   Mat                    global_schur_subsets,*submat_global_schur_subsets,work_mat;
13   ISLocalToGlobalMapping l2gmap_subsets;
14   IS                     is_I,*is_subset_B,temp_is;
15   PetscInt               *nnz,*all_local_idx_G,*all_local_idx_B,*all_local_idx_N,*all_permutation_G;
16   PetscInt               i,subset_size,max_subset_size;
17   PetscInt               local_size,global_size;
18   PetscBool              implicit_schurs;
19   PetscErrorCode         ierr;
20 
21   PetscFunctionBegin;
22   //ierr = PetscObjectTypeCompare((PetscObject)sub_schurs->S,MATSCHURCOMPLEMENT,&implicit_schurs);CHKERRQ(ierr);
23   implicit_schurs = PETSC_TRUE;
24   /* allocate space for schur complements */
25   ierr = PetscMalloc4(sub_schurs->n_subs,&sub_schurs->is_AEj_B,
26                       sub_schurs->n_subs,&sub_schurs->S_Ej,
27                       sub_schurs->n_subs,&sub_schurs->work1,
28                       sub_schurs->n_subs,&sub_schurs->work2);CHKERRQ(ierr);
29 
30   /* get Schur complement matrices */
31   if (implicit_schurs) {
32     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&A_IB,&A_BI,&A_BB);CHKERRQ(ierr);
33     ierr = PetscMalloc4(sub_schurs->n_subs,&is_subset_B,
34                         sub_schurs->n_subs,&AE_IE,
35                         sub_schurs->n_subs,&AE_EI,
36                         sub_schurs->n_subs,&AE_EE);CHKERRQ(ierr);
37   }
38 
39   /* determine interior problems */
40   if (nlayers >= 0 && xadj != NULL && adjncy != NULL) { /* Interior problems can be different from the original one */
41     PetscBT                touched;
42     const PetscInt*        idx_B;
43     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
44 
45     /* get sizes */
46     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
47     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
48 
49     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
50     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
51     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
52 
53     /* all boundary dofs must be skipped when adding layers */
54     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
55     for (j=0;j<n_B;j++) {
56       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
57     }
58     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
59     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
60 
61     /* add prescribed number of layers of dofs */
62     n_local_dofs = n_B;
63     n_prev_added = n_B;
64     for (layer=0;layer<nlayers;layer++) {
65       PetscInt n_added;
66       if (n_local_dofs == n_I+n_B) break;
67       if (n_local_dofs > n_I+n_B) {
68         SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error querying layer %d. Out of bound access (%d > %d)",layer,n_local_dofs,n_I+n_B);
69       }
70       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
71       n_prev_added = n_added;
72       n_local_dofs += n_added;
73       if (!n_added) break;
74     }
75     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
76 
77     /* IS for I dofs in original numbering */
78     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I),n_local_dofs-n_B,local_numbering+n_B,PETSC_COPY_VALUES,&sub_schurs->is_I_layer);CHKERRQ(ierr);
79     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
80     ierr = ISSort(sub_schurs->is_I_layer);CHKERRQ(ierr);
81     /* IS for I dofs in boundary numbering */
82     if (implicit_schurs) {
83       ISLocalToGlobalMapping ItoNmap;
84       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
85       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,sub_schurs->is_I_layer,&is_I);CHKERRQ(ierr);
86       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
87 
88       /* II block */
89       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
90     }
91   } else {
92     PetscInt n_I;
93 
94     /* IS for I dofs in original numbering */
95     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
96     sub_schurs->is_I_layer = sub_schurs->is_I;
97 
98     /* IS for I dofs in I numbering (strided 1) */
99     if (implicit_schurs) {
100       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
101       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
102 
103       /* II block is the same */
104       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
105       AE_II = A_II;
106     }
107   }
108 
109   if (implicit_schurs) {
110     /* subsets in original and boundary numbering */
111     for (i=0;i<sub_schurs->n_subs;i++) {
112       ierr = ISDuplicate(sub_schurs->is_subs[i],&sub_schurs->is_AEj_B[i]);CHKERRQ(ierr);
113       ierr = ISSort(sub_schurs->is_AEj_B[i]);CHKERRQ(ierr);
114       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_AEj_B[i],&is_subset_B[i]);CHKERRQ(ierr);
115     }
116 
117     /* EE block */
118     for (i=0;i<sub_schurs->n_subs;i++) {
119       ierr = MatGetSubMatrix(A_BB,is_subset_B[i],is_subset_B[i],MAT_INITIAL_MATRIX,&AE_EE[i]);CHKERRQ(ierr);
120     }
121     /* IE block */
122     for (i=0;i<sub_schurs->n_subs;i++) {
123       ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B[i],MAT_INITIAL_MATRIX,&AE_IE[i]);CHKERRQ(ierr);
124     }
125     /* EI block */
126     for (i=0;i<sub_schurs->n_subs;i++) {
127       ierr = MatGetSubMatrix(A_BI,is_subset_B[i],is_I,MAT_INITIAL_MATRIX,&AE_EI[i]);CHKERRQ(ierr);
128     }
129 
130     /* setup Schur complements on subset */
131     for (i=0;i<sub_schurs->n_subs;i++) {
132       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE[i],AE_EI[i],AE_EE[i],&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
133       if (AE_II == A_II) { /* we can reuse the same ksp */
134         KSP ksp;
135         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
136         ierr = MatSchurComplementSetKSP(sub_schurs->S_Ej[i],ksp);CHKERRQ(ierr);
137       } else { /* build new ksp object which inherits ksp and pc types from the original one */
138         KSP      origksp,schurksp;
139         PC       origpc,schurpc;
140         KSPType  ksp_type;
141         PCType   pc_type;
142         PetscInt n_internal;
143 
144         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
145         ierr = MatSchurComplementGetKSP(sub_schurs->S_Ej[i],&schurksp);CHKERRQ(ierr);
146         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
147         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
148         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
149         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
150         ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
151         ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
152         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
153         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
154           MatSolverPackage solver=NULL;
155           ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
156           if (solver) {
157             ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
158           }
159         }
160         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
161       }
162     }
163     /* free */
164     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
165     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
166     for (i=0;i<sub_schurs->n_subs;i++) {
167       ierr = MatDestroy(&AE_EE[i]);CHKERRQ(ierr);
168       ierr = MatDestroy(&AE_IE[i]);CHKERRQ(ierr);
169       ierr = MatDestroy(&AE_EI[i]);CHKERRQ(ierr);
170       ierr = ISDestroy(&is_subset_B[i]);CHKERRQ(ierr);
171     }
172     ierr = PetscFree4(is_subset_B,AE_IE,AE_EI,AE_EE);CHKERRQ(ierr);
173   }
174 
175   /* TODO: just for compatibility with the previous version, needs to be fixed */
176   for (i=0;i<sub_schurs->n_subs_par;i++) {
177     PetscInt j = sub_schurs->index_parallel[i];
178     ierr = MatCreateVecs(sub_schurs->S_Ej[j],&sub_schurs->work1[j],&sub_schurs->work2[j]);CHKERRQ(ierr);
179   }
180   for (i=0;i<sub_schurs->n_subs_seq;i++) {
181      sub_schurs->work1[sub_schurs->index_sequential[i]] = 0;
182      sub_schurs->work2[sub_schurs->index_sequential[i]] = 0;
183   }
184 
185   if (!sub_schurs->n_subs_seq_g) {
186     sub_schurs->S_Ej_all = 0;
187     sub_schurs->sum_S_Ej_all = 0;
188     sub_schurs->is_Ej_all = 0;
189     PetscFunctionReturn(0);
190   }
191 
192   /* Get info on subset sizes and sum of all subsets sizes */
193   max_subset_size = 0;
194   local_size = 0;
195   for (i=0;i<sub_schurs->n_subs_seq;i++) {
196     PetscInt j = sub_schurs->index_sequential[i];
197     ierr = ISGetLocalSize(sub_schurs->is_AEj_B[j],&subset_size);CHKERRQ(ierr);
198     max_subset_size = PetscMax(subset_size,max_subset_size);
199     local_size += subset_size;
200   }
201 
202   /* Work arrays for local indices */
203   ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
204   ierr = PetscMalloc1(local_size,&all_local_idx_N);CHKERRQ(ierr);
205   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
206 
207   /* Get local indices in local whole numbering and local boundary numbering */
208   local_size = 0;
209   for (i=0;i<sub_schurs->n_subs_seq;i++) {
210     PetscInt j;
211     const    PetscInt *idxs;
212 
213     PetscInt local_problem_index = sub_schurs->index_sequential[i];
214     ierr = ISGetLocalSize(sub_schurs->is_AEj_B[local_problem_index],&subset_size);CHKERRQ(ierr);
215     ierr = ISGetIndices(sub_schurs->is_AEj_B[local_problem_index],&idxs);CHKERRQ(ierr);
216     /* subset indices in local numbering */
217     ierr = PetscMemcpy(all_local_idx_N+local_size,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
218     ierr = ISRestoreIndices(sub_schurs->is_AEj_B[local_problem_index],&idxs);CHKERRQ(ierr);
219     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
220     local_size += subset_size;
221   }
222 
223   /* subset indices in local boundary numbering */
224   ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N,&subset_size,all_local_idx_B);CHKERRQ(ierr);
225   if (subset_size != local_size) {
226     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %d != %d\n",subset_size,local_size);
227   }
228   ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
229 
230   /* Number dofs on all subsets (parallel) and sort numbering */
231   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)sub_schurs->l2gmap),sub_schurs->l2gmap,local_size,all_local_idx_N,PETSC_NULL,&global_size,&all_local_idx_G);CHKERRQ(ierr);
232   ierr = PetscMalloc1(local_size,&all_permutation_G);CHKERRQ(ierr);
233   for (i=0;i<local_size;i++) {
234     all_permutation_G[i]=i;
235   }
236   ierr = PetscSortIntWithPermutation(local_size,all_local_idx_G,all_permutation_G);CHKERRQ(ierr);
237 
238   /* Local matrix of all local Schur on subsets */
239   ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
240   ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
241   ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
242   ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
243   ierr = PetscFree(nnz);CHKERRQ(ierr);
244 
245   if (implicit_schurs) {
246     PetscScalar *fill_vals;
247     PetscInt    *dummy_idx;
248 
249     ierr = MatSetOption(sub_schurs->S_Ej_all,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
250 
251     /* Work arrays */
252     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&fill_vals);CHKERRQ(ierr);
253 
254     /* Loop on local problems to compute Schur complements explicitly (TODO; optimize)*/
255     local_size = 0;
256     for (i=0;i<sub_schurs->n_subs_seq;i++) {
257       Vec work1,work2;
258       PetscInt j,local_problem_index = sub_schurs->index_sequential[i];
259 
260       ierr = MatCreateVecs(sub_schurs->S_Ej[local_problem_index],&work1,&work2);CHKERRQ(ierr);
261       ierr = ISGetLocalSize(sub_schurs->is_AEj_B[local_problem_index],&subset_size);CHKERRQ(ierr);
262       /* local Schur */
263       for (j=0;j<subset_size;j++) {
264         ierr = VecSet(work1,0.0);CHKERRQ(ierr);
265         ierr = VecSetValue(work1,j,1.0,INSERT_VALUES);CHKERRQ(ierr);
266         ierr = VecPlaceArray(work2,&fill_vals[j*subset_size]);CHKERRQ(ierr);
267         ierr = MatMult(sub_schurs->S_Ej[local_problem_index],work1,work2);CHKERRQ(ierr);
268         ierr = VecResetArray(work2);CHKERRQ(ierr);
269       }
270       for (j=0;j<subset_size;j++) {
271         dummy_idx[j]=local_size+j;
272       }
273       ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,fill_vals,INSERT_VALUES);CHKERRQ(ierr);
274       local_size += subset_size;
275       ierr = VecDestroy(&work1);CHKERRQ(ierr);
276       ierr = VecDestroy(&work2);CHKERRQ(ierr);
277     }
278     ierr = PetscFree2(dummy_idx,fill_vals);CHKERRQ(ierr);
279   }
280   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
281   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
282 
283   /* Global matrix of all assembled Schur on subsets */
284   ierr = ISLocalToGlobalMappingCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,local_size,all_local_idx_G,PETSC_COPY_VALUES,&l2gmap_subsets);CHKERRQ(ierr);
285   ierr = MatCreateIS(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,&work_mat);CHKERRQ(ierr);
286   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
287   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
288   ierr = MatISGetMPIXAIJ(work_mat,MAT_INITIAL_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
289   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
290 
291   /* Get local part of (\sum_j S_Ej) */
292   for (i=0;i<local_size;i++) {
293     all_local_idx_N[i] = all_local_idx_G[all_permutation_G[i]];
294   }
295   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->l2gmap),local_size,all_local_idx_N,PETSC_OWN_POINTER,&temp_is);CHKERRQ(ierr);
296   ierr = MatGetSubMatrices(global_schur_subsets,1,&temp_is,&temp_is,MAT_INITIAL_MATRIX,&submat_global_schur_subsets);CHKERRQ(ierr);
297   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
298   ierr = ISDestroy(&temp_is);CHKERRQ(ierr);
299   for (i=0;i<local_size;i++) {
300     all_local_idx_G[all_permutation_G[i]] = i;
301   }
302   ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_G,PETSC_OWN_POINTER,&temp_is);CHKERRQ(ierr);
303   ierr = ISSetPermutation(temp_is);CHKERRQ(ierr);
304   ierr = MatPermute(submat_global_schur_subsets[0],temp_is,temp_is,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
305   ierr = MatDestroyMatrices(1,&submat_global_schur_subsets);CHKERRQ(ierr);
306   ierr = ISDestroy(&temp_is);CHKERRQ(ierr);
307   ierr = PetscFree(all_permutation_G);CHKERRQ(ierr);
308   PetscFunctionReturn(0);
309 }
310 
311 #undef __FUNCT__
312 #define __FUNCT__ "PCBDDCSubSchursInit"
313 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, Mat A, Mat S, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscInt seqthreshold)
314 {
315   IS                  *faces,*edges,*all_cc;
316   PetscInt            *index_sequential,*index_parallel;
317   PetscInt            *auxlocal_sequential,*auxlocal_parallel;
318   PetscInt            *auxglobal_sequential,*auxglobal_parallel;
319   PetscInt            *auxmapping;//,*idxs;
320   PetscInt            i,max_subset_size;
321   PetscInt            n_sequential_problems,n_local_sequential_problems,n_parallel_problems,n_local_parallel_problems;
322   PetscInt            n_faces,n_edges,n_all_cc;
323   PetscBool           is_sorted;
324   PetscErrorCode  ierr;
325 
326   PetscFunctionBegin;
327   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
328   if (!is_sorted) {
329     SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
330   }
331   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
332   if (!is_sorted) {
333     SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
334   }
335 
336   /* reset any previous data */
337   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
338 
339   /* get index sets for faces and edges */
340   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,NULL);CHKERRQ(ierr);
341   n_all_cc = n_faces+n_edges;
342   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
343   for (i=0;i<n_faces;i++) {
344     all_cc[i] = faces[i];
345   }
346   for (i=0;i<n_edges;i++) {
347     all_cc[n_faces+i] = edges[i];
348   }
349   ierr = PetscFree(faces);CHKERRQ(ierr);
350   ierr = PetscFree(edges);CHKERRQ(ierr);
351 
352   /* map interface's subsets */
353   max_subset_size = 0;
354   for (i=0;i<n_all_cc;i++) {
355     PetscInt subset_size;
356     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
357     max_subset_size = PetscMax(max_subset_size,subset_size);
358   }
359   ierr = PetscMalloc1(max_subset_size,&auxmapping);CHKERRQ(ierr);
360   ierr = PetscMalloc2(graph->ncc,&auxlocal_sequential,
361                       graph->ncc,&auxlocal_parallel);CHKERRQ(ierr);
362   ierr = PetscMalloc2(graph->ncc,&index_sequential,
363                       graph->ncc,&index_parallel);CHKERRQ(ierr);
364 
365   /* if threshold is negative, uses all sequential problems */
366   if (seqthreshold < 0) seqthreshold = max_subset_size;
367 
368   /* determine which problem has to be solved in parallel or sequentially */
369   n_local_sequential_problems = 0;
370   n_local_parallel_problems = 0;
371   for (i=0;i<n_all_cc;i++) {
372     PetscInt       subset_size,j,min_loc = 0;
373     const PetscInt *idxs;
374 
375     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
376     ierr = ISGetIndices(all_cc[i],&idxs);CHKERRQ(ierr);
377     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,subset_size,idxs,auxmapping);CHKERRQ(ierr);
378     for (j=1;j<subset_size;j++) {
379       if (auxmapping[j]<auxmapping[min_loc]) {
380         min_loc = j;
381       }
382     }
383     if (subset_size > seqthreshold) {
384       index_parallel[n_local_parallel_problems] = i;
385       auxlocal_parallel[n_local_parallel_problems] = idxs[min_loc];
386       n_local_parallel_problems++;
387     } else {
388       index_sequential[n_local_sequential_problems] = i;
389       auxlocal_sequential[n_local_sequential_problems] = idxs[min_loc];
390       n_local_sequential_problems++;
391     }
392     ierr = ISRestoreIndices(all_cc[i],&idxs);CHKERRQ(ierr);
393   }
394 
395   /* Number parallel problems */
396   auxglobal_parallel = 0;
397   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_parallel_problems,auxlocal_parallel,PETSC_NULL,&n_parallel_problems,&auxglobal_parallel);CHKERRQ(ierr);
398 
399   /* Number sequential problems */
400   auxglobal_sequential = 0;
401   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_sequential_problems,auxlocal_sequential,PETSC_NULL,&n_sequential_problems,&auxglobal_sequential);CHKERRQ(ierr);
402 
403   /* update info in sub_schurs */
404   if (A) {
405     ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
406     sub_schurs->A = A;
407   }
408   ierr = PetscObjectReference((PetscObject)S);CHKERRQ(ierr);
409   sub_schurs->S = S;
410   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
411   sub_schurs->is_I = is_I;
412   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
413   sub_schurs->is_B = is_B;
414   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
415   sub_schurs->l2gmap = graph->l2gmap;
416   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
417   sub_schurs->BtoNmap = BtoNmap;
418   sub_schurs->n_subs_seq = n_local_sequential_problems;
419   sub_schurs->n_subs_par = n_local_parallel_problems;
420   sub_schurs->n_subs_seq_g = n_sequential_problems;
421   sub_schurs->n_subs_par_g = n_parallel_problems;
422   sub_schurs->n_subs = sub_schurs->n_subs_seq + sub_schurs->n_subs_par;
423   sub_schurs->is_subs = all_cc;
424   sub_schurs->index_sequential = index_sequential;
425   sub_schurs->index_parallel = index_parallel;
426   sub_schurs->auxglobal_sequential = auxglobal_sequential;
427   sub_schurs->auxglobal_parallel = auxglobal_parallel;
428 
429   /* free workspace */
430   ierr = PetscFree(auxmapping);CHKERRQ(ierr);
431   ierr = PetscFree2(auxlocal_sequential,auxlocal_parallel);CHKERRQ(ierr);
432 
433   PetscFunctionReturn(0);
434 }
435 
436 #undef __FUNCT__
437 #define __FUNCT__ "PCBDDCSubSchursCreate"
438 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
439 {
440   PCBDDCSubSchurs schurs_ctx;
441   PetscErrorCode  ierr;
442 
443   PetscFunctionBegin;
444   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
445   schurs_ctx->n_subs = 0;
446   *sub_schurs = schurs_ctx;
447   PetscFunctionReturn(0);
448 }
449 
450 #undef __FUNCT__
451 #define __FUNCT__ "PCBDDCSubSchursDestroy"
452 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
453 {
454   PetscErrorCode ierr;
455 
456   PetscFunctionBegin;
457   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
458   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
459   PetscFunctionReturn(0);
460 }
461 
462 #undef __FUNCT__
463 #define __FUNCT__ "PCBDDCSubSchursReset"
464 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
465 {
466   PetscInt       i;
467   PetscErrorCode ierr;
468 
469   PetscFunctionBegin;
470   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
471   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
472   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
473   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
474   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
475   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
476   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
477   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
478   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
479   for (i=0;i<sub_schurs->n_subs;i++) {
480     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
481     ierr = ISDestroy(&sub_schurs->is_AEj_B[i]);CHKERRQ(ierr);
482     ierr = MatDestroy(&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
483     ierr = VecDestroy(&sub_schurs->work1[i]);CHKERRQ(ierr);
484     ierr = VecDestroy(&sub_schurs->work2[i]);CHKERRQ(ierr);
485   }
486   ierr = ISDestroy(&sub_schurs->is_I_layer);CHKERRQ(ierr);
487   if (sub_schurs->n_subs) {
488     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
489     ierr = PetscFree4(sub_schurs->is_AEj_B,sub_schurs->S_Ej,sub_schurs->work1,sub_schurs->work2);CHKERRQ(ierr);
490     ierr = PetscFree2(sub_schurs->index_sequential,sub_schurs->index_parallel);CHKERRQ(ierr);
491     ierr = PetscFree(sub_schurs->auxglobal_sequential);CHKERRQ(ierr);
492     ierr = PetscFree(sub_schurs->auxglobal_parallel);CHKERRQ(ierr);
493   }
494   sub_schurs->n_subs = 0;
495   PetscFunctionReturn(0);
496 }
497 
498 #undef __FUNCT__
499 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
500 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
501 {
502   PetscInt       i,j,n;
503   PetscErrorCode ierr;
504 
505   PetscFunctionBegin;
506   n = 0;
507   for (i=-n_prev;i<0;i++) {
508     PetscInt start_dof = queue_tip[i];
509     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
510       PetscInt dof = adjncy[j];
511       if (!PetscBTLookup(touched,dof)) {
512         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
513         queue_tip[n] = dof;
514         n++;
515       }
516     }
517   }
518   *n_added = n;
519   PetscFunctionReturn(0);
520 }
521 
522 #undef __FUNCT__
523 #define __FUNCT__ "PCBDDCSubSchursSetUp"
524 PetscErrorCode PCBDDCSubSchursSetUp(PCBDDCSubSchurs sub_schurs, Mat S, IS is_A_I, IS is_A_B, PetscInt ncc, IS is_cc[], PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers)
525 {
526   Mat                    A_II,A_IB,A_BI,A_BB;
527   Mat                    AE_II,*AE_IE,*AE_EI,*AE_EE;
528   IS                     is_I,*is_subset_B;
529   ISLocalToGlobalMapping BtoNmap;
530   PetscInt               i;
531   PetscBool              is_sorted;
532   PetscErrorCode         ierr;
533 
534   PetscFunctionBegin;
535   ierr = ISSorted(is_A_I,&is_sorted);CHKERRQ(ierr);
536   if (!is_sorted) {
537     SETERRQ(PetscObjectComm((PetscObject)is_A_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
538   }
539   ierr = ISSorted(is_A_B,&is_sorted);CHKERRQ(ierr);
540   if (!is_sorted) {
541     SETERRQ(PetscObjectComm((PetscObject)is_A_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
542   }
543 
544   /* get Schur complement matrices */
545   ierr = MatSchurComplementGetSubMatrices(S,&A_II,NULL,&A_IB,&A_BI,&A_BB);CHKERRQ(ierr);
546 
547   /* allocate space for schur complements */
548   sub_schurs->n_subs = ncc;
549   ierr = PetscMalloc4(sub_schurs->n_subs,&sub_schurs->is_AEj_B,
550                       sub_schurs->n_subs,&sub_schurs->S_Ej,
551                       sub_schurs->n_subs,&sub_schurs->work1,
552                       sub_schurs->n_subs,&sub_schurs->work2);CHKERRQ(ierr);
553   ierr = PetscMalloc4(ncc,&is_subset_B,ncc,&AE_IE,ncc,&AE_EI,ncc,&AE_EE);CHKERRQ(ierr);
554 
555   /* maps */
556   if (sub_schurs->n_subs && nlayers >= 0 && xadj != NULL && adjncy != NULL) { /* Interior problems can be different from the original one */
557     ISLocalToGlobalMapping ItoNmap;
558     PetscBT                touched;
559     const PetscInt*        idx_B;
560     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
561 
562     /* get sizes */
563     ierr = ISGetLocalSize(is_A_I,&n_I);CHKERRQ(ierr);
564     ierr = ISGetLocalSize(is_A_B,&n_B);CHKERRQ(ierr);
565 
566     ierr = ISLocalToGlobalMappingCreateIS(is_A_I,&ItoNmap);CHKERRQ(ierr);
567     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
568     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
569     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
570 
571     /* all boundary dofs must be skipped when adding layers */
572     ierr = ISGetIndices(is_A_B,&idx_B);CHKERRQ(ierr);
573     for (j=0;j<n_B;j++) {
574       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
575     }
576     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
577     ierr = ISRestoreIndices(is_A_B,&idx_B);CHKERRQ(ierr);
578 
579     /* add next layers of dofs */
580     n_local_dofs = n_B;
581     n_prev_added = n_B;
582     for (layer=0;layer<nlayers;layer++) {
583       PetscInt n_added;
584       if (n_local_dofs == n_I+n_B) break;
585       if (n_local_dofs > n_I+n_B) {
586         SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error querying layer %d. Out of bound access (%d > %d)",layer,n_local_dofs,n_I+n_B);
587       }
588       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
589       n_prev_added = n_added;
590       n_local_dofs += n_added;
591       if (!n_added) break;
592     }
593     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
594 
595     /* IS for I dofs in original numbering and in I numbering */
596     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)ItoNmap),n_local_dofs-n_B,local_numbering+n_B,PETSC_COPY_VALUES,&sub_schurs->is_I_layer);CHKERRQ(ierr);
597     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
598     ierr = ISSort(sub_schurs->is_I_layer);CHKERRQ(ierr);
599     ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,sub_schurs->is_I_layer,&is_I);CHKERRQ(ierr);
600     ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
601 
602     /* II block */
603     ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
604   } else {
605     PetscInt n_I;
606 
607     /* IS for I dofs in original numbering */
608     ierr = PetscObjectReference((PetscObject)is_A_I);CHKERRQ(ierr);
609     sub_schurs->is_I_layer = is_A_I;
610 
611     /* IS for I dofs in I numbering (strided 1) */
612     ierr = ISGetSize(is_A_I,&n_I);CHKERRQ(ierr);
613     ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_I),n_I,0,1,&is_I);CHKERRQ(ierr);
614 
615     /* II block is the same */
616     ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
617     AE_II = A_II;
618   }
619 
620   /* subsets in original and boundary numbering */
621   ierr = ISLocalToGlobalMappingCreateIS(is_A_B,&BtoNmap);CHKERRQ(ierr);
622   for (i=0;i<sub_schurs->n_subs;i++) {
623     ierr = ISDuplicate(is_cc[i],&sub_schurs->is_AEj_B[i]);CHKERRQ(ierr);
624     ierr = ISSort(sub_schurs->is_AEj_B[i]);CHKERRQ(ierr);
625     ierr = ISGlobalToLocalMappingApplyIS(BtoNmap,IS_GTOLM_DROP,sub_schurs->is_AEj_B[i],&is_subset_B[i]);CHKERRQ(ierr);
626   }
627   ierr = ISLocalToGlobalMappingDestroy(&BtoNmap);CHKERRQ(ierr);
628 
629   /* EE block */
630   for (i=0;i<sub_schurs->n_subs;i++) {
631     ierr = MatGetSubMatrix(A_BB,is_subset_B[i],is_subset_B[i],MAT_INITIAL_MATRIX,&AE_EE[i]);CHKERRQ(ierr);
632   }
633   /* IE block */
634   for (i=0;i<sub_schurs->n_subs;i++) {
635     ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B[i],MAT_INITIAL_MATRIX,&AE_IE[i]);CHKERRQ(ierr);
636   }
637   /* EI block */
638   for (i=0;i<sub_schurs->n_subs;i++) {
639     ierr = MatGetSubMatrix(A_BI,is_subset_B[i],is_I,MAT_INITIAL_MATRIX,&AE_EI[i]);CHKERRQ(ierr);
640   }
641 
642   /* setup Schur complements on subset */
643   for (i=0;i<sub_schurs->n_subs;i++) {
644     ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE[i],AE_EI[i],AE_EE[i],&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
645     ierr = MatCreateVecs(sub_schurs->S_Ej[i],&sub_schurs->work1[i],&sub_schurs->work2[i]);CHKERRQ(ierr);
646     if (AE_II == A_II) { /* we can reuse the same ksp */
647       KSP ksp;
648       ierr = MatSchurComplementGetKSP(S,&ksp);CHKERRQ(ierr);
649       ierr = MatSchurComplementSetKSP(sub_schurs->S_Ej[i],ksp);CHKERRQ(ierr);
650     } else { /* build new ksp object which inherits ksp and pc types from the original one */
651       KSP      origksp,schurksp;
652       PC       origpc,schurpc;
653       KSPType  ksp_type;
654       PCType   pc_type;
655       PetscInt n_internal;
656 
657       ierr = MatSchurComplementGetKSP(S,&origksp);CHKERRQ(ierr);
658       ierr = MatSchurComplementGetKSP(sub_schurs->S_Ej[i],&schurksp);CHKERRQ(ierr);
659       ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
660       ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
661       ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
662       ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
663       ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
664       ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
665       ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
666       if (n_internal) { /* UMFPACK gives error with 0 sized problems */
667         MatSolverPackage solver=NULL;
668         ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
669         if (solver) {
670           ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
671         }
672       }
673       ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
674     }
675   }
676   /* free */
677   ierr = ISDestroy(&is_I);CHKERRQ(ierr);
678   ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
679   for (i=0;i<sub_schurs->n_subs;i++) {
680     ierr = MatDestroy(&AE_EE[i]);CHKERRQ(ierr);
681     ierr = MatDestroy(&AE_IE[i]);CHKERRQ(ierr);
682     ierr = MatDestroy(&AE_EI[i]);CHKERRQ(ierr);
683     ierr = ISDestroy(&is_subset_B[i]);CHKERRQ(ierr);
684   }
685   ierr = PetscFree4(is_subset_B,AE_IE,AE_EI,AE_EE);CHKERRQ(ierr);
686   PetscFunctionReturn(0);
687 }
688