xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 6816873a55b70635a36c8ab78c96f47555ca6ab6)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <petscblaslapack.h>
4 
5 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt*,PetscInt,PetscBT,PetscInt*,PetscInt*,PetscInt*);
6 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat,PetscBool,MatReuse,Mat*);
7 static PetscErrorCode PCBDDCMumpsInteriorSolve(PC,Vec,Vec);
8 static PetscErrorCode PCBDDCMumpsCorrectionSolve(PC,Vec,Vec);
9 
10 #undef __FUNCT__
11 #define __FUNCT__ "PCBDDCMumpsCorrectionSolve"
12 static PetscErrorCode PCBDDCMumpsCorrectionSolve(PC pc, Vec rhs, Vec sol)
13 {
14   PCBDDCReuseMumps ctx;
15   PetscInt         ival;
16   PetscErrorCode   ierr;
17 
18   PetscFunctionBegin;
19   ierr = PCShellGetContext(pc,(void **)&ctx);CHKERRQ(ierr);
20 #if defined(PETSC_HAVE_MUMPS)
21   ierr = MatMumpsGetIcntl(ctx->F,26,&ival);CHKERRQ(ierr);
22   ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
23 #endif
24   ierr = MatSolve(ctx->F,rhs,sol);CHKERRQ(ierr);
25 #if defined(PETSC_HAVE_MUMPS)
26   ierr = MatMumpsSetIcntl(ctx->F,26,ival);CHKERRQ(ierr);
27 #endif
28   PetscFunctionReturn(0);
29 }
30 
31 #undef __FUNCT__
32 #define __FUNCT__ "PCBDDCReuseMumpsReset"
33 static PetscErrorCode PCBDDCReuseMumpsReset(PCBDDCReuseMumps reuse)
34 {
35   PetscErrorCode ierr;
36 
37   PetscFunctionBegin;
38   ierr = MatDestroy(&reuse->F);CHKERRQ(ierr);
39   ierr = MatDestroy(&reuse->S_inv);CHKERRQ(ierr);
40   ierr = VecDestroy(&reuse->sol);CHKERRQ(ierr);
41   ierr = VecDestroy(&reuse->rhs);CHKERRQ(ierr);
42   ierr = PCDestroy(&reuse->interior_solver);CHKERRQ(ierr);
43   ierr = PCDestroy(&reuse->correction_solver);CHKERRQ(ierr);
44   ierr = VecScatterDestroy(&reuse->correction_scatter_B);CHKERRQ(ierr);
45   ierr = VecDestroy(&reuse->solB);CHKERRQ(ierr);
46   ierr = VecDestroy(&reuse->rhsB);CHKERRQ(ierr);
47   PetscFunctionReturn(0);
48 }
49 
50 #undef __FUNCT__
51 #define __FUNCT__ "PCBDDCMumpsInteriorSolve"
52 static PetscErrorCode PCBDDCMumpsInteriorSolve(PC pc, Vec rhs, Vec sol)
53 {
54   PCBDDCReuseMumps ctx;
55   PetscScalar      *array,*array_mumps;
56   PetscInt         ival;
57   PetscErrorCode   ierr;
58 
59   PetscFunctionBegin;
60   ierr = PCShellGetContext(pc,(void **)&ctx);CHKERRQ(ierr);
61 #if defined(PETSC_HAVE_MUMPS)
62   ierr = MatMumpsGetIcntl(ctx->F,26,&ival);CHKERRQ(ierr);
63   ierr = MatMumpsSetIcntl(ctx->F,26,0);CHKERRQ(ierr);
64 #endif
65   /* copy rhs into factored matrix workspace (can it be avoided?, MatSolve_MUMPS has another copy b->x internally) */
66   ierr = VecGetArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
67   ierr = VecGetArray(ctx->rhs,&array_mumps);CHKERRQ(ierr);
68   ierr = PetscMemcpy(array_mumps,array,ctx->n_I*sizeof(PetscScalar));CHKERRQ(ierr);
69   ierr = VecRestoreArray(ctx->rhs,&array_mumps);CHKERRQ(ierr);
70   ierr = VecRestoreArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
71 
72   ierr = MatSolve(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
73 
74   /* get back data to caller worskpace */
75   ierr = VecGetArrayRead(ctx->sol,(const PetscScalar**)&array_mumps);CHKERRQ(ierr);
76   ierr = VecGetArray(sol,&array);CHKERRQ(ierr);
77   ierr = PetscMemcpy(array,array_mumps,ctx->n_I*sizeof(PetscScalar));CHKERRQ(ierr);
78   ierr = VecRestoreArray(sol,&array);CHKERRQ(ierr);
79   ierr = VecRestoreArrayRead(ctx->sol,(const PetscScalar**)&array_mumps);CHKERRQ(ierr);
80 #if defined(PETSC_HAVE_MUMPS)
81   ierr = MatMumpsSetIcntl(ctx->F,26,ival);CHKERRQ(ierr);
82 #endif
83   PetscFunctionReturn(0);
84 }
85 
86 #undef __FUNCT__
87 #define __FUNCT__ "PCBDDCComputeExplicitSchur"
88 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
89 {
90   Mat            B, C, D, Bd, Cd, AinvBd;
91   KSP            ksp;
92   PC             pc;
93   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
94   PetscReal      fill = 2.0;
95   PetscInt       n_I;
96   PetscMPIInt    size;
97   PetscErrorCode ierr;
98 
99   PetscFunctionBegin;
100   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRQ(ierr);
101   if (size != 1) {
102     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
103   }
104   if (reuse == MAT_REUSE_MATRIX) {
105     PetscBool Sdense;
106 
107     ierr = PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);CHKERRQ(ierr);
108     if (!Sdense) {
109       SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"S should dense");
110     }
111   }
112   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
113   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
114   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
115   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
116   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
117   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
118   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
119   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
120   ierr = MatGetSize(B,&n_I,NULL);CHKERRQ(ierr);
121   if (n_I) {
122     if (!Bdense) {
123       ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
124     } else {
125       Bd = B;
126     }
127 
128     if (isLU || isILU || isCHOL) {
129       Mat fact;
130       ierr = KSPSetUp(ksp);CHKERRQ(ierr);
131       ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
132       ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
133       ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
134     } else {
135       PetscBool ex = PETSC_TRUE;
136 
137       if (ex) {
138         Mat Ainvd;
139 
140         ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
141         ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
142         ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
143       } else {
144         Vec         sol,rhs;
145         PetscScalar *arrayrhs,*arraysol;
146         PetscInt    i,nrhs,n;
147 
148         ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
149         ierr = MatGetSize(Bd,&n,&nrhs);CHKERRQ(ierr);
150         ierr = MatDenseGetArray(Bd,&arrayrhs);CHKERRQ(ierr);
151         ierr = MatDenseGetArray(AinvBd,&arraysol);CHKERRQ(ierr);
152         ierr = KSPGetSolution(ksp,&sol);CHKERRQ(ierr);
153         ierr = KSPGetRhs(ksp,&rhs);CHKERRQ(ierr);
154         for (i=0;i<nrhs;i++) {
155           ierr = VecPlaceArray(rhs,arrayrhs+i*n);CHKERRQ(ierr);
156           ierr = VecPlaceArray(sol,arraysol+i*n);CHKERRQ(ierr);
157           ierr = KSPSolve(ksp,rhs,sol);CHKERRQ(ierr);
158           ierr = VecResetArray(rhs);CHKERRQ(ierr);
159           ierr = VecResetArray(sol);CHKERRQ(ierr);
160         }
161         ierr = MatDenseRestoreArray(Bd,&arrayrhs);CHKERRQ(ierr);
162         ierr = MatDenseRestoreArray(AinvBd,&arrayrhs);CHKERRQ(ierr);
163       }
164     }
165     if (!Bdense & !issym) {
166       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
167     }
168 
169     if (!issym) {
170       if (!Cdense) {
171         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
172       } else {
173         Cd = C;
174       }
175       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
176       if (!Cdense) {
177         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
178       }
179     } else {
180       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
181       if (!Bdense) {
182         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
183       }
184     }
185     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
186   }
187 
188   if (D) {
189     Mat       Dd;
190     PetscBool Ddense;
191 
192     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
193     if (!Ddense) {
194       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
195     } else {
196       Dd = D;
197     }
198     if (n_I) {
199       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
200     } else {
201       if (reuse == MAT_INITIAL_MATRIX) {
202         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
203       } else {
204         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
205       }
206     }
207     if (!Ddense) {
208       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
209     }
210   } else {
211     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
212   }
213   PetscFunctionReturn(0);
214 }
215 
216 #undef __FUNCT__
217 #define __FUNCT__ "PCBDDCSubSchursSetUp"
218 PetscErrorCode PCBDDCSubSchursSetUp(PCBDDCSubSchurs sub_schurs, Mat Ain, Mat Sin, PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers, PetscBool faster_deluxe, PetscBool compute_Stilda, PetscBool reuse_solvers,PetscBool use_edges, PetscBool use_faces)
219 {
220   Mat                    A_II,A_IB,A_BI,A_BB,AE_II;
221   Mat                    S_all,S_all_inv;
222   Mat                    global_schur_subsets,work_mat;
223   Mat                    S_Ej_tilda_all,S_Ej_inv_all;
224   ISLocalToGlobalMapping l2gmap_subsets;
225   IS                     is_I,is_I_layer,temp_is;
226   PetscInt               *nnz,*all_local_idx_G,*all_local_idx_N;
227   PetscInt               *auxnum1,*auxnum2,*all_local_idx_G_rep;
228   PetscInt               i,subset_size,max_subset_size;
229   PetscInt               extra,local_size,global_size;
230   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
231   PetscScalar            *Bwork;
232   PetscSubcomm           subcomm;
233   PetscMPIInt            color,rank;
234   MPI_Comm               comm_n;
235   PetscErrorCode         ierr;
236 
237   PetscFunctionBegin;
238   /* update info in sub_schurs */
239   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
240   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
241   if (Ain) {
242     PetscBool isseqaij;
243 
244     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
245     if (isseqaij) {
246       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
247       sub_schurs->A = Ain;
248     } else { /* SeqBAIJ matrices does not support symmetry checking, SeqSBAIJ does not support MatPermute */
249       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
250     }
251   }
252   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
253   sub_schurs->S = Sin;
254   if (sub_schurs->use_mumps) {
255     sub_schurs->use_mumps = (PetscBool)(!!sub_schurs->A);
256   }
257 
258   /* preliminary checks */
259   if (!sub_schurs->use_mumps && compute_Stilda) {
260     SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS");
261   }
262   /* determine if we are dealing with hermitian positive definite problems */
263   sub_schurs->is_hermitian = PETSC_FALSE;
264   sub_schurs->is_posdef = PETSC_FALSE;
265   if (sub_schurs->A) {
266     PetscInt lsize;
267 
268     ierr = MatGetSize(sub_schurs->A,&lsize,NULL);CHKERRQ(ierr);
269     if (lsize) {
270       ierr = MatIsHermitian(sub_schurs->A,0.0,&sub_schurs->is_hermitian);CHKERRQ(ierr);
271       if (sub_schurs->is_hermitian) {
272         PetscScalar val;
273         Vec         vec1,vec2;
274 
275         ierr = MatCreateVecs(sub_schurs->A,&vec1,&vec2);CHKERRQ(ierr);
276         ierr = VecSetRandom(vec1,NULL);
277         ierr = VecCopy(vec1,vec2);CHKERRQ(ierr);
278         ierr = MatMult(sub_schurs->A,vec2,vec1);CHKERRQ(ierr);
279         ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
280         if (PetscRealPart(val) > 0. && PetscImaginaryPart(val) == 0.) sub_schurs->is_posdef = PETSC_TRUE;
281         ierr = VecDestroy(&vec1);CHKERRQ(ierr);
282         ierr = VecDestroy(&vec2);CHKERRQ(ierr);
283       }
284     } else {
285       sub_schurs->is_hermitian = PETSC_TRUE;
286       sub_schurs->is_posdef = PETSC_TRUE;
287     }
288     if (compute_Stilda && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
289       SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"General matrix pencils are not currently supported");
290     }
291   }
292   /* restrict work on active processes */
293   color = 0;
294   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
295   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
296   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
297   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
298   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
299   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
300   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
301   if (!sub_schurs->n_subs) {
302     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
303     PetscFunctionReturn(0);
304   }
305 
306   /* get Schur complement matrices */
307   if (!sub_schurs->use_mumps) {
308     Mat       tA_IB,tA_BI,tA_BB;
309     PetscBool isseqaij;
310     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
311     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
312     if (!isseqaij) {
313       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
314       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
315       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
316     } else {
317       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
318       A_BB = tA_BB;
319       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
320       A_IB = tA_IB;
321       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
322       A_BI = tA_BI;
323     }
324   } else {
325     A_II = NULL;
326     A_IB = NULL;
327     A_BI = NULL;
328     A_BB = NULL;
329   }
330   S_all = NULL;
331   S_all_inv = NULL;
332   S_Ej_tilda_all = NULL;
333   S_Ej_inv_all = NULL;
334 
335   /* determine interior problems */
336   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
337   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
338     PetscBT                touched;
339     const PetscInt*        idx_B;
340     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
341 
342     if (xadj == NULL || adjncy == NULL) {
343       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
344     }
345     /* get sizes */
346     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
347     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
348 
349     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
350     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
351     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
352 
353     /* all boundary dofs must be skipped when adding layers */
354     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
355     for (j=0;j<n_B;j++) {
356       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
357     }
358     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
359     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
360 
361     /* add prescribed number of layers of dofs */
362     n_local_dofs = n_B;
363     n_prev_added = n_B;
364     for (layer=0;layer<nlayers;layer++) {
365       PetscInt n_added;
366       if (n_local_dofs == n_I+n_B) break;
367       if (n_local_dofs > n_I+n_B) {
368         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);
369       }
370       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
371       n_prev_added = n_added;
372       n_local_dofs += n_added;
373       if (!n_added) break;
374     }
375     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
376 
377     /* IS for I layer dofs in original numbering */
378     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I),n_local_dofs-n_B,local_numbering+n_B,PETSC_COPY_VALUES,&is_I_layer);CHKERRQ(ierr);
379     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
380     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
381     /* IS for I layer dofs in I numbering */
382     if (!sub_schurs->use_mumps) {
383       ISLocalToGlobalMapping ItoNmap;
384       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
385       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
386       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
387 
388       /* II block */
389       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
390     }
391   } else {
392     PetscInt n_I;
393 
394     /* IS for I dofs in original numbering */
395     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
396     is_I_layer = sub_schurs->is_I;
397 
398     /* IS for I dofs in I numbering (strided 1) */
399     if (!sub_schurs->use_mumps) {
400       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
401       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
402 
403       /* II block is the same */
404       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
405       AE_II = A_II;
406     }
407   }
408 
409   /* Get info on subset sizes and sum of all subsets sizes */
410   max_subset_size = 0;
411   local_size = 0;
412   for (i=0;i<sub_schurs->n_subs;i++) {
413     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
414     max_subset_size = PetscMax(subset_size,max_subset_size);
415     local_size += subset_size;
416   }
417 
418   /* Work arrays for local indices */
419   extra = 0;
420   if (sub_schurs->use_mumps) {
421     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
422   }
423   ierr = PetscMalloc1(local_size+extra,&all_local_idx_N);CHKERRQ(ierr);
424   if (extra) {
425     const PetscInt *idxs;
426     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
427     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
428     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
429   }
430   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
431   ierr = PetscMalloc2(sub_schurs->n_subs,&auxnum1,sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
432 
433   /* Get local indices in local numbering */
434   local_size = 0;
435   for (i=0;i<sub_schurs->n_subs;i++) {
436     PetscInt j;
437     const    PetscInt *idxs;
438 
439     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
440     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
441     /* start (smallest in global ordering) and multiplicity */
442     auxnum1[i] = idxs[0];
443     auxnum2[i] = subset_size;
444     /* subset indices in local numbering */
445     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
446     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
447     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
448     local_size += subset_size;
449   }
450 
451   /* allocate extra workspace needed only for GETRI */
452   Bwork = NULL;
453   pivots = NULL;
454   if (sub_schurs->n_subs && !sub_schurs->is_hermitian) {
455     PetscScalar lwork;
456 
457     B_lwork = -1;
458     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
459     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
460     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
461     ierr = PetscFPTrapPop();CHKERRQ(ierr);
462     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
463     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
464     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
465   }
466 
467   /* prepare parallel matrices for summing up properly schurs on subsets */
468   ierr = PCBDDCSubsetNumbering(comm_n,sub_schurs->l2gmap,sub_schurs->n_subs,auxnum1,auxnum2,&global_size,&all_local_idx_G_rep);CHKERRQ(ierr);
469   ierr = PetscMalloc1(local_size,&all_local_idx_G);CHKERRQ(ierr);
470   local_size = 0;
471   for (i=0;i<sub_schurs->n_subs;i++) {
472     PetscInt j;
473     for (j=0;j<auxnum2[i];j++) all_local_idx_G[local_size++] = all_local_idx_G_rep[i] + j;
474   }
475   ierr = PetscFree(all_local_idx_G_rep);CHKERRQ(ierr);
476   ierr = PetscFree2(auxnum1,auxnum2);CHKERRQ(ierr);
477   ierr = ISLocalToGlobalMappingCreate(comm_n,1,local_size,all_local_idx_G,PETSC_COPY_VALUES,&l2gmap_subsets);CHKERRQ(ierr);
478   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,&work_mat);CHKERRQ(ierr);
479   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
480   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
481   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
482   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
483 
484   /* subset indices in local boundary numbering */
485   if (!sub_schurs->is_Ej_all) {
486     PetscInt *all_local_idx_B;
487 
488     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
489     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
490     if (subset_size != local_size) {
491       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %d != %d\n",subset_size,local_size);
492     }
493     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
494   }
495 
496   /* Local matrix of all local Schur on subsets (transposed) */
497   if (!sub_schurs->S_Ej_all) {
498     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
499     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
500     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
501     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
502   } else {
503     ierr = MatZeroEntries(sub_schurs->S_Ej_all);CHKERRQ(ierr);
504   }
505 
506   /* Compute Schur complements explicitly */
507   ierr = PetscBTMemzero(sub_schurs->n_subs,sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
508   if (!sub_schurs->use_mumps) {
509     Mat         S_Ej_expl;
510     PetscScalar *work;
511     PetscInt    j,*dummy_idx;
512     PetscBool   Sdense;
513 
514     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
515     local_size = 0;
516     for (i=0;i<sub_schurs->n_subs;i++) {
517       IS  is_subset_B;
518       Mat AE_EE,AE_IE,AE_EI,S_Ej;
519 
520       /* subsets in original and boundary numbering */
521       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
522       /* EE block */
523       ierr = MatGetSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
524       /* IE block */
525       ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
526       /* EI block */
527       if (sub_schurs->is_hermitian) {
528         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
529       } else {
530         ierr = MatGetSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
531       }
532       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
533       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
534       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
535       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
536       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
537       if (AE_II == A_II) { /* we can reuse the same ksp */
538         KSP ksp;
539         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
540         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
541       } else { /* build new ksp object which inherits ksp and pc types from the original one */
542         KSP       origksp,schurksp;
543         PC        origpc,schurpc;
544         KSPType   ksp_type;
545         PetscInt  n_internal;
546         PetscBool ispcnone;
547 
548         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
549         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
550         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
551         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
552         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
553         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
554         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
555         if (!ispcnone) {
556           PCType pc_type;
557           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
558           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
559         } else {
560           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
561         }
562         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
563         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
564           MatSolverPackage solver=NULL;
565           ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
566           if (solver) {
567             ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
568           }
569         }
570         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
571       }
572       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
573       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
574       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
575       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
576       if (Sdense) {
577         for (j=0;j<subset_size;j++) {
578           dummy_idx[j]=local_size+j;
579         }
580         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
581       } else {
582         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
583       }
584       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
585       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
586       local_size += subset_size;
587     }
588     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
589     /* free */
590     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
591     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
592     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
593   } else {
594     Mat         A,F;
595     IS          is_A_all;
596     PetscScalar *work;
597     PetscInt    *idxs_schur,n_I,n_I_all,*dummy_idx,size_schur,size_active_schur;
598 
599     /* get working mat */
600     ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
601     if (!sub_schurs->is_dir) {
602       ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size+n_I,all_local_idx_N,PETSC_COPY_VALUES,&is_A_all);CHKERRQ(ierr);
603       size_schur = local_size;
604     } else {
605       IS list[2];
606 
607       ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size+n_I,all_local_idx_N,PETSC_COPY_VALUES,&list[0]);CHKERRQ(ierr);
608       list[1] = sub_schurs->is_dir;
609       ierr = ISConcatenate(PETSC_COMM_SELF,2,list,&is_A_all);CHKERRQ(ierr);
610       ierr = ISDestroy(&list[0]);CHKERRQ(ierr);
611       ierr = ISGetLocalSize(sub_schurs->is_dir,&size_schur);CHKERRQ(ierr);
612       size_schur += local_size;
613     }
614     size_active_schur = local_size;
615     ierr = MatGetSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
616     ierr = MatSetOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
617 
618     if (n_I) {
619       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
620         ierr = MatSetOption(A,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
621         ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
622       } else {
623         ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
624         ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
625       }
626 
627       /* subsets ordered last */
628       ierr = PetscMalloc1(size_schur,&idxs_schur);CHKERRQ(ierr);
629       for (i=0;i<size_schur;i++) {
630         idxs_schur[i] = n_I+i+1;
631       }
632 #if defined(PETSC_HAVE_MUMPS)
633       ierr = MatMumpsSetSchurIndices(F,size_schur,idxs_schur);CHKERRQ(ierr);
634 #endif
635       ierr = PetscFree(idxs_schur);CHKERRQ(ierr);
636 
637       /* factorization step */
638       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
639         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
640         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
641       } else {
642         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
643         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
644       }
645 
646       /* get explicit Schur Complement computed during numeric factorization */
647 #if defined(PETSC_HAVE_MUMPS)
648       ierr = MatMumpsGetSchurComplement(F,&S_all);CHKERRQ(ierr);
649 #endif
650 
651       /* we can reuse the solvers if we are not using the economic version */
652       ierr = ISGetLocalSize(sub_schurs->is_I,&n_I_all);CHKERRQ(ierr);
653       if (n_I == n_I_all && reuse_solvers) {
654         Mat              A_II;
655         PCBDDCReuseMumps msolv_ctx;
656 
657         if (sub_schurs->reuse_mumps) {
658           ierr = PCBDDCReuseMumpsReset(sub_schurs->reuse_mumps);CHKERRQ(ierr);
659           ierr = PetscFree(sub_schurs->reuse_mumps);CHKERRQ(ierr);
660         }
661         ierr = PetscNew(&msolv_ctx);CHKERRQ(ierr);
662         msolv_ctx->n_I = n_I;
663         ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
664         msolv_ctx->F = F;
665         ierr = MatCreateVecs(F,&msolv_ctx->sol,&msolv_ctx->rhs);CHKERRQ(ierr);
666         ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
667 
668         /* interior solver */
669         ierr = PCCreate(PETSC_COMM_SELF,&msolv_ctx->interior_solver);CHKERRQ(ierr);
670         ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
671         ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
672         ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
673         ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCMumpsInteriorSolve);CHKERRQ(ierr);
674 
675         /* correction solver */
676         /* auxiliary scatters are needed and are created in PCBDDCSetUpLocalScatters */
677         ierr = PCCreate(PETSC_COMM_SELF,&msolv_ctx->correction_solver);CHKERRQ(ierr);
678         ierr = PCSetOperators(msolv_ctx->correction_solver,A,A);CHKERRQ(ierr);
679         ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
680         ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
681         ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCMumpsCorrectionSolve);CHKERRQ(ierr);
682         sub_schurs->reuse_mumps = msolv_ctx;
683       }
684       ierr = MatDestroy(&F);CHKERRQ(ierr);
685     } else {
686       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
687     }
688     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
689     ierr = MatDestroy(&A);CHKERRQ(ierr);
690     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
691 
692     if (compute_Stilda) {
693       ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_tilda_all);CHKERRQ(ierr);
694       ierr = MatSetSizes(S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
695       ierr = MatSetType(S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
696       ierr = MatSeqAIJSetPreallocation(S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
697       ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_inv_all);CHKERRQ(ierr);
698       ierr = MatSetSizes(S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
699       ierr = MatSetType(S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
700       ierr = MatSeqAIJSetPreallocation(S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
701 
702       /* compute St^-1 */
703       if (size_active_schur) { /* multilevel guard */
704         PetscScalar *vals;
705 
706         ierr = PetscBLASIntCast(size_active_schur,&B_N);CHKERRQ(ierr);
707         ierr = MatDuplicate(S_all,MAT_COPY_VALUES,&S_all_inv);CHKERRQ(ierr);
708         ierr = MatDenseGetArray(S_all_inv,&vals);CHKERRQ(ierr);
709         if (!sub_schurs->is_hermitian) {
710           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,vals,&B_N,pivots,&B_ierr));
711           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
712           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,vals,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
713           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
714         } else {
715           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,vals,&B_N,&B_ierr));
716           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
717           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,vals,&B_N,&B_ierr));
718           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
719         }
720         ierr = MatDenseRestoreArray(S_all_inv,&vals);CHKERRQ(ierr);
721       }
722     }
723 
724     /* S_all_inv (if any) inside PCBDDCReuseMumps */
725     if (sub_schurs->reuse_mumps && S_all_inv) {
726       PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;
727 
728       ierr = PetscObjectReference((PetscObject)S_all_inv);CHKERRQ(ierr);
729       reuse_mumps->S_inv = S_all_inv;
730       ierr = MatCreateVecs(S_all_inv,&reuse_mumps->solB,&reuse_mumps->rhsB);CHKERRQ(ierr);
731     }
732 
733     /* Work arrays */
734     if (sub_schurs->n_subs == 1) {
735       ierr = PetscMalloc1(max_subset_size,&dummy_idx);CHKERRQ(ierr);
736     } else {
737       ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
738     }
739 
740     local_size = 0;
741     for (i=0;i<sub_schurs->n_subs;i++) {
742       Mat S_Ej;
743       IS  is_E;
744       PetscInt j;
745 
746       /* get S_E */
747       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
748       if (sub_schurs->n_subs == 1) {
749         ierr = MatDenseGetArray(S_all,&work);CHKERRQ(ierr);
750         S_Ej = NULL;
751         is_E = NULL;
752       } else {
753         ierr = ISCreateStride(PETSC_COMM_SELF,subset_size,local_size,1,&is_E);CHKERRQ(ierr);
754         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej);CHKERRQ(ierr);
755         ierr = MatGetSubMatrix(S_all,is_E,is_E,MAT_REUSE_MATRIX,&S_Ej);CHKERRQ(ierr);
756       }
757       /* insert S_E values */
758       for (j=0;j<subset_size;j++) {
759         dummy_idx[j]=local_size+j;
760       }
761       ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
762 
763       /* if adaptivity is requested, invert S_E and insert St_E^-1 blocks */
764       if (compute_Stilda && ((PetscBTLookup(sub_schurs->is_edge,i) && use_edges) || (!PetscBTLookup(sub_schurs->is_edge,i) && use_faces))) {
765         /* get S_E^-1 */
766         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
767         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
768         if (!sub_schurs->is_hermitian) {
769           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
770           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
771           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
772           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
773         } else {
774           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
775           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
776           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
777           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
778         }
779         ierr = PetscFPTrapPop();CHKERRQ(ierr);
780         ierr = MatSetValues(S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
781 
782         /* get St_E^-1 */
783         if (sub_schurs->n_subs == 1) {
784           ierr = MatDenseRestoreArray(S_all,&work);CHKERRQ(ierr);
785           ierr = MatDenseGetArray(S_all_inv,&work);CHKERRQ(ierr);
786         } else {
787           ierr = MatGetSubMatrix(S_all_inv,is_E,is_E,MAT_REUSE_MATRIX,&S_Ej);CHKERRQ(ierr);
788         }
789         ierr = MatSetValues(S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
790         if (sub_schurs->n_subs == 1) {
791           ierr = MatDenseRestoreArray(S_all_inv,&work);CHKERRQ(ierr);
792         }
793         ierr = PetscBTSet(sub_schurs->computed_Stilda_subs,i);CHKERRQ(ierr);
794       } else if (sub_schurs->n_subs == 1) {
795         ierr = MatDenseRestoreArray(S_all,&work);CHKERRQ(ierr);
796       }
797       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
798       ierr = ISDestroy(&is_E);CHKERRQ(ierr);
799       local_size += subset_size;
800     }
801     if (sub_schurs->n_subs == 1) {
802       ierr = PetscFree(dummy_idx);CHKERRQ(ierr);
803     } else {
804       ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
805     }
806   }
807   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
808   ierr = PetscFree(nnz);CHKERRQ(ierr);
809   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
810   ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
811   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
812   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
813   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
814   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
815   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
816   if (compute_Stilda) {
817     ierr = MatAssemblyBegin(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
818     ierr = MatAssemblyEnd(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
819     ierr = MatAssemblyBegin(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
820     ierr = MatAssemblyEnd(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
821   }
822 
823   /* Global matrix of all assembled Schur on subsets */
824   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
825   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
826   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
827 
828   /* Get local part of (\sum_j S_Ej) */
829   ierr = ISCreateGeneral(comm_n,local_size,all_local_idx_G,PETSC_OWN_POINTER,&temp_is);CHKERRQ(ierr);
830   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
831   ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
832 
833   /* Compute explicitly (\sum_j S_Ej)^-1 (faster scaling during PCApply, needs extra work when doing setup) */
834   if (faster_deluxe) {
835     Mat         tmpmat;
836     PetscScalar *array;
837     PetscInt    cum;
838 
839     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all,&array);CHKERRQ(ierr);
840     cum = 0;
841     for (i=0;i<sub_schurs->n_subs;i++) {
842       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
843       ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
844       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
845       if (!sub_schurs->is_hermitian) {
846         PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
847         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
848         PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
849         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
850       } else {
851         PetscInt j,k;
852 
853         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
854         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
855         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
856         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
857         for (j=0;j<B_N;j++) {
858           for (k=j+1;k<B_N;k++) {
859             array[k*B_N+j+cum] = array[j*B_N+k+cum];
860           }
861         }
862       }
863       ierr = PetscFPTrapPop();CHKERRQ(ierr);
864       cum += subset_size*subset_size;
865     }
866     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all,&array);CHKERRQ(ierr);
867     ierr = MatMatMult(sub_schurs->S_Ej_all,sub_schurs->sum_S_Ej_all,MAT_INITIAL_MATRIX,1.0,&tmpmat);CHKERRQ(ierr);
868     ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
869     ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
870     sub_schurs->S_Ej_all = tmpmat;
871   }
872 
873   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
874   if (compute_Stilda) {
875     ierr = MatISSetLocalMat(work_mat,S_Ej_tilda_all);CHKERRQ(ierr);
876     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
877     ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
878     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
879     ierr = MatISSetLocalMat(work_mat,S_Ej_inv_all);CHKERRQ(ierr);
880     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
881     ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
882     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
883   }
884 
885   /* free workspace */
886   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
887   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
888   ierr = MatDestroy(&S_Ej_tilda_all);CHKERRQ(ierr);
889   ierr = MatDestroy(&S_Ej_inv_all);CHKERRQ(ierr);
890   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
891   ierr = ISDestroy(&temp_is);CHKERRQ(ierr);
892   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
893   PetscFunctionReturn(0);
894 }
895 
896 #undef __FUNCT__
897 #define __FUNCT__ "PCBDDCSubSchursInit"
898 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap)
899 {
900   IS              *faces,*edges,*all_cc,vertices;
901   PetscInt        i,n_faces,n_edges,n_all_cc;
902   PetscBool       is_sorted;
903   PetscErrorCode  ierr;
904 
905   PetscFunctionBegin;
906   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
907   if (!is_sorted) {
908     SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
909   }
910   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
911   if (!is_sorted) {
912     SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
913   }
914 
915   /* reset any previous data */
916   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
917 
918   /* get index sets for faces and edges (already sorted by global ordering) */
919   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
920   n_all_cc = n_faces+n_edges;
921   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
922   ierr = PetscBTCreate(n_all_cc,&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
923   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
924   for (i=0;i<n_faces;i++) {
925     all_cc[i] = faces[i];
926   }
927   for (i=0;i<n_edges;i++) {
928     all_cc[n_faces+i] = edges[i];
929     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
930   }
931   ierr = PetscFree(faces);CHKERRQ(ierr);
932   ierr = PetscFree(edges);CHKERRQ(ierr);
933   sub_schurs->is_dir = NULL;
934   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
935 
936   /* Determine if MUMPS can be used */
937   sub_schurs->use_mumps = PETSC_FALSE;
938 #if defined(PETSC_HAVE_MUMPS)
939   sub_schurs->use_mumps = PETSC_TRUE;
940 #endif
941 
942   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
943   sub_schurs->is_I = is_I;
944   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
945   sub_schurs->is_B = is_B;
946   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
947   sub_schurs->l2gmap = graph->l2gmap;
948   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
949   sub_schurs->BtoNmap = BtoNmap;
950   sub_schurs->n_subs = n_all_cc;
951   sub_schurs->is_subs = all_cc;
952   if (!sub_schurs->use_mumps) { /* sort by local ordering mumps is not present */
953     for (i=0;i<sub_schurs->n_subs;i++) {
954       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
955     }
956   }
957   sub_schurs->is_vertices = vertices;
958   sub_schurs->S_Ej_all = NULL;
959   sub_schurs->sum_S_Ej_all = NULL;
960   sub_schurs->sum_S_Ej_inv_all = NULL;
961   sub_schurs->sum_S_Ej_tilda_all = NULL;
962   sub_schurs->is_Ej_all = NULL;
963   PetscFunctionReturn(0);
964 }
965 
966 #undef __FUNCT__
967 #define __FUNCT__ "PCBDDCSubSchursCreate"
968 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
969 {
970   PCBDDCSubSchurs schurs_ctx;
971   PetscErrorCode  ierr;
972 
973   PetscFunctionBegin;
974   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
975   schurs_ctx->n_subs = 0;
976   *sub_schurs = schurs_ctx;
977   PetscFunctionReturn(0);
978 }
979 
980 #undef __FUNCT__
981 #define __FUNCT__ "PCBDDCSubSchursDestroy"
982 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
983 {
984   PetscErrorCode ierr;
985 
986   PetscFunctionBegin;
987   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
988   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
989   PetscFunctionReturn(0);
990 }
991 
992 #undef __FUNCT__
993 #define __FUNCT__ "PCBDDCSubSchursReset"
994 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
995 {
996   PetscInt       i;
997   PetscErrorCode ierr;
998 
999   PetscFunctionBegin;
1000   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1001   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1002   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1003   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1004   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1005   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1006   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1007   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1008   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1009   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1010   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1011   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1012   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1013   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1014   ierr = PetscBTDestroy(&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
1015   for (i=0;i<sub_schurs->n_subs;i++) {
1016     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1017   }
1018   if (sub_schurs->n_subs) {
1019     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1020   }
1021   if (sub_schurs->reuse_mumps) {
1022     ierr = PCBDDCReuseMumpsReset(sub_schurs->reuse_mumps);CHKERRQ(ierr);
1023   }
1024   ierr = PetscFree(sub_schurs->reuse_mumps);CHKERRQ(ierr);
1025   sub_schurs->n_subs = 0;
1026   PetscFunctionReturn(0);
1027 }
1028 
1029 #undef __FUNCT__
1030 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
1031 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1032 {
1033   PetscInt       i,j,n;
1034   PetscErrorCode ierr;
1035 
1036   PetscFunctionBegin;
1037   n = 0;
1038   for (i=-n_prev;i<0;i++) {
1039     PetscInt start_dof = queue_tip[i];
1040     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1041       PetscInt dof = adjncy[j];
1042       if (!PetscBTLookup(touched,dof)) {
1043         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1044         queue_tip[n] = dof;
1045         n++;
1046       }
1047     }
1048   }
1049   *n_added = n;
1050   PetscFunctionReturn(0);
1051 }
1052