xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 17d7d9258a1c6f50bcce6bd41950d5afced449e8)
1 /* TODOLIST
2    DofSplitting and DM attached to pc?
3    Change SetNeumannBoundaries to SetNeumannBoundariesLocal and provide new SetNeumannBoundaries (same Dirichlet)
4      - change prec_type to switch_inexact_prec_type
5    Inexact solvers: global preconditioner application is ready, ask to developers (Jed?) on how to best implement Dohrmann's approach (PCSHELL?)
6    change how to deal with the coarse problem (PCBDDCSetCoarseEnvironment):
7      - mind the problem with coarsening_factor
8      - simplify coarse problem structure -> PCBDDC or PCREDUDANT, nothing else -> same comm for all levels?
9      - remove coarse enums and allow use of PCBDDCGetCoarseKSP
10      - remove metis dependency -> use MatPartitioning for multilevel -> Assemble serial adjacency in ManageLocalBoundaries?
11      - Add levels' slot to bddc data structure and associated Set/Get functions
12    code refactoring:
13      - pick up better names for static functions
14    change options structure:
15      - insert BDDC into MG framework?
16    provide other ops? Ask to developers
17    remove all unused printf
18    man pages
19 */
20 
21 /* ----------------------------------------------------------------------------------------------------------------------------------------------
22    Implementation of BDDC preconditioner based on:
23    C. Dohrmann "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
24    ---------------------------------------------------------------------------------------------------------------------------------------------- */
25 
26 #include "bddc.h" /*I "petscpc.h" I*/  /* includes for fortran wrappers */
27 #include <petscblaslapack.h>
28 /* -------------------------------------------------------------------------- */
29 #undef __FUNCT__
30 #define __FUNCT__ "PCSetFromOptions_BDDC"
31 PetscErrorCode PCSetFromOptions_BDDC(PC pc)
32 {
33   PC_BDDC         *pcbddc = (PC_BDDC*)pc->data;
34   PetscErrorCode ierr;
35 
36   PetscFunctionBegin;
37   ierr = PetscOptionsHead("BDDC options");CHKERRQ(ierr);
38   /* Verbose debugging of main data structures */
39   ierr = PetscOptionsBool("-pc_bddc_check_all"       ,"Verbose (debugging) output for PCBDDC"                       ,"none",pcbddc->dbg_flag      ,&pcbddc->dbg_flag      ,PETSC_NULL);CHKERRQ(ierr);
40   /* Some customization for default primal space */
41   ierr = PetscOptionsBool("-pc_bddc_vertices_only"   ,"Use only vertices in coarse space (i.e. discard constraints)","none",pcbddc->vertices_flag   ,&pcbddc->vertices_flag   ,PETSC_NULL);CHKERRQ(ierr);
42   ierr = PetscOptionsBool("-pc_bddc_constraints_only","Use only constraints in coarse space (i.e. discard vertices)","none",pcbddc->constraints_flag,&pcbddc->constraints_flag,PETSC_NULL);CHKERRQ(ierr);
43   ierr = PetscOptionsBool("-pc_bddc_faces_only"      ,"Use only faces among constraints of coarse space (i.e. discard edges)"         ,"none",pcbddc->faces_flag      ,&pcbddc->faces_flag      ,PETSC_NULL);CHKERRQ(ierr);
44   ierr = PetscOptionsBool("-pc_bddc_edges_only"      ,"Use only edges among constraints of coarse space (i.e. discard faces)"         ,"none",pcbddc->edges_flag      ,&pcbddc->edges_flag      ,PETSC_NULL);CHKERRQ(ierr);
45   /* Coarse solver context */
46   static const char *avail_coarse_problems[] = {"sequential","replicated","parallel","multilevel",""}; /*order of choiches depends on ENUM defined in bddc.h */
47   ierr = PetscOptionsEnum("-pc_bddc_coarse_problem_type","Set coarse problem type","none",avail_coarse_problems,(PetscEnum)pcbddc->coarse_problem_type,(PetscEnum*)&pcbddc->coarse_problem_type,PETSC_NULL);CHKERRQ(ierr);
48   /* Two different application of BDDC to the whole set of dofs, internal and interface */
49   ierr = PetscOptionsBool("-pc_bddc_switch_preconditioning_type","Switch between M_2 (default) and M_3 preconditioners (as defined by Dohrmann)","none",pcbddc->prec_type,&pcbddc->prec_type,PETSC_NULL);CHKERRQ(ierr);
50   ierr = PetscOptionsBool("-pc_bddc_use_change_of_basis","Use change of basis approach for primal space","none",pcbddc->usechangeofbasis,&pcbddc->usechangeofbasis,PETSC_NULL);CHKERRQ(ierr);
51   ierr = PetscOptionsBool("-pc_bddc_use_change_on_faces","Use change of basis approach for face constraints","none",pcbddc->usechangeonfaces,&pcbddc->usechangeonfaces,PETSC_NULL);CHKERRQ(ierr);
52   pcbddc->usechangeonfaces = pcbddc->usechangeonfaces && pcbddc->usechangeofbasis;
53   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,PETSC_NULL);CHKERRQ(ierr);
54   ierr = PetscOptionsTail();CHKERRQ(ierr);
55   PetscFunctionReturn(0);
56 }
57 /* -------------------------------------------------------------------------- */
58 EXTERN_C_BEGIN
59 #undef __FUNCT__
60 #define __FUNCT__ "PCBDDCSetCoarseProblemType_BDDC"
61 static PetscErrorCode PCBDDCSetCoarseProblemType_BDDC(PC pc, CoarseProblemType CPT)
62 {
63   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
64 
65   PetscFunctionBegin;
66   pcbddc->coarse_problem_type = CPT;
67   PetscFunctionReturn(0);
68 }
69 EXTERN_C_END
70 #undef __FUNCT__
71 #define __FUNCT__ "PCBDDCSetCoarseProblemType"
72 /*@
73  PCBDDCSetCoarseProblemType - Set coarse problem type in PCBDDC.
74 
75    Not collective
76 
77    Input Parameters:
78 +  pc - the preconditioning context
79 -  CoarseProblemType - pick a better name and explain what this is
80 
81    Level: intermediate
82 
83    Notes:
84    Not collective but all procs must call with same arguments.
85 
86 .seealso: PCBDDC
87 @*/
88 PetscErrorCode PCBDDCSetCoarseProblemType(PC pc, CoarseProblemType CPT)
89 {
90   PetscErrorCode ierr;
91 
92   PetscFunctionBegin;
93   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
94   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseProblemType_C",(PC,CoarseProblemType),(pc,CPT));CHKERRQ(ierr);
95   PetscFunctionReturn(0);
96 }
97 /* -------------------------------------------------------------------------- */
98 EXTERN_C_BEGIN
99 #undef __FUNCT__
100 #define __FUNCT__ "PCBDDCSetDirichletBoundaries_BDDC"
101 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
102 {
103   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
104   PetscErrorCode ierr;
105 
106   PetscFunctionBegin;
107   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
108   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
109   pcbddc->DirichletBoundaries=DirichletBoundaries;
110   PetscFunctionReturn(0);
111 }
112 EXTERN_C_END
113 #undef __FUNCT__
114 #define __FUNCT__ "PCBDDCSetDirichletBoundaries"
115 /*@
116  PCBDDCSetDirichletBoundaries - Set index set defining subdomain part (in local ordering)
117                               of Dirichlet boundaries for the global problem.
118 
119    Not collective
120 
121    Input Parameters:
122 +  pc - the preconditioning context
123 -  DirichletBoundaries - sequential index set defining the subdomain part of Dirichlet boundaries (can be PETSC_NULL)
124 
125    Level: intermediate
126 
127    Notes:
128 
129 .seealso: PCBDDC
130 @*/
131 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
132 {
133   PetscErrorCode ierr;
134 
135   PetscFunctionBegin;
136   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
137   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
138   PetscFunctionReturn(0);
139 }
140 /* -------------------------------------------------------------------------- */
141 EXTERN_C_BEGIN
142 #undef __FUNCT__
143 #define __FUNCT__ "PCBDDCSetNeumannBoundaries_BDDC"
144 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
145 {
146   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
147   PetscErrorCode ierr;
148 
149   PetscFunctionBegin;
150   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
151   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
152   pcbddc->NeumannBoundaries=NeumannBoundaries;
153   PetscFunctionReturn(0);
154 }
155 EXTERN_C_END
156 #undef __FUNCT__
157 #define __FUNCT__ "PCBDDCSetNeumannBoundaries"
158 /*@
159  PCBDDCSetNeumannBoundaries - Set index set defining subdomain part (in local ordering)
160                               of Neumann boundaries for the global problem.
161 
162    Not collective
163 
164    Input Parameters:
165 +  pc - the preconditioning context
166 -  NeumannBoundaries - sequential index set defining the subdomain part of Neumann boundaries (can be PETSC_NULL)
167 
168    Level: intermediate
169 
170    Notes:
171 
172 .seealso: PCBDDC
173 @*/
174 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
175 {
176   PetscErrorCode ierr;
177 
178   PetscFunctionBegin;
179   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
180   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
181   PetscFunctionReturn(0);
182 }
183 /* -------------------------------------------------------------------------- */
184 EXTERN_C_BEGIN
185 #undef __FUNCT__
186 #define __FUNCT__ "PCBDDCGetDirichletBoundaries_BDDC"
187 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
188 {
189   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
190 
191   PetscFunctionBegin;
192   *DirichletBoundaries = pcbddc->DirichletBoundaries;
193   PetscFunctionReturn(0);
194 }
195 EXTERN_C_END
196 #undef __FUNCT__
197 #define __FUNCT__ "PCBDDCGetDirichletBoundaries"
198 /*@
199  PCBDDCGetDirichletBoundaries - Get index set defining subdomain part (in local ordering)
200                                 of Dirichlet boundaries for the global problem.
201 
202    Not collective
203 
204    Input Parameters:
205 +  pc - the preconditioning context
206 
207    Output Parameters:
208 +  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
209 
210    Level: intermediate
211 
212    Notes:
213 
214 .seealso: PCBDDC
215 @*/
216 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
217 {
218   PetscErrorCode ierr;
219 
220   PetscFunctionBegin;
221   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
222   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
223   PetscFunctionReturn(0);
224 }
225 /* -------------------------------------------------------------------------- */
226 EXTERN_C_BEGIN
227 #undef __FUNCT__
228 #define __FUNCT__ "PCBDDCGetNeumannBoundaries_BDDC"
229 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
230 {
231   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
232 
233   PetscFunctionBegin;
234   *NeumannBoundaries = pcbddc->NeumannBoundaries;
235   PetscFunctionReturn(0);
236 }
237 EXTERN_C_END
238 #undef __FUNCT__
239 #define __FUNCT__ "PCBDDCGetNeumannBoundaries"
240 /*@
241  PCBDDCGetNeumannBoundaries - Get index set defining subdomain part (in local ordering)
242                               of Neumann boundaries for the global problem.
243 
244    Not collective
245 
246    Input Parameters:
247 +  pc - the preconditioning context
248 
249    Output Parameters:
250 +  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
251 
252    Level: intermediate
253 
254    Notes:
255 
256 .seealso: PCBDDC
257 @*/
258 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
259 {
260   PetscErrorCode ierr;
261 
262   PetscFunctionBegin;
263   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
264   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
265   PetscFunctionReturn(0);
266 }
267 /* -------------------------------------------------------------------------- */
268 EXTERN_C_BEGIN
269 #undef __FUNCT__
270 #define __FUNCT__ "PCBDDCSetLocalAdjacencyGraph_BDDC"
271 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs, PetscInt xadj[], PetscInt adjncy[], PetscCopyMode copymode)
272 {
273   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
274   PCBDDCGraph    mat_graph=pcbddc->mat_graph;
275   PetscErrorCode ierr;
276 
277   PetscFunctionBegin;
278   mat_graph->nvtxs=nvtxs;
279   ierr = PetscFree(mat_graph->xadj);CHKERRQ(ierr);
280   ierr = PetscFree(mat_graph->adjncy);CHKERRQ(ierr);
281   if(copymode == PETSC_COPY_VALUES) {
282     ierr = PetscMalloc((mat_graph->nvtxs+1)*sizeof(PetscInt),&mat_graph->xadj);CHKERRQ(ierr);
283     ierr = PetscMalloc(xadj[mat_graph->nvtxs]*sizeof(PetscInt),&mat_graph->adjncy);CHKERRQ(ierr);
284     ierr = PetscMemcpy(mat_graph->xadj,xadj,(mat_graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
285     ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[mat_graph->nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
286   } else if(copymode == PETSC_OWN_POINTER) {
287     mat_graph->xadj=xadj;
288     mat_graph->adjncy=adjncy;
289   } else {
290     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %d in %s\n",copymode,__FUNCT__);
291   }
292   PetscFunctionReturn(0);
293 }
294 EXTERN_C_END
295 #undef __FUNCT__
296 #define __FUNCT__ "PCBDDCSetLocalAdjacencyGraph"
297 /*@
298  PCBDDCSetLocalAdjacencyGraph - Set CSR graph of local matrix for use of PCBDDC.
299 
300    Not collective
301 
302    Input Parameters:
303 +  pc - the preconditioning context
304 -  nvtxs - number of local vertices of the graph
305 -  xadj, adjncy - the CSR graph
306 -  copymode - either PETSC_COPY_VALUES or PETSC_OWN_POINTER. In the former case the user must free the array passed in;
307                                                              in the latter case, memory must be obtained with PetscMalloc.
308 
309    Level: intermediate
310 
311    Notes:
312 
313 .seealso: PCBDDC
314 @*/
315 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,PetscInt xadj[],PetscInt adjncy[], PetscCopyMode copymode)
316 {
317   PetscInt       nrows,ncols;
318   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
319   PetscErrorCode ierr;
320 
321   PetscFunctionBegin;
322   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
323   ierr = MatGetSize(matis->A,&nrows,&ncols);CHKERRQ(ierr);
324   if(nvtxs != nrows) {
325     SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local adjacency size %d passed in %s differs from local problem size %d!\n",nvtxs,__FUNCT__,nrows);
326   } else {
327     ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,PetscInt[],PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
328   }
329   PetscFunctionReturn(0);
330 }
331 /* -------------------------------------------------------------------------- */
332 EXTERN_C_BEGIN
333 #undef __FUNCT__
334 #define __FUNCT__ "PCBDDCSetDofsSplitting_BDDC"
335 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
336 {
337   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
338   PetscInt i;
339   PetscErrorCode ierr;
340 
341   PetscFunctionBegin;
342   /* Destroy ISes if they were already set */
343   for(i=0;i<pcbddc->n_ISForDofs;i++) {
344     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
345   }
346   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
347   /* allocate space then set */
348   ierr = PetscMalloc(n_is*sizeof(IS),&pcbddc->ISForDofs);CHKERRQ(ierr);
349   for(i=0;i<n_is;i++) {
350     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
351     pcbddc->ISForDofs[i]=ISForDofs[i];
352   }
353   pcbddc->n_ISForDofs=n_is;
354   PetscFunctionReturn(0);
355 }
356 EXTERN_C_END
357 #undef __FUNCT__
358 #define __FUNCT__ "PCBDDCSetDofsSplitting"
359 /*@
360  PCBDDCSetDofsSplitting - Set index sets defining fields of local mat.
361 
362    Not collective
363 
364    Input Parameters:
365 +  pc - the preconditioning context
366 -  n - number of index sets defining the fields
367 -  IS[] - array of IS describing the fields
368 
369    Level: intermediate
370 
371    Notes:
372 
373 .seealso: PCBDDC
374 @*/
375 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
376 {
377   PetscErrorCode ierr;
378 
379   PetscFunctionBegin;
380   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
381   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
382   PetscFunctionReturn(0);
383 }
384 /* -------------------------------------------------------------------------- */
385 #undef __FUNCT__
386 #define __FUNCT__ "PCPreSolve_BDDC"
387 /* -------------------------------------------------------------------------- */
388 /*
389    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
390                      guess if a transformation of basis approach has been selected.
391 
392    Input Parameter:
393 +  pc - the preconditioner contex
394 
395    Application Interface Routine: PCPreSolve()
396 
397    Notes:
398    The interface routine PCPreSolve() is not usually called directly by
399    the user, but instead is called by KSPSolve().
400 */
401 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
402 {
403   PetscErrorCode ierr;
404   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
405   PC_IS          *pcis = (PC_IS*)(pc->data);
406   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
407   Mat            temp_mat;
408   IS             dirIS;
409   PetscInt       dirsize,i,*is_indices;
410   PetscScalar    *array_x,*array_diagonal;
411   Vec            used_vec;
412   PetscBool      guess_nonzero;
413 
414   PetscFunctionBegin;
415   if(x) {
416     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
417     used_vec = x;
418   } else {
419     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
420     used_vec = pcbddc->temp_solution;
421     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
422   }
423   /* hack into ksp data structure PCPreSolve comes earlier in src/ksp/ksp/interface/itfunc.c */
424   if (ksp) {
425     ierr = KSPGetInitialGuessNonzero(ksp,&guess_nonzero);CHKERRQ(ierr);
426     if( !guess_nonzero ) {
427       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
428     }
429   }
430   /* store the original rhs */
431   ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
432 
433   /* Take into account zeroed rows -> change rhs and store solution removed */
434   ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
435   ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
436   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
437   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
438   ierr = VecScatterBegin(matis->ctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
439   ierr = VecScatterEnd  (matis->ctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
440   ierr = PCBDDCGetDirichletBoundaries(pc,&dirIS);CHKERRQ(ierr);
441   if(dirIS) {
442     ierr = ISGetSize(dirIS,&dirsize);CHKERRQ(ierr);
443     ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
444     ierr = VecGetArray(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
445     ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
446     for(i=0;i<dirsize;i++) {
447       array_x[is_indices[i]]=array_diagonal[is_indices[i]];
448     }
449     ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
450     ierr = VecRestoreArray(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
451     ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
452   }
453   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
454   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
455 
456   /* remove the computed solution from the rhs */
457   ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
458   ierr = MatMultAdd(pc->pmat,used_vec,rhs,rhs);CHKERRQ(ierr);
459   ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
460 
461   /* store partially computed solution and set initial guess */
462   if(x) {
463     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
464     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
465     if(pcbddc->use_exact_dirichlet) {
466       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
467       ierr = VecScatterEnd  (pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
468       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
469       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
470       ierr = VecScatterEnd  (pcis->global_to_D,pcis->vec2_D,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
471       if(ksp) {
472         ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
473       }
474     }
475   }
476   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
477 
478   /* rhs change of basis */
479   if(pcbddc->usechangeofbasis) {
480     /* swap pointers for local matrices */
481     temp_mat = matis->A;
482     matis->A = pcbddc->local_mat;
483     pcbddc->local_mat = temp_mat;
484     /* Get local rhs and apply transformation of basis */
485     ierr = VecScatterBegin(pcis->global_to_B,rhs,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
486     ierr = VecScatterEnd  (pcis->global_to_B,rhs,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
487     /* from original basis to modified basis */
488     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcis->vec1_B,pcis->vec2_B);CHKERRQ(ierr);
489     /* put back modified values into the global vec using INSERT_VALUES copy mode */
490     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec2_B,rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
491     ierr = VecScatterEnd  (pcis->global_to_B,pcis->vec2_B,rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
492   }
493   PetscFunctionReturn(0);
494 }
495 /* -------------------------------------------------------------------------- */
496 #undef __FUNCT__
497 #define __FUNCT__ "PCPostSolve_BDDC"
498 /* -------------------------------------------------------------------------- */
499 /*
500    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
501                      approach has been selected. Also, restores rhs to its original state.
502 
503    Input Parameter:
504 +  pc - the preconditioner contex
505 
506    Application Interface Routine: PCPostSolve()
507 
508    Notes:
509    The interface routine PCPostSolve() is not usually called directly by
510    the user, but instead is called by KSPSolve().
511 */
512 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
513 {
514   PetscErrorCode ierr;
515   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
516   PC_IS          *pcis = (PC_IS*)(pc->data);
517   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
518   Mat            temp_mat;
519 
520   PetscFunctionBegin;
521   if(pcbddc->usechangeofbasis) {
522     /* swap pointers for local matrices */
523     temp_mat = matis->A;
524     matis->A = pcbddc->local_mat;
525     pcbddc->local_mat = temp_mat;
526     /* restore rhs to its original state */
527     if(rhs) {
528       ierr = VecCopy(pcbddc->original_rhs,rhs);CHKERRQ(ierr);
529     }
530     /* Get Local boundary and apply transformation of basis to solution vector */
531     ierr = VecScatterBegin(pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
532     ierr = VecScatterEnd  (pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
533     /* from modified basis to original basis */
534     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_B,pcis->vec2_B);CHKERRQ(ierr);
535     /* put back modified values into the global vec using INSERT_VALUES copy mode */
536     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
537     ierr = VecScatterEnd  (pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
538   }
539   /* add solution removed in presolve */
540   if(x) {
541     ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
542   }
543   PetscFunctionReturn(0);
544 }
545 /* -------------------------------------------------------------------------- */
546 #undef __FUNCT__
547 #define __FUNCT__ "PCSetUp_BDDC"
548 /* -------------------------------------------------------------------------- */
549 /*
550    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
551                   by setting data structures and options.
552 
553    Input Parameter:
554 +  pc - the preconditioner context
555 
556    Application Interface Routine: PCSetUp()
557 
558    Notes:
559    The interface routine PCSetUp() is not usually called directly by
560    the user, but instead is called by PCApply() if necessary.
561 */
562 PetscErrorCode PCSetUp_BDDC(PC pc)
563 {
564   PetscErrorCode ierr;
565   PC_BDDC*       pcbddc   = (PC_BDDC*)pc->data;
566   PC_IS            *pcis = (PC_IS*)(pc->data);
567 
568   PetscFunctionBegin;
569   if (!pc->setupcalled) {
570     /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
571        So, we set to pcnone the Neumann problem of pcis in order to avoid unneeded computation
572        Also, we decide to directly build the (same) Dirichlet problem */
573     ierr = PetscOptionsSetValue("-is_localN_pc_type","none");CHKERRQ(ierr);
574     ierr = PetscOptionsSetValue("-is_localD_pc_type","none");CHKERRQ(ierr);
575     /* Set up all the "iterative substructuring" common block */
576     ierr = PCISSetUp(pc);CHKERRQ(ierr);
577     /* Get stdout for dbg */
578     if(pcbddc->dbg_flag) {
579       ierr = PetscViewerASCIIGetStdout(((PetscObject)pc)->comm,&pcbddc->dbg_viewer);CHKERRQ(ierr);
580       ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
581     }
582     /* TODO MOVE CODE FRAGMENT */
583     PetscInt im_active=0;
584     if(pcis->n) im_active = 1;
585     ierr = MPI_Allreduce(&im_active,&pcbddc->active_procs,1,MPIU_INT,MPI_SUM,((PetscObject)pc)->comm);CHKERRQ(ierr);
586     /* Analyze local interface */
587     ierr = PCBDDCManageLocalBoundaries(pc);CHKERRQ(ierr);
588     /* Set up local constraint matrix */
589     ierr = PCBDDCCreateConstraintMatrix(pc);CHKERRQ(ierr);
590     /* Create coarse and local stuffs used for evaluating action of preconditioner */
591     ierr = PCBDDCCoarseSetUp(pc);CHKERRQ(ierr);
592     /* Processes fakely involved in multilevel should not call ISLocalToGlobalMappingRestoreInfo */
593     if ( !pcis->n_neigh ) pcis->ISLocalToGlobalMappingGetInfoWasCalled=PETSC_FALSE;
594   }
595   PetscFunctionReturn(0);
596 }
597 
598 /* -------------------------------------------------------------------------- */
599 /*
600    PCApply_BDDC - Applies the BDDC preconditioner to a vector.
601 
602    Input Parameters:
603 .  pc - the preconditioner context
604 .  r - input vector (global)
605 
606    Output Parameter:
607 .  z - output vector (global)
608 
609    Application Interface Routine: PCApply()
610  */
611 #undef __FUNCT__
612 #define __FUNCT__ "PCApply_BDDC"
613 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
614 {
615   PC_IS             *pcis = (PC_IS*)(pc->data);
616   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
617   PetscErrorCode    ierr;
618   const PetscScalar one = 1.0;
619   const PetscScalar m_one = -1.0;
620   const PetscScalar zero = 0.0;
621 
622 /* This code is similar to that provided in nn.c for PCNN
623    NN interface preconditioner changed to BDDC
624    Added support for M_3 preconditioenr in the reference article (code is active if pcbddc->prec_type = PETSC_TRUE) */
625 
626   PetscFunctionBegin;
627   if(!pcbddc->use_exact_dirichlet) {
628     /* First Dirichlet solve */
629     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
630     ierr = VecScatterEnd  (pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
631     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
632     /*
633       Assembling right hand side for BDDC operator
634       - vec1_D for the Dirichlet part (if needed, i.e. prec_flag=PETSC_TRUE)
635       - the interface part of the global vector z
636     */
637     ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
638     ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
639     if(pcbddc->prec_type) { ierr = MatMultAdd(pcis->A_II,pcis->vec2_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
640     ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
641     ierr = VecCopy(r,z);CHKERRQ(ierr);
642     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
643     ierr = VecScatterEnd  (pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
644     ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
645     ierr = VecScatterEnd  (pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
646   } else {
647     ierr = VecScatterBegin(pcis->global_to_B,r,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
648     ierr = VecScatterEnd  (pcis->global_to_B,r,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
649     ierr = VecSet(pcis->vec2_D,zero);CHKERRQ(ierr);
650   }
651 
652   /* Apply partition of unity */
653   ierr = VecPointwiseMult(pcis->vec1_B,pcis->D,pcis->vec1_B);CHKERRQ(ierr);
654 
655   /* Apply interface preconditioner
656      input/output vecs: pcis->vec1_B and pcis->vec1_D */
657   ierr = PCBDDCApplyInterfacePreconditioner(pc);CHKERRQ(ierr);
658 
659   /* Apply partition of unity and sum boundary values */
660   ierr = VecPointwiseMult(pcis->vec1_B,pcis->D,pcis->vec1_B);CHKERRQ(ierr);
661   ierr = VecSet(z,zero);CHKERRQ(ierr);
662   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
663   ierr = VecScatterEnd  (pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
664 
665   /* Second Dirichlet solve and assembling of output */
666   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
667   ierr = VecScatterEnd  (pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
668   ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
669   if(pcbddc->prec_type) { ierr = MatMultAdd(pcis->A_II,pcis->vec1_D,pcis->vec3_D,pcis->vec3_D);CHKERRQ(ierr); }
670   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcbddc->vec4_D);CHKERRQ(ierr);
671   ierr = VecScale(pcbddc->vec4_D,m_one);CHKERRQ(ierr);
672   if(pcbddc->prec_type) { ierr = VecAXPY (pcbddc->vec4_D,one,pcis->vec1_D);CHKERRQ(ierr); }
673   ierr = VecAXPY (pcis->vec2_D,one,pcbddc->vec4_D);CHKERRQ(ierr);
674   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
675   ierr = VecScatterEnd  (pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
676   PetscFunctionReturn(0);
677 
678 }
679 /* -------------------------------------------------------------------------- */
680 #undef __FUNCT__
681 #define __FUNCT__ "PCDestroy_BDDC"
682 PetscErrorCode PCDestroy_BDDC(PC pc)
683 {
684   PC_BDDC          *pcbddc = (PC_BDDC*)pc->data;
685   PetscErrorCode ierr;
686 
687   PetscFunctionBegin;
688   /* free data created by PCIS */
689   ierr = PCISDestroy(pc);CHKERRQ(ierr);
690   /* free BDDC data  */
691   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
692   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
693   ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
694   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
695   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
696   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
697   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
698   ierr = MatDestroy(&pcbddc->coarse_mat);CHKERRQ(ierr);
699   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
700   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
701   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
702   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
703   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
704   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
705   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
706   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
707   ierr = VecDestroy(&pcbddc->vec4_D);CHKERRQ(ierr);
708   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
709   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
710   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
711   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
712   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
713   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
714   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
715   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
716   ierr = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
717   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
718   if (pcbddc->replicated_local_primal_values)    { free(pcbddc->replicated_local_primal_values); }
719   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
720   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
721   PetscInt i;
722   for(i=0;i<pcbddc->n_ISForDofs;i++) { ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr); }
723   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
724   for(i=0;i<pcbddc->n_ISForFaces;i++) { ierr = ISDestroy(&pcbddc->ISForFaces[i]);CHKERRQ(ierr); }
725   ierr = PetscFree(pcbddc->ISForFaces);CHKERRQ(ierr);
726   for(i=0;i<pcbddc->n_ISForEdges;i++) { ierr = ISDestroy(&pcbddc->ISForEdges[i]);CHKERRQ(ierr); }
727   ierr = PetscFree(pcbddc->ISForEdges);CHKERRQ(ierr);
728   ierr = ISDestroy(&pcbddc->ISForVertices);CHKERRQ(ierr);
729   /* Free graph structure */
730   ierr = PetscFree(pcbddc->mat_graph->xadj);CHKERRQ(ierr);
731   ierr = PetscFree(pcbddc->mat_graph->adjncy);CHKERRQ(ierr);
732   ierr = PetscFree(pcbddc->mat_graph->neighbours_set[0]);CHKERRQ(ierr);
733   ierr = PetscFree(pcbddc->mat_graph->neighbours_set);CHKERRQ(ierr);
734   ierr = PetscFree4(pcbddc->mat_graph->where,pcbddc->mat_graph->count,pcbddc->mat_graph->cptr,pcbddc->mat_graph->queue);CHKERRQ(ierr);
735   ierr = PetscFree2(pcbddc->mat_graph->which_dof,pcbddc->mat_graph->touched);CHKERRQ(ierr);
736   ierr = PetscFree(pcbddc->mat_graph->where_ncmps);CHKERRQ(ierr);
737   ierr = PetscFree(pcbddc->mat_graph);CHKERRQ(ierr);
738   /* remove functions */
739   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C","",PETSC_NULL);CHKERRQ(ierr);
740   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C","",PETSC_NULL);CHKERRQ(ierr);
741   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C","",PETSC_NULL);CHKERRQ(ierr);
742   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C","",PETSC_NULL);CHKERRQ(ierr);
743   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetCoarseProblemType_C","",PETSC_NULL);CHKERRQ(ierr);
744   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetDofsSplitting_C","",PETSC_NULL);CHKERRQ(ierr);
745   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C","",PETSC_NULL);CHKERRQ(ierr);
746   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCPreSolve_C","",PETSC_NULL);CHKERRQ(ierr);
747   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCPostSolve_C","",PETSC_NULL);CHKERRQ(ierr);
748   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C","",PETSC_NULL);CHKERRQ(ierr);
749   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C","",PETSC_NULL);CHKERRQ(ierr);
750   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C","",PETSC_NULL);CHKERRQ(ierr);
751   /* Free the private data structure that was hanging off the PC */
752   ierr = PetscFree(pcbddc);CHKERRQ(ierr);
753   PetscFunctionReturn(0);
754 }
755 /* -------------------------------------------------------------------------- */
756 EXTERN_C_BEGIN
757 #undef __FUNCT__
758 #define __FUNCT__ "PCBDDCMatFETIDPGetRHS_BDDC"
759 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
760 {
761   FETIDPMat_ctx  *mat_ctx;
762   PC_IS*         pcis;
763   PC_BDDC*       pcbddc;
764   Mat_IS*        matis;
765   PetscErrorCode ierr;
766 
767   PetscFunctionBegin;
768   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
769   pcis = (PC_IS*)mat_ctx->pc->data;
770   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
771   matis = (Mat_IS*)mat_ctx->pc->pmat->data;
772 
773   /* change of basis for physical rhs if needed
774      It also changes the rhs in case of dirichlet boundaries */
775   (*mat_ctx->pc->ops->presolve)(mat_ctx->pc,PETSC_NULL,standard_rhs,PETSC_NULL);
776   /* store vectors for computation of fetidp final solution */
777   ierr = VecScatterBegin(pcis->global_to_D,standard_rhs,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
778   ierr = VecScatterEnd  (pcis->global_to_D,standard_rhs,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
779   ierr = VecScatterBegin(pcis->global_to_B,standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
780   ierr = VecScatterEnd  (pcis->global_to_B,standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
781   /* scale rhs since it should be unassembled */
782   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
783   if(!pcbddc->prec_type) {
784     /* compute partially subassembled Schur complement right-hand side */
785     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
786     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
787     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
788     ierr = VecSet(standard_rhs,0.0);CHKERRQ(ierr);
789     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,standard_rhs,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
790     ierr = VecScatterEnd  (pcis->global_to_B,mat_ctx->temp_solution_B,standard_rhs,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
791     ierr = VecScatterBegin(pcis->global_to_B,standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
792     ierr = VecScatterEnd  (pcis->global_to_B,standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
793     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
794   }
795   /* BDDC rhs */
796   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
797   if(pcbddc->prec_type) {
798     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
799   }
800   /* apply BDDC */
801   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc);CHKERRQ(ierr);
802   /* Application of B_delta and assembling of rhs for fetidp fluxes */
803   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
804   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
805   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
806   ierr = VecScatterEnd  (mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
807   /* restore original rhs */
808   ierr = VecCopy(pcbddc->original_rhs,standard_rhs);CHKERRQ(ierr);
809   PetscFunctionReturn(0);
810 }
811 EXTERN_C_END
812 #undef __FUNCT__
813 #define __FUNCT__ "PCBDDCMatFETIDPGetRHS"
814 /*@
815  PCBDDCMatFETIDPGetRHS - Get rhs for FETIDP linear system.
816 
817    Collective
818 
819    Input Parameters:
820 +  fetidp_mat   - the FETIDP mat obtained by a call to PCBDDCCreateFETIDPOperators
821 +  standard_rhs - the rhs of your linear system
822 
823    Output Parameters:
824 +  fetidp_flux_rhs   - the rhs of the FETIDP linear system
825 
826    Level: developer
827 
828    Notes:
829 
830 .seealso: PCBDDC
831 @*/
832 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
833 {
834   FETIDPMat_ctx  *mat_ctx;
835   PetscErrorCode ierr;
836 
837   PetscFunctionBegin;
838   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
839   ierr = PetscTryMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
840   PetscFunctionReturn(0);
841 }
842 /* -------------------------------------------------------------------------- */
843 EXTERN_C_BEGIN
844 #undef __FUNCT__
845 #define __FUNCT__ "PCBDDCMatFETIDPGetSolution_BDDC"
846 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
847 {
848   FETIDPMat_ctx  *mat_ctx;
849   PC_IS*         pcis;
850   PC_BDDC*       pcbddc;
851   Mat_IS*        matis;
852   PetscErrorCode ierr;
853 
854   PetscFunctionBegin;
855   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
856   pcis = (PC_IS*)mat_ctx->pc->data;
857   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
858   matis = (Mat_IS*)mat_ctx->pc->pmat->data;
859 
860   /* apply B_delta^T */
861   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
862   ierr = VecScatterEnd  (mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
863   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
864   /* compute rhs for BDDC application */
865   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
866   if(pcbddc->prec_type) {
867     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
868   }
869   /* apply BDDC */
870   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc);CHKERRQ(ierr);
871   /* put values into standard global vector */
872   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
873   ierr = VecScatterEnd  (pcis->global_to_B,pcis->vec1_B,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
874   if(!pcbddc->prec_type) {
875     /* compute values into the interior if solved for the partially subassembled Schur complement */
876     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
877     ierr = VecAXPY(mat_ctx->temp_solution_D,-1.0,pcis->vec1_D);CHKERRQ(ierr);
878     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
879   }
880   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
881   ierr = VecScatterEnd  (pcis->global_to_D,pcis->vec1_D,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
882   /* final change of basis if needed
883      Is also sums the dirichlet part removed during RHS assembling */
884   (*mat_ctx->pc->ops->postsolve)(mat_ctx->pc,PETSC_NULL,PETSC_NULL,standard_sol);
885   PetscFunctionReturn(0);
886 
887 }
888 EXTERN_C_END
889 #undef __FUNCT__
890 #define __FUNCT__ "PCBDDCMatFETIDPGetSolution"
891 /*@
892  PCBDDCMatFETIDPGetSolution - Get Solution for FETIDP linear system.
893 
894    Collective
895 
896    Input Parameters:
897 +  fetidp_mat        - the FETIDP mat obtained by a call to PCBDDCCreateFETIDPOperators
898 +  fetidp_flux_sol - the solution of the FETIDP linear system
899 
900    Output Parameters:
901 +  standard_sol      - the solution on the global domain
902 
903    Level: developer
904 
905    Notes:
906 
907 .seealso: PCBDDC
908 @*/
909 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
910 {
911   FETIDPMat_ctx  *mat_ctx;
912   PetscErrorCode ierr;
913 
914   PetscFunctionBegin;
915   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
916   ierr = PetscTryMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
917   PetscFunctionReturn(0);
918 }
919 /* -------------------------------------------------------------------------- */
920 EXTERN_C_BEGIN
921 #undef __FUNCT__
922 #define __FUNCT__ "PCBDDCCreateFETIDPOperators_BDDC"
923 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, Mat *fetidp_mat, PC *fetidp_pc)
924 {
925   PETSC_EXTERN PetscErrorCode FETIDPMatMult(Mat,Vec,Vec);
926   PETSC_EXTERN PetscErrorCode PCBDDCDestroyFETIDPMat(Mat);
927   PETSC_EXTERN PetscErrorCode FETIDPPCApply(PC,Vec,Vec);
928   PETSC_EXTERN PetscErrorCode PCBDDCDestroyFETIDPPC(PC);
929 
930   FETIDPMat_ctx  *fetidpmat_ctx;
931   Mat            newmat;
932   FETIDPPC_ctx  *fetidppc_ctx;
933   PC             newpc;
934   MPI_Comm       comm = ((PetscObject)pc)->comm;
935   PetscErrorCode ierr;
936 
937   PetscFunctionBegin;
938   /* FETIDP linear matrix */
939   ierr = PCBDDCCreateFETIDPMatContext(pc, &fetidpmat_ctx);CHKERRQ(ierr);
940   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
941   ierr = MatCreateShell(comm,PETSC_DECIDE,PETSC_DECIDE,fetidpmat_ctx->n_lambda,fetidpmat_ctx->n_lambda,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
942   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
943   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
944   ierr = MatSetUp(newmat);CHKERRQ(ierr);
945   /* FETIDP preconditioner */
946   ierr = PCBDDCCreateFETIDPPCContext(pc, &fetidppc_ctx);CHKERRQ(ierr);
947   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
948   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
949   ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
950   ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
951   ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
952   ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
953   ierr = PCSetOperators(newpc,newmat,newmat,SAME_PRECONDITIONER);CHKERRQ(ierr);
954   ierr = PCSetUp(newpc);CHKERRQ(ierr);
955   /* return pointers for objects created */
956   *fetidp_mat=newmat;
957   *fetidp_pc=newpc;
958 
959   PetscFunctionReturn(0);
960 }
961 EXTERN_C_END
962 #undef __FUNCT__
963 #define __FUNCT__ "PCBDDCCreateFETIDPOperators"
964 /*@
965  PCBDDCCreateFETIDPOperators - Create operators for FETIDP.
966 
967    Collective
968 
969    Input Parameters:
970 +  pc - the BDDC preconditioning context (setup must be already called)
971 
972    Level: developer
973 
974    Notes:
975 
976 .seealso: PCBDDC
977 @*/
978 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, Mat *fetidp_mat, PC *fetidp_pc)
979 {
980   PetscErrorCode ierr;
981 
982   PetscFunctionBegin;
983   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
984   if (pc->setupcalled) {
985     ierr = PetscTryMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,Mat*,PC*),(pc,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
986   } else {
987     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"You must call PCSetup_BDDC before calling %s\n",__FUNCT__);
988   }
989   PetscFunctionReturn(0);
990 }
991 /* -------------------------------------------------------------------------- */
992 /*MC
993    PCBDDC - Balancing Domain Decomposition by Constraints.
994 
995    Options Database Keys:
996 .    -pcbddc ??? -
997 
998    Level: intermediate
999 
1000    Notes: The matrix used with this preconditioner must be of type MATIS
1001 
1002           Unlike more 'conventional' interface preconditioners, this iterates over ALL the
1003           degrees of freedom, NOT just those on the interface (this allows the use of approximate solvers
1004           on the subdomains).
1005 
1006           Options for the coarse grid preconditioner can be set with -
1007           Options for the Dirichlet subproblem can be set with -
1008           Options for the Neumann subproblem can be set with -
1009 
1010    Contributed by Stefano Zampini
1011 
1012 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
1013 M*/
1014 EXTERN_C_BEGIN
1015 #undef __FUNCT__
1016 #define __FUNCT__ "PCCreate_BDDC"
1017 PetscErrorCode PCCreate_BDDC(PC pc)
1018 {
1019   PetscErrorCode ierr;
1020   PC_BDDC        *pcbddc;
1021   PCBDDCGraph    mat_graph;
1022 
1023   PetscFunctionBegin;
1024   /* Creates the private data structure for this preconditioner and attach it to the PC object. */
1025   ierr      = PetscNewLog(pc,PC_BDDC,&pcbddc);CHKERRQ(ierr);
1026   pc->data  = (void*)pcbddc;
1027 
1028   /* create PCIS data structure */
1029   ierr = PCISCreate(pc);CHKERRQ(ierr);
1030 
1031   /* BDDC specific */
1032   pcbddc->temp_solution              = 0;
1033   pcbddc->original_rhs               = 0;
1034   pcbddc->local_mat                  = 0;
1035   pcbddc->ChangeOfBasisMatrix        = 0;
1036   pcbddc->usechangeofbasis           = PETSC_TRUE;
1037   pcbddc->usechangeonfaces           = PETSC_FALSE;
1038   pcbddc->coarse_vec                 = 0;
1039   pcbddc->coarse_rhs                 = 0;
1040   pcbddc->coarse_ksp                 = 0;
1041   pcbddc->coarse_phi_B               = 0;
1042   pcbddc->coarse_phi_D               = 0;
1043   pcbddc->vec1_P                     = 0;
1044   pcbddc->vec1_R                     = 0;
1045   pcbddc->vec2_R                     = 0;
1046   pcbddc->local_auxmat1              = 0;
1047   pcbddc->local_auxmat2              = 0;
1048   pcbddc->R_to_B                     = 0;
1049   pcbddc->R_to_D                     = 0;
1050   pcbddc->ksp_D                      = 0;
1051   pcbddc->ksp_R                      = 0;
1052   pcbddc->local_primal_indices       = 0;
1053   pcbddc->prec_type                  = PETSC_FALSE;
1054   pcbddc->NeumannBoundaries          = 0;
1055   pcbddc->ISForDofs                  = 0;
1056   pcbddc->ISForVertices              = 0;
1057   pcbddc->n_ISForFaces               = 0;
1058   pcbddc->n_ISForEdges               = 0;
1059   pcbddc->ConstraintMatrix           = 0;
1060   pcbddc->use_nnsp_true              = PETSC_FALSE;
1061   pcbddc->local_primal_sizes         = 0;
1062   pcbddc->local_primal_displacements = 0;
1063   pcbddc->replicated_local_primal_indices = 0;
1064   pcbddc->replicated_local_primal_values  = 0;
1065   pcbddc->coarse_loc_to_glob         = 0;
1066   pcbddc->dbg_flag                   = PETSC_FALSE;
1067   pcbddc->coarsening_ratio           = 8;
1068   pcbddc->use_exact_dirichlet        = PETSC_TRUE;
1069 
1070   /* allocate and initialize needed graph structure */
1071   ierr = PetscMalloc(sizeof(*mat_graph),&pcbddc->mat_graph);CHKERRQ(ierr);
1072   pcbddc->mat_graph->xadj            = 0;
1073   pcbddc->mat_graph->adjncy          = 0;
1074 
1075   /* function pointers */
1076   pc->ops->apply               = PCApply_BDDC;
1077   pc->ops->applytranspose      = 0;
1078   pc->ops->setup               = PCSetUp_BDDC;
1079   pc->ops->destroy             = PCDestroy_BDDC;
1080   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
1081   pc->ops->view                = 0;
1082   pc->ops->applyrichardson     = 0;
1083   pc->ops->applysymmetricleft  = 0;
1084   pc->ops->applysymmetricright = 0;
1085   pc->ops->presolve            = PCPreSolve_BDDC;
1086   pc->ops->postsolve           = PCPostSolve_BDDC;
1087 
1088   /* composing function */
1089   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C","PCBDDCSetDirichletBoundaries_BDDC",
1090                     PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
1091   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C","PCBDDCSetNeumannBoundaries_BDDC",
1092                     PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
1093   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C","PCBDDCGetDirichletBoundaries_BDDC",
1094                     PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
1095   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C","PCBDDCGetNeumannBoundaries_BDDC",
1096                     PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
1097   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetCoarseProblemType_C","PCBDDCSetCoarseProblemType_BDDC",
1098                     PCBDDCSetCoarseProblemType_BDDC);CHKERRQ(ierr);
1099   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetDofsSplitting_C","PCBDDCSetDofsSplitting_BDDC",
1100                     PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
1101   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C","PCBDDCSetLocalAdjacencyGraph_BDDC",
1102                     PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
1103   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCPreSolve_C","PCPreSolve_BDDC",
1104                     PCPreSolve_BDDC);CHKERRQ(ierr);
1105   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCPostSolve_C","PCPostSolve_BDDC",
1106                     PCPostSolve_BDDC);CHKERRQ(ierr);
1107   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C","PCBDDCCreateFETIDPOperators_BDDC",
1108                     PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
1109   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C","PCBDDCMatFETIDPGetRHS_BDDC",
1110                     PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
1111   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C","PCBDDCMatFETIDPGetSolution_BDDC",
1112                     PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
1113   PetscFunctionReturn(0);
1114 }
1115 EXTERN_C_END
1116 
1117 /* -------------------------------------------------------------------------- */
1118 /* All static functions from now on                                           */
1119 /* -------------------------------------------------------------------------- */
1120 
1121 #undef __FUNCT__
1122 #define __FUNCT__ "PCBDDCCreateFETIDPMatContext"
1123 static PetscErrorCode PCBDDCCreateFETIDPMatContext(PC pc, FETIDPMat_ctx **fetidpmat_ctx)
1124 {
1125   FETIDPMat_ctx  *newctx;
1126   PetscErrorCode ierr;
1127 
1128   PetscFunctionBegin;
1129   ierr = PetscMalloc(sizeof(*newctx),&newctx);CHKERRQ(ierr);
1130   newctx->lambda_local    = 0;
1131   newctx->temp_solution_B = 0;
1132   newctx->temp_solution_D = 0;
1133   newctx->B_delta         = 0;
1134   newctx->B_Ddelta        = 0; /* theoretically belongs to the FETIDP preconditioner */
1135   newctx->l2g_lambda      = 0;
1136   /* increase the reference count for BDDC preconditioner */
1137   ierr = PetscObjectReference((PetscObject)pc);CHKERRQ(ierr);
1138   newctx->pc              = pc;
1139   *fetidpmat_ctx          = newctx;
1140   PetscFunctionReturn(0);
1141 }
1142 
1143 #undef __FUNCT__
1144 #define __FUNCT__ "PCBDDCCreateFETIDPPCContext"
1145 static PetscErrorCode PCBDDCCreateFETIDPPCContext(PC pc, FETIDPPC_ctx **fetidppc_ctx)
1146 {
1147   FETIDPPC_ctx  *newctx;
1148   PetscErrorCode ierr;
1149 
1150   PetscFunctionBegin;
1151   ierr = PetscMalloc(sizeof(*newctx),&newctx);CHKERRQ(ierr);
1152   newctx->lambda_local    = 0;
1153   newctx->B_Ddelta        = 0;
1154   newctx->l2g_lambda      = 0;
1155   /* increase the reference count for BDDC preconditioner */
1156   ierr = PetscObjectReference((PetscObject)pc);CHKERRQ(ierr);
1157   newctx->pc              = pc;
1158   *fetidppc_ctx           = newctx;
1159   PetscFunctionReturn(0);
1160 }
1161 
1162 #undef __FUNCT__
1163 #define __FUNCT__ "PCBDDCDestroyFETIDPMat"
1164 static PetscErrorCode PCBDDCDestroyFETIDPMat(Mat A)
1165 {
1166   FETIDPMat_ctx  *mat_ctx;
1167   PetscErrorCode ierr;
1168 
1169   PetscFunctionBegin;
1170   ierr = MatShellGetContext(A,(void**)&mat_ctx);CHKERRQ(ierr);
1171   ierr = VecDestroy(&mat_ctx->lambda_local);CHKERRQ(ierr);
1172   ierr = VecDestroy(&mat_ctx->temp_solution_D);CHKERRQ(ierr);
1173   ierr = VecDestroy(&mat_ctx->temp_solution_B);CHKERRQ(ierr);
1174   ierr = MatDestroy(&mat_ctx->B_delta);CHKERRQ(ierr);
1175   ierr = MatDestroy(&mat_ctx->B_Ddelta);CHKERRQ(ierr);
1176   ierr = VecScatterDestroy(&mat_ctx->l2g_lambda);CHKERRQ(ierr);
1177   ierr = PCDestroy(&mat_ctx->pc);CHKERRQ(ierr); /* actually it does not destroy BDDC, only decrease its reference count */
1178   ierr = PetscFree(mat_ctx);CHKERRQ(ierr);
1179   PetscFunctionReturn(0);
1180 }
1181 
1182 #undef __FUNCT__
1183 #define __FUNCT__ "PCBDDCDestroyFETIDPPC"
1184 static PetscErrorCode PCBDDCDestroyFETIDPPC(PC pc)
1185 {
1186   FETIDPPC_ctx  *pc_ctx;
1187   PetscErrorCode ierr;
1188 
1189   PetscFunctionBegin;
1190   ierr = PCShellGetContext(pc,(void**)&pc_ctx);CHKERRQ(ierr);
1191   ierr = VecDestroy(&pc_ctx->lambda_local);CHKERRQ(ierr);
1192   ierr = MatDestroy(&pc_ctx->B_Ddelta);CHKERRQ(ierr);
1193   ierr = VecScatterDestroy(&pc_ctx->l2g_lambda);CHKERRQ(ierr);
1194   ierr = PCDestroy(&pc_ctx->pc);CHKERRQ(ierr); /* actually it does not destroy BDDC, only decrease its reference count */
1195   ierr = PetscFree(pc_ctx);CHKERRQ(ierr);
1196   PetscFunctionReturn(0);
1197 }
1198 
1199 #undef __FUNCT__
1200 #define __FUNCT__ "PCBDDCSetupFETIDPMatContext"
1201 static PetscErrorCode PCBDDCSetupFETIDPMatContext(FETIDPMat_ctx *fetidpmat_ctx )
1202 {
1203   PetscErrorCode ierr;
1204   PC_IS          *pcis=(PC_IS*)fetidpmat_ctx->pc->data;
1205   PC_BDDC        *pcbddc=(PC_BDDC*)fetidpmat_ctx->pc->data;
1206   PCBDDCGraph    mat_graph=pcbddc->mat_graph;
1207   Mat_IS         *matis  = (Mat_IS*)fetidpmat_ctx->pc->pmat->data;
1208   MPI_Comm       comm = ((PetscObject)(fetidpmat_ctx->pc))->comm;
1209 
1210   Mat            ScalingMat;
1211   Vec            lambda_global;
1212   IS             IS_l2g_lambda;
1213 
1214   PetscBool      skip_node,fully_redundant;
1215   PetscInt       i,j,k,s,n_boundary_dofs,sum_dof_sizes,n_global_lambda,n_vertices;
1216   PetscInt       n_local_lambda,n_lambda_for_dof,dual_size,n_neg_values,n_pos_values;
1217   PetscMPIInt    rank,nprocs,partial_sum;
1218   PetscScalar    scalar_value;
1219 
1220   PetscInt       *vertex_indices,*temp_indices;
1221   PetscInt       *dual_dofs_boundary_indices,*aux_local_numbering_1,*aux_global_numbering;
1222   PetscInt       *aux_sums,*cols_B_delta,*l2g_indices;
1223   PetscMPIInt    *aux_local_numbering_2,*aux_global_numbering_mpi,*dof_sizes,*dof_displs;
1224   PetscMPIInt    *all_aux_global_numbering_mpi_1,*all_aux_global_numbering_mpi_2,*global_dofs_numbering;
1225   PetscScalar    *array,*scaling_factors,*vals_B_delta;
1226 
1227   /* For communication of scaling factors */
1228   PetscInt       *ptrs_buffer,neigh_position;
1229   PetscScalar    **all_factors,*send_buffer,*recv_buffer;
1230   MPI_Request    *send_reqs,*recv_reqs;
1231 
1232   /* tests */
1233   Vec            test_vec;
1234   PetscBool      test_fetidp;
1235   PetscViewer    viewer;
1236 
1237   PetscFunctionBegin;
1238   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1239   ierr = MPI_Comm_size(comm,&nprocs);CHKERRQ(ierr);
1240 
1241   /* Default type of lagrange multipliers is non-redundant */
1242   fully_redundant = PETSC_FALSE;
1243   ierr = PetscOptionsGetBool(PETSC_NULL,"-fetidp_fullyredundant",&fully_redundant,PETSC_NULL);CHKERRQ(ierr);
1244 
1245   /* Evaluate local and global number of lagrange multipliers */
1246   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
1247   n_local_lambda = 0;
1248   partial_sum = 0;
1249   n_boundary_dofs = 0;
1250   s = 0;
1251   n_vertices = 0;
1252   /* Get Vertices used to define the BDDC */
1253   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(*vertex_indices),&vertex_indices);CHKERRQ(ierr);
1254   for(i=0;i<pcbddc->local_primal_size;i++) {
1255     ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&j,(const PetscInt**)&temp_indices,PETSC_NULL);CHKERRQ(ierr);
1256     if(j == 1) {
1257       vertex_indices[n_vertices]=temp_indices[0];
1258       n_vertices++;
1259     }
1260     ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&j,(const PetscInt**)&temp_indices,PETSC_NULL);CHKERRQ(ierr);
1261   }
1262   dual_size = pcis->n_B-n_vertices;
1263   ierr = PetscMalloc(dual_size*sizeof(*dual_dofs_boundary_indices),&dual_dofs_boundary_indices);CHKERRQ(ierr);
1264   ierr = PetscMalloc(dual_size*sizeof(*aux_local_numbering_1),&aux_local_numbering_1);CHKERRQ(ierr);
1265   ierr = PetscMalloc(dual_size*sizeof(*aux_local_numbering_2),&aux_local_numbering_2);CHKERRQ(ierr);
1266 
1267   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1268   for(i=0;i<pcis->n;i++){
1269     j = mat_graph->count[i]; /* RECALL: mat_graph->count[i] does not count myself */
1270     k = 0;
1271     if(j > 0) {
1272       k = (mat_graph->neighbours_set[i][0] == -1 ?  1 : 0);
1273     }
1274     j = j - k ;
1275     if( j > 0 ) { n_boundary_dofs++; }
1276 
1277     skip_node = PETSC_FALSE;
1278     if( s < n_vertices && vertex_indices[s]==i) { /* it works for a sorted set of vertices */
1279       skip_node = PETSC_TRUE;
1280       s++;
1281     }
1282     if(j < 1) {skip_node = PETSC_TRUE;}
1283     if( !skip_node ) {
1284       if(fully_redundant) {
1285         /* fully redundant set of lagrange multipliers */
1286         n_lambda_for_dof = (j*(j+1))/2;
1287       } else {
1288         n_lambda_for_dof = j;
1289       }
1290       n_local_lambda += j;
1291       /* needed to evaluate global number of lagrange multipliers */
1292       array[i]=(1.0*n_lambda_for_dof)/(j+1.0); /* already scaled for the next global sum */
1293       /* store some data needed */
1294       dual_dofs_boundary_indices[partial_sum] = n_boundary_dofs-1;
1295       aux_local_numbering_1[partial_sum] = i;
1296       aux_local_numbering_2[partial_sum] = (PetscMPIInt)n_lambda_for_dof;
1297       partial_sum++;
1298     }
1299   }
1300   /*printf("I found %d local lambda dofs\n",n_local_lambda);
1301   printf("I found %d boundary dofs (should be %d)\n",n_boundary_dofs,pcis->n_B);
1302   printf("Partial sum %d should be %d\n",partial_sum,dual_size);*/
1303   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1304   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
1305   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1306   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1307   ierr = VecSum(pcis->vec1_global,&scalar_value);CHKERRQ(ierr);
1308   fetidpmat_ctx->n_lambda = (PetscInt) scalar_value;
1309   /* printf("I found %d global multipliers (%f)\n",fetidpmat_ctx->n_lambda,scalar_value); */
1310   ierr = VecCreate(PETSC_COMM_SELF,&fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
1311   ierr = VecSetSizes(fetidpmat_ctx->lambda_local,n_local_lambda,n_local_lambda);CHKERRQ(ierr);
1312   ierr = VecSetType(fetidpmat_ctx->lambda_local,VECSEQ);CHKERRQ(ierr);
1313   ierr = VecCreate(comm,&lambda_global);CHKERRQ(ierr);
1314   ierr = VecSetSizes(lambda_global,PETSC_DECIDE,fetidpmat_ctx->n_lambda);CHKERRQ(ierr);
1315   ierr = VecSetType(lambda_global,VECMPI);CHKERRQ(ierr);
1316 
1317   /* compute global ordering of lagrange multipliers and associate l2g map */
1318 
1319   ierr = PetscMalloc(dual_size*sizeof(*aux_global_numbering),&aux_global_numbering);CHKERRQ(ierr);
1320   ierr = PetscMalloc(dual_size*sizeof(*aux_global_numbering_mpi),&aux_global_numbering_mpi);CHKERRQ(ierr);
1321   j = (rank == 0 ? nprocs : 0);
1322   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1323   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1324   ierr = ISLocalToGlobalMappingApply(matis->mapping,dual_size,aux_local_numbering_1,aux_global_numbering);CHKERRQ(ierr);
1325   ierr = MPI_Gather(&dual_size,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1326   sum_dof_sizes=0;
1327   if ( rank == 0 ) {
1328     dof_displs[0]=0;
1329     sum_dof_sizes=dual_size;
1330     for(i=1;i<nprocs;i++) {
1331       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1332       sum_dof_sizes += dof_sizes[i];
1333     }
1334   }
1335   for(i=0;i<dual_size;i++) {
1336     aux_global_numbering_mpi[i]=(PetscMPIInt)aux_global_numbering[i];
1337   }
1338   ierr = PetscMalloc(sum_dof_sizes*sizeof(*all_aux_global_numbering_mpi_1),&all_aux_global_numbering_mpi_1);CHKERRQ(ierr);
1339   ierr = PetscMalloc(sum_dof_sizes*sizeof(*all_aux_global_numbering_mpi_2),&all_aux_global_numbering_mpi_2);CHKERRQ(ierr);
1340   ierr = MPI_Gatherv(aux_global_numbering_mpi,dual_size,MPIU_INT,all_aux_global_numbering_mpi_1,dof_sizes,dof_displs,MPIU_INT,0,comm);CHKERRQ(ierr);
1341   ierr = MPI_Gatherv(aux_local_numbering_2,dual_size,MPIU_INT,all_aux_global_numbering_mpi_2,dof_sizes,dof_displs,MPIU_INT,0,comm);CHKERRQ(ierr);
1342 
1343   ierr = PetscMalloc(fetidpmat_ctx->n_lambda*sizeof(*global_dofs_numbering),&global_dofs_numbering);CHKERRQ(ierr);
1344   if( rank == 0 ) {
1345     ierr = PetscSortMPIIntWithArray(sum_dof_sizes,all_aux_global_numbering_mpi_1,all_aux_global_numbering_mpi_2);CHKERRQ(ierr);
1346     j=-1;
1347     partial_sum = 0;
1348     for(i=0;i<sum_dof_sizes;i++) {
1349       if(j != all_aux_global_numbering_mpi_1[i] ) {
1350         j=all_aux_global_numbering_mpi_1[i];
1351         for(k=0;k<all_aux_global_numbering_mpi_2[i];k++) {
1352           global_dofs_numbering[partial_sum+k]=all_aux_global_numbering_mpi_1[i];
1353         }
1354         partial_sum += all_aux_global_numbering_mpi_2[i];
1355       }
1356     }
1357     /* printf("Partial sum for global dofs %d should be %d\n",partial_sum,fetidpmat_ctx->n_lambda); */
1358   }
1359   ierr = MPI_Bcast(global_dofs_numbering,fetidpmat_ctx->n_lambda,MPIU_INT,0,comm);CHKERRQ(ierr);
1360 
1361   /* init data for scaling factors exchange */
1362   partial_sum = 0;
1363   j = 0;
1364   ierr = PetscMalloc( pcis->n_neigh*sizeof(PetscInt),&ptrs_buffer);CHKERRQ(ierr);
1365   ierr = PetscMalloc( (pcis->n_neigh-1)*sizeof(MPI_Request),&send_reqs);CHKERRQ(ierr);
1366   ierr = PetscMalloc( (pcis->n_neigh-1)*sizeof(MPI_Request),&recv_reqs);CHKERRQ(ierr);
1367   ierr = PetscMalloc( pcis->n*sizeof(PetscScalar*),&all_factors);CHKERRQ(ierr);
1368   ptrs_buffer[0]=0;
1369   for(i=1;i<pcis->n_neigh;i++) {
1370     partial_sum += pcis->n_shared[i];
1371     ptrs_buffer[i] = ptrs_buffer[i-1]+pcis->n_shared[i];
1372   }
1373   ierr = PetscMalloc( partial_sum*sizeof(PetscScalar),&send_buffer);CHKERRQ(ierr);
1374   ierr = PetscMalloc( partial_sum*sizeof(PetscScalar),&recv_buffer);CHKERRQ(ierr);
1375   ierr = PetscMalloc( partial_sum*sizeof(PetscScalar),&all_factors[0]);CHKERRQ(ierr);
1376   for(i=0;i<pcis->n-1;i++) {
1377     j = mat_graph->count[i];
1378     if(j>0) {
1379       k = (mat_graph->neighbours_set[i][0] == -1 ?  1 : 0);
1380       j = j - k;
1381     }
1382     all_factors[i+1]=all_factors[i]+j;
1383   }
1384   /* scatter B scaling to N vec */
1385   ierr = VecScatterBegin(pcis->N_to_B,pcis->D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1386   ierr = VecScatterEnd  (pcis->N_to_B,pcis->D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1387   /* communications */
1388   k = 0;
1389   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1390   for(i=1;i<pcis->n_neigh;i++) {
1391     for(j=0;j<pcis->n_shared[i];j++) {
1392       send_buffer[ptrs_buffer[i-1]+j]=array[pcis->shared[i][j]];
1393     }
1394     j = ptrs_buffer[i]-ptrs_buffer[i-1];
1395     ierr = MPI_Isend(&send_buffer[ptrs_buffer[i-1]],j,MPIU_SCALAR,pcis->neigh[i],0,comm,&send_reqs[k]);CHKERRQ(ierr);
1396     ierr = MPI_Irecv(&recv_buffer[ptrs_buffer[i-1]],j,MPIU_SCALAR,pcis->neigh[i],0,comm,&recv_reqs[k]);CHKERRQ(ierr);
1397     k++;
1398   }
1399   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1400   ierr = MPI_Waitall(k,recv_reqs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
1401   ierr = MPI_Waitall(k,send_reqs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
1402   /* put values in correct places */
1403   for(i=1;i<pcis->n_neigh;i++) {
1404     for(j=0;j<pcis->n_shared[i];j++) {
1405       k = pcis->shared[i][j];
1406       neigh_position = 0;
1407       while(mat_graph->neighbours_set[k][neigh_position] != pcis->neigh[i]) {neigh_position++;}
1408       s = (mat_graph->neighbours_set[k][0] == -1 ?  1 : 0);
1409       neigh_position = neigh_position - s;
1410       all_factors[k][neigh_position]=recv_buffer[ptrs_buffer[i-1]+j];
1411     }
1412   }
1413   ierr = PetscFree(send_reqs);CHKERRQ(ierr);
1414   ierr = PetscFree(recv_reqs);CHKERRQ(ierr);
1415   ierr = PetscFree(send_buffer);CHKERRQ(ierr);
1416   ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
1417   ierr = PetscFree(ptrs_buffer);CHKERRQ(ierr);
1418 
1419   /* Compute B and B_delta (local actions) */
1420   ierr = PetscMalloc(pcis->n_neigh*sizeof(*aux_sums),&aux_sums);CHKERRQ(ierr);
1421   ierr = PetscMalloc(n_local_lambda*sizeof(*l2g_indices),&l2g_indices);CHKERRQ(ierr);
1422   ierr = PetscMalloc(n_local_lambda*sizeof(*vals_B_delta),&vals_B_delta);CHKERRQ(ierr);
1423   ierr = PetscMalloc(n_local_lambda*sizeof(*cols_B_delta),&cols_B_delta);CHKERRQ(ierr);
1424   ierr = PetscMalloc(n_local_lambda*sizeof(*scaling_factors),&scaling_factors);CHKERRQ(ierr);
1425   n_global_lambda=0;
1426   partial_sum=0;
1427   for(i=0;i<dual_size;i++) {
1428     while( global_dofs_numbering[n_global_lambda] != aux_global_numbering_mpi[i] ) { n_global_lambda++; }
1429     j = mat_graph->count[aux_local_numbering_1[i]];
1430     k = (mat_graph->neighbours_set[aux_local_numbering_1[i]][0] == -1 ?  1 : 0);
1431     j = j - k;
1432     aux_sums[0]=0;
1433     for(s=1;s<j;s++) {
1434       aux_sums[s]=aux_sums[s-1]+j-s+1;
1435     }
1436     array = all_factors[aux_local_numbering_1[i]];
1437     n_neg_values = 0;
1438     while(n_neg_values < j && mat_graph->neighbours_set[aux_local_numbering_1[i]][n_neg_values+k] < rank) {n_neg_values++;}
1439     n_pos_values = j - n_neg_values;
1440     if(fully_redundant) {
1441       for(s=0;s<n_neg_values;s++) {
1442         l2g_indices    [partial_sum+s]=aux_sums[s]+n_neg_values-s-1+n_global_lambda;
1443         cols_B_delta   [partial_sum+s]=dual_dofs_boundary_indices[i];
1444         vals_B_delta   [partial_sum+s]=-1.0;
1445         scaling_factors[partial_sum+s]=array[s];
1446       }
1447       for(s=0;s<n_pos_values;s++) {
1448         l2g_indices    [partial_sum+s+n_neg_values]=aux_sums[n_neg_values]+s+n_global_lambda;
1449         cols_B_delta   [partial_sum+s+n_neg_values]=dual_dofs_boundary_indices[i];
1450         vals_B_delta   [partial_sum+s+n_neg_values]=1.0;
1451         scaling_factors[partial_sum+s+n_neg_values]=array[s+n_neg_values];
1452       }
1453       partial_sum += j;
1454     } else {
1455       /* l2g_indices and default cols and vals of B_delta */
1456       for(s=0;s<j;s++) {
1457         l2g_indices    [partial_sum+s]=n_global_lambda+s;
1458         cols_B_delta   [partial_sum+s]=dual_dofs_boundary_indices[i];
1459         vals_B_delta   [partial_sum+s]=0.0;
1460       }
1461       /* B_delta */
1462       if( n_neg_values > 0 ) { /* there's a rank next to me to the left */
1463         vals_B_delta   [partial_sum+n_neg_values-1]=-1.0;
1464       }
1465       if ( n_neg_values < j ) { /* there's a rank next to me to the right */
1466         vals_B_delta   [partial_sum+n_neg_values]=1.0;
1467       }
1468       /* scaling as in Klawonn-Widlund 1999*/
1469       for(s=0;s<n_neg_values;s++) {
1470         scalar_value = 0.0;
1471         for(k=0;k<s+1;k++) {
1472           scalar_value += array[k];
1473         }
1474         scalar_value = -scalar_value;
1475         scaling_factors[partial_sum+s] = scalar_value;
1476       }
1477       for(s=0;s<n_pos_values;s++) {
1478         scalar_value = 0.0;
1479         for(k=s+n_neg_values;k<j;k++) {
1480           scalar_value += array[k];
1481         }
1482         scaling_factors[partial_sum+s+n_neg_values] = scalar_value;
1483       }
1484       partial_sum += j;
1485     }
1486   }
1487   ierr = PetscFree(all_factors[0]);CHKERRQ(ierr);
1488   ierr = PetscFree(all_factors);CHKERRQ(ierr);
1489   /* printf("I found %d local lambda dofs when numbering them (should be %d)\n",partial_sum,n_local_lambda); */
1490   ierr = ISCreateGeneral(comm,n_local_lambda,l2g_indices,PETSC_OWN_POINTER,&IS_l2g_lambda);CHKERRQ(ierr);
1491   ierr = VecScatterCreate(fetidpmat_ctx->lambda_local,(IS)0,lambda_global,IS_l2g_lambda,&fetidpmat_ctx->l2g_lambda);CHKERRQ(ierr);
1492 
1493   /* Create local part of B_delta */
1494   ierr = MatCreate(PETSC_COMM_SELF,&fetidpmat_ctx->B_delta);
1495   ierr = MatSetSizes(fetidpmat_ctx->B_delta,n_local_lambda,pcis->n_B,n_local_lambda,pcis->n_B);CHKERRQ(ierr);
1496   ierr = MatSetType(fetidpmat_ctx->B_delta,MATSEQAIJ);CHKERRQ(ierr);
1497   ierr = MatSeqAIJSetPreallocation(fetidpmat_ctx->B_delta,1,PETSC_NULL);CHKERRQ(ierr);
1498   ierr = MatSetOption(fetidpmat_ctx->B_delta,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
1499   for(i=0;i<n_local_lambda;i++) {
1500     ierr = MatSetValue(fetidpmat_ctx->B_delta,i,cols_B_delta[i],vals_B_delta[i],INSERT_VALUES);CHKERRQ(ierr);
1501   }
1502   ierr = MatAssemblyBegin(fetidpmat_ctx->B_delta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1503   ierr = MatAssemblyEnd  (fetidpmat_ctx->B_delta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1504 
1505   if(fully_redundant) {
1506     ierr = MatCreate(PETSC_COMM_SELF,&ScalingMat);
1507     ierr = MatSetSizes(ScalingMat,n_local_lambda,n_local_lambda,n_local_lambda,n_local_lambda);CHKERRQ(ierr);
1508     ierr = MatSetType(ScalingMat,MATSEQAIJ);CHKERRQ(ierr);
1509     ierr = MatSeqAIJSetPreallocation(ScalingMat,1,PETSC_NULL);CHKERRQ(ierr);
1510     for(i=0;i<n_local_lambda;i++) {
1511       ierr = MatSetValue(ScalingMat,i,i,scaling_factors[i],INSERT_VALUES);CHKERRQ(ierr);
1512     }
1513     ierr = MatAssemblyBegin(ScalingMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1514     ierr = MatAssemblyEnd  (ScalingMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1515     ierr = MatMatMult(ScalingMat,fetidpmat_ctx->B_delta,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&fetidpmat_ctx->B_Ddelta);CHKERRQ(ierr);
1516     ierr = MatDestroy(&ScalingMat);CHKERRQ(ierr);
1517   } else {
1518     ierr = MatCreate(PETSC_COMM_SELF,&fetidpmat_ctx->B_Ddelta);
1519     ierr = MatSetSizes(fetidpmat_ctx->B_Ddelta,n_local_lambda,pcis->n_B,n_local_lambda,pcis->n_B);CHKERRQ(ierr);
1520     ierr = MatSetType(fetidpmat_ctx->B_Ddelta,MATSEQAIJ);CHKERRQ(ierr);
1521     ierr = MatSeqAIJSetPreallocation(fetidpmat_ctx->B_Ddelta,1,PETSC_NULL);CHKERRQ(ierr);
1522     for(i=0;i<n_local_lambda;i++) {
1523       ierr = MatSetValue(fetidpmat_ctx->B_Ddelta,i,cols_B_delta[i],scaling_factors[i],INSERT_VALUES);CHKERRQ(ierr);
1524     }
1525     ierr = MatAssemblyBegin(fetidpmat_ctx->B_Ddelta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1526     ierr = MatAssemblyEnd  (fetidpmat_ctx->B_Ddelta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1527   }
1528 
1529   /* Create some vectors needed by fetidp */
1530   ierr = VecDuplicate(pcis->vec1_B,&fetidpmat_ctx->temp_solution_B);CHKERRQ(ierr);
1531   ierr = VecDuplicate(pcis->vec1_D,&fetidpmat_ctx->temp_solution_D);CHKERRQ(ierr);
1532 
1533   test_fetidp = PETSC_FALSE;
1534   ierr = PetscOptionsGetBool(PETSC_NULL,"-fetidp_check",&test_fetidp,PETSC_NULL);CHKERRQ(ierr);
1535 
1536   if(test_fetidp) {
1537 
1538     ierr = PetscViewerASCIIGetStdout(((PetscObject)(fetidpmat_ctx->pc))->comm,&viewer);CHKERRQ(ierr);
1539     ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
1540     ierr = PetscViewerASCIIPrintf(viewer,"----------FETI_DP TESTS--------------\n");CHKERRQ(ierr);
1541     ierr = PetscViewerASCIIPrintf(viewer,"All tests should return zero!\n");CHKERRQ(ierr);
1542     ierr = PetscViewerASCIIPrintf(viewer,"FETIDP MAT context in the ");CHKERRQ(ierr);
1543     if(fully_redundant) {
1544       ierr = PetscViewerASCIIPrintf(viewer,"fully redundant case for lagrange multipliers.\n");CHKERRQ(ierr);
1545     } else {
1546       ierr = PetscViewerASCIIPrintf(viewer,"Non-fully redundant case for lagrange multiplier.\n");CHKERRQ(ierr);
1547     }
1548     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1549 
1550     /******************************************************************/
1551     /* TEST A/B: Test numbering of global lambda dofs             */
1552     /******************************************************************/
1553 
1554     ierr = VecDuplicate(fetidpmat_ctx->lambda_local,&test_vec);CHKERRQ(ierr);
1555     ierr = VecSet(lambda_global,1.0);CHKERRQ(ierr);
1556     ierr = VecSet(test_vec,1.0);CHKERRQ(ierr);
1557     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1558     ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1559     scalar_value = -1.0;
1560     ierr = VecAXPY(test_vec,scalar_value,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
1561     ierr = VecNorm(test_vec,NORM_INFINITY,&scalar_value);CHKERRQ(ierr);
1562     ierr = VecDestroy(&test_vec);CHKERRQ(ierr);
1563     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"A[%04d]: CHECK glob to loc: % 1.14e\n",rank,scalar_value);CHKERRQ(ierr);
1564     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1565     if(fully_redundant) {
1566       ierr = VecSet(lambda_global,0.0);CHKERRQ(ierr);
1567       ierr = VecSet(fetidpmat_ctx->lambda_local,0.5);CHKERRQ(ierr);
1568       ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1569       ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1570       ierr = VecSum(lambda_global,&scalar_value);CHKERRQ(ierr);
1571       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"B[%04d]: CHECK loc to glob: % 1.14e\n",rank,scalar_value-fetidpmat_ctx->n_lambda);CHKERRQ(ierr);
1572       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1573     }
1574 
1575     /******************************************************************/
1576     /* TEST C: It should holds B_delta*w=0, w\in\widehat{W}           */
1577     /* This is the meaning of the B matrix                            */
1578     /******************************************************************/
1579 
1580     ierr = VecSetRandom(pcis->vec1_N,PETSC_NULL);CHKERRQ(ierr);
1581     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
1582     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1583     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1584     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1585     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1586     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1587     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1588     /* Action of B_delta */
1589     ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
1590     ierr = VecSet(lambda_global,0.0);CHKERRQ(ierr);
1591     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1592     ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1593     ierr = VecNorm(lambda_global,NORM_INFINITY,&scalar_value);CHKERRQ(ierr);
1594     ierr = PetscViewerASCIIPrintf(viewer,"C[coll]: CHECK infty norm of B_delta*w (w continuous): % 1.14e\n",scalar_value);CHKERRQ(ierr);
1595     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1596 
1597     /******************************************************************/
1598     /* TEST D: It should holds E_Dw = w - P_Dw w\in\widetilde{W}     */
1599     /* E_D = R_D^TR                                                   */
1600     /* P_D = B_{D,delta}^T B_{delta}                                  */
1601     /* eq.44 Mandel Tezaur and Dohrmann 2005                          */
1602     /******************************************************************/
1603 
1604     /* compute a random vector in \widetilde{W} */
1605     ierr = VecSetRandom(pcis->vec1_N,PETSC_NULL);CHKERRQ(ierr);
1606     scalar_value = 0.0;  /* set zero at vertices */
1607     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1608     for(i=0;i<n_vertices;i++) { array[vertex_indices[i]]=scalar_value; }
1609     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1610     /* store w for final comparison */
1611     ierr = VecDuplicate(pcis->vec1_B,&test_vec);CHKERRQ(ierr);
1612     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,test_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1613     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,test_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1614 
1615     /* Jump operator P_D : results stored in pcis->vec1_B */
1616 
1617     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1618     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1619     /* Action of B_delta */
1620     ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
1621     ierr = VecSet(lambda_global,0.0);CHKERRQ(ierr);
1622     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1623     ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1624     /* Action of B_Ddelta^T */
1625     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1626     ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1627     ierr = MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
1628 
1629     /* Average operator E_D : results stored in pcis->vec2_B */
1630 
1631     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1632     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1633     ierr = VecPointwiseMult(pcis->vec2_B,pcis->D,pcis->vec2_B);CHKERRQ(ierr);
1634     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1635     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec2_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1636     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
1637     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1638     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1639     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1640     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1641     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1642     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1643 
1644     /* test E_D=I-P_D */
1645     scalar_value = 1.0;
1646     ierr = VecAXPY(pcis->vec1_B,scalar_value,pcis->vec2_B);CHKERRQ(ierr);
1647     scalar_value = -1.0;
1648     ierr = VecAXPY(pcis->vec1_B,scalar_value,test_vec);CHKERRQ(ierr);
1649     ierr = VecNorm(pcis->vec1_B,NORM_INFINITY,&scalar_value);CHKERRQ(ierr);
1650     ierr = VecDestroy(&test_vec);CHKERRQ(ierr);
1651     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"D[%04d] CHECK infty norm of E_D + P_D - I: % 1.14e\n",rank,scalar_value);CHKERRQ(ierr);
1652     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1653 
1654     /******************************************************************/
1655     /* TEST E: It should holds R_D^TP_Dw=0 w\in\widetilde{W}          */
1656     /* eq.48 Mandel Tezaur and Dohrmann 2005                          */
1657     /******************************************************************/
1658 
1659     ierr = VecSetRandom(pcis->vec1_N,PETSC_NULL);CHKERRQ(ierr);
1660     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1661     scalar_value = 0.0;  /* set zero at vertices */
1662     for(i=0;i<n_vertices;i++) { array[vertex_indices[i]]=scalar_value; }
1663     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1664 
1665     /* Jump operator P_D : results stored in pcis->vec1_B */
1666 
1667     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1668     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1669     /* Action of B_delta */
1670     ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
1671     ierr = VecSet(lambda_global,0.0);CHKERRQ(ierr);
1672     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1673     ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1674     /* Action of B_Ddelta^T */
1675     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1676     ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1677     ierr = MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
1678     /* diagonal scaling */
1679     ierr = VecPointwiseMult(pcis->vec1_B,pcis->D,pcis->vec1_B);CHKERRQ(ierr);
1680     /* sum on the interface */
1681     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
1682     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1683     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1684     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
1685     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1686     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1687     ierr = VecNorm(pcis->vec1_global,NORM_INFINITY,&scalar_value);CHKERRQ(ierr);
1688     ierr = PetscViewerASCIIPrintf(viewer,"E[coll]: CHECK infty norm of R^T_D P_D: % 1.14e\n",scalar_value);CHKERRQ(ierr);
1689     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1690 
1691     if(!fully_redundant) {
1692       /******************************************************************/
1693       /* TEST F: It should holds B_{delta}B^T_{D,delta}=I               */
1694       /* Corollary thm 14 Mandel Tezaur and Dohrmann 2005               */
1695       /******************************************************************/
1696       ierr = VecDuplicate(lambda_global,&test_vec);CHKERRQ(ierr);
1697       ierr = VecSetRandom(lambda_global,PETSC_NULL);CHKERRQ(ierr);
1698       /* Action of B_Ddelta^T */
1699       ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1700       ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1701       ierr = MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
1702       /* Action of B_delta */
1703       ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
1704       ierr = VecSet(test_vec,0.0);CHKERRQ(ierr);
1705       ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,test_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1706       ierr = VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,test_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1707       scalar_value = -1.0;
1708       ierr = VecAXPY(lambda_global,scalar_value,test_vec);CHKERRQ(ierr);
1709       ierr = VecNorm(lambda_global,NORM_INFINITY,&scalar_value);CHKERRQ(ierr);
1710       ierr = PetscViewerASCIIPrintf(viewer,"E[coll]: CHECK infty norm of P^T_D - I: % 1.14e\n",scalar_value);CHKERRQ(ierr);
1711       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1712       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1713       ierr = VecDestroy(&test_vec);CHKERRQ(ierr);
1714     }
1715   }
1716   /* final cleanup */
1717   ierr = PetscFree(dual_dofs_boundary_indices);CHKERRQ(ierr);
1718   ierr = PetscFree(vertex_indices);CHKERRQ(ierr);
1719   ierr = PetscFree(aux_local_numbering_1);CHKERRQ(ierr);
1720   ierr = PetscFree(aux_local_numbering_2);CHKERRQ(ierr);
1721   ierr = PetscFree(aux_global_numbering);CHKERRQ(ierr);
1722   ierr = PetscFree(aux_global_numbering_mpi);CHKERRQ(ierr);
1723   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1724   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1725   ierr = PetscFree(all_aux_global_numbering_mpi_1);CHKERRQ(ierr);
1726   ierr = PetscFree(all_aux_global_numbering_mpi_2);CHKERRQ(ierr);
1727   ierr = PetscFree(global_dofs_numbering);CHKERRQ(ierr);
1728   ierr = PetscFree(aux_sums);CHKERRQ(ierr);
1729   ierr = PetscFree(cols_B_delta);CHKERRQ(ierr);
1730   ierr = PetscFree(vals_B_delta);CHKERRQ(ierr);
1731   ierr = PetscFree(scaling_factors);CHKERRQ(ierr);
1732   ierr = VecDestroy(&lambda_global);CHKERRQ(ierr);
1733   ierr = ISDestroy(&IS_l2g_lambda);CHKERRQ(ierr);
1734 
1735   PetscFunctionReturn(0);
1736 }
1737 
1738 #undef __FUNCT__
1739 #define __FUNCT__ "PCBDDCSetupFETIDPPCContext"
1740 static PetscErrorCode PCBDDCSetupFETIDPPCContext(Mat fetimat, FETIDPPC_ctx *fetidppc_ctx)
1741 {
1742   FETIDPMat_ctx  *mat_ctx;
1743   PetscErrorCode ierr;
1744 
1745   PetscFunctionBegin;
1746   ierr = MatShellGetContext(fetimat,&mat_ctx);CHKERRQ(ierr);
1747   /* get references from objects created when setting up feti mat context */
1748   ierr = PetscObjectReference((PetscObject)mat_ctx->lambda_local);CHKERRQ(ierr);
1749   fetidppc_ctx->lambda_local = mat_ctx->lambda_local;
1750   ierr = PetscObjectReference((PetscObject)mat_ctx->B_Ddelta);CHKERRQ(ierr);
1751   fetidppc_ctx->B_Ddelta = mat_ctx->B_Ddelta;
1752   ierr = PetscObjectReference((PetscObject)mat_ctx->l2g_lambda);CHKERRQ(ierr);
1753   fetidppc_ctx->l2g_lambda = mat_ctx->l2g_lambda;
1754   PetscFunctionReturn(0);
1755 }
1756 
1757 #undef __FUNCT__
1758 #define __FUNCT__ "FETIDPMatMult"
1759 static PetscErrorCode FETIDPMatMult(Mat fetimat, Vec x, Vec y)
1760 {
1761   FETIDPMat_ctx  *mat_ctx;
1762   PC_IS          *pcis;
1763   PetscErrorCode ierr;
1764 
1765   PetscFunctionBegin;
1766   ierr = MatShellGetContext(fetimat,&mat_ctx);CHKERRQ(ierr);
1767   pcis = (PC_IS*)mat_ctx->pc->data;
1768   /* Application of B_delta^T */
1769   ierr = VecScatterBegin(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1770   ierr = VecScatterEnd(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1771   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
1772   /* Application of \widetilde{S}^-1 */
1773   ierr = VecSet(pcis->vec1_D,0.0);CHKERRQ(ierr);
1774   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc);CHKERRQ(ierr);
1775   /* Application of B_delta */
1776   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
1777   ierr = VecSet(y,0.0);CHKERRQ(ierr);
1778   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1779   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1780   PetscFunctionReturn(0);
1781 }
1782 
1783 #undef __FUNCT__
1784 #define __FUNCT__ "FETIDPPCApply"
1785 static PetscErrorCode FETIDPPCApply(PC fetipc, Vec x, Vec y)
1786 {
1787   FETIDPPC_ctx   *pc_ctx;
1788   PC_IS          *pcis;
1789   PetscErrorCode ierr;
1790 
1791   PetscFunctionBegin;
1792   ierr = PCShellGetContext(fetipc,(void**)&pc_ctx);
1793   pcis = (PC_IS*)pc_ctx->pc->data;
1794   /* Application of B_Ddelta^T */
1795   ierr = VecScatterBegin(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1796   ierr = VecScatterEnd(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1797   ierr = VecSet(pcis->vec2_B,0.0);CHKERRQ(ierr);
1798   ierr = MatMultTranspose(pc_ctx->B_Ddelta,pc_ctx->lambda_local,pcis->vec2_B);CHKERRQ(ierr);
1799   /* Application of S */
1800   ierr = PCISApplySchur(pc_ctx->pc,pcis->vec2_B,pcis->vec1_B,(Vec)0,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1801   /* Application of B_Ddelta */
1802   ierr = MatMult(pc_ctx->B_Ddelta,pcis->vec1_B,pc_ctx->lambda_local);CHKERRQ(ierr);
1803   ierr = VecSet(y,0.0);CHKERRQ(ierr);
1804   ierr = VecScatterBegin(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1805   ierr = VecScatterEnd(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1806   PetscFunctionReturn(0);
1807 }
1808 
1809 #undef __FUNCT__
1810 #define __FUNCT__ "PCBDDCSetupLocalAdjacencyGraph"
1811 static PetscErrorCode PCBDDCSetupLocalAdjacencyGraph(PC pc)
1812 {
1813   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1814   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
1815   PetscInt       nvtxs,*xadj,*adjncy;
1816   Mat            mat_adj;
1817   PetscBool      symmetrize_rowij=PETSC_TRUE,compressed_rowij=PETSC_FALSE,flg_row=PETSC_TRUE;
1818   PCBDDCGraph    mat_graph=pcbddc->mat_graph;
1819   PetscErrorCode ierr;
1820 
1821   PetscFunctionBegin;
1822   /* get CSR adjacency from local matrix if user has not yet provided local graph using PCBDDCSetLocalAdjacencyGraph function */
1823   if(!mat_graph->xadj) {
1824     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1825     ierr = MatGetRowIJ(mat_adj,0,symmetrize_rowij,compressed_rowij,&nvtxs,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1826     if(!flg_row) {
1827       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1828     }
1829     /* Get adjacency into BDDC workspace */
1830     ierr = PCBDDCSetLocalAdjacencyGraph(pc,nvtxs,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1831     ierr = MatRestoreRowIJ(mat_adj,0,symmetrize_rowij,compressed_rowij,&nvtxs,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1832     if(!flg_row) {
1833       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
1834     }
1835     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1836   }
1837   PetscFunctionReturn(0);
1838 }
1839 /* -------------------------------------------------------------------------- */
1840 #undef __FUNCT__
1841 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
1842 static PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
1843 {
1844   PetscErrorCode ierr;
1845   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
1846   PC_IS*            pcis = (PC_IS*)  (pc->data);
1847   const PetscScalar zero = 0.0;
1848 
1849   PetscFunctionBegin;
1850   /* Application of PHI^T  */
1851   ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1852   if(pcbddc->prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1853 
1854   /* Scatter data of coarse_rhs */
1855   if(pcbddc->coarse_rhs) ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr);
1856   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1857 
1858   /* Local solution on R nodes */
1859   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
1860   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1861   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1862   if(pcbddc->prec_type) {
1863     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1864     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1865   }
1866   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
1867   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1868   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1869   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1870   if(pcbddc->prec_type) {
1871     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1872     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1873   }
1874 
1875   /* Coarse solution */
1876   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1877   if(pcbddc->coarse_rhs) ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
1878   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1879   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1880 
1881   /* Sum contributions from two levels */
1882   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1883   if(pcbddc->prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1884   PetscFunctionReturn(0);
1885 }
1886 /* -------------------------------------------------------------------------- */
1887 #undef __FUNCT__
1888 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
1889 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
1890 {
1891   PetscErrorCode ierr;
1892   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1893 
1894   PetscFunctionBegin;
1895   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
1896   if(pcbddc->local_auxmat1) {
1897     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
1898     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
1899   }
1900   PetscFunctionReturn(0);
1901 }
1902 /* -------------------------------------------------------------------------- */
1903 #undef __FUNCT__
1904 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
1905 static PetscErrorCode  PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
1906 {
1907   PetscErrorCode ierr;
1908   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1909 
1910   PetscFunctionBegin;
1911   switch(pcbddc->coarse_communications_type){
1912     case SCATTERS_BDDC:
1913       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
1914       break;
1915     case GATHERS_BDDC:
1916       break;
1917   }
1918   PetscFunctionReturn(0);
1919 }
1920 /* -------------------------------------------------------------------------- */
1921 #undef __FUNCT__
1922 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
1923 static PetscErrorCode  PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
1924 {
1925   PetscErrorCode ierr;
1926   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1927   PetscScalar*   array_to;
1928   PetscScalar*   array_from;
1929   MPI_Comm       comm=((PetscObject)pc)->comm;
1930   PetscInt i;
1931 
1932   PetscFunctionBegin;
1933 
1934   switch(pcbddc->coarse_communications_type){
1935     case SCATTERS_BDDC:
1936       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
1937       break;
1938     case GATHERS_BDDC:
1939       if(vec_from) VecGetArray(vec_from,&array_from);
1940       if(vec_to)   VecGetArray(vec_to,&array_to);
1941       switch(pcbddc->coarse_problem_type){
1942         case SEQUENTIAL_BDDC:
1943           if(smode == SCATTER_FORWARD) {
1944             ierr = MPI_Gatherv(&array_from[0],pcbddc->local_primal_size,MPIU_SCALAR,&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,0,comm);CHKERRQ(ierr);
1945             if(vec_to) {
1946               for(i=0;i<pcbddc->replicated_primal_size;i++)
1947                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
1948             }
1949           } else {
1950             if(vec_from)
1951               for(i=0;i<pcbddc->replicated_primal_size;i++)
1952                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
1953             ierr = MPI_Scatterv(&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,&array_to[0],pcbddc->local_primal_size,MPIU_SCALAR,0,comm);CHKERRQ(ierr);
1954           }
1955           break;
1956         case REPLICATED_BDDC:
1957           if(smode == SCATTER_FORWARD) {
1958             ierr = MPI_Allgatherv(&array_from[0],pcbddc->local_primal_size,MPIU_SCALAR,&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,comm);CHKERRQ(ierr);
1959             for(i=0;i<pcbddc->replicated_primal_size;i++)
1960               array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
1961           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
1962             for(i=0;i<pcbddc->local_primal_size;i++)
1963               array_to[i]=array_from[pcbddc->local_primal_indices[i]];
1964           }
1965           break;
1966         case MULTILEVEL_BDDC:
1967           break;
1968         case PARALLEL_BDDC:
1969           break;
1970       }
1971       if(vec_from) VecRestoreArray(vec_from,&array_from);
1972       if(vec_to)   VecRestoreArray(vec_to,&array_to);
1973       break;
1974   }
1975   PetscFunctionReturn(0);
1976 }
1977 /* -------------------------------------------------------------------------- */
1978 #undef __FUNCT__
1979 #define __FUNCT__ "PCBDDCCreateConstraintMatrix"
1980 static PetscErrorCode PCBDDCCreateConstraintMatrix(PC pc)
1981 {
1982   PetscErrorCode ierr;
1983   PC_IS*         pcis = (PC_IS*)(pc->data);
1984   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
1985   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
1986   PetscInt       *nnz,*is_indices;
1987   PetscScalar    *temp_quadrature_constraint;
1988   PetscInt       *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B,*local_to_B;
1989   PetscInt       local_primal_size,i,j,k,total_counts,max_size_of_constraint;
1990   PetscInt       n_constraints,n_vertices,size_of_constraint;
1991   PetscScalar    quad_value;
1992   PetscBool      nnsp_has_cnst=PETSC_FALSE,use_nnsp_true=pcbddc->use_nnsp_true;
1993   PetscInt       nnsp_size=0,nnsp_addone=0,temp_constraints,temp_start_ptr;
1994   IS             *used_IS;
1995   const MatType  impMatType=MATSEQAIJ;
1996   PetscBLASInt   Bs,Bt,lwork,lierr;
1997   PetscReal      tol=1.0e-8;
1998   MatNullSpace   nearnullsp;
1999   const Vec      *nearnullvecs;
2000   Vec            *localnearnullsp;
2001   PetscScalar    *work,*temp_basis,*array_vector,*correlation_mat;
2002   PetscReal      *rwork,*singular_vals;
2003   PetscBLASInt   Bone=1,*ipiv;
2004   Vec            temp_vec;
2005   Mat            temp_mat;
2006   KSP            temp_ksp;
2007   PC             temp_pc;
2008   PetscInt       s,start_constraint,dual_dofs;
2009   PetscBool      compute_submatrix,useksp=PETSC_FALSE;
2010   PetscInt       *aux_primal_permutation,*aux_primal_numbering;
2011   PetscBool      boolforface,*change_basis;
2012 /* some ugly conditional declarations */
2013 #if defined(PETSC_MISSING_LAPACK_GESVD)
2014   PetscScalar    dot_result;
2015   PetscScalar    one=1.0,zero=0.0;
2016   PetscInt       ii;
2017   PetscScalar    *singular_vectors;
2018   PetscBLASInt   *iwork,*ifail;
2019   PetscReal      dummy_real,abs_tol;
2020   PetscBLASInt   eigs_found;
2021 #if defined(PETSC_USE_COMPLEX)
2022   PetscScalar    val1,val2;
2023 #endif
2024 #endif
2025   PetscBLASInt   dummy_int;
2026   PetscScalar    dummy_scalar;
2027 
2028   PetscFunctionBegin;
2029   /* check if near null space is attached to global mat */
2030   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
2031   if (nearnullsp) {
2032     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
2033   } else { /* if near null space is not provided it uses constants */
2034     nnsp_has_cnst = PETSC_TRUE;
2035     use_nnsp_true = PETSC_TRUE;
2036   }
2037   if(nnsp_has_cnst) {
2038     nnsp_addone = 1;
2039   }
2040   /*
2041        Evaluate maximum storage size needed by the procedure
2042        - temp_indices will contain start index of each constraint stored as follows
2043        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
2044        - temp_indices_to_constraint_B[temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in boundary numbering) on which the constraint acts
2045        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
2046                                                                                                                                                          */
2047 
2048   total_counts = pcbddc->n_ISForFaces+pcbddc->n_ISForEdges;
2049   total_counts *= (nnsp_addone+nnsp_size);
2050   ierr = ISGetSize(pcbddc->ISForVertices,&n_vertices);CHKERRQ(ierr);
2051   total_counts += n_vertices;
2052   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
2053   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
2054   total_counts = 0;
2055   max_size_of_constraint = 0;
2056   for(i=0;i<pcbddc->n_ISForEdges+pcbddc->n_ISForFaces;i++){
2057     if(i<pcbddc->n_ISForEdges){
2058       used_IS = &pcbddc->ISForEdges[i];
2059     } else {
2060       used_IS = &pcbddc->ISForFaces[i-pcbddc->n_ISForEdges];
2061     }
2062     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
2063     total_counts += j;
2064     if(j>max_size_of_constraint) max_size_of_constraint=j;
2065   }
2066   total_counts *= (nnsp_addone+nnsp_size);
2067   total_counts += n_vertices;
2068   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
2069   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
2070   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
2071   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
2072   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2073   for(i=0;i<pcis->n;i++) {
2074     local_to_B[i]=-1;
2075   }
2076   for(i=0;i<pcis->n_B;i++) {
2077     local_to_B[is_indices[i]]=i;
2078   }
2079   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2080 
2081   /* First we issue queries to allocate optimal workspace for LAPACKgesvd or LAPACKsyev/LAPACKheev */
2082   rwork = 0;
2083   work = 0;
2084   singular_vals = 0;
2085   temp_basis = 0;
2086   correlation_mat = 0;
2087   if(!pcbddc->use_nnsp_true) {
2088     PetscScalar temp_work;
2089 #if defined(PETSC_MISSING_LAPACK_GESVD)
2090     /* POD */
2091     PetscInt max_n;
2092     max_n = nnsp_addone+nnsp_size;
2093     /* using some techniques borrowed from Proper Orthogonal Decomposition */
2094     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
2095     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&singular_vectors);CHKERRQ(ierr);
2096     ierr = PetscMalloc(max_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
2097     ierr = PetscMalloc(max_size_of_constraint*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
2098 #if defined(PETSC_USE_COMPLEX)
2099     ierr = PetscMalloc(3*max_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
2100 #endif
2101     ierr = PetscMalloc(5*max_n*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
2102     ierr = PetscMalloc(max_n*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
2103     /* now we evaluate the optimal workspace using query with lwork=-1 */
2104     Bt = PetscBLASIntCast(max_n);
2105     lwork=-1;
2106     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2107 #if !defined(PETSC_USE_COMPLEX)
2108     abs_tol=1.e-8;
2109 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr); */
2110     LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,
2111                  &abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,&temp_work,&lwork,iwork,ifail,&lierr);
2112 #else
2113 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr); */
2114 /*  LAPACK call is missing here! TODO */
2115     SETERRQ(((PetscObject) pc)->comm, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
2116 #endif
2117     if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEVX Lapack routine %d",(int)lierr);
2118     ierr = PetscFPTrapPop();CHKERRQ(ierr);
2119 #else /* on missing GESVD */
2120     /* SVD */
2121     PetscInt max_n,min_n;
2122     max_n = max_size_of_constraint;
2123     min_n = nnsp_addone+nnsp_size;
2124     if(max_size_of_constraint < ( nnsp_addone+nnsp_size ) ) {
2125       min_n = max_size_of_constraint;
2126       max_n = nnsp_addone+nnsp_size;
2127     }
2128     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
2129 #if defined(PETSC_USE_COMPLEX)
2130     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
2131 #endif
2132     /* now we evaluate the optimal workspace using query with lwork=-1 */
2133     lwork=-1;
2134     Bs = PetscBLASIntCast(max_n);
2135     Bt = PetscBLASIntCast(min_n);
2136     dummy_int = Bs;
2137     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2138 #if !defined(PETSC_USE_COMPLEX)
2139     LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,
2140                  &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,&lierr);
2141 #else
2142     LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,
2143                  &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,rwork,&lierr);
2144 #endif
2145     if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SVD Lapack routine %d",(int)lierr);
2146     ierr = PetscFPTrapPop();CHKERRQ(ierr);
2147 #endif
2148     /* Allocate optimal workspace */
2149     lwork = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work));
2150     total_counts = (PetscInt)lwork;
2151     ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&work);CHKERRQ(ierr);
2152   }
2153   /* get local part of global near null space vectors */
2154   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
2155   for(k=0;k<nnsp_size;k++) {
2156     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
2157     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2158     ierr = VecScatterEnd  (matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2159   }
2160   /* Now we can loop on constraining sets */
2161   total_counts=0;
2162   temp_indices[0]=0;
2163   /* vertices */
2164   PetscBool used_vertex;
2165   ierr = ISGetIndices(pcbddc->ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2166   if(nnsp_has_cnst) { /* consider all vertices */
2167     for(i=0;i<n_vertices;i++) {
2168       temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
2169       temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
2170       temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
2171       temp_indices[total_counts+1]=temp_indices[total_counts]+1;
2172       change_basis[total_counts]=PETSC_FALSE;
2173       total_counts++;
2174     }
2175   } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
2176     for(i=0;i<n_vertices;i++) {
2177       used_vertex=PETSC_FALSE;
2178       k=0;
2179       while(!used_vertex && k<nnsp_size) {
2180         ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2181         if(PetscAbsScalar(array_vector[is_indices[i]])>0.0) {
2182           temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
2183           temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
2184           temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
2185           temp_indices[total_counts+1]=temp_indices[total_counts]+1;
2186           change_basis[total_counts]=PETSC_FALSE;
2187           total_counts++;
2188           used_vertex=PETSC_TRUE;
2189         }
2190         ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2191         k++;
2192       }
2193     }
2194   }
2195   ierr = ISRestoreIndices(pcbddc->ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2196   n_vertices=total_counts;
2197   /* edges and faces */
2198   for(i=0;i<pcbddc->n_ISForEdges+pcbddc->n_ISForFaces;i++){
2199     if(i<pcbddc->n_ISForEdges){
2200       used_IS = &pcbddc->ISForEdges[i];
2201       boolforface = pcbddc->usechangeofbasis;
2202     } else {
2203       used_IS = &pcbddc->ISForFaces[i-pcbddc->n_ISForEdges];
2204       boolforface = pcbddc->usechangeonfaces;
2205     }
2206     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
2207     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
2208     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
2209     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2210     if(nnsp_has_cnst) {
2211       temp_constraints++;
2212       quad_value = (PetscScalar) (1.0/PetscSqrtReal((PetscReal)size_of_constraint));
2213       for(j=0;j<size_of_constraint;j++) {
2214         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
2215         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
2216         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
2217       }
2218       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
2219       change_basis[total_counts]=boolforface;
2220       total_counts++;
2221     }
2222     for(k=0;k<nnsp_size;k++) {
2223       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2224       for(j=0;j<size_of_constraint;j++) {
2225         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
2226         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
2227         temp_quadrature_constraint[temp_indices[total_counts]+j]=array_vector[is_indices[j]];
2228       }
2229       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2230       quad_value = 1.0;
2231       if( use_nnsp_true ) { /* check if array is null on the connected component in case use_nnsp_true has been requested */
2232         Bs = PetscBLASIntCast(size_of_constraint);
2233         quad_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone);
2234       }
2235       if ( quad_value > 0.0 ) { /* keep indices and values */
2236         temp_constraints++;
2237         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
2238         change_basis[total_counts]=boolforface;
2239         total_counts++;
2240       }
2241     }
2242     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2243     /* perform SVD on the constraint if use_nnsp_true has not be requested by the user */
2244     if(!use_nnsp_true) {
2245 
2246       Bs = PetscBLASIntCast(size_of_constraint);
2247       Bt = PetscBLASIntCast(temp_constraints);
2248 
2249 #if defined(PETSC_MISSING_LAPACK_GESVD)
2250       ierr = PetscMemzero(correlation_mat,Bt*Bt*sizeof(PetscScalar));CHKERRQ(ierr);
2251       /* Store upper triangular part of correlation matrix */
2252       for(j=0;j<temp_constraints;j++) {
2253         for(k=0;k<j+1;k++) {
2254 #if defined(PETSC_USE_COMPLEX)
2255           /* hand made complex dot product -> replace */
2256           dot_result = 0.0;
2257           for (ii=0; ii<size_of_constraint; ii++) {
2258             val1 = temp_quadrature_constraint[temp_indices[temp_start_ptr+j]+ii];
2259             val2 = temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii];
2260             dot_result += val1*PetscConj(val2);
2261           }
2262 #else
2263           dot_result = BLASdot_(&Bs,&temp_quadrature_constraint[temp_indices[temp_start_ptr+j]],&Bone,
2264                                     &temp_quadrature_constraint[temp_indices[temp_start_ptr+k]],&Bone);
2265 #endif
2266           correlation_mat[j*temp_constraints+k]=dot_result;
2267         }
2268       }
2269       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2270 #if !defined(PETSC_USE_COMPLEX)
2271 /*      LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr); */
2272       LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,
2273                  &abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,work,&lwork,iwork,ifail,&lierr);
2274 #else
2275 /*  LAPACK call is missing here! TODO */
2276       SETERRQ(((PetscObject) pc)->comm, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
2277 #endif
2278       if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEVX Lapack routine %d",(int)lierr);
2279       ierr = PetscFPTrapPop();CHKERRQ(ierr);
2280       /* retain eigenvalues greater than tol: note that lapack SYEV gives eigs in ascending order */
2281       j=0;
2282       while( j < Bt && singular_vals[j] < tol) j++;
2283       total_counts=total_counts-j;
2284       if(j<temp_constraints) {
2285         for(k=j;k<Bt;k++) { singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]); }
2286         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2287         BLASgemm_("N","N",&Bs,&Bt,&Bt,&one,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,correlation_mat,&Bt,&zero,temp_basis,&Bs);
2288         ierr = PetscFPTrapPop();CHKERRQ(ierr);
2289         /* copy POD basis into used quadrature memory */
2290         for(k=0;k<Bt-j;k++) {
2291           for(ii=0;ii<size_of_constraint;ii++) {
2292             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[Bt-1-k]*temp_basis[(Bt-1-k)*size_of_constraint+ii];
2293           }
2294         }
2295       }
2296 
2297 #else  /* on missing GESVD */
2298       PetscInt min_n = temp_constraints;
2299       if(min_n > size_of_constraint) min_n = size_of_constraint;
2300       dummy_int = Bs;
2301       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2302 #if !defined(PETSC_USE_COMPLEX)
2303       LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,
2304                    &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,&lierr);
2305 #else
2306       LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,
2307                    &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,rwork,&lierr);
2308 #endif
2309       if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD Lapack routine %d",(int)lierr);
2310       ierr = PetscFPTrapPop();CHKERRQ(ierr);
2311       /* retain eigenvalues greater than tol: note that lapack SVD gives eigs in descending order */
2312       j=0;
2313       while( j < min_n && singular_vals[min_n-j-1] < tol) j++;
2314       total_counts = total_counts-(PetscInt)Bt+(min_n-j);
2315 #endif
2316     }
2317   }
2318 
2319   n_constraints=total_counts-n_vertices;
2320   local_primal_size = total_counts;
2321   /* set quantities in pcbddc data structure */
2322   pcbddc->n_vertices = n_vertices;
2323   pcbddc->n_constraints = n_constraints;
2324   pcbddc->local_primal_size = local_primal_size;
2325 
2326   /* Create constraint matrix */
2327   /* The constraint matrix is used to compute the l2g map of primal dofs */
2328   /* so we need to set it up properly either with or without change of basis */
2329   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
2330   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
2331   ierr = MatSetSizes(pcbddc->ConstraintMatrix,local_primal_size,pcis->n,local_primal_size,pcis->n);CHKERRQ(ierr);
2332   /* compute a local numbering of constraints : vertices first then constraints */
2333   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
2334   ierr = VecGetArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
2335   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
2336   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_permutation);CHKERRQ(ierr);
2337   total_counts=0;
2338   /* find vertices: subdomain corners plus dofs with basis changed */
2339   for(i=0;i<local_primal_size;i++) {
2340     size_of_constraint=temp_indices[i+1]-temp_indices[i];
2341     if(change_basis[i] || size_of_constraint == 1) {
2342       k=0;
2343       while(k < size_of_constraint && array_vector[temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1]] != 0.0) {
2344         k=k+1;
2345       }
2346       j=temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1];
2347       array_vector[j] = 1.0;
2348       aux_primal_numbering[total_counts]=j;
2349       aux_primal_permutation[total_counts]=total_counts;
2350       total_counts++;
2351     }
2352   }
2353   ierr = VecRestoreArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
2354   /* permute indices in order to have a sorted set of vertices */
2355   ierr = PetscSortIntWithPermutation(total_counts,aux_primal_numbering,aux_primal_permutation);
2356   /* nonzero structure */
2357   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2358   for(i=0;i<total_counts;i++) {
2359     nnz[i]=1;
2360   }
2361   j=total_counts;
2362   for(i=n_vertices;i<local_primal_size;i++) {
2363     if(!change_basis[i]) {
2364       nnz[j]=temp_indices[i+1]-temp_indices[i];
2365       j++;
2366     }
2367   }
2368   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
2369   ierr = PetscFree(nnz);CHKERRQ(ierr);
2370   /* set values in constraint matrix */
2371   for(i=0;i<total_counts;i++) {
2372     j = aux_primal_permutation[i];
2373     k = aux_primal_numbering[j];
2374     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,k,1.0,INSERT_VALUES);CHKERRQ(ierr);
2375   }
2376   for(i=n_vertices;i<local_primal_size;i++) {
2377     if(!change_basis[i]) {
2378       size_of_constraint=temp_indices[i+1]-temp_indices[i];
2379       ierr = MatSetValues(pcbddc->ConstraintMatrix,1,&total_counts,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],&temp_quadrature_constraint[temp_indices[i]],INSERT_VALUES);CHKERRQ(ierr);
2380       total_counts++;
2381     }
2382   }
2383   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2384   ierr = PetscFree(aux_primal_permutation);CHKERRQ(ierr);
2385   /* assembling */
2386   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2387   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2388 
2389   /* Create matrix for change of basis. We don't need it in case pcbddc->usechangeofbasis is FALSE */
2390   if(pcbddc->usechangeofbasis) {
2391     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2392     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
2393     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
2394     /* work arrays */
2395     /* we need to reuse these arrays, so we free them */
2396     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
2397     ierr = PetscFree(work);CHKERRQ(ierr);
2398     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2399     ierr = PetscMalloc((nnsp_addone+nnsp_size)*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
2400     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscScalar),&work);CHKERRQ(ierr);
2401     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscBLASInt),&ipiv);CHKERRQ(ierr);
2402     for(i=0;i<pcis->n_B;i++) {
2403       nnz[i]=1;
2404     }
2405     /* Overestimated nonzeros per row */
2406     k=1;
2407     for(i=pcbddc->n_vertices;i<local_primal_size;i++) {
2408       if(change_basis[i]) {
2409         size_of_constraint = temp_indices[i+1]-temp_indices[i];
2410         if(k < size_of_constraint) {
2411           k = size_of_constraint;
2412         }
2413         for(j=0;j<size_of_constraint;j++) {
2414           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
2415         }
2416       }
2417     }
2418     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
2419     ierr = PetscFree(nnz);CHKERRQ(ierr);
2420     /* Temporary array to store indices */
2421     ierr = PetscMalloc(k*sizeof(PetscInt),&is_indices);CHKERRQ(ierr);
2422     /* Set initial identity in the matrix */
2423     for(i=0;i<pcis->n_B;i++) {
2424       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
2425     }
2426     /* Now we loop on the constraints which need a change of basis */
2427     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
2428     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (6.2.1) */
2429     temp_constraints = 0;
2430     if(pcbddc->n_vertices < local_primal_size) {
2431       temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
2432     }
2433     for(i=pcbddc->n_vertices;i<local_primal_size;i++) {
2434       if(change_basis[i]) {
2435         compute_submatrix = PETSC_FALSE;
2436         useksp = PETSC_FALSE;
2437         if(temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
2438           temp_constraints++;
2439           if(i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
2440             compute_submatrix = PETSC_TRUE;
2441           }
2442         }
2443         if(compute_submatrix) {
2444           if(temp_constraints > 1 || pcbddc->use_nnsp_true) {
2445             useksp = PETSC_TRUE;
2446           }
2447           size_of_constraint = temp_indices[i+1]-temp_indices[i];
2448           if(useksp) { /* experimental */
2449             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
2450             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
2451             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
2452             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,PETSC_NULL);CHKERRQ(ierr);
2453           }
2454           /* First _size_of_constraint-temp_constraints_ columns */
2455           dual_dofs = size_of_constraint-temp_constraints;
2456           start_constraint = i+1-temp_constraints;
2457           for(s=0;s<dual_dofs;s++) {
2458             is_indices[0] = s;
2459             for(j=0;j<temp_constraints;j++) {
2460               for(k=0;k<temp_constraints;k++) {
2461                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
2462               }
2463               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
2464               is_indices[j+1]=s+j+1;
2465             }
2466             Bt = temp_constraints;
2467             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2468             LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr);
2469             if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
2470             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2471             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
2472             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
2473             if(useksp) {
2474               /* temp mat with transposed rows and columns */
2475               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
2476               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
2477             }
2478           }
2479           if(useksp) {
2480             /* last rows of temp_mat */
2481             for(j=0;j<size_of_constraint;j++) {
2482               is_indices[j] = j;
2483             }
2484             for(s=0;s<temp_constraints;s++) {
2485               k = s + dual_dofs;
2486               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
2487             }
2488             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2489             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2490             ierr = MatGetVecs(temp_mat,&temp_vec,PETSC_NULL);CHKERRQ(ierr);
2491             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
2492             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
2493             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
2494             ierr = KSPGetPC(temp_ksp,&temp_pc);CHKERRQ(ierr);
2495             ierr = PCSetType(temp_pc,PCLU);CHKERRQ(ierr);
2496             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
2497             for(s=0;s<temp_constraints;s++) {
2498               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
2499               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
2500               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
2501               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
2502               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
2503               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
2504               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
2505               /* last columns of change of basis matrix associated to new primal dofs */
2506               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,&temp_indices_to_constraint_B[temp_indices[start_constraint+s]],1,&j,array_vector,INSERT_VALUES);CHKERRQ(ierr);
2507               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
2508             }
2509             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
2510             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
2511             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2512           } else {
2513             /* last columns of change of basis matrix associated to new primal dofs */
2514             for(s=0;s<temp_constraints;s++) {
2515               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
2516               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,&temp_indices_to_constraint_B[temp_indices[start_constraint+s]],1,&j,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
2517             }
2518           }
2519           /* prepare for the next cycle */
2520           temp_constraints = 0;
2521           if(i != local_primal_size -1 ) {
2522             temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
2523           }
2524         }
2525       }
2526     }
2527     /* assembling */
2528     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2529     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2530     ierr = PetscFree(ipiv);CHKERRQ(ierr);
2531     ierr = PetscFree(is_indices);CHKERRQ(ierr);
2532   }
2533   /* free workspace no longer needed */
2534   ierr = PetscFree(rwork);CHKERRQ(ierr);
2535   ierr = PetscFree(work);CHKERRQ(ierr);
2536   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
2537   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
2538   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
2539   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2540   ierr = PetscFree(change_basis);CHKERRQ(ierr);
2541   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
2542   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
2543   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
2544   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
2545 #if defined(PETSC_MISSING_LAPACK_GESVD)
2546   ierr = PetscFree(iwork);CHKERRQ(ierr);
2547   ierr = PetscFree(ifail);CHKERRQ(ierr);
2548   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
2549 #endif
2550   for(k=0;k<nnsp_size;k++) {
2551     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
2552   }
2553   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
2554   PetscFunctionReturn(0);
2555 }
2556 /* -------------------------------------------------------------------------- */
2557 #undef __FUNCT__
2558 #define __FUNCT__ "PCBDDCCoarseSetUp"
2559 static PetscErrorCode PCBDDCCoarseSetUp(PC pc)
2560 {
2561   PetscErrorCode  ierr;
2562 
2563   PC_IS*            pcis = (PC_IS*)(pc->data);
2564   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
2565   Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
2566   Mat               change_mat_all;
2567   IS                is_R_local;
2568   IS                is_V_local;
2569   IS                is_C_local;
2570   IS                is_aux1;
2571   IS                is_aux2;
2572   const VecType     impVecType;
2573   const MatType     impMatType;
2574   PetscInt          n_R=0;
2575   PetscInt          n_D=0;
2576   PetscInt          n_B=0;
2577   PetscScalar       zero=0.0;
2578   PetscScalar       one=1.0;
2579   PetscScalar       m_one=-1.0;
2580   PetscScalar*      array;
2581   PetscScalar       *coarse_submat_vals;
2582   PetscInt          *idx_R_local;
2583   PetscInt          *idx_V_B;
2584   PetscScalar       *coarsefunctions_errors;
2585   PetscScalar       *constraints_errors;
2586   /* auxiliary indices */
2587   PetscInt i,j,k;
2588   /* for verbose output of bddc */
2589   PetscViewer       viewer=pcbddc->dbg_viewer;
2590   PetscBool         dbg_flag=pcbddc->dbg_flag;
2591   /* for counting coarse dofs */
2592   PetscInt          n_vertices,n_constraints;
2593   PetscInt          size_of_constraint;
2594   PetscInt          *row_cmat_indices;
2595   PetscScalar       *row_cmat_values;
2596   PetscInt          *vertices,*nnz,*is_indices,*temp_indices;
2597 
2598   PetscFunctionBegin;
2599   /* Set Non-overlapping dimensions */
2600   n_B = pcis->n_B; n_D = pcis->n - n_B;
2601   /* Set types for local objects needed by BDDC precondtioner */
2602   impMatType = MATSEQDENSE;
2603   impVecType = VECSEQ;
2604   /* get vertex indices from constraint matrix */
2605   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
2606   n_vertices=0;
2607   for(i=0;i<pcbddc->local_primal_size;i++) {
2608     ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
2609     if(size_of_constraint == 1) {
2610       vertices[n_vertices]=row_cmat_indices[0];
2611       n_vertices++;
2612     }
2613     ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
2614   }
2615   /* Set number of constraints */
2616   n_constraints = pcbddc->local_primal_size-n_vertices;
2617 
2618   /* vertices in boundary numbering */
2619   if(n_vertices) {
2620     ierr = VecSet(pcis->vec1_N,m_one);CHKERRQ(ierr);
2621     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2622     for (i=0; i<n_vertices; i++) { array[ vertices[i] ] = i; }
2623     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2624     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2625     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2626     ierr = PetscMalloc(n_vertices*sizeof(PetscInt),&idx_V_B);CHKERRQ(ierr);
2627     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2628     for (i=0; i<n_vertices; i++) {
2629       j=0;
2630       while (array[j] != i ) {j++;}
2631       idx_V_B[i]=j;
2632     }
2633     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2634   }
2635 
2636   /* transform local matrices if needed */
2637   if(pcbddc->usechangeofbasis) {
2638     ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2639     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2640     for(i=0;i<n_D;i++) {
2641       nnz[is_indices[i]]=1;
2642     }
2643     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2644     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2645     k=1;
2646     for(i=0;i<n_B;i++) {
2647       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
2648       nnz[is_indices[i]]=j;
2649       if( k < j) {
2650         k = j;
2651       }
2652       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
2653     }
2654     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2655     /* assemble change of basis matrix on the whole set of local dofs */
2656     ierr = PetscMalloc(k*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
2657     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
2658     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
2659     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
2660     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
2661     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2662     for(i=0;i<n_D;i++) {
2663       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
2664     }
2665     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2666     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2667     for(i=0;i<n_B;i++) {
2668       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2669       for(k=0;k<j;k++) {
2670         temp_indices[k]=is_indices[row_cmat_indices[k]];
2671       }
2672       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
2673       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2674     }
2675     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2676     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2677     ierr = MatPtAP(matis->A,change_mat_all,MAT_INITIAL_MATRIX,1.0,&pcbddc->local_mat);CHKERRQ(ierr);
2678     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
2679     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
2680     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
2681     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
2682     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
2683     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
2684     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
2685     ierr = PetscFree(nnz);CHKERRQ(ierr);
2686     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2687   } else {
2688     /* without change of basis, the local matrix is unchanged */
2689     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
2690     pcbddc->local_mat = matis->A;
2691   }
2692 
2693   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
2694   ierr = VecSet(pcis->vec1_N,one);CHKERRQ(ierr);
2695   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2696   for (i=0;i<n_vertices;i++) { array[ vertices[i] ] = zero; }
2697   ierr = PetscMalloc(( pcis->n - n_vertices )*sizeof(PetscInt),&idx_R_local);CHKERRQ(ierr);
2698   for (i=0, n_R=0; i<pcis->n; i++) { if (array[i] == one) { idx_R_local[n_R] = i; n_R++; } }
2699   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2700   if(dbg_flag) {
2701     ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
2702     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2703     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
2704     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
2705     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"r_size = %d, v_size = %d, constraints = %d, local_primal_size = %d\n",n_R,n_vertices,n_constraints,pcbddc->local_primal_size);CHKERRQ(ierr);
2706     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
2707     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2708   }
2709 
2710   /* Allocate needed vectors */
2711   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2712   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
2713   ierr = VecDuplicate(pcis->vec1_D,&pcbddc->vec4_D);CHKERRQ(ierr);
2714   ierr = VecCreate(PETSC_COMM_SELF,&pcbddc->vec1_R);CHKERRQ(ierr);
2715   ierr = VecSetSizes(pcbddc->vec1_R,n_R,n_R);CHKERRQ(ierr);
2716   ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
2717   ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
2718   ierr = VecCreate(PETSC_COMM_SELF,&pcbddc->vec1_P);CHKERRQ(ierr);
2719   ierr = VecSetSizes(pcbddc->vec1_P,pcbddc->local_primal_size,pcbddc->local_primal_size);CHKERRQ(ierr);
2720   ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
2721 
2722   /* Creating some index sets needed  */
2723   /* For submatrices */
2724   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_R,idx_R_local,PETSC_OWN_POINTER,&is_R_local);CHKERRQ(ierr);
2725   if(n_vertices)    {
2726     ierr = ISCreateGeneral(PETSC_COMM_SELF,n_vertices,vertices,PETSC_OWN_POINTER,&is_V_local);CHKERRQ(ierr);
2727   }
2728   if(n_constraints) {
2729     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_C_local);CHKERRQ(ierr);
2730   }
2731 
2732   /* For VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
2733   {
2734     PetscInt   *aux_array1;
2735     PetscInt   *aux_array2;
2736 
2737     ierr = PetscMalloc( (pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
2738     ierr = PetscMalloc( (pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array2);CHKERRQ(ierr);
2739 
2740     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
2741     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2742     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2743     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2744     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2745     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2746     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2747     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2748     for (i=0, j=0; i<n_R; i++) { if (array[idx_R_local[i]] > one) { aux_array1[j] = i; j++; } }
2749     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2750     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_COPY_VALUES,&is_aux1);CHKERRQ(ierr);
2751     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2752     for (i=0, j=0; i<n_B; i++) { if (array[i] > one) { aux_array2[j] = i; j++; } }
2753     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2754     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_COPY_VALUES,&is_aux2);CHKERRQ(ierr);
2755     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
2756     ierr = PetscFree(aux_array1);CHKERRQ(ierr);
2757     ierr = PetscFree(aux_array2);CHKERRQ(ierr);
2758     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2759     ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
2760 
2761     if(pcbddc->prec_type || dbg_flag ) {
2762       ierr = PetscMalloc(n_D*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
2763       ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2764       for (i=0, j=0; i<n_R; i++) { if (array[idx_R_local[i]] == one) { aux_array1[j] = i; j++; } }
2765       ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2766       ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_COPY_VALUES,&is_aux1);CHKERRQ(ierr);
2767       ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
2768       ierr = PetscFree(aux_array1);CHKERRQ(ierr);
2769       ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2770     }
2771   }
2772 
2773   /* Creating PC contexts for local Dirichlet and Neumann problems */
2774   {
2775     Mat  A_RR;
2776     PC   pc_temp;
2777     /* Matrix for Dirichlet problem is A_II -> we already have it from pcis.c code */
2778     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
2779     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
2780     ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,SAME_PRECONDITIONER);CHKERRQ(ierr);
2781     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
2782     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
2783     /* default */
2784     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
2785     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
2786     /* Allow user's customization */
2787     ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
2788     /* Set Up KSP for Dirichlet problem of BDDC */
2789     ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
2790     /* set ksp_D into pcis data */
2791     ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
2792     ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
2793     pcis->ksp_D = pcbddc->ksp_D;
2794     /* Matrix for Neumann problem is A_RR -> we need to create it */
2795     ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
2796     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
2797     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
2798     ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,SAME_PRECONDITIONER);CHKERRQ(ierr);
2799     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
2800     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
2801     /* default */
2802     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
2803     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
2804     /* Allow user's customization */
2805     ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
2806     /* Set Up KSP for Neumann problem of BDDC */
2807     ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
2808     /* check Dirichlet and Neumann solvers */
2809     {
2810       Vec         temp_vec;
2811       PetscReal   value;
2812       PetscMPIInt use_exact,use_exact_reduced;
2813 
2814       ierr = VecDuplicate(pcis->vec1_D,&temp_vec);CHKERRQ(ierr);
2815       ierr = VecSetRandom(pcis->vec1_D,PETSC_NULL);CHKERRQ(ierr);
2816       ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
2817       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,temp_vec);CHKERRQ(ierr);
2818       ierr = VecAXPY(temp_vec,m_one,pcis->vec1_D);CHKERRQ(ierr);
2819       ierr = VecNorm(temp_vec,NORM_INFINITY,&value);CHKERRQ(ierr);
2820       use_exact = 1;
2821       if(PetscAbsReal(value) > 1.e-4) {
2822         use_exact = 0;
2823       }
2824       ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,((PetscObject)pc)->comm);CHKERRQ(ierr);
2825       pcbddc->use_exact_dirichlet = (PetscBool) use_exact_reduced;
2826       ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2827       if(dbg_flag) {
2828         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2829         ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
2830         ierr = PetscViewerASCIIPrintf(viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
2831         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
2832         ierr = VecDuplicate(pcbddc->vec1_R,&temp_vec);CHKERRQ(ierr);
2833         ierr = VecSetRandom(pcbddc->vec1_R,PETSC_NULL);CHKERRQ(ierr);
2834         ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2835         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,temp_vec);CHKERRQ(ierr);
2836         ierr = VecAXPY(temp_vec,m_one,pcbddc->vec1_R);CHKERRQ(ierr);
2837         ierr = VecNorm(temp_vec,NORM_INFINITY,&value);CHKERRQ(ierr);
2838         ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2839         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
2840         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2841       }
2842     }
2843     /* free Neumann problem's matrix */
2844     ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
2845   }
2846 
2847   /* Assemble all remaining stuff needed to apply BDDC  */
2848   {
2849     Mat          A_RV,A_VR,A_VV;
2850     Mat          M1,M2;
2851     Mat          C_CR;
2852     Mat          AUXMAT;
2853     Vec          vec1_C;
2854     Vec          vec2_C;
2855     Vec          vec1_V;
2856     Vec          vec2_V;
2857     PetscInt     *nnz;
2858     PetscInt     *auxindices;
2859     PetscInt     index;
2860     PetscScalar* array2;
2861     MatFactorInfo matinfo;
2862 
2863     /* Allocating some extra storage just to be safe */
2864     ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2865     ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&auxindices);CHKERRQ(ierr);
2866     for(i=0;i<pcis->n;i++) {auxindices[i]=i;}
2867 
2868     /* some work vectors on vertices and/or constraints */
2869     if(n_vertices) {
2870       ierr = VecCreate(PETSC_COMM_SELF,&vec1_V);CHKERRQ(ierr);
2871       ierr = VecSetSizes(vec1_V,n_vertices,n_vertices);CHKERRQ(ierr);
2872       ierr = VecSetType(vec1_V,impVecType);CHKERRQ(ierr);
2873       ierr = VecDuplicate(vec1_V,&vec2_V);CHKERRQ(ierr);
2874     }
2875     if(n_constraints) {
2876       ierr = VecCreate(PETSC_COMM_SELF,&vec1_C);CHKERRQ(ierr);
2877       ierr = VecSetSizes(vec1_C,n_constraints,n_constraints);CHKERRQ(ierr);
2878       ierr = VecSetType(vec1_C,impVecType);CHKERRQ(ierr);
2879       ierr = VecDuplicate(vec1_C,&vec2_C);CHKERRQ(ierr);
2880       ierr = VecDuplicate(vec1_C,&pcbddc->vec1_C);CHKERRQ(ierr);
2881     }
2882     /* Precompute stuffs needed for preprocessing and application of BDDC*/
2883     if(n_constraints) {
2884       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->local_auxmat2);CHKERRQ(ierr);
2885       ierr = MatSetSizes(pcbddc->local_auxmat2,n_R,n_constraints,n_R,n_constraints);CHKERRQ(ierr);
2886       ierr = MatSetType(pcbddc->local_auxmat2,impMatType);CHKERRQ(ierr);
2887       ierr = MatSeqDenseSetPreallocation(pcbddc->local_auxmat2,PETSC_NULL);CHKERRQ(ierr);
2888 
2889       /* Create Constraint matrix on R nodes: C_{CR}  */
2890       ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_C_local,is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
2891       ierr = ISDestroy(&is_C_local);CHKERRQ(ierr);
2892 
2893       /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
2894       for(i=0;i<n_constraints;i++) {
2895         ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
2896         /* Get row of constraint matrix in R numbering */
2897         ierr = VecGetArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
2898         ierr = MatGetRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2899         for(j=0;j<size_of_constraint;j++) { array[ row_cmat_indices[j] ] = - row_cmat_values[j]; }
2900         ierr = MatRestoreRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2901         ierr = VecRestoreArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
2902         /* Solve for row of constraint matrix in R numbering */
2903         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2904         /* Set values */
2905         ierr = VecGetArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2906         ierr = MatSetValues(pcbddc->local_auxmat2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2907         ierr = VecRestoreArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2908       }
2909       ierr = MatAssemblyBegin(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2910       ierr = MatAssemblyEnd(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2911 
2912       /* Assemble AUXMAT = ( LUFactor )( -C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} */
2913       ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AUXMAT);CHKERRQ(ierr);
2914       ierr = MatFactorInfoInitialize(&matinfo);CHKERRQ(ierr);
2915       ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,0,1,&is_aux1);CHKERRQ(ierr);
2916       ierr = MatLUFactor(AUXMAT,is_aux1,is_aux1,&matinfo);CHKERRQ(ierr);
2917       ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2918 
2919       /* Assemble explicitly M1 = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} needed in preproc  */
2920       ierr = MatCreate(PETSC_COMM_SELF,&M1);CHKERRQ(ierr);
2921       ierr = MatSetSizes(M1,n_constraints,n_constraints,n_constraints,n_constraints);CHKERRQ(ierr);
2922       ierr = MatSetType(M1,impMatType);CHKERRQ(ierr);
2923       ierr = MatSeqDenseSetPreallocation(M1,PETSC_NULL);CHKERRQ(ierr);
2924       for(i=0;i<n_constraints;i++) {
2925         ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
2926         ierr = VecSetValue(vec1_C,i,one,INSERT_VALUES);CHKERRQ(ierr);
2927         ierr = VecAssemblyBegin(vec1_C);CHKERRQ(ierr);
2928         ierr = VecAssemblyEnd(vec1_C);CHKERRQ(ierr);
2929         ierr = MatSolve(AUXMAT,vec1_C,vec2_C);CHKERRQ(ierr);
2930         ierr = VecScale(vec2_C,m_one);CHKERRQ(ierr);
2931         ierr = VecGetArray(vec2_C,&array);CHKERRQ(ierr);
2932         ierr = MatSetValues(M1,n_constraints,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2933         ierr = VecRestoreArray(vec2_C,&array);CHKERRQ(ierr);
2934       }
2935       ierr = MatAssemblyBegin(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2936       ierr = MatAssemblyEnd(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2937       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
2938       /* Assemble local_auxmat1 = M1*C_{CR} needed by BDDC application in KSP and in preproc */
2939       ierr = MatMatMult(M1,C_CR,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
2940 
2941     }
2942 
2943     /* Get submatrices from subdomain matrix */
2944     if(n_vertices){
2945       ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_V_local,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
2946       ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
2947       ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_V_local,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
2948       /* Assemble M2 = A_RR^{-1}A_RV */
2949       ierr = MatCreate(PETSC_COMM_SELF,&M2);CHKERRQ(ierr);
2950       ierr = MatSetSizes(M2,n_R,n_vertices,n_R,n_vertices);CHKERRQ(ierr);
2951       ierr = MatSetType(M2,impMatType);CHKERRQ(ierr);
2952       ierr = MatSeqDenseSetPreallocation(M2,PETSC_NULL);CHKERRQ(ierr);
2953       for(i=0;i<n_vertices;i++) {
2954         ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
2955         ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
2956         ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
2957         ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
2958         ierr = MatMult(A_RV,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
2959         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2960         ierr = VecGetArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2961         ierr = MatSetValues(M2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2962         ierr = VecRestoreArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2963       }
2964       ierr = MatAssemblyBegin(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2965       ierr = MatAssemblyEnd(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2966     }
2967 
2968     /* Matrix of coarse basis functions (local) */
2969     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
2970     ierr = MatSetSizes(pcbddc->coarse_phi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
2971     ierr = MatSetType(pcbddc->coarse_phi_B,impMatType);CHKERRQ(ierr);
2972     ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_B,PETSC_NULL);CHKERRQ(ierr);
2973     if(pcbddc->prec_type || dbg_flag ) {
2974       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
2975       ierr = MatSetSizes(pcbddc->coarse_phi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
2976       ierr = MatSetType(pcbddc->coarse_phi_D,impMatType);CHKERRQ(ierr);
2977       ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_D,PETSC_NULL);CHKERRQ(ierr);
2978     }
2979 
2980     if(dbg_flag) {
2981       ierr = PetscMalloc( pcbddc->local_primal_size*sizeof(PetscScalar),&coarsefunctions_errors);CHKERRQ(ierr);
2982       ierr = PetscMalloc( pcbddc->local_primal_size*sizeof(PetscScalar),&constraints_errors);CHKERRQ(ierr);
2983     }
2984     /* Subdomain contribution (Non-overlapping) to coarse matrix  */
2985     ierr = PetscMalloc ((pcbddc->local_primal_size)*(pcbddc->local_primal_size)*sizeof(PetscScalar),&coarse_submat_vals);CHKERRQ(ierr);
2986 
2987     /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
2988     for(i=0;i<n_vertices;i++){
2989       ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
2990       ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
2991       ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
2992       ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
2993       /* solution of saddle point problem */
2994       ierr = MatMult(M2,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
2995       ierr = VecScale(pcbddc->vec1_R,m_one);CHKERRQ(ierr);
2996       if(n_constraints) {
2997         ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec1_R,vec1_C);CHKERRQ(ierr);
2998         ierr = MatMultAdd(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
2999         ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
3000       }
3001       ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
3002       ierr = MatMultAdd(A_VV,vec1_V,vec2_V,vec2_V);CHKERRQ(ierr);
3003 
3004       /* Set values in coarse basis function and subdomain part of coarse_mat */
3005       /* coarse basis functions */
3006       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
3007       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3008       ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3009       ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3010       ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
3011       ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3012       ierr = MatSetValue(pcbddc->coarse_phi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
3013       if( pcbddc->prec_type || dbg_flag  ) {
3014         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3015         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3016         ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3017         ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
3018         ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3019       }
3020       /* subdomain contribution to coarse matrix */
3021       ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3022       for(j=0;j<n_vertices;j++) { coarse_submat_vals[i*pcbddc->local_primal_size+j] = array[j]; } /* WARNING -> column major ordering */
3023       ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3024       if(n_constraints) {
3025         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3026         for(j=0;j<n_constraints;j++) { coarse_submat_vals[i*pcbddc->local_primal_size+j+n_vertices] = array[j]; } /* WARNING -> column major ordering */
3027         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3028       }
3029 
3030       if( dbg_flag ) {
3031         /* assemble subdomain vector on nodes */
3032         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3033         ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3034         ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3035         for(j=0;j<n_R;j++) { array[idx_R_local[j]] = array2[j]; }
3036         array[ vertices[i] ] = one;
3037         ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3038         ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3039         /* assemble subdomain vector of lagrange multipliers (i.e. primal nodes) */
3040         ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
3041         ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3042         ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3043         for(j=0;j<n_vertices;j++) { array2[j]=array[j]; }
3044         ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3045         if(n_constraints) {
3046           ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3047           for(j=0;j<n_constraints;j++) { array2[j+n_vertices]=array[j]; }
3048           ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3049         }
3050         ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3051         ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
3052         /* check saddle point solution */
3053         ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
3054         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
3055         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i]);CHKERRQ(ierr);
3056         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
3057         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3058         array[i]=array[i]+m_one;  /* shift by the identity matrix */
3059         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3060         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i]);CHKERRQ(ierr);
3061       }
3062     }
3063 
3064     for(i=0;i<n_constraints;i++){
3065       ierr = VecSet(vec2_C,zero);CHKERRQ(ierr);
3066       ierr = VecSetValue(vec2_C,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
3067       ierr = VecAssemblyBegin(vec2_C);CHKERRQ(ierr);
3068       ierr = VecAssemblyEnd(vec2_C);CHKERRQ(ierr);
3069       /* solution of saddle point problem */
3070       ierr = MatMult(M1,vec2_C,vec1_C);CHKERRQ(ierr);
3071       ierr = MatMult(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
3072       ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
3073       if(n_vertices) { ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr); }
3074       /* Set values in coarse basis function and subdomain part of coarse_mat */
3075       /* coarse basis functions */
3076       index=i+n_vertices;
3077       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
3078       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3079       ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3080       ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3081       ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
3082       ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3083       if( pcbddc->prec_type || dbg_flag ) {
3084         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3085         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3086         ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3087         ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
3088         ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3089       }
3090       /* subdomain contribution to coarse matrix */
3091       if(n_vertices) {
3092         ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3093         for(j=0;j<n_vertices;j++) {coarse_submat_vals[index*pcbddc->local_primal_size+j]=array[j];} /* WARNING -> column major ordering */
3094         ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3095       }
3096       ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3097       for(j=0;j<n_constraints;j++) {coarse_submat_vals[index*pcbddc->local_primal_size+j+n_vertices]=array[j];} /* WARNING -> column major ordering */
3098       ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3099 
3100       if( dbg_flag ) {
3101         /* assemble subdomain vector on nodes */
3102         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3103         ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3104         ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3105         for(j=0;j<n_R;j++){ array[ idx_R_local[j] ] = array2[j]; }
3106         ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3107         ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3108         /* assemble subdomain vector of lagrange multipliers */
3109         ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
3110         ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3111         if( n_vertices) {
3112           ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3113           for(j=0;j<n_vertices;j++) {array2[j]=-array[j];}
3114           ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3115         }
3116         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3117         for(j=0;j<n_constraints;j++) {array2[j+n_vertices]=-array[j];}
3118         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3119         ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3120         /* check saddle point solution */
3121         ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
3122         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
3123         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[index]);CHKERRQ(ierr);
3124         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
3125         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3126         array[index]=array[index]+m_one; /* shift by the identity matrix */
3127         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3128         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[index]);CHKERRQ(ierr);
3129       }
3130     }
3131     ierr = MatAssemblyBegin(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3132     ierr = MatAssemblyEnd  (pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3133     if( pcbddc->prec_type || dbg_flag ) {
3134       ierr = MatAssemblyBegin(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3135       ierr = MatAssemblyEnd  (pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3136     }
3137     /* Checking coarse_sub_mat and coarse basis functios */
3138     /* It shuld be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
3139     if(dbg_flag) {
3140 
3141       Mat coarse_sub_mat;
3142       Mat TM1,TM2,TM3,TM4;
3143       Mat coarse_phi_D,coarse_phi_B,A_II,A_BB,A_IB,A_BI;
3144       const MatType checkmattype=MATSEQAIJ;
3145       PetscScalar      value;
3146 
3147       ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
3148       ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
3149       ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
3150       ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
3151       ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
3152       ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
3153       ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
3154       ierr = MatConvert(coarse_sub_mat,checkmattype,MAT_REUSE_MATRIX,&coarse_sub_mat);CHKERRQ(ierr);
3155 
3156       /*PetscViewer view_out;
3157       PetscMPIInt myrank;
3158       char filename[256];
3159       MPI_Comm_rank(((PetscObject)pc)->comm,&myrank);
3160       sprintf(filename,"coarsesubmat_%04d.m",myrank);
3161       ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&view_out);CHKERRQ(ierr);
3162       ierr = PetscViewerSetFormat(view_out,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3163       ierr = MatView(coarse_sub_mat,view_out);CHKERRQ(ierr);
3164       ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);*/
3165 
3166       ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3167       ierr = PetscViewerASCIIPrintf(viewer,"Check coarse sub mat and local basis functions\n");CHKERRQ(ierr);
3168       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3169       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
3170       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
3171       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
3172       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
3173       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
3174       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
3175       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
3176       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
3177       ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3178       ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3179       ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3180       ierr = MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3181       ierr = MatNorm(TM1,NORM_INFINITY,&value);CHKERRQ(ierr);
3182       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"----------------------------------\n");CHKERRQ(ierr);
3183       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d \n",PetscGlobalRank);CHKERRQ(ierr);
3184       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"matrix error = % 1.14e\n",value);CHKERRQ(ierr);
3185       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"coarse functions errors\n");CHKERRQ(ierr);
3186       for(i=0;i<pcbddc->local_primal_size;i++) { ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local %02d-th function error = % 1.14e\n",i,coarsefunctions_errors[i]);CHKERRQ(ierr); }
3187       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"constraints errors\n");CHKERRQ(ierr);
3188       for(i=0;i<pcbddc->local_primal_size;i++) { ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local %02d-th function error = % 1.14e\n",i,constraints_errors[i]);CHKERRQ(ierr); }
3189       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3190       ierr = MatDestroy(&A_II);CHKERRQ(ierr);
3191       ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
3192       ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
3193       ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
3194       ierr = MatDestroy(&TM1);CHKERRQ(ierr);
3195       ierr = MatDestroy(&TM2);CHKERRQ(ierr);
3196       ierr = MatDestroy(&TM3);CHKERRQ(ierr);
3197       ierr = MatDestroy(&TM4);CHKERRQ(ierr);
3198       ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
3199       ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
3200       ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
3201       ierr = PetscFree(coarsefunctions_errors);CHKERRQ(ierr);
3202       ierr = PetscFree(constraints_errors);CHKERRQ(ierr);
3203     }
3204 
3205     /* create coarse matrix and data structures for message passing associated actual choice of coarse problem type */
3206     ierr = PCBDDCSetupCoarseEnvironment(pc,coarse_submat_vals);CHKERRQ(ierr);
3207     /* free memory */
3208     ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
3209     ierr = PetscFree(auxindices);CHKERRQ(ierr);
3210     ierr = PetscFree(nnz);CHKERRQ(ierr);
3211     if(n_vertices) {
3212       ierr = VecDestroy(&vec1_V);CHKERRQ(ierr);
3213       ierr = VecDestroy(&vec2_V);CHKERRQ(ierr);
3214       ierr = MatDestroy(&M2);CHKERRQ(ierr);
3215       ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
3216       ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
3217       ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
3218     }
3219     if(n_constraints) {
3220       ierr = VecDestroy(&vec1_C);CHKERRQ(ierr);
3221       ierr = VecDestroy(&vec2_C);CHKERRQ(ierr);
3222       ierr = MatDestroy(&M1);CHKERRQ(ierr);
3223       ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
3224     }
3225   }
3226   /* free memory */
3227   if(n_vertices) {
3228     ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
3229     ierr = ISDestroy(&is_V_local);CHKERRQ(ierr);
3230   }
3231   ierr = ISDestroy(&is_R_local);CHKERRQ(ierr);
3232 
3233   PetscFunctionReturn(0);
3234 }
3235 
3236 /* -------------------------------------------------------------------------- */
3237 
3238 #undef __FUNCT__
3239 #define __FUNCT__ "PCBDDCSetupCoarseEnvironment"
3240 static PetscErrorCode PCBDDCSetupCoarseEnvironment(PC pc,PetscScalar* coarse_submat_vals)
3241 {
3242 
3243 
3244   Mat_IS    *matis    = (Mat_IS*)pc->pmat->data;
3245   PC_BDDC   *pcbddc   = (PC_BDDC*)pc->data;
3246   PC_IS     *pcis     = (PC_IS*)pc->data;
3247   MPI_Comm  prec_comm = ((PetscObject)pc)->comm;
3248   MPI_Comm  coarse_comm;
3249 
3250   /* common to all choiches */
3251   PetscScalar *temp_coarse_mat_vals;
3252   PetscScalar *ins_coarse_mat_vals;
3253   PetscInt    *ins_local_primal_indices;
3254   PetscMPIInt *localsizes2,*localdispl2;
3255   PetscMPIInt size_prec_comm;
3256   PetscMPIInt rank_prec_comm;
3257   PetscMPIInt active_rank=MPI_PROC_NULL;
3258   PetscMPIInt master_proc=0;
3259   PetscInt    ins_local_primal_size;
3260   /* specific to MULTILEVEL_BDDC */
3261   PetscMPIInt *ranks_recv;
3262   PetscMPIInt count_recv=0;
3263   PetscMPIInt rank_coarse_proc_send_to;
3264   PetscMPIInt coarse_color = MPI_UNDEFINED;
3265   ISLocalToGlobalMapping coarse_ISLG;
3266   /* some other variables */
3267   PetscErrorCode ierr;
3268   const MatType coarse_mat_type;
3269   const PCType  coarse_pc_type;
3270   const KSPType  coarse_ksp_type;
3271   PC pc_temp;
3272   PetscInt i,j,k,bs;
3273   PetscInt max_it_coarse_ksp=1;  /* don't increase this value */
3274   /* verbose output viewer */
3275   PetscViewer viewer=pcbddc->dbg_viewer;
3276   PetscBool   dbg_flag=pcbddc->dbg_flag;
3277 
3278   PetscFunctionBegin;
3279 
3280   ins_local_primal_indices = 0;
3281   ins_coarse_mat_vals      = 0;
3282   localsizes2              = 0;
3283   localdispl2              = 0;
3284   temp_coarse_mat_vals     = 0;
3285   coarse_ISLG              = 0;
3286 
3287   ierr = MPI_Comm_size(prec_comm,&size_prec_comm);CHKERRQ(ierr);
3288   ierr = MPI_Comm_rank(prec_comm,&rank_prec_comm);CHKERRQ(ierr);
3289   ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
3290 
3291   /* adapt coarse problem type */
3292   if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC && pcbddc->active_procs < MIN_PROCS_FOR_BDDC )
3293     pcbddc->coarse_problem_type = PARALLEL_BDDC;
3294 
3295   /* Assign global numbering to coarse dofs */
3296   {
3297     PetscScalar    one=1.,zero=0.;
3298     PetscScalar    *array;
3299     PetscMPIInt    *auxlocal_primal;
3300     PetscMPIInt    *auxglobal_primal;
3301     PetscMPIInt    *all_auxglobal_primal;
3302     PetscMPIInt    mpi_local_primal_size = (PetscMPIInt)pcbddc->local_primal_size;
3303     PetscInt       *row_cmat_indices;
3304     PetscInt       size_of_constraint;
3305     PetscScalar    coarsesum;
3306 
3307     /* Construct needed data structures for message passing */
3308     ierr = PetscMalloc(mpi_local_primal_size*sizeof(PetscMPIInt),&pcbddc->local_primal_indices);CHKERRQ(ierr);
3309     j = 0;
3310     if(rank_prec_comm == 0 || pcbddc->coarse_problem_type == REPLICATED_BDDC) {
3311       j = size_prec_comm;
3312     }
3313     ierr = PetscMalloc(j*sizeof(PetscMPIInt),&pcbddc->local_primal_sizes);CHKERRQ(ierr);
3314     ierr = PetscMalloc(j*sizeof(PetscMPIInt),&pcbddc->local_primal_displacements);CHKERRQ(ierr);
3315     /* Gather local_primal_size information for all processes  */
3316     if(pcbddc->coarse_problem_type == REPLICATED_BDDC) {
3317       ierr = MPI_Allgather(&mpi_local_primal_size,1,MPIU_INT,&pcbddc->local_primal_sizes[0],1,MPIU_INT,prec_comm);CHKERRQ(ierr);
3318     } else {
3319       ierr = MPI_Gather(&mpi_local_primal_size,1,MPIU_INT,&pcbddc->local_primal_sizes[0],1,MPIU_INT,0,prec_comm);CHKERRQ(ierr);
3320     }
3321     pcbddc->replicated_primal_size = 0;
3322     for (i=0; i<j; i++) {
3323       pcbddc->local_primal_displacements[i] = pcbddc->replicated_primal_size ;
3324       pcbddc->replicated_primal_size += pcbddc->local_primal_sizes[i];
3325     }
3326     if(rank_prec_comm == 0) {
3327       /* allocate some auxiliary space */
3328       ierr = PetscMalloc(pcbddc->replicated_primal_size*sizeof(*all_auxglobal_primal),&all_auxglobal_primal);CHKERRQ(ierr);
3329     }
3330     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscMPIInt),&auxlocal_primal);CHKERRQ(ierr);
3331     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscMPIInt),&auxglobal_primal);CHKERRQ(ierr);
3332 
3333     /* First let's count coarse dofs.
3334        This code fragment assumes that the number of local constraints per connected component
3335        is not greater than the number of nodes defined for the connected component
3336        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
3337     /* auxlocal_primal      : primal indices in local nodes numbering (internal and interface) with complete queue sorted by global ordering */
3338     ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3339     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3340     for(i=0;i<pcbddc->local_primal_size;i++) {
3341       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
3342       for (j=0; j<size_of_constraint; j++) {
3343         k = row_cmat_indices[j];
3344         if( array[k] == zero ) {
3345           array[k] = one;
3346           auxlocal_primal[i] = k;
3347           break;
3348         }
3349       }
3350       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
3351     }
3352     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3353     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
3354     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3355     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3356     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3357     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3358     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3359     for(i=0;i<pcis->n;i++) { if( array[i] > zero) array[i] = one/array[i]; }
3360     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3361     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
3362     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3363     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3364     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
3365     pcbddc->coarse_size = (PetscInt) coarsesum;
3366 
3367     /* Now assign them a global numbering */
3368     /* auxglobal_primal contains indices in global nodes numbering (internal and interface) */
3369     ierr = ISLocalToGlobalMappingApply(matis->mapping,pcbddc->local_primal_size,auxlocal_primal,auxglobal_primal);CHKERRQ(ierr);
3370     /* all_auxglobal_primal contains all primal nodes indices in global nodes numbering (internal and interface) */
3371     ierr = MPI_Gatherv(&auxglobal_primal[0],pcbddc->local_primal_size,MPIU_INT,&all_auxglobal_primal[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_INT,0,prec_comm);CHKERRQ(ierr);
3372 
3373     /* After this block all_auxglobal_primal should contains one copy of each primal node's indices in global nodes numbering */
3374     if(rank_prec_comm==0) {
3375       j=pcbddc->replicated_primal_size;
3376       ierr = PetscSortRemoveDupsMPIInt(&j,all_auxglobal_primal);CHKERRQ(ierr);
3377     } else {
3378       ierr = PetscMalloc(pcbddc->coarse_size*sizeof(PetscMPIInt),&all_auxglobal_primal);CHKERRQ(ierr);
3379     }
3380     /* We only need to broadcast the indices from 0 to pcbddc->coarse_size. Remaning elements of array all_aux_global_primal are garbage. */
3381     ierr = MPI_Bcast(all_auxglobal_primal,pcbddc->coarse_size,MPIU_INT,0,prec_comm);CHKERRQ(ierr);
3382 
3383     /* Now get global coarse numbering of local primal nodes */
3384     for(i=0;i<pcbddc->local_primal_size;i++) {
3385       k=0;
3386       while( all_auxglobal_primal[k] != auxglobal_primal[i] ) { k++;}
3387       pcbddc->local_primal_indices[i]=k;
3388     }
3389     if(dbg_flag) {
3390       ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3391       ierr = PetscViewerASCIIPrintf(viewer,"Size of coarse problem %d\n",pcbddc->coarse_size);CHKERRQ(ierr);
3392       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3393     }
3394     /* free allocated memory */
3395     ierr = PetscFree(auxlocal_primal);CHKERRQ(ierr);
3396     ierr = PetscFree(auxglobal_primal);CHKERRQ(ierr);
3397     ierr = PetscFree(all_auxglobal_primal);CHKERRQ(ierr);
3398   }
3399 
3400   switch(pcbddc->coarse_problem_type){
3401 
3402     case(MULTILEVEL_BDDC):   /* we define a coarse mesh where subdomains are elements */
3403     {
3404       /* we need additional variables */
3405       MetisInt   n_subdomains,n_parts,objval,ncon,faces_nvtxs;
3406       MetisInt   *metis_coarse_subdivision;
3407       MetisInt   options[METIS_NOPTIONS];
3408       PetscMPIInt size_coarse_comm,rank_coarse_comm;
3409       PetscMPIInt procs_jumps_coarse_comm;
3410       PetscMPIInt *coarse_subdivision;
3411       PetscMPIInt *total_count_recv;
3412       PetscMPIInt *total_ranks_recv;
3413       PetscMPIInt *displacements_recv;
3414       PetscMPIInt *my_faces_connectivity;
3415       PetscMPIInt *petsc_faces_adjncy;
3416       MetisInt    *faces_adjncy;
3417       MetisInt    *faces_xadj;
3418       PetscMPIInt *number_of_faces;
3419       PetscMPIInt *faces_displacements;
3420       PetscInt    *array_int;
3421       PetscMPIInt my_faces=0;
3422       PetscMPIInt total_faces=0;
3423       PetscInt    ranks_stretching_ratio;
3424 
3425       /* define some quantities */
3426       pcbddc->coarse_communications_type = SCATTERS_BDDC;
3427       coarse_mat_type = MATIS;
3428       coarse_pc_type  = PCBDDC;
3429       coarse_ksp_type  = KSPCHEBYSHEV;
3430 
3431       /* details of coarse decomposition */
3432       n_subdomains = pcbddc->active_procs;
3433       n_parts      = n_subdomains/pcbddc->coarsening_ratio;
3434       ranks_stretching_ratio = size_prec_comm/pcbddc->active_procs;
3435       procs_jumps_coarse_comm = pcbddc->coarsening_ratio*ranks_stretching_ratio;
3436 
3437       /*printf("Coarse algorithm details: \n");
3438       printf("n_subdomains %d, n_parts %d\nstretch %d,jumps %d,coarse_ratio %d\nlevel should be log_%d(%d)\n",n_subdomains,n_parts,ranks_stretching_ratio,procs_jumps_coarse_comm,pcbddc->coarsening_ratio,pcbddc->coarsening_ratio,(ranks_stretching_ratio/pcbddc->coarsening_ratio+1));*/
3439 
3440       /* build CSR graph of subdomains' connectivity through faces */
3441       ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&array_int);CHKERRQ(ierr);
3442       ierr = PetscMemzero(array_int,pcis->n*sizeof(PetscInt));CHKERRQ(ierr);
3443       for(i=1;i<pcis->n_neigh;i++){/* i=1 so I don't count myself -> faces nodes counts to 1 */
3444         for(j=0;j<pcis->n_shared[i];j++){
3445           array_int[ pcis->shared[i][j] ]+=1;
3446         }
3447       }
3448       for(i=1;i<pcis->n_neigh;i++){
3449         for(j=0;j<pcis->n_shared[i];j++){
3450           if(array_int[ pcis->shared[i][j] ] == 1 ){
3451             my_faces++;
3452             break;
3453           }
3454         }
3455       }
3456 
3457       ierr = MPI_Reduce(&my_faces,&total_faces,1,MPIU_INT,MPI_SUM,master_proc,prec_comm);CHKERRQ(ierr);
3458       ierr = PetscMalloc (my_faces*sizeof(PetscInt),&my_faces_connectivity);CHKERRQ(ierr);
3459       my_faces=0;
3460       for(i=1;i<pcis->n_neigh;i++){
3461         for(j=0;j<pcis->n_shared[i];j++){
3462           if(array_int[ pcis->shared[i][j] ] == 1 ){
3463             my_faces_connectivity[my_faces]=pcis->neigh[i];
3464             my_faces++;
3465             break;
3466           }
3467         }
3468       }
3469       if(rank_prec_comm == master_proc) {
3470         ierr = PetscMalloc (total_faces*sizeof(PetscMPIInt),&petsc_faces_adjncy);CHKERRQ(ierr);
3471         ierr = PetscMalloc (size_prec_comm*sizeof(PetscMPIInt),&number_of_faces);CHKERRQ(ierr);
3472         ierr = PetscMalloc (total_faces*sizeof(MetisInt),&faces_adjncy);CHKERRQ(ierr);
3473         ierr = PetscMalloc ((n_subdomains+1)*sizeof(MetisInt),&faces_xadj);CHKERRQ(ierr);
3474         ierr = PetscMalloc ((size_prec_comm+1)*sizeof(PetscMPIInt),&faces_displacements);CHKERRQ(ierr);
3475       }
3476       ierr = MPI_Gather(&my_faces,1,MPIU_INT,&number_of_faces[0],1,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3477       if(rank_prec_comm == master_proc) {
3478         faces_xadj[0]=0;
3479         faces_displacements[0]=0;
3480         j=0;
3481         for(i=1;i<size_prec_comm+1;i++) {
3482           faces_displacements[i]=faces_displacements[i-1]+number_of_faces[i-1];
3483           if(number_of_faces[i-1]) {
3484             j++;
3485             faces_xadj[j]=faces_xadj[j-1]+number_of_faces[i-1];
3486           }
3487         }
3488         /*printf("The J I count is %d and should be %d\n",j,n_subdomains);
3489         printf("Total faces seem %d and should be %d\n",faces_xadj[j],total_faces);*/
3490       }
3491       ierr = MPI_Gatherv(&my_faces_connectivity[0],my_faces,MPIU_INT,&petsc_faces_adjncy[0],number_of_faces,faces_displacements,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3492       ierr = PetscFree(my_faces_connectivity);CHKERRQ(ierr);
3493       ierr = PetscFree(array_int);CHKERRQ(ierr);
3494       if(rank_prec_comm == master_proc) {
3495         for(i=0;i<total_faces;i++) faces_adjncy[i]=(MetisInt)(petsc_faces_adjncy[i]/ranks_stretching_ratio); /* cast to MetisInt */
3496         /*printf("This is the face connectivity (actual ranks)\n");
3497         for(i=0;i<n_subdomains;i++){
3498           printf("proc %d is connected with \n",i);
3499           for(j=faces_xadj[i];j<faces_xadj[i+1];j++)
3500             printf("%d ",faces_adjncy[j]);
3501           printf("\n");
3502         }*/
3503         ierr = PetscFree(faces_displacements);CHKERRQ(ierr);
3504         ierr = PetscFree(number_of_faces);CHKERRQ(ierr);
3505         ierr = PetscFree(petsc_faces_adjncy);CHKERRQ(ierr);
3506       }
3507 
3508       if( rank_prec_comm == master_proc ) {
3509 
3510         PetscInt heuristic_for_metis=3;
3511 
3512         ncon=1;
3513         faces_nvtxs=n_subdomains;
3514         /* partition graoh induced by face connectivity */
3515         ierr = PetscMalloc (n_subdomains*sizeof(MetisInt),&metis_coarse_subdivision);CHKERRQ(ierr);
3516         ierr = METIS_SetDefaultOptions(options);
3517         /* we need a contiguous partition of the coarse mesh */
3518         options[METIS_OPTION_CONTIG]=1;
3519         options[METIS_OPTION_DBGLVL]=1;
3520         options[METIS_OPTION_NITER]=30;
3521         if(n_subdomains>n_parts*heuristic_for_metis) {
3522           options[METIS_OPTION_IPTYPE]=METIS_IPTYPE_EDGE;
3523           options[METIS_OPTION_OBJTYPE]=METIS_OBJTYPE_CUT;
3524           ierr = METIS_PartGraphKway(&faces_nvtxs,&ncon,faces_xadj,faces_adjncy,NULL,NULL,NULL,&n_parts,NULL,NULL,options,&objval,metis_coarse_subdivision);
3525         } else {
3526           ierr = METIS_PartGraphRecursive(&faces_nvtxs,&ncon,faces_xadj,faces_adjncy,NULL,NULL,NULL,&n_parts,NULL,NULL,options,&objval,metis_coarse_subdivision);
3527         }
3528         if(ierr != METIS_OK) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in METIS_PartGraphKway (metis error code %D) called from PCBDDCSetupCoarseEnvironment\n",ierr);
3529         ierr = PetscFree(faces_xadj);CHKERRQ(ierr);
3530         ierr = PetscFree(faces_adjncy);CHKERRQ(ierr);
3531         coarse_subdivision = (PetscMPIInt*)calloc(size_prec_comm,sizeof(PetscMPIInt)); /* calloc for contiguous memory since we need to scatter these values later */
3532         /* copy/cast values avoiding possible type conflicts between PETSc, MPI and METIS */
3533         for(i=0;i<size_prec_comm;i++) coarse_subdivision[i]=MPI_PROC_NULL;
3534         for(i=0;i<n_subdomains;i++)   coarse_subdivision[ranks_stretching_ratio*i]=(PetscInt)(metis_coarse_subdivision[i]);
3535         ierr = PetscFree(metis_coarse_subdivision);CHKERRQ(ierr);
3536       }
3537 
3538       /* Create new communicator for coarse problem splitting the old one */
3539       if( !(rank_prec_comm%procs_jumps_coarse_comm) && rank_prec_comm < procs_jumps_coarse_comm*n_parts ){
3540         coarse_color=0;              /* for communicator splitting */
3541         active_rank=rank_prec_comm;  /* for insertion of matrix values */
3542       }
3543       /* procs with coarse_color = MPI_UNDEFINED will have coarse_comm = MPI_COMM_NULL (from mpi standards)
3544          key = rank_prec_comm -> keep same ordering of ranks from the old to the new communicator */
3545       ierr = MPI_Comm_split(prec_comm,coarse_color,rank_prec_comm,&coarse_comm);CHKERRQ(ierr);
3546 
3547       if( coarse_color == 0 ) {
3548         ierr = MPI_Comm_size(coarse_comm,&size_coarse_comm);CHKERRQ(ierr);
3549         ierr = MPI_Comm_rank(coarse_comm,&rank_coarse_comm);CHKERRQ(ierr);
3550         /*printf("Details of coarse comm\n");
3551         printf("size = %d, myrank = %d\n",size_coarse_comm,rank_coarse_comm);
3552         printf("jumps = %d, coarse_color = %d, n_parts = %d\n",procs_jumps_coarse_comm,coarse_color,n_parts);*/
3553       } else {
3554         rank_coarse_comm = MPI_PROC_NULL;
3555       }
3556 
3557       /* master proc take care of arranging and distributing coarse informations */
3558       if(rank_coarse_comm == master_proc) {
3559         ierr = PetscMalloc (size_coarse_comm*sizeof(PetscMPIInt),&displacements_recv);CHKERRQ(ierr);
3560         /*ierr = PetscMalloc (size_coarse_comm*sizeof(PetscMPIInt),&total_count_recv);CHKERRQ(ierr);
3561           ierr = PetscMalloc (n_subdomains*sizeof(PetscMPIInt),&total_ranks_recv);CHKERRQ(ierr);*/
3562         total_count_recv = (PetscMPIInt*)calloc(size_prec_comm,sizeof(PetscMPIInt));
3563         total_ranks_recv = (PetscMPIInt*)calloc(n_subdomains,sizeof(PetscMPIInt));
3564         /* some initializations */
3565         displacements_recv[0]=0;
3566         /* PetscMemzero(total_count_recv,size_coarse_comm*sizeof(PetscMPIInt)); not needed -> calloc initializes to zero */
3567         /* count from how many processes the j-th process of the coarse decomposition will receive data */
3568         for(j=0;j<size_coarse_comm;j++)
3569           for(i=0;i<size_prec_comm;i++)
3570             if(coarse_subdivision[i]==j)
3571               total_count_recv[j]++;
3572         /* displacements needed for scatterv of total_ranks_recv */
3573         for(i=1;i<size_coarse_comm;i++) displacements_recv[i]=displacements_recv[i-1]+total_count_recv[i-1];
3574         /* Now fill properly total_ranks_recv -> each coarse process will receive the ranks (in prec_comm communicator) of its friend (sending) processes */
3575         ierr = PetscMemzero(total_count_recv,size_coarse_comm*sizeof(PetscMPIInt));CHKERRQ(ierr);
3576         for(j=0;j<size_coarse_comm;j++) {
3577           for(i=0;i<size_prec_comm;i++) {
3578             if(coarse_subdivision[i]==j) {
3579               total_ranks_recv[displacements_recv[j]+total_count_recv[j]]=i;
3580               total_count_recv[j]+=1;
3581             }
3582           }
3583         }
3584         /*for(j=0;j<size_coarse_comm;j++) {
3585           printf("process %d in new rank will receive from %d processes (original ranks follows)\n",j,total_count_recv[j]);
3586           for(i=0;i<total_count_recv[j];i++) {
3587             printf("%d ",total_ranks_recv[displacements_recv[j]+i]);
3588           }
3589           printf("\n");
3590         }*/
3591 
3592         /* identify new decomposition in terms of ranks in the old communicator */
3593         for(i=0;i<n_subdomains;i++) coarse_subdivision[ranks_stretching_ratio*i]=coarse_subdivision[ranks_stretching_ratio*i]*procs_jumps_coarse_comm;
3594         /*printf("coarse_subdivision in old end new ranks\n");
3595         for(i=0;i<size_prec_comm;i++)
3596           if(coarse_subdivision[i]!=MPI_PROC_NULL) {
3597             printf("%d=(%d %d), ",i,coarse_subdivision[i],coarse_subdivision[i]/procs_jumps_coarse_comm);
3598           } else {
3599             printf("%d=(%d %d), ",i,coarse_subdivision[i],coarse_subdivision[i]);
3600           }
3601         printf("\n");*/
3602       }
3603 
3604       /* Scatter new decomposition for send details */
3605       ierr = MPI_Scatter(&coarse_subdivision[0],1,MPIU_INT,&rank_coarse_proc_send_to,1,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3606       /* Scatter receiving details to members of coarse decomposition */
3607       if( coarse_color == 0) {
3608         ierr = MPI_Scatter(&total_count_recv[0],1,MPIU_INT,&count_recv,1,MPIU_INT,master_proc,coarse_comm);CHKERRQ(ierr);
3609         ierr = PetscMalloc (count_recv*sizeof(PetscMPIInt),&ranks_recv);CHKERRQ(ierr);
3610         ierr = MPI_Scatterv(&total_ranks_recv[0],total_count_recv,displacements_recv,MPIU_INT,&ranks_recv[0],count_recv,MPIU_INT,master_proc,coarse_comm);CHKERRQ(ierr);
3611       }
3612 
3613       /*printf("I will send my matrix data to proc  %d\n",rank_coarse_proc_send_to);
3614       if(coarse_color == 0) {
3615         printf("I will receive some matrix data from %d processes (ranks follows)\n",count_recv);
3616         for(i=0;i<count_recv;i++)
3617           printf("%d ",ranks_recv[i]);
3618         printf("\n");
3619       }*/
3620 
3621       if(rank_prec_comm == master_proc) {
3622         /*ierr = PetscFree(coarse_subdivision);CHKERRQ(ierr);
3623         ierr = PetscFree(total_count_recv);CHKERRQ(ierr);
3624         ierr = PetscFree(total_ranks_recv);CHKERRQ(ierr);*/
3625         free(coarse_subdivision);
3626         free(total_count_recv);
3627         free(total_ranks_recv);
3628         ierr = PetscFree(displacements_recv);CHKERRQ(ierr);
3629       }
3630       break;
3631     }
3632 
3633     case(REPLICATED_BDDC):
3634 
3635       pcbddc->coarse_communications_type = GATHERS_BDDC;
3636       coarse_mat_type = MATSEQAIJ;
3637       coarse_pc_type  = PCLU;
3638       coarse_ksp_type  = KSPPREONLY;
3639       coarse_comm = PETSC_COMM_SELF;
3640       active_rank = rank_prec_comm;
3641       break;
3642 
3643     case(PARALLEL_BDDC):
3644 
3645       pcbddc->coarse_communications_type = SCATTERS_BDDC;
3646       coarse_mat_type = MATMPIAIJ;
3647       coarse_pc_type  = PCREDUNDANT;
3648       coarse_ksp_type  = KSPPREONLY;
3649       coarse_comm = prec_comm;
3650       active_rank = rank_prec_comm;
3651       break;
3652 
3653     case(SEQUENTIAL_BDDC):
3654       pcbddc->coarse_communications_type = GATHERS_BDDC;
3655       coarse_mat_type = MATSEQAIJ;
3656       coarse_pc_type = PCLU;
3657       coarse_ksp_type  = KSPPREONLY;
3658       coarse_comm = PETSC_COMM_SELF;
3659       active_rank = master_proc;
3660       break;
3661   }
3662 
3663   switch(pcbddc->coarse_communications_type){
3664 
3665     case(SCATTERS_BDDC):
3666       {
3667         if(pcbddc->coarse_problem_type==MULTILEVEL_BDDC) {
3668 
3669           PetscMPIInt send_size;
3670           PetscInt    *aux_ins_indices;
3671           PetscInt    ii,jj;
3672           MPI_Request *requests;
3673 
3674           /* allocate auxiliary space */
3675           ierr = PetscMalloc (pcbddc->replicated_primal_size*sizeof(PetscMPIInt),&pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
3676           ierr = MPI_Allgatherv(&pcbddc->local_primal_indices[0],pcbddc->local_primal_size,MPIU_INT,&pcbddc->replicated_local_primal_indices[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_INT,prec_comm);CHKERRQ(ierr);
3677           ierr = PetscMalloc ( pcbddc->coarse_size*sizeof(PetscInt),&aux_ins_indices);CHKERRQ(ierr);
3678           ierr = PetscMemzero(aux_ins_indices,pcbddc->coarse_size*sizeof(PetscInt));CHKERRQ(ierr);
3679           /* allocate stuffs for message massing */
3680           ierr = PetscMalloc ( (count_recv+1)*sizeof(MPI_Request),&requests);CHKERRQ(ierr);
3681           for(i=0;i<count_recv+1;i++) requests[i]=MPI_REQUEST_NULL;
3682           ierr = PetscMalloc ( count_recv*sizeof(PetscMPIInt),&localsizes2);CHKERRQ(ierr);
3683           ierr = PetscMalloc ( count_recv*sizeof(PetscMPIInt),&localdispl2);CHKERRQ(ierr);
3684           /* fill up quantities */
3685           j=0;
3686           for(i=0;i<count_recv;i++){
3687             ii = ranks_recv[i];
3688             localsizes2[i]=pcbddc->local_primal_sizes[ii]*pcbddc->local_primal_sizes[ii];
3689             localdispl2[i]=j;
3690             j+=localsizes2[i];
3691             jj = pcbddc->local_primal_displacements[ii];
3692             for(k=0;k<pcbddc->local_primal_sizes[ii];k++) aux_ins_indices[pcbddc->replicated_local_primal_indices[jj+k]]+=1;  /* it counts the coarse subdomains sharing the coarse node */
3693           }
3694           /*printf("aux_ins_indices 1\n");
3695           for(i=0;i<pcbddc->coarse_size;i++)
3696             printf("%d ",aux_ins_indices[i]);
3697           printf("\n");*/
3698           /* temp_coarse_mat_vals used to store temporarly received matrix values */
3699           ierr = PetscMalloc ( j*sizeof(PetscScalar),&temp_coarse_mat_vals);CHKERRQ(ierr);
3700           /* evaluate how many values I will insert in coarse mat */
3701           ins_local_primal_size=0;
3702           for(i=0;i<pcbddc->coarse_size;i++)
3703             if(aux_ins_indices[i])
3704               ins_local_primal_size++;
3705           /* evaluate indices I will insert in coarse mat */
3706           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscInt),&ins_local_primal_indices);CHKERRQ(ierr);
3707           j=0;
3708           for(i=0;i<pcbddc->coarse_size;i++)
3709             if(aux_ins_indices[i])
3710               ins_local_primal_indices[j++]=i;
3711           /* use aux_ins_indices to realize a global to local mapping */
3712           j=0;
3713           for(i=0;i<pcbddc->coarse_size;i++){
3714             if(aux_ins_indices[i]==0){
3715               aux_ins_indices[i]=-1;
3716             } else {
3717               aux_ins_indices[i]=j;
3718               j++;
3719             }
3720           }
3721 
3722           /*printf("New details localsizes2 localdispl2\n");
3723           for(i=0;i<count_recv;i++)
3724             printf("(%d %d) ",localsizes2[i],localdispl2[i]);
3725           printf("\n");
3726           printf("aux_ins_indices 2\n");
3727           for(i=0;i<pcbddc->coarse_size;i++)
3728             printf("%d ",aux_ins_indices[i]);
3729           printf("\n");
3730           printf("ins_local_primal_indices\n");
3731           for(i=0;i<ins_local_primal_size;i++)
3732             printf("%d ",ins_local_primal_indices[i]);
3733           printf("\n");
3734           printf("coarse_submat_vals\n");
3735           for(i=0;i<pcbddc->local_primal_size;i++)
3736             for(j=0;j<pcbddc->local_primal_size;j++)
3737               printf("(%lf %d %d)\n",coarse_submat_vals[j*pcbddc->local_primal_size+i],pcbddc->local_primal_indices[i],pcbddc->local_primal_indices[j]);
3738           printf("\n");*/
3739 
3740           /* processes partecipating in coarse problem receive matrix data from their friends */
3741           for(i=0;i<count_recv;i++) ierr = MPI_Irecv(&temp_coarse_mat_vals[localdispl2[i]],localsizes2[i],MPIU_SCALAR,ranks_recv[i],666,prec_comm,&requests[i]);CHKERRQ(ierr);
3742           if(rank_coarse_proc_send_to != MPI_PROC_NULL ) {
3743             send_size=pcbddc->local_primal_size*pcbddc->local_primal_size;
3744             ierr = MPI_Isend(&coarse_submat_vals[0],send_size,MPIU_SCALAR,rank_coarse_proc_send_to,666,prec_comm,&requests[count_recv]);CHKERRQ(ierr);
3745           }
3746           ierr = MPI_Waitall(count_recv+1,requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3747 
3748           /*if(coarse_color == 0) {
3749             printf("temp_coarse_mat_vals\n");
3750             for(k=0;k<count_recv;k++){
3751               printf("---- %d ----\n",ranks_recv[k]);
3752               for(i=0;i<pcbddc->local_primal_sizes[ranks_recv[k]];i++)
3753                 for(j=0;j<pcbddc->local_primal_sizes[ranks_recv[k]];j++)
3754                   printf("(%lf %d %d)\n",temp_coarse_mat_vals[localdispl2[k]+j*pcbddc->local_primal_sizes[ranks_recv[k]]+i],pcbddc->replicated_local_primal_indices[pcbddc->local_primal_displacements[ranks_recv[k]]+i],pcbddc->replicated_local_primal_indices[pcbddc->local_primal_displacements[ranks_recv[k]]+j]);
3755               printf("\n");
3756             }
3757           }*/
3758           /* calculate data to insert in coarse mat */
3759           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3760           PetscMemzero(ins_coarse_mat_vals,ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar));
3761 
3762           PetscMPIInt rr,kk,lps,lpd;
3763           PetscInt row_ind,col_ind;
3764           for(k=0;k<count_recv;k++){
3765             rr = ranks_recv[k];
3766             kk = localdispl2[k];
3767             lps = pcbddc->local_primal_sizes[rr];
3768             lpd = pcbddc->local_primal_displacements[rr];
3769             /*printf("Inserting the following indices (received from %d)\n",rr);*/
3770             for(j=0;j<lps;j++){
3771               col_ind=aux_ins_indices[pcbddc->replicated_local_primal_indices[lpd+j]];
3772               for(i=0;i<lps;i++){
3773                 row_ind=aux_ins_indices[pcbddc->replicated_local_primal_indices[lpd+i]];
3774                 /*printf("%d %d\n",row_ind,col_ind);*/
3775                 ins_coarse_mat_vals[col_ind*ins_local_primal_size+row_ind]+=temp_coarse_mat_vals[kk+j*lps+i];
3776               }
3777             }
3778           }
3779           ierr = PetscFree(requests);CHKERRQ(ierr);
3780           ierr = PetscFree(aux_ins_indices);CHKERRQ(ierr);
3781           ierr = PetscFree(temp_coarse_mat_vals);CHKERRQ(ierr);
3782           if(coarse_color == 0) { ierr = PetscFree(ranks_recv);CHKERRQ(ierr); }
3783 
3784           /* create local to global mapping needed by coarse MATIS */
3785           {
3786             IS coarse_IS;
3787             if(coarse_comm != MPI_COMM_NULL ) ierr = MPI_Comm_free(&coarse_comm);CHKERRQ(ierr);
3788             coarse_comm = prec_comm;
3789             active_rank=rank_prec_comm;
3790             ierr = ISCreateGeneral(coarse_comm,ins_local_primal_size,ins_local_primal_indices,PETSC_COPY_VALUES,&coarse_IS);CHKERRQ(ierr);
3791             ierr = ISLocalToGlobalMappingCreateIS(coarse_IS,&coarse_ISLG);CHKERRQ(ierr);
3792             ierr = ISDestroy(&coarse_IS);CHKERRQ(ierr);
3793           }
3794         }
3795         if(pcbddc->coarse_problem_type==PARALLEL_BDDC) {
3796           /* arrays for values insertion */
3797           ins_local_primal_size = pcbddc->local_primal_size;
3798           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscMPIInt),&ins_local_primal_indices);CHKERRQ(ierr);
3799           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3800           for(j=0;j<ins_local_primal_size;j++){
3801             ins_local_primal_indices[j]=pcbddc->local_primal_indices[j];
3802             for(i=0;i<ins_local_primal_size;i++) ins_coarse_mat_vals[j*ins_local_primal_size+i]=coarse_submat_vals[j*ins_local_primal_size+i];
3803           }
3804         }
3805         break;
3806 
3807     }
3808 
3809     case(GATHERS_BDDC):
3810       {
3811 
3812         PetscMPIInt mysize,mysize2;
3813 
3814         if(rank_prec_comm==active_rank) {
3815           ierr = PetscMalloc ( pcbddc->replicated_primal_size*sizeof(PetscMPIInt),&pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
3816           pcbddc->replicated_local_primal_values = (PetscScalar*)calloc(pcbddc->replicated_primal_size,sizeof(PetscScalar));
3817           ierr = PetscMalloc ( size_prec_comm*sizeof(PetscMPIInt),&localsizes2);CHKERRQ(ierr);
3818           ierr = PetscMalloc ( size_prec_comm*sizeof(PetscMPIInt),&localdispl2);CHKERRQ(ierr);
3819           /* arrays for values insertion */
3820           ins_local_primal_size = pcbddc->coarse_size;
3821           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscMPIInt),&ins_local_primal_indices);CHKERRQ(ierr);
3822           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3823           for(i=0;i<size_prec_comm;i++) localsizes2[i]=pcbddc->local_primal_sizes[i]*pcbddc->local_primal_sizes[i];
3824           localdispl2[0]=0;
3825           for(i=1;i<size_prec_comm;i++) localdispl2[i]=localsizes2[i-1]+localdispl2[i-1];
3826           j=0;
3827           for(i=0;i<size_prec_comm;i++) j+=localsizes2[i];
3828           ierr = PetscMalloc ( j*sizeof(PetscScalar),&temp_coarse_mat_vals);CHKERRQ(ierr);
3829         }
3830 
3831         mysize=pcbddc->local_primal_size;
3832         mysize2=pcbddc->local_primal_size*pcbddc->local_primal_size;
3833         if(pcbddc->coarse_problem_type == SEQUENTIAL_BDDC){
3834           ierr = MPI_Gatherv(&pcbddc->local_primal_indices[0],mysize,MPIU_INT,&pcbddc->replicated_local_primal_indices[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3835           ierr = MPI_Gatherv(&coarse_submat_vals[0],mysize2,MPIU_SCALAR,&temp_coarse_mat_vals[0],localsizes2,localdispl2,MPIU_SCALAR,master_proc,prec_comm);CHKERRQ(ierr);
3836         } else {
3837           ierr = MPI_Allgatherv(&pcbddc->local_primal_indices[0],mysize,MPIU_INT,&pcbddc->replicated_local_primal_indices[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_INT,prec_comm);CHKERRQ(ierr);
3838           ierr = MPI_Allgatherv(&coarse_submat_vals[0],mysize2,MPIU_SCALAR,&temp_coarse_mat_vals[0],localsizes2,localdispl2,MPIU_SCALAR,prec_comm);CHKERRQ(ierr);
3839         }
3840 
3841   /* free data structures no longer needed and allocate some space which will be needed in BDDC application */
3842         if(rank_prec_comm==active_rank) {
3843           PetscInt offset,offset2,row_ind,col_ind;
3844           for(j=0;j<ins_local_primal_size;j++){
3845             ins_local_primal_indices[j]=j;
3846             for(i=0;i<ins_local_primal_size;i++) ins_coarse_mat_vals[j*ins_local_primal_size+i]=0.0;
3847           }
3848           for(k=0;k<size_prec_comm;k++){
3849             offset=pcbddc->local_primal_displacements[k];
3850             offset2=localdispl2[k];
3851             for(j=0;j<pcbddc->local_primal_sizes[k];j++){
3852               col_ind=pcbddc->replicated_local_primal_indices[offset+j];
3853               for(i=0;i<pcbddc->local_primal_sizes[k];i++){
3854                 row_ind=pcbddc->replicated_local_primal_indices[offset+i];
3855                 ins_coarse_mat_vals[col_ind*pcbddc->coarse_size+row_ind]+=temp_coarse_mat_vals[offset2+j*pcbddc->local_primal_sizes[k]+i];
3856               }
3857             }
3858           }
3859         }
3860         break;
3861       }/* switch on coarse problem and communications associated with finished */
3862   }
3863 
3864   /* Now create and fill up coarse matrix */
3865   if( rank_prec_comm == active_rank ) {
3866     if(pcbddc->coarse_problem_type != MULTILEVEL_BDDC) {
3867       ierr = MatCreate(coarse_comm,&pcbddc->coarse_mat);CHKERRQ(ierr);
3868       ierr = MatSetSizes(pcbddc->coarse_mat,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size);CHKERRQ(ierr);
3869       ierr = MatSetType(pcbddc->coarse_mat,coarse_mat_type);CHKERRQ(ierr);
3870       ierr = MatSetUp(pcbddc->coarse_mat);CHKERRQ(ierr);
3871       ierr = MatSetOption(pcbddc->coarse_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr); /* local values stored in column major */
3872       ierr = MatSetOption(pcbddc->coarse_mat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3873     } else {
3874       Mat matis_coarse_local_mat;
3875       /* remind bs */
3876       ierr = MatCreateIS(coarse_comm,bs,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_ISLG,&pcbddc->coarse_mat);CHKERRQ(ierr);
3877       ierr = MatSetUp(pcbddc->coarse_mat);CHKERRQ(ierr);
3878       ierr = MatISGetLocalMat(pcbddc->coarse_mat,&matis_coarse_local_mat);CHKERRQ(ierr);
3879       ierr = MatSetUp(matis_coarse_local_mat);CHKERRQ(ierr);
3880       ierr = MatSetOption(matis_coarse_local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr); /* local values stored in column major */
3881       ierr = MatSetOption(matis_coarse_local_mat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3882     }
3883     ierr = MatSetOption(pcbddc->coarse_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
3884     ierr = MatSetValues(pcbddc->coarse_mat,ins_local_primal_size,ins_local_primal_indices,ins_local_primal_size,ins_local_primal_indices,ins_coarse_mat_vals,ADD_VALUES);CHKERRQ(ierr);
3885     ierr = MatAssemblyBegin(pcbddc->coarse_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3886     ierr = MatAssemblyEnd(pcbddc->coarse_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3887 
3888     /*  PetscViewer view_out;
3889       ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,"coarsematfull.m",&view_out);CHKERRQ(ierr);
3890       ierr = PetscViewerSetFormat(view_out,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3891       ierr = MatView(pcbddc->coarse_mat,view_out);CHKERRQ(ierr);
3892       ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);*/
3893 
3894     ierr = MatGetVecs(pcbddc->coarse_mat,&pcbddc->coarse_vec,&pcbddc->coarse_rhs);CHKERRQ(ierr);
3895     /* Preconditioner for coarse problem */
3896     ierr = KSPCreate(coarse_comm,&pcbddc->coarse_ksp);CHKERRQ(ierr);
3897     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3898     ierr = KSPSetOperators(pcbddc->coarse_ksp,pcbddc->coarse_mat,pcbddc->coarse_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
3899     ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,max_it_coarse_ksp);CHKERRQ(ierr);
3900     ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3901     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3902     ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3903     /* Allow user's customization */
3904     ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,"coarse_");CHKERRQ(ierr);
3905     ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3906     /* Set Up PC for coarse problem BDDC */
3907     if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC) {
3908       if(dbg_flag) {
3909         ierr = PetscViewerASCIIPrintf(viewer,"----------------Setting up a new level---------------\n");CHKERRQ(ierr);
3910         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3911       }
3912       ierr = PCBDDCSetCoarseProblemType(pc_temp,MULTILEVEL_BDDC);CHKERRQ(ierr);
3913     }
3914     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3915     if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC) {
3916       if(dbg_flag) {
3917         ierr = PetscViewerASCIIPrintf(viewer,"----------------New level set------------------------\n");CHKERRQ(ierr);
3918         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3919       }
3920     }
3921   }
3922   if(pcbddc->coarse_communications_type == SCATTERS_BDDC) {
3923      IS local_IS,global_IS;
3924      ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size,0,1,&local_IS);CHKERRQ(ierr);
3925      ierr = ISCreateGeneral(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_indices,PETSC_COPY_VALUES,&global_IS);CHKERRQ(ierr);
3926      ierr = VecScatterCreate(pcbddc->vec1_P,local_IS,pcbddc->coarse_vec,global_IS,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3927      ierr = ISDestroy(&local_IS);CHKERRQ(ierr);
3928      ierr = ISDestroy(&global_IS);CHKERRQ(ierr);
3929   }
3930 
3931 
3932   /* Evaluate condition number of coarse problem for cheby (and verbose output if requested) */
3933   if( pcbddc->coarse_problem_type == MULTILEVEL_BDDC && rank_prec_comm == active_rank ) {
3934     PetscScalar m_one=-1.0;
3935     PetscReal   infty_error,lambda_min,lambda_max,kappa_2;
3936     const KSPType check_ksp_type=KSPGMRES;
3937 
3938     /* change coarse ksp object to an iterative method suitable for extreme eigenvalues' estimation */
3939     ierr = KSPSetType(pcbddc->coarse_ksp,check_ksp_type);CHKERRQ(ierr);
3940     ierr = KSPSetComputeSingularValues(pcbddc->coarse_ksp,PETSC_TRUE);CHKERRQ(ierr);
3941     ierr = KSPSetTolerances(pcbddc->coarse_ksp,1.e-8,1.e-8,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3942     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3943     ierr = VecSetRandom(pcbddc->coarse_rhs,PETSC_NULL);CHKERRQ(ierr);
3944     ierr = MatMult(pcbddc->coarse_mat,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
3945     ierr = MatMult(pcbddc->coarse_mat,pcbddc->coarse_vec,pcbddc->coarse_rhs);CHKERRQ(ierr);
3946     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_rhs);CHKERRQ(ierr);
3947     ierr = KSPComputeExtremeSingularValues(pcbddc->coarse_ksp,&lambda_max,&lambda_min);CHKERRQ(ierr);
3948     if(dbg_flag) {
3949       kappa_2=lambda_max/lambda_min;
3950       ierr = KSPGetIterationNumber(pcbddc->coarse_ksp,&k);CHKERRQ(ierr);
3951       ierr = VecAXPY(pcbddc->coarse_rhs,m_one,pcbddc->coarse_vec);CHKERRQ(ierr);
3952       ierr = VecNorm(pcbddc->coarse_rhs,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3953       ierr = PetscViewerASCIIPrintf(viewer,"Coarse problem condition number estimated with %d iterations of %s is: % 1.14e\n",k,check_ksp_type,kappa_2);CHKERRQ(ierr);
3954       ierr = PetscViewerASCIIPrintf(viewer,"Coarse problem eigenvalues: % 1.14e %1.14e\n",lambda_min,lambda_max);CHKERRQ(ierr);
3955       ierr = PetscViewerASCIIPrintf(viewer,"Coarse problem infty_error: %1.14e\n",infty_error);CHKERRQ(ierr);
3956     }
3957     /* restore coarse ksp to default values */
3958     ierr = KSPSetComputeSingularValues(pcbddc->coarse_ksp,PETSC_FALSE);CHKERRQ(ierr);
3959     ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3960     ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3961     ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,max_it_coarse_ksp);CHKERRQ(ierr);
3962     ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3963     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3964   }
3965 
3966   /* free data structures no longer needed */
3967   if(coarse_ISLG)                { ierr = ISLocalToGlobalMappingDestroy(&coarse_ISLG);CHKERRQ(ierr); }
3968   if(ins_local_primal_indices)   { ierr = PetscFree(ins_local_primal_indices);CHKERRQ(ierr);  }
3969   if(ins_coarse_mat_vals)        { ierr = PetscFree(ins_coarse_mat_vals);CHKERRQ(ierr);}
3970   if(localsizes2)                { ierr = PetscFree(localsizes2);CHKERRQ(ierr);}
3971   if(localdispl2)                { ierr = PetscFree(localdispl2);CHKERRQ(ierr);}
3972   if(temp_coarse_mat_vals)       { ierr = PetscFree(temp_coarse_mat_vals);CHKERRQ(ierr);}
3973 
3974   PetscFunctionReturn(0);
3975 }
3976 
3977 #undef __FUNCT__
3978 #define __FUNCT__ "PCBDDCManageLocalBoundaries"
3979 static PetscErrorCode PCBDDCManageLocalBoundaries(PC pc)
3980 {
3981 
3982   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
3983   PC_IS         *pcis = (PC_IS*)pc->data;
3984   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
3985   PCBDDCGraph mat_graph=pcbddc->mat_graph;
3986   PetscInt    *queue_in_global_numbering,*is_indices,*auxis;
3987   PetscInt    bs,ierr,i,j,s,k,iindex,neumann_bsize,dirichlet_bsize;
3988   PetscInt    total_counts,nodes_touched,where_values=1,vertex_size;
3989   PetscMPIInt adapt_interface=0,adapt_interface_reduced=0,NEUMANNCNT=0;
3990   PetscBool   same_set;
3991   MPI_Comm    interface_comm=((PetscObject)pc)->comm;
3992   PetscBool   use_faces=PETSC_FALSE,use_edges=PETSC_FALSE;
3993   const PetscInt *neumann_nodes;
3994   const PetscInt *dirichlet_nodes;
3995   IS          used_IS,*custom_ISForDofs;
3996   PetscScalar *array;
3997   PetscScalar *array2;
3998   PetscViewer viewer=pcbddc->dbg_viewer;
3999 
4000   PetscFunctionBegin;
4001   /* Setup local adjacency graph */
4002   mat_graph->nvtxs=pcis->n;
4003   if(!mat_graph->xadj) { NEUMANNCNT = 1; }
4004   ierr = PCBDDCSetupLocalAdjacencyGraph(pc);CHKERRQ(ierr);
4005   i = mat_graph->nvtxs;
4006   ierr = PetscMalloc4(i,PetscInt,&mat_graph->where,i,PetscInt,&mat_graph->count,i+1,PetscInt,&mat_graph->cptr,i,PetscInt,&mat_graph->queue);CHKERRQ(ierr);
4007   ierr = PetscMalloc2(i,PetscInt,&mat_graph->which_dof,i,PetscBool,&mat_graph->touched);CHKERRQ(ierr);
4008   ierr = PetscMalloc(i*sizeof(PetscInt),&queue_in_global_numbering);CHKERRQ(ierr);
4009   ierr = PetscMemzero(mat_graph->where,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4010   ierr = PetscMemzero(mat_graph->count,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4011   ierr = PetscMemzero(mat_graph->which_dof,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4012   ierr = PetscMemzero(mat_graph->queue,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4013   ierr = PetscMemzero(mat_graph->cptr,(mat_graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
4014 
4015   /* Setting dofs splitting in mat_graph->which_dof
4016      Get information about dofs' splitting if provided by the user
4017      Otherwise it assumes a constant block size */
4018   vertex_size=0;
4019   if(!pcbddc->n_ISForDofs) {
4020     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
4021     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
4022     for(i=0;i<bs;i++) {
4023       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
4024     }
4025     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
4026     vertex_size=1;
4027     /* remove my references to IS objects */
4028     for(i=0;i<bs;i++) {
4029       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
4030     }
4031     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
4032   }
4033   for(i=0;i<pcbddc->n_ISForDofs;i++) {
4034     ierr = ISGetSize(pcbddc->ISForDofs[i],&k);CHKERRQ(ierr);
4035     ierr = ISGetIndices(pcbddc->ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
4036     for(j=0;j<k;j++) {
4037       mat_graph->which_dof[is_indices[j]]=i;
4038     }
4039     ierr = ISRestoreIndices(pcbddc->ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
4040   }
4041   /* use mat block size as vertex size if it has not yet set */
4042   if(!vertex_size) {
4043     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
4044   }
4045 
4046   /* count number of neigh per node */
4047   total_counts=0;
4048   for(i=1;i<pcis->n_neigh;i++){
4049     s=pcis->n_shared[i];
4050     total_counts+=s;
4051     for(j=0;j<s;j++){
4052       mat_graph->count[pcis->shared[i][j]] += 1;
4053     }
4054   }
4055   /* Take into account Neumann data -> it increments number of sharing subdomains for nodes lying on the interface */
4056   ierr = PCBDDCGetNeumannBoundaries(pc,&used_IS);CHKERRQ(ierr);
4057   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
4058   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4059   if(used_IS) {
4060     ierr = ISGetSize(used_IS,&neumann_bsize);CHKERRQ(ierr);
4061     ierr = ISGetIndices(used_IS,&neumann_nodes);CHKERRQ(ierr);
4062     for(i=0;i<neumann_bsize;i++){
4063       iindex = neumann_nodes[i];
4064       if(mat_graph->count[iindex] > NEUMANNCNT && array[iindex]==0.0){
4065         mat_graph->count[iindex]+=1;
4066         total_counts++;
4067         array[iindex]=array[iindex]+1.0;
4068       } else if(array[iindex]>0.0) {
4069         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_USER,"Error for neumann nodes provided to BDDC! They must be uniquely listed! Found duplicate node %d\n",iindex);
4070       }
4071     }
4072   }
4073   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4074   /* allocate space for storing the set of neighbours for each node */
4075   ierr = PetscMalloc(mat_graph->nvtxs*sizeof(PetscInt*),&mat_graph->neighbours_set);CHKERRQ(ierr);
4076   if(mat_graph->nvtxs) { ierr = PetscMalloc(total_counts*sizeof(PetscInt),&mat_graph->neighbours_set[0]);CHKERRQ(ierr); }
4077   for(i=1;i<mat_graph->nvtxs;i++) mat_graph->neighbours_set[i]=mat_graph->neighbours_set[i-1]+mat_graph->count[i-1];
4078   ierr = PetscMemzero(mat_graph->count,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4079   for(i=1;i<pcis->n_neigh;i++){
4080     s=pcis->n_shared[i];
4081     for(j=0;j<s;j++) {
4082       k=pcis->shared[i][j];
4083       mat_graph->neighbours_set[k][mat_graph->count[k]] = pcis->neigh[i];
4084       mat_graph->count[k]+=1;
4085     }
4086   }
4087   /* Check consistency of Neumann nodes */
4088   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4089   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4090   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4091   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4092   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4093   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4094   /* set -1 fake neighbour to mimic Neumann boundary */
4095   if(used_IS) {
4096     for(i=0;i<neumann_bsize;i++){
4097       iindex = neumann_nodes[i];
4098       if(mat_graph->count[iindex] > NEUMANNCNT){
4099         if(mat_graph->count[iindex]+1 != (PetscInt)array[iindex]) {
4100           SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_USER,"Neumann nodes provided to BDDC must be consistent among neighbours!\nNode %d: number of sharing subdomains %d != number of subdomains for which it is a neumann node %d\n",iindex,mat_graph->count[iindex]+1,(PetscInt)array[iindex]);
4101         }
4102         mat_graph->neighbours_set[iindex][mat_graph->count[iindex]] = -1;
4103         mat_graph->count[iindex]+=1;
4104       }
4105     }
4106     ierr = ISRestoreIndices(used_IS,&neumann_nodes);CHKERRQ(ierr);
4107   }
4108   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4109   /* sort set of sharing subdomains */
4110   for(i=0;i<mat_graph->nvtxs;i++) { ierr = PetscSortInt(mat_graph->count[i],mat_graph->neighbours_set[i]);CHKERRQ(ierr); }
4111   /* remove interior nodes and dirichlet boundary nodes from the next search into the graph */
4112   for(i=0;i<mat_graph->nvtxs;i++){mat_graph->touched[i]=PETSC_FALSE;}
4113   nodes_touched=0;
4114   ierr = PCBDDCGetDirichletBoundaries(pc,&used_IS);CHKERRQ(ierr);
4115   ierr = VecSet(pcis->vec2_N,0.0);CHKERRQ(ierr);
4116   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4117   ierr = VecGetArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4118   if(used_IS) {
4119     ierr = ISGetSize(used_IS,&dirichlet_bsize);CHKERRQ(ierr);
4120     if(dirichlet_bsize && matis->pure_neumann) {
4121       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Dirichlet boundaries are intended to be used with matrices with zeroed rows!\n");
4122     }
4123     ierr = ISGetIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4124     for(i=0;i<dirichlet_bsize;i++){
4125       iindex=dirichlet_nodes[i];
4126       if(mat_graph->count[iindex] && !mat_graph->touched[iindex]) {
4127         if(array[iindex]>0.0) {
4128           SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_USER,"BDDC cannot have nodes which are marked as Neumann and Dirichlet at the same time! Wrong node %d\n",iindex);
4129         }
4130         mat_graph->touched[iindex]=PETSC_TRUE;
4131         mat_graph->where[iindex]=0;
4132         nodes_touched++;
4133         array2[iindex]=array2[iindex]+1.0;
4134       }
4135     }
4136     ierr = ISRestoreIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4137   }
4138   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4139   ierr = VecRestoreArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4140   /* Check consistency of Dirichlet nodes */
4141   ierr = VecSet(pcis->vec1_N,1.0);CHKERRQ(ierr);
4142   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4143   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4144   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4145   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4146   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4147   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4148   ierr = VecScatterBegin(matis->ctx,pcis->vec2_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4149   ierr = VecScatterEnd  (matis->ctx,pcis->vec2_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4150   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4151   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4152   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4153   ierr = VecGetArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4154   if(used_IS) {
4155     ierr = ISGetSize(used_IS,&dirichlet_bsize);CHKERRQ(ierr);
4156     ierr = ISGetIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4157     for(i=0;i<dirichlet_bsize;i++){
4158       iindex=dirichlet_nodes[i];
4159       if(array[iindex]>1.0 && array[iindex]!=array2[iindex] ) {
4160          SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_USER,"Dirichlet nodes provided to BDDC must be consistent among neighbours!\nNode %d: number of sharing subdomains %d != number of subdomains for which it is a neumann node %d\n",iindex,(PetscInt)array[iindex],(PetscInt)array2[iindex]);
4161       }
4162     }
4163     ierr = ISRestoreIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4164   }
4165   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4166   ierr = VecRestoreArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4167 
4168   for(i=0;i<mat_graph->nvtxs;i++){
4169     if(!mat_graph->count[i]){  /* interior nodes */
4170       mat_graph->touched[i]=PETSC_TRUE;
4171       mat_graph->where[i]=0;
4172       nodes_touched++;
4173     }
4174   }
4175   mat_graph->ncmps = 0;
4176   i=0;
4177   while(nodes_touched<mat_graph->nvtxs) {
4178     /*  find first untouched node in local ordering */
4179     while(mat_graph->touched[i]) i++;
4180     mat_graph->touched[i]=PETSC_TRUE;
4181     mat_graph->where[i]=where_values;
4182     nodes_touched++;
4183     /* now find all other nodes having the same set of sharing subdomains */
4184     for(j=i+1;j<mat_graph->nvtxs;j++){
4185       /* check for same number of sharing subdomains and dof number */
4186       if(!mat_graph->touched[j] && mat_graph->count[i]==mat_graph->count[j] && mat_graph->which_dof[i] == mat_graph->which_dof[j] ){
4187         /* check for same set of sharing subdomains */
4188         same_set=PETSC_TRUE;
4189         for(k=0;k<mat_graph->count[j];k++){
4190           if(mat_graph->neighbours_set[i][k]!=mat_graph->neighbours_set[j][k]) {
4191             same_set=PETSC_FALSE;
4192           }
4193         }
4194         /* I found a friend of mine */
4195         if(same_set) {
4196           mat_graph->where[j]=where_values;
4197           mat_graph->touched[j]=PETSC_TRUE;
4198           nodes_touched++;
4199         }
4200       }
4201     }
4202     where_values++;
4203   }
4204   where_values--; if(where_values<0) where_values=0;
4205   ierr = PetscMalloc(where_values*sizeof(PetscMPIInt),&mat_graph->where_ncmps);CHKERRQ(ierr);
4206   /* Find connected components defined on the shared interface */
4207   if(where_values) {
4208     ierr = PCBDDCFindConnectedComponents(mat_graph, where_values);
4209     /* For consistency among neughbouring procs, I need to sort (by global ordering) each connected component */
4210     for(i=0;i<mat_graph->ncmps;i++) {
4211       ierr = ISLocalToGlobalMappingApply(matis->mapping,mat_graph->cptr[i+1]-mat_graph->cptr[i],&mat_graph->queue[mat_graph->cptr[i]],&queue_in_global_numbering[mat_graph->cptr[i]]);CHKERRQ(ierr);
4212       ierr = PetscSortIntWithArray(mat_graph->cptr[i+1]-mat_graph->cptr[i],&queue_in_global_numbering[mat_graph->cptr[i]],&mat_graph->queue[mat_graph->cptr[i]]);CHKERRQ(ierr);
4213     }
4214   }
4215   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
4216   for(i=0;i<where_values;i++) {
4217     /* We are not sure that two connected components will be the same among subdomains sharing a subset of local interface */
4218     if(mat_graph->where_ncmps[i]>1) {
4219       adapt_interface=1;
4220       break;
4221     }
4222   }
4223   ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_INT,MPI_LOR,interface_comm);CHKERRQ(ierr);
4224   if(pcbddc->dbg_flag && adapt_interface_reduced) {
4225     ierr = PetscViewerASCIIPrintf(viewer,"Interface adapted\n");CHKERRQ(ierr);
4226     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
4227   }
4228   if(where_values && adapt_interface_reduced) {
4229 
4230     PetscInt sum_requests=0,my_rank;
4231     PetscInt buffer_size,start_of_recv,size_of_recv,start_of_send;
4232     PetscInt temp_buffer_size,ins_val,global_where_counter;
4233     PetscInt *cum_recv_counts;
4234     PetscInt *where_to_nodes_indices;
4235     PetscInt *petsc_buffer;
4236     PetscMPIInt *recv_buffer;
4237     PetscMPIInt *recv_buffer_where;
4238     PetscMPIInt *send_buffer;
4239     PetscMPIInt size_of_send;
4240     PetscInt *sizes_of_sends;
4241     MPI_Request *send_requests;
4242     MPI_Request *recv_requests;
4243     PetscInt *where_cc_adapt;
4244     PetscInt **temp_buffer;
4245     PetscInt *nodes_to_temp_buffer_indices;
4246     PetscInt *add_to_where;
4247 
4248     ierr = MPI_Comm_rank(interface_comm,&my_rank);CHKERRQ(ierr);
4249     ierr = PetscMalloc((where_values+1)*sizeof(PetscInt),&cum_recv_counts);CHKERRQ(ierr);
4250     ierr = PetscMemzero(cum_recv_counts,(where_values+1)*sizeof(PetscInt));CHKERRQ(ierr);
4251     ierr = PetscMalloc(where_values*sizeof(PetscInt),&where_to_nodes_indices);CHKERRQ(ierr);
4252     /* first count how many neighbours per connected component I will receive from */
4253     cum_recv_counts[0]=0;
4254     for(i=1;i<where_values+1;i++){
4255       j=0;
4256       while(mat_graph->where[j] != i) j++;
4257       where_to_nodes_indices[i-1]=j;
4258       if(mat_graph->neighbours_set[j][0]!=-1) { cum_recv_counts[i]=cum_recv_counts[i-1]+mat_graph->count[j]; } /* We don't want sends/recvs_to/from_self -> here I don't count myself  */
4259       else { cum_recv_counts[i]=cum_recv_counts[i-1]+mat_graph->count[j]-1; }
4260     }
4261     buffer_size=2*cum_recv_counts[where_values]+mat_graph->nvtxs;
4262     ierr = PetscMalloc(2*cum_recv_counts[where_values]*sizeof(PetscMPIInt),&recv_buffer_where);CHKERRQ(ierr);
4263     ierr = PetscMalloc(buffer_size*sizeof(PetscMPIInt),&send_buffer);CHKERRQ(ierr);
4264     ierr = PetscMalloc(cum_recv_counts[where_values]*sizeof(MPI_Request),&send_requests);CHKERRQ(ierr);
4265     ierr = PetscMalloc(cum_recv_counts[where_values]*sizeof(MPI_Request),&recv_requests);CHKERRQ(ierr);
4266     for(i=0;i<cum_recv_counts[where_values];i++) {
4267       send_requests[i]=MPI_REQUEST_NULL;
4268       recv_requests[i]=MPI_REQUEST_NULL;
4269     }
4270     /* exchange with my neighbours the number of my connected components on the shared interface */
4271     for(i=0;i<where_values;i++){
4272       j=where_to_nodes_indices[i];
4273       k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4274       for(;k<mat_graph->count[j];k++){
4275         ierr = MPI_Isend(&mat_graph->where_ncmps[i],1,MPIU_INT,mat_graph->neighbours_set[j][k],(my_rank+1)*mat_graph->count[j],interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
4276         ierr = MPI_Irecv(&recv_buffer_where[sum_requests],1,MPIU_INT,mat_graph->neighbours_set[j][k],(mat_graph->neighbours_set[j][k]+1)*mat_graph->count[j],interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
4277         sum_requests++;
4278       }
4279     }
4280     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4281     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4282     /* determine the connected component I need to adapt */
4283     ierr = PetscMalloc(where_values*sizeof(PetscInt),&where_cc_adapt);CHKERRQ(ierr);
4284     ierr = PetscMemzero(where_cc_adapt,where_values*sizeof(PetscInt));CHKERRQ(ierr);
4285     for(i=0;i<where_values;i++){
4286       for(j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
4287         /* The first condition is natural (i.e someone has a different number of cc than me), the second one is just to be safe */
4288         if( mat_graph->where_ncmps[i]!=recv_buffer_where[j] || mat_graph->where_ncmps[i] > 1 ) {
4289           where_cc_adapt[i]=PETSC_TRUE;
4290           break;
4291         }
4292       }
4293     }
4294     /* now get from neighbours their ccs (in global numbering) and adapt them (in case it is needed) */
4295     /* first determine how much data to send (size of each queue plus the global indices) and communicate it to neighbours */
4296     ierr = PetscMalloc(where_values*sizeof(PetscInt),&sizes_of_sends);CHKERRQ(ierr);
4297     ierr = PetscMemzero(sizes_of_sends,where_values*sizeof(PetscInt));CHKERRQ(ierr);
4298     sum_requests=0;
4299     start_of_send=0;
4300     start_of_recv=cum_recv_counts[where_values];
4301     for(i=0;i<where_values;i++) {
4302       if(where_cc_adapt[i]) {
4303         size_of_send=0;
4304         for(j=i;j<mat_graph->ncmps;j++) {
4305           if(mat_graph->where[mat_graph->queue[mat_graph->cptr[j]]] == i+1) { /* WARNING -> where values goes from 1 to where_values included */
4306             send_buffer[start_of_send+size_of_send]=mat_graph->cptr[j+1]-mat_graph->cptr[j];
4307             size_of_send+=1;
4308             for(k=0;k<mat_graph->cptr[j+1]-mat_graph->cptr[j];k++) {
4309               send_buffer[start_of_send+size_of_send+k]=queue_in_global_numbering[mat_graph->cptr[j]+k];
4310             }
4311             size_of_send=size_of_send+mat_graph->cptr[j+1]-mat_graph->cptr[j];
4312           }
4313         }
4314         j = where_to_nodes_indices[i];
4315         k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4316         sizes_of_sends[i]=size_of_send;
4317         for(;k<mat_graph->count[j];k++){
4318           ierr = MPI_Isend(&sizes_of_sends[i],1,MPIU_INT,mat_graph->neighbours_set[j][k],(my_rank+1)*mat_graph->count[j],interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
4319           ierr = MPI_Irecv(&recv_buffer_where[sum_requests+start_of_recv],1,MPIU_INT,mat_graph->neighbours_set[j][k],(mat_graph->neighbours_set[j][k]+1)*mat_graph->count[j],interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
4320           sum_requests++;
4321         }
4322         start_of_send+=size_of_send;
4323       }
4324     }
4325     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4326     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4327     buffer_size=0;
4328     for(k=0;k<sum_requests;k++) { buffer_size+=recv_buffer_where[start_of_recv+k]; }
4329     ierr = PetscMalloc(buffer_size*sizeof(PetscMPIInt),&recv_buffer);CHKERRQ(ierr);
4330     /* now exchange the data */
4331     start_of_recv=0;
4332     start_of_send=0;
4333     sum_requests=0;
4334     for(i=0;i<where_values;i++) {
4335       if(where_cc_adapt[i]) {
4336         size_of_send = sizes_of_sends[i];
4337         j = where_to_nodes_indices[i];
4338         k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4339         for(;k<mat_graph->count[j];k++){
4340           ierr = MPI_Isend(&send_buffer[start_of_send],size_of_send,MPIU_INT,mat_graph->neighbours_set[j][k],(my_rank+1)*mat_graph->count[j],interface_comm,&send_requests[sum_requests]);CHKERRQ(ierr);
4341           size_of_recv=recv_buffer_where[cum_recv_counts[where_values]+sum_requests];
4342           ierr = MPI_Irecv(&recv_buffer[start_of_recv],size_of_recv,MPIU_INT,mat_graph->neighbours_set[j][k],(mat_graph->neighbours_set[j][k]+1)*mat_graph->count[j],interface_comm,&recv_requests[sum_requests]);CHKERRQ(ierr);
4343           start_of_recv+=size_of_recv;
4344           sum_requests++;
4345         }
4346         start_of_send+=size_of_send;
4347       }
4348     }
4349     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4350     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4351     ierr = PetscMalloc(buffer_size*sizeof(PetscInt),&petsc_buffer);CHKERRQ(ierr);
4352     for(k=0;k<start_of_recv;k++) { petsc_buffer[k]=(PetscInt)recv_buffer[k]; }
4353     for(j=0;j<buffer_size;) {
4354        ierr = ISGlobalToLocalMappingApply(matis->mapping,IS_GTOLM_MASK,petsc_buffer[j],&petsc_buffer[j+1],&petsc_buffer[j],&petsc_buffer[j+1]);CHKERRQ(ierr);
4355        k=petsc_buffer[j]+1;
4356        j+=k;
4357     }
4358     sum_requests=cum_recv_counts[where_values];
4359     start_of_recv=0;
4360     ierr = PetscMalloc(mat_graph->nvtxs*sizeof(PetscInt),&nodes_to_temp_buffer_indices);CHKERRQ(ierr);
4361     global_where_counter=0;
4362     for(i=0;i<where_values;i++){
4363       if(where_cc_adapt[i]){
4364         temp_buffer_size=0;
4365         /* find nodes on the shared interface we need to adapt */
4366         for(j=0;j<mat_graph->nvtxs;j++){
4367           if(mat_graph->where[j]==i+1) {
4368             nodes_to_temp_buffer_indices[j]=temp_buffer_size;
4369             temp_buffer_size++;
4370           } else {
4371             nodes_to_temp_buffer_indices[j]=-1;
4372           }
4373         }
4374         /* allocate some temporary space */
4375         ierr = PetscMalloc(temp_buffer_size*sizeof(PetscInt*),&temp_buffer);CHKERRQ(ierr);
4376         ierr = PetscMalloc(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt),&temp_buffer[0]);CHKERRQ(ierr);
4377         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
4378         for(j=1;j<temp_buffer_size;j++){
4379           temp_buffer[j]=temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
4380         }
4381         /* analyze contributions from neighbouring subdomains for i-th conn comp
4382            temp buffer structure:
4383            supposing part of the interface has dimension 5 (global nodes 0,1,2,3,4)
4384            3 neighs procs with structured connected components:
4385              neigh 0: [0 1 4], [2 3];  (2 connected components)
4386              neigh 1: [0 1], [2 3 4];  (2 connected components)
4387              neigh 2: [0 4], [1], [2 3]; (3 connected components)
4388            tempbuffer (row-oriented) should be filled as:
4389              [ 0, 0, 0;
4390                0, 0, 1;
4391                1, 1, 2;
4392                1, 1, 2;
4393                0, 1, 0; ];
4394            This way we can simply recover the resulting structure account for possible intersections of ccs among neighs.
4395            The mat_graph->where array will be modified to reproduce the following 4 connected components [0], [1], [2 3], [4];
4396                                                                                                                                    */
4397         for(j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
4398           ins_val=0;
4399           size_of_recv=recv_buffer_where[sum_requests];  /* total size of recv from neighs */
4400           for(buffer_size=0;buffer_size<size_of_recv;) {  /* loop until all data from neighs has been taken into account */
4401             for(k=1;k<petsc_buffer[buffer_size+start_of_recv]+1;k++) { /* filling properly temp_buffer using data from a single recv */
4402               temp_buffer[ nodes_to_temp_buffer_indices[ petsc_buffer[ start_of_recv+buffer_size+k ] ] ][j]=ins_val;
4403             }
4404             buffer_size+=k;
4405             ins_val++;
4406           }
4407           start_of_recv+=size_of_recv;
4408           sum_requests++;
4409         }
4410         ierr = PetscMalloc(temp_buffer_size*sizeof(PetscInt),&add_to_where);CHKERRQ(ierr);
4411         ierr = PetscMemzero(add_to_where,temp_buffer_size*sizeof(PetscInt));CHKERRQ(ierr);
4412         for(j=0;j<temp_buffer_size;j++){
4413           if(!add_to_where[j]){ /* found a new cc  */
4414             global_where_counter++;
4415             add_to_where[j]=global_where_counter;
4416             for(k=j+1;k<temp_buffer_size;k++){ /* check for other nodes in new cc */
4417               same_set=PETSC_TRUE;
4418               for(s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++){
4419                 if(temp_buffer[j][s]!=temp_buffer[k][s]) {
4420                   same_set=PETSC_FALSE;
4421                   break;
4422                 }
4423               }
4424               if(same_set) add_to_where[k]=global_where_counter;
4425             }
4426           }
4427         }
4428         /* insert new data in where array */
4429         temp_buffer_size=0;
4430         for(j=0;j<mat_graph->nvtxs;j++){
4431           if(mat_graph->where[j]==i+1) {
4432             mat_graph->where[j]=where_values+add_to_where[temp_buffer_size];
4433             temp_buffer_size++;
4434           }
4435         }
4436         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
4437         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
4438         ierr = PetscFree(add_to_where);CHKERRQ(ierr);
4439       }
4440     }
4441     ierr = PetscFree(nodes_to_temp_buffer_indices);CHKERRQ(ierr);
4442     ierr = PetscFree(sizes_of_sends);CHKERRQ(ierr);
4443     ierr = PetscFree(send_requests);CHKERRQ(ierr);
4444     ierr = PetscFree(recv_requests);CHKERRQ(ierr);
4445     ierr = PetscFree(petsc_buffer);CHKERRQ(ierr);
4446     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
4447     ierr = PetscFree(recv_buffer_where);CHKERRQ(ierr);
4448     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
4449     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
4450     ierr = PetscFree(where_to_nodes_indices);CHKERRQ(ierr);
4451     ierr = PetscFree(where_cc_adapt);CHKERRQ(ierr);
4452     /* We are ready to evaluate consistent connected components on each part of the shared interface */
4453     if(global_where_counter) {
4454       for(i=0;i<mat_graph->nvtxs;i++){ mat_graph->touched[i]=PETSC_FALSE; }
4455       global_where_counter=0;
4456       for(i=0;i<mat_graph->nvtxs;i++){
4457         if(mat_graph->where[i] && !mat_graph->touched[i]) {
4458           global_where_counter++;
4459           for(j=i+1;j<mat_graph->nvtxs;j++){
4460             if(!mat_graph->touched[j] && mat_graph->where[j]==mat_graph->where[i]) {
4461               mat_graph->where[j]=global_where_counter;
4462               mat_graph->touched[j]=PETSC_TRUE;
4463             }
4464           }
4465           mat_graph->where[i]=global_where_counter;
4466           mat_graph->touched[i]=PETSC_TRUE;
4467         }
4468       }
4469       where_values=global_where_counter;
4470     }
4471     if(global_where_counter) {
4472       ierr = PetscMemzero(mat_graph->cptr,(mat_graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
4473       ierr = PetscMemzero(mat_graph->queue,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4474       ierr = PetscFree(mat_graph->where_ncmps);CHKERRQ(ierr);
4475       ierr = PetscMalloc(where_values*sizeof(PetscMPIInt),&mat_graph->where_ncmps);CHKERRQ(ierr);
4476       ierr = PCBDDCFindConnectedComponents(mat_graph, where_values);
4477       for(i=0;i<mat_graph->ncmps;i++) {
4478         ierr = ISLocalToGlobalMappingApply(matis->mapping,mat_graph->cptr[i+1]-mat_graph->cptr[i],&mat_graph->queue[mat_graph->cptr[i]],&queue_in_global_numbering[mat_graph->cptr[i]]);CHKERRQ(ierr);
4479         ierr = PetscSortIntWithArray(mat_graph->cptr[i+1]-mat_graph->cptr[i],&queue_in_global_numbering[mat_graph->cptr[i]],&mat_graph->queue[mat_graph->cptr[i]]);CHKERRQ(ierr);
4480       }
4481     }
4482   } /* Finished adapting interface */
4483   PetscInt nfc=0;
4484   PetscInt nec=0;
4485   PetscInt nvc=0;
4486   PetscBool twodim_flag=PETSC_FALSE;
4487   for (i=0; i<mat_graph->ncmps; i++) {
4488     if( mat_graph->cptr[i+1]-mat_graph->cptr[i] > vertex_size ){
4489       if(mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]==1){ /* 1 neigh Neumann fake included */
4490         nfc++;
4491       } else { /* note that nec will be zero in 2d */
4492         nec++;
4493       }
4494     } else {
4495       nvc+=mat_graph->cptr[i+1]-mat_graph->cptr[i];
4496     }
4497   }
4498 
4499   if(!nec) { /* we are in a 2d case -> no faces, only edges */
4500     nec = nfc;
4501     nfc = 0;
4502     twodim_flag = PETSC_TRUE;
4503   }
4504   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
4505   k=0;
4506   for (i=0; i<mat_graph->ncmps; i++) {
4507     j=mat_graph->cptr[i+1]-mat_graph->cptr[i];
4508     if( j > k) {
4509       k=j;
4510     }
4511     if(j<=vertex_size) {
4512       k+=vertex_size;
4513     }
4514   }
4515   ierr = PetscMalloc(k*sizeof(PetscInt),&auxis);CHKERRQ(ierr);
4516 
4517   if(!pcbddc->vertices_flag && !pcbddc->edges_flag) {
4518     ierr = PetscMalloc(nfc*sizeof(IS),&pcbddc->ISForFaces);CHKERRQ(ierr);
4519     use_faces=PETSC_TRUE;
4520   }
4521   if(!pcbddc->vertices_flag && !pcbddc->faces_flag) {
4522     ierr = PetscMalloc(nec*sizeof(IS),&pcbddc->ISForEdges);CHKERRQ(ierr);
4523     use_edges=PETSC_TRUE;
4524   }
4525   nfc=0;
4526   nec=0;
4527   for (i=0; i<mat_graph->ncmps; i++) {
4528     if( mat_graph->cptr[i+1]-mat_graph->cptr[i] > vertex_size ){
4529       for(j=0;j<mat_graph->cptr[i+1]-mat_graph->cptr[i];j++) {
4530         auxis[j]=mat_graph->queue[mat_graph->cptr[i]+j];
4531       }
4532       if(mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]==1){
4533         if(twodim_flag) {
4534           if(use_edges) {
4535             ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForEdges[nec]);CHKERRQ(ierr);
4536             nec++;
4537           }
4538         } else {
4539           if(use_faces) {
4540             ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForFaces[nfc]);CHKERRQ(ierr);
4541             nfc++;
4542           }
4543         }
4544       } else {
4545         if(use_edges) {
4546           ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForEdges[nec]);CHKERRQ(ierr);
4547           nec++;
4548         }
4549       }
4550     }
4551   }
4552   pcbddc->n_ISForFaces=nfc;
4553   pcbddc->n_ISForEdges=nec;
4554   nvc=0;
4555   if( !pcbddc->constraints_flag ) {
4556     for (i=0; i<mat_graph->ncmps; i++) {
4557       if( mat_graph->cptr[i+1]-mat_graph->cptr[i] <= vertex_size ){
4558         for( j=mat_graph->cptr[i];j<mat_graph->cptr[i+1];j++) {
4559           auxis[nvc]=mat_graph->queue[j];
4560           nvc++;
4561         }
4562       }
4563     }
4564   }
4565   /* sort vertex set (by local ordering) */
4566   ierr = PetscSortInt(nvc,auxis);CHKERRQ(ierr);
4567   ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,auxis,PETSC_COPY_VALUES,&pcbddc->ISForVertices);CHKERRQ(ierr);
4568 
4569   if(pcbddc->dbg_flag) {
4570 
4571     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4572     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Details from PCBDDCManageLocalBoundaries for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
4573     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4574 /*    ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Graph (adjacency structure) of local Neumann mat\n");CHKERRQ(ierr);
4575     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4576     for(i=0;i<mat_graph->nvtxs;i++) {
4577       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Nodes connected to node number %d are %d\n",i,mat_graph->xadj[i+1]-mat_graph->xadj[i]);CHKERRQ(ierr);
4578       for(j=mat_graph->xadj[i];j<mat_graph->xadj[i+1];j++){
4579         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d ",mat_graph->adjncy[j]);CHKERRQ(ierr);
4580       }
4581       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n--------------------------------------------------------------\n");CHKERRQ(ierr);
4582     }*/
4583     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Matrix graph has %d connected components", mat_graph->ncmps);CHKERRQ(ierr);
4584     for(i=0;i<mat_graph->ncmps;i++) {
4585       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\nDetails for connected component number %02d: size %04d, count %01d. Nodes follow.\n",
4586              i,mat_graph->cptr[i+1]-mat_graph->cptr[i],mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]);CHKERRQ(ierr);
4587       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"subdomains: ");
4588       for (j=0;j<mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]; j++) {
4589         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d ",mat_graph->neighbours_set[mat_graph->queue[mat_graph->cptr[i]]][j]);
4590       }
4591       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");
4592       for (j=mat_graph->cptr[i]; j<mat_graph->cptr[i+1]; j++){
4593         /* ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d (%d), ",queue_in_global_numbering[j],mat_graph->queue[j]);CHKERRQ(ierr); */
4594         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d, ",mat_graph->queue[j]);CHKERRQ(ierr);
4595       }
4596     }
4597     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n--------------------------------------------------------------\n");CHKERRQ(ierr);
4598     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local vertices\n",PetscGlobalRank,nvc);CHKERRQ(ierr);
4599     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local faces\n",PetscGlobalRank,nfc);CHKERRQ(ierr);
4600     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local edges\n",PetscGlobalRank,nec);CHKERRQ(ierr);
4601     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
4602   }
4603 
4604   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
4605   ierr = PetscFree(auxis);CHKERRQ(ierr);
4606   PetscFunctionReturn(0);
4607 
4608 }
4609 
4610 /* -------------------------------------------------------------------------- */
4611 
4612 /* The following code has been adapted from function IsConnectedSubdomain contained
4613    in source file contig.c of METIS library (version 5.0.1)
4614    It finds connected components of each partition labeled from 1 to n_dist  */
4615 
4616 #undef __FUNCT__
4617 #define __FUNCT__ "PCBDDCFindConnectedComponents"
4618 static PetscErrorCode PCBDDCFindConnectedComponents(PCBDDCGraph graph, PetscInt n_dist )
4619 {
4620   PetscInt i, j, k, nvtxs, first, last, nleft, ncmps,pid,cum_queue,n,ncmps_pid;
4621   PetscInt *xadj, *adjncy, *where, *queue;
4622   PetscInt *cptr;
4623   PetscBool *touched;
4624 
4625   PetscFunctionBegin;
4626 
4627   nvtxs   = graph->nvtxs;
4628   xadj    = graph->xadj;
4629   adjncy  = graph->adjncy;
4630   where   = graph->where;
4631   touched = graph->touched;
4632   queue   = graph->queue;
4633   cptr    = graph->cptr;
4634 
4635   for (i=0; i<nvtxs; i++)
4636     touched[i] = PETSC_FALSE;
4637 
4638   cum_queue=0;
4639   ncmps=0;
4640 
4641   for(n=0; n<n_dist; n++) {
4642     pid = n+1;  /* partition labeled by 0 is discarded */
4643     nleft = 0;
4644     for (i=0; i<nvtxs; i++) {
4645       if (where[i] == pid)
4646         nleft++;
4647     }
4648     for (i=0; i<nvtxs; i++) {
4649       if (where[i] == pid)
4650         break;
4651     }
4652     touched[i] = PETSC_TRUE;
4653     queue[cum_queue] = i;
4654     first = 0; last = 1;
4655     cptr[ncmps] = cum_queue;  /* This actually points to queue */
4656     ncmps_pid = 0;
4657     while (first != nleft) {
4658       if (first == last) { /* Find another starting vertex */
4659         cptr[++ncmps] = first+cum_queue;
4660         ncmps_pid++;
4661         for (i=0; i<nvtxs; i++) {
4662           if (where[i] == pid && !touched[i])
4663             break;
4664         }
4665         queue[cum_queue+last] = i;
4666         last++;
4667         touched[i] = PETSC_TRUE;
4668       }
4669       i = queue[cum_queue+first];
4670       first++;
4671       for (j=xadj[i]; j<xadj[i+1]; j++) {
4672         k = adjncy[j];
4673         if (where[k] == pid && !touched[k]) {
4674           queue[cum_queue+last] = k;
4675           last++;
4676           touched[k] = PETSC_TRUE;
4677         }
4678       }
4679     }
4680     cptr[++ncmps] = first+cum_queue;
4681     ncmps_pid++;
4682     cum_queue=cptr[ncmps];
4683     graph->where_ncmps[n] = ncmps_pid;
4684   }
4685   graph->ncmps = ncmps;
4686 
4687   PetscFunctionReturn(0);
4688 }
4689