xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision b76ba3228293fdd80ac8346c012ee0e4167e0aa9)
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   PetscInt       s,start_constraint,dual_dofs;
2008   PetscBool      compute_submatrix,useksp=PETSC_FALSE;
2009   PetscInt       *aux_primal_permutation,*aux_primal_numbering;
2010   PetscBool      boolforface,*change_basis;
2011 /* some ugly conditional declarations */
2012 #if defined(PETSC_MISSING_LAPACK_GESVD)
2013   PetscScalar    dot_result;
2014   PetscScalar    one=1.0,zero=0.0;
2015   PetscInt       ii;
2016   PetscScalar    *singular_vectors;
2017   PetscBLASInt   *iwork,*ifail;
2018   PetscReal      dummy_real,abs_tol;
2019   PetscBLASInt   eigs_found;
2020 #if defined(PETSC_USE_COMPLEX)
2021   PetscScalar    val1,val2;
2022 #endif
2023 #endif
2024   PetscBLASInt   dummy_int;
2025   PetscScalar    dummy_scalar;
2026 
2027   PetscFunctionBegin;
2028   /* check if near null space is attached to global mat */
2029   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
2030   if (nearnullsp) {
2031     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
2032   } else { /* if near null space is not provided it uses constants */
2033     nnsp_has_cnst = PETSC_TRUE;
2034     use_nnsp_true = PETSC_TRUE;
2035   }
2036   if(nnsp_has_cnst) {
2037     nnsp_addone = 1;
2038   }
2039   /*
2040        Evaluate maximum storage size needed by the procedure
2041        - temp_indices will contain start index of each constraint stored as follows
2042        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
2043        - 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
2044        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
2045                                                                                                                                                          */
2046 
2047   total_counts = pcbddc->n_ISForFaces+pcbddc->n_ISForEdges;
2048   total_counts *= (nnsp_addone+nnsp_size);
2049   ierr = ISGetSize(pcbddc->ISForVertices,&n_vertices);CHKERRQ(ierr);
2050   total_counts += n_vertices;
2051   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
2052   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
2053   total_counts = 0;
2054   max_size_of_constraint = 0;
2055   for(i=0;i<pcbddc->n_ISForEdges+pcbddc->n_ISForFaces;i++){
2056     if(i<pcbddc->n_ISForEdges){
2057       used_IS = &pcbddc->ISForEdges[i];
2058     } else {
2059       used_IS = &pcbddc->ISForFaces[i-pcbddc->n_ISForEdges];
2060     }
2061     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
2062     total_counts += j;
2063     if(j>max_size_of_constraint) max_size_of_constraint=j;
2064   }
2065   total_counts *= (nnsp_addone+nnsp_size);
2066   total_counts += n_vertices;
2067   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
2068   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
2069   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
2070   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
2071   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2072   for(i=0;i<pcis->n;i++) {
2073     local_to_B[i]=-1;
2074   }
2075   for(i=0;i<pcis->n_B;i++) {
2076     local_to_B[is_indices[i]]=i;
2077   }
2078   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2079 
2080   /* First we issue queries to allocate optimal workspace for LAPACKgesvd or LAPACKsyev/LAPACKheev */
2081   rwork = 0;
2082   work = 0;
2083   singular_vals = 0;
2084   temp_basis = 0;
2085   correlation_mat = 0;
2086   if(!pcbddc->use_nnsp_true) {
2087     PetscScalar temp_work;
2088 #if defined(PETSC_MISSING_LAPACK_GESVD)
2089     /* POD */
2090     PetscInt max_n;
2091     max_n = nnsp_addone+nnsp_size;
2092     /* using some techniques borrowed from Proper Orthogonal Decomposition */
2093     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
2094     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&singular_vectors);CHKERRQ(ierr);
2095     ierr = PetscMalloc(max_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
2096     ierr = PetscMalloc(max_size_of_constraint*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
2097 #if defined(PETSC_USE_COMPLEX)
2098     ierr = PetscMalloc(3*max_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
2099 #endif
2100     ierr = PetscMalloc(5*max_n*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
2101     ierr = PetscMalloc(max_n*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
2102     /* now we evaluate the optimal workspace using query with lwork=-1 */
2103     Bt = PetscBLASIntCast(max_n);
2104     lwork=-1;
2105     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2106 #if !defined(PETSC_USE_COMPLEX)
2107     abs_tol=1.e-8;
2108 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr); */
2109     LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,
2110                  &abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,&temp_work,&lwork,iwork,ifail,&lierr);
2111 #else
2112 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr); */
2113 /*  LAPACK call is missing here! TODO */
2114     SETERRQ(((PetscObject) pc)->comm, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
2115 #endif
2116     if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEVX Lapack routine %d",(int)lierr);
2117     ierr = PetscFPTrapPop();CHKERRQ(ierr);
2118 #else /* on missing GESVD */
2119     /* SVD */
2120     PetscInt max_n,min_n;
2121     max_n = max_size_of_constraint;
2122     min_n = nnsp_addone+nnsp_size;
2123     if(max_size_of_constraint < ( nnsp_addone+nnsp_size ) ) {
2124       min_n = max_size_of_constraint;
2125       max_n = nnsp_addone+nnsp_size;
2126     }
2127     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
2128 #if defined(PETSC_USE_COMPLEX)
2129     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
2130 #endif
2131     /* now we evaluate the optimal workspace using query with lwork=-1 */
2132     lwork=-1;
2133     Bs = PetscBLASIntCast(max_n);
2134     Bt = PetscBLASIntCast(min_n);
2135     dummy_int = Bs;
2136     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2137 #if !defined(PETSC_USE_COMPLEX)
2138     LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,
2139                  &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,&lierr);
2140 #else
2141     LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,
2142                  &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,rwork,&lierr);
2143 #endif
2144     if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SVD Lapack routine %d",(int)lierr);
2145     ierr = PetscFPTrapPop();CHKERRQ(ierr);
2146 #endif
2147     /* Allocate optimal workspace */
2148     lwork = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work));
2149     total_counts = (PetscInt)lwork;
2150     ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&work);CHKERRQ(ierr);
2151   }
2152   /* get local part of global near null space vectors */
2153   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
2154   for(k=0;k<nnsp_size;k++) {
2155     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
2156     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2157     ierr = VecScatterEnd  (matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2158   }
2159   /* Now we can loop on constraining sets */
2160   total_counts=0;
2161   temp_indices[0]=0;
2162   /* vertices */
2163   PetscBool used_vertex;
2164   ierr = ISGetIndices(pcbddc->ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2165   if(nnsp_has_cnst) { /* consider all vertices */
2166     for(i=0;i<n_vertices;i++) {
2167       temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
2168       temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
2169       temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
2170       temp_indices[total_counts+1]=temp_indices[total_counts]+1;
2171       change_basis[total_counts]=PETSC_FALSE;
2172       total_counts++;
2173     }
2174   } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
2175     for(i=0;i<n_vertices;i++) {
2176       used_vertex=PETSC_FALSE;
2177       k=0;
2178       while(!used_vertex && k<nnsp_size) {
2179         ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2180         if(PetscAbsScalar(array_vector[is_indices[i]])>0.0) {
2181           temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
2182           temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
2183           temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
2184           temp_indices[total_counts+1]=temp_indices[total_counts]+1;
2185           change_basis[total_counts]=PETSC_FALSE;
2186           total_counts++;
2187           used_vertex=PETSC_TRUE;
2188         }
2189         ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2190         k++;
2191       }
2192     }
2193   }
2194   ierr = ISRestoreIndices(pcbddc->ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2195   n_vertices=total_counts;
2196   /* edges and faces */
2197   for(i=0;i<pcbddc->n_ISForEdges+pcbddc->n_ISForFaces;i++){
2198     if(i<pcbddc->n_ISForEdges){
2199       used_IS = &pcbddc->ISForEdges[i];
2200       boolforface = pcbddc->usechangeofbasis;
2201     } else {
2202       used_IS = &pcbddc->ISForFaces[i-pcbddc->n_ISForEdges];
2203       boolforface = pcbddc->usechangeonfaces;
2204     }
2205     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
2206     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
2207     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
2208     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2209     if(nnsp_has_cnst) {
2210       temp_constraints++;
2211       quad_value = (PetscScalar) (1.0/PetscSqrtReal((PetscReal)size_of_constraint));
2212       for(j=0;j<size_of_constraint;j++) {
2213         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
2214         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
2215         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
2216       }
2217       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
2218       change_basis[total_counts]=boolforface;
2219       total_counts++;
2220     }
2221     for(k=0;k<nnsp_size;k++) {
2222       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2223       for(j=0;j<size_of_constraint;j++) {
2224         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
2225         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
2226         temp_quadrature_constraint[temp_indices[total_counts]+j]=array_vector[is_indices[j]];
2227       }
2228       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
2229       quad_value = 1.0;
2230       if( use_nnsp_true ) { /* check if array is null on the connected component in case use_nnsp_true has been requested */
2231         Bs = PetscBLASIntCast(size_of_constraint);
2232         quad_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone);
2233       }
2234       if ( quad_value > 0.0 ) { /* keep indices and values */
2235         temp_constraints++;
2236         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
2237         change_basis[total_counts]=boolforface;
2238         total_counts++;
2239       }
2240     }
2241     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2242     /* perform SVD on the constraint if use_nnsp_true has not be requested by the user */
2243     if(!use_nnsp_true) {
2244 
2245       Bs = PetscBLASIntCast(size_of_constraint);
2246       Bt = PetscBLASIntCast(temp_constraints);
2247 
2248 #if defined(PETSC_MISSING_LAPACK_GESVD)
2249       ierr = PetscMemzero(correlation_mat,Bt*Bt*sizeof(PetscScalar));CHKERRQ(ierr);
2250       /* Store upper triangular part of correlation matrix */
2251       for(j=0;j<temp_constraints;j++) {
2252         for(k=0;k<j+1;k++) {
2253 #if defined(PETSC_USE_COMPLEX)
2254           /* hand made complex dot product -> replace */
2255           dot_result = 0.0;
2256           for (ii=0; ii<size_of_constraint; ii++) {
2257             val1 = temp_quadrature_constraint[temp_indices[temp_start_ptr+j]+ii];
2258             val2 = temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii];
2259             dot_result += val1*PetscConj(val2);
2260           }
2261 #else
2262           dot_result = BLASdot_(&Bs,&temp_quadrature_constraint[temp_indices[temp_start_ptr+j]],&Bone,
2263                                     &temp_quadrature_constraint[temp_indices[temp_start_ptr+k]],&Bone);
2264 #endif
2265           correlation_mat[j*temp_constraints+k]=dot_result;
2266         }
2267       }
2268       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2269 #if !defined(PETSC_USE_COMPLEX)
2270 /*      LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr); */
2271       LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,
2272                  &abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,work,&lwork,iwork,ifail,&lierr);
2273 #else
2274 /*  LAPACK call is missing here! TODO */
2275       SETERRQ(((PetscObject) pc)->comm, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
2276 #endif
2277       if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEVX Lapack routine %d",(int)lierr);
2278       ierr = PetscFPTrapPop();CHKERRQ(ierr);
2279       /* retain eigenvalues greater than tol: note that lapack SYEV gives eigs in ascending order */
2280       j=0;
2281       while( j < Bt && singular_vals[j] < tol) j++;
2282       total_counts=total_counts-j;
2283       if(j<temp_constraints) {
2284         for(k=j;k<Bt;k++) { singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]); }
2285         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2286         BLASgemm_("N","N",&Bs,&Bt,&Bt,&one,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,correlation_mat,&Bt,&zero,temp_basis,&Bs);
2287         ierr = PetscFPTrapPop();CHKERRQ(ierr);
2288         /* copy POD basis into used quadrature memory */
2289         for(k=0;k<Bt-j;k++) {
2290           for(ii=0;ii<size_of_constraint;ii++) {
2291             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[Bt-1-k]*temp_basis[(Bt-1-k)*size_of_constraint+ii];
2292           }
2293         }
2294       }
2295 
2296 #else  /* on missing GESVD */
2297       PetscInt min_n = temp_constraints;
2298       if(min_n > size_of_constraint) min_n = size_of_constraint;
2299       dummy_int = Bs;
2300       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2301 #if !defined(PETSC_USE_COMPLEX)
2302       LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,
2303                    &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,&lierr);
2304 #else
2305       LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,
2306                    &dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,rwork,&lierr);
2307 #endif
2308       if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD Lapack routine %d",(int)lierr);
2309       ierr = PetscFPTrapPop();CHKERRQ(ierr);
2310       /* retain eigenvalues greater than tol: note that lapack SVD gives eigs in descending order */
2311       j=0;
2312       while( j < min_n && singular_vals[min_n-j-1] < tol) j++;
2313       total_counts = total_counts-(PetscInt)Bt+(min_n-j);
2314 #endif
2315     }
2316   }
2317 
2318   n_constraints=total_counts-n_vertices;
2319   local_primal_size = total_counts;
2320   /* set quantities in pcbddc data structure */
2321   pcbddc->n_vertices = n_vertices;
2322   pcbddc->n_constraints = n_constraints;
2323   pcbddc->local_primal_size = local_primal_size;
2324 
2325   /* Create constraint matrix */
2326   /* The constraint matrix is used to compute the l2g map of primal dofs */
2327   /* so we need to set it up properly either with or without change of basis */
2328   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
2329   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
2330   ierr = MatSetSizes(pcbddc->ConstraintMatrix,local_primal_size,pcis->n,local_primal_size,pcis->n);CHKERRQ(ierr);
2331   /* compute a local numbering of constraints : vertices first then constraints */
2332   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
2333   ierr = VecGetArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
2334   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
2335   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_permutation);CHKERRQ(ierr);
2336   total_counts=0;
2337   /* find vertices: subdomain corners plus dofs with basis changed */
2338   for(i=0;i<local_primal_size;i++) {
2339     size_of_constraint=temp_indices[i+1]-temp_indices[i];
2340     if(change_basis[i] || size_of_constraint == 1) {
2341       k=0;
2342       while(k < size_of_constraint && array_vector[temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1]] != 0.0) {
2343         k=k+1;
2344       }
2345       j=temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1];
2346       array_vector[j] = 1.0;
2347       aux_primal_numbering[total_counts]=j;
2348       aux_primal_permutation[total_counts]=total_counts;
2349       total_counts++;
2350     }
2351   }
2352   ierr = VecRestoreArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
2353   /* permute indices in order to have a sorted set of vertices */
2354   ierr = PetscSortIntWithPermutation(total_counts,aux_primal_numbering,aux_primal_permutation);
2355   /* nonzero structure */
2356   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2357   for(i=0;i<total_counts;i++) {
2358     nnz[i]=1;
2359   }
2360   j=total_counts;
2361   for(i=n_vertices;i<local_primal_size;i++) {
2362     if(!change_basis[i]) {
2363       nnz[j]=temp_indices[i+1]-temp_indices[i];
2364       j++;
2365     }
2366   }
2367   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
2368   ierr = PetscFree(nnz);CHKERRQ(ierr);
2369   /* set values in constraint matrix */
2370   for(i=0;i<total_counts;i++) {
2371     j = aux_primal_permutation[i];
2372     k = aux_primal_numbering[j];
2373     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,k,1.0,INSERT_VALUES);CHKERRQ(ierr);
2374   }
2375   for(i=n_vertices;i<local_primal_size;i++) {
2376     if(!change_basis[i]) {
2377       size_of_constraint=temp_indices[i+1]-temp_indices[i];
2378       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);
2379       total_counts++;
2380     }
2381   }
2382   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2383   ierr = PetscFree(aux_primal_permutation);CHKERRQ(ierr);
2384   /* assembling */
2385   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2386   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2387 
2388   /* Create matrix for change of basis. We don't need it in case pcbddc->usechangeofbasis is FALSE */
2389   if(pcbddc->usechangeofbasis) {
2390     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2391     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
2392     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
2393     /* work arrays */
2394     /* we need to reuse these arrays, so we free them */
2395     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
2396     ierr = PetscFree(work);CHKERRQ(ierr);
2397     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2398     ierr = PetscMalloc((nnsp_addone+nnsp_size)*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
2399     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscScalar),&work);CHKERRQ(ierr);
2400     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscBLASInt),&ipiv);CHKERRQ(ierr);
2401     for(i=0;i<pcis->n_B;i++) {
2402       nnz[i]=1;
2403     }
2404     /* Overestimated nonzeros per row */
2405     k=1;
2406     for(i=pcbddc->n_vertices;i<local_primal_size;i++) {
2407       if(change_basis[i]) {
2408         size_of_constraint = temp_indices[i+1]-temp_indices[i];
2409         if(k < size_of_constraint) {
2410           k = size_of_constraint;
2411         }
2412         for(j=0;j<size_of_constraint;j++) {
2413           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
2414         }
2415       }
2416     }
2417     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
2418     ierr = PetscFree(nnz);CHKERRQ(ierr);
2419     /* Temporary array to store indices */
2420     ierr = PetscMalloc(k*sizeof(PetscInt),&is_indices);CHKERRQ(ierr);
2421     /* Set initial identity in the matrix */
2422     for(i=0;i<pcis->n_B;i++) {
2423       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
2424     }
2425     /* Now we loop on the constraints which need a change of basis */
2426     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
2427     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (6.2.1) */
2428     temp_constraints = 0;
2429     temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
2430     for(i=pcbddc->n_vertices;i<local_primal_size;i++) {
2431       if(change_basis[i]) {
2432         compute_submatrix = PETSC_FALSE;
2433         useksp = PETSC_FALSE;
2434         if(temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
2435           temp_constraints++;
2436           if(i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
2437             compute_submatrix = PETSC_TRUE;
2438           }
2439         }
2440         if(compute_submatrix) {
2441           if(temp_constraints > 1 || pcbddc->use_nnsp_true) {
2442             useksp = PETSC_TRUE;
2443           }
2444           size_of_constraint = temp_indices[i+1]-temp_indices[i];
2445           if(useksp) { /* experimental */
2446             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
2447             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
2448             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
2449             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,PETSC_NULL);CHKERRQ(ierr);
2450           }
2451           /* First _size_of_constraint-temp_constraints_ columns */
2452           dual_dofs = size_of_constraint-temp_constraints;
2453           start_constraint = i+1-temp_constraints;
2454           for(s=0;s<dual_dofs;s++) {
2455             is_indices[0] = s;
2456             for(j=0;j<temp_constraints;j++) {
2457               for(k=0;k<temp_constraints;k++) {
2458                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
2459               }
2460               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
2461               is_indices[j+1]=s+j+1;
2462             }
2463             Bt = temp_constraints;
2464             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2465             LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr);
2466             if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
2467             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2468             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
2469             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
2470             if(useksp) {
2471               /* temp mat with transposed rows and columns */
2472               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
2473               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
2474             }
2475           }
2476           if(useksp) {
2477             /* last rows of temp_mat */
2478             for(j=0;j<size_of_constraint;j++) {
2479               is_indices[j] = j;
2480             }
2481             for(s=0;s<temp_constraints;s++) {
2482               k = s + dual_dofs;
2483               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
2484             }
2485             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2486             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2487             ierr = MatGetVecs(temp_mat,&temp_vec,PETSC_NULL);CHKERRQ(ierr);
2488             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
2489             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
2490             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
2491             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
2492             for(s=0;s<temp_constraints;s++) {
2493               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
2494               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
2495               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
2496               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
2497               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
2498               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
2499               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
2500               /* last columns of change of basis matrix associated to new primal dofs */
2501               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);
2502               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
2503             }
2504             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
2505             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
2506             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2507           } else {
2508             /* last columns of change of basis matrix associated to new primal dofs */
2509             for(s=0;s<temp_constraints;s++) {
2510               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
2511               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);
2512             }
2513           }
2514           /* prepare for the next cycle */
2515           temp_constraints = 0;
2516           if(i != local_primal_size -1 ) {
2517           temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
2518         }
2519       }
2520     }
2521     }
2522     /* assembling */
2523     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2524     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2525     ierr = PetscFree(ipiv);CHKERRQ(ierr);
2526     ierr = PetscFree(is_indices);CHKERRQ(ierr);
2527   }
2528   /* free workspace no longer needed */
2529   ierr = PetscFree(rwork);CHKERRQ(ierr);
2530   ierr = PetscFree(work);CHKERRQ(ierr);
2531   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
2532   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
2533   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
2534   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2535   ierr = PetscFree(change_basis);CHKERRQ(ierr);
2536   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
2537   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
2538   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
2539   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
2540 #if defined(PETSC_MISSING_LAPACK_GESVD)
2541   ierr = PetscFree(iwork);CHKERRQ(ierr);
2542   ierr = PetscFree(ifail);CHKERRQ(ierr);
2543   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
2544 #endif
2545   for(k=0;k<nnsp_size;k++) {
2546     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
2547   }
2548   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
2549   PetscFunctionReturn(0);
2550 }
2551 /* -------------------------------------------------------------------------- */
2552 #undef __FUNCT__
2553 #define __FUNCT__ "PCBDDCCoarseSetUp"
2554 static PetscErrorCode PCBDDCCoarseSetUp(PC pc)
2555 {
2556   PetscErrorCode  ierr;
2557 
2558   PC_IS*            pcis = (PC_IS*)(pc->data);
2559   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
2560   Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
2561   Mat               change_mat_all;
2562   IS                is_R_local;
2563   IS                is_V_local;
2564   IS                is_C_local;
2565   IS                is_aux1;
2566   IS                is_aux2;
2567   const VecType     impVecType;
2568   const MatType     impMatType;
2569   PetscInt          n_R=0;
2570   PetscInt          n_D=0;
2571   PetscInt          n_B=0;
2572   PetscScalar       zero=0.0;
2573   PetscScalar       one=1.0;
2574   PetscScalar       m_one=-1.0;
2575   PetscScalar*      array;
2576   PetscScalar       *coarse_submat_vals;
2577   PetscInt          *idx_R_local;
2578   PetscInt          *idx_V_B;
2579   PetscScalar       *coarsefunctions_errors;
2580   PetscScalar       *constraints_errors;
2581   /* auxiliary indices */
2582   PetscInt i,j,k;
2583   /* for verbose output of bddc */
2584   PetscViewer       viewer=pcbddc->dbg_viewer;
2585   PetscBool         dbg_flag=pcbddc->dbg_flag;
2586   /* for counting coarse dofs */
2587   PetscInt          n_vertices,n_constraints;
2588   PetscInt          size_of_constraint;
2589   PetscInt          *row_cmat_indices;
2590   PetscScalar       *row_cmat_values;
2591   PetscInt          *vertices,*nnz,*is_indices,*temp_indices;
2592 
2593   PetscFunctionBegin;
2594   /* Set Non-overlapping dimensions */
2595   n_B = pcis->n_B; n_D = pcis->n - n_B;
2596   /* Set types for local objects needed by BDDC precondtioner */
2597   impMatType = MATSEQDENSE;
2598   impVecType = VECSEQ;
2599   /* get vertex indices from constraint matrix */
2600   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
2601   n_vertices=0;
2602   for(i=0;i<pcbddc->local_primal_size;i++) {
2603     ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
2604     if(size_of_constraint == 1) {
2605       vertices[n_vertices]=row_cmat_indices[0];
2606       n_vertices++;
2607     }
2608     ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
2609   }
2610   /* Set number of constraints */
2611   n_constraints = pcbddc->local_primal_size-n_vertices;
2612 
2613   /* vertices in boundary numbering */
2614   if(n_vertices) {
2615     ierr = VecSet(pcis->vec1_N,m_one);CHKERRQ(ierr);
2616     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2617     for (i=0; i<n_vertices; i++) { array[ vertices[i] ] = i; }
2618     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2619     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2620     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2621     ierr = PetscMalloc(n_vertices*sizeof(PetscInt),&idx_V_B);CHKERRQ(ierr);
2622     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2623     for (i=0; i<n_vertices; i++) {
2624       j=0;
2625       while (array[j] != i ) {j++;}
2626       idx_V_B[i]=j;
2627     }
2628     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2629   }
2630 
2631   /* transform local matrices if needed */
2632   if(pcbddc->usechangeofbasis) {
2633     ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2634     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2635     for(i=0;i<n_D;i++) {
2636       nnz[is_indices[i]]=1;
2637     }
2638     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2639     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2640     k=1;
2641     for(i=0;i<n_B;i++) {
2642       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
2643       nnz[is_indices[i]]=j;
2644       if( k < j) {
2645         k = j;
2646       }
2647       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
2648     }
2649     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2650     /* assemble change of basis matrix on the whole set of local dofs */
2651     ierr = PetscMalloc(k*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
2652     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
2653     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
2654     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
2655     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
2656     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2657     for(i=0;i<n_D;i++) {
2658       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
2659     }
2660     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2661     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2662     for(i=0;i<n_B;i++) {
2663       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2664       for(k=0;k<j;k++) {
2665         temp_indices[k]=is_indices[row_cmat_indices[k]];
2666       }
2667       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
2668       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2669     }
2670     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2671     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2672     ierr = MatPtAP(matis->A,change_mat_all,MAT_INITIAL_MATRIX,1.0,&pcbddc->local_mat);CHKERRQ(ierr);
2673     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
2674     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
2675     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
2676     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
2677     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
2678     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
2679     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
2680     ierr = PetscFree(nnz);CHKERRQ(ierr);
2681     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2682   } else {
2683     /* without change of basis, the local matrix is unchanged */
2684     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
2685     pcbddc->local_mat = matis->A;
2686   }
2687 
2688   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
2689   ierr = VecSet(pcis->vec1_N,one);CHKERRQ(ierr);
2690   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2691   for (i=0;i<n_vertices;i++) { array[ vertices[i] ] = zero; }
2692   ierr = PetscMalloc(( pcis->n - n_vertices )*sizeof(PetscInt),&idx_R_local);CHKERRQ(ierr);
2693   for (i=0, n_R=0; i<pcis->n; i++) { if (array[i] == one) { idx_R_local[n_R] = i; n_R++; } }
2694   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2695   if(dbg_flag) {
2696     ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
2697     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2698     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
2699     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
2700     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);
2701     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
2702     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2703   }
2704 
2705   /* Allocate needed vectors */
2706   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2707   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
2708   ierr = VecDuplicate(pcis->vec1_D,&pcbddc->vec4_D);CHKERRQ(ierr);
2709   ierr = VecCreate(PETSC_COMM_SELF,&pcbddc->vec1_R);CHKERRQ(ierr);
2710   ierr = VecSetSizes(pcbddc->vec1_R,n_R,n_R);CHKERRQ(ierr);
2711   ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
2712   ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
2713   ierr = VecCreate(PETSC_COMM_SELF,&pcbddc->vec1_P);CHKERRQ(ierr);
2714   ierr = VecSetSizes(pcbddc->vec1_P,pcbddc->local_primal_size,pcbddc->local_primal_size);CHKERRQ(ierr);
2715   ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
2716 
2717   /* Creating some index sets needed  */
2718   /* For submatrices */
2719   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_R,idx_R_local,PETSC_OWN_POINTER,&is_R_local);CHKERRQ(ierr);
2720   if(n_vertices)    {
2721     ierr = ISCreateGeneral(PETSC_COMM_SELF,n_vertices,vertices,PETSC_OWN_POINTER,&is_V_local);CHKERRQ(ierr);
2722   }
2723   if(n_constraints) {
2724     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_C_local);CHKERRQ(ierr);
2725   }
2726 
2727   /* For VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
2728   {
2729     PetscInt   *aux_array1;
2730     PetscInt   *aux_array2;
2731 
2732     ierr = PetscMalloc( (pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
2733     ierr = PetscMalloc( (pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array2);CHKERRQ(ierr);
2734 
2735     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
2736     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2737     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2738     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2739     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2740     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2741     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2742     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2743     for (i=0, j=0; i<n_R; i++) { if (array[idx_R_local[i]] > one) { aux_array1[j] = i; j++; } }
2744     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2745     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_COPY_VALUES,&is_aux1);CHKERRQ(ierr);
2746     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2747     for (i=0, j=0; i<n_B; i++) { if (array[i] > one) { aux_array2[j] = i; j++; } }
2748     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2749     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_COPY_VALUES,&is_aux2);CHKERRQ(ierr);
2750     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
2751     ierr = PetscFree(aux_array1);CHKERRQ(ierr);
2752     ierr = PetscFree(aux_array2);CHKERRQ(ierr);
2753     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2754     ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
2755 
2756     if(pcbddc->prec_type || dbg_flag ) {
2757       ierr = PetscMalloc(n_D*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
2758       ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2759       for (i=0, j=0; i<n_R; i++) { if (array[idx_R_local[i]] == one) { aux_array1[j] = i; j++; } }
2760       ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2761       ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_COPY_VALUES,&is_aux1);CHKERRQ(ierr);
2762       ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
2763       ierr = PetscFree(aux_array1);CHKERRQ(ierr);
2764       ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2765     }
2766   }
2767 
2768   /* Creating PC contexts for local Dirichlet and Neumann problems */
2769   {
2770     Mat  A_RR;
2771     PC   pc_temp;
2772     /* Matrix for Dirichlet problem is A_II -> we already have it from pcis.c code */
2773     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
2774     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
2775     ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,SAME_PRECONDITIONER);CHKERRQ(ierr);
2776     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
2777     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
2778     /* default */
2779     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
2780     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
2781     /* Allow user's customization */
2782     ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
2783     /* Set Up KSP for Dirichlet problem of BDDC */
2784     ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
2785     /* set ksp_D into pcis data */
2786     ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
2787     ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
2788     pcis->ksp_D = pcbddc->ksp_D;
2789     /* Matrix for Neumann problem is A_RR -> we need to create it */
2790     ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
2791     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
2792     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
2793     ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,SAME_PRECONDITIONER);CHKERRQ(ierr);
2794     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
2795     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
2796     /* default */
2797     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
2798     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
2799     /* Allow user's customization */
2800     ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
2801     /* Set Up KSP for Neumann problem of BDDC */
2802     ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
2803     /* check Dirichlet and Neumann solvers */
2804     {
2805       Vec         temp_vec;
2806       PetscReal   value;
2807       PetscMPIInt use_exact,use_exact_reduced;
2808 
2809       ierr = VecDuplicate(pcis->vec1_D,&temp_vec);CHKERRQ(ierr);
2810       ierr = VecSetRandom(pcis->vec1_D,PETSC_NULL);CHKERRQ(ierr);
2811       ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
2812       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,temp_vec);CHKERRQ(ierr);
2813       ierr = VecAXPY(temp_vec,m_one,pcis->vec1_D);CHKERRQ(ierr);
2814       ierr = VecNorm(temp_vec,NORM_INFINITY,&value);CHKERRQ(ierr);
2815       use_exact = 1;
2816       if(PetscAbsReal(value) > 1.e-4) {
2817         use_exact = 0;
2818       }
2819       ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,((PetscObject)pc)->comm);CHKERRQ(ierr);
2820       pcbddc->use_exact_dirichlet = (PetscBool) use_exact_reduced;
2821       ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2822       if(dbg_flag) {
2823         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2824         ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
2825         ierr = PetscViewerASCIIPrintf(viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
2826         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
2827         ierr = VecDuplicate(pcbddc->vec1_R,&temp_vec);CHKERRQ(ierr);
2828         ierr = VecSetRandom(pcbddc->vec1_R,PETSC_NULL);CHKERRQ(ierr);
2829         ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2830         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,temp_vec);CHKERRQ(ierr);
2831         ierr = VecAXPY(temp_vec,m_one,pcbddc->vec1_R);CHKERRQ(ierr);
2832         ierr = VecNorm(temp_vec,NORM_INFINITY,&value);CHKERRQ(ierr);
2833         ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2834         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
2835         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2836       }
2837     }
2838     /* free Neumann problem's matrix */
2839     ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
2840   }
2841 
2842   /* Assemble all remaining stuff needed to apply BDDC  */
2843   {
2844     Mat          A_RV,A_VR,A_VV;
2845     Mat          M1,M2;
2846     Mat          C_CR;
2847     Mat          AUXMAT;
2848     Vec          vec1_C;
2849     Vec          vec2_C;
2850     Vec          vec1_V;
2851     Vec          vec2_V;
2852     PetscInt     *nnz;
2853     PetscInt     *auxindices;
2854     PetscInt     index;
2855     PetscScalar* array2;
2856     MatFactorInfo matinfo;
2857 
2858     /* Allocating some extra storage just to be safe */
2859     ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2860     ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&auxindices);CHKERRQ(ierr);
2861     for(i=0;i<pcis->n;i++) {auxindices[i]=i;}
2862 
2863     /* some work vectors on vertices and/or constraints */
2864     if(n_vertices) {
2865       ierr = VecCreate(PETSC_COMM_SELF,&vec1_V);CHKERRQ(ierr);
2866       ierr = VecSetSizes(vec1_V,n_vertices,n_vertices);CHKERRQ(ierr);
2867       ierr = VecSetType(vec1_V,impVecType);CHKERRQ(ierr);
2868       ierr = VecDuplicate(vec1_V,&vec2_V);CHKERRQ(ierr);
2869     }
2870     if(n_constraints) {
2871       ierr = VecCreate(PETSC_COMM_SELF,&vec1_C);CHKERRQ(ierr);
2872       ierr = VecSetSizes(vec1_C,n_constraints,n_constraints);CHKERRQ(ierr);
2873       ierr = VecSetType(vec1_C,impVecType);CHKERRQ(ierr);
2874       ierr = VecDuplicate(vec1_C,&vec2_C);CHKERRQ(ierr);
2875       ierr = VecDuplicate(vec1_C,&pcbddc->vec1_C);CHKERRQ(ierr);
2876     }
2877     /* Precompute stuffs needed for preprocessing and application of BDDC*/
2878     if(n_constraints) {
2879       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->local_auxmat2);CHKERRQ(ierr);
2880       ierr = MatSetSizes(pcbddc->local_auxmat2,n_R,n_constraints,n_R,n_constraints);CHKERRQ(ierr);
2881       ierr = MatSetType(pcbddc->local_auxmat2,impMatType);CHKERRQ(ierr);
2882       ierr = MatSeqDenseSetPreallocation(pcbddc->local_auxmat2,PETSC_NULL);CHKERRQ(ierr);
2883 
2884       /* Create Constraint matrix on R nodes: C_{CR}  */
2885       ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_C_local,is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
2886       ierr = ISDestroy(&is_C_local);CHKERRQ(ierr);
2887 
2888       /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
2889       for(i=0;i<n_constraints;i++) {
2890         ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
2891         /* Get row of constraint matrix in R numbering */
2892         ierr = VecGetArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
2893         ierr = MatGetRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2894         for(j=0;j<size_of_constraint;j++) { array[ row_cmat_indices[j] ] = - row_cmat_values[j]; }
2895         ierr = MatRestoreRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2896         ierr = VecRestoreArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
2897         /* Solve for row of constraint matrix in R numbering */
2898         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2899         /* Set values */
2900         ierr = VecGetArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2901         ierr = MatSetValues(pcbddc->local_auxmat2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2902         ierr = VecRestoreArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2903       }
2904       ierr = MatAssemblyBegin(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2905       ierr = MatAssemblyEnd(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2906 
2907       /* Assemble AUXMAT = ( LUFactor )( -C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} */
2908       ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AUXMAT);CHKERRQ(ierr);
2909       ierr = MatFactorInfoInitialize(&matinfo);CHKERRQ(ierr);
2910       ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,0,1,&is_aux1);CHKERRQ(ierr);
2911       ierr = MatLUFactor(AUXMAT,is_aux1,is_aux1,&matinfo);CHKERRQ(ierr);
2912       ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2913 
2914       /* Assemble explicitly M1 = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} needed in preproc  */
2915       ierr = MatCreate(PETSC_COMM_SELF,&M1);CHKERRQ(ierr);
2916       ierr = MatSetSizes(M1,n_constraints,n_constraints,n_constraints,n_constraints);CHKERRQ(ierr);
2917       ierr = MatSetType(M1,impMatType);CHKERRQ(ierr);
2918       ierr = MatSeqDenseSetPreallocation(M1,PETSC_NULL);CHKERRQ(ierr);
2919       for(i=0;i<n_constraints;i++) {
2920         ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
2921         ierr = VecSetValue(vec1_C,i,one,INSERT_VALUES);CHKERRQ(ierr);
2922         ierr = VecAssemblyBegin(vec1_C);CHKERRQ(ierr);
2923         ierr = VecAssemblyEnd(vec1_C);CHKERRQ(ierr);
2924         ierr = MatSolve(AUXMAT,vec1_C,vec2_C);CHKERRQ(ierr);
2925         ierr = VecScale(vec2_C,m_one);CHKERRQ(ierr);
2926         ierr = VecGetArray(vec2_C,&array);CHKERRQ(ierr);
2927         ierr = MatSetValues(M1,n_constraints,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2928         ierr = VecRestoreArray(vec2_C,&array);CHKERRQ(ierr);
2929       }
2930       ierr = MatAssemblyBegin(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2931       ierr = MatAssemblyEnd(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2932       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
2933       /* Assemble local_auxmat1 = M1*C_{CR} needed by BDDC application in KSP and in preproc */
2934       ierr = MatMatMult(M1,C_CR,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
2935 
2936     }
2937 
2938     /* Get submatrices from subdomain matrix */
2939     if(n_vertices){
2940       ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_V_local,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
2941       ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
2942       ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_V_local,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
2943       /* Assemble M2 = A_RR^{-1}A_RV */
2944       ierr = MatCreate(PETSC_COMM_SELF,&M2);CHKERRQ(ierr);
2945       ierr = MatSetSizes(M2,n_R,n_vertices,n_R,n_vertices);CHKERRQ(ierr);
2946       ierr = MatSetType(M2,impMatType);CHKERRQ(ierr);
2947       ierr = MatSeqDenseSetPreallocation(M2,PETSC_NULL);CHKERRQ(ierr);
2948       for(i=0;i<n_vertices;i++) {
2949         ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
2950         ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
2951         ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
2952         ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
2953         ierr = MatMult(A_RV,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
2954         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2955         ierr = VecGetArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2956         ierr = MatSetValues(M2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2957         ierr = VecRestoreArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2958       }
2959       ierr = MatAssemblyBegin(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2960       ierr = MatAssemblyEnd(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2961     }
2962 
2963     /* Matrix of coarse basis functions (local) */
2964     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
2965     ierr = MatSetSizes(pcbddc->coarse_phi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
2966     ierr = MatSetType(pcbddc->coarse_phi_B,impMatType);CHKERRQ(ierr);
2967     ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_B,PETSC_NULL);CHKERRQ(ierr);
2968     if(pcbddc->prec_type || dbg_flag ) {
2969       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
2970       ierr = MatSetSizes(pcbddc->coarse_phi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
2971       ierr = MatSetType(pcbddc->coarse_phi_D,impMatType);CHKERRQ(ierr);
2972       ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_D,PETSC_NULL);CHKERRQ(ierr);
2973     }
2974 
2975     if(dbg_flag) {
2976       ierr = PetscMalloc( pcbddc->local_primal_size*sizeof(PetscScalar),&coarsefunctions_errors);CHKERRQ(ierr);
2977       ierr = PetscMalloc( pcbddc->local_primal_size*sizeof(PetscScalar),&constraints_errors);CHKERRQ(ierr);
2978     }
2979     /* Subdomain contribution (Non-overlapping) to coarse matrix  */
2980     ierr = PetscMalloc ((pcbddc->local_primal_size)*(pcbddc->local_primal_size)*sizeof(PetscScalar),&coarse_submat_vals);CHKERRQ(ierr);
2981 
2982     /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
2983     for(i=0;i<n_vertices;i++){
2984       ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
2985       ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
2986       ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
2987       ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
2988       /* solution of saddle point problem */
2989       ierr = MatMult(M2,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
2990       ierr = VecScale(pcbddc->vec1_R,m_one);CHKERRQ(ierr);
2991       if(n_constraints) {
2992         ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec1_R,vec1_C);CHKERRQ(ierr);
2993         ierr = MatMultAdd(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
2994         ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
2995       }
2996       ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
2997       ierr = MatMultAdd(A_VV,vec1_V,vec2_V,vec2_V);CHKERRQ(ierr);
2998 
2999       /* Set values in coarse basis function and subdomain part of coarse_mat */
3000       /* coarse basis functions */
3001       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
3002       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3003       ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3004       ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3005       ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
3006       ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3007       ierr = MatSetValue(pcbddc->coarse_phi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
3008       if( pcbddc->prec_type || dbg_flag  ) {
3009         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3010         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3011         ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3012         ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
3013         ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3014       }
3015       /* subdomain contribution to coarse matrix */
3016       ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3017       for(j=0;j<n_vertices;j++) { coarse_submat_vals[i*pcbddc->local_primal_size+j] = array[j]; } /* WARNING -> column major ordering */
3018       ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3019       if(n_constraints) {
3020         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3021         for(j=0;j<n_constraints;j++) { coarse_submat_vals[i*pcbddc->local_primal_size+j+n_vertices] = array[j]; } /* WARNING -> column major ordering */
3022         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3023       }
3024 
3025       if( dbg_flag ) {
3026         /* assemble subdomain vector on nodes */
3027         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3028         ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3029         ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3030         for(j=0;j<n_R;j++) { array[idx_R_local[j]] = array2[j]; }
3031         array[ vertices[i] ] = one;
3032         ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3033         ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3034         /* assemble subdomain vector of lagrange multipliers (i.e. primal nodes) */
3035         ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
3036         ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3037         ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3038         for(j=0;j<n_vertices;j++) { array2[j]=array[j]; }
3039         ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3040         if(n_constraints) {
3041           ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3042           for(j=0;j<n_constraints;j++) { array2[j+n_vertices]=array[j]; }
3043           ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3044         }
3045         ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3046         ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
3047         /* check saddle point solution */
3048         ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
3049         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
3050         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i]);CHKERRQ(ierr);
3051         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
3052         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3053         array[i]=array[i]+m_one;  /* shift by the identity matrix */
3054         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3055         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i]);CHKERRQ(ierr);
3056       }
3057     }
3058 
3059     for(i=0;i<n_constraints;i++){
3060       ierr = VecSet(vec2_C,zero);CHKERRQ(ierr);
3061       ierr = VecSetValue(vec2_C,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
3062       ierr = VecAssemblyBegin(vec2_C);CHKERRQ(ierr);
3063       ierr = VecAssemblyEnd(vec2_C);CHKERRQ(ierr);
3064       /* solution of saddle point problem */
3065       ierr = MatMult(M1,vec2_C,vec1_C);CHKERRQ(ierr);
3066       ierr = MatMult(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
3067       ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
3068       if(n_vertices) { ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr); }
3069       /* Set values in coarse basis function and subdomain part of coarse_mat */
3070       /* coarse basis functions */
3071       index=i+n_vertices;
3072       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
3073       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3074       ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3075       ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3076       ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
3077       ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3078       if( pcbddc->prec_type || dbg_flag ) {
3079         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3080         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3081         ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3082         ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
3083         ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3084       }
3085       /* subdomain contribution to coarse matrix */
3086       if(n_vertices) {
3087         ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3088         for(j=0;j<n_vertices;j++) {coarse_submat_vals[index*pcbddc->local_primal_size+j]=array[j];} /* WARNING -> column major ordering */
3089         ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3090       }
3091       ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3092       for(j=0;j<n_constraints;j++) {coarse_submat_vals[index*pcbddc->local_primal_size+j+n_vertices]=array[j];} /* WARNING -> column major ordering */
3093       ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3094 
3095       if( dbg_flag ) {
3096         /* assemble subdomain vector on nodes */
3097         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3098         ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3099         ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3100         for(j=0;j<n_R;j++){ array[ idx_R_local[j] ] = array2[j]; }
3101         ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3102         ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3103         /* assemble subdomain vector of lagrange multipliers */
3104         ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
3105         ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3106         if( n_vertices) {
3107           ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3108           for(j=0;j<n_vertices;j++) {array2[j]=-array[j];}
3109           ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3110         }
3111         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3112         for(j=0;j<n_constraints;j++) {array2[j+n_vertices]=-array[j];}
3113         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3114         ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3115         /* check saddle point solution */
3116         ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
3117         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
3118         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[index]);CHKERRQ(ierr);
3119         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
3120         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3121         array[index]=array[index]+m_one; /* shift by the identity matrix */
3122         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3123         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[index]);CHKERRQ(ierr);
3124       }
3125     }
3126     ierr = MatAssemblyBegin(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3127     ierr = MatAssemblyEnd  (pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3128     if( pcbddc->prec_type || dbg_flag ) {
3129       ierr = MatAssemblyBegin(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3130       ierr = MatAssemblyEnd  (pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3131     }
3132     /* Checking coarse_sub_mat and coarse basis functios */
3133     /* It shuld be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
3134     if(dbg_flag) {
3135 
3136       Mat coarse_sub_mat;
3137       Mat TM1,TM2,TM3,TM4;
3138       Mat coarse_phi_D,coarse_phi_B,A_II,A_BB,A_IB,A_BI;
3139       const MatType checkmattype=MATSEQAIJ;
3140       PetscScalar      value;
3141 
3142       ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
3143       ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
3144       ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
3145       ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
3146       ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
3147       ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
3148       ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
3149       ierr = MatConvert(coarse_sub_mat,checkmattype,MAT_REUSE_MATRIX,&coarse_sub_mat);CHKERRQ(ierr);
3150 
3151       /*PetscViewer view_out;
3152       PetscMPIInt myrank;
3153       char filename[256];
3154       MPI_Comm_rank(((PetscObject)pc)->comm,&myrank);
3155       sprintf(filename,"coarsesubmat_%04d.m",myrank);
3156       ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&view_out);CHKERRQ(ierr);
3157       ierr = PetscViewerSetFormat(view_out,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3158       ierr = MatView(coarse_sub_mat,view_out);CHKERRQ(ierr);
3159       ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);*/
3160 
3161       ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3162       ierr = PetscViewerASCIIPrintf(viewer,"Check coarse sub mat and local basis functions\n");CHKERRQ(ierr);
3163       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3164       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
3165       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
3166       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
3167       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
3168       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
3169       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
3170       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
3171       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
3172       ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3173       ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3174       ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3175       ierr = MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3176       ierr = MatNorm(TM1,NORM_INFINITY,&value);CHKERRQ(ierr);
3177       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"----------------------------------\n");CHKERRQ(ierr);
3178       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d \n",PetscGlobalRank);CHKERRQ(ierr);
3179       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"matrix error = % 1.14e\n",value);CHKERRQ(ierr);
3180       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"coarse functions errors\n");CHKERRQ(ierr);
3181       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); }
3182       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"constraints errors\n");CHKERRQ(ierr);
3183       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); }
3184       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3185       ierr = MatDestroy(&A_II);CHKERRQ(ierr);
3186       ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
3187       ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
3188       ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
3189       ierr = MatDestroy(&TM1);CHKERRQ(ierr);
3190       ierr = MatDestroy(&TM2);CHKERRQ(ierr);
3191       ierr = MatDestroy(&TM3);CHKERRQ(ierr);
3192       ierr = MatDestroy(&TM4);CHKERRQ(ierr);
3193       ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
3194       ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
3195       ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
3196       ierr = PetscFree(coarsefunctions_errors);CHKERRQ(ierr);
3197       ierr = PetscFree(constraints_errors);CHKERRQ(ierr);
3198     }
3199 
3200     /* create coarse matrix and data structures for message passing associated actual choice of coarse problem type */
3201     ierr = PCBDDCSetupCoarseEnvironment(pc,coarse_submat_vals);CHKERRQ(ierr);
3202     /* free memory */
3203     ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
3204     ierr = PetscFree(auxindices);CHKERRQ(ierr);
3205     ierr = PetscFree(nnz);CHKERRQ(ierr);
3206     if(n_vertices) {
3207       ierr = VecDestroy(&vec1_V);CHKERRQ(ierr);
3208       ierr = VecDestroy(&vec2_V);CHKERRQ(ierr);
3209       ierr = MatDestroy(&M2);CHKERRQ(ierr);
3210       ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
3211       ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
3212       ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
3213     }
3214     if(n_constraints) {
3215       ierr = VecDestroy(&vec1_C);CHKERRQ(ierr);
3216       ierr = VecDestroy(&vec2_C);CHKERRQ(ierr);
3217       ierr = MatDestroy(&M1);CHKERRQ(ierr);
3218       ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
3219     }
3220   }
3221   /* free memory */
3222   if(n_vertices) {
3223     ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
3224     ierr = ISDestroy(&is_V_local);CHKERRQ(ierr);
3225   }
3226   ierr = ISDestroy(&is_R_local);CHKERRQ(ierr);
3227 
3228   PetscFunctionReturn(0);
3229 }
3230 
3231 /* -------------------------------------------------------------------------- */
3232 
3233 #undef __FUNCT__
3234 #define __FUNCT__ "PCBDDCSetupCoarseEnvironment"
3235 static PetscErrorCode PCBDDCSetupCoarseEnvironment(PC pc,PetscScalar* coarse_submat_vals)
3236 {
3237 
3238 
3239   Mat_IS    *matis    = (Mat_IS*)pc->pmat->data;
3240   PC_BDDC   *pcbddc   = (PC_BDDC*)pc->data;
3241   PC_IS     *pcis     = (PC_IS*)pc->data;
3242   MPI_Comm  prec_comm = ((PetscObject)pc)->comm;
3243   MPI_Comm  coarse_comm;
3244 
3245   /* common to all choiches */
3246   PetscScalar *temp_coarse_mat_vals;
3247   PetscScalar *ins_coarse_mat_vals;
3248   PetscInt    *ins_local_primal_indices;
3249   PetscMPIInt *localsizes2,*localdispl2;
3250   PetscMPIInt size_prec_comm;
3251   PetscMPIInt rank_prec_comm;
3252   PetscMPIInt active_rank=MPI_PROC_NULL;
3253   PetscMPIInt master_proc=0;
3254   PetscInt    ins_local_primal_size;
3255   /* specific to MULTILEVEL_BDDC */
3256   PetscMPIInt *ranks_recv;
3257   PetscMPIInt count_recv=0;
3258   PetscMPIInt rank_coarse_proc_send_to;
3259   PetscMPIInt coarse_color = MPI_UNDEFINED;
3260   ISLocalToGlobalMapping coarse_ISLG;
3261   /* some other variables */
3262   PetscErrorCode ierr;
3263   const MatType coarse_mat_type;
3264   const PCType  coarse_pc_type;
3265   const KSPType  coarse_ksp_type;
3266   PC pc_temp;
3267   PetscInt i,j,k,bs;
3268   PetscInt max_it_coarse_ksp=1;  /* don't increase this value */
3269   /* verbose output viewer */
3270   PetscViewer viewer=pcbddc->dbg_viewer;
3271   PetscBool   dbg_flag=pcbddc->dbg_flag;
3272 
3273   PetscFunctionBegin;
3274 
3275   ins_local_primal_indices = 0;
3276   ins_coarse_mat_vals      = 0;
3277   localsizes2              = 0;
3278   localdispl2              = 0;
3279   temp_coarse_mat_vals     = 0;
3280   coarse_ISLG              = 0;
3281 
3282   ierr = MPI_Comm_size(prec_comm,&size_prec_comm);CHKERRQ(ierr);
3283   ierr = MPI_Comm_rank(prec_comm,&rank_prec_comm);CHKERRQ(ierr);
3284   ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
3285 
3286   /* Assign global numbering to coarse dofs */
3287   {
3288     PetscScalar    one=1.,zero=0.;
3289     PetscScalar    *array;
3290     PetscMPIInt    *auxlocal_primal;
3291     PetscMPIInt    *auxglobal_primal;
3292     PetscMPIInt    *all_auxglobal_primal;
3293     PetscMPIInt    *all_auxglobal_primal_dummy;
3294     PetscMPIInt    mpi_local_primal_size = (PetscMPIInt)pcbddc->local_primal_size;
3295     PetscInt       *row_cmat_indices;
3296     PetscInt       size_of_constraint;
3297     PetscScalar    coarsesum;
3298 
3299     /* Construct needed data structures for message passing */
3300     ierr = PetscMalloc(mpi_local_primal_size*sizeof(PetscMPIInt),&pcbddc->local_primal_indices);CHKERRQ(ierr);
3301     ierr = PetscMalloc(size_prec_comm*sizeof(PetscMPIInt),&pcbddc->local_primal_sizes);CHKERRQ(ierr);
3302     ierr = PetscMalloc(size_prec_comm*sizeof(PetscMPIInt),&pcbddc->local_primal_displacements);CHKERRQ(ierr);
3303     /* Gather local_primal_size information for all processes  */
3304     ierr = MPI_Allgather(&mpi_local_primal_size,1,MPIU_INT,&pcbddc->local_primal_sizes[0],1,MPIU_INT,prec_comm);CHKERRQ(ierr);
3305     pcbddc->replicated_primal_size = 0;
3306     for (i=0; i<size_prec_comm; i++) {
3307       pcbddc->local_primal_displacements[i] = pcbddc->replicated_primal_size ;
3308       pcbddc->replicated_primal_size += pcbddc->local_primal_sizes[i];
3309     }
3310     if(rank_prec_comm == 0) {
3311       /* allocate some auxiliary space */
3312       ierr = PetscMalloc(pcbddc->replicated_primal_size*sizeof(*all_auxglobal_primal),&all_auxglobal_primal);CHKERRQ(ierr);
3313       ierr = PetscMalloc(pcbddc->replicated_primal_size*sizeof(*all_auxglobal_primal_dummy),&all_auxglobal_primal_dummy);CHKERRQ(ierr);
3314     }
3315     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscMPIInt),&auxlocal_primal);CHKERRQ(ierr);
3316     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscMPIInt),&auxglobal_primal);CHKERRQ(ierr);
3317 
3318     /* First let's count coarse dofs.
3319        This code fragment assumes that the number of local constraints per connected component
3320        is not greater than the number of nodes defined for the connected component
3321        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
3322     /* auxlocal_primal      : primal indices in local nodes numbering (internal and interface) with complete queue sorted by global ordering */
3323     ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3324     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3325     for(i=0;i<pcbddc->local_primal_size;i++) {
3326       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
3327       for (j=0; j<size_of_constraint; j++) {
3328         k = row_cmat_indices[j];
3329         if( array[k] == zero ) {
3330           array[k] = one;
3331           auxlocal_primal[i] = k;
3332           break;
3333         }
3334       }
3335       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
3336     }
3337     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3338     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
3339     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3340     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3341     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3342     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3343     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3344     for(i=0;i<pcis->n;i++) { if( array[i] > zero) array[i] = one/array[i]; }
3345     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3346     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
3347     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3348     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3349     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
3350     pcbddc->coarse_size = (PetscInt) coarsesum;
3351 
3352     /* Now assign them a global numbering */
3353     /* auxglobal_primal contains indices in global nodes numbering (internal and interface) */
3354     ierr = ISLocalToGlobalMappingApply(matis->mapping,pcbddc->local_primal_size,auxlocal_primal,auxglobal_primal);CHKERRQ(ierr);
3355     /* all_auxglobal_primal contains all primal nodes indices in global nodes numbering (internal and interface) */
3356     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);
3357 
3358     /* After this block all_auxglobal_primal should contains one copy of each primal node's indices in global nodes numbering */
3359     /* It implements a function similar to PetscSortRemoveDupsInt */
3360     if(rank_prec_comm==0) {
3361       /* dummy argument since PetscSortMPIInt doesn't exist! */
3362       ierr = PetscSortMPIIntWithArray(pcbddc->replicated_primal_size,all_auxglobal_primal,all_auxglobal_primal_dummy);CHKERRQ(ierr);
3363       k=1;
3364       j=all_auxglobal_primal[0];  /* first dof in global numbering */
3365       for(i=1;i< pcbddc->replicated_primal_size ;i++) {
3366         if(j != all_auxglobal_primal[i] ) {
3367           all_auxglobal_primal[k]=all_auxglobal_primal[i];
3368           k++;
3369           j=all_auxglobal_primal[i];
3370         }
3371       }
3372     } else {
3373       ierr = PetscMalloc(pcbddc->coarse_size*sizeof(PetscMPIInt),&all_auxglobal_primal);CHKERRQ(ierr);
3374     }
3375     /* We only need to broadcast the indices from 0 to pcbddc->coarse_size. Remaning elements of array all_aux_global_primal are garbage. */
3376     ierr = MPI_Bcast(all_auxglobal_primal,pcbddc->coarse_size,MPIU_INT,0,prec_comm);CHKERRQ(ierr);
3377 
3378     /* Now get global coarse numbering of local primal nodes */
3379     for(i=0;i<pcbddc->local_primal_size;i++) {
3380       k=0;
3381       while( all_auxglobal_primal[k] != auxglobal_primal[i] ) { k++;}
3382       pcbddc->local_primal_indices[i]=k;
3383     }
3384     if(dbg_flag) {
3385       ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3386       ierr = PetscViewerASCIIPrintf(viewer,"Size of coarse problem %d\n",pcbddc->coarse_size);CHKERRQ(ierr);
3387       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3388     }
3389     /* free allocated memory */
3390     ierr = PetscFree(auxlocal_primal);CHKERRQ(ierr);
3391     ierr = PetscFree(auxglobal_primal);CHKERRQ(ierr);
3392     ierr = PetscFree(all_auxglobal_primal);CHKERRQ(ierr);
3393     if(rank_prec_comm == 0) {
3394       ierr = PetscFree(all_auxglobal_primal_dummy);CHKERRQ(ierr);
3395     }
3396   }
3397 
3398   /* adapt coarse problem type */
3399   if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC && pcbddc->active_procs < MIN_PROCS_FOR_BDDC )
3400     pcbddc->coarse_problem_type = PARALLEL_BDDC;
3401 
3402   switch(pcbddc->coarse_problem_type){
3403 
3404     case(MULTILEVEL_BDDC):   /* we define a coarse mesh where subdomains are elements */
3405     {
3406       /* we need additional variables */
3407       MetisInt   n_subdomains,n_parts,objval,ncon,faces_nvtxs;
3408       MetisInt   *metis_coarse_subdivision;
3409       MetisInt   options[METIS_NOPTIONS];
3410       PetscMPIInt size_coarse_comm,rank_coarse_comm;
3411       PetscMPIInt procs_jumps_coarse_comm;
3412       PetscMPIInt *coarse_subdivision;
3413       PetscMPIInt *total_count_recv;
3414       PetscMPIInt *total_ranks_recv;
3415       PetscMPIInt *displacements_recv;
3416       PetscMPIInt *my_faces_connectivity;
3417       PetscMPIInt *petsc_faces_adjncy;
3418       MetisInt    *faces_adjncy;
3419       MetisInt    *faces_xadj;
3420       PetscMPIInt *number_of_faces;
3421       PetscMPIInt *faces_displacements;
3422       PetscInt    *array_int;
3423       PetscMPIInt my_faces=0;
3424       PetscMPIInt total_faces=0;
3425       PetscInt    ranks_stretching_ratio;
3426 
3427       /* define some quantities */
3428       pcbddc->coarse_communications_type = SCATTERS_BDDC;
3429       coarse_mat_type = MATIS;
3430       coarse_pc_type  = PCBDDC;
3431       coarse_ksp_type  = KSPCHEBYSHEV;
3432 
3433       /* details of coarse decomposition */
3434       n_subdomains = pcbddc->active_procs;
3435       n_parts      = n_subdomains/pcbddc->coarsening_ratio;
3436       ranks_stretching_ratio = size_prec_comm/pcbddc->active_procs;
3437       procs_jumps_coarse_comm = pcbddc->coarsening_ratio*ranks_stretching_ratio;
3438 
3439       /*printf("Coarse algorithm details: \n");
3440       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));*/
3441 
3442       /* build CSR graph of subdomains' connectivity through faces */
3443       ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&array_int);CHKERRQ(ierr);
3444       ierr = PetscMemzero(array_int,pcis->n*sizeof(PetscInt));CHKERRQ(ierr);
3445       for(i=1;i<pcis->n_neigh;i++){/* i=1 so I don't count myself -> faces nodes counts to 1 */
3446         for(j=0;j<pcis->n_shared[i];j++){
3447           array_int[ pcis->shared[i][j] ]+=1;
3448         }
3449       }
3450       for(i=1;i<pcis->n_neigh;i++){
3451         for(j=0;j<pcis->n_shared[i];j++){
3452           if(array_int[ pcis->shared[i][j] ] == 1 ){
3453             my_faces++;
3454             break;
3455           }
3456         }
3457       }
3458 
3459       ierr = MPI_Reduce(&my_faces,&total_faces,1,MPIU_INT,MPI_SUM,master_proc,prec_comm);CHKERRQ(ierr);
3460       ierr = PetscMalloc (my_faces*sizeof(PetscInt),&my_faces_connectivity);CHKERRQ(ierr);
3461       my_faces=0;
3462       for(i=1;i<pcis->n_neigh;i++){
3463         for(j=0;j<pcis->n_shared[i];j++){
3464           if(array_int[ pcis->shared[i][j] ] == 1 ){
3465             my_faces_connectivity[my_faces]=pcis->neigh[i];
3466             my_faces++;
3467             break;
3468           }
3469         }
3470       }
3471       if(rank_prec_comm == master_proc) {
3472         ierr = PetscMalloc (total_faces*sizeof(PetscMPIInt),&petsc_faces_adjncy);CHKERRQ(ierr);
3473         ierr = PetscMalloc (size_prec_comm*sizeof(PetscMPIInt),&number_of_faces);CHKERRQ(ierr);
3474         ierr = PetscMalloc (total_faces*sizeof(MetisInt),&faces_adjncy);CHKERRQ(ierr);
3475         ierr = PetscMalloc ((n_subdomains+1)*sizeof(MetisInt),&faces_xadj);CHKERRQ(ierr);
3476         ierr = PetscMalloc ((size_prec_comm+1)*sizeof(PetscMPIInt),&faces_displacements);CHKERRQ(ierr);
3477       }
3478       ierr = MPI_Gather(&my_faces,1,MPIU_INT,&number_of_faces[0],1,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3479       if(rank_prec_comm == master_proc) {
3480         faces_xadj[0]=0;
3481         faces_displacements[0]=0;
3482         j=0;
3483         for(i=1;i<size_prec_comm+1;i++) {
3484           faces_displacements[i]=faces_displacements[i-1]+number_of_faces[i-1];
3485           if(number_of_faces[i-1]) {
3486             j++;
3487             faces_xadj[j]=faces_xadj[j-1]+number_of_faces[i-1];
3488           }
3489         }
3490         /*printf("The J I count is %d and should be %d\n",j,n_subdomains);
3491         printf("Total faces seem %d and should be %d\n",faces_xadj[j],total_faces);*/
3492       }
3493       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);
3494       ierr = PetscFree(my_faces_connectivity);CHKERRQ(ierr);
3495       ierr = PetscFree(array_int);CHKERRQ(ierr);
3496       if(rank_prec_comm == master_proc) {
3497         for(i=0;i<total_faces;i++) faces_adjncy[i]=(MetisInt)(petsc_faces_adjncy[i]/ranks_stretching_ratio); /* cast to MetisInt */
3498         /*printf("This is the face connectivity (actual ranks)\n");
3499         for(i=0;i<n_subdomains;i++){
3500           printf("proc %d is connected with \n",i);
3501           for(j=faces_xadj[i];j<faces_xadj[i+1];j++)
3502             printf("%d ",faces_adjncy[j]);
3503           printf("\n");
3504         }*/
3505         ierr = PetscFree(faces_displacements);CHKERRQ(ierr);
3506         ierr = PetscFree(number_of_faces);CHKERRQ(ierr);
3507         ierr = PetscFree(petsc_faces_adjncy);CHKERRQ(ierr);
3508       }
3509 
3510       if( rank_prec_comm == master_proc ) {
3511 
3512         PetscInt heuristic_for_metis=3;
3513 
3514         ncon=1;
3515         faces_nvtxs=n_subdomains;
3516         /* partition graoh induced by face connectivity */
3517         ierr = PetscMalloc (n_subdomains*sizeof(MetisInt),&metis_coarse_subdivision);CHKERRQ(ierr);
3518         ierr = METIS_SetDefaultOptions(options);
3519         /* we need a contiguous partition of the coarse mesh */
3520         options[METIS_OPTION_CONTIG]=1;
3521         options[METIS_OPTION_DBGLVL]=1;
3522         options[METIS_OPTION_NITER]=30;
3523         if(n_subdomains>n_parts*heuristic_for_metis) {
3524           options[METIS_OPTION_IPTYPE]=METIS_IPTYPE_EDGE;
3525           options[METIS_OPTION_OBJTYPE]=METIS_OBJTYPE_CUT;
3526           ierr = METIS_PartGraphKway(&faces_nvtxs,&ncon,faces_xadj,faces_adjncy,NULL,NULL,NULL,&n_parts,NULL,NULL,options,&objval,metis_coarse_subdivision);
3527         } else {
3528           ierr = METIS_PartGraphRecursive(&faces_nvtxs,&ncon,faces_xadj,faces_adjncy,NULL,NULL,NULL,&n_parts,NULL,NULL,options,&objval,metis_coarse_subdivision);
3529         }
3530         if(ierr != METIS_OK) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in METIS_PartGraphKway (metis error code %D) called from PCBDDCSetupCoarseEnvironment\n",ierr);
3531         ierr = PetscFree(faces_xadj);CHKERRQ(ierr);
3532         ierr = PetscFree(faces_adjncy);CHKERRQ(ierr);
3533         coarse_subdivision = (PetscMPIInt*)calloc(size_prec_comm,sizeof(PetscMPIInt)); /* calloc for contiguous memory since we need to scatter these values later */
3534         /* copy/cast values avoiding possible type conflicts between PETSc, MPI and METIS */
3535         for(i=0;i<size_prec_comm;i++) coarse_subdivision[i]=MPI_PROC_NULL;
3536         for(i=0;i<n_subdomains;i++)   coarse_subdivision[ranks_stretching_ratio*i]=(PetscInt)(metis_coarse_subdivision[i]);
3537         ierr = PetscFree(metis_coarse_subdivision);CHKERRQ(ierr);
3538       }
3539 
3540       /* Create new communicator for coarse problem splitting the old one */
3541       if( !(rank_prec_comm%procs_jumps_coarse_comm) && rank_prec_comm < procs_jumps_coarse_comm*n_parts ){
3542         coarse_color=0;              /* for communicator splitting */
3543         active_rank=rank_prec_comm;  /* for insertion of matrix values */
3544       }
3545       /* procs with coarse_color = MPI_UNDEFINED will have coarse_comm = MPI_COMM_NULL (from mpi standards)
3546          key = rank_prec_comm -> keep same ordering of ranks from the old to the new communicator */
3547       ierr = MPI_Comm_split(prec_comm,coarse_color,rank_prec_comm,&coarse_comm);CHKERRQ(ierr);
3548 
3549       if( coarse_color == 0 ) {
3550         ierr = MPI_Comm_size(coarse_comm,&size_coarse_comm);CHKERRQ(ierr);
3551         ierr = MPI_Comm_rank(coarse_comm,&rank_coarse_comm);CHKERRQ(ierr);
3552         /*printf("Details of coarse comm\n");
3553         printf("size = %d, myrank = %d\n",size_coarse_comm,rank_coarse_comm);
3554         printf("jumps = %d, coarse_color = %d, n_parts = %d\n",procs_jumps_coarse_comm,coarse_color,n_parts);*/
3555       } else {
3556         rank_coarse_comm = MPI_PROC_NULL;
3557       }
3558 
3559       /* master proc take care of arranging and distributing coarse informations */
3560       if(rank_coarse_comm == master_proc) {
3561         ierr = PetscMalloc (size_coarse_comm*sizeof(PetscMPIInt),&displacements_recv);CHKERRQ(ierr);
3562         /*ierr = PetscMalloc (size_coarse_comm*sizeof(PetscMPIInt),&total_count_recv);CHKERRQ(ierr);
3563           ierr = PetscMalloc (n_subdomains*sizeof(PetscMPIInt),&total_ranks_recv);CHKERRQ(ierr);*/
3564         total_count_recv = (PetscMPIInt*)calloc(size_prec_comm,sizeof(PetscMPIInt));
3565         total_ranks_recv = (PetscMPIInt*)calloc(n_subdomains,sizeof(PetscMPIInt));
3566         /* some initializations */
3567         displacements_recv[0]=0;
3568         /* PetscMemzero(total_count_recv,size_coarse_comm*sizeof(PetscMPIInt)); not needed -> calloc initializes to zero */
3569         /* count from how many processes the j-th process of the coarse decomposition will receive data */
3570         for(j=0;j<size_coarse_comm;j++)
3571           for(i=0;i<size_prec_comm;i++)
3572             if(coarse_subdivision[i]==j)
3573               total_count_recv[j]++;
3574         /* displacements needed for scatterv of total_ranks_recv */
3575         for(i=1;i<size_coarse_comm;i++) displacements_recv[i]=displacements_recv[i-1]+total_count_recv[i-1];
3576         /* Now fill properly total_ranks_recv -> each coarse process will receive the ranks (in prec_comm communicator) of its friend (sending) processes */
3577         ierr = PetscMemzero(total_count_recv,size_coarse_comm*sizeof(PetscMPIInt));CHKERRQ(ierr);
3578         for(j=0;j<size_coarse_comm;j++) {
3579           for(i=0;i<size_prec_comm;i++) {
3580             if(coarse_subdivision[i]==j) {
3581               total_ranks_recv[displacements_recv[j]+total_count_recv[j]]=i;
3582               total_count_recv[j]+=1;
3583             }
3584           }
3585         }
3586         /*for(j=0;j<size_coarse_comm;j++) {
3587           printf("process %d in new rank will receive from %d processes (original ranks follows)\n",j,total_count_recv[j]);
3588           for(i=0;i<total_count_recv[j];i++) {
3589             printf("%d ",total_ranks_recv[displacements_recv[j]+i]);
3590           }
3591           printf("\n");
3592         }*/
3593 
3594         /* identify new decomposition in terms of ranks in the old communicator */
3595         for(i=0;i<n_subdomains;i++) coarse_subdivision[ranks_stretching_ratio*i]=coarse_subdivision[ranks_stretching_ratio*i]*procs_jumps_coarse_comm;
3596         /*printf("coarse_subdivision in old end new ranks\n");
3597         for(i=0;i<size_prec_comm;i++)
3598           if(coarse_subdivision[i]!=MPI_PROC_NULL) {
3599             printf("%d=(%d %d), ",i,coarse_subdivision[i],coarse_subdivision[i]/procs_jumps_coarse_comm);
3600           } else {
3601             printf("%d=(%d %d), ",i,coarse_subdivision[i],coarse_subdivision[i]);
3602           }
3603         printf("\n");*/
3604       }
3605 
3606       /* Scatter new decomposition for send details */
3607       ierr = MPI_Scatter(&coarse_subdivision[0],1,MPIU_INT,&rank_coarse_proc_send_to,1,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3608       /* Scatter receiving details to members of coarse decomposition */
3609       if( coarse_color == 0) {
3610         ierr = MPI_Scatter(&total_count_recv[0],1,MPIU_INT,&count_recv,1,MPIU_INT,master_proc,coarse_comm);CHKERRQ(ierr);
3611         ierr = PetscMalloc (count_recv*sizeof(PetscMPIInt),&ranks_recv);CHKERRQ(ierr);
3612         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);
3613       }
3614 
3615       /*printf("I will send my matrix data to proc  %d\n",rank_coarse_proc_send_to);
3616       if(coarse_color == 0) {
3617         printf("I will receive some matrix data from %d processes (ranks follows)\n",count_recv);
3618         for(i=0;i<count_recv;i++)
3619           printf("%d ",ranks_recv[i]);
3620         printf("\n");
3621       }*/
3622 
3623       if(rank_prec_comm == master_proc) {
3624         /*ierr = PetscFree(coarse_subdivision);CHKERRQ(ierr);
3625         ierr = PetscFree(total_count_recv);CHKERRQ(ierr);
3626         ierr = PetscFree(total_ranks_recv);CHKERRQ(ierr);*/
3627         free(coarse_subdivision);
3628         free(total_count_recv);
3629         free(total_ranks_recv);
3630         ierr = PetscFree(displacements_recv);CHKERRQ(ierr);
3631       }
3632       break;
3633     }
3634 
3635     case(REPLICATED_BDDC):
3636 
3637       pcbddc->coarse_communications_type = GATHERS_BDDC;
3638       coarse_mat_type = MATSEQAIJ;
3639       coarse_pc_type  = PCLU;
3640       coarse_ksp_type  = KSPPREONLY;
3641       coarse_comm = PETSC_COMM_SELF;
3642       active_rank = rank_prec_comm;
3643       break;
3644 
3645     case(PARALLEL_BDDC):
3646 
3647       pcbddc->coarse_communications_type = SCATTERS_BDDC;
3648       coarse_mat_type = MATMPIAIJ;
3649       coarse_pc_type  = PCREDUNDANT;
3650       coarse_ksp_type  = KSPPREONLY;
3651       coarse_comm = prec_comm;
3652       active_rank = rank_prec_comm;
3653       break;
3654 
3655     case(SEQUENTIAL_BDDC):
3656       pcbddc->coarse_communications_type = GATHERS_BDDC;
3657       coarse_mat_type = MATSEQAIJ;
3658       coarse_pc_type = PCLU;
3659       coarse_ksp_type  = KSPPREONLY;
3660       coarse_comm = PETSC_COMM_SELF;
3661       active_rank = master_proc;
3662       break;
3663   }
3664 
3665   switch(pcbddc->coarse_communications_type){
3666 
3667     case(SCATTERS_BDDC):
3668       {
3669         if(pcbddc->coarse_problem_type==MULTILEVEL_BDDC) {
3670 
3671           PetscMPIInt send_size;
3672           PetscInt    *aux_ins_indices;
3673           PetscInt    ii,jj;
3674           MPI_Request *requests;
3675 
3676           /* allocate auxiliary space */
3677           ierr = PetscMalloc (pcbddc->replicated_primal_size*sizeof(PetscMPIInt),&pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
3678           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);
3679           ierr = PetscMalloc ( pcbddc->coarse_size*sizeof(PetscInt),&aux_ins_indices);CHKERRQ(ierr);
3680           ierr = PetscMemzero(aux_ins_indices,pcbddc->coarse_size*sizeof(PetscInt));CHKERRQ(ierr);
3681           /* allocate stuffs for message massing */
3682           ierr = PetscMalloc ( (count_recv+1)*sizeof(MPI_Request),&requests);CHKERRQ(ierr);
3683           for(i=0;i<count_recv+1;i++) requests[i]=MPI_REQUEST_NULL;
3684           ierr = PetscMalloc ( count_recv*sizeof(PetscMPIInt),&localsizes2);CHKERRQ(ierr);
3685           ierr = PetscMalloc ( count_recv*sizeof(PetscMPIInt),&localdispl2);CHKERRQ(ierr);
3686           /* fill up quantities */
3687           j=0;
3688           for(i=0;i<count_recv;i++){
3689             ii = ranks_recv[i];
3690             localsizes2[i]=pcbddc->local_primal_sizes[ii]*pcbddc->local_primal_sizes[ii];
3691             localdispl2[i]=j;
3692             j+=localsizes2[i];
3693             jj = pcbddc->local_primal_displacements[ii];
3694             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 */
3695           }
3696           /*printf("aux_ins_indices 1\n");
3697           for(i=0;i<pcbddc->coarse_size;i++)
3698             printf("%d ",aux_ins_indices[i]);
3699           printf("\n");*/
3700           /* temp_coarse_mat_vals used to store temporarly received matrix values */
3701           ierr = PetscMalloc ( j*sizeof(PetscScalar),&temp_coarse_mat_vals);CHKERRQ(ierr);
3702           /* evaluate how many values I will insert in coarse mat */
3703           ins_local_primal_size=0;
3704           for(i=0;i<pcbddc->coarse_size;i++)
3705             if(aux_ins_indices[i])
3706               ins_local_primal_size++;
3707           /* evaluate indices I will insert in coarse mat */
3708           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscInt),&ins_local_primal_indices);CHKERRQ(ierr);
3709           j=0;
3710           for(i=0;i<pcbddc->coarse_size;i++)
3711             if(aux_ins_indices[i])
3712               ins_local_primal_indices[j++]=i;
3713           /* use aux_ins_indices to realize a global to local mapping */
3714           j=0;
3715           for(i=0;i<pcbddc->coarse_size;i++){
3716             if(aux_ins_indices[i]==0){
3717               aux_ins_indices[i]=-1;
3718             } else {
3719               aux_ins_indices[i]=j;
3720               j++;
3721             }
3722           }
3723 
3724           /*printf("New details localsizes2 localdispl2\n");
3725           for(i=0;i<count_recv;i++)
3726             printf("(%d %d) ",localsizes2[i],localdispl2[i]);
3727           printf("\n");
3728           printf("aux_ins_indices 2\n");
3729           for(i=0;i<pcbddc->coarse_size;i++)
3730             printf("%d ",aux_ins_indices[i]);
3731           printf("\n");
3732           printf("ins_local_primal_indices\n");
3733           for(i=0;i<ins_local_primal_size;i++)
3734             printf("%d ",ins_local_primal_indices[i]);
3735           printf("\n");
3736           printf("coarse_submat_vals\n");
3737           for(i=0;i<pcbddc->local_primal_size;i++)
3738             for(j=0;j<pcbddc->local_primal_size;j++)
3739               printf("(%lf %d %d)\n",coarse_submat_vals[j*pcbddc->local_primal_size+i],pcbddc->local_primal_indices[i],pcbddc->local_primal_indices[j]);
3740           printf("\n");*/
3741 
3742           /* processes partecipating in coarse problem receive matrix data from their friends */
3743           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);
3744           if(rank_coarse_proc_send_to != MPI_PROC_NULL ) {
3745             send_size=pcbddc->local_primal_size*pcbddc->local_primal_size;
3746             ierr = MPI_Isend(&coarse_submat_vals[0],send_size,MPIU_SCALAR,rank_coarse_proc_send_to,666,prec_comm,&requests[count_recv]);CHKERRQ(ierr);
3747           }
3748           ierr = MPI_Waitall(count_recv+1,requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3749 
3750           /*if(coarse_color == 0) {
3751             printf("temp_coarse_mat_vals\n");
3752             for(k=0;k<count_recv;k++){
3753               printf("---- %d ----\n",ranks_recv[k]);
3754               for(i=0;i<pcbddc->local_primal_sizes[ranks_recv[k]];i++)
3755                 for(j=0;j<pcbddc->local_primal_sizes[ranks_recv[k]];j++)
3756                   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]);
3757               printf("\n");
3758             }
3759           }*/
3760           /* calculate data to insert in coarse mat */
3761           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3762           PetscMemzero(ins_coarse_mat_vals,ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar));
3763 
3764           PetscMPIInt rr,kk,lps,lpd;
3765           PetscInt row_ind,col_ind;
3766           for(k=0;k<count_recv;k++){
3767             rr = ranks_recv[k];
3768             kk = localdispl2[k];
3769             lps = pcbddc->local_primal_sizes[rr];
3770             lpd = pcbddc->local_primal_displacements[rr];
3771             /*printf("Inserting the following indices (received from %d)\n",rr);*/
3772             for(j=0;j<lps;j++){
3773               col_ind=aux_ins_indices[pcbddc->replicated_local_primal_indices[lpd+j]];
3774               for(i=0;i<lps;i++){
3775                 row_ind=aux_ins_indices[pcbddc->replicated_local_primal_indices[lpd+i]];
3776                 /*printf("%d %d\n",row_ind,col_ind);*/
3777                 ins_coarse_mat_vals[col_ind*ins_local_primal_size+row_ind]+=temp_coarse_mat_vals[kk+j*lps+i];
3778               }
3779             }
3780           }
3781           ierr = PetscFree(requests);CHKERRQ(ierr);
3782           ierr = PetscFree(aux_ins_indices);CHKERRQ(ierr);
3783           ierr = PetscFree(temp_coarse_mat_vals);CHKERRQ(ierr);
3784           if(coarse_color == 0) { ierr = PetscFree(ranks_recv);CHKERRQ(ierr); }
3785 
3786           /* create local to global mapping needed by coarse MATIS */
3787           {
3788             IS coarse_IS;
3789             if(coarse_comm != MPI_COMM_NULL ) ierr = MPI_Comm_free(&coarse_comm);CHKERRQ(ierr);
3790             coarse_comm = prec_comm;
3791             active_rank=rank_prec_comm;
3792             ierr = ISCreateGeneral(coarse_comm,ins_local_primal_size,ins_local_primal_indices,PETSC_COPY_VALUES,&coarse_IS);CHKERRQ(ierr);
3793             ierr = ISLocalToGlobalMappingCreateIS(coarse_IS,&coarse_ISLG);CHKERRQ(ierr);
3794             ierr = ISDestroy(&coarse_IS);CHKERRQ(ierr);
3795           }
3796         }
3797         if(pcbddc->coarse_problem_type==PARALLEL_BDDC) {
3798           /* arrays for values insertion */
3799           ins_local_primal_size = pcbddc->local_primal_size;
3800           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscMPIInt),&ins_local_primal_indices);CHKERRQ(ierr);
3801           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3802           for(j=0;j<ins_local_primal_size;j++){
3803             ins_local_primal_indices[j]=pcbddc->local_primal_indices[j];
3804             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];
3805           }
3806         }
3807         break;
3808 
3809     }
3810 
3811     case(GATHERS_BDDC):
3812       {
3813 
3814         PetscMPIInt mysize,mysize2;
3815 
3816         if(rank_prec_comm==active_rank) {
3817           ierr = PetscMalloc ( pcbddc->replicated_primal_size*sizeof(PetscMPIInt),&pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
3818           pcbddc->replicated_local_primal_values = (PetscScalar*)calloc(pcbddc->replicated_primal_size,sizeof(PetscScalar));
3819           ierr = PetscMalloc ( size_prec_comm*sizeof(PetscMPIInt),&localsizes2);CHKERRQ(ierr);
3820           ierr = PetscMalloc ( size_prec_comm*sizeof(PetscMPIInt),&localdispl2);CHKERRQ(ierr);
3821           /* arrays for values insertion */
3822           ins_local_primal_size = pcbddc->coarse_size;
3823           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscMPIInt),&ins_local_primal_indices);CHKERRQ(ierr);
3824           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3825           for(i=0;i<size_prec_comm;i++) localsizes2[i]=pcbddc->local_primal_sizes[i]*pcbddc->local_primal_sizes[i];
3826           localdispl2[0]=0;
3827           for(i=1;i<size_prec_comm;i++) localdispl2[i]=localsizes2[i-1]+localdispl2[i-1];
3828           j=0;
3829           for(i=0;i<size_prec_comm;i++) j+=localsizes2[i];
3830           ierr = PetscMalloc ( j*sizeof(PetscScalar),&temp_coarse_mat_vals);CHKERRQ(ierr);
3831         }
3832 
3833         mysize=pcbddc->local_primal_size;
3834         mysize2=pcbddc->local_primal_size*pcbddc->local_primal_size;
3835         if(pcbddc->coarse_problem_type == SEQUENTIAL_BDDC){
3836           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);
3837           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);
3838         } else {
3839           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);
3840           ierr = MPI_Allgatherv(&coarse_submat_vals[0],mysize2,MPIU_SCALAR,&temp_coarse_mat_vals[0],localsizes2,localdispl2,MPIU_SCALAR,prec_comm);CHKERRQ(ierr);
3841         }
3842 
3843   /* free data structures no longer needed and allocate some space which will be needed in BDDC application */
3844         if(rank_prec_comm==active_rank) {
3845           PetscInt offset,offset2,row_ind,col_ind;
3846           for(j=0;j<ins_local_primal_size;j++){
3847             ins_local_primal_indices[j]=j;
3848             for(i=0;i<ins_local_primal_size;i++) ins_coarse_mat_vals[j*ins_local_primal_size+i]=0.0;
3849           }
3850           for(k=0;k<size_prec_comm;k++){
3851             offset=pcbddc->local_primal_displacements[k];
3852             offset2=localdispl2[k];
3853             for(j=0;j<pcbddc->local_primal_sizes[k];j++){
3854               col_ind=pcbddc->replicated_local_primal_indices[offset+j];
3855               for(i=0;i<pcbddc->local_primal_sizes[k];i++){
3856                 row_ind=pcbddc->replicated_local_primal_indices[offset+i];
3857                 ins_coarse_mat_vals[col_ind*pcbddc->coarse_size+row_ind]+=temp_coarse_mat_vals[offset2+j*pcbddc->local_primal_sizes[k]+i];
3858               }
3859             }
3860           }
3861         }
3862         break;
3863       }/* switch on coarse problem and communications associated with finished */
3864   }
3865 
3866   /* Now create and fill up coarse matrix */
3867   if( rank_prec_comm == active_rank ) {
3868     if(pcbddc->coarse_problem_type != MULTILEVEL_BDDC) {
3869       ierr = MatCreate(coarse_comm,&pcbddc->coarse_mat);CHKERRQ(ierr);
3870       ierr = MatSetSizes(pcbddc->coarse_mat,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size);CHKERRQ(ierr);
3871       ierr = MatSetType(pcbddc->coarse_mat,coarse_mat_type);CHKERRQ(ierr);
3872       ierr = MatSetUp(pcbddc->coarse_mat);CHKERRQ(ierr);
3873       ierr = MatSetOption(pcbddc->coarse_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr); /* local values stored in column major */
3874       ierr = MatSetOption(pcbddc->coarse_mat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3875     } else {
3876       Mat matis_coarse_local_mat;
3877       /* remind bs */
3878       ierr = MatCreateIS(coarse_comm,bs,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_ISLG,&pcbddc->coarse_mat);CHKERRQ(ierr);
3879       ierr = MatSetUp(pcbddc->coarse_mat);CHKERRQ(ierr);
3880       ierr = MatISGetLocalMat(pcbddc->coarse_mat,&matis_coarse_local_mat);CHKERRQ(ierr);
3881       ierr = MatSetUp(matis_coarse_local_mat);CHKERRQ(ierr);
3882       ierr = MatSetOption(matis_coarse_local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr); /* local values stored in column major */
3883       ierr = MatSetOption(matis_coarse_local_mat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3884     }
3885     ierr = MatSetOption(pcbddc->coarse_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
3886     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);
3887     ierr = MatAssemblyBegin(pcbddc->coarse_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3888     ierr = MatAssemblyEnd(pcbddc->coarse_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3889 
3890     /*  PetscViewer view_out;
3891       ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,"coarsematfull.m",&view_out);CHKERRQ(ierr);
3892       ierr = PetscViewerSetFormat(view_out,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3893       ierr = MatView(pcbddc->coarse_mat,view_out);CHKERRQ(ierr);
3894       ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);*/
3895 
3896     ierr = MatGetVecs(pcbddc->coarse_mat,&pcbddc->coarse_vec,&pcbddc->coarse_rhs);CHKERRQ(ierr);
3897     /* Preconditioner for coarse problem */
3898     ierr = KSPCreate(coarse_comm,&pcbddc->coarse_ksp);CHKERRQ(ierr);
3899     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3900     ierr = KSPSetOperators(pcbddc->coarse_ksp,pcbddc->coarse_mat,pcbddc->coarse_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
3901     ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,max_it_coarse_ksp);CHKERRQ(ierr);
3902     ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3903     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3904     ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3905     /* Allow user's customization */
3906     ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,"coarse_");CHKERRQ(ierr);
3907     ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3908     /* Set Up PC for coarse problem BDDC */
3909     if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC) {
3910       if(dbg_flag) {
3911         ierr = PetscViewerASCIIPrintf(viewer,"----------------Setting up a new level---------------\n");CHKERRQ(ierr);
3912         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3913       }
3914       ierr = PCBDDCSetCoarseProblemType(pc_temp,MULTILEVEL_BDDC);CHKERRQ(ierr);
3915     }
3916     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3917     if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC) {
3918       if(dbg_flag) {
3919         ierr = PetscViewerASCIIPrintf(viewer,"----------------New level set------------------------\n");CHKERRQ(ierr);
3920         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3921       }
3922     }
3923   }
3924   if(pcbddc->coarse_communications_type == SCATTERS_BDDC) {
3925      IS local_IS,global_IS;
3926      ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size,0,1,&local_IS);CHKERRQ(ierr);
3927      ierr = ISCreateGeneral(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_indices,PETSC_COPY_VALUES,&global_IS);CHKERRQ(ierr);
3928      ierr = VecScatterCreate(pcbddc->vec1_P,local_IS,pcbddc->coarse_vec,global_IS,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3929      ierr = ISDestroy(&local_IS);CHKERRQ(ierr);
3930      ierr = ISDestroy(&global_IS);CHKERRQ(ierr);
3931   }
3932 
3933 
3934   /* Evaluate condition number of coarse problem for cheby (and verbose output if requested) */
3935   if( pcbddc->coarse_problem_type == MULTILEVEL_BDDC && rank_prec_comm == active_rank ) {
3936     PetscScalar m_one=-1.0;
3937     PetscReal   infty_error,lambda_min,lambda_max,kappa_2;
3938     const KSPType check_ksp_type=KSPGMRES;
3939 
3940     /* change coarse ksp object to an iterative method suitable for extreme eigenvalues' estimation */
3941     ierr = KSPSetType(pcbddc->coarse_ksp,check_ksp_type);CHKERRQ(ierr);
3942     ierr = KSPSetComputeSingularValues(pcbddc->coarse_ksp,PETSC_TRUE);CHKERRQ(ierr);
3943     ierr = KSPSetTolerances(pcbddc->coarse_ksp,1.e-8,1.e-8,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3944     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3945     ierr = VecSetRandom(pcbddc->coarse_rhs,PETSC_NULL);CHKERRQ(ierr);
3946     ierr = MatMult(pcbddc->coarse_mat,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
3947     ierr = MatMult(pcbddc->coarse_mat,pcbddc->coarse_vec,pcbddc->coarse_rhs);CHKERRQ(ierr);
3948     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_rhs);CHKERRQ(ierr);
3949     ierr = KSPComputeExtremeSingularValues(pcbddc->coarse_ksp,&lambda_max,&lambda_min);CHKERRQ(ierr);
3950     if(dbg_flag) {
3951       kappa_2=lambda_max/lambda_min;
3952       ierr = KSPGetIterationNumber(pcbddc->coarse_ksp,&k);CHKERRQ(ierr);
3953       ierr = VecAXPY(pcbddc->coarse_rhs,m_one,pcbddc->coarse_vec);CHKERRQ(ierr);
3954       ierr = VecNorm(pcbddc->coarse_rhs,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3955       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);
3956       ierr = PetscViewerASCIIPrintf(viewer,"Coarse problem eigenvalues: % 1.14e %1.14e\n",lambda_min,lambda_max);CHKERRQ(ierr);
3957       ierr = PetscViewerASCIIPrintf(viewer,"Coarse problem infty_error: %1.14e\n",infty_error);CHKERRQ(ierr);
3958     }
3959     /* restore coarse ksp to default values */
3960     ierr = KSPSetComputeSingularValues(pcbddc->coarse_ksp,PETSC_FALSE);CHKERRQ(ierr);
3961     ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3962     ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3963     ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,max_it_coarse_ksp);CHKERRQ(ierr);
3964     ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3965     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3966   }
3967 
3968   /* free data structures no longer needed */
3969   if(coarse_ISLG)                { ierr = ISLocalToGlobalMappingDestroy(&coarse_ISLG);CHKERRQ(ierr); }
3970   if(ins_local_primal_indices)   { ierr = PetscFree(ins_local_primal_indices);CHKERRQ(ierr);  }
3971   if(ins_coarse_mat_vals)        { ierr = PetscFree(ins_coarse_mat_vals);CHKERRQ(ierr);}
3972   if(localsizes2)                { ierr = PetscFree(localsizes2);CHKERRQ(ierr);}
3973   if(localdispl2)                { ierr = PetscFree(localdispl2);CHKERRQ(ierr);}
3974   if(temp_coarse_mat_vals)       { ierr = PetscFree(temp_coarse_mat_vals);CHKERRQ(ierr);}
3975 
3976   PetscFunctionReturn(0);
3977 }
3978 
3979 #undef __FUNCT__
3980 #define __FUNCT__ "PCBDDCManageLocalBoundaries"
3981 static PetscErrorCode PCBDDCManageLocalBoundaries(PC pc)
3982 {
3983 
3984   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
3985   PC_IS         *pcis = (PC_IS*)pc->data;
3986   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
3987   PCBDDCGraph mat_graph=pcbddc->mat_graph;
3988   PetscInt    *queue_in_global_numbering,*is_indices,*auxis;
3989   PetscInt    bs,ierr,i,j,s,k,iindex,neumann_bsize,dirichlet_bsize;
3990   PetscInt    total_counts,nodes_touched,where_values=1,vertex_size;
3991   PetscMPIInt adapt_interface=0,adapt_interface_reduced=0,NEUMANNCNT=0;
3992   PetscBool   same_set;
3993   MPI_Comm    interface_comm=((PetscObject)pc)->comm;
3994   PetscBool   use_faces=PETSC_FALSE,use_edges=PETSC_FALSE;
3995   const PetscInt *neumann_nodes;
3996   const PetscInt *dirichlet_nodes;
3997   IS          used_IS,*custom_ISForDofs;
3998   PetscScalar *array;
3999   PetscScalar *array2;
4000   PetscViewer viewer=pcbddc->dbg_viewer;
4001 
4002   PetscFunctionBegin;
4003   /* Setup local adjacency graph */
4004   mat_graph->nvtxs=pcis->n;
4005   if(!mat_graph->xadj) { NEUMANNCNT = 1; }
4006   ierr = PCBDDCSetupLocalAdjacencyGraph(pc);CHKERRQ(ierr);
4007   i = mat_graph->nvtxs;
4008   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);
4009   ierr = PetscMalloc2(i,PetscInt,&mat_graph->which_dof,i,PetscBool,&mat_graph->touched);CHKERRQ(ierr);
4010   ierr = PetscMalloc(i*sizeof(PetscInt),&queue_in_global_numbering);CHKERRQ(ierr);
4011   ierr = PetscMemzero(mat_graph->where,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4012   ierr = PetscMemzero(mat_graph->count,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4013   ierr = PetscMemzero(mat_graph->which_dof,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4014   ierr = PetscMemzero(mat_graph->queue,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4015   ierr = PetscMemzero(mat_graph->cptr,(mat_graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
4016 
4017   /* Setting dofs splitting in mat_graph->which_dof
4018      Get information about dofs' splitting if provided by the user
4019      Otherwise it assumes a constant block size */
4020   vertex_size=0;
4021   if(!pcbddc->n_ISForDofs) {
4022     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
4023     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
4024     for(i=0;i<bs;i++) {
4025       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
4026     }
4027     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
4028     vertex_size=1;
4029     /* remove my references to IS objects */
4030     for(i=0;i<bs;i++) {
4031       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
4032     }
4033     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
4034   }
4035   for(i=0;i<pcbddc->n_ISForDofs;i++) {
4036     ierr = ISGetSize(pcbddc->ISForDofs[i],&k);CHKERRQ(ierr);
4037     ierr = ISGetIndices(pcbddc->ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
4038     for(j=0;j<k;j++) {
4039       mat_graph->which_dof[is_indices[j]]=i;
4040     }
4041     ierr = ISRestoreIndices(pcbddc->ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
4042   }
4043   /* use mat block size as vertex size if it has not yet set */
4044   if(!vertex_size) {
4045     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
4046   }
4047 
4048   /* count number of neigh per node */
4049   total_counts=0;
4050   for(i=1;i<pcis->n_neigh;i++){
4051     s=pcis->n_shared[i];
4052     total_counts+=s;
4053     for(j=0;j<s;j++){
4054       mat_graph->count[pcis->shared[i][j]] += 1;
4055     }
4056   }
4057   /* Take into account Neumann data -> it increments number of sharing subdomains for nodes lying on the interface */
4058   ierr = PCBDDCGetNeumannBoundaries(pc,&used_IS);CHKERRQ(ierr);
4059   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
4060   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4061   if(used_IS) {
4062     ierr = ISGetSize(used_IS,&neumann_bsize);CHKERRQ(ierr);
4063     ierr = ISGetIndices(used_IS,&neumann_nodes);CHKERRQ(ierr);
4064     for(i=0;i<neumann_bsize;i++){
4065       iindex = neumann_nodes[i];
4066       if(mat_graph->count[iindex] > NEUMANNCNT && array[iindex]==0.0){
4067         mat_graph->count[iindex]+=1;
4068         total_counts++;
4069         array[iindex]=array[iindex]+1.0;
4070       } else if(array[iindex]>0.0) {
4071         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);
4072       }
4073     }
4074   }
4075   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4076   /* allocate space for storing the set of neighbours for each node */
4077   ierr = PetscMalloc(mat_graph->nvtxs*sizeof(PetscInt*),&mat_graph->neighbours_set);CHKERRQ(ierr);
4078   if(mat_graph->nvtxs) { ierr = PetscMalloc(total_counts*sizeof(PetscInt),&mat_graph->neighbours_set[0]);CHKERRQ(ierr); }
4079   for(i=1;i<mat_graph->nvtxs;i++) mat_graph->neighbours_set[i]=mat_graph->neighbours_set[i-1]+mat_graph->count[i-1];
4080   ierr = PetscMemzero(mat_graph->count,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4081   for(i=1;i<pcis->n_neigh;i++){
4082     s=pcis->n_shared[i];
4083     for(j=0;j<s;j++) {
4084       k=pcis->shared[i][j];
4085       mat_graph->neighbours_set[k][mat_graph->count[k]] = pcis->neigh[i];
4086       mat_graph->count[k]+=1;
4087     }
4088   }
4089   /* Check consistency of Neumann nodes */
4090   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4091   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4092   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4093   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4094   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4095   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4096   /* set -1 fake neighbour to mimic Neumann boundary */
4097   if(used_IS) {
4098     for(i=0;i<neumann_bsize;i++){
4099       iindex = neumann_nodes[i];
4100       if(mat_graph->count[iindex] > NEUMANNCNT){
4101         if(mat_graph->count[iindex]+1 != (PetscInt)array[iindex]) {
4102           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]);
4103         }
4104         mat_graph->neighbours_set[iindex][mat_graph->count[iindex]] = -1;
4105         mat_graph->count[iindex]+=1;
4106       }
4107     }
4108     ierr = ISRestoreIndices(used_IS,&neumann_nodes);CHKERRQ(ierr);
4109   }
4110   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4111   /* sort set of sharing subdomains */
4112   for(i=0;i<mat_graph->nvtxs;i++) { ierr = PetscSortInt(mat_graph->count[i],mat_graph->neighbours_set[i]);CHKERRQ(ierr); }
4113   /* remove interior nodes and dirichlet boundary nodes from the next search into the graph */
4114   for(i=0;i<mat_graph->nvtxs;i++){mat_graph->touched[i]=PETSC_FALSE;}
4115   nodes_touched=0;
4116   ierr = PCBDDCGetDirichletBoundaries(pc,&used_IS);CHKERRQ(ierr);
4117   ierr = VecSet(pcis->vec2_N,0.0);CHKERRQ(ierr);
4118   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4119   ierr = VecGetArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4120   if(used_IS) {
4121     ierr = ISGetSize(used_IS,&dirichlet_bsize);CHKERRQ(ierr);
4122     if(dirichlet_bsize && matis->pure_neumann) {
4123       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Dirichlet boundaries are intended to be used with matrices with zeroed rows!\n");
4124     }
4125     ierr = ISGetIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4126     for(i=0;i<dirichlet_bsize;i++){
4127       iindex=dirichlet_nodes[i];
4128       if(mat_graph->count[iindex] && !mat_graph->touched[iindex]) {
4129         if(array[iindex]>0.0) {
4130           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);
4131         }
4132         mat_graph->touched[iindex]=PETSC_TRUE;
4133         mat_graph->where[iindex]=0;
4134         nodes_touched++;
4135         array2[iindex]=array2[iindex]+1.0;
4136       }
4137     }
4138     ierr = ISRestoreIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4139   }
4140   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4141   ierr = VecRestoreArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4142   /* Check consistency of Dirichlet nodes */
4143   ierr = VecSet(pcis->vec1_N,1.0);CHKERRQ(ierr);
4144   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4145   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4146   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4147   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4148   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4149   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4150   ierr = VecScatterBegin(matis->ctx,pcis->vec2_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4151   ierr = VecScatterEnd  (matis->ctx,pcis->vec2_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4152   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4153   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4154   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4155   ierr = VecGetArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4156   if(used_IS) {
4157     ierr = ISGetSize(used_IS,&dirichlet_bsize);CHKERRQ(ierr);
4158     ierr = ISGetIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4159     for(i=0;i<dirichlet_bsize;i++){
4160       iindex=dirichlet_nodes[i];
4161       if(array[iindex]>1.0 && array[iindex]!=array2[iindex] ) {
4162          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]);
4163       }
4164     }
4165     ierr = ISRestoreIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4166   }
4167   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4168   ierr = VecRestoreArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4169 
4170   for(i=0;i<mat_graph->nvtxs;i++){
4171     if(!mat_graph->count[i]){  /* interior nodes */
4172       mat_graph->touched[i]=PETSC_TRUE;
4173       mat_graph->where[i]=0;
4174       nodes_touched++;
4175     }
4176   }
4177   mat_graph->ncmps = 0;
4178   i=0;
4179   while(nodes_touched<mat_graph->nvtxs) {
4180     /*  find first untouched node in local ordering */
4181     while(mat_graph->touched[i]) i++;
4182     mat_graph->touched[i]=PETSC_TRUE;
4183     mat_graph->where[i]=where_values;
4184     nodes_touched++;
4185     /* now find all other nodes having the same set of sharing subdomains */
4186     for(j=i+1;j<mat_graph->nvtxs;j++){
4187       /* check for same number of sharing subdomains and dof number */
4188       if(!mat_graph->touched[j] && mat_graph->count[i]==mat_graph->count[j] && mat_graph->which_dof[i] == mat_graph->which_dof[j] ){
4189         /* check for same set of sharing subdomains */
4190         same_set=PETSC_TRUE;
4191         for(k=0;k<mat_graph->count[j];k++){
4192           if(mat_graph->neighbours_set[i][k]!=mat_graph->neighbours_set[j][k]) {
4193             same_set=PETSC_FALSE;
4194           }
4195         }
4196         /* I found a friend of mine */
4197         if(same_set) {
4198           mat_graph->where[j]=where_values;
4199           mat_graph->touched[j]=PETSC_TRUE;
4200           nodes_touched++;
4201         }
4202       }
4203     }
4204     where_values++;
4205   }
4206   where_values--; if(where_values<0) where_values=0;
4207   ierr = PetscMalloc(where_values*sizeof(PetscMPIInt),&mat_graph->where_ncmps);CHKERRQ(ierr);
4208   /* Find connected components defined on the shared interface */
4209   if(where_values) {
4210     ierr = PCBDDCFindConnectedComponents(mat_graph, where_values);
4211     /* For consistency among neughbouring procs, I need to sort (by global ordering) each connected component */
4212     for(i=0;i<mat_graph->ncmps;i++) {
4213       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);
4214       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);
4215     }
4216   }
4217   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
4218   for(i=0;i<where_values;i++) {
4219     /* We are not sure that two connected components will be the same among subdomains sharing a subset of local interface */
4220     if(mat_graph->where_ncmps[i]>1) {
4221       adapt_interface=1;
4222       break;
4223     }
4224   }
4225   ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_INT,MPI_LOR,interface_comm);CHKERRQ(ierr);
4226   if(pcbddc->dbg_flag && adapt_interface_reduced) {
4227     ierr = PetscViewerASCIIPrintf(viewer,"Interface adapted\n");CHKERRQ(ierr);
4228     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
4229   }
4230   if(where_values && adapt_interface_reduced) {
4231 
4232     PetscInt sum_requests=0,my_rank;
4233     PetscInt buffer_size,start_of_recv,size_of_recv,start_of_send;
4234     PetscInt temp_buffer_size,ins_val,global_where_counter;
4235     PetscInt *cum_recv_counts;
4236     PetscInt *where_to_nodes_indices;
4237     PetscInt *petsc_buffer;
4238     PetscMPIInt *recv_buffer;
4239     PetscMPIInt *recv_buffer_where;
4240     PetscMPIInt *send_buffer;
4241     PetscMPIInt size_of_send;
4242     PetscInt *sizes_of_sends;
4243     MPI_Request *send_requests;
4244     MPI_Request *recv_requests;
4245     PetscInt *where_cc_adapt;
4246     PetscInt **temp_buffer;
4247     PetscInt *nodes_to_temp_buffer_indices;
4248     PetscInt *add_to_where;
4249 
4250     ierr = MPI_Comm_rank(interface_comm,&my_rank);CHKERRQ(ierr);
4251     ierr = PetscMalloc((where_values+1)*sizeof(PetscInt),&cum_recv_counts);CHKERRQ(ierr);
4252     ierr = PetscMemzero(cum_recv_counts,(where_values+1)*sizeof(PetscInt));CHKERRQ(ierr);
4253     ierr = PetscMalloc(where_values*sizeof(PetscInt),&where_to_nodes_indices);CHKERRQ(ierr);
4254     /* first count how many neighbours per connected component I will receive from */
4255     cum_recv_counts[0]=0;
4256     for(i=1;i<where_values+1;i++){
4257       j=0;
4258       while(mat_graph->where[j] != i) j++;
4259       where_to_nodes_indices[i-1]=j;
4260       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  */
4261       else { cum_recv_counts[i]=cum_recv_counts[i-1]+mat_graph->count[j]-1; }
4262     }
4263     buffer_size=2*cum_recv_counts[where_values]+mat_graph->nvtxs;
4264     ierr = PetscMalloc(2*cum_recv_counts[where_values]*sizeof(PetscMPIInt),&recv_buffer_where);CHKERRQ(ierr);
4265     ierr = PetscMalloc(buffer_size*sizeof(PetscMPIInt),&send_buffer);CHKERRQ(ierr);
4266     ierr = PetscMalloc(cum_recv_counts[where_values]*sizeof(MPI_Request),&send_requests);CHKERRQ(ierr);
4267     ierr = PetscMalloc(cum_recv_counts[where_values]*sizeof(MPI_Request),&recv_requests);CHKERRQ(ierr);
4268     for(i=0;i<cum_recv_counts[where_values];i++) {
4269       send_requests[i]=MPI_REQUEST_NULL;
4270       recv_requests[i]=MPI_REQUEST_NULL;
4271     }
4272     /* exchange with my neighbours the number of my connected components on the shared interface */
4273     for(i=0;i<where_values;i++){
4274       j=where_to_nodes_indices[i];
4275       k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4276       for(;k<mat_graph->count[j];k++){
4277         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);
4278         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);
4279         sum_requests++;
4280       }
4281     }
4282     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4283     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4284     /* determine the connected component I need to adapt */
4285     ierr = PetscMalloc(where_values*sizeof(PetscInt),&where_cc_adapt);CHKERRQ(ierr);
4286     ierr = PetscMemzero(where_cc_adapt,where_values*sizeof(PetscInt));CHKERRQ(ierr);
4287     for(i=0;i<where_values;i++){
4288       for(j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
4289         /* The first condition is natural (i.e someone has a different number of cc than me), the second one is just to be safe */
4290         if( mat_graph->where_ncmps[i]!=recv_buffer_where[j] || mat_graph->where_ncmps[i] > 1 ) {
4291           where_cc_adapt[i]=PETSC_TRUE;
4292           break;
4293         }
4294       }
4295     }
4296     /* now get from neighbours their ccs (in global numbering) and adapt them (in case it is needed) */
4297     /* first determine how much data to send (size of each queue plus the global indices) and communicate it to neighbours */
4298     ierr = PetscMalloc(where_values*sizeof(PetscInt),&sizes_of_sends);CHKERRQ(ierr);
4299     ierr = PetscMemzero(sizes_of_sends,where_values*sizeof(PetscInt));CHKERRQ(ierr);
4300     sum_requests=0;
4301     start_of_send=0;
4302     start_of_recv=cum_recv_counts[where_values];
4303     for(i=0;i<where_values;i++) {
4304       if(where_cc_adapt[i]) {
4305         size_of_send=0;
4306         for(j=i;j<mat_graph->ncmps;j++) {
4307           if(mat_graph->where[mat_graph->queue[mat_graph->cptr[j]]] == i+1) { /* WARNING -> where values goes from 1 to where_values included */
4308             send_buffer[start_of_send+size_of_send]=mat_graph->cptr[j+1]-mat_graph->cptr[j];
4309             size_of_send+=1;
4310             for(k=0;k<mat_graph->cptr[j+1]-mat_graph->cptr[j];k++) {
4311               send_buffer[start_of_send+size_of_send+k]=queue_in_global_numbering[mat_graph->cptr[j]+k];
4312             }
4313             size_of_send=size_of_send+mat_graph->cptr[j+1]-mat_graph->cptr[j];
4314           }
4315         }
4316         j = where_to_nodes_indices[i];
4317         k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4318         sizes_of_sends[i]=size_of_send;
4319         for(;k<mat_graph->count[j];k++){
4320           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);
4321           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);
4322           sum_requests++;
4323         }
4324         start_of_send+=size_of_send;
4325       }
4326     }
4327     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4328     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4329     buffer_size=0;
4330     for(k=0;k<sum_requests;k++) { buffer_size+=recv_buffer_where[start_of_recv+k]; }
4331     ierr = PetscMalloc(buffer_size*sizeof(PetscMPIInt),&recv_buffer);CHKERRQ(ierr);
4332     /* now exchange the data */
4333     start_of_recv=0;
4334     start_of_send=0;
4335     sum_requests=0;
4336     for(i=0;i<where_values;i++) {
4337       if(where_cc_adapt[i]) {
4338         size_of_send = sizes_of_sends[i];
4339         j = where_to_nodes_indices[i];
4340         k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4341         for(;k<mat_graph->count[j];k++){
4342           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);
4343           size_of_recv=recv_buffer_where[cum_recv_counts[where_values]+sum_requests];
4344           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);
4345           start_of_recv+=size_of_recv;
4346           sum_requests++;
4347         }
4348         start_of_send+=size_of_send;
4349       }
4350     }
4351     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4352     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4353     ierr = PetscMalloc(buffer_size*sizeof(PetscInt),&petsc_buffer);CHKERRQ(ierr);
4354     for(k=0;k<start_of_recv;k++) { petsc_buffer[k]=(PetscInt)recv_buffer[k]; }
4355     for(j=0;j<buffer_size;) {
4356        ierr = ISGlobalToLocalMappingApply(matis->mapping,IS_GTOLM_MASK,petsc_buffer[j],&petsc_buffer[j+1],&petsc_buffer[j],&petsc_buffer[j+1]);CHKERRQ(ierr);
4357        k=petsc_buffer[j]+1;
4358        j+=k;
4359     }
4360     sum_requests=cum_recv_counts[where_values];
4361     start_of_recv=0;
4362     ierr = PetscMalloc(mat_graph->nvtxs*sizeof(PetscInt),&nodes_to_temp_buffer_indices);CHKERRQ(ierr);
4363     global_where_counter=0;
4364     for(i=0;i<where_values;i++){
4365       if(where_cc_adapt[i]){
4366         temp_buffer_size=0;
4367         /* find nodes on the shared interface we need to adapt */
4368         for(j=0;j<mat_graph->nvtxs;j++){
4369           if(mat_graph->where[j]==i+1) {
4370             nodes_to_temp_buffer_indices[j]=temp_buffer_size;
4371             temp_buffer_size++;
4372           } else {
4373             nodes_to_temp_buffer_indices[j]=-1;
4374           }
4375         }
4376         /* allocate some temporary space */
4377         ierr = PetscMalloc(temp_buffer_size*sizeof(PetscInt*),&temp_buffer);CHKERRQ(ierr);
4378         ierr = PetscMalloc(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt),&temp_buffer[0]);CHKERRQ(ierr);
4379         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
4380         for(j=1;j<temp_buffer_size;j++){
4381           temp_buffer[j]=temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
4382         }
4383         /* analyze contributions from neighbouring subdomains for i-th conn comp
4384            temp buffer structure:
4385            supposing part of the interface has dimension 5 (global nodes 0,1,2,3,4)
4386            3 neighs procs with structured connected components:
4387              neigh 0: [0 1 4], [2 3];  (2 connected components)
4388              neigh 1: [0 1], [2 3 4];  (2 connected components)
4389              neigh 2: [0 4], [1], [2 3]; (3 connected components)
4390            tempbuffer (row-oriented) should be filled as:
4391              [ 0, 0, 0;
4392                0, 0, 1;
4393                1, 1, 2;
4394                1, 1, 2;
4395                0, 1, 0; ];
4396            This way we can simply recover the resulting structure account for possible intersections of ccs among neighs.
4397            The mat_graph->where array will be modified to reproduce the following 4 connected components [0], [1], [2 3], [4];
4398                                                                                                                                    */
4399         for(j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
4400           ins_val=0;
4401           size_of_recv=recv_buffer_where[sum_requests];  /* total size of recv from neighs */
4402           for(buffer_size=0;buffer_size<size_of_recv;) {  /* loop until all data from neighs has been taken into account */
4403             for(k=1;k<petsc_buffer[buffer_size+start_of_recv]+1;k++) { /* filling properly temp_buffer using data from a single recv */
4404               temp_buffer[ nodes_to_temp_buffer_indices[ petsc_buffer[ start_of_recv+buffer_size+k ] ] ][j]=ins_val;
4405             }
4406             buffer_size+=k;
4407             ins_val++;
4408           }
4409           start_of_recv+=size_of_recv;
4410           sum_requests++;
4411         }
4412         ierr = PetscMalloc(temp_buffer_size*sizeof(PetscInt),&add_to_where);CHKERRQ(ierr);
4413         ierr = PetscMemzero(add_to_where,temp_buffer_size*sizeof(PetscInt));CHKERRQ(ierr);
4414         for(j=0;j<temp_buffer_size;j++){
4415           if(!add_to_where[j]){ /* found a new cc  */
4416             global_where_counter++;
4417             add_to_where[j]=global_where_counter;
4418             for(k=j+1;k<temp_buffer_size;k++){ /* check for other nodes in new cc */
4419               same_set=PETSC_TRUE;
4420               for(s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++){
4421                 if(temp_buffer[j][s]!=temp_buffer[k][s]) {
4422                   same_set=PETSC_FALSE;
4423                   break;
4424                 }
4425               }
4426               if(same_set) add_to_where[k]=global_where_counter;
4427             }
4428           }
4429         }
4430         /* insert new data in where array */
4431         temp_buffer_size=0;
4432         for(j=0;j<mat_graph->nvtxs;j++){
4433           if(mat_graph->where[j]==i+1) {
4434             mat_graph->where[j]=where_values+add_to_where[temp_buffer_size];
4435             temp_buffer_size++;
4436           }
4437         }
4438         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
4439         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
4440         ierr = PetscFree(add_to_where);CHKERRQ(ierr);
4441       }
4442     }
4443     ierr = PetscFree(nodes_to_temp_buffer_indices);CHKERRQ(ierr);
4444     ierr = PetscFree(sizes_of_sends);CHKERRQ(ierr);
4445     ierr = PetscFree(send_requests);CHKERRQ(ierr);
4446     ierr = PetscFree(recv_requests);CHKERRQ(ierr);
4447     ierr = PetscFree(petsc_buffer);CHKERRQ(ierr);
4448     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
4449     ierr = PetscFree(recv_buffer_where);CHKERRQ(ierr);
4450     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
4451     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
4452     ierr = PetscFree(where_to_nodes_indices);CHKERRQ(ierr);
4453     ierr = PetscFree(where_cc_adapt);CHKERRQ(ierr);
4454     /* We are ready to evaluate consistent connected components on each part of the shared interface */
4455     if(global_where_counter) {
4456       for(i=0;i<mat_graph->nvtxs;i++){ mat_graph->touched[i]=PETSC_FALSE; }
4457       global_where_counter=0;
4458       for(i=0;i<mat_graph->nvtxs;i++){
4459         if(mat_graph->where[i] && !mat_graph->touched[i]) {
4460           global_where_counter++;
4461           for(j=i+1;j<mat_graph->nvtxs;j++){
4462             if(!mat_graph->touched[j] && mat_graph->where[j]==mat_graph->where[i]) {
4463               mat_graph->where[j]=global_where_counter;
4464               mat_graph->touched[j]=PETSC_TRUE;
4465             }
4466           }
4467           mat_graph->where[i]=global_where_counter;
4468           mat_graph->touched[i]=PETSC_TRUE;
4469         }
4470       }
4471       where_values=global_where_counter;
4472     }
4473     if(global_where_counter) {
4474       ierr = PetscMemzero(mat_graph->cptr,(mat_graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
4475       ierr = PetscMemzero(mat_graph->queue,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4476       ierr = PetscFree(mat_graph->where_ncmps);CHKERRQ(ierr);
4477       ierr = PetscMalloc(where_values*sizeof(PetscMPIInt),&mat_graph->where_ncmps);CHKERRQ(ierr);
4478       ierr = PCBDDCFindConnectedComponents(mat_graph, where_values);
4479       for(i=0;i<mat_graph->ncmps;i++) {
4480         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);
4481         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);
4482       }
4483     }
4484   } /* Finished adapting interface */
4485   PetscInt nfc=0;
4486   PetscInt nec=0;
4487   PetscInt nvc=0;
4488   PetscBool twodim_flag=PETSC_FALSE;
4489   for (i=0; i<mat_graph->ncmps; i++) {
4490     if( mat_graph->cptr[i+1]-mat_graph->cptr[i] > vertex_size ){
4491       if(mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]==1){ /* 1 neigh Neumann fake included */
4492         nfc++;
4493       } else { /* note that nec will be zero in 2d */
4494         nec++;
4495       }
4496     } else {
4497       nvc+=mat_graph->cptr[i+1]-mat_graph->cptr[i];
4498     }
4499   }
4500 
4501   if(!nec) { /* we are in a 2d case -> no faces, only edges */
4502     nec = nfc;
4503     nfc = 0;
4504     twodim_flag = PETSC_TRUE;
4505   }
4506   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
4507   k=0;
4508   for (i=0; i<mat_graph->ncmps; i++) {
4509     j=mat_graph->cptr[i+1]-mat_graph->cptr[i];
4510     if( j > k) {
4511       k=j;
4512     }
4513     if(j<=vertex_size) {
4514       k+=vertex_size;
4515     }
4516   }
4517   ierr = PetscMalloc(k*sizeof(PetscInt),&auxis);CHKERRQ(ierr);
4518 
4519   if(!pcbddc->vertices_flag && !pcbddc->edges_flag) {
4520     ierr = PetscMalloc(nfc*sizeof(IS),&pcbddc->ISForFaces);CHKERRQ(ierr);
4521     use_faces=PETSC_TRUE;
4522   }
4523   if(!pcbddc->vertices_flag && !pcbddc->faces_flag) {
4524     ierr = PetscMalloc(nec*sizeof(IS),&pcbddc->ISForEdges);CHKERRQ(ierr);
4525     use_edges=PETSC_TRUE;
4526   }
4527   nfc=0;
4528   nec=0;
4529   for (i=0; i<mat_graph->ncmps; i++) {
4530     if( mat_graph->cptr[i+1]-mat_graph->cptr[i] > vertex_size ){
4531       for(j=0;j<mat_graph->cptr[i+1]-mat_graph->cptr[i];j++) {
4532         auxis[j]=mat_graph->queue[mat_graph->cptr[i]+j];
4533       }
4534       if(mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]==1){
4535         if(twodim_flag) {
4536           if(use_edges) {
4537             ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForEdges[nec]);CHKERRQ(ierr);
4538             nec++;
4539           }
4540         } else {
4541           if(use_faces) {
4542             ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForFaces[nfc]);CHKERRQ(ierr);
4543             nfc++;
4544           }
4545         }
4546       } else {
4547         if(use_edges) {
4548           ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForEdges[nec]);CHKERRQ(ierr);
4549           nec++;
4550         }
4551       }
4552     }
4553   }
4554   pcbddc->n_ISForFaces=nfc;
4555   pcbddc->n_ISForEdges=nec;
4556   nvc=0;
4557   if( !pcbddc->constraints_flag ) {
4558     for (i=0; i<mat_graph->ncmps; i++) {
4559       if( mat_graph->cptr[i+1]-mat_graph->cptr[i] <= vertex_size ){
4560         for( j=mat_graph->cptr[i];j<mat_graph->cptr[i+1];j++) {
4561           auxis[nvc]=mat_graph->queue[j];
4562           nvc++;
4563         }
4564       }
4565     }
4566   }
4567   /* sort vertex set (by local ordering) */
4568   ierr = PetscSortInt(nvc,auxis);CHKERRQ(ierr);
4569   ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,auxis,PETSC_COPY_VALUES,&pcbddc->ISForVertices);CHKERRQ(ierr);
4570 
4571   if(pcbddc->dbg_flag) {
4572 
4573     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4574     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Details from PCBDDCManageLocalBoundaries for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
4575     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4576 /*    ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Graph (adjacency structure) of local Neumann mat\n");CHKERRQ(ierr);
4577     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4578     for(i=0;i<mat_graph->nvtxs;i++) {
4579       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Nodes connected to node number %d are %d\n",i,mat_graph->xadj[i+1]-mat_graph->xadj[i]);CHKERRQ(ierr);
4580       for(j=mat_graph->xadj[i];j<mat_graph->xadj[i+1];j++){
4581         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d ",mat_graph->adjncy[j]);CHKERRQ(ierr);
4582       }
4583       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n--------------------------------------------------------------\n");CHKERRQ(ierr);
4584     }*/
4585     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Matrix graph has %d connected components", mat_graph->ncmps);CHKERRQ(ierr);
4586     for(i=0;i<mat_graph->ncmps;i++) {
4587       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\nDetails for connected component number %02d: size %04d, count %01d. Nodes follow.\n",
4588              i,mat_graph->cptr[i+1]-mat_graph->cptr[i],mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]);CHKERRQ(ierr);
4589       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"subdomains: ");
4590       for (j=0;j<mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]; j++) {
4591         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d ",mat_graph->neighbours_set[mat_graph->queue[mat_graph->cptr[i]]][j]);
4592       }
4593       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");
4594       for (j=mat_graph->cptr[i]; j<mat_graph->cptr[i+1]; j++){
4595         /* ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d (%d), ",queue_in_global_numbering[j],mat_graph->queue[j]);CHKERRQ(ierr); */
4596         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d, ",mat_graph->queue[j]);CHKERRQ(ierr);
4597       }
4598     }
4599     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n--------------------------------------------------------------\n");CHKERRQ(ierr);
4600     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local vertices\n",PetscGlobalRank,nvc);CHKERRQ(ierr);
4601     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local faces\n",PetscGlobalRank,nfc);CHKERRQ(ierr);
4602     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local edges\n",PetscGlobalRank,nec);CHKERRQ(ierr);
4603     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
4604   }
4605 
4606   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
4607   ierr = PetscFree(auxis);CHKERRQ(ierr);
4608   PetscFunctionReturn(0);
4609 
4610 }
4611 
4612 /* -------------------------------------------------------------------------- */
4613 
4614 /* The following code has been adapted from function IsConnectedSubdomain contained
4615    in source file contig.c of METIS library (version 5.0.1)
4616    It finds connected components of each partition labeled from 1 to n_dist  */
4617 
4618 #undef __FUNCT__
4619 #define __FUNCT__ "PCBDDCFindConnectedComponents"
4620 static PetscErrorCode PCBDDCFindConnectedComponents(PCBDDCGraph graph, PetscInt n_dist )
4621 {
4622   PetscInt i, j, k, nvtxs, first, last, nleft, ncmps,pid,cum_queue,n,ncmps_pid;
4623   PetscInt *xadj, *adjncy, *where, *queue;
4624   PetscInt *cptr;
4625   PetscBool *touched;
4626 
4627   PetscFunctionBegin;
4628 
4629   nvtxs   = graph->nvtxs;
4630   xadj    = graph->xadj;
4631   adjncy  = graph->adjncy;
4632   where   = graph->where;
4633   touched = graph->touched;
4634   queue   = graph->queue;
4635   cptr    = graph->cptr;
4636 
4637   for (i=0; i<nvtxs; i++)
4638     touched[i] = PETSC_FALSE;
4639 
4640   cum_queue=0;
4641   ncmps=0;
4642 
4643   for(n=0; n<n_dist; n++) {
4644     pid = n+1;  /* partition labeled by 0 is discarded */
4645     nleft = 0;
4646     for (i=0; i<nvtxs; i++) {
4647       if (where[i] == pid)
4648         nleft++;
4649     }
4650     for (i=0; i<nvtxs; i++) {
4651       if (where[i] == pid)
4652         break;
4653     }
4654     touched[i] = PETSC_TRUE;
4655     queue[cum_queue] = i;
4656     first = 0; last = 1;
4657     cptr[ncmps] = cum_queue;  /* This actually points to queue */
4658     ncmps_pid = 0;
4659     while (first != nleft) {
4660       if (first == last) { /* Find another starting vertex */
4661         cptr[++ncmps] = first+cum_queue;
4662         ncmps_pid++;
4663         for (i=0; i<nvtxs; i++) {
4664           if (where[i] == pid && !touched[i])
4665             break;
4666         }
4667         queue[cum_queue+last] = i;
4668         last++;
4669         touched[i] = PETSC_TRUE;
4670       }
4671       i = queue[cum_queue+first];
4672       first++;
4673       for (j=xadj[i]; j<xadj[i+1]; j++) {
4674         k = adjncy[j];
4675         if (where[k] == pid && !touched[k]) {
4676           queue[cum_queue+last] = k;
4677           last++;
4678           touched[k] = PETSC_TRUE;
4679         }
4680       }
4681     }
4682     cptr[++ncmps] = first+cum_queue;
4683     ncmps_pid++;
4684     cum_queue=cptr[ncmps];
4685     graph->where_ncmps[n] = ncmps_pid;
4686   }
4687   graph->ncmps = ncmps;
4688 
4689   PetscFunctionReturn(0);
4690 }
4691