xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 93dc3b609793c36ad3d3a530f4e276bb50cf9238)
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     if(pcbddc->n_vertices < local_primal_size) {
2430       temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
2431     }
2432     for(i=pcbddc->n_vertices;i<local_primal_size;i++) {
2433       if(change_basis[i]) {
2434         compute_submatrix = PETSC_FALSE;
2435         useksp = PETSC_FALSE;
2436         if(temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
2437           temp_constraints++;
2438           if(i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
2439             compute_submatrix = PETSC_TRUE;
2440           }
2441         }
2442         if(compute_submatrix) {
2443           if(temp_constraints > 1 || pcbddc->use_nnsp_true) {
2444             useksp = PETSC_TRUE;
2445           }
2446           size_of_constraint = temp_indices[i+1]-temp_indices[i];
2447           if(useksp) { /* experimental */
2448             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
2449             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
2450             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
2451             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,PETSC_NULL);CHKERRQ(ierr);
2452           }
2453           /* First _size_of_constraint-temp_constraints_ columns */
2454           dual_dofs = size_of_constraint-temp_constraints;
2455           start_constraint = i+1-temp_constraints;
2456           for(s=0;s<dual_dofs;s++) {
2457             is_indices[0] = s;
2458             for(j=0;j<temp_constraints;j++) {
2459               for(k=0;k<temp_constraints;k++) {
2460                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
2461               }
2462               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
2463               is_indices[j+1]=s+j+1;
2464             }
2465             Bt = temp_constraints;
2466             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2467             LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr);
2468             if ( lierr ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
2469             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2470             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
2471             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
2472             if(useksp) {
2473               /* temp mat with transposed rows and columns */
2474               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
2475               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
2476             }
2477           }
2478           if(useksp) {
2479             /* last rows of temp_mat */
2480             for(j=0;j<size_of_constraint;j++) {
2481               is_indices[j] = j;
2482             }
2483             for(s=0;s<temp_constraints;s++) {
2484               k = s + dual_dofs;
2485               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
2486             }
2487             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2488             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2489             ierr = MatGetVecs(temp_mat,&temp_vec,PETSC_NULL);CHKERRQ(ierr);
2490             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
2491             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
2492             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
2493             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
2494             for(s=0;s<temp_constraints;s++) {
2495               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
2496               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
2497               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
2498               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
2499               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
2500               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
2501               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
2502               /* last columns of change of basis matrix associated to new primal dofs */
2503               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);
2504               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
2505             }
2506             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
2507             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
2508             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2509           } else {
2510             /* last columns of change of basis matrix associated to new primal dofs */
2511             for(s=0;s<temp_constraints;s++) {
2512               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
2513               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);
2514             }
2515           }
2516           /* prepare for the next cycle */
2517           temp_constraints = 0;
2518           if(i != local_primal_size -1 ) {
2519             temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
2520           }
2521         }
2522       }
2523     }
2524     /* assembling */
2525     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2526     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2527     ierr = PetscFree(ipiv);CHKERRQ(ierr);
2528     ierr = PetscFree(is_indices);CHKERRQ(ierr);
2529   }
2530   /* free workspace no longer needed */
2531   ierr = PetscFree(rwork);CHKERRQ(ierr);
2532   ierr = PetscFree(work);CHKERRQ(ierr);
2533   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
2534   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
2535   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
2536   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2537   ierr = PetscFree(change_basis);CHKERRQ(ierr);
2538   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
2539   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
2540   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
2541   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
2542 #if defined(PETSC_MISSING_LAPACK_GESVD)
2543   ierr = PetscFree(iwork);CHKERRQ(ierr);
2544   ierr = PetscFree(ifail);CHKERRQ(ierr);
2545   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
2546 #endif
2547   for(k=0;k<nnsp_size;k++) {
2548     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
2549   }
2550   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
2551   PetscFunctionReturn(0);
2552 }
2553 /* -------------------------------------------------------------------------- */
2554 #undef __FUNCT__
2555 #define __FUNCT__ "PCBDDCCoarseSetUp"
2556 static PetscErrorCode PCBDDCCoarseSetUp(PC pc)
2557 {
2558   PetscErrorCode  ierr;
2559 
2560   PC_IS*            pcis = (PC_IS*)(pc->data);
2561   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
2562   Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
2563   Mat               change_mat_all;
2564   IS                is_R_local;
2565   IS                is_V_local;
2566   IS                is_C_local;
2567   IS                is_aux1;
2568   IS                is_aux2;
2569   const VecType     impVecType;
2570   const MatType     impMatType;
2571   PetscInt          n_R=0;
2572   PetscInt          n_D=0;
2573   PetscInt          n_B=0;
2574   PetscScalar       zero=0.0;
2575   PetscScalar       one=1.0;
2576   PetscScalar       m_one=-1.0;
2577   PetscScalar*      array;
2578   PetscScalar       *coarse_submat_vals;
2579   PetscInt          *idx_R_local;
2580   PetscInt          *idx_V_B;
2581   PetscScalar       *coarsefunctions_errors;
2582   PetscScalar       *constraints_errors;
2583   /* auxiliary indices */
2584   PetscInt i,j,k;
2585   /* for verbose output of bddc */
2586   PetscViewer       viewer=pcbddc->dbg_viewer;
2587   PetscBool         dbg_flag=pcbddc->dbg_flag;
2588   /* for counting coarse dofs */
2589   PetscInt          n_vertices,n_constraints;
2590   PetscInt          size_of_constraint;
2591   PetscInt          *row_cmat_indices;
2592   PetscScalar       *row_cmat_values;
2593   PetscInt          *vertices,*nnz,*is_indices,*temp_indices;
2594 
2595   PetscFunctionBegin;
2596   /* Set Non-overlapping dimensions */
2597   n_B = pcis->n_B; n_D = pcis->n - n_B;
2598   /* Set types for local objects needed by BDDC precondtioner */
2599   impMatType = MATSEQDENSE;
2600   impVecType = VECSEQ;
2601   /* get vertex indices from constraint matrix */
2602   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
2603   n_vertices=0;
2604   for(i=0;i<pcbddc->local_primal_size;i++) {
2605     ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
2606     if(size_of_constraint == 1) {
2607       vertices[n_vertices]=row_cmat_indices[0];
2608       n_vertices++;
2609     }
2610     ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
2611   }
2612   /* Set number of constraints */
2613   n_constraints = pcbddc->local_primal_size-n_vertices;
2614 
2615   /* vertices in boundary numbering */
2616   if(n_vertices) {
2617     ierr = VecSet(pcis->vec1_N,m_one);CHKERRQ(ierr);
2618     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2619     for (i=0; i<n_vertices; i++) { array[ vertices[i] ] = i; }
2620     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2621     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2622     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2623     ierr = PetscMalloc(n_vertices*sizeof(PetscInt),&idx_V_B);CHKERRQ(ierr);
2624     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2625     for (i=0; i<n_vertices; i++) {
2626       j=0;
2627       while (array[j] != i ) {j++;}
2628       idx_V_B[i]=j;
2629     }
2630     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2631   }
2632 
2633   /* transform local matrices if needed */
2634   if(pcbddc->usechangeofbasis) {
2635     ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2636     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2637     for(i=0;i<n_D;i++) {
2638       nnz[is_indices[i]]=1;
2639     }
2640     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2641     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2642     k=1;
2643     for(i=0;i<n_B;i++) {
2644       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
2645       nnz[is_indices[i]]=j;
2646       if( k < j) {
2647         k = j;
2648       }
2649       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
2650     }
2651     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2652     /* assemble change of basis matrix on the whole set of local dofs */
2653     ierr = PetscMalloc(k*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
2654     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
2655     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
2656     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
2657     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
2658     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2659     for(i=0;i<n_D;i++) {
2660       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
2661     }
2662     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2663     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2664     for(i=0;i<n_B;i++) {
2665       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2666       for(k=0;k<j;k++) {
2667         temp_indices[k]=is_indices[row_cmat_indices[k]];
2668       }
2669       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
2670       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2671     }
2672     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2673     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2674     ierr = MatPtAP(matis->A,change_mat_all,MAT_INITIAL_MATRIX,1.0,&pcbddc->local_mat);CHKERRQ(ierr);
2675     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
2676     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
2677     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
2678     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
2679     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
2680     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
2681     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
2682     ierr = PetscFree(nnz);CHKERRQ(ierr);
2683     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2684   } else {
2685     /* without change of basis, the local matrix is unchanged */
2686     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
2687     pcbddc->local_mat = matis->A;
2688   }
2689 
2690   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
2691   ierr = VecSet(pcis->vec1_N,one);CHKERRQ(ierr);
2692   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2693   for (i=0;i<n_vertices;i++) { array[ vertices[i] ] = zero; }
2694   ierr = PetscMalloc(( pcis->n - n_vertices )*sizeof(PetscInt),&idx_R_local);CHKERRQ(ierr);
2695   for (i=0, n_R=0; i<pcis->n; i++) { if (array[i] == one) { idx_R_local[n_R] = i; n_R++; } }
2696   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2697   if(dbg_flag) {
2698     ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
2699     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2700     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
2701     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
2702     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);
2703     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
2704     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2705   }
2706 
2707   /* Allocate needed vectors */
2708   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2709   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
2710   ierr = VecDuplicate(pcis->vec1_D,&pcbddc->vec4_D);CHKERRQ(ierr);
2711   ierr = VecCreate(PETSC_COMM_SELF,&pcbddc->vec1_R);CHKERRQ(ierr);
2712   ierr = VecSetSizes(pcbddc->vec1_R,n_R,n_R);CHKERRQ(ierr);
2713   ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
2714   ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
2715   ierr = VecCreate(PETSC_COMM_SELF,&pcbddc->vec1_P);CHKERRQ(ierr);
2716   ierr = VecSetSizes(pcbddc->vec1_P,pcbddc->local_primal_size,pcbddc->local_primal_size);CHKERRQ(ierr);
2717   ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
2718 
2719   /* Creating some index sets needed  */
2720   /* For submatrices */
2721   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_R,idx_R_local,PETSC_OWN_POINTER,&is_R_local);CHKERRQ(ierr);
2722   if(n_vertices)    {
2723     ierr = ISCreateGeneral(PETSC_COMM_SELF,n_vertices,vertices,PETSC_OWN_POINTER,&is_V_local);CHKERRQ(ierr);
2724   }
2725   if(n_constraints) {
2726     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_C_local);CHKERRQ(ierr);
2727   }
2728 
2729   /* For VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
2730   {
2731     PetscInt   *aux_array1;
2732     PetscInt   *aux_array2;
2733 
2734     ierr = PetscMalloc( (pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
2735     ierr = PetscMalloc( (pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array2);CHKERRQ(ierr);
2736 
2737     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
2738     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2739     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2740     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2741     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2742     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2743     ierr = VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2744     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2745     for (i=0, j=0; i<n_R; i++) { if (array[idx_R_local[i]] > one) { aux_array1[j] = i; j++; } }
2746     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2747     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_COPY_VALUES,&is_aux1);CHKERRQ(ierr);
2748     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2749     for (i=0, j=0; i<n_B; i++) { if (array[i] > one) { aux_array2[j] = i; j++; } }
2750     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
2751     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_COPY_VALUES,&is_aux2);CHKERRQ(ierr);
2752     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
2753     ierr = PetscFree(aux_array1);CHKERRQ(ierr);
2754     ierr = PetscFree(aux_array2);CHKERRQ(ierr);
2755     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2756     ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
2757 
2758     if(pcbddc->prec_type || dbg_flag ) {
2759       ierr = PetscMalloc(n_D*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
2760       ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2761       for (i=0, j=0; i<n_R; i++) { if (array[idx_R_local[i]] == one) { aux_array1[j] = i; j++; } }
2762       ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
2763       ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_COPY_VALUES,&is_aux1);CHKERRQ(ierr);
2764       ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
2765       ierr = PetscFree(aux_array1);CHKERRQ(ierr);
2766       ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2767     }
2768   }
2769 
2770   /* Creating PC contexts for local Dirichlet and Neumann problems */
2771   {
2772     Mat  A_RR;
2773     PC   pc_temp;
2774     /* Matrix for Dirichlet problem is A_II -> we already have it from pcis.c code */
2775     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
2776     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
2777     ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,SAME_PRECONDITIONER);CHKERRQ(ierr);
2778     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
2779     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
2780     /* default */
2781     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
2782     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
2783     /* Allow user's customization */
2784     ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
2785     /* Set Up KSP for Dirichlet problem of BDDC */
2786     ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
2787     /* set ksp_D into pcis data */
2788     ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
2789     ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
2790     pcis->ksp_D = pcbddc->ksp_D;
2791     /* Matrix for Neumann problem is A_RR -> we need to create it */
2792     ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
2793     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
2794     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
2795     ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,SAME_PRECONDITIONER);CHKERRQ(ierr);
2796     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
2797     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
2798     /* default */
2799     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
2800     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
2801     /* Allow user's customization */
2802     ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
2803     /* Set Up KSP for Neumann problem of BDDC */
2804     ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
2805     /* check Dirichlet and Neumann solvers */
2806     {
2807       Vec         temp_vec;
2808       PetscReal   value;
2809       PetscMPIInt use_exact,use_exact_reduced;
2810 
2811       ierr = VecDuplicate(pcis->vec1_D,&temp_vec);CHKERRQ(ierr);
2812       ierr = VecSetRandom(pcis->vec1_D,PETSC_NULL);CHKERRQ(ierr);
2813       ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
2814       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,temp_vec);CHKERRQ(ierr);
2815       ierr = VecAXPY(temp_vec,m_one,pcis->vec1_D);CHKERRQ(ierr);
2816       ierr = VecNorm(temp_vec,NORM_INFINITY,&value);CHKERRQ(ierr);
2817       use_exact = 1;
2818       if(PetscAbsReal(value) > 1.e-4) {
2819         use_exact = 0;
2820       }
2821       ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,((PetscObject)pc)->comm);CHKERRQ(ierr);
2822       pcbddc->use_exact_dirichlet = (PetscBool) use_exact_reduced;
2823       ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2824       if(dbg_flag) {
2825         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2826         ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
2827         ierr = PetscViewerASCIIPrintf(viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
2828         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
2829         ierr = VecDuplicate(pcbddc->vec1_R,&temp_vec);CHKERRQ(ierr);
2830         ierr = VecSetRandom(pcbddc->vec1_R,PETSC_NULL);CHKERRQ(ierr);
2831         ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2832         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,temp_vec);CHKERRQ(ierr);
2833         ierr = VecAXPY(temp_vec,m_one,pcbddc->vec1_R);CHKERRQ(ierr);
2834         ierr = VecNorm(temp_vec,NORM_INFINITY,&value);CHKERRQ(ierr);
2835         ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
2836         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
2837         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
2838       }
2839     }
2840     /* free Neumann problem's matrix */
2841     ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
2842   }
2843 
2844   /* Assemble all remaining stuff needed to apply BDDC  */
2845   {
2846     Mat          A_RV,A_VR,A_VV;
2847     Mat          M1,M2;
2848     Mat          C_CR;
2849     Mat          AUXMAT;
2850     Vec          vec1_C;
2851     Vec          vec2_C;
2852     Vec          vec1_V;
2853     Vec          vec2_V;
2854     PetscInt     *nnz;
2855     PetscInt     *auxindices;
2856     PetscInt     index;
2857     PetscScalar* array2;
2858     MatFactorInfo matinfo;
2859 
2860     /* Allocating some extra storage just to be safe */
2861     ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
2862     ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&auxindices);CHKERRQ(ierr);
2863     for(i=0;i<pcis->n;i++) {auxindices[i]=i;}
2864 
2865     /* some work vectors on vertices and/or constraints */
2866     if(n_vertices) {
2867       ierr = VecCreate(PETSC_COMM_SELF,&vec1_V);CHKERRQ(ierr);
2868       ierr = VecSetSizes(vec1_V,n_vertices,n_vertices);CHKERRQ(ierr);
2869       ierr = VecSetType(vec1_V,impVecType);CHKERRQ(ierr);
2870       ierr = VecDuplicate(vec1_V,&vec2_V);CHKERRQ(ierr);
2871     }
2872     if(n_constraints) {
2873       ierr = VecCreate(PETSC_COMM_SELF,&vec1_C);CHKERRQ(ierr);
2874       ierr = VecSetSizes(vec1_C,n_constraints,n_constraints);CHKERRQ(ierr);
2875       ierr = VecSetType(vec1_C,impVecType);CHKERRQ(ierr);
2876       ierr = VecDuplicate(vec1_C,&vec2_C);CHKERRQ(ierr);
2877       ierr = VecDuplicate(vec1_C,&pcbddc->vec1_C);CHKERRQ(ierr);
2878     }
2879     /* Precompute stuffs needed for preprocessing and application of BDDC*/
2880     if(n_constraints) {
2881       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->local_auxmat2);CHKERRQ(ierr);
2882       ierr = MatSetSizes(pcbddc->local_auxmat2,n_R,n_constraints,n_R,n_constraints);CHKERRQ(ierr);
2883       ierr = MatSetType(pcbddc->local_auxmat2,impMatType);CHKERRQ(ierr);
2884       ierr = MatSeqDenseSetPreallocation(pcbddc->local_auxmat2,PETSC_NULL);CHKERRQ(ierr);
2885 
2886       /* Create Constraint matrix on R nodes: C_{CR}  */
2887       ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_C_local,is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
2888       ierr = ISDestroy(&is_C_local);CHKERRQ(ierr);
2889 
2890       /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
2891       for(i=0;i<n_constraints;i++) {
2892         ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
2893         /* Get row of constraint matrix in R numbering */
2894         ierr = VecGetArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
2895         ierr = MatGetRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2896         for(j=0;j<size_of_constraint;j++) { array[ row_cmat_indices[j] ] = - row_cmat_values[j]; }
2897         ierr = MatRestoreRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
2898         ierr = VecRestoreArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
2899         /* Solve for row of constraint matrix in R numbering */
2900         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2901         /* Set values */
2902         ierr = VecGetArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2903         ierr = MatSetValues(pcbddc->local_auxmat2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2904         ierr = VecRestoreArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2905       }
2906       ierr = MatAssemblyBegin(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2907       ierr = MatAssemblyEnd(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2908 
2909       /* Assemble AUXMAT = ( LUFactor )( -C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} */
2910       ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AUXMAT);CHKERRQ(ierr);
2911       ierr = MatFactorInfoInitialize(&matinfo);CHKERRQ(ierr);
2912       ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,0,1,&is_aux1);CHKERRQ(ierr);
2913       ierr = MatLUFactor(AUXMAT,is_aux1,is_aux1,&matinfo);CHKERRQ(ierr);
2914       ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
2915 
2916       /* Assemble explicitly M1 = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} needed in preproc  */
2917       ierr = MatCreate(PETSC_COMM_SELF,&M1);CHKERRQ(ierr);
2918       ierr = MatSetSizes(M1,n_constraints,n_constraints,n_constraints,n_constraints);CHKERRQ(ierr);
2919       ierr = MatSetType(M1,impMatType);CHKERRQ(ierr);
2920       ierr = MatSeqDenseSetPreallocation(M1,PETSC_NULL);CHKERRQ(ierr);
2921       for(i=0;i<n_constraints;i++) {
2922         ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
2923         ierr = VecSetValue(vec1_C,i,one,INSERT_VALUES);CHKERRQ(ierr);
2924         ierr = VecAssemblyBegin(vec1_C);CHKERRQ(ierr);
2925         ierr = VecAssemblyEnd(vec1_C);CHKERRQ(ierr);
2926         ierr = MatSolve(AUXMAT,vec1_C,vec2_C);CHKERRQ(ierr);
2927         ierr = VecScale(vec2_C,m_one);CHKERRQ(ierr);
2928         ierr = VecGetArray(vec2_C,&array);CHKERRQ(ierr);
2929         ierr = MatSetValues(M1,n_constraints,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2930         ierr = VecRestoreArray(vec2_C,&array);CHKERRQ(ierr);
2931       }
2932       ierr = MatAssemblyBegin(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2933       ierr = MatAssemblyEnd(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2934       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
2935       /* Assemble local_auxmat1 = M1*C_{CR} needed by BDDC application in KSP and in preproc */
2936       ierr = MatMatMult(M1,C_CR,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
2937 
2938     }
2939 
2940     /* Get submatrices from subdomain matrix */
2941     if(n_vertices){
2942       ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_V_local,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
2943       ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
2944       ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_V_local,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
2945       /* Assemble M2 = A_RR^{-1}A_RV */
2946       ierr = MatCreate(PETSC_COMM_SELF,&M2);CHKERRQ(ierr);
2947       ierr = MatSetSizes(M2,n_R,n_vertices,n_R,n_vertices);CHKERRQ(ierr);
2948       ierr = MatSetType(M2,impMatType);CHKERRQ(ierr);
2949       ierr = MatSeqDenseSetPreallocation(M2,PETSC_NULL);CHKERRQ(ierr);
2950       for(i=0;i<n_vertices;i++) {
2951         ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
2952         ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
2953         ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
2954         ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
2955         ierr = MatMult(A_RV,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
2956         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
2957         ierr = VecGetArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2958         ierr = MatSetValues(M2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2959         ierr = VecRestoreArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
2960       }
2961       ierr = MatAssemblyBegin(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2962       ierr = MatAssemblyEnd(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2963     }
2964 
2965     /* Matrix of coarse basis functions (local) */
2966     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
2967     ierr = MatSetSizes(pcbddc->coarse_phi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
2968     ierr = MatSetType(pcbddc->coarse_phi_B,impMatType);CHKERRQ(ierr);
2969     ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_B,PETSC_NULL);CHKERRQ(ierr);
2970     if(pcbddc->prec_type || dbg_flag ) {
2971       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
2972       ierr = MatSetSizes(pcbddc->coarse_phi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
2973       ierr = MatSetType(pcbddc->coarse_phi_D,impMatType);CHKERRQ(ierr);
2974       ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_D,PETSC_NULL);CHKERRQ(ierr);
2975     }
2976 
2977     if(dbg_flag) {
2978       ierr = PetscMalloc( pcbddc->local_primal_size*sizeof(PetscScalar),&coarsefunctions_errors);CHKERRQ(ierr);
2979       ierr = PetscMalloc( pcbddc->local_primal_size*sizeof(PetscScalar),&constraints_errors);CHKERRQ(ierr);
2980     }
2981     /* Subdomain contribution (Non-overlapping) to coarse matrix  */
2982     ierr = PetscMalloc ((pcbddc->local_primal_size)*(pcbddc->local_primal_size)*sizeof(PetscScalar),&coarse_submat_vals);CHKERRQ(ierr);
2983 
2984     /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
2985     for(i=0;i<n_vertices;i++){
2986       ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
2987       ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
2988       ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
2989       ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
2990       /* solution of saddle point problem */
2991       ierr = MatMult(M2,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
2992       ierr = VecScale(pcbddc->vec1_R,m_one);CHKERRQ(ierr);
2993       if(n_constraints) {
2994         ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec1_R,vec1_C);CHKERRQ(ierr);
2995         ierr = MatMultAdd(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
2996         ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
2997       }
2998       ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
2999       ierr = MatMultAdd(A_VV,vec1_V,vec2_V,vec2_V);CHKERRQ(ierr);
3000 
3001       /* Set values in coarse basis function and subdomain part of coarse_mat */
3002       /* coarse basis functions */
3003       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
3004       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3005       ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3006       ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3007       ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
3008       ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3009       ierr = MatSetValue(pcbddc->coarse_phi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
3010       if( pcbddc->prec_type || dbg_flag  ) {
3011         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3012         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3013         ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3014         ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
3015         ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3016       }
3017       /* subdomain contribution to coarse matrix */
3018       ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3019       for(j=0;j<n_vertices;j++) { coarse_submat_vals[i*pcbddc->local_primal_size+j] = array[j]; } /* WARNING -> column major ordering */
3020       ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3021       if(n_constraints) {
3022         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3023         for(j=0;j<n_constraints;j++) { coarse_submat_vals[i*pcbddc->local_primal_size+j+n_vertices] = array[j]; } /* WARNING -> column major ordering */
3024         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3025       }
3026 
3027       if( dbg_flag ) {
3028         /* assemble subdomain vector on nodes */
3029         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3030         ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3031         ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3032         for(j=0;j<n_R;j++) { array[idx_R_local[j]] = array2[j]; }
3033         array[ vertices[i] ] = one;
3034         ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3035         ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3036         /* assemble subdomain vector of lagrange multipliers (i.e. primal nodes) */
3037         ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
3038         ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3039         ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3040         for(j=0;j<n_vertices;j++) { array2[j]=array[j]; }
3041         ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3042         if(n_constraints) {
3043           ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3044           for(j=0;j<n_constraints;j++) { array2[j+n_vertices]=array[j]; }
3045           ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3046         }
3047         ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3048         ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
3049         /* check saddle point solution */
3050         ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
3051         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
3052         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i]);CHKERRQ(ierr);
3053         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
3054         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3055         array[i]=array[i]+m_one;  /* shift by the identity matrix */
3056         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3057         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i]);CHKERRQ(ierr);
3058       }
3059     }
3060 
3061     for(i=0;i<n_constraints;i++){
3062       ierr = VecSet(vec2_C,zero);CHKERRQ(ierr);
3063       ierr = VecSetValue(vec2_C,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
3064       ierr = VecAssemblyBegin(vec2_C);CHKERRQ(ierr);
3065       ierr = VecAssemblyEnd(vec2_C);CHKERRQ(ierr);
3066       /* solution of saddle point problem */
3067       ierr = MatMult(M1,vec2_C,vec1_C);CHKERRQ(ierr);
3068       ierr = MatMult(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
3069       ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
3070       if(n_vertices) { ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr); }
3071       /* Set values in coarse basis function and subdomain part of coarse_mat */
3072       /* coarse basis functions */
3073       index=i+n_vertices;
3074       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
3075       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3076       ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3077       ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3078       ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
3079       ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
3080       if( pcbddc->prec_type || dbg_flag ) {
3081         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3082         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3083         ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3084         ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
3085         ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
3086       }
3087       /* subdomain contribution to coarse matrix */
3088       if(n_vertices) {
3089         ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3090         for(j=0;j<n_vertices;j++) {coarse_submat_vals[index*pcbddc->local_primal_size+j]=array[j];} /* WARNING -> column major ordering */
3091         ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3092       }
3093       ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3094       for(j=0;j<n_constraints;j++) {coarse_submat_vals[index*pcbddc->local_primal_size+j+n_vertices]=array[j];} /* WARNING -> column major ordering */
3095       ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3096 
3097       if( dbg_flag ) {
3098         /* assemble subdomain vector on nodes */
3099         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3100         ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3101         ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3102         for(j=0;j<n_R;j++){ array[ idx_R_local[j] ] = array2[j]; }
3103         ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
3104         ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3105         /* assemble subdomain vector of lagrange multipliers */
3106         ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
3107         ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3108         if( n_vertices) {
3109           ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
3110           for(j=0;j<n_vertices;j++) {array2[j]=-array[j];}
3111           ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
3112         }
3113         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
3114         for(j=0;j<n_constraints;j++) {array2[j+n_vertices]=-array[j];}
3115         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
3116         ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
3117         /* check saddle point solution */
3118         ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
3119         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
3120         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[index]);CHKERRQ(ierr);
3121         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
3122         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3123         array[index]=array[index]+m_one; /* shift by the identity matrix */
3124         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
3125         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[index]);CHKERRQ(ierr);
3126       }
3127     }
3128     ierr = MatAssemblyBegin(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3129     ierr = MatAssemblyEnd  (pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3130     if( pcbddc->prec_type || dbg_flag ) {
3131       ierr = MatAssemblyBegin(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3132       ierr = MatAssemblyEnd  (pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3133     }
3134     /* Checking coarse_sub_mat and coarse basis functios */
3135     /* It shuld be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
3136     if(dbg_flag) {
3137 
3138       Mat coarse_sub_mat;
3139       Mat TM1,TM2,TM3,TM4;
3140       Mat coarse_phi_D,coarse_phi_B,A_II,A_BB,A_IB,A_BI;
3141       const MatType checkmattype=MATSEQAIJ;
3142       PetscScalar      value;
3143 
3144       ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
3145       ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
3146       ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
3147       ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
3148       ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
3149       ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
3150       ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
3151       ierr = MatConvert(coarse_sub_mat,checkmattype,MAT_REUSE_MATRIX,&coarse_sub_mat);CHKERRQ(ierr);
3152 
3153       /*PetscViewer view_out;
3154       PetscMPIInt myrank;
3155       char filename[256];
3156       MPI_Comm_rank(((PetscObject)pc)->comm,&myrank);
3157       sprintf(filename,"coarsesubmat_%04d.m",myrank);
3158       ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&view_out);CHKERRQ(ierr);
3159       ierr = PetscViewerSetFormat(view_out,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3160       ierr = MatView(coarse_sub_mat,view_out);CHKERRQ(ierr);
3161       ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);*/
3162 
3163       ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3164       ierr = PetscViewerASCIIPrintf(viewer,"Check coarse sub mat and local basis functions\n");CHKERRQ(ierr);
3165       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3166       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
3167       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
3168       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
3169       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
3170       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
3171       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
3172       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
3173       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
3174       ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3175       ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3176       ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3177       ierr = MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
3178       ierr = MatNorm(TM1,NORM_INFINITY,&value);CHKERRQ(ierr);
3179       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"----------------------------------\n");CHKERRQ(ierr);
3180       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d \n",PetscGlobalRank);CHKERRQ(ierr);
3181       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"matrix error = % 1.14e\n",value);CHKERRQ(ierr);
3182       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"coarse functions 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,coarsefunctions_errors[i]);CHKERRQ(ierr); }
3184       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"constraints errors\n");CHKERRQ(ierr);
3185       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); }
3186       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3187       ierr = MatDestroy(&A_II);CHKERRQ(ierr);
3188       ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
3189       ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
3190       ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
3191       ierr = MatDestroy(&TM1);CHKERRQ(ierr);
3192       ierr = MatDestroy(&TM2);CHKERRQ(ierr);
3193       ierr = MatDestroy(&TM3);CHKERRQ(ierr);
3194       ierr = MatDestroy(&TM4);CHKERRQ(ierr);
3195       ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
3196       ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
3197       ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
3198       ierr = PetscFree(coarsefunctions_errors);CHKERRQ(ierr);
3199       ierr = PetscFree(constraints_errors);CHKERRQ(ierr);
3200     }
3201 
3202     /* create coarse matrix and data structures for message passing associated actual choice of coarse problem type */
3203     ierr = PCBDDCSetupCoarseEnvironment(pc,coarse_submat_vals);CHKERRQ(ierr);
3204     /* free memory */
3205     ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
3206     ierr = PetscFree(auxindices);CHKERRQ(ierr);
3207     ierr = PetscFree(nnz);CHKERRQ(ierr);
3208     if(n_vertices) {
3209       ierr = VecDestroy(&vec1_V);CHKERRQ(ierr);
3210       ierr = VecDestroy(&vec2_V);CHKERRQ(ierr);
3211       ierr = MatDestroy(&M2);CHKERRQ(ierr);
3212       ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
3213       ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
3214       ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
3215     }
3216     if(n_constraints) {
3217       ierr = VecDestroy(&vec1_C);CHKERRQ(ierr);
3218       ierr = VecDestroy(&vec2_C);CHKERRQ(ierr);
3219       ierr = MatDestroy(&M1);CHKERRQ(ierr);
3220       ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
3221     }
3222   }
3223   /* free memory */
3224   if(n_vertices) {
3225     ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
3226     ierr = ISDestroy(&is_V_local);CHKERRQ(ierr);
3227   }
3228   ierr = ISDestroy(&is_R_local);CHKERRQ(ierr);
3229 
3230   PetscFunctionReturn(0);
3231 }
3232 
3233 /* -------------------------------------------------------------------------- */
3234 
3235 #undef __FUNCT__
3236 #define __FUNCT__ "PCBDDCSetupCoarseEnvironment"
3237 static PetscErrorCode PCBDDCSetupCoarseEnvironment(PC pc,PetscScalar* coarse_submat_vals)
3238 {
3239 
3240 
3241   Mat_IS    *matis    = (Mat_IS*)pc->pmat->data;
3242   PC_BDDC   *pcbddc   = (PC_BDDC*)pc->data;
3243   PC_IS     *pcis     = (PC_IS*)pc->data;
3244   MPI_Comm  prec_comm = ((PetscObject)pc)->comm;
3245   MPI_Comm  coarse_comm;
3246 
3247   /* common to all choiches */
3248   PetscScalar *temp_coarse_mat_vals;
3249   PetscScalar *ins_coarse_mat_vals;
3250   PetscInt    *ins_local_primal_indices;
3251   PetscMPIInt *localsizes2,*localdispl2;
3252   PetscMPIInt size_prec_comm;
3253   PetscMPIInt rank_prec_comm;
3254   PetscMPIInt active_rank=MPI_PROC_NULL;
3255   PetscMPIInt master_proc=0;
3256   PetscInt    ins_local_primal_size;
3257   /* specific to MULTILEVEL_BDDC */
3258   PetscMPIInt *ranks_recv;
3259   PetscMPIInt count_recv=0;
3260   PetscMPIInt rank_coarse_proc_send_to;
3261   PetscMPIInt coarse_color = MPI_UNDEFINED;
3262   ISLocalToGlobalMapping coarse_ISLG;
3263   /* some other variables */
3264   PetscErrorCode ierr;
3265   const MatType coarse_mat_type;
3266   const PCType  coarse_pc_type;
3267   const KSPType  coarse_ksp_type;
3268   PC pc_temp;
3269   PetscInt i,j,k,bs;
3270   PetscInt max_it_coarse_ksp=1;  /* don't increase this value */
3271   /* verbose output viewer */
3272   PetscViewer viewer=pcbddc->dbg_viewer;
3273   PetscBool   dbg_flag=pcbddc->dbg_flag;
3274 
3275   PetscFunctionBegin;
3276 
3277   ins_local_primal_indices = 0;
3278   ins_coarse_mat_vals      = 0;
3279   localsizes2              = 0;
3280   localdispl2              = 0;
3281   temp_coarse_mat_vals     = 0;
3282   coarse_ISLG              = 0;
3283 
3284   ierr = MPI_Comm_size(prec_comm,&size_prec_comm);CHKERRQ(ierr);
3285   ierr = MPI_Comm_rank(prec_comm,&rank_prec_comm);CHKERRQ(ierr);
3286   ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
3287 
3288   /* Assign global numbering to coarse dofs */
3289   {
3290     PetscScalar    one=1.,zero=0.;
3291     PetscScalar    *array;
3292     PetscMPIInt    *auxlocal_primal;
3293     PetscMPIInt    *auxglobal_primal;
3294     PetscMPIInt    *all_auxglobal_primal;
3295     PetscMPIInt    *all_auxglobal_primal_dummy;
3296     PetscMPIInt    mpi_local_primal_size = (PetscMPIInt)pcbddc->local_primal_size;
3297     PetscInt       *row_cmat_indices;
3298     PetscInt       size_of_constraint;
3299     PetscScalar    coarsesum;
3300 
3301     /* Construct needed data structures for message passing */
3302     ierr = PetscMalloc(mpi_local_primal_size*sizeof(PetscMPIInt),&pcbddc->local_primal_indices);CHKERRQ(ierr);
3303     ierr = PetscMalloc(size_prec_comm*sizeof(PetscMPIInt),&pcbddc->local_primal_sizes);CHKERRQ(ierr);
3304     ierr = PetscMalloc(size_prec_comm*sizeof(PetscMPIInt),&pcbddc->local_primal_displacements);CHKERRQ(ierr);
3305     /* Gather local_primal_size information for all processes  */
3306     ierr = MPI_Allgather(&mpi_local_primal_size,1,MPIU_INT,&pcbddc->local_primal_sizes[0],1,MPIU_INT,prec_comm);CHKERRQ(ierr);
3307     pcbddc->replicated_primal_size = 0;
3308     for (i=0; i<size_prec_comm; i++) {
3309       pcbddc->local_primal_displacements[i] = pcbddc->replicated_primal_size ;
3310       pcbddc->replicated_primal_size += pcbddc->local_primal_sizes[i];
3311     }
3312     if(rank_prec_comm == 0) {
3313       /* allocate some auxiliary space */
3314       ierr = PetscMalloc(pcbddc->replicated_primal_size*sizeof(*all_auxglobal_primal),&all_auxglobal_primal);CHKERRQ(ierr);
3315       ierr = PetscMalloc(pcbddc->replicated_primal_size*sizeof(*all_auxglobal_primal_dummy),&all_auxglobal_primal_dummy);CHKERRQ(ierr);
3316     }
3317     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscMPIInt),&auxlocal_primal);CHKERRQ(ierr);
3318     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscMPIInt),&auxglobal_primal);CHKERRQ(ierr);
3319 
3320     /* First let's count coarse dofs.
3321        This code fragment assumes that the number of local constraints per connected component
3322        is not greater than the number of nodes defined for the connected component
3323        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
3324     /* auxlocal_primal      : primal indices in local nodes numbering (internal and interface) with complete queue sorted by global ordering */
3325     ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
3326     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3327     for(i=0;i<pcbddc->local_primal_size;i++) {
3328       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
3329       for (j=0; j<size_of_constraint; j++) {
3330         k = row_cmat_indices[j];
3331         if( array[k] == zero ) {
3332           array[k] = one;
3333           auxlocal_primal[i] = k;
3334           break;
3335         }
3336       }
3337       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,PETSC_NULL);CHKERRQ(ierr);
3338     }
3339     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3340     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
3341     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3342     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3343     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3344     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3345     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3346     for(i=0;i<pcis->n;i++) { if( array[i] > zero) array[i] = one/array[i]; }
3347     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3348     ierr = VecSet(pcis->vec1_global,zero);CHKERRQ(ierr);
3349     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3350     ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3351     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
3352     pcbddc->coarse_size = (PetscInt) coarsesum;
3353 
3354     /* Now assign them a global numbering */
3355     /* auxglobal_primal contains indices in global nodes numbering (internal and interface) */
3356     ierr = ISLocalToGlobalMappingApply(matis->mapping,pcbddc->local_primal_size,auxlocal_primal,auxglobal_primal);CHKERRQ(ierr);
3357     /* all_auxglobal_primal contains all primal nodes indices in global nodes numbering (internal and interface) */
3358     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);
3359 
3360     /* After this block all_auxglobal_primal should contains one copy of each primal node's indices in global nodes numbering */
3361     /* It implements a function similar to PetscSortRemoveDupsInt */
3362     if(rank_prec_comm==0) {
3363       /* dummy argument since PetscSortMPIInt doesn't exist! */
3364       ierr = PetscSortMPIIntWithArray(pcbddc->replicated_primal_size,all_auxglobal_primal,all_auxglobal_primal_dummy);CHKERRQ(ierr);
3365       k=1;
3366       j=all_auxglobal_primal[0];  /* first dof in global numbering */
3367       for(i=1;i< pcbddc->replicated_primal_size ;i++) {
3368         if(j != all_auxglobal_primal[i] ) {
3369           all_auxglobal_primal[k]=all_auxglobal_primal[i];
3370           k++;
3371           j=all_auxglobal_primal[i];
3372         }
3373       }
3374     } else {
3375       ierr = PetscMalloc(pcbddc->coarse_size*sizeof(PetscMPIInt),&all_auxglobal_primal);CHKERRQ(ierr);
3376     }
3377     /* We only need to broadcast the indices from 0 to pcbddc->coarse_size. Remaning elements of array all_aux_global_primal are garbage. */
3378     ierr = MPI_Bcast(all_auxglobal_primal,pcbddc->coarse_size,MPIU_INT,0,prec_comm);CHKERRQ(ierr);
3379 
3380     /* Now get global coarse numbering of local primal nodes */
3381     for(i=0;i<pcbddc->local_primal_size;i++) {
3382       k=0;
3383       while( all_auxglobal_primal[k] != auxglobal_primal[i] ) { k++;}
3384       pcbddc->local_primal_indices[i]=k;
3385     }
3386     if(dbg_flag) {
3387       ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3388       ierr = PetscViewerASCIIPrintf(viewer,"Size of coarse problem %d\n",pcbddc->coarse_size);CHKERRQ(ierr);
3389       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3390     }
3391     /* free allocated memory */
3392     ierr = PetscFree(auxlocal_primal);CHKERRQ(ierr);
3393     ierr = PetscFree(auxglobal_primal);CHKERRQ(ierr);
3394     ierr = PetscFree(all_auxglobal_primal);CHKERRQ(ierr);
3395     if(rank_prec_comm == 0) {
3396       ierr = PetscFree(all_auxglobal_primal_dummy);CHKERRQ(ierr);
3397     }
3398   }
3399 
3400   /* adapt coarse problem type */
3401   if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC && pcbddc->active_procs < MIN_PROCS_FOR_BDDC )
3402     pcbddc->coarse_problem_type = PARALLEL_BDDC;
3403 
3404   switch(pcbddc->coarse_problem_type){
3405 
3406     case(MULTILEVEL_BDDC):   /* we define a coarse mesh where subdomains are elements */
3407     {
3408       /* we need additional variables */
3409       MetisInt   n_subdomains,n_parts,objval,ncon,faces_nvtxs;
3410       MetisInt   *metis_coarse_subdivision;
3411       MetisInt   options[METIS_NOPTIONS];
3412       PetscMPIInt size_coarse_comm,rank_coarse_comm;
3413       PetscMPIInt procs_jumps_coarse_comm;
3414       PetscMPIInt *coarse_subdivision;
3415       PetscMPIInt *total_count_recv;
3416       PetscMPIInt *total_ranks_recv;
3417       PetscMPIInt *displacements_recv;
3418       PetscMPIInt *my_faces_connectivity;
3419       PetscMPIInt *petsc_faces_adjncy;
3420       MetisInt    *faces_adjncy;
3421       MetisInt    *faces_xadj;
3422       PetscMPIInt *number_of_faces;
3423       PetscMPIInt *faces_displacements;
3424       PetscInt    *array_int;
3425       PetscMPIInt my_faces=0;
3426       PetscMPIInt total_faces=0;
3427       PetscInt    ranks_stretching_ratio;
3428 
3429       /* define some quantities */
3430       pcbddc->coarse_communications_type = SCATTERS_BDDC;
3431       coarse_mat_type = MATIS;
3432       coarse_pc_type  = PCBDDC;
3433       coarse_ksp_type  = KSPCHEBYSHEV;
3434 
3435       /* details of coarse decomposition */
3436       n_subdomains = pcbddc->active_procs;
3437       n_parts      = n_subdomains/pcbddc->coarsening_ratio;
3438       ranks_stretching_ratio = size_prec_comm/pcbddc->active_procs;
3439       procs_jumps_coarse_comm = pcbddc->coarsening_ratio*ranks_stretching_ratio;
3440 
3441       /*printf("Coarse algorithm details: \n");
3442       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));*/
3443 
3444       /* build CSR graph of subdomains' connectivity through faces */
3445       ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&array_int);CHKERRQ(ierr);
3446       ierr = PetscMemzero(array_int,pcis->n*sizeof(PetscInt));CHKERRQ(ierr);
3447       for(i=1;i<pcis->n_neigh;i++){/* i=1 so I don't count myself -> faces nodes counts to 1 */
3448         for(j=0;j<pcis->n_shared[i];j++){
3449           array_int[ pcis->shared[i][j] ]+=1;
3450         }
3451       }
3452       for(i=1;i<pcis->n_neigh;i++){
3453         for(j=0;j<pcis->n_shared[i];j++){
3454           if(array_int[ pcis->shared[i][j] ] == 1 ){
3455             my_faces++;
3456             break;
3457           }
3458         }
3459       }
3460 
3461       ierr = MPI_Reduce(&my_faces,&total_faces,1,MPIU_INT,MPI_SUM,master_proc,prec_comm);CHKERRQ(ierr);
3462       ierr = PetscMalloc (my_faces*sizeof(PetscInt),&my_faces_connectivity);CHKERRQ(ierr);
3463       my_faces=0;
3464       for(i=1;i<pcis->n_neigh;i++){
3465         for(j=0;j<pcis->n_shared[i];j++){
3466           if(array_int[ pcis->shared[i][j] ] == 1 ){
3467             my_faces_connectivity[my_faces]=pcis->neigh[i];
3468             my_faces++;
3469             break;
3470           }
3471         }
3472       }
3473       if(rank_prec_comm == master_proc) {
3474         ierr = PetscMalloc (total_faces*sizeof(PetscMPIInt),&petsc_faces_adjncy);CHKERRQ(ierr);
3475         ierr = PetscMalloc (size_prec_comm*sizeof(PetscMPIInt),&number_of_faces);CHKERRQ(ierr);
3476         ierr = PetscMalloc (total_faces*sizeof(MetisInt),&faces_adjncy);CHKERRQ(ierr);
3477         ierr = PetscMalloc ((n_subdomains+1)*sizeof(MetisInt),&faces_xadj);CHKERRQ(ierr);
3478         ierr = PetscMalloc ((size_prec_comm+1)*sizeof(PetscMPIInt),&faces_displacements);CHKERRQ(ierr);
3479       }
3480       ierr = MPI_Gather(&my_faces,1,MPIU_INT,&number_of_faces[0],1,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3481       if(rank_prec_comm == master_proc) {
3482         faces_xadj[0]=0;
3483         faces_displacements[0]=0;
3484         j=0;
3485         for(i=1;i<size_prec_comm+1;i++) {
3486           faces_displacements[i]=faces_displacements[i-1]+number_of_faces[i-1];
3487           if(number_of_faces[i-1]) {
3488             j++;
3489             faces_xadj[j]=faces_xadj[j-1]+number_of_faces[i-1];
3490           }
3491         }
3492         /*printf("The J I count is %d and should be %d\n",j,n_subdomains);
3493         printf("Total faces seem %d and should be %d\n",faces_xadj[j],total_faces);*/
3494       }
3495       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);
3496       ierr = PetscFree(my_faces_connectivity);CHKERRQ(ierr);
3497       ierr = PetscFree(array_int);CHKERRQ(ierr);
3498       if(rank_prec_comm == master_proc) {
3499         for(i=0;i<total_faces;i++) faces_adjncy[i]=(MetisInt)(petsc_faces_adjncy[i]/ranks_stretching_ratio); /* cast to MetisInt */
3500         /*printf("This is the face connectivity (actual ranks)\n");
3501         for(i=0;i<n_subdomains;i++){
3502           printf("proc %d is connected with \n",i);
3503           for(j=faces_xadj[i];j<faces_xadj[i+1];j++)
3504             printf("%d ",faces_adjncy[j]);
3505           printf("\n");
3506         }*/
3507         ierr = PetscFree(faces_displacements);CHKERRQ(ierr);
3508         ierr = PetscFree(number_of_faces);CHKERRQ(ierr);
3509         ierr = PetscFree(petsc_faces_adjncy);CHKERRQ(ierr);
3510       }
3511 
3512       if( rank_prec_comm == master_proc ) {
3513 
3514         PetscInt heuristic_for_metis=3;
3515 
3516         ncon=1;
3517         faces_nvtxs=n_subdomains;
3518         /* partition graoh induced by face connectivity */
3519         ierr = PetscMalloc (n_subdomains*sizeof(MetisInt),&metis_coarse_subdivision);CHKERRQ(ierr);
3520         ierr = METIS_SetDefaultOptions(options);
3521         /* we need a contiguous partition of the coarse mesh */
3522         options[METIS_OPTION_CONTIG]=1;
3523         options[METIS_OPTION_DBGLVL]=1;
3524         options[METIS_OPTION_NITER]=30;
3525         if(n_subdomains>n_parts*heuristic_for_metis) {
3526           options[METIS_OPTION_IPTYPE]=METIS_IPTYPE_EDGE;
3527           options[METIS_OPTION_OBJTYPE]=METIS_OBJTYPE_CUT;
3528           ierr = METIS_PartGraphKway(&faces_nvtxs,&ncon,faces_xadj,faces_adjncy,NULL,NULL,NULL,&n_parts,NULL,NULL,options,&objval,metis_coarse_subdivision);
3529         } else {
3530           ierr = METIS_PartGraphRecursive(&faces_nvtxs,&ncon,faces_xadj,faces_adjncy,NULL,NULL,NULL,&n_parts,NULL,NULL,options,&objval,metis_coarse_subdivision);
3531         }
3532         if(ierr != METIS_OK) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in METIS_PartGraphKway (metis error code %D) called from PCBDDCSetupCoarseEnvironment\n",ierr);
3533         ierr = PetscFree(faces_xadj);CHKERRQ(ierr);
3534         ierr = PetscFree(faces_adjncy);CHKERRQ(ierr);
3535         coarse_subdivision = (PetscMPIInt*)calloc(size_prec_comm,sizeof(PetscMPIInt)); /* calloc for contiguous memory since we need to scatter these values later */
3536         /* copy/cast values avoiding possible type conflicts between PETSc, MPI and METIS */
3537         for(i=0;i<size_prec_comm;i++) coarse_subdivision[i]=MPI_PROC_NULL;
3538         for(i=0;i<n_subdomains;i++)   coarse_subdivision[ranks_stretching_ratio*i]=(PetscInt)(metis_coarse_subdivision[i]);
3539         ierr = PetscFree(metis_coarse_subdivision);CHKERRQ(ierr);
3540       }
3541 
3542       /* Create new communicator for coarse problem splitting the old one */
3543       if( !(rank_prec_comm%procs_jumps_coarse_comm) && rank_prec_comm < procs_jumps_coarse_comm*n_parts ){
3544         coarse_color=0;              /* for communicator splitting */
3545         active_rank=rank_prec_comm;  /* for insertion of matrix values */
3546       }
3547       /* procs with coarse_color = MPI_UNDEFINED will have coarse_comm = MPI_COMM_NULL (from mpi standards)
3548          key = rank_prec_comm -> keep same ordering of ranks from the old to the new communicator */
3549       ierr = MPI_Comm_split(prec_comm,coarse_color,rank_prec_comm,&coarse_comm);CHKERRQ(ierr);
3550 
3551       if( coarse_color == 0 ) {
3552         ierr = MPI_Comm_size(coarse_comm,&size_coarse_comm);CHKERRQ(ierr);
3553         ierr = MPI_Comm_rank(coarse_comm,&rank_coarse_comm);CHKERRQ(ierr);
3554         /*printf("Details of coarse comm\n");
3555         printf("size = %d, myrank = %d\n",size_coarse_comm,rank_coarse_comm);
3556         printf("jumps = %d, coarse_color = %d, n_parts = %d\n",procs_jumps_coarse_comm,coarse_color,n_parts);*/
3557       } else {
3558         rank_coarse_comm = MPI_PROC_NULL;
3559       }
3560 
3561       /* master proc take care of arranging and distributing coarse informations */
3562       if(rank_coarse_comm == master_proc) {
3563         ierr = PetscMalloc (size_coarse_comm*sizeof(PetscMPIInt),&displacements_recv);CHKERRQ(ierr);
3564         /*ierr = PetscMalloc (size_coarse_comm*sizeof(PetscMPIInt),&total_count_recv);CHKERRQ(ierr);
3565           ierr = PetscMalloc (n_subdomains*sizeof(PetscMPIInt),&total_ranks_recv);CHKERRQ(ierr);*/
3566         total_count_recv = (PetscMPIInt*)calloc(size_prec_comm,sizeof(PetscMPIInt));
3567         total_ranks_recv = (PetscMPIInt*)calloc(n_subdomains,sizeof(PetscMPIInt));
3568         /* some initializations */
3569         displacements_recv[0]=0;
3570         /* PetscMemzero(total_count_recv,size_coarse_comm*sizeof(PetscMPIInt)); not needed -> calloc initializes to zero */
3571         /* count from how many processes the j-th process of the coarse decomposition will receive data */
3572         for(j=0;j<size_coarse_comm;j++)
3573           for(i=0;i<size_prec_comm;i++)
3574             if(coarse_subdivision[i]==j)
3575               total_count_recv[j]++;
3576         /* displacements needed for scatterv of total_ranks_recv */
3577         for(i=1;i<size_coarse_comm;i++) displacements_recv[i]=displacements_recv[i-1]+total_count_recv[i-1];
3578         /* Now fill properly total_ranks_recv -> each coarse process will receive the ranks (in prec_comm communicator) of its friend (sending) processes */
3579         ierr = PetscMemzero(total_count_recv,size_coarse_comm*sizeof(PetscMPIInt));CHKERRQ(ierr);
3580         for(j=0;j<size_coarse_comm;j++) {
3581           for(i=0;i<size_prec_comm;i++) {
3582             if(coarse_subdivision[i]==j) {
3583               total_ranks_recv[displacements_recv[j]+total_count_recv[j]]=i;
3584               total_count_recv[j]+=1;
3585             }
3586           }
3587         }
3588         /*for(j=0;j<size_coarse_comm;j++) {
3589           printf("process %d in new rank will receive from %d processes (original ranks follows)\n",j,total_count_recv[j]);
3590           for(i=0;i<total_count_recv[j];i++) {
3591             printf("%d ",total_ranks_recv[displacements_recv[j]+i]);
3592           }
3593           printf("\n");
3594         }*/
3595 
3596         /* identify new decomposition in terms of ranks in the old communicator */
3597         for(i=0;i<n_subdomains;i++) coarse_subdivision[ranks_stretching_ratio*i]=coarse_subdivision[ranks_stretching_ratio*i]*procs_jumps_coarse_comm;
3598         /*printf("coarse_subdivision in old end new ranks\n");
3599         for(i=0;i<size_prec_comm;i++)
3600           if(coarse_subdivision[i]!=MPI_PROC_NULL) {
3601             printf("%d=(%d %d), ",i,coarse_subdivision[i],coarse_subdivision[i]/procs_jumps_coarse_comm);
3602           } else {
3603             printf("%d=(%d %d), ",i,coarse_subdivision[i],coarse_subdivision[i]);
3604           }
3605         printf("\n");*/
3606       }
3607 
3608       /* Scatter new decomposition for send details */
3609       ierr = MPI_Scatter(&coarse_subdivision[0],1,MPIU_INT,&rank_coarse_proc_send_to,1,MPIU_INT,master_proc,prec_comm);CHKERRQ(ierr);
3610       /* Scatter receiving details to members of coarse decomposition */
3611       if( coarse_color == 0) {
3612         ierr = MPI_Scatter(&total_count_recv[0],1,MPIU_INT,&count_recv,1,MPIU_INT,master_proc,coarse_comm);CHKERRQ(ierr);
3613         ierr = PetscMalloc (count_recv*sizeof(PetscMPIInt),&ranks_recv);CHKERRQ(ierr);
3614         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);
3615       }
3616 
3617       /*printf("I will send my matrix data to proc  %d\n",rank_coarse_proc_send_to);
3618       if(coarse_color == 0) {
3619         printf("I will receive some matrix data from %d processes (ranks follows)\n",count_recv);
3620         for(i=0;i<count_recv;i++)
3621           printf("%d ",ranks_recv[i]);
3622         printf("\n");
3623       }*/
3624 
3625       if(rank_prec_comm == master_proc) {
3626         /*ierr = PetscFree(coarse_subdivision);CHKERRQ(ierr);
3627         ierr = PetscFree(total_count_recv);CHKERRQ(ierr);
3628         ierr = PetscFree(total_ranks_recv);CHKERRQ(ierr);*/
3629         free(coarse_subdivision);
3630         free(total_count_recv);
3631         free(total_ranks_recv);
3632         ierr = PetscFree(displacements_recv);CHKERRQ(ierr);
3633       }
3634       break;
3635     }
3636 
3637     case(REPLICATED_BDDC):
3638 
3639       pcbddc->coarse_communications_type = GATHERS_BDDC;
3640       coarse_mat_type = MATSEQAIJ;
3641       coarse_pc_type  = PCLU;
3642       coarse_ksp_type  = KSPPREONLY;
3643       coarse_comm = PETSC_COMM_SELF;
3644       active_rank = rank_prec_comm;
3645       break;
3646 
3647     case(PARALLEL_BDDC):
3648 
3649       pcbddc->coarse_communications_type = SCATTERS_BDDC;
3650       coarse_mat_type = MATMPIAIJ;
3651       coarse_pc_type  = PCREDUNDANT;
3652       coarse_ksp_type  = KSPPREONLY;
3653       coarse_comm = prec_comm;
3654       active_rank = rank_prec_comm;
3655       break;
3656 
3657     case(SEQUENTIAL_BDDC):
3658       pcbddc->coarse_communications_type = GATHERS_BDDC;
3659       coarse_mat_type = MATSEQAIJ;
3660       coarse_pc_type = PCLU;
3661       coarse_ksp_type  = KSPPREONLY;
3662       coarse_comm = PETSC_COMM_SELF;
3663       active_rank = master_proc;
3664       break;
3665   }
3666 
3667   switch(pcbddc->coarse_communications_type){
3668 
3669     case(SCATTERS_BDDC):
3670       {
3671         if(pcbddc->coarse_problem_type==MULTILEVEL_BDDC) {
3672 
3673           PetscMPIInt send_size;
3674           PetscInt    *aux_ins_indices;
3675           PetscInt    ii,jj;
3676           MPI_Request *requests;
3677 
3678           /* allocate auxiliary space */
3679           ierr = PetscMalloc (pcbddc->replicated_primal_size*sizeof(PetscMPIInt),&pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
3680           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);
3681           ierr = PetscMalloc ( pcbddc->coarse_size*sizeof(PetscInt),&aux_ins_indices);CHKERRQ(ierr);
3682           ierr = PetscMemzero(aux_ins_indices,pcbddc->coarse_size*sizeof(PetscInt));CHKERRQ(ierr);
3683           /* allocate stuffs for message massing */
3684           ierr = PetscMalloc ( (count_recv+1)*sizeof(MPI_Request),&requests);CHKERRQ(ierr);
3685           for(i=0;i<count_recv+1;i++) requests[i]=MPI_REQUEST_NULL;
3686           ierr = PetscMalloc ( count_recv*sizeof(PetscMPIInt),&localsizes2);CHKERRQ(ierr);
3687           ierr = PetscMalloc ( count_recv*sizeof(PetscMPIInt),&localdispl2);CHKERRQ(ierr);
3688           /* fill up quantities */
3689           j=0;
3690           for(i=0;i<count_recv;i++){
3691             ii = ranks_recv[i];
3692             localsizes2[i]=pcbddc->local_primal_sizes[ii]*pcbddc->local_primal_sizes[ii];
3693             localdispl2[i]=j;
3694             j+=localsizes2[i];
3695             jj = pcbddc->local_primal_displacements[ii];
3696             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 */
3697           }
3698           /*printf("aux_ins_indices 1\n");
3699           for(i=0;i<pcbddc->coarse_size;i++)
3700             printf("%d ",aux_ins_indices[i]);
3701           printf("\n");*/
3702           /* temp_coarse_mat_vals used to store temporarly received matrix values */
3703           ierr = PetscMalloc ( j*sizeof(PetscScalar),&temp_coarse_mat_vals);CHKERRQ(ierr);
3704           /* evaluate how many values I will insert in coarse mat */
3705           ins_local_primal_size=0;
3706           for(i=0;i<pcbddc->coarse_size;i++)
3707             if(aux_ins_indices[i])
3708               ins_local_primal_size++;
3709           /* evaluate indices I will insert in coarse mat */
3710           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscInt),&ins_local_primal_indices);CHKERRQ(ierr);
3711           j=0;
3712           for(i=0;i<pcbddc->coarse_size;i++)
3713             if(aux_ins_indices[i])
3714               ins_local_primal_indices[j++]=i;
3715           /* use aux_ins_indices to realize a global to local mapping */
3716           j=0;
3717           for(i=0;i<pcbddc->coarse_size;i++){
3718             if(aux_ins_indices[i]==0){
3719               aux_ins_indices[i]=-1;
3720             } else {
3721               aux_ins_indices[i]=j;
3722               j++;
3723             }
3724           }
3725 
3726           /*printf("New details localsizes2 localdispl2\n");
3727           for(i=0;i<count_recv;i++)
3728             printf("(%d %d) ",localsizes2[i],localdispl2[i]);
3729           printf("\n");
3730           printf("aux_ins_indices 2\n");
3731           for(i=0;i<pcbddc->coarse_size;i++)
3732             printf("%d ",aux_ins_indices[i]);
3733           printf("\n");
3734           printf("ins_local_primal_indices\n");
3735           for(i=0;i<ins_local_primal_size;i++)
3736             printf("%d ",ins_local_primal_indices[i]);
3737           printf("\n");
3738           printf("coarse_submat_vals\n");
3739           for(i=0;i<pcbddc->local_primal_size;i++)
3740             for(j=0;j<pcbddc->local_primal_size;j++)
3741               printf("(%lf %d %d)\n",coarse_submat_vals[j*pcbddc->local_primal_size+i],pcbddc->local_primal_indices[i],pcbddc->local_primal_indices[j]);
3742           printf("\n");*/
3743 
3744           /* processes partecipating in coarse problem receive matrix data from their friends */
3745           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);
3746           if(rank_coarse_proc_send_to != MPI_PROC_NULL ) {
3747             send_size=pcbddc->local_primal_size*pcbddc->local_primal_size;
3748             ierr = MPI_Isend(&coarse_submat_vals[0],send_size,MPIU_SCALAR,rank_coarse_proc_send_to,666,prec_comm,&requests[count_recv]);CHKERRQ(ierr);
3749           }
3750           ierr = MPI_Waitall(count_recv+1,requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3751 
3752           /*if(coarse_color == 0) {
3753             printf("temp_coarse_mat_vals\n");
3754             for(k=0;k<count_recv;k++){
3755               printf("---- %d ----\n",ranks_recv[k]);
3756               for(i=0;i<pcbddc->local_primal_sizes[ranks_recv[k]];i++)
3757                 for(j=0;j<pcbddc->local_primal_sizes[ranks_recv[k]];j++)
3758                   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]);
3759               printf("\n");
3760             }
3761           }*/
3762           /* calculate data to insert in coarse mat */
3763           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3764           PetscMemzero(ins_coarse_mat_vals,ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar));
3765 
3766           PetscMPIInt rr,kk,lps,lpd;
3767           PetscInt row_ind,col_ind;
3768           for(k=0;k<count_recv;k++){
3769             rr = ranks_recv[k];
3770             kk = localdispl2[k];
3771             lps = pcbddc->local_primal_sizes[rr];
3772             lpd = pcbddc->local_primal_displacements[rr];
3773             /*printf("Inserting the following indices (received from %d)\n",rr);*/
3774             for(j=0;j<lps;j++){
3775               col_ind=aux_ins_indices[pcbddc->replicated_local_primal_indices[lpd+j]];
3776               for(i=0;i<lps;i++){
3777                 row_ind=aux_ins_indices[pcbddc->replicated_local_primal_indices[lpd+i]];
3778                 /*printf("%d %d\n",row_ind,col_ind);*/
3779                 ins_coarse_mat_vals[col_ind*ins_local_primal_size+row_ind]+=temp_coarse_mat_vals[kk+j*lps+i];
3780               }
3781             }
3782           }
3783           ierr = PetscFree(requests);CHKERRQ(ierr);
3784           ierr = PetscFree(aux_ins_indices);CHKERRQ(ierr);
3785           ierr = PetscFree(temp_coarse_mat_vals);CHKERRQ(ierr);
3786           if(coarse_color == 0) { ierr = PetscFree(ranks_recv);CHKERRQ(ierr); }
3787 
3788           /* create local to global mapping needed by coarse MATIS */
3789           {
3790             IS coarse_IS;
3791             if(coarse_comm != MPI_COMM_NULL ) ierr = MPI_Comm_free(&coarse_comm);CHKERRQ(ierr);
3792             coarse_comm = prec_comm;
3793             active_rank=rank_prec_comm;
3794             ierr = ISCreateGeneral(coarse_comm,ins_local_primal_size,ins_local_primal_indices,PETSC_COPY_VALUES,&coarse_IS);CHKERRQ(ierr);
3795             ierr = ISLocalToGlobalMappingCreateIS(coarse_IS,&coarse_ISLG);CHKERRQ(ierr);
3796             ierr = ISDestroy(&coarse_IS);CHKERRQ(ierr);
3797           }
3798         }
3799         if(pcbddc->coarse_problem_type==PARALLEL_BDDC) {
3800           /* arrays for values insertion */
3801           ins_local_primal_size = pcbddc->local_primal_size;
3802           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscMPIInt),&ins_local_primal_indices);CHKERRQ(ierr);
3803           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3804           for(j=0;j<ins_local_primal_size;j++){
3805             ins_local_primal_indices[j]=pcbddc->local_primal_indices[j];
3806             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];
3807           }
3808         }
3809         break;
3810 
3811     }
3812 
3813     case(GATHERS_BDDC):
3814       {
3815 
3816         PetscMPIInt mysize,mysize2;
3817 
3818         if(rank_prec_comm==active_rank) {
3819           ierr = PetscMalloc ( pcbddc->replicated_primal_size*sizeof(PetscMPIInt),&pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
3820           pcbddc->replicated_local_primal_values = (PetscScalar*)calloc(pcbddc->replicated_primal_size,sizeof(PetscScalar));
3821           ierr = PetscMalloc ( size_prec_comm*sizeof(PetscMPIInt),&localsizes2);CHKERRQ(ierr);
3822           ierr = PetscMalloc ( size_prec_comm*sizeof(PetscMPIInt),&localdispl2);CHKERRQ(ierr);
3823           /* arrays for values insertion */
3824           ins_local_primal_size = pcbddc->coarse_size;
3825           ierr = PetscMalloc ( ins_local_primal_size*sizeof(PetscMPIInt),&ins_local_primal_indices);CHKERRQ(ierr);
3826           ierr = PetscMalloc ( ins_local_primal_size*ins_local_primal_size*sizeof(PetscScalar),&ins_coarse_mat_vals);CHKERRQ(ierr);
3827           for(i=0;i<size_prec_comm;i++) localsizes2[i]=pcbddc->local_primal_sizes[i]*pcbddc->local_primal_sizes[i];
3828           localdispl2[0]=0;
3829           for(i=1;i<size_prec_comm;i++) localdispl2[i]=localsizes2[i-1]+localdispl2[i-1];
3830           j=0;
3831           for(i=0;i<size_prec_comm;i++) j+=localsizes2[i];
3832           ierr = PetscMalloc ( j*sizeof(PetscScalar),&temp_coarse_mat_vals);CHKERRQ(ierr);
3833         }
3834 
3835         mysize=pcbddc->local_primal_size;
3836         mysize2=pcbddc->local_primal_size*pcbddc->local_primal_size;
3837         if(pcbddc->coarse_problem_type == SEQUENTIAL_BDDC){
3838           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);
3839           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);
3840         } else {
3841           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);
3842           ierr = MPI_Allgatherv(&coarse_submat_vals[0],mysize2,MPIU_SCALAR,&temp_coarse_mat_vals[0],localsizes2,localdispl2,MPIU_SCALAR,prec_comm);CHKERRQ(ierr);
3843         }
3844 
3845   /* free data structures no longer needed and allocate some space which will be needed in BDDC application */
3846         if(rank_prec_comm==active_rank) {
3847           PetscInt offset,offset2,row_ind,col_ind;
3848           for(j=0;j<ins_local_primal_size;j++){
3849             ins_local_primal_indices[j]=j;
3850             for(i=0;i<ins_local_primal_size;i++) ins_coarse_mat_vals[j*ins_local_primal_size+i]=0.0;
3851           }
3852           for(k=0;k<size_prec_comm;k++){
3853             offset=pcbddc->local_primal_displacements[k];
3854             offset2=localdispl2[k];
3855             for(j=0;j<pcbddc->local_primal_sizes[k];j++){
3856               col_ind=pcbddc->replicated_local_primal_indices[offset+j];
3857               for(i=0;i<pcbddc->local_primal_sizes[k];i++){
3858                 row_ind=pcbddc->replicated_local_primal_indices[offset+i];
3859                 ins_coarse_mat_vals[col_ind*pcbddc->coarse_size+row_ind]+=temp_coarse_mat_vals[offset2+j*pcbddc->local_primal_sizes[k]+i];
3860               }
3861             }
3862           }
3863         }
3864         break;
3865       }/* switch on coarse problem and communications associated with finished */
3866   }
3867 
3868   /* Now create and fill up coarse matrix */
3869   if( rank_prec_comm == active_rank ) {
3870     if(pcbddc->coarse_problem_type != MULTILEVEL_BDDC) {
3871       ierr = MatCreate(coarse_comm,&pcbddc->coarse_mat);CHKERRQ(ierr);
3872       ierr = MatSetSizes(pcbddc->coarse_mat,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size);CHKERRQ(ierr);
3873       ierr = MatSetType(pcbddc->coarse_mat,coarse_mat_type);CHKERRQ(ierr);
3874       ierr = MatSetUp(pcbddc->coarse_mat);CHKERRQ(ierr);
3875       ierr = MatSetOption(pcbddc->coarse_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr); /* local values stored in column major */
3876       ierr = MatSetOption(pcbddc->coarse_mat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3877     } else {
3878       Mat matis_coarse_local_mat;
3879       /* remind bs */
3880       ierr = MatCreateIS(coarse_comm,bs,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_ISLG,&pcbddc->coarse_mat);CHKERRQ(ierr);
3881       ierr = MatSetUp(pcbddc->coarse_mat);CHKERRQ(ierr);
3882       ierr = MatISGetLocalMat(pcbddc->coarse_mat,&matis_coarse_local_mat);CHKERRQ(ierr);
3883       ierr = MatSetUp(matis_coarse_local_mat);CHKERRQ(ierr);
3884       ierr = MatSetOption(matis_coarse_local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr); /* local values stored in column major */
3885       ierr = MatSetOption(matis_coarse_local_mat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3886     }
3887     ierr = MatSetOption(pcbddc->coarse_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
3888     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);
3889     ierr = MatAssemblyBegin(pcbddc->coarse_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3890     ierr = MatAssemblyEnd(pcbddc->coarse_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3891 
3892     /*  PetscViewer view_out;
3893       ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,"coarsematfull.m",&view_out);CHKERRQ(ierr);
3894       ierr = PetscViewerSetFormat(view_out,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3895       ierr = MatView(pcbddc->coarse_mat,view_out);CHKERRQ(ierr);
3896       ierr = PetscViewerDestroy(&view_out);CHKERRQ(ierr);*/
3897 
3898     ierr = MatGetVecs(pcbddc->coarse_mat,&pcbddc->coarse_vec,&pcbddc->coarse_rhs);CHKERRQ(ierr);
3899     /* Preconditioner for coarse problem */
3900     ierr = KSPCreate(coarse_comm,&pcbddc->coarse_ksp);CHKERRQ(ierr);
3901     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3902     ierr = KSPSetOperators(pcbddc->coarse_ksp,pcbddc->coarse_mat,pcbddc->coarse_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
3903     ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,max_it_coarse_ksp);CHKERRQ(ierr);
3904     ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3905     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3906     ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3907     /* Allow user's customization */
3908     ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,"coarse_");CHKERRQ(ierr);
3909     ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3910     /* Set Up PC for coarse problem BDDC */
3911     if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC) {
3912       if(dbg_flag) {
3913         ierr = PetscViewerASCIIPrintf(viewer,"----------------Setting up a new level---------------\n");CHKERRQ(ierr);
3914         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3915       }
3916       ierr = PCBDDCSetCoarseProblemType(pc_temp,MULTILEVEL_BDDC);CHKERRQ(ierr);
3917     }
3918     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3919     if(pcbddc->coarse_problem_type == MULTILEVEL_BDDC) {
3920       if(dbg_flag) {
3921         ierr = PetscViewerASCIIPrintf(viewer,"----------------New level set------------------------\n");CHKERRQ(ierr);
3922         ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
3923       }
3924     }
3925   }
3926   if(pcbddc->coarse_communications_type == SCATTERS_BDDC) {
3927      IS local_IS,global_IS;
3928      ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size,0,1,&local_IS);CHKERRQ(ierr);
3929      ierr = ISCreateGeneral(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_indices,PETSC_COPY_VALUES,&global_IS);CHKERRQ(ierr);
3930      ierr = VecScatterCreate(pcbddc->vec1_P,local_IS,pcbddc->coarse_vec,global_IS,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3931      ierr = ISDestroy(&local_IS);CHKERRQ(ierr);
3932      ierr = ISDestroy(&global_IS);CHKERRQ(ierr);
3933   }
3934 
3935 
3936   /* Evaluate condition number of coarse problem for cheby (and verbose output if requested) */
3937   if( pcbddc->coarse_problem_type == MULTILEVEL_BDDC && rank_prec_comm == active_rank ) {
3938     PetscScalar m_one=-1.0;
3939     PetscReal   infty_error,lambda_min,lambda_max,kappa_2;
3940     const KSPType check_ksp_type=KSPGMRES;
3941 
3942     /* change coarse ksp object to an iterative method suitable for extreme eigenvalues' estimation */
3943     ierr = KSPSetType(pcbddc->coarse_ksp,check_ksp_type);CHKERRQ(ierr);
3944     ierr = KSPSetComputeSingularValues(pcbddc->coarse_ksp,PETSC_TRUE);CHKERRQ(ierr);
3945     ierr = KSPSetTolerances(pcbddc->coarse_ksp,1.e-8,1.e-8,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3946     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3947     ierr = VecSetRandom(pcbddc->coarse_rhs,PETSC_NULL);CHKERRQ(ierr);
3948     ierr = MatMult(pcbddc->coarse_mat,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
3949     ierr = MatMult(pcbddc->coarse_mat,pcbddc->coarse_vec,pcbddc->coarse_rhs);CHKERRQ(ierr);
3950     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_rhs);CHKERRQ(ierr);
3951     ierr = KSPComputeExtremeSingularValues(pcbddc->coarse_ksp,&lambda_max,&lambda_min);CHKERRQ(ierr);
3952     if(dbg_flag) {
3953       kappa_2=lambda_max/lambda_min;
3954       ierr = KSPGetIterationNumber(pcbddc->coarse_ksp,&k);CHKERRQ(ierr);
3955       ierr = VecAXPY(pcbddc->coarse_rhs,m_one,pcbddc->coarse_vec);CHKERRQ(ierr);
3956       ierr = VecNorm(pcbddc->coarse_rhs,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3957       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);
3958       ierr = PetscViewerASCIIPrintf(viewer,"Coarse problem eigenvalues: % 1.14e %1.14e\n",lambda_min,lambda_max);CHKERRQ(ierr);
3959       ierr = PetscViewerASCIIPrintf(viewer,"Coarse problem infty_error: %1.14e\n",infty_error);CHKERRQ(ierr);
3960     }
3961     /* restore coarse ksp to default values */
3962     ierr = KSPSetComputeSingularValues(pcbddc->coarse_ksp,PETSC_FALSE);CHKERRQ(ierr);
3963     ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3964     ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3965     ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,max_it_coarse_ksp);CHKERRQ(ierr);
3966     ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3967     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3968   }
3969 
3970   /* free data structures no longer needed */
3971   if(coarse_ISLG)                { ierr = ISLocalToGlobalMappingDestroy(&coarse_ISLG);CHKERRQ(ierr); }
3972   if(ins_local_primal_indices)   { ierr = PetscFree(ins_local_primal_indices);CHKERRQ(ierr);  }
3973   if(ins_coarse_mat_vals)        { ierr = PetscFree(ins_coarse_mat_vals);CHKERRQ(ierr);}
3974   if(localsizes2)                { ierr = PetscFree(localsizes2);CHKERRQ(ierr);}
3975   if(localdispl2)                { ierr = PetscFree(localdispl2);CHKERRQ(ierr);}
3976   if(temp_coarse_mat_vals)       { ierr = PetscFree(temp_coarse_mat_vals);CHKERRQ(ierr);}
3977 
3978   PetscFunctionReturn(0);
3979 }
3980 
3981 #undef __FUNCT__
3982 #define __FUNCT__ "PCBDDCManageLocalBoundaries"
3983 static PetscErrorCode PCBDDCManageLocalBoundaries(PC pc)
3984 {
3985 
3986   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
3987   PC_IS         *pcis = (PC_IS*)pc->data;
3988   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
3989   PCBDDCGraph mat_graph=pcbddc->mat_graph;
3990   PetscInt    *queue_in_global_numbering,*is_indices,*auxis;
3991   PetscInt    bs,ierr,i,j,s,k,iindex,neumann_bsize,dirichlet_bsize;
3992   PetscInt    total_counts,nodes_touched,where_values=1,vertex_size;
3993   PetscMPIInt adapt_interface=0,adapt_interface_reduced=0,NEUMANNCNT=0;
3994   PetscBool   same_set;
3995   MPI_Comm    interface_comm=((PetscObject)pc)->comm;
3996   PetscBool   use_faces=PETSC_FALSE,use_edges=PETSC_FALSE;
3997   const PetscInt *neumann_nodes;
3998   const PetscInt *dirichlet_nodes;
3999   IS          used_IS,*custom_ISForDofs;
4000   PetscScalar *array;
4001   PetscScalar *array2;
4002   PetscViewer viewer=pcbddc->dbg_viewer;
4003 
4004   PetscFunctionBegin;
4005   /* Setup local adjacency graph */
4006   mat_graph->nvtxs=pcis->n;
4007   if(!mat_graph->xadj) { NEUMANNCNT = 1; }
4008   ierr = PCBDDCSetupLocalAdjacencyGraph(pc);CHKERRQ(ierr);
4009   i = mat_graph->nvtxs;
4010   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);
4011   ierr = PetscMalloc2(i,PetscInt,&mat_graph->which_dof,i,PetscBool,&mat_graph->touched);CHKERRQ(ierr);
4012   ierr = PetscMalloc(i*sizeof(PetscInt),&queue_in_global_numbering);CHKERRQ(ierr);
4013   ierr = PetscMemzero(mat_graph->where,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4014   ierr = PetscMemzero(mat_graph->count,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4015   ierr = PetscMemzero(mat_graph->which_dof,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4016   ierr = PetscMemzero(mat_graph->queue,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4017   ierr = PetscMemzero(mat_graph->cptr,(mat_graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
4018 
4019   /* Setting dofs splitting in mat_graph->which_dof
4020      Get information about dofs' splitting if provided by the user
4021      Otherwise it assumes a constant block size */
4022   vertex_size=0;
4023   if(!pcbddc->n_ISForDofs) {
4024     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
4025     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
4026     for(i=0;i<bs;i++) {
4027       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
4028     }
4029     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
4030     vertex_size=1;
4031     /* remove my references to IS objects */
4032     for(i=0;i<bs;i++) {
4033       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
4034     }
4035     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
4036   }
4037   for(i=0;i<pcbddc->n_ISForDofs;i++) {
4038     ierr = ISGetSize(pcbddc->ISForDofs[i],&k);CHKERRQ(ierr);
4039     ierr = ISGetIndices(pcbddc->ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
4040     for(j=0;j<k;j++) {
4041       mat_graph->which_dof[is_indices[j]]=i;
4042     }
4043     ierr = ISRestoreIndices(pcbddc->ISForDofs[i],(const PetscInt**)&is_indices);CHKERRQ(ierr);
4044   }
4045   /* use mat block size as vertex size if it has not yet set */
4046   if(!vertex_size) {
4047     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
4048   }
4049 
4050   /* count number of neigh per node */
4051   total_counts=0;
4052   for(i=1;i<pcis->n_neigh;i++){
4053     s=pcis->n_shared[i];
4054     total_counts+=s;
4055     for(j=0;j<s;j++){
4056       mat_graph->count[pcis->shared[i][j]] += 1;
4057     }
4058   }
4059   /* Take into account Neumann data -> it increments number of sharing subdomains for nodes lying on the interface */
4060   ierr = PCBDDCGetNeumannBoundaries(pc,&used_IS);CHKERRQ(ierr);
4061   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
4062   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4063   if(used_IS) {
4064     ierr = ISGetSize(used_IS,&neumann_bsize);CHKERRQ(ierr);
4065     ierr = ISGetIndices(used_IS,&neumann_nodes);CHKERRQ(ierr);
4066     for(i=0;i<neumann_bsize;i++){
4067       iindex = neumann_nodes[i];
4068       if(mat_graph->count[iindex] > NEUMANNCNT && array[iindex]==0.0){
4069         mat_graph->count[iindex]+=1;
4070         total_counts++;
4071         array[iindex]=array[iindex]+1.0;
4072       } else if(array[iindex]>0.0) {
4073         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);
4074       }
4075     }
4076   }
4077   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4078   /* allocate space for storing the set of neighbours for each node */
4079   ierr = PetscMalloc(mat_graph->nvtxs*sizeof(PetscInt*),&mat_graph->neighbours_set);CHKERRQ(ierr);
4080   if(mat_graph->nvtxs) { ierr = PetscMalloc(total_counts*sizeof(PetscInt),&mat_graph->neighbours_set[0]);CHKERRQ(ierr); }
4081   for(i=1;i<mat_graph->nvtxs;i++) mat_graph->neighbours_set[i]=mat_graph->neighbours_set[i-1]+mat_graph->count[i-1];
4082   ierr = PetscMemzero(mat_graph->count,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4083   for(i=1;i<pcis->n_neigh;i++){
4084     s=pcis->n_shared[i];
4085     for(j=0;j<s;j++) {
4086       k=pcis->shared[i][j];
4087       mat_graph->neighbours_set[k][mat_graph->count[k]] = pcis->neigh[i];
4088       mat_graph->count[k]+=1;
4089     }
4090   }
4091   /* Check consistency of Neumann nodes */
4092   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4093   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4094   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4095   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4096   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4097   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4098   /* set -1 fake neighbour to mimic Neumann boundary */
4099   if(used_IS) {
4100     for(i=0;i<neumann_bsize;i++){
4101       iindex = neumann_nodes[i];
4102       if(mat_graph->count[iindex] > NEUMANNCNT){
4103         if(mat_graph->count[iindex]+1 != (PetscInt)array[iindex]) {
4104           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]);
4105         }
4106         mat_graph->neighbours_set[iindex][mat_graph->count[iindex]] = -1;
4107         mat_graph->count[iindex]+=1;
4108       }
4109     }
4110     ierr = ISRestoreIndices(used_IS,&neumann_nodes);CHKERRQ(ierr);
4111   }
4112   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4113   /* sort set of sharing subdomains */
4114   for(i=0;i<mat_graph->nvtxs;i++) { ierr = PetscSortInt(mat_graph->count[i],mat_graph->neighbours_set[i]);CHKERRQ(ierr); }
4115   /* remove interior nodes and dirichlet boundary nodes from the next search into the graph */
4116   for(i=0;i<mat_graph->nvtxs;i++){mat_graph->touched[i]=PETSC_FALSE;}
4117   nodes_touched=0;
4118   ierr = PCBDDCGetDirichletBoundaries(pc,&used_IS);CHKERRQ(ierr);
4119   ierr = VecSet(pcis->vec2_N,0.0);CHKERRQ(ierr);
4120   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4121   ierr = VecGetArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4122   if(used_IS) {
4123     ierr = ISGetSize(used_IS,&dirichlet_bsize);CHKERRQ(ierr);
4124     if(dirichlet_bsize && matis->pure_neumann) {
4125       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Dirichlet boundaries are intended to be used with matrices with zeroed rows!\n");
4126     }
4127     ierr = ISGetIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4128     for(i=0;i<dirichlet_bsize;i++){
4129       iindex=dirichlet_nodes[i];
4130       if(mat_graph->count[iindex] && !mat_graph->touched[iindex]) {
4131         if(array[iindex]>0.0) {
4132           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);
4133         }
4134         mat_graph->touched[iindex]=PETSC_TRUE;
4135         mat_graph->where[iindex]=0;
4136         nodes_touched++;
4137         array2[iindex]=array2[iindex]+1.0;
4138       }
4139     }
4140     ierr = ISRestoreIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4141   }
4142   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4143   ierr = VecRestoreArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4144   /* Check consistency of Dirichlet nodes */
4145   ierr = VecSet(pcis->vec1_N,1.0);CHKERRQ(ierr);
4146   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4147   ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4148   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4149   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4150   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4151   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4152   ierr = VecScatterBegin(matis->ctx,pcis->vec2_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4153   ierr = VecScatterEnd  (matis->ctx,pcis->vec2_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4154   ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4155   ierr = VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4156   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4157   ierr = VecGetArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4158   if(used_IS) {
4159     ierr = ISGetSize(used_IS,&dirichlet_bsize);CHKERRQ(ierr);
4160     ierr = ISGetIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4161     for(i=0;i<dirichlet_bsize;i++){
4162       iindex=dirichlet_nodes[i];
4163       if(array[iindex]>1.0 && array[iindex]!=array2[iindex] ) {
4164          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]);
4165       }
4166     }
4167     ierr = ISRestoreIndices(used_IS,&dirichlet_nodes);CHKERRQ(ierr);
4168   }
4169   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4170   ierr = VecRestoreArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
4171 
4172   for(i=0;i<mat_graph->nvtxs;i++){
4173     if(!mat_graph->count[i]){  /* interior nodes */
4174       mat_graph->touched[i]=PETSC_TRUE;
4175       mat_graph->where[i]=0;
4176       nodes_touched++;
4177     }
4178   }
4179   mat_graph->ncmps = 0;
4180   i=0;
4181   while(nodes_touched<mat_graph->nvtxs) {
4182     /*  find first untouched node in local ordering */
4183     while(mat_graph->touched[i]) i++;
4184     mat_graph->touched[i]=PETSC_TRUE;
4185     mat_graph->where[i]=where_values;
4186     nodes_touched++;
4187     /* now find all other nodes having the same set of sharing subdomains */
4188     for(j=i+1;j<mat_graph->nvtxs;j++){
4189       /* check for same number of sharing subdomains and dof number */
4190       if(!mat_graph->touched[j] && mat_graph->count[i]==mat_graph->count[j] && mat_graph->which_dof[i] == mat_graph->which_dof[j] ){
4191         /* check for same set of sharing subdomains */
4192         same_set=PETSC_TRUE;
4193         for(k=0;k<mat_graph->count[j];k++){
4194           if(mat_graph->neighbours_set[i][k]!=mat_graph->neighbours_set[j][k]) {
4195             same_set=PETSC_FALSE;
4196           }
4197         }
4198         /* I found a friend of mine */
4199         if(same_set) {
4200           mat_graph->where[j]=where_values;
4201           mat_graph->touched[j]=PETSC_TRUE;
4202           nodes_touched++;
4203         }
4204       }
4205     }
4206     where_values++;
4207   }
4208   where_values--; if(where_values<0) where_values=0;
4209   ierr = PetscMalloc(where_values*sizeof(PetscMPIInt),&mat_graph->where_ncmps);CHKERRQ(ierr);
4210   /* Find connected components defined on the shared interface */
4211   if(where_values) {
4212     ierr = PCBDDCFindConnectedComponents(mat_graph, where_values);
4213     /* For consistency among neughbouring procs, I need to sort (by global ordering) each connected component */
4214     for(i=0;i<mat_graph->ncmps;i++) {
4215       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);
4216       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);
4217     }
4218   }
4219   /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
4220   for(i=0;i<where_values;i++) {
4221     /* We are not sure that two connected components will be the same among subdomains sharing a subset of local interface */
4222     if(mat_graph->where_ncmps[i]>1) {
4223       adapt_interface=1;
4224       break;
4225     }
4226   }
4227   ierr = MPI_Allreduce(&adapt_interface,&adapt_interface_reduced,1,MPIU_INT,MPI_LOR,interface_comm);CHKERRQ(ierr);
4228   if(pcbddc->dbg_flag && adapt_interface_reduced) {
4229     ierr = PetscViewerASCIIPrintf(viewer,"Interface adapted\n");CHKERRQ(ierr);
4230     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
4231   }
4232   if(where_values && adapt_interface_reduced) {
4233 
4234     PetscInt sum_requests=0,my_rank;
4235     PetscInt buffer_size,start_of_recv,size_of_recv,start_of_send;
4236     PetscInt temp_buffer_size,ins_val,global_where_counter;
4237     PetscInt *cum_recv_counts;
4238     PetscInt *where_to_nodes_indices;
4239     PetscInt *petsc_buffer;
4240     PetscMPIInt *recv_buffer;
4241     PetscMPIInt *recv_buffer_where;
4242     PetscMPIInt *send_buffer;
4243     PetscMPIInt size_of_send;
4244     PetscInt *sizes_of_sends;
4245     MPI_Request *send_requests;
4246     MPI_Request *recv_requests;
4247     PetscInt *where_cc_adapt;
4248     PetscInt **temp_buffer;
4249     PetscInt *nodes_to_temp_buffer_indices;
4250     PetscInt *add_to_where;
4251 
4252     ierr = MPI_Comm_rank(interface_comm,&my_rank);CHKERRQ(ierr);
4253     ierr = PetscMalloc((where_values+1)*sizeof(PetscInt),&cum_recv_counts);CHKERRQ(ierr);
4254     ierr = PetscMemzero(cum_recv_counts,(where_values+1)*sizeof(PetscInt));CHKERRQ(ierr);
4255     ierr = PetscMalloc(where_values*sizeof(PetscInt),&where_to_nodes_indices);CHKERRQ(ierr);
4256     /* first count how many neighbours per connected component I will receive from */
4257     cum_recv_counts[0]=0;
4258     for(i=1;i<where_values+1;i++){
4259       j=0;
4260       while(mat_graph->where[j] != i) j++;
4261       where_to_nodes_indices[i-1]=j;
4262       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  */
4263       else { cum_recv_counts[i]=cum_recv_counts[i-1]+mat_graph->count[j]-1; }
4264     }
4265     buffer_size=2*cum_recv_counts[where_values]+mat_graph->nvtxs;
4266     ierr = PetscMalloc(2*cum_recv_counts[where_values]*sizeof(PetscMPIInt),&recv_buffer_where);CHKERRQ(ierr);
4267     ierr = PetscMalloc(buffer_size*sizeof(PetscMPIInt),&send_buffer);CHKERRQ(ierr);
4268     ierr = PetscMalloc(cum_recv_counts[where_values]*sizeof(MPI_Request),&send_requests);CHKERRQ(ierr);
4269     ierr = PetscMalloc(cum_recv_counts[where_values]*sizeof(MPI_Request),&recv_requests);CHKERRQ(ierr);
4270     for(i=0;i<cum_recv_counts[where_values];i++) {
4271       send_requests[i]=MPI_REQUEST_NULL;
4272       recv_requests[i]=MPI_REQUEST_NULL;
4273     }
4274     /* exchange with my neighbours the number of my connected components on the shared interface */
4275     for(i=0;i<where_values;i++){
4276       j=where_to_nodes_indices[i];
4277       k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4278       for(;k<mat_graph->count[j];k++){
4279         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);
4280         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);
4281         sum_requests++;
4282       }
4283     }
4284     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4285     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4286     /* determine the connected component I need to adapt */
4287     ierr = PetscMalloc(where_values*sizeof(PetscInt),&where_cc_adapt);CHKERRQ(ierr);
4288     ierr = PetscMemzero(where_cc_adapt,where_values*sizeof(PetscInt));CHKERRQ(ierr);
4289     for(i=0;i<where_values;i++){
4290       for(j=cum_recv_counts[i];j<cum_recv_counts[i+1];j++){
4291         /* The first condition is natural (i.e someone has a different number of cc than me), the second one is just to be safe */
4292         if( mat_graph->where_ncmps[i]!=recv_buffer_where[j] || mat_graph->where_ncmps[i] > 1 ) {
4293           where_cc_adapt[i]=PETSC_TRUE;
4294           break;
4295         }
4296       }
4297     }
4298     /* now get from neighbours their ccs (in global numbering) and adapt them (in case it is needed) */
4299     /* first determine how much data to send (size of each queue plus the global indices) and communicate it to neighbours */
4300     ierr = PetscMalloc(where_values*sizeof(PetscInt),&sizes_of_sends);CHKERRQ(ierr);
4301     ierr = PetscMemzero(sizes_of_sends,where_values*sizeof(PetscInt));CHKERRQ(ierr);
4302     sum_requests=0;
4303     start_of_send=0;
4304     start_of_recv=cum_recv_counts[where_values];
4305     for(i=0;i<where_values;i++) {
4306       if(where_cc_adapt[i]) {
4307         size_of_send=0;
4308         for(j=i;j<mat_graph->ncmps;j++) {
4309           if(mat_graph->where[mat_graph->queue[mat_graph->cptr[j]]] == i+1) { /* WARNING -> where values goes from 1 to where_values included */
4310             send_buffer[start_of_send+size_of_send]=mat_graph->cptr[j+1]-mat_graph->cptr[j];
4311             size_of_send+=1;
4312             for(k=0;k<mat_graph->cptr[j+1]-mat_graph->cptr[j];k++) {
4313               send_buffer[start_of_send+size_of_send+k]=queue_in_global_numbering[mat_graph->cptr[j]+k];
4314             }
4315             size_of_send=size_of_send+mat_graph->cptr[j+1]-mat_graph->cptr[j];
4316           }
4317         }
4318         j = where_to_nodes_indices[i];
4319         k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4320         sizes_of_sends[i]=size_of_send;
4321         for(;k<mat_graph->count[j];k++){
4322           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);
4323           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);
4324           sum_requests++;
4325         }
4326         start_of_send+=size_of_send;
4327       }
4328     }
4329     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4330     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4331     buffer_size=0;
4332     for(k=0;k<sum_requests;k++) { buffer_size+=recv_buffer_where[start_of_recv+k]; }
4333     ierr = PetscMalloc(buffer_size*sizeof(PetscMPIInt),&recv_buffer);CHKERRQ(ierr);
4334     /* now exchange the data */
4335     start_of_recv=0;
4336     start_of_send=0;
4337     sum_requests=0;
4338     for(i=0;i<where_values;i++) {
4339       if(where_cc_adapt[i]) {
4340         size_of_send = sizes_of_sends[i];
4341         j = where_to_nodes_indices[i];
4342         k = (mat_graph->neighbours_set[j][0] == -1 ?  1 : 0);
4343         for(;k<mat_graph->count[j];k++){
4344           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);
4345           size_of_recv=recv_buffer_where[cum_recv_counts[where_values]+sum_requests];
4346           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);
4347           start_of_recv+=size_of_recv;
4348           sum_requests++;
4349         }
4350         start_of_send+=size_of_send;
4351       }
4352     }
4353     ierr = MPI_Waitall(sum_requests,recv_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4354     ierr = MPI_Waitall(sum_requests,send_requests,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
4355     ierr = PetscMalloc(buffer_size*sizeof(PetscInt),&petsc_buffer);CHKERRQ(ierr);
4356     for(k=0;k<start_of_recv;k++) { petsc_buffer[k]=(PetscInt)recv_buffer[k]; }
4357     for(j=0;j<buffer_size;) {
4358        ierr = ISGlobalToLocalMappingApply(matis->mapping,IS_GTOLM_MASK,petsc_buffer[j],&petsc_buffer[j+1],&petsc_buffer[j],&petsc_buffer[j+1]);CHKERRQ(ierr);
4359        k=petsc_buffer[j]+1;
4360        j+=k;
4361     }
4362     sum_requests=cum_recv_counts[where_values];
4363     start_of_recv=0;
4364     ierr = PetscMalloc(mat_graph->nvtxs*sizeof(PetscInt),&nodes_to_temp_buffer_indices);CHKERRQ(ierr);
4365     global_where_counter=0;
4366     for(i=0;i<where_values;i++){
4367       if(where_cc_adapt[i]){
4368         temp_buffer_size=0;
4369         /* find nodes on the shared interface we need to adapt */
4370         for(j=0;j<mat_graph->nvtxs;j++){
4371           if(mat_graph->where[j]==i+1) {
4372             nodes_to_temp_buffer_indices[j]=temp_buffer_size;
4373             temp_buffer_size++;
4374           } else {
4375             nodes_to_temp_buffer_indices[j]=-1;
4376           }
4377         }
4378         /* allocate some temporary space */
4379         ierr = PetscMalloc(temp_buffer_size*sizeof(PetscInt*),&temp_buffer);CHKERRQ(ierr);
4380         ierr = PetscMalloc(temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt),&temp_buffer[0]);CHKERRQ(ierr);
4381         ierr = PetscMemzero(temp_buffer[0],temp_buffer_size*(cum_recv_counts[i+1]-cum_recv_counts[i])*sizeof(PetscInt));CHKERRQ(ierr);
4382         for(j=1;j<temp_buffer_size;j++){
4383           temp_buffer[j]=temp_buffer[j-1]+cum_recv_counts[i+1]-cum_recv_counts[i];
4384         }
4385         /* analyze contributions from neighbouring subdomains for i-th conn comp
4386            temp buffer structure:
4387            supposing part of the interface has dimension 5 (global nodes 0,1,2,3,4)
4388            3 neighs procs with structured connected components:
4389              neigh 0: [0 1 4], [2 3];  (2 connected components)
4390              neigh 1: [0 1], [2 3 4];  (2 connected components)
4391              neigh 2: [0 4], [1], [2 3]; (3 connected components)
4392            tempbuffer (row-oriented) should be filled as:
4393              [ 0, 0, 0;
4394                0, 0, 1;
4395                1, 1, 2;
4396                1, 1, 2;
4397                0, 1, 0; ];
4398            This way we can simply recover the resulting structure account for possible intersections of ccs among neighs.
4399            The mat_graph->where array will be modified to reproduce the following 4 connected components [0], [1], [2 3], [4];
4400                                                                                                                                    */
4401         for(j=0;j<cum_recv_counts[i+1]-cum_recv_counts[i];j++) {
4402           ins_val=0;
4403           size_of_recv=recv_buffer_where[sum_requests];  /* total size of recv from neighs */
4404           for(buffer_size=0;buffer_size<size_of_recv;) {  /* loop until all data from neighs has been taken into account */
4405             for(k=1;k<petsc_buffer[buffer_size+start_of_recv]+1;k++) { /* filling properly temp_buffer using data from a single recv */
4406               temp_buffer[ nodes_to_temp_buffer_indices[ petsc_buffer[ start_of_recv+buffer_size+k ] ] ][j]=ins_val;
4407             }
4408             buffer_size+=k;
4409             ins_val++;
4410           }
4411           start_of_recv+=size_of_recv;
4412           sum_requests++;
4413         }
4414         ierr = PetscMalloc(temp_buffer_size*sizeof(PetscInt),&add_to_where);CHKERRQ(ierr);
4415         ierr = PetscMemzero(add_to_where,temp_buffer_size*sizeof(PetscInt));CHKERRQ(ierr);
4416         for(j=0;j<temp_buffer_size;j++){
4417           if(!add_to_where[j]){ /* found a new cc  */
4418             global_where_counter++;
4419             add_to_where[j]=global_where_counter;
4420             for(k=j+1;k<temp_buffer_size;k++){ /* check for other nodes in new cc */
4421               same_set=PETSC_TRUE;
4422               for(s=0;s<cum_recv_counts[i+1]-cum_recv_counts[i];s++){
4423                 if(temp_buffer[j][s]!=temp_buffer[k][s]) {
4424                   same_set=PETSC_FALSE;
4425                   break;
4426                 }
4427               }
4428               if(same_set) add_to_where[k]=global_where_counter;
4429             }
4430           }
4431         }
4432         /* insert new data in where array */
4433         temp_buffer_size=0;
4434         for(j=0;j<mat_graph->nvtxs;j++){
4435           if(mat_graph->where[j]==i+1) {
4436             mat_graph->where[j]=where_values+add_to_where[temp_buffer_size];
4437             temp_buffer_size++;
4438           }
4439         }
4440         ierr = PetscFree(temp_buffer[0]);CHKERRQ(ierr);
4441         ierr = PetscFree(temp_buffer);CHKERRQ(ierr);
4442         ierr = PetscFree(add_to_where);CHKERRQ(ierr);
4443       }
4444     }
4445     ierr = PetscFree(nodes_to_temp_buffer_indices);CHKERRQ(ierr);
4446     ierr = PetscFree(sizes_of_sends);CHKERRQ(ierr);
4447     ierr = PetscFree(send_requests);CHKERRQ(ierr);
4448     ierr = PetscFree(recv_requests);CHKERRQ(ierr);
4449     ierr = PetscFree(petsc_buffer);CHKERRQ(ierr);
4450     ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
4451     ierr = PetscFree(recv_buffer_where);CHKERRQ(ierr);
4452     ierr = PetscFree(send_buffer);CHKERRQ(ierr);
4453     ierr = PetscFree(cum_recv_counts);CHKERRQ(ierr);
4454     ierr = PetscFree(where_to_nodes_indices);CHKERRQ(ierr);
4455     ierr = PetscFree(where_cc_adapt);CHKERRQ(ierr);
4456     /* We are ready to evaluate consistent connected components on each part of the shared interface */
4457     if(global_where_counter) {
4458       for(i=0;i<mat_graph->nvtxs;i++){ mat_graph->touched[i]=PETSC_FALSE; }
4459       global_where_counter=0;
4460       for(i=0;i<mat_graph->nvtxs;i++){
4461         if(mat_graph->where[i] && !mat_graph->touched[i]) {
4462           global_where_counter++;
4463           for(j=i+1;j<mat_graph->nvtxs;j++){
4464             if(!mat_graph->touched[j] && mat_graph->where[j]==mat_graph->where[i]) {
4465               mat_graph->where[j]=global_where_counter;
4466               mat_graph->touched[j]=PETSC_TRUE;
4467             }
4468           }
4469           mat_graph->where[i]=global_where_counter;
4470           mat_graph->touched[i]=PETSC_TRUE;
4471         }
4472       }
4473       where_values=global_where_counter;
4474     }
4475     if(global_where_counter) {
4476       ierr = PetscMemzero(mat_graph->cptr,(mat_graph->nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
4477       ierr = PetscMemzero(mat_graph->queue,mat_graph->nvtxs*sizeof(PetscInt));CHKERRQ(ierr);
4478       ierr = PetscFree(mat_graph->where_ncmps);CHKERRQ(ierr);
4479       ierr = PetscMalloc(where_values*sizeof(PetscMPIInt),&mat_graph->where_ncmps);CHKERRQ(ierr);
4480       ierr = PCBDDCFindConnectedComponents(mat_graph, where_values);
4481       for(i=0;i<mat_graph->ncmps;i++) {
4482         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);
4483         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);
4484       }
4485     }
4486   } /* Finished adapting interface */
4487   PetscInt nfc=0;
4488   PetscInt nec=0;
4489   PetscInt nvc=0;
4490   PetscBool twodim_flag=PETSC_FALSE;
4491   for (i=0; i<mat_graph->ncmps; i++) {
4492     if( mat_graph->cptr[i+1]-mat_graph->cptr[i] > vertex_size ){
4493       if(mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]==1){ /* 1 neigh Neumann fake included */
4494         nfc++;
4495       } else { /* note that nec will be zero in 2d */
4496         nec++;
4497       }
4498     } else {
4499       nvc+=mat_graph->cptr[i+1]-mat_graph->cptr[i];
4500     }
4501   }
4502 
4503   if(!nec) { /* we are in a 2d case -> no faces, only edges */
4504     nec = nfc;
4505     nfc = 0;
4506     twodim_flag = PETSC_TRUE;
4507   }
4508   /* allocate IS arrays for faces, edges. Vertices need a single index set. */
4509   k=0;
4510   for (i=0; i<mat_graph->ncmps; i++) {
4511     j=mat_graph->cptr[i+1]-mat_graph->cptr[i];
4512     if( j > k) {
4513       k=j;
4514     }
4515     if(j<=vertex_size) {
4516       k+=vertex_size;
4517     }
4518   }
4519   ierr = PetscMalloc(k*sizeof(PetscInt),&auxis);CHKERRQ(ierr);
4520 
4521   if(!pcbddc->vertices_flag && !pcbddc->edges_flag) {
4522     ierr = PetscMalloc(nfc*sizeof(IS),&pcbddc->ISForFaces);CHKERRQ(ierr);
4523     use_faces=PETSC_TRUE;
4524   }
4525   if(!pcbddc->vertices_flag && !pcbddc->faces_flag) {
4526     ierr = PetscMalloc(nec*sizeof(IS),&pcbddc->ISForEdges);CHKERRQ(ierr);
4527     use_edges=PETSC_TRUE;
4528   }
4529   nfc=0;
4530   nec=0;
4531   for (i=0; i<mat_graph->ncmps; i++) {
4532     if( mat_graph->cptr[i+1]-mat_graph->cptr[i] > vertex_size ){
4533       for(j=0;j<mat_graph->cptr[i+1]-mat_graph->cptr[i];j++) {
4534         auxis[j]=mat_graph->queue[mat_graph->cptr[i]+j];
4535       }
4536       if(mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]==1){
4537         if(twodim_flag) {
4538           if(use_edges) {
4539             ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForEdges[nec]);CHKERRQ(ierr);
4540             nec++;
4541           }
4542         } else {
4543           if(use_faces) {
4544             ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForFaces[nfc]);CHKERRQ(ierr);
4545             nfc++;
4546           }
4547         }
4548       } else {
4549         if(use_edges) {
4550           ierr = ISCreateGeneral(PETSC_COMM_SELF,j,auxis,PETSC_COPY_VALUES,&pcbddc->ISForEdges[nec]);CHKERRQ(ierr);
4551           nec++;
4552         }
4553       }
4554     }
4555   }
4556   pcbddc->n_ISForFaces=nfc;
4557   pcbddc->n_ISForEdges=nec;
4558   nvc=0;
4559   if( !pcbddc->constraints_flag ) {
4560     for (i=0; i<mat_graph->ncmps; i++) {
4561       if( mat_graph->cptr[i+1]-mat_graph->cptr[i] <= vertex_size ){
4562         for( j=mat_graph->cptr[i];j<mat_graph->cptr[i+1];j++) {
4563           auxis[nvc]=mat_graph->queue[j];
4564           nvc++;
4565         }
4566       }
4567     }
4568   }
4569   /* sort vertex set (by local ordering) */
4570   ierr = PetscSortInt(nvc,auxis);CHKERRQ(ierr);
4571   ierr = ISCreateGeneral(PETSC_COMM_SELF,nvc,auxis,PETSC_COPY_VALUES,&pcbddc->ISForVertices);CHKERRQ(ierr);
4572 
4573   if(pcbddc->dbg_flag) {
4574 
4575     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4576     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Details from PCBDDCManageLocalBoundaries for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
4577     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4578 /*    ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Graph (adjacency structure) of local Neumann mat\n");CHKERRQ(ierr);
4579     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
4580     for(i=0;i<mat_graph->nvtxs;i++) {
4581       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Nodes connected to node number %d are %d\n",i,mat_graph->xadj[i+1]-mat_graph->xadj[i]);CHKERRQ(ierr);
4582       for(j=mat_graph->xadj[i];j<mat_graph->xadj[i+1];j++){
4583         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d ",mat_graph->adjncy[j]);CHKERRQ(ierr);
4584       }
4585       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n--------------------------------------------------------------\n");CHKERRQ(ierr);
4586     }*/
4587     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Matrix graph has %d connected components", mat_graph->ncmps);CHKERRQ(ierr);
4588     for(i=0;i<mat_graph->ncmps;i++) {
4589       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\nDetails for connected component number %02d: size %04d, count %01d. Nodes follow.\n",
4590              i,mat_graph->cptr[i+1]-mat_graph->cptr[i],mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]);CHKERRQ(ierr);
4591       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"subdomains: ");
4592       for (j=0;j<mat_graph->count[mat_graph->queue[mat_graph->cptr[i]]]; j++) {
4593         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d ",mat_graph->neighbours_set[mat_graph->queue[mat_graph->cptr[i]]][j]);
4594       }
4595       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n");
4596       for (j=mat_graph->cptr[i]; j<mat_graph->cptr[i+1]; j++){
4597         /* ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d (%d), ",queue_in_global_numbering[j],mat_graph->queue[j]);CHKERRQ(ierr); */
4598         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"%d, ",mat_graph->queue[j]);CHKERRQ(ierr);
4599       }
4600     }
4601     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"\n--------------------------------------------------------------\n");CHKERRQ(ierr);
4602     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local vertices\n",PetscGlobalRank,nvc);CHKERRQ(ierr);
4603     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local faces\n",PetscGlobalRank,nfc);CHKERRQ(ierr);
4604     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d detected %02d local edges\n",PetscGlobalRank,nec);CHKERRQ(ierr);
4605     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
4606   }
4607 
4608   ierr = PetscFree(queue_in_global_numbering);CHKERRQ(ierr);
4609   ierr = PetscFree(auxis);CHKERRQ(ierr);
4610   PetscFunctionReturn(0);
4611 
4612 }
4613 
4614 /* -------------------------------------------------------------------------- */
4615 
4616 /* The following code has been adapted from function IsConnectedSubdomain contained
4617    in source file contig.c of METIS library (version 5.0.1)
4618    It finds connected components of each partition labeled from 1 to n_dist  */
4619 
4620 #undef __FUNCT__
4621 #define __FUNCT__ "PCBDDCFindConnectedComponents"
4622 static PetscErrorCode PCBDDCFindConnectedComponents(PCBDDCGraph graph, PetscInt n_dist )
4623 {
4624   PetscInt i, j, k, nvtxs, first, last, nleft, ncmps,pid,cum_queue,n,ncmps_pid;
4625   PetscInt *xadj, *adjncy, *where, *queue;
4626   PetscInt *cptr;
4627   PetscBool *touched;
4628 
4629   PetscFunctionBegin;
4630 
4631   nvtxs   = graph->nvtxs;
4632   xadj    = graph->xadj;
4633   adjncy  = graph->adjncy;
4634   where   = graph->where;
4635   touched = graph->touched;
4636   queue   = graph->queue;
4637   cptr    = graph->cptr;
4638 
4639   for (i=0; i<nvtxs; i++)
4640     touched[i] = PETSC_FALSE;
4641 
4642   cum_queue=0;
4643   ncmps=0;
4644 
4645   for(n=0; n<n_dist; n++) {
4646     pid = n+1;  /* partition labeled by 0 is discarded */
4647     nleft = 0;
4648     for (i=0; i<nvtxs; i++) {
4649       if (where[i] == pid)
4650         nleft++;
4651     }
4652     for (i=0; i<nvtxs; i++) {
4653       if (where[i] == pid)
4654         break;
4655     }
4656     touched[i] = PETSC_TRUE;
4657     queue[cum_queue] = i;
4658     first = 0; last = 1;
4659     cptr[ncmps] = cum_queue;  /* This actually points to queue */
4660     ncmps_pid = 0;
4661     while (first != nleft) {
4662       if (first == last) { /* Find another starting vertex */
4663         cptr[++ncmps] = first+cum_queue;
4664         ncmps_pid++;
4665         for (i=0; i<nvtxs; i++) {
4666           if (where[i] == pid && !touched[i])
4667             break;
4668         }
4669         queue[cum_queue+last] = i;
4670         last++;
4671         touched[i] = PETSC_TRUE;
4672       }
4673       i = queue[cum_queue+first];
4674       first++;
4675       for (j=xadj[i]; j<xadj[i+1]; j++) {
4676         k = adjncy[j];
4677         if (where[k] == pid && !touched[k]) {
4678           queue[cum_queue+last] = k;
4679           last++;
4680           touched[k] = PETSC_TRUE;
4681         }
4682       }
4683     }
4684     cptr[++ncmps] = first+cum_queue;
4685     ncmps_pid++;
4686     cum_queue=cptr[ncmps];
4687     graph->where_ncmps[n] = ncmps_pid;
4688   }
4689   graph->ncmps = ncmps;
4690 
4691   PetscFunctionReturn(0);
4692 }
4693