xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 8666afb4586210a41db396957f4305e39960f1ad)
1 /* TODOLIST
2 
3    Solvers
4    - Add support for cholesky for coarse solver (similar to local solvers)
5    - Propagate ksp prefixes for solvers to mat objects?
6 
7    User interface
8    - ** DM attached to pc?
9 
10    Debugging output
11    - * Better management of verbosity levels of debugging output
12 
13    Extra
14    - *** Is it possible to work with PCBDDCGraph on boundary indices only (less memory consumed)?
15    - BDDC with MG framework?
16 
17    FETIDP
18    - Move FETIDP code to its own classes
19 
20    MATIS related operations contained in BDDC code
21    - Provide general case for subassembling
22 
23 */
24 
25 #include <../src/ksp/pc/impls/bddc/bddc.h> /*I "petscpc.h" I*/  /* includes for fortran wrappers */
26 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
27 #include <petscblaslapack.h>
28 
29 /* temporarily declare it */
30 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
31 
32 /* -------------------------------------------------------------------------- */
33 #undef __FUNCT__
34 #define __FUNCT__ "PCSetFromOptions_BDDC"
35 PetscErrorCode PCSetFromOptions_BDDC(PetscOptions *PetscOptionsObject,PC pc)
36 {
37   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
38   PetscErrorCode ierr;
39 
40   PetscFunctionBegin;
41   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
42   /* Verbose debugging */
43   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
44   /* Primal space cumstomization */
45   ierr = PetscOptionsBool("-pc_bddc_use_local_mat_graph","Use or not adjacency graph of local mat for interface analysis","none",pcbddc->use_local_adj,&pcbddc->use_local_adj,NULL);CHKERRQ(ierr);
46   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
47   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
48   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
49   ierr = PetscOptionsBool("-pc_bddc_use_true_nnsp","Use near null space attached to the matrix without modifications","none",pcbddc->use_nnsp_true,&pcbddc->use_nnsp_true,NULL);CHKERRQ(ierr);
50   ierr = PetscOptionsBool("-pc_bddc_use_qr_single","Use QR factorization for single constraints on cc (QR is used when multiple constraints are present)","none",pcbddc->use_qr_single,&pcbddc->use_qr_single,NULL);CHKERRQ(ierr);
51   /* Change of basis */
52   ierr = PetscOptionsBool("-pc_bddc_use_change_of_basis","Use or not internal change of basis on local edge nodes","none",pcbddc->use_change_of_basis,&pcbddc->use_change_of_basis,NULL);CHKERRQ(ierr);
53   ierr = PetscOptionsBool("-pc_bddc_use_change_on_faces","Use or not internal change of basis on local face nodes","none",pcbddc->use_change_on_faces,&pcbddc->use_change_on_faces,NULL);CHKERRQ(ierr);
54   if (!pcbddc->use_change_of_basis) {
55     pcbddc->use_change_on_faces = PETSC_FALSE;
56   }
57   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
58   ierr = PetscOptionsBool("-pc_bddc_switch_static","Switch on static condensation ops around the interface preconditioner","none",pcbddc->switch_static,&pcbddc->switch_static,NULL);CHKERRQ(ierr);
59   ierr = PetscOptionsInt("-pc_bddc_coarse_redistribute","Number of procs where to redistribute coarse problem","none",pcbddc->redistribute_coarse,&pcbddc->redistribute_coarse,NULL);CHKERRQ(ierr);
60   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,NULL);CHKERRQ(ierr);
61   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","none",pcbddc->max_levels,&pcbddc->max_levels,NULL);CHKERRQ(ierr);
62   ierr = PetscOptionsBool("-pc_bddc_use_coarse_estimates","Use estimated eigenvalues for coarse problem","none",pcbddc->use_coarse_estimates,&pcbddc->use_coarse_estimates,NULL);CHKERRQ(ierr);
63   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
64   ierr = PetscOptionsBool("-pc_bddc_schur_rebuild","Whether or not the interface graph for Schur principal minors has to be rebuilt (i.e. define the interface without any adjacency)","none",pcbddc->sub_schurs_rebuild,&pcbddc->sub_schurs_rebuild,NULL);CHKERRQ(ierr);
65   ierr = PetscOptionsInt("-pc_bddc_schur_layers","Number of dofs' layers for the computation of principal minors (i.e. -1 uses all dofs)","none",pcbddc->sub_schurs_layers,&pcbddc->sub_schurs_layers,NULL);CHKERRQ(ierr);
66   ierr = PetscOptionsBool("-pc_bddc_schur_use_useradj","Whether or not the CSR graph specified by the user should be used for computing successive layers (default is to use adj of local mat)","none",pcbddc->sub_schurs_use_useradj,&pcbddc->sub_schurs_use_useradj,NULL);CHKERRQ(ierr);
67   ierr = PetscOptionsBool("-pc_bddc_deluxe_faster","Faster application of deluxe scaling (requires extra work during setup)","none",pcbddc->faster_deluxe,&pcbddc->faster_deluxe,NULL);CHKERRQ(ierr);
68   ierr = PetscOptionsReal("-pc_bddc_adaptive_threshold","Threshold to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&pcbddc->adaptive_threshold,NULL);CHKERRQ(ierr);
69   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
70   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
71   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
72   ierr = PetscOptionsInt("-pc_bddc_coarse_adj","Number of processors where to map the coarse adjacency list","none",pcbddc->coarse_adj_red,&pcbddc->coarse_adj_red,NULL);CHKERRQ(ierr);
73   ierr = PetscOptionsBool("-pc_bddc_benign_trick","Apply the benign subspace trick to a class of saddle point problems","none",pcbddc->benign_saddle_point,&pcbddc->benign_saddle_point,NULL);CHKERRQ(ierr);
74   ierr = PetscOptionsTail();CHKERRQ(ierr);
75   PetscFunctionReturn(0);
76 }
77 /* -------------------------------------------------------------------------- */
78 #undef __FUNCT__
79 #define __FUNCT__ "PCBDDCSetChangeOfBasisMat_BDDC"
80 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change)
81 {
82   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
83   PetscErrorCode ierr;
84 
85   PetscFunctionBegin;
86   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
87   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
88   pcbddc->user_ChangeOfBasisMatrix = change;
89   PetscFunctionReturn(0);
90 }
91 #undef __FUNCT__
92 #define __FUNCT__ "PCBDDCSetChangeOfBasisMat"
93 /*@
94  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
95 
96    Collective on PC
97 
98    Input Parameters:
99 +  pc - the preconditioning context
100 -  change - the change of basis matrix
101 
102    Level: intermediate
103 
104    Notes:
105 
106 .seealso: PCBDDC
107 @*/
108 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change)
109 {
110   PetscErrorCode ierr;
111 
112   PetscFunctionBegin;
113   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
114   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
115   PetscCheckSameComm(pc,1,change,2);
116   if (pc->mat) {
117     PetscInt rows_c,cols_c,rows,cols;
118     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
119     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
120     if (rows_c != rows) {
121       SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of rows for change of basis matrix! %d != %d",rows_c,rows);
122     }
123     if (cols_c != cols) {
124       SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of columns for change of basis matrix! %d != %d",cols_c,cols);
125     }
126     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
127     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
128     if (rows_c != rows) {
129       SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local rows for change of basis matrix! %d != %d",rows_c,rows);
130     }
131     if (cols_c != cols) {
132       SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local columns for change of basis matrix! %d != %d",cols_c,cols);
133     }
134   }
135   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat),(pc,change));CHKERRQ(ierr);
136   PetscFunctionReturn(0);
137 }
138 /* -------------------------------------------------------------------------- */
139 #undef __FUNCT__
140 #define __FUNCT__ "PCBDDCSetPrimalVerticesLocalIS_BDDC"
141 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
142 {
143   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
144   PetscErrorCode ierr;
145 
146   PetscFunctionBegin;
147   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
148   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
149   pcbddc->user_primal_vertices = PrimalVertices;
150   PetscFunctionReturn(0);
151 }
152 #undef __FUNCT__
153 #define __FUNCT__ "PCBDDCSetPrimalVerticesLocalIS"
154 /*@
155  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
156 
157    Collective
158 
159    Input Parameters:
160 +  pc - the preconditioning context
161 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
162 
163    Level: intermediate
164 
165    Notes:
166 
167 .seealso: PCBDDC
168 @*/
169 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
170 {
171   PetscErrorCode ierr;
172 
173   PetscFunctionBegin;
174   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
175   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
176   PetscCheckSameComm(pc,1,PrimalVertices,2);
177   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
178   PetscFunctionReturn(0);
179 }
180 /* -------------------------------------------------------------------------- */
181 #undef __FUNCT__
182 #define __FUNCT__ "PCBDDCSetCoarseningRatio_BDDC"
183 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
184 {
185   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
186 
187   PetscFunctionBegin;
188   pcbddc->coarsening_ratio = k;
189   PetscFunctionReturn(0);
190 }
191 
192 #undef __FUNCT__
193 #define __FUNCT__ "PCBDDCSetCoarseningRatio"
194 /*@
195  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
196 
197    Logically collective on PC
198 
199    Input Parameters:
200 +  pc - the preconditioning context
201 -  k - coarsening ratio (H/h at the coarser level)
202 
203    Options Database Keys:
204 .    -pc_bddc_coarsening_ratio
205 
206    Level: intermediate
207 
208    Notes:
209      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
210 
211 .seealso: PCBDDC, PCBDDCSetLevels()
212 @*/
213 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
214 {
215   PetscErrorCode ierr;
216 
217   PetscFunctionBegin;
218   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
219   PetscValidLogicalCollectiveInt(pc,k,2);
220   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
221   PetscFunctionReturn(0);
222 }
223 
224 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
225 #undef __FUNCT__
226 #define __FUNCT__ "PCBDDCSetUseExactDirichlet_BDDC"
227 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
228 {
229   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
230 
231   PetscFunctionBegin;
232   pcbddc->use_exact_dirichlet_trick = flg;
233   PetscFunctionReturn(0);
234 }
235 
236 #undef __FUNCT__
237 #define __FUNCT__ "PCBDDCSetUseExactDirichlet"
238 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
239 {
240   PetscErrorCode ierr;
241 
242   PetscFunctionBegin;
243   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
244   PetscValidLogicalCollectiveBool(pc,flg,2);
245   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
246   PetscFunctionReturn(0);
247 }
248 
249 #undef __FUNCT__
250 #define __FUNCT__ "PCBDDCSetLevel_BDDC"
251 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
252 {
253   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
254 
255   PetscFunctionBegin;
256   pcbddc->current_level = level;
257   PetscFunctionReturn(0);
258 }
259 
260 #undef __FUNCT__
261 #define __FUNCT__ "PCBDDCSetLevel"
262 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
263 {
264   PetscErrorCode ierr;
265 
266   PetscFunctionBegin;
267   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
268   PetscValidLogicalCollectiveInt(pc,level,2);
269   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
270   PetscFunctionReturn(0);
271 }
272 
273 #undef __FUNCT__
274 #define __FUNCT__ "PCBDDCSetLevels_BDDC"
275 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
276 {
277   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
278 
279   PetscFunctionBegin;
280   pcbddc->max_levels = levels;
281   PetscFunctionReturn(0);
282 }
283 
284 #undef __FUNCT__
285 #define __FUNCT__ "PCBDDCSetLevels"
286 /*@
287  PCBDDCSetLevels - Sets the maximum number of levels for multilevel
288 
289    Logically collective on PC
290 
291    Input Parameters:
292 +  pc - the preconditioning context
293 -  levels - the maximum number of levels (max 9)
294 
295    Options Database Keys:
296 .    -pc_bddc_levels
297 
298    Level: intermediate
299 
300    Notes:
301      Default value is 0, i.e. traditional one-level BDDC
302 
303 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
304 @*/
305 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
306 {
307   PetscErrorCode ierr;
308 
309   PetscFunctionBegin;
310   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
311   PetscValidLogicalCollectiveInt(pc,levels,2);
312   if (levels > 99) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of levels for bddc is 99\n");
313   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
314   PetscFunctionReturn(0);
315 }
316 /* -------------------------------------------------------------------------- */
317 
318 #undef __FUNCT__
319 #define __FUNCT__ "PCBDDCSetNullSpace_BDDC"
320 static PetscErrorCode PCBDDCSetNullSpace_BDDC(PC pc,MatNullSpace NullSpace)
321 {
322   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
323   PetscErrorCode ierr;
324 
325   PetscFunctionBegin;
326   ierr = PetscObjectReference((PetscObject)NullSpace);CHKERRQ(ierr);
327   ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
328   pcbddc->NullSpace = NullSpace;
329   PetscFunctionReturn(0);
330 }
331 
332 #undef __FUNCT__
333 #define __FUNCT__ "PCBDDCSetNullSpace"
334 /*@
335  PCBDDCSetNullSpace - Set nullspace for BDDC operator
336 
337    Logically collective on PC and MatNullSpace
338 
339    Input Parameters:
340 +  pc - the preconditioning context
341 -  NullSpace - Null space of the linear operator to be preconditioned (Pmat)
342 
343    Level: intermediate
344 
345    Notes:
346 
347 .seealso: PCBDDC
348 @*/
349 PetscErrorCode PCBDDCSetNullSpace(PC pc,MatNullSpace NullSpace)
350 {
351   PetscErrorCode ierr;
352 
353   PetscFunctionBegin;
354   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
355   PetscValidHeaderSpecific(NullSpace,MAT_NULLSPACE_CLASSID,2);
356   PetscCheckSameComm(pc,1,NullSpace,2);
357   ierr = PetscTryMethod(pc,"PCBDDCSetNullSpace_C",(PC,MatNullSpace),(pc,NullSpace));CHKERRQ(ierr);
358   PetscFunctionReturn(0);
359 }
360 /* -------------------------------------------------------------------------- */
361 
362 #undef __FUNCT__
363 #define __FUNCT__ "PCBDDCSetDirichletBoundaries_BDDC"
364 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
365 {
366   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
367   PetscErrorCode ierr;
368 
369   PetscFunctionBegin;
370   /* last user setting takes precendence -> destroy any other customization */
371   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
372   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
373   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
374   pcbddc->DirichletBoundaries = DirichletBoundaries;
375   pcbddc->recompute_topography = PETSC_TRUE;
376   PetscFunctionReturn(0);
377 }
378 
379 #undef __FUNCT__
380 #define __FUNCT__ "PCBDDCSetDirichletBoundaries"
381 /*@
382  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
383 
384    Collective
385 
386    Input Parameters:
387 +  pc - the preconditioning context
388 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
389 
390    Level: intermediate
391 
392    Notes:
393      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
394 
395 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
396 @*/
397 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
398 {
399   PetscErrorCode ierr;
400 
401   PetscFunctionBegin;
402   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
403   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
404   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
405   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
406   PetscFunctionReturn(0);
407 }
408 /* -------------------------------------------------------------------------- */
409 
410 #undef __FUNCT__
411 #define __FUNCT__ "PCBDDCSetDirichletBoundariesLocal_BDDC"
412 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
413 {
414   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
415   PetscErrorCode ierr;
416 
417   PetscFunctionBegin;
418   /* last user setting takes precendence -> destroy any other customization */
419   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
420   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
421   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
422   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
423   pcbddc->recompute_topography = PETSC_TRUE;
424   PetscFunctionReturn(0);
425 }
426 
427 #undef __FUNCT__
428 #define __FUNCT__ "PCBDDCSetDirichletBoundariesLocal"
429 /*@
430  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
431 
432    Collective
433 
434    Input Parameters:
435 +  pc - the preconditioning context
436 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
437 
438    Level: intermediate
439 
440    Notes:
441 
442 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
443 @*/
444 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
445 {
446   PetscErrorCode ierr;
447 
448   PetscFunctionBegin;
449   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
450   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
451   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
452   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
453   PetscFunctionReturn(0);
454 }
455 /* -------------------------------------------------------------------------- */
456 
457 #undef __FUNCT__
458 #define __FUNCT__ "PCBDDCSetNeumannBoundaries_BDDC"
459 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
460 {
461   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
462   PetscErrorCode ierr;
463 
464   PetscFunctionBegin;
465   /* last user setting takes precendence -> destroy any other customization */
466   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
467   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
468   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
469   pcbddc->NeumannBoundaries = NeumannBoundaries;
470   pcbddc->recompute_topography = PETSC_TRUE;
471   PetscFunctionReturn(0);
472 }
473 
474 #undef __FUNCT__
475 #define __FUNCT__ "PCBDDCSetNeumannBoundaries"
476 /*@
477  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
478 
479    Collective
480 
481    Input Parameters:
482 +  pc - the preconditioning context
483 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
484 
485    Level: intermediate
486 
487    Notes:
488      Any process can list any global node
489 
490 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
491 @*/
492 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
493 {
494   PetscErrorCode ierr;
495 
496   PetscFunctionBegin;
497   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
498   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
499   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
500   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
501   PetscFunctionReturn(0);
502 }
503 /* -------------------------------------------------------------------------- */
504 
505 #undef __FUNCT__
506 #define __FUNCT__ "PCBDDCSetNeumannBoundariesLocal_BDDC"
507 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
508 {
509   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
510   PetscErrorCode ierr;
511 
512   PetscFunctionBegin;
513   /* last user setting takes precendence -> destroy any other customization */
514   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
515   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
516   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
517   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
518   pcbddc->recompute_topography = PETSC_TRUE;
519   PetscFunctionReturn(0);
520 }
521 
522 #undef __FUNCT__
523 #define __FUNCT__ "PCBDDCSetNeumannBoundariesLocal"
524 /*@
525  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
526 
527    Collective
528 
529    Input Parameters:
530 +  pc - the preconditioning context
531 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
532 
533    Level: intermediate
534 
535    Notes:
536 
537 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
538 @*/
539 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
540 {
541   PetscErrorCode ierr;
542 
543   PetscFunctionBegin;
544   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
545   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
546   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
547   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
548   PetscFunctionReturn(0);
549 }
550 /* -------------------------------------------------------------------------- */
551 
552 #undef __FUNCT__
553 #define __FUNCT__ "PCBDDCGetDirichletBoundaries_BDDC"
554 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
555 {
556   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
557 
558   PetscFunctionBegin;
559   *DirichletBoundaries = pcbddc->DirichletBoundaries;
560   PetscFunctionReturn(0);
561 }
562 
563 #undef __FUNCT__
564 #define __FUNCT__ "PCBDDCGetDirichletBoundaries"
565 /*@
566  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
567 
568    Collective
569 
570    Input Parameters:
571 .  pc - the preconditioning context
572 
573    Output Parameters:
574 .  DirichletBoundaries - index set defining the Dirichlet boundaries
575 
576    Level: intermediate
577 
578    Notes:
579      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
580 
581 .seealso: PCBDDC
582 @*/
583 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
584 {
585   PetscErrorCode ierr;
586 
587   PetscFunctionBegin;
588   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
589   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
590   PetscFunctionReturn(0);
591 }
592 /* -------------------------------------------------------------------------- */
593 
594 #undef __FUNCT__
595 #define __FUNCT__ "PCBDDCGetDirichletBoundariesLocal_BDDC"
596 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
597 {
598   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
599 
600   PetscFunctionBegin;
601   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
602   PetscFunctionReturn(0);
603 }
604 
605 #undef __FUNCT__
606 #define __FUNCT__ "PCBDDCGetDirichletBoundariesLocal"
607 /*@
608  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
609 
610    Collective
611 
612    Input Parameters:
613 .  pc - the preconditioning context
614 
615    Output Parameters:
616 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
617 
618    Level: intermediate
619 
620    Notes:
621      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetDirichletBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetDirichletBoundaries).
622           In the latter case, the IS will be available after PCSetUp.
623 
624 .seealso: PCBDDC
625 @*/
626 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
627 {
628   PetscErrorCode ierr;
629 
630   PetscFunctionBegin;
631   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
632   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
633   PetscFunctionReturn(0);
634 }
635 /* -------------------------------------------------------------------------- */
636 
637 #undef __FUNCT__
638 #define __FUNCT__ "PCBDDCGetNeumannBoundaries_BDDC"
639 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
640 {
641   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
642 
643   PetscFunctionBegin;
644   *NeumannBoundaries = pcbddc->NeumannBoundaries;
645   PetscFunctionReturn(0);
646 }
647 
648 #undef __FUNCT__
649 #define __FUNCT__ "PCBDDCGetNeumannBoundaries"
650 /*@
651  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
652 
653    Collective
654 
655    Input Parameters:
656 .  pc - the preconditioning context
657 
658    Output Parameters:
659 .  NeumannBoundaries - index set defining the Neumann boundaries
660 
661    Level: intermediate
662 
663    Notes:
664      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
665 
666 .seealso: PCBDDC
667 @*/
668 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
669 {
670   PetscErrorCode ierr;
671 
672   PetscFunctionBegin;
673   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
674   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
675   PetscFunctionReturn(0);
676 }
677 /* -------------------------------------------------------------------------- */
678 
679 #undef __FUNCT__
680 #define __FUNCT__ "PCBDDCGetNeumannBoundariesLocal_BDDC"
681 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
682 {
683   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
684 
685   PetscFunctionBegin;
686   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
687   PetscFunctionReturn(0);
688 }
689 
690 #undef __FUNCT__
691 #define __FUNCT__ "PCBDDCGetNeumannBoundariesLocal"
692 /*@
693  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
694 
695    Collective
696 
697    Input Parameters:
698 .  pc - the preconditioning context
699 
700    Output Parameters:
701 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
702 
703    Level: intermediate
704 
705    Notes:
706      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetNeumannBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetNeumannBoundaries).
707           In the latter case, the IS will be available after PCSetUp.
708 
709 .seealso: PCBDDC
710 @*/
711 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
712 {
713   PetscErrorCode ierr;
714 
715   PetscFunctionBegin;
716   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
717   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
718   PetscFunctionReturn(0);
719 }
720 /* -------------------------------------------------------------------------- */
721 
722 #undef __FUNCT__
723 #define __FUNCT__ "PCBDDCSetLocalAdjacencyGraph_BDDC"
724 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
725 {
726   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
727   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
728   PetscErrorCode ierr;
729 
730   PetscFunctionBegin;
731   /* free old CSR */
732   ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
733   /* TODO: PCBDDCGraphSetAdjacency */
734   /* get CSR into graph structure */
735   if (copymode == PETSC_COPY_VALUES) {
736     ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
737     ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
738     ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
739     ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
740   } else if (copymode == PETSC_OWN_POINTER) {
741     mat_graph->xadj = (PetscInt*)xadj;
742     mat_graph->adjncy = (PetscInt*)adjncy;
743   }
744   mat_graph->nvtxs_csr = nvtxs;
745   PetscFunctionReturn(0);
746 }
747 
748 #undef __FUNCT__
749 #define __FUNCT__ "PCBDDCSetLocalAdjacencyGraph"
750 /*@
751  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local matrix
752 
753    Not collective
754 
755    Input Parameters:
756 +  pc - the preconditioning context
757 .  nvtxs - number of local vertices of the graph (i.e., the size of the local problem)
758 .  xadj, adjncy - the CSR graph
759 -  copymode - either PETSC_COPY_VALUES or PETSC_OWN_POINTER.
760 
761    Level: intermediate
762 
763    Notes:
764 
765 .seealso: PCBDDC,PetscCopyMode
766 @*/
767 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
768 {
769   void (*f)(void) = 0;
770   PetscErrorCode ierr;
771 
772   PetscFunctionBegin;
773   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
774   PetscValidIntPointer(xadj,3);
775   PetscValidIntPointer(adjncy,4);
776   if (copymode != PETSC_COPY_VALUES && copymode != PETSC_OWN_POINTER) {
777     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %d in %s\n",copymode,__FUNCT__);
778   }
779   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
780   /* free arrays if PCBDDC is not the PC type */
781   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
782   if (!f && copymode == PETSC_OWN_POINTER) {
783     ierr = PetscFree(xadj);CHKERRQ(ierr);
784     ierr = PetscFree(adjncy);CHKERRQ(ierr);
785   }
786   PetscFunctionReturn(0);
787 }
788 /* -------------------------------------------------------------------------- */
789 
790 #undef __FUNCT__
791 #define __FUNCT__ "PCBDDCSetDofsSplittingLocal_BDDC"
792 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
793 {
794   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
795   PetscInt i;
796   PetscErrorCode ierr;
797 
798   PetscFunctionBegin;
799   /* Destroy ISes if they were already set */
800   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
801     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
802   }
803   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
804   /* last user setting takes precendence -> destroy any other customization */
805   for (i=0;i<pcbddc->n_ISForDofs;i++) {
806     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
807   }
808   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
809   pcbddc->n_ISForDofs = 0;
810   /* allocate space then set */
811   if (n_is) {
812     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
813   }
814   for (i=0;i<n_is;i++) {
815     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
816     pcbddc->ISForDofsLocal[i]=ISForDofs[i];
817   }
818   pcbddc->n_ISForDofsLocal=n_is;
819   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
820   pcbddc->recompute_topography = PETSC_TRUE;
821   PetscFunctionReturn(0);
822 }
823 
824 #undef __FUNCT__
825 #define __FUNCT__ "PCBDDCSetDofsSplittingLocal"
826 /*@
827  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
828 
829    Collective
830 
831    Input Parameters:
832 +  pc - the preconditioning context
833 .  n_is - number of index sets defining the fields
834 -  ISForDofs - array of IS describing the fields in local ordering
835 
836    Level: intermediate
837 
838    Notes:
839      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
840 
841 .seealso: PCBDDC
842 @*/
843 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
844 {
845   PetscInt       i;
846   PetscErrorCode ierr;
847 
848   PetscFunctionBegin;
849   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
850   PetscValidLogicalCollectiveInt(pc,n_is,2);
851   for (i=0;i<n_is;i++) {
852     PetscCheckSameComm(pc,1,ISForDofs[i],3);
853     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
854   }
855   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
856   PetscFunctionReturn(0);
857 }
858 /* -------------------------------------------------------------------------- */
859 
860 #undef __FUNCT__
861 #define __FUNCT__ "PCBDDCSetDofsSplitting_BDDC"
862 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
863 {
864   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
865   PetscInt i;
866   PetscErrorCode ierr;
867 
868   PetscFunctionBegin;
869   /* Destroy ISes if they were already set */
870   for (i=0;i<pcbddc->n_ISForDofs;i++) {
871     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
872   }
873   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
874   /* last user setting takes precendence -> destroy any other customization */
875   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
876     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
877   }
878   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
879   pcbddc->n_ISForDofsLocal = 0;
880   /* allocate space then set */
881   if (n_is) {
882     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
883   }
884   for (i=0;i<n_is;i++) {
885     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
886     pcbddc->ISForDofs[i]=ISForDofs[i];
887   }
888   pcbddc->n_ISForDofs=n_is;
889   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
890   pcbddc->recompute_topography = PETSC_TRUE;
891   PetscFunctionReturn(0);
892 }
893 
894 #undef __FUNCT__
895 #define __FUNCT__ "PCBDDCSetDofsSplitting"
896 /*@
897  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
898 
899    Collective
900 
901    Input Parameters:
902 +  pc - the preconditioning context
903 .  n_is - number of index sets defining the fields
904 -  ISForDofs - array of IS describing the fields in global ordering
905 
906    Level: intermediate
907 
908    Notes:
909      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
910 
911 .seealso: PCBDDC
912 @*/
913 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
914 {
915   PetscInt       i;
916   PetscErrorCode ierr;
917 
918   PetscFunctionBegin;
919   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
920   PetscValidLogicalCollectiveInt(pc,n_is,2);
921   for (i=0;i<n_is;i++) {
922     PetscCheckSameComm(pc,1,ISForDofs[i],3);
923     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
924   }
925   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
926   PetscFunctionReturn(0);
927 }
928 
929 /* -------------------------------------------------------------------------- */
930 #undef __FUNCT__
931 #define __FUNCT__ "PCPreSolve_BDDC"
932 /* -------------------------------------------------------------------------- */
933 /*
934    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
935                      guess if a transformation of basis approach has been selected.
936 
937    Input Parameter:
938 +  pc - the preconditioner contex
939 
940    Application Interface Routine: PCPreSolve()
941 
942    Notes:
943      The interface routine PCPreSolve() is not usually called directly by
944    the user, but instead is called by KSPSolve().
945 */
946 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
947 {
948   PetscErrorCode ierr;
949   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
950   PC_IS          *pcis = (PC_IS*)(pc->data);
951   Vec            used_vec;
952   PetscBool      copy_rhs = PETSC_TRUE;
953 
954   PetscFunctionBegin;
955   /* if we are working with cg, one dirichlet solve can be avoided during Krylov iterations */
956   if (ksp) {
957     PetscBool iscg;
958     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
959     if (!iscg) {
960       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
961     }
962   }
963   /* Creates parallel work vectors used in presolve */
964   if (!pcbddc->original_rhs) {
965     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
966   }
967   if (!pcbddc->temp_solution) {
968     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
969   }
970 
971   if (x) {
972     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
973     used_vec = x;
974   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
975     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
976     used_vec = pcbddc->temp_solution;
977     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
978   }
979 
980   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
981   if (ksp) {
982     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
983     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
984     if (!pcbddc->ksp_guess_nonzero) {
985       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
986     }
987   }
988 
989   pcbddc->rhs_change = PETSC_FALSE;
990   /* Take into account zeroed rows -> change rhs and store solution removed */
991   if (rhs) {
992     IS dirIS = NULL;
993 
994     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
995     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
996     if (dirIS) {
997       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
998       PetscInt          dirsize,i,*is_indices;
999       PetscScalar       *array_x;
1000       const PetscScalar *array_diagonal;
1001 
1002       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1003       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1004       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1005       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1006       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1007       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1008       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1009       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1010       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1011       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1012       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1013       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1014       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1015       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1016       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1017       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1018       pcbddc->rhs_change = PETSC_TRUE;
1019       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1020     }
1021   }
1022 
1023   /* remove the computed solution or the initial guess from the rhs */
1024   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1025     /* store the original rhs */
1026     if (copy_rhs) {
1027       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1028       copy_rhs = PETSC_FALSE;
1029     }
1030     pcbddc->rhs_change = PETSC_TRUE;
1031     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1032     ierr = MatMultAdd(pc->mat,used_vec,rhs,rhs);CHKERRQ(ierr);
1033     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1034     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1035     if (ksp) {
1036       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1037     }
1038   }
1039   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1040 
1041   /* When using the benign trick: (TODO: what about FETI-DP?)
1042      - change rhs on pressures (iteration matrix is surely of type MATIS)
1043      - compute initial vector in benign space
1044   */
1045   if (rhs && pcbddc->benign_saddle_point) {
1046     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1047 
1048     /* store the original rhs */
1049     if (copy_rhs) {
1050       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1051       copy_rhs = PETSC_FALSE;
1052     }
1053 
1054     /* now change (locally) the basis */
1055     ierr = VecScatterBegin(matis->rctx,rhs,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1056     ierr = VecScatterEnd(matis->rctx,rhs,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1057     if (pcbddc->benign_change) {
1058       ierr = MatMultTranspose(pcbddc->benign_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1059       ierr = VecScatterBegin(matis->rctx,pcis->vec2_N,rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1060       ierr = VecScatterEnd(matis->rctx,pcis->vec2_N,rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1061       /* change local iteration matrix */
1062       ierr = MatPtAP(matis->A,pcbddc->benign_change,MAT_REUSE_MATRIX,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
1063       ierr = MatDestroy(&pcbddc->benign_original_mat);CHKERRQ(ierr);
1064       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1065       pcbddc->benign_original_mat = matis->A;
1066       ierr = MatDestroy(&matis->A);CHKERRQ(ierr);
1067       ierr = PetscObjectReference((PetscObject)pcbddc->local_mat);CHKERRQ(ierr);
1068       matis->A = pcbddc->local_mat;
1069       ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1070     } else {
1071       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1072       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1073     }
1074     pcbddc->rhs_change = PETSC_TRUE;
1075 
1076     /* compute u^*_h as in Xuemin Tu's thesis (see Section 4.8.1) */
1077     /* TODO: what about Stokes? */
1078     if (!pcbddc->benign_vec) {
1079       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1080     }
1081     ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1082     pcbddc->benign_p0 = 0.;
1083     if (pcbddc->benign_p0_lidx >= 0) {
1084       const PetscScalar *array;
1085 
1086       ierr = VecGetArrayRead(pcis->vec2_N,&array);CHKERRQ(ierr);
1087       pcbddc->benign_p0 = array[pcbddc->benign_p0_lidx];
1088       ierr = VecRestoreArrayRead(pcis->vec2_N,&array);CHKERRQ(ierr);
1089     }
1090 #if 0
1091     ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] benign u* should be %1.4e\n",PetscGlobalRank,pcbddc->benign_p0);CHKERRQ(ierr);
1092 #endif
1093     ierr = PCBDDCBenignPopOrPushP0(pc,pcis->vec1_global,PETSC_FALSE);CHKERRQ(ierr);
1094     ierr = PCApply_BDDC(pc,pcis->vec1_global,pcbddc->benign_vec);CHKERRQ(ierr);
1095     pcbddc->benign_p0 = 0.;
1096     ierr = PCBDDCBenignPopOrPushP0(pc,pcbddc->benign_vec,PETSC_FALSE);CHKERRQ(ierr);
1097     if (pcbddc->benign_saddle_point) {
1098       Mat_IS* matis = (Mat_IS*)(pc->mat->data);
1099       ierr = VecScatterBegin(matis->rctx,pcbddc->benign_vec,matis->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1100       ierr = VecScatterEnd(matis->rctx,pcbddc->benign_vec,matis->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1101 
1102 #if 0
1103       if (pcbddc->benign_p0_lidx >=0) {
1104         Mat B0;
1105         Vec dummy_vec;
1106         PetscScalar *array;
1107         PetscInt ii[2];
1108 
1109         ii[0] = 0;
1110         ii[1] = pcbddc->B0_ncol;
1111         ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,1,pcis->n,ii,pcbddc->B0_cols,pcbddc->B0_vals,&B0);CHKERRQ(ierr);
1112         ierr = MatCreateVecs(B0,NULL,&dummy_vec);CHKERRQ(ierr);
1113         ierr = MatMult(B0,matis->x,dummy_vec);CHKERRQ(ierr);
1114         ierr = VecGetArray(dummy_vec,&array);CHKERRQ(ierr);
1115         ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] benign u* is %1.4e\n",PetscGlobalRank,array[0]);CHKERRQ(ierr);
1116         ierr = VecRestoreArray(dummy_vec,&array);CHKERRQ(ierr);
1117         ierr = MatDestroy(&B0);CHKERRQ(ierr);
1118         ierr = VecDestroy(&dummy_vec);CHKERRQ(ierr);
1119       }
1120 #endif
1121     }
1122   }
1123 
1124   /* change rhs and iteration matrix if using the change of basis */
1125   if (pcbddc->ChangeOfBasisMatrix) {
1126     PCBDDCChange_ctx change_ctx;
1127 
1128     /* get change ctx */
1129     ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
1130 
1131     /* set current iteration matrix inside change context (change of basis has been already set into the ctx during PCSetUp) */
1132     ierr = MatDestroy(&change_ctx->original_mat);CHKERRQ(ierr);
1133     ierr = PetscObjectReference((PetscObject)pc->mat);CHKERRQ(ierr);
1134     change_ctx->original_mat = pc->mat;
1135 
1136     /* change iteration matrix */
1137     ierr = MatDestroy(&pc->mat);CHKERRQ(ierr);
1138     ierr = PetscObjectReference((PetscObject)pcbddc->new_global_mat);CHKERRQ(ierr);
1139     pc->mat = pcbddc->new_global_mat;
1140 
1141     /* store the original rhs */
1142     if (copy_rhs) {
1143       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1144       copy_rhs = PETSC_FALSE;
1145     }
1146 
1147     /* change rhs */
1148     ierr = MatMultTranspose(change_ctx->global_change,rhs,pcis->vec1_global);CHKERRQ(ierr);
1149     ierr = VecCopy(pcis->vec1_global,rhs);CHKERRQ(ierr);
1150     pcbddc->rhs_change = PETSC_TRUE;
1151   }
1152 
1153   /* remove non-benign solution from the rhs */
1154   if (pcbddc->benign_saddle_point) {
1155     /* store the original rhs */
1156     if (copy_rhs) {
1157       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1158       copy_rhs = PETSC_FALSE;
1159     }
1160     ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1161     ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1162     pcbddc->rhs_change = PETSC_TRUE;
1163   }
1164 
1165   /* set initial guess if using PCG */
1166   if (x && pcbddc->use_exact_dirichlet_trick) {
1167     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1168     ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1169     ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1170     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1171     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1172     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1173     if (ksp) {
1174       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1175     }
1176   }
1177 
1178   /* remove nullspace if present */
1179   if (ksp && x && pcbddc->NullSpace) {
1180     ierr = MatNullSpaceRemove(pcbddc->NullSpace,x);CHKERRQ(ierr);
1181     /* store the original rhs */
1182     if (copy_rhs) {
1183       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1184       copy_rhs = PETSC_FALSE;
1185     }
1186     pcbddc->rhs_change = PETSC_TRUE;
1187     ierr = MatNullSpaceRemove(pcbddc->NullSpace,rhs);CHKERRQ(ierr);
1188   }
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 /* -------------------------------------------------------------------------- */
1193 #undef __FUNCT__
1194 #define __FUNCT__ "PCPostSolve_BDDC"
1195 /* -------------------------------------------------------------------------- */
1196 /*
1197    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1198                      approach has been selected. Also, restores rhs to its original state.
1199 
1200    Input Parameter:
1201 +  pc - the preconditioner contex
1202 
1203    Application Interface Routine: PCPostSolve()
1204 
1205    Notes:
1206      The interface routine PCPostSolve() is not usually called directly by
1207      the user, but instead is called by KSPSolve().
1208 */
1209 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1210 {
1211   PetscErrorCode ierr;
1212   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1213 
1214   PetscFunctionBegin;
1215   if (pcbddc->ChangeOfBasisMatrix) {
1216     PCBDDCChange_ctx change_ctx;
1217 
1218     /* get change ctx */
1219     ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
1220 
1221     /* restore iteration matrix */
1222     ierr = MatDestroy(&pc->mat);CHKERRQ(ierr);
1223     ierr = PetscObjectReference((PetscObject)change_ctx->original_mat);CHKERRQ(ierr);
1224     pc->mat = change_ctx->original_mat;
1225 
1226     /* need to restore the local matrices */
1227     if (pcbddc->benign_saddle_point && pcbddc->benign_change) {
1228       Mat_IS *matis = (Mat_IS*)pc->mat->data;
1229 
1230       ierr = MatDestroy(&matis->A);CHKERRQ(ierr);
1231       ierr = PetscObjectReference((PetscObject)pcbddc->benign_original_mat);CHKERRQ(ierr);
1232       matis->A = pcbddc->benign_original_mat;
1233       ierr = MatDestroy(&pcbddc->benign_original_mat);CHKERRQ(ierr);
1234     }
1235 
1236     /* get solution in original basis */
1237     if (x) {
1238       PC_IS *pcis = (PC_IS*)(pc->data);
1239 
1240 
1241       /* restore solution on pressures */
1242       if (pcbddc->benign_saddle_point) {
1243         Mat_IS *matis = (Mat_IS*)pc->mat->data;
1244 
1245         /* add non-benign solution */
1246         ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1247 
1248         /* change basis on pressures for x */
1249         ierr = VecScatterBegin(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1250         ierr = VecScatterEnd(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1251         if (pcbddc->benign_change) {
1252 
1253           ierr = MatMult(pcbddc->benign_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1254           ierr = VecScatterBegin(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1255           ierr = VecScatterEnd(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1256         } else {
1257           ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1258           ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1259         }
1260       }
1261       /* change basis on x */
1262       ierr = MatMult(change_ctx->global_change,x,pcis->vec1_global);CHKERRQ(ierr);
1263       ierr = VecCopy(pcis->vec1_global,x);CHKERRQ(ierr);
1264     }
1265   }
1266 
1267   /* add solution removed in presolve */
1268   if (x && pcbddc->rhs_change) {
1269     ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1270   }
1271 
1272   /* restore rhs to its original state */
1273   if (rhs && pcbddc->rhs_change) {
1274     ierr = VecCopy(pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1275   }
1276   pcbddc->rhs_change = PETSC_FALSE;
1277 
1278   /* restore ksp guess state */
1279   if (ksp) {
1280     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1281   }
1282   PetscFunctionReturn(0);
1283 }
1284 /* -------------------------------------------------------------------------- */
1285 #undef __FUNCT__
1286 #define __FUNCT__ "PCSetUp_BDDC"
1287 /* -------------------------------------------------------------------------- */
1288 /*
1289    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1290                   by setting data structures and options.
1291 
1292    Input Parameter:
1293 +  pc - the preconditioner context
1294 
1295    Application Interface Routine: PCSetUp()
1296 
1297    Notes:
1298      The interface routine PCSetUp() is not usually called directly by
1299      the user, but instead is called by PCApply() if necessary.
1300 */
1301 PetscErrorCode PCSetUp_BDDC(PC pc)
1302 {
1303   PetscErrorCode ierr;
1304   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
1305   Mat_IS*        matis;
1306   MatNullSpace   nearnullspace;
1307   IS             zerodiag = NULL;
1308   PetscInt       nrows,ncols;
1309   PetscBool      computetopography,computesolvers,computesubschurs;
1310   PetscBool      computeconstraintsmatrix;
1311   PetscBool      new_nearnullspace_provided,ismatis;
1312 
1313   PetscFunctionBegin;
1314   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1315   if (!ismatis) {
1316     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1317   }
1318   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1319   if (nrows != ncols) {
1320     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1321   }
1322   matis = (Mat_IS*)pc->pmat->data;
1323   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1324   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1325      Also, BDDC directly build the Dirichlet problem */
1326   /* split work */
1327   if (pc->setupcalled) {
1328     if (pc->flag == SAME_NONZERO_PATTERN) {
1329       computetopography = PETSC_FALSE;
1330       computesolvers = PETSC_TRUE;
1331     } else { /* DIFFERENT_NONZERO_PATTERN */
1332       computetopography = PETSC_TRUE;
1333       computesolvers = PETSC_TRUE;
1334     }
1335   } else {
1336     computetopography = PETSC_TRUE;
1337     computesolvers = PETSC_TRUE;
1338   }
1339   if (pcbddc->recompute_topography) {
1340     computetopography = PETSC_TRUE;
1341   }
1342   computeconstraintsmatrix = PETSC_FALSE;
1343   if (pcbddc->adaptive_threshold > 0.0 && !pcbddc->use_deluxe_scaling) {
1344     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute adaptive constraints without deluxe scaling. Rerun with -pc_bddc_use_deluxe_scaling");
1345   }
1346   pcbddc->adaptive_selection = (PetscBool)(pcbddc->adaptive_threshold > 0.0 && pcbddc->use_deluxe_scaling);
1347   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1348 
1349   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1350   if (pcbddc->faster_deluxe && pcbddc->adaptive_selection && pcbddc->use_change_of_basis) {
1351     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute faster deluxe if adaptivity and change of basis are both requested. Rerun with -pc_bddc_deluxe_faster false");
1352   }
1353 
1354   /* check if the iteration matrix is of type MATIS in case the benign trick has been requested */
1355   ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1356   if (pcbddc->benign_saddle_point && !ismatis) {
1357     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner with benign subspace trick requires the iteration matrix to be of type MATIS");
1358   }
1359 
1360   /* Get stdout for dbg */
1361   if (pcbddc->dbg_flag) {
1362     if (!pcbddc->dbg_viewer) {
1363       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1364       ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1365     }
1366     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1367   }
1368 
1369   if (pcbddc->user_ChangeOfBasisMatrix) {
1370     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1371     pcbddc->use_change_of_basis = PETSC_FALSE;
1372     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1373   } else {
1374     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1375     if (!pcbddc->benign_saddle_point) {
1376       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1377       pcbddc->local_mat = matis->A;
1378     } else { /* TODO: handle user change of basis */
1379       PetscInt  nz;
1380       PetscBool sorted;
1381 
1382       ierr = MatFindZeroDiagonals(matis->A,&zerodiag);CHKERRQ(ierr);
1383       ierr = ISSorted(zerodiag,&sorted);CHKERRQ(ierr);
1384       if (!sorted) {
1385         ierr = ISSort(zerodiag);CHKERRQ(ierr);
1386       }
1387       ierr = ISGetLocalSize(zerodiag,&nz);CHKERRQ(ierr);
1388       if (nz) {
1389         IS                zerodiagc;
1390         PetscScalar       *array;
1391         const PetscInt    *idxs,*idxsc;
1392         PetscInt          i,n,*nnz;
1393 
1394         /* TODO: add check for shared dofs */
1395         pcbddc->use_change_of_basis = PETSC_TRUE;
1396         pcbddc->use_change_on_faces = PETSC_TRUE;
1397         ierr = MatGetLocalSize(matis->A,&n,NULL);CHKERRQ(ierr);
1398         ierr = ISComplement(zerodiag,0,n,&zerodiagc);CHKERRQ(ierr);
1399         ierr = ISGetIndices(zerodiag,&idxs);CHKERRQ(ierr);
1400         ierr = ISGetIndices(zerodiagc,&idxsc);CHKERRQ(ierr);
1401         /* local change of basis for pressures */
1402         ierr = MatDestroy(&pcbddc->benign_change);CHKERRQ(ierr);
1403         ierr = MatCreate(PetscObjectComm((PetscObject)matis->A),&pcbddc->benign_change);CHKERRQ(ierr);
1404         ierr = MatSetType(pcbddc->benign_change,MATAIJ);CHKERRQ(ierr);
1405         ierr = MatSetSizes(pcbddc->benign_change,n,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
1406         ierr = PetscMalloc1(n,&nnz);CHKERRQ(ierr);
1407         for (i=0;i<n-nz;i++) nnz[idxsc[i]] = 1; /* identity on velocities */
1408         for (i=0;i<nz-1;i++) nnz[idxs[i]] = 2; /* change on pressures */
1409         nnz[idxs[nz-1]] = nz; /* last local pressure dof: _0 set */
1410         ierr = MatSeqAIJSetPreallocation(pcbddc->benign_change,0,nnz);CHKERRQ(ierr);
1411         ierr = PetscFree(nnz);CHKERRQ(ierr);
1412         /* set identity on velocities */
1413         for (i=0;i<n-nz;i++) {
1414           ierr = MatSetValue(pcbddc->benign_change,idxsc[i],idxsc[i],1.,INSERT_VALUES);CHKERRQ(ierr);
1415         }
1416         /* set change on pressures */
1417         for (i=0;i<nz-1;i++) {
1418           PetscScalar vals[2];
1419           PetscInt    cols[2];
1420 
1421           /* TODO: add quadrature */
1422           cols[0] = idxs[i];
1423           cols[1] = idxs[nz-1];
1424           vals[0] = 1.;
1425           vals[1] = 1./nz;
1426           ierr = MatSetValues(pcbddc->benign_change,1,idxs+i,2,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
1427         }
1428         ierr = PetscMalloc1(nz,&array);CHKERRQ(ierr);
1429         for (i=0;i<nz-1;i++) array[i] = -1.;
1430         array[nz-1] = 1./nz;
1431         ierr = MatSetValues(pcbddc->benign_change,1,idxs+nz-1,nz,idxs,array,INSERT_VALUES);CHKERRQ(ierr);
1432         ierr = PetscFree(array);CHKERRQ(ierr);
1433         ierr = MatAssemblyBegin(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1434         ierr = MatAssemblyEnd(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1435         /* TODO: need optimization? */
1436         ierr = MatPtAP(matis->A,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
1437         /* store local and global idxs for p0 */
1438         pcbddc->benign_p0_lidx = idxs[nz-1];
1439         ierr = ISLocalToGlobalMappingApply(pc->pmat->rmap->mapping,1,&idxs[nz-1],&pcbddc->benign_p0_gidx);CHKERRQ(ierr);
1440         ierr = ISRestoreIndices(zerodiag,&idxs);CHKERRQ(ierr);
1441         ierr = ISRestoreIndices(zerodiagc,&idxsc);CHKERRQ(ierr);
1442         ierr = ISDestroy(&zerodiagc);CHKERRQ(ierr);
1443         /* pop B0 mat from pcbddc->local_mat */
1444         ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1445       } else { /* this is unlikely to happen but, just in case, destroy the empty IS */
1446         ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1447         ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1448         pcbddc->local_mat = matis->A;
1449       }
1450     }
1451   }
1452 
1453   /* workaround for reals */
1454 #if !defined(PETSC_USE_COMPLEX)
1455   if (matis->A->symmetric_set) {
1456     ierr = MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);CHKERRQ(ierr);
1457   }
1458 #endif
1459   if (matis->A->symmetric_set) {
1460     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1461   }
1462   if (matis->A->spd_set) {
1463     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1464   }
1465 
1466   /* Set up all the "iterative substructuring" common block without computing solvers */
1467   {
1468     Mat temp_mat;
1469 
1470     temp_mat = matis->A;
1471     matis->A = pcbddc->local_mat;
1472     ierr = PCISSetUp(pc,PETSC_FALSE);CHKERRQ(ierr);
1473     pcbddc->local_mat = matis->A;
1474     matis->A = temp_mat;
1475   }
1476 
1477   /* Analyze interface */
1478   if (computetopography) {
1479     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1480     computeconstraintsmatrix = PETSC_TRUE;
1481   }
1482 
1483   /* check b(v_I,p_0) = 0 for all v_I */
1484   if (pcbddc->dbg_flag && zerodiag) {
1485     PC_IS          *pcis = (PC_IS*)(pc->data);
1486     IS             dirIS = NULL;
1487     PetscScalar    *vals;
1488     const PetscInt *idxs;
1489     PetscInt       i,nz;
1490 
1491     /* p0 */
1492     ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1493     ierr = PetscMalloc1(pcis->n,&vals);CHKERRQ(ierr);
1494     ierr = ISGetLocalSize(zerodiag,&nz);CHKERRQ(ierr);
1495     ierr = ISGetIndices(zerodiag,&idxs);CHKERRQ(ierr);
1496     for (i=0;i<nz;i++) vals[i] = 1.;
1497     ierr = VecSetValues(pcis->vec1_N,nz,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
1498     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
1499     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
1500     /* v_I */
1501     ierr = VecSetRandom(pcis->vec2_N,NULL);CHKERRQ(ierr);
1502     for (i=0;i<nz;i++) vals[i] = 0.;
1503     ierr = VecSetValues(pcis->vec2_N,nz,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
1504     ierr = ISRestoreIndices(zerodiag,&idxs);CHKERRQ(ierr);
1505     ierr = ISGetIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
1506     for (i=0;i<pcis->n_B;i++) vals[i] = 0.;
1507     ierr = VecSetValues(pcis->vec2_N,pcis->n_B,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
1508     ierr = ISRestoreIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
1509     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1510     if (dirIS) {
1511       PetscInt n;
1512 
1513       ierr = ISGetLocalSize(dirIS,&n);CHKERRQ(ierr);
1514       ierr = ISGetIndices(dirIS,&idxs);CHKERRQ(ierr);
1515       for (i=0;i<n;i++) vals[i] = 0.;
1516       ierr = VecSetValues(pcis->vec2_N,n,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
1517       ierr = ISRestoreIndices(dirIS,&idxs);CHKERRQ(ierr);
1518     }
1519     ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1520     ierr = VecAssemblyBegin(pcis->vec2_N);CHKERRQ(ierr);
1521     ierr = VecAssemblyEnd(pcis->vec2_N);CHKERRQ(ierr);
1522     ierr = VecSet(matis->x,0.);CHKERRQ(ierr);
1523     ierr = MatMult(matis->A,pcis->vec1_N,matis->x);CHKERRQ(ierr);
1524     ierr = VecDot(matis->x,pcis->vec2_N,&vals[0]);CHKERRQ(ierr);
1525     ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] check original mat: %1.4e\n",PetscGlobalRank,vals[0]);CHKERRQ(ierr);
1526     ierr = PetscFree(vals);CHKERRQ(ierr);
1527   }
1528 
1529   /* check PCBDDCBenignPopOrPush */
1530   if (pcbddc->dbg_flag && pcbddc->benign_saddle_point) {
1531     PC_IS  *pcis = (PC_IS*)(pc->data);
1532 
1533     ierr = VecSetRandom(pcis->vec1_global,NULL);CHKERRQ(ierr);
1534     pcbddc->benign_p0 = -PetscGlobalRank;
1535     ierr = PCBDDCBenignPopOrPushP0(pc,pcis->vec1_global,PETSC_FALSE);CHKERRQ(ierr);
1536     pcbddc->benign_p0 = 1;
1537     ierr = PCBDDCBenignPopOrPushP0(pc,pcis->vec1_global,PETSC_TRUE);CHKERRQ(ierr);
1538     if (pcbddc->benign_p0_gidx >=0 && pcbddc->benign_p0 != -PetscGlobalRank) {
1539       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error testing PCBDDCBenignPopOrPushP0! Found %1.4e instead of %1.4e\n",pcbddc->benign_p0,-PetscGlobalRank);CHKERRQ(ierr);
1540     }
1541   }
1542 
1543   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1544   if (computesolvers) {
1545     PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;
1546 
1547     if (computesubschurs && computetopography) {
1548       ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1549     }
1550     if (sub_schurs->use_mumps) {
1551       if (computesubschurs) {
1552         ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1553       }
1554       ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1555     } else {
1556       ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1557       if (computesubschurs) {
1558         ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1559       }
1560     }
1561     if (pcbddc->adaptive_selection) {
1562       ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1563       computeconstraintsmatrix = PETSC_TRUE;
1564     }
1565   }
1566 
1567   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1568   new_nearnullspace_provided = PETSC_FALSE;
1569   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1570   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1571     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1572       new_nearnullspace_provided = PETSC_TRUE;
1573     } else {
1574       /* determine if the two nullspaces are different (should be lightweight) */
1575       if (nearnullspace != pcbddc->onearnullspace) {
1576         new_nearnullspace_provided = PETSC_TRUE;
1577       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1578         PetscInt         i;
1579         const Vec        *nearnullvecs;
1580         PetscObjectState state;
1581         PetscInt         nnsp_size;
1582         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1583         for (i=0;i<nnsp_size;i++) {
1584           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1585           if (pcbddc->onearnullvecs_state[i] != state) {
1586             new_nearnullspace_provided = PETSC_TRUE;
1587             break;
1588           }
1589         }
1590       }
1591     }
1592   } else {
1593     if (!nearnullspace) { /* both nearnullspaces are null */
1594       new_nearnullspace_provided = PETSC_FALSE;
1595     } else { /* nearnullspace attached later */
1596       new_nearnullspace_provided = PETSC_TRUE;
1597     }
1598   }
1599 
1600   /* Setup constraints and related work vectors */
1601   /* reset primal space flags */
1602   pcbddc->new_primal_space = PETSC_FALSE;
1603   pcbddc->new_primal_space_local = PETSC_FALSE;
1604   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1605     /* It also sets the primal space flags */
1606     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1607     /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1608     ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1609   }
1610 
1611   if (computesolvers || pcbddc->new_primal_space) {
1612     if (pcbddc->use_change_of_basis) {
1613       PC_IS *pcis = (PC_IS*)(pc->data);
1614       Mat   temp_mat = NULL;
1615 
1616       if (zerodiag) {
1617         /* insert B0 in pcbddc->local_mat */
1618         ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_FALSE);CHKERRQ(ierr);
1619         if (pcbddc->dbg_flag) {
1620           PC_IS          *pcis = (PC_IS*)(pc->data);
1621           IS             dirIS = NULL;
1622           PetscScalar    *vals;
1623           const PetscInt *idxs;
1624           PetscInt       i,nz;
1625 
1626           /* p0 */
1627           ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1628           ierr = PetscMalloc1(pcis->n,&vals);CHKERRQ(ierr);
1629           ierr = ISGetLocalSize(zerodiag,&nz);CHKERRQ(ierr);
1630           ierr = ISGetIndices(zerodiag,&idxs);CHKERRQ(ierr);
1631           vals[0] = 1.;
1632           ierr = VecSetValues(pcis->vec1_N,1,&idxs[nz-1],vals,INSERT_VALUES);CHKERRQ(ierr);
1633           ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
1634           ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
1635           /* v_I */
1636           ierr = VecSetRandom(pcis->vec2_N,NULL);CHKERRQ(ierr);
1637           for (i=0;i<nz;i++) vals[i] = 0.;
1638           ierr = VecSetValues(pcis->vec2_N,nz,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
1639           ierr = ISRestoreIndices(zerodiag,&idxs);CHKERRQ(ierr);
1640           ierr = ISGetIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
1641           for (i=0;i<pcis->n_B;i++) vals[i] = 0.;
1642           ierr = VecSetValues(pcis->vec2_N,pcis->n_B,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
1643           ierr = ISRestoreIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
1644           ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1645           if (dirIS) {
1646             PetscInt n;
1647 
1648             ierr = ISGetLocalSize(dirIS,&n);CHKERRQ(ierr);
1649             ierr = ISGetIndices(dirIS,&idxs);CHKERRQ(ierr);
1650             for (i=0;i<n;i++) vals[i] = 0.;
1651             ierr = VecSetValues(pcis->vec2_N,n,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
1652             ierr = ISRestoreIndices(dirIS,&idxs);CHKERRQ(ierr);
1653           }
1654           ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1655           ierr = VecAssemblyBegin(pcis->vec2_N);CHKERRQ(ierr);
1656           ierr = VecAssemblyEnd(pcis->vec2_N);CHKERRQ(ierr);
1657           ierr = VecSet(matis->x,0.);CHKERRQ(ierr);
1658           ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,matis->x);CHKERRQ(ierr);
1659           ierr = VecDot(matis->x,pcis->vec2_N,&vals[0]);CHKERRQ(ierr);
1660           ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] check new mat: %1.4e\n",PetscGlobalRank,vals[0]);CHKERRQ(ierr);
1661           ierr = PetscFree(vals);CHKERRQ(ierr);
1662         }
1663         /* hack: swap pointers */
1664         temp_mat = matis->A;
1665         matis->A = pcbddc->local_mat;
1666         pcbddc->local_mat = NULL;
1667       }
1668       ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1669       if (zerodiag) {
1670         /* restore original matrix */
1671         ierr = MatDestroy(&matis->A);CHKERRQ(ierr);
1672         matis->A = temp_mat;
1673         /* pop B0 from pcbddc->local_mat */
1674         ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1675       }
1676       /* get submatrices */
1677       ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1678       ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1679       ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1680       ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1681       ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1682       ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1683       /* set flag in pcis to not reuse submatrices during PCISCreate */
1684       pcis->reusesubmatrices = PETSC_FALSE;
1685     } else if (!pcbddc->user_ChangeOfBasisMatrix) {
1686       ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1687       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1688       pcbddc->local_mat = matis->A;
1689     }
1690     /* SetUp coarse and local Neumann solvers */
1691     ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1692     /* SetUp Scaling operator */
1693     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1694   }
1695 
1696   /* check BDDC operator */
1697   if (pcbddc->dbg_flag && (
1698       (pcbddc->n_vertices == pcbddc->local_primal_size) || pcbddc->benign_saddle_point) ) {
1699     PC_IS          *pcis = (PC_IS*)(pc->data);
1700     Mat            S_j,B0=NULL,B0_B=NULL;
1701     Vec            dummy_vec=NULL,vec_check_B,vec_scale_P;
1702     PetscScalar    norm,p0_check,*array,*array2;
1703     PetscInt       i;
1704 
1705     /* B0 and B0_B */
1706     if (zerodiag) {
1707       IS       dummy;
1708       PetscInt ii[2];
1709 
1710       ii[0] = 0;
1711       ii[1] = pcbddc->B0_ncol;
1712       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,1,pcis->n,ii,pcbddc->B0_cols,pcbddc->B0_vals,&B0);CHKERRQ(ierr);
1713       ierr = ISCreateStride(PETSC_COMM_SELF,1,0,1,&dummy);CHKERRQ(ierr);
1714       ierr = MatGetSubMatrix(B0,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);CHKERRQ(ierr);
1715       ierr = MatCreateVecs(B0_B,NULL,&dummy_vec);CHKERRQ(ierr);
1716       ierr = ISDestroy(&dummy);CHKERRQ(ierr);
1717     }
1718     /* I need a primal vector to scale primal nodes since BDDC sums contibutions */
1719     ierr = VecDuplicate(pcbddc->vec1_P,&vec_scale_P);CHKERRQ(ierr);
1720     ierr = VecSet(pcbddc->vec1_P,1.0);CHKERRQ(ierr);
1721     ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1722     ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1723     ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1724     ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1725     ierr = VecReciprocal(vec_scale_P);CHKERRQ(ierr);
1726     /* S_j */
1727     ierr = MatCreateSchurComplement(pcis->A_II,pcis->A_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);CHKERRQ(ierr);
1728     ierr = MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);CHKERRQ(ierr);
1729 
1730     /* mimic vector in \widetilde{W}_\Gamma */
1731     ierr = VecSetRandom(pcis->vec1_N,NULL);CHKERRQ(ierr);
1732     /* continuous in primal space */
1733     ierr = VecSetRandom(pcbddc->coarse_vec,NULL);CHKERRQ(ierr);
1734     ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1735     ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1736     ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
1737     if (zerodiag) {
1738       p0_check = array[pcbddc->local_primal_size-1];
1739     } else {
1740       p0_check = 0;
1741     }
1742     ierr = VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);CHKERRQ(ierr);
1743     ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
1744     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
1745     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
1746     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1747     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1748     ierr = VecDuplicate(pcis->vec2_B,&vec_check_B);CHKERRQ(ierr);
1749     ierr = VecCopy(pcis->vec2_B,vec_check_B);CHKERRQ(ierr);
1750 
1751     /* assemble rhs for coarse problem */
1752     /* widetilde{S}_\Gamma w_\Gamma + \widetilde{B0}^T_B p0 */
1753     /* local with Schur */
1754     ierr = MatMult(S_j,pcis->vec2_B,pcis->vec1_B);CHKERRQ(ierr);
1755     if (zerodiag) {
1756       ierr = VecGetArray(dummy_vec,&array);CHKERRQ(ierr);
1757       array[0] = p0_check;
1758       ierr = VecRestoreArray(dummy_vec,&array);CHKERRQ(ierr);
1759       ierr = MatMultTransposeAdd(B0_B,dummy_vec,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1760     }
1761     /* sum on primal nodes the local contributions */
1762     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1763     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1764     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1765     ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
1766     for (i=0;i<pcbddc->local_primal_size;i++) array2[i] = array[pcbddc->local_primal_ref_node[i]];
1767     ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
1768     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
1769     ierr = VecSet(pcbddc->coarse_vec,0.);CHKERRQ(ierr);
1770     ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1771     ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1772     ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1773     ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1774     ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
1775     /* scale primal nodes (BDDC sums contibutions) */
1776     ierr = VecPointwiseMult(pcbddc->vec1_P,vec_scale_P,pcbddc->vec1_P);CHKERRQ(ierr);
1777     ierr = VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);CHKERRQ(ierr);
1778     ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
1779     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
1780     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
1781     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1782     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1783     /* global: \widetilde{B0}_B w_\Gamma */
1784     if (zerodiag) {
1785       ierr = MatMult(B0_B,pcis->vec2_B,dummy_vec);CHKERRQ(ierr);
1786       ierr = VecGetArray(dummy_vec,&array);CHKERRQ(ierr);
1787       pcbddc->benign_p0 = array[0];
1788       ierr = VecRestoreArray(dummy_vec,&array);CHKERRQ(ierr);
1789     } else {
1790       pcbddc->benign_p0 = 0.;
1791     }
1792     /* BDDC */
1793     ierr = VecSet(pcis->vec1_D,0.);CHKERRQ(ierr);
1794     ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1795 
1796     ierr = VecCopy(pcis->vec1_B,pcis->vec2_B);CHKERRQ(ierr);
1797     ierr = VecAXPY(pcis->vec1_B,-1.0,vec_check_B);CHKERRQ(ierr);
1798     ierr = VecNorm(pcis->vec1_B,NORM_INFINITY,&norm);CHKERRQ(ierr);
1799     PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC local error is %1.4e\n",PetscGlobalRank,norm);
1800     if (pcbddc->benign_p0_lidx >= 0) {
1801       PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC p0 error is %1.4e\n",PetscGlobalRank,PetscAbsScalar(pcbddc->benign_p0-p0_check));
1802     }
1803 
1804     ierr = VecDestroy(&vec_scale_P);CHKERRQ(ierr);
1805     ierr = VecDestroy(&vec_check_B);CHKERRQ(ierr);
1806     ierr = VecDestroy(&dummy_vec);CHKERRQ(ierr);
1807     ierr = MatDestroy(&S_j);CHKERRQ(ierr);
1808     ierr = MatDestroy(&B0);CHKERRQ(ierr);
1809     ierr = MatDestroy(&B0_B);CHKERRQ(ierr);
1810   }
1811   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1812 
1813   if (pcbddc->dbg_flag) {
1814     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1815   }
1816   PetscFunctionReturn(0);
1817 }
1818 
1819 /* -------------------------------------------------------------------------- */
1820 /*
1821    PCApply_BDDC - Applies the BDDC operator to a vector.
1822 
1823    Input Parameters:
1824 +  pc - the preconditioner context
1825 -  r - input vector (global)
1826 
1827    Output Parameter:
1828 .  z - output vector (global)
1829 
1830    Application Interface Routine: PCApply()
1831  */
1832 #undef __FUNCT__
1833 #define __FUNCT__ "PCApply_BDDC"
1834 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1835 {
1836   PC_IS             *pcis = (PC_IS*)(pc->data);
1837   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1838   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1839   PetscErrorCode    ierr;
1840   const PetscScalar one = 1.0;
1841   const PetscScalar m_one = -1.0;
1842   const PetscScalar zero = 0.0;
1843 
1844 /* This code is similar to that provided in nn.c for PCNN
1845    NN interface preconditioner changed to BDDC
1846    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1847 
1848   PetscFunctionBegin;
1849   if (pcbddc->benign_saddle_point) { /* extract p0 from r */
1850     ierr = PCBDDCBenignPopOrPushP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1851   }
1852   if (!pcbddc->use_exact_dirichlet_trick) {
1853     ierr = VecCopy(r,z);CHKERRQ(ierr);
1854     /* First Dirichlet solve */
1855     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1856     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1857     /*
1858       Assembling right hand side for BDDC operator
1859       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1860       - pcis->vec1_B the interface part of the global vector z
1861     */
1862     if (n_D) {
1863       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1864       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1865       if (pcbddc->switch_static) { ierr = MatMultAdd(pcis->A_II,pcis->vec2_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1866       ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1867     } else {
1868       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1869     }
1870     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1871     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1872     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1873   } else {
1874     if (pcbddc->switch_static) {
1875       ierr = VecSet(pcis->vec1_D,zero);CHKERRQ(ierr);
1876     }
1877     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1878   }
1879 
1880   /* Apply interface preconditioner
1881      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1882   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1883 
1884   /* Apply transpose of partition of unity operator */
1885   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1886 
1887   /* Second Dirichlet solve and assembling of output */
1888   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1889   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1890   if (n_B) {
1891     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1892     if (pcbddc->switch_static) { ierr = MatMultAdd(pcis->A_II,pcis->vec1_D,pcis->vec3_D,pcis->vec3_D);CHKERRQ(ierr); }
1893   } else if (pcbddc->switch_static) {
1894     ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1895   }
1896   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1897 
1898   if (!pcbddc->use_exact_dirichlet_trick) {
1899     if (pcbddc->switch_static) {
1900       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1901     } else {
1902       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1903     }
1904     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1905     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1906   } else {
1907     if (pcbddc->switch_static) {
1908       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1909     } else {
1910       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1911     }
1912     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1913     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1914   }
1915 
1916   if (pcbddc->benign_saddle_point) { /* push p0 (computed in PCBDDCApplyInterface) */
1917     ierr = PCBDDCBenignPopOrPushP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1918   }
1919   PetscFunctionReturn(0);
1920 }
1921 
1922 /* -------------------------------------------------------------------------- */
1923 /*
1924    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1925 
1926    Input Parameters:
1927 +  pc - the preconditioner context
1928 -  r - input vector (global)
1929 
1930    Output Parameter:
1931 .  z - output vector (global)
1932 
1933    Application Interface Routine: PCApplyTranspose()
1934  */
1935 #undef __FUNCT__
1936 #define __FUNCT__ "PCApplyTranspose_BDDC"
1937 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1938 {
1939   PC_IS             *pcis = (PC_IS*)(pc->data);
1940   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1941   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1942   PetscErrorCode    ierr;
1943   const PetscScalar one = 1.0;
1944   const PetscScalar m_one = -1.0;
1945   const PetscScalar zero = 0.0;
1946 
1947   PetscFunctionBegin;
1948   if (!pcbddc->use_exact_dirichlet_trick) {
1949     ierr = VecCopy(r,z);CHKERRQ(ierr);
1950     /* First Dirichlet solve */
1951     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1952     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1953     /*
1954       Assembling right hand side for BDDC operator
1955       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1956       - pcis->vec1_B the interface part of the global vector z
1957     */
1958     if (n_D) {
1959       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1960       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1961       if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcis->A_II,pcis->vec2_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1962       ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1963     } else {
1964       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1965     }
1966     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1967     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1968     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1969   } else {
1970     if (pcbddc->switch_static) {
1971       ierr = VecSet(pcis->vec1_D,zero);CHKERRQ(ierr);
1972     }
1973     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1974   }
1975 
1976   /* Apply interface preconditioner
1977      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1978   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
1979 
1980   /* Apply transpose of partition of unity operator */
1981   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1982 
1983   /* Second Dirichlet solve and assembling of output */
1984   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1985   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1986   if (n_B) {
1987     ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1988     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcis->A_II,pcis->vec1_D,pcis->vec3_D,pcis->vec3_D);CHKERRQ(ierr); }
1989   } else if (pcbddc->switch_static) {
1990     ierr = MatMultTranspose(pcis->A_II,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1991   }
1992   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1993   if (!pcbddc->use_exact_dirichlet_trick) {
1994     if (pcbddc->switch_static) {
1995       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1996     } else {
1997       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1998     }
1999     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2000     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2001   } else {
2002     if (pcbddc->switch_static) {
2003       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2004     } else {
2005       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2006     }
2007     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2008     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2009   }
2010   PetscFunctionReturn(0);
2011 }
2012 /* -------------------------------------------------------------------------- */
2013 
2014 #undef __FUNCT__
2015 #define __FUNCT__ "PCDestroy_BDDC"
2016 PetscErrorCode PCDestroy_BDDC(PC pc)
2017 {
2018   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2019   PetscErrorCode ierr;
2020 
2021   PetscFunctionBegin;
2022   /* free data created by PCIS */
2023   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2024   /* free BDDC custom data  */
2025   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2026   /* destroy objects related to topography */
2027   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2028   /* free allocated graph structure */
2029   ierr = PetscFree(pcbddc->mat_graph);CHKERRQ(ierr);
2030   /* free allocated sub schurs structure */
2031   ierr = PetscFree(pcbddc->sub_schurs);CHKERRQ(ierr);
2032   /* destroy objects for scaling operator */
2033   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2034   ierr = PetscFree(pcbddc->deluxe_ctx);CHKERRQ(ierr);
2035   /* free solvers stuff */
2036   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2037   /* free global vectors needed in presolve */
2038   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2039   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2040   /* free stuff for change of basis hooks */
2041   if (pcbddc->new_global_mat) {
2042     PCBDDCChange_ctx change_ctx;
2043     ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
2044     ierr = MatDestroy(&change_ctx->original_mat);CHKERRQ(ierr);
2045     ierr = MatDestroy(&change_ctx->global_change);CHKERRQ(ierr);
2046     ierr = VecDestroyVecs(2,&change_ctx->work);CHKERRQ(ierr);
2047     ierr = PetscFree(change_ctx);CHKERRQ(ierr);
2048   }
2049   ierr = MatDestroy(&pcbddc->new_global_mat);CHKERRQ(ierr);
2050   /* remove functions */
2051   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2052   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2053   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2054   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2055   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2056   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2057   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNullSpace_C",NULL);CHKERRQ(ierr);
2058   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2059   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2060   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2061   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2062   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2063   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2064   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2065   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2066   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2067   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2068   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2069   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2070   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2071   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2072   /* Free the private data structure */
2073   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2074   PetscFunctionReturn(0);
2075 }
2076 /* -------------------------------------------------------------------------- */
2077 
2078 #undef __FUNCT__
2079 #define __FUNCT__ "PCBDDCMatFETIDPGetRHS_BDDC"
2080 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2081 {
2082   FETIDPMat_ctx  mat_ctx;
2083   Vec            copy_standard_rhs;
2084   PC_IS*         pcis;
2085   PC_BDDC*       pcbddc;
2086   PetscErrorCode ierr;
2087 
2088   PetscFunctionBegin;
2089   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2090   pcis = (PC_IS*)mat_ctx->pc->data;
2091   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2092 
2093   /*
2094      change of basis for physical rhs if needed
2095      It also changes the rhs in case of dirichlet boundaries
2096      TODO: better management when FETIDP will have its own class
2097   */
2098   ierr = VecDuplicate(standard_rhs,&copy_standard_rhs);CHKERRQ(ierr);
2099   ierr = VecCopy(standard_rhs,copy_standard_rhs);CHKERRQ(ierr);
2100   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,copy_standard_rhs,NULL);CHKERRQ(ierr);
2101   /* store vectors for computation of fetidp final solution */
2102   ierr = VecScatterBegin(pcis->global_to_D,copy_standard_rhs,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2103   ierr = VecScatterEnd(pcis->global_to_D,copy_standard_rhs,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2104   /* scale rhs since it should be unassembled */
2105   /* TODO use counter scaling? (also below) */
2106   ierr = VecScatterBegin(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2107   ierr = VecScatterEnd(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2108   /* Apply partition of unity */
2109   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2110   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,copy_standard_rhs,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2111   if (!pcbddc->switch_static) {
2112     /* compute partially subassembled Schur complement right-hand side */
2113     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2114     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2115     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2116     ierr = VecSet(copy_standard_rhs,0.0);CHKERRQ(ierr);
2117     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,copy_standard_rhs,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2118     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,copy_standard_rhs,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2119     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,copy_standard_rhs,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2120     ierr = VecScatterBegin(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2121     ierr = VecScatterEnd(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2122     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2123   }
2124   ierr = VecDestroy(&copy_standard_rhs);CHKERRQ(ierr);
2125   /* BDDC rhs */
2126   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2127   if (pcbddc->switch_static) {
2128     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2129   }
2130   /* apply BDDC */
2131   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2132   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2133   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2134   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2135   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2136   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2137   PetscFunctionReturn(0);
2138 }
2139 
2140 #undef __FUNCT__
2141 #define __FUNCT__ "PCBDDCMatFETIDPGetRHS"
2142 /*@
2143  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2144 
2145    Collective
2146 
2147    Input Parameters:
2148 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2149 -  standard_rhs    - the right-hand side of the original linear system
2150 
2151    Output Parameters:
2152 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2153 
2154    Level: developer
2155 
2156    Notes:
2157 
2158 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2159 @*/
2160 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2161 {
2162   FETIDPMat_ctx  mat_ctx;
2163   PetscErrorCode ierr;
2164 
2165   PetscFunctionBegin;
2166   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2167   ierr = PetscTryMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2168   PetscFunctionReturn(0);
2169 }
2170 /* -------------------------------------------------------------------------- */
2171 
2172 #undef __FUNCT__
2173 #define __FUNCT__ "PCBDDCMatFETIDPGetSolution_BDDC"
2174 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2175 {
2176   FETIDPMat_ctx  mat_ctx;
2177   PC_IS*         pcis;
2178   PC_BDDC*       pcbddc;
2179   PetscErrorCode ierr;
2180 
2181   PetscFunctionBegin;
2182   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2183   pcis = (PC_IS*)mat_ctx->pc->data;
2184   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2185 
2186   /* apply B_delta^T */
2187   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2188   ierr = VecScatterEnd  (mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2189   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2190   /* compute rhs for BDDC application */
2191   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2192   if (pcbddc->switch_static) {
2193     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2194   }
2195   /* apply BDDC */
2196   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2197   /* put values into standard global vector */
2198   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2199   ierr = VecScatterEnd  (pcis->global_to_B,pcis->vec1_B,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2200   if (!pcbddc->switch_static) {
2201     /* compute values into the interior if solved for the partially subassembled Schur complement */
2202     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2203     ierr = VecAXPY(mat_ctx->temp_solution_D,-1.0,pcis->vec1_D);CHKERRQ(ierr);
2204     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2205   }
2206   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2207   ierr = VecScatterEnd  (pcis->global_to_D,pcis->vec1_D,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2208   /* final change of basis if needed
2209      Is also sums the dirichlet part removed during RHS assembling */
2210   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2211   PetscFunctionReturn(0);
2212 }
2213 
2214 #undef __FUNCT__
2215 #define __FUNCT__ "PCBDDCMatFETIDPGetSolution"
2216 /*@
2217  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2218 
2219    Collective
2220 
2221    Input Parameters:
2222 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2223 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2224 
2225    Output Parameters:
2226 .  standard_sol    - the solution defined on the physical domain
2227 
2228    Level: developer
2229 
2230    Notes:
2231 
2232 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2233 @*/
2234 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2235 {
2236   FETIDPMat_ctx  mat_ctx;
2237   PetscErrorCode ierr;
2238 
2239   PetscFunctionBegin;
2240   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2241   ierr = PetscTryMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2242   PetscFunctionReturn(0);
2243 }
2244 /* -------------------------------------------------------------------------- */
2245 
2246 extern PetscErrorCode FETIDPMatMult(Mat,Vec,Vec);
2247 extern PetscErrorCode FETIDPMatMultTranspose(Mat,Vec,Vec);
2248 extern PetscErrorCode PCBDDCDestroyFETIDPMat(Mat);
2249 extern PetscErrorCode FETIDPPCApply(PC,Vec,Vec);
2250 extern PetscErrorCode FETIDPPCApplyTranspose(PC,Vec,Vec);
2251 extern PetscErrorCode PCBDDCDestroyFETIDPPC(PC);
2252 
2253 #undef __FUNCT__
2254 #define __FUNCT__ "PCBDDCCreateFETIDPOperators_BDDC"
2255 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, Mat *fetidp_mat, PC *fetidp_pc)
2256 {
2257 
2258   FETIDPMat_ctx  fetidpmat_ctx;
2259   Mat            newmat;
2260   FETIDPPC_ctx   fetidppc_ctx;
2261   PC             newpc;
2262   MPI_Comm       comm;
2263   PetscErrorCode ierr;
2264 
2265   PetscFunctionBegin;
2266   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2267   /* FETIDP linear matrix */
2268   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2269   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2270   ierr = MatCreateShell(comm,PETSC_DECIDE,PETSC_DECIDE,fetidpmat_ctx->n_lambda,fetidpmat_ctx->n_lambda,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2271   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2272   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2273   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2274   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2275   /* FETIDP preconditioner */
2276   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2277   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2278   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2279   ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2280   ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2281   ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2282   ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2283   ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2284   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2285   ierr = PCSetUp(newpc);CHKERRQ(ierr);
2286   /* return pointers for objects created */
2287   *fetidp_mat=newmat;
2288   *fetidp_pc=newpc;
2289   PetscFunctionReturn(0);
2290 }
2291 
2292 #undef __FUNCT__
2293 #define __FUNCT__ "PCBDDCCreateFETIDPOperators"
2294 /*@
2295  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2296 
2297    Collective
2298 
2299    Input Parameters:
2300 .  pc - the BDDC preconditioning context (setup should have been called before)
2301 
2302    Output Parameters:
2303 +  fetidp_mat - shell FETI-DP matrix object
2304 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2305 
2306    Options Database Keys:
2307 .    -fetidp_fullyredundant <false> - use or not a fully redundant set of Lagrange multipliers
2308 
2309    Level: developer
2310 
2311    Notes:
2312      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2313 
2314 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2315 @*/
2316 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, Mat *fetidp_mat, PC *fetidp_pc)
2317 {
2318   PetscErrorCode ierr;
2319 
2320   PetscFunctionBegin;
2321   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2322   if (pc->setupcalled) {
2323     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,Mat*,PC*),(pc,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2324   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2325   PetscFunctionReturn(0);
2326 }
2327 /* -------------------------------------------------------------------------- */
2328 /*MC
2329    PCBDDC - Balancing Domain Decomposition by Constraints.
2330 
2331    An implementation of the BDDC preconditioner based on
2332 
2333 .vb
2334    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2335    [2] A. Klawonn and O. B. Widlund. "Dual-Primal FETI Methods for Linear Elasticity", http://cs.nyu.edu/csweb/Research/TechReports/TR2004-855/TR2004-855.pdf
2336    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2337    [4] C. Pechstein and C. R. Dohrmann. "Modern domain decomposition methods BDDC, deluxe scaling, and an algebraic approach", Seminar talk, Linz, December 2013, http://people.ricam.oeaw.ac.at/c.pechstein/pechstein-bddc2013.pdf
2338 .ve
2339 
2340    The matrix to be preconditioned (Pmat) must be of type MATIS.
2341 
2342    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2343 
2344    It also works with unsymmetric and indefinite problems.
2345 
2346    Unlike 'conventional' interface preconditioners, PCBDDC iterates over all degrees of freedom, not just those on the interface. This allows the use of approximate solvers on the subdomains.
2347 
2348    Approximate local solvers are automatically adapted for singular linear problems (see [1]) if the user has provided the nullspace using PCBDDCSetNullSpace()
2349 
2350    Boundary nodes are split in vertices, edges and faces classes using information from the local to global mapping of dofs and the local connectivity graph of nodes. The latter can be customized by using PCBDDCSetLocalAdjacencyGraph()
2351    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesLocalIS()
2352 
2353    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2354 
2355    Change of basis is performed similarly to [2] when requested. When more than one constraint is present on a single connected component (i.e. an edge or a face), a robust method based on local QR factorizations is used.
2356    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2357 
2358    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2359 
2360    Adaptive selection of primal constraints [4] is supported for SPD systems with high-contrast in the coefficients if MUMPS is present. Future versions of the code will also consider using MKL_PARDISO or PASTIX.
2361 
2362    An experimental interface to the FETI-DP method is available. FETI-DP operators could be created using PCBDDCCreateFETIDPOperators(). A stand-alone class for the FETI-DP method will be provided in the next releases.
2363    Deluxe scaling is not supported yet for FETI-DP.
2364 
2365    Options Database Keys (some of them, run with -h for a complete list):
2366 
2367 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2368 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2369 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2370 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2371 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2372 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2373 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2374 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2375 .    -pc_bddc_coarsening_ratio <8> - number of subdomains which will be aggregated together at the coarser level (e.g. H/h ratio at the coarser level, significative only in the multilevel case)
2376 .    -pc_bddc_redistribute <0> - size of a subset of processors where the coarse problem will be remapped (the value is ignored if not at the coarsest level)
2377 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2378 .    -pc_bddc_schur_layers <-1> - select the economic version of deluxe scaling by specifying the number of layers (-1 corresponds to the original deluxe scaling)
2379 .    -pc_bddc_adaptive_threshold <0.0> - when a value greater than one is specified, adaptive selection of constraints is performed on edges and faces (requires deluxe scaling and MUMPS installed)
2380 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2381 
2382    Options for Dirichlet, Neumann or coarse solver can be set with
2383 .vb
2384       -pc_bddc_dirichlet_
2385       -pc_bddc_neumann_
2386       -pc_bddc_coarse_
2387 .ve
2388    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2389 
2390    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2391 .vb
2392       -pc_bddc_dirichlet_lN_
2393       -pc_bddc_neumann_lN_
2394       -pc_bddc_coarse_lN_
2395 .ve
2396    Note that level number ranges from the finest (0) to the coarsest (N).
2397    In order to specify options for the BDDC operators at the coarser levels (and not for the solvers), prepend -pc_bddc_coarse_ or -pc_bddc_coarse_l to the option, e.g.
2398 .vb
2399      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2400 .ve
2401    will use a threshold of 5 for constraints' selection at the first coarse level and will redistribute the coarse problem of the first coarse level on 3 processors
2402 
2403    Level: intermediate
2404 
2405    Developer notes:
2406 
2407    Contributed by Stefano Zampini
2408 
2409 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2410 M*/
2411 
2412 #undef __FUNCT__
2413 #define __FUNCT__ "PCCreate_BDDC"
2414 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2415 {
2416   PetscErrorCode      ierr;
2417   PC_BDDC             *pcbddc;
2418 
2419   PetscFunctionBegin;
2420   /* Creates the private data structure for this preconditioner and attach it to the PC object. */
2421   ierr      = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2422   pc->data  = (void*)pcbddc;
2423 
2424   /* create PCIS data structure */
2425   ierr = PCISCreate(pc);CHKERRQ(ierr);
2426 
2427   /* BDDC customization */
2428   pcbddc->use_local_adj       = PETSC_TRUE;
2429   pcbddc->use_vertices        = PETSC_TRUE;
2430   pcbddc->use_edges           = PETSC_TRUE;
2431   pcbddc->use_faces           = PETSC_FALSE;
2432   pcbddc->use_change_of_basis = PETSC_FALSE;
2433   pcbddc->use_change_on_faces = PETSC_FALSE;
2434   pcbddc->switch_static       = PETSC_FALSE;
2435   pcbddc->use_nnsp_true       = PETSC_FALSE;
2436   pcbddc->use_qr_single       = PETSC_FALSE;
2437   pcbddc->symmetric_primal    = PETSC_TRUE;
2438   pcbddc->benign_saddle_point = PETSC_FALSE;
2439   pcbddc->dbg_flag            = 0;
2440   /* private */
2441   pcbddc->local_primal_size          = 0;
2442   pcbddc->local_primal_size_cc       = 0;
2443   pcbddc->local_primal_ref_node      = 0;
2444   pcbddc->local_primal_ref_mult      = 0;
2445   pcbddc->n_vertices                 = 0;
2446   pcbddc->primal_indices_local_idxs  = 0;
2447   pcbddc->recompute_topography       = PETSC_FALSE;
2448   pcbddc->coarse_size                = -1;
2449   pcbddc->new_primal_space           = PETSC_FALSE;
2450   pcbddc->new_primal_space_local     = PETSC_FALSE;
2451   pcbddc->global_primal_indices      = 0;
2452   pcbddc->onearnullspace             = 0;
2453   pcbddc->onearnullvecs_state        = 0;
2454   pcbddc->user_primal_vertices       = 0;
2455   pcbddc->NullSpace                  = 0;
2456   pcbddc->temp_solution              = 0;
2457   pcbddc->original_rhs               = 0;
2458   pcbddc->local_mat                  = 0;
2459   pcbddc->ChangeOfBasisMatrix        = 0;
2460   pcbddc->user_ChangeOfBasisMatrix   = 0;
2461   pcbddc->new_global_mat             = 0;
2462   pcbddc->coarse_vec                 = 0;
2463   pcbddc->coarse_ksp                 = 0;
2464   pcbddc->coarse_phi_B               = 0;
2465   pcbddc->coarse_phi_D               = 0;
2466   pcbddc->coarse_psi_B               = 0;
2467   pcbddc->coarse_psi_D               = 0;
2468   pcbddc->vec1_P                     = 0;
2469   pcbddc->vec1_R                     = 0;
2470   pcbddc->vec2_R                     = 0;
2471   pcbddc->local_auxmat1              = 0;
2472   pcbddc->local_auxmat2              = 0;
2473   pcbddc->R_to_B                     = 0;
2474   pcbddc->R_to_D                     = 0;
2475   pcbddc->ksp_D                      = 0;
2476   pcbddc->ksp_R                      = 0;
2477   pcbddc->NeumannBoundaries          = 0;
2478   pcbddc->NeumannBoundariesLocal     = 0;
2479   pcbddc->DirichletBoundaries        = 0;
2480   pcbddc->DirichletBoundariesLocal   = 0;
2481   pcbddc->user_provided_isfordofs    = PETSC_FALSE;
2482   pcbddc->n_ISForDofs                = 0;
2483   pcbddc->n_ISForDofsLocal           = 0;
2484   pcbddc->ISForDofs                  = 0;
2485   pcbddc->ISForDofsLocal             = 0;
2486   pcbddc->ConstraintMatrix           = 0;
2487   pcbddc->use_exact_dirichlet_trick  = PETSC_TRUE;
2488   pcbddc->coarse_loc_to_glob         = 0;
2489   pcbddc->coarsening_ratio           = 8;
2490   pcbddc->coarse_adj_red             = 0;
2491   pcbddc->current_level              = 0;
2492   pcbddc->max_levels                 = 0;
2493   pcbddc->use_coarse_estimates       = PETSC_FALSE;
2494   pcbddc->redistribute_coarse        = 0;
2495   pcbddc->coarse_subassembling       = 0;
2496   pcbddc->coarse_subassembling_init  = 0;
2497 
2498   /* benign subspace trick */
2499   pcbddc->B0_ncol                    = 0;
2500   pcbddc->B0_cols                    = NULL;
2501   pcbddc->B0_vals                    = NULL;
2502   pcbddc->benign_change              = 0;
2503   pcbddc->benign_vec                 = 0;
2504   pcbddc->benign_original_mat        = 0;
2505   pcbddc->benign_sf                  = 0;
2506   pcbddc->benign_p0_lidx             = -1;
2507   pcbddc->benign_p0_gidx             = -1;
2508 
2509   /* create local graph structure */
2510   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2511 
2512   /* scaling */
2513   pcbddc->work_scaling          = 0;
2514   pcbddc->use_deluxe_scaling    = PETSC_FALSE;
2515   pcbddc->faster_deluxe         = PETSC_FALSE;
2516 
2517   /* create sub schurs structure */
2518   ierr = PCBDDCSubSchursCreate(&pcbddc->sub_schurs);CHKERRQ(ierr);
2519   pcbddc->sub_schurs_rebuild     = PETSC_FALSE;
2520   pcbddc->sub_schurs_layers      = -1;
2521   pcbddc->sub_schurs_use_useradj = PETSC_FALSE;
2522 
2523   pcbddc->computed_rowadj = PETSC_FALSE;
2524 
2525   /* adaptivity */
2526   pcbddc->adaptive_threshold      = 0.0;
2527   pcbddc->adaptive_nmax           = 0;
2528   pcbddc->adaptive_nmin           = 0;
2529 
2530   /* function pointers */
2531   pc->ops->apply               = PCApply_BDDC;
2532   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2533   pc->ops->setup               = PCSetUp_BDDC;
2534   pc->ops->destroy             = PCDestroy_BDDC;
2535   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2536   pc->ops->view                = 0;
2537   pc->ops->applyrichardson     = 0;
2538   pc->ops->applysymmetricleft  = 0;
2539   pc->ops->applysymmetricright = 0;
2540   pc->ops->presolve            = PCPreSolve_BDDC;
2541   pc->ops->postsolve           = PCPostSolve_BDDC;
2542 
2543   /* composing function */
2544   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2545   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2546   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2547   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2548   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2549   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2550   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNullSpace_C",PCBDDCSetNullSpace_BDDC);CHKERRQ(ierr);
2551   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2552   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2553   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2554   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2555   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2556   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2557   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2558   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2559   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2560   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2561   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2562   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2563   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2564   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2565   PetscFunctionReturn(0);
2566 }
2567 
2568