xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision e5a47cbf7a0ea2f3162c91eaca9c3f50ebb42cd0)
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     ierr = PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_FALSE);CHKERRQ(ierr);
1091     ierr = PCApply_BDDC(pc,pcis->vec1_global,pcbddc->benign_vec);CHKERRQ(ierr);
1092     pcbddc->benign_p0 = 0.;
1093     ierr = PCBDDCBenignGetOrSetP0(pc,pcbddc->benign_vec,PETSC_FALSE);CHKERRQ(ierr);
1094   }
1095 
1096   /* change rhs and iteration matrix if using the change of basis */
1097   if (pcbddc->ChangeOfBasisMatrix) {
1098     PCBDDCChange_ctx change_ctx;
1099 
1100     /* get change ctx */
1101     ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
1102 
1103     /* set current iteration matrix inside change context (change of basis has been already set into the ctx during PCSetUp) */
1104     ierr = MatDestroy(&change_ctx->original_mat);CHKERRQ(ierr);
1105     ierr = PetscObjectReference((PetscObject)pc->mat);CHKERRQ(ierr);
1106     change_ctx->original_mat = pc->mat;
1107 
1108     /* change iteration matrix */
1109     ierr = MatDestroy(&pc->mat);CHKERRQ(ierr);
1110     ierr = PetscObjectReference((PetscObject)pcbddc->new_global_mat);CHKERRQ(ierr);
1111     pc->mat = pcbddc->new_global_mat;
1112 
1113     /* store the original rhs */
1114     if (copy_rhs) {
1115       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1116       copy_rhs = PETSC_FALSE;
1117     }
1118 
1119     /* change rhs */
1120     ierr = MatMultTranspose(change_ctx->global_change,rhs,pcis->vec1_global);CHKERRQ(ierr);
1121     ierr = VecCopy(pcis->vec1_global,rhs);CHKERRQ(ierr);
1122     pcbddc->rhs_change = PETSC_TRUE;
1123   }
1124 
1125   /* remove non-benign solution from the rhs */
1126   if (pcbddc->benign_saddle_point) {
1127     /* store the original rhs */
1128     if (copy_rhs) {
1129       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1130       copy_rhs = PETSC_FALSE;
1131     }
1132     ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1133     ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1134     pcbddc->rhs_change = PETSC_TRUE;
1135   }
1136 
1137   /* set initial guess if using PCG */
1138   if (x && pcbddc->use_exact_dirichlet_trick) {
1139     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1140     ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1141     ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1142     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1143     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1144     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1145     if (ksp) {
1146       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1147     }
1148   }
1149 
1150   /* remove nullspace if present */
1151   if (ksp && x && pcbddc->NullSpace) {
1152     ierr = MatNullSpaceRemove(pcbddc->NullSpace,x);CHKERRQ(ierr);
1153     /* store the original rhs */
1154     if (copy_rhs) {
1155       ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1156       copy_rhs = PETSC_FALSE;
1157     }
1158     pcbddc->rhs_change = PETSC_TRUE;
1159     ierr = MatNullSpaceRemove(pcbddc->NullSpace,rhs);CHKERRQ(ierr);
1160   }
1161   PetscFunctionReturn(0);
1162 }
1163 
1164 /* -------------------------------------------------------------------------- */
1165 #undef __FUNCT__
1166 #define __FUNCT__ "PCPostSolve_BDDC"
1167 /* -------------------------------------------------------------------------- */
1168 /*
1169    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1170                      approach has been selected. Also, restores rhs to its original state.
1171 
1172    Input Parameter:
1173 +  pc - the preconditioner contex
1174 
1175    Application Interface Routine: PCPostSolve()
1176 
1177    Notes:
1178      The interface routine PCPostSolve() is not usually called directly by
1179      the user, but instead is called by KSPSolve().
1180 */
1181 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1182 {
1183   PetscErrorCode ierr;
1184   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1185 
1186   PetscFunctionBegin;
1187   if (pcbddc->ChangeOfBasisMatrix) {
1188     PCBDDCChange_ctx change_ctx;
1189 
1190     /* get change ctx */
1191     ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
1192 
1193     /* restore iteration matrix */
1194     ierr = MatDestroy(&pc->mat);CHKERRQ(ierr);
1195     ierr = PetscObjectReference((PetscObject)change_ctx->original_mat);CHKERRQ(ierr);
1196     pc->mat = change_ctx->original_mat;
1197 
1198     /* need to restore the local matrices */
1199     if (pcbddc->benign_saddle_point && pcbddc->benign_change) {
1200       Mat_IS *matis = (Mat_IS*)pc->mat->data;
1201 
1202       ierr = MatDestroy(&matis->A);CHKERRQ(ierr);
1203       ierr = PetscObjectReference((PetscObject)pcbddc->benign_original_mat);CHKERRQ(ierr);
1204       matis->A = pcbddc->benign_original_mat;
1205       ierr = MatDestroy(&pcbddc->benign_original_mat);CHKERRQ(ierr);
1206     }
1207 
1208     /* get solution in original basis */
1209     if (x) {
1210       PC_IS *pcis = (PC_IS*)(pc->data);
1211 
1212       /* restore solution on pressures */
1213       if (pcbddc->benign_saddle_point) {
1214         Mat_IS *matis = (Mat_IS*)pc->mat->data;
1215 
1216         /* add non-benign solution */
1217         ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1218 
1219         /* change basis on pressures for x */
1220         ierr = VecScatterBegin(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1221         ierr = VecScatterEnd(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1222         if (pcbddc->benign_change) {
1223 
1224           ierr = MatMult(pcbddc->benign_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1225           ierr = VecScatterBegin(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1226           ierr = VecScatterEnd(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1227         } else {
1228           ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1229           ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1230         }
1231       }
1232       /* change basis on x */
1233       ierr = MatMult(change_ctx->global_change,x,pcis->vec1_global);CHKERRQ(ierr);
1234       ierr = VecCopy(pcis->vec1_global,x);CHKERRQ(ierr);
1235     }
1236   }
1237 
1238   /* add solution removed in presolve */
1239   if (x && pcbddc->rhs_change) {
1240     ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1241   }
1242 
1243   /* restore rhs to its original state */
1244   if (rhs && pcbddc->rhs_change) {
1245     ierr = VecCopy(pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1246   }
1247   pcbddc->rhs_change = PETSC_FALSE;
1248 
1249   /* restore ksp guess state */
1250   if (ksp) {
1251     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1252   }
1253   PetscFunctionReturn(0);
1254 }
1255 /* -------------------------------------------------------------------------- */
1256 #undef __FUNCT__
1257 #define __FUNCT__ "PCSetUp_BDDC"
1258 /* -------------------------------------------------------------------------- */
1259 /*
1260    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1261                   by setting data structures and options.
1262 
1263    Input Parameter:
1264 +  pc - the preconditioner context
1265 
1266    Application Interface Routine: PCSetUp()
1267 
1268    Notes:
1269      The interface routine PCSetUp() is not usually called directly by
1270      the user, but instead is called by PCApply() if necessary.
1271 */
1272 PetscErrorCode PCSetUp_BDDC(PC pc)
1273 {
1274   PetscErrorCode ierr;
1275   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
1276   Mat_IS*        matis;
1277   MatNullSpace   nearnullspace;
1278   IS             zerodiag = NULL;
1279   PetscInt       nrows,ncols;
1280   PetscBool      computetopography,computesolvers,computesubschurs;
1281   PetscBool      computeconstraintsmatrix;
1282   PetscBool      new_nearnullspace_provided,ismatis;
1283 
1284   PetscFunctionBegin;
1285   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1286   if (!ismatis) {
1287     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1288   }
1289   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1290   if (nrows != ncols) {
1291     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1292   }
1293   matis = (Mat_IS*)pc->pmat->data;
1294   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1295   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1296      Also, BDDC directly build the Dirichlet problem */
1297   /* split work */
1298   if (pc->setupcalled) {
1299     if (pc->flag == SAME_NONZERO_PATTERN) {
1300       computetopography = PETSC_FALSE;
1301       computesolvers = PETSC_TRUE;
1302     } else { /* DIFFERENT_NONZERO_PATTERN */
1303       computetopography = PETSC_TRUE;
1304       computesolvers = PETSC_TRUE;
1305     }
1306   } else {
1307     computetopography = PETSC_TRUE;
1308     computesolvers = PETSC_TRUE;
1309   }
1310   if (pcbddc->recompute_topography) {
1311     computetopography = PETSC_TRUE;
1312   }
1313   computeconstraintsmatrix = PETSC_FALSE;
1314 
1315   /* check parameters' compatibility */
1316   if (pcbddc->adaptive_threshold > 0.0 && !pcbddc->use_deluxe_scaling) {
1317     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute adaptive constraints without deluxe scaling. Rerun with -pc_bddc_use_deluxe_scaling");
1318   }
1319   pcbddc->adaptive_selection = (PetscBool)(pcbddc->adaptive_threshold > 0.0 && pcbddc->use_deluxe_scaling);
1320   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1321 
1322   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1323   if (pcbddc->faster_deluxe && pcbddc->adaptive_selection && pcbddc->use_change_of_basis) {
1324     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");
1325   }
1326 
1327   /* check if the iteration matrix is of type MATIS in case the benign trick has been requested */
1328   ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1329   if (pcbddc->benign_saddle_point && !ismatis) {
1330     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner with benign subspace trick requires the iteration matrix to be of type MATIS");
1331   }
1332 
1333   /* Get stdout for dbg */
1334   if (pcbddc->dbg_flag) {
1335     if (!pcbddc->dbg_viewer) {
1336       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1337       ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1338     }
1339     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1340   }
1341 
1342   if (pcbddc->user_ChangeOfBasisMatrix) {
1343     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1344     pcbddc->use_change_of_basis = PETSC_FALSE;
1345     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1346   } else {
1347     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1348     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1349     pcbddc->local_mat = matis->A;
1350   }
1351 
1352   /* change basis on local pressures (aka zerodiag dofs) */
1353   if (pcbddc->benign_saddle_point) {
1354     /* detect local saddle point and change the basis in pcbddc->local_mat */
1355     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1356     /* pop B0 mat from pcbddc->local_mat */
1357     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1358   }
1359 
1360   /* propagate relevant information */
1361   /* workaround for reals */
1362 #if !defined(PETSC_USE_COMPLEX)
1363   if (matis->A->symmetric_set) {
1364     ierr = MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);CHKERRQ(ierr);
1365   }
1366 #endif
1367   if (matis->A->symmetric_set) {
1368     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1369   }
1370   if (matis->A->spd_set) {
1371     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1372   }
1373 
1374   /* Set up all the "iterative substructuring" common block without computing solvers */
1375   {
1376     Mat temp_mat;
1377 
1378     temp_mat = matis->A;
1379     matis->A = pcbddc->local_mat;
1380     ierr = PCISSetUp(pc,PETSC_FALSE);CHKERRQ(ierr);
1381     pcbddc->local_mat = matis->A;
1382     matis->A = temp_mat;
1383   }
1384 
1385   /* Analyze interface */
1386   if (computetopography) {
1387     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1388     computeconstraintsmatrix = PETSC_TRUE;
1389   }
1390 
1391   /* check existence of a divergence free extension, i.e.
1392      b(v_I,p_0) = 0 for all v_I (raise error if not).
1393      Also, check that PCBDDCBenignGetOrSetP0 works */
1394 #if defined(PETSC_USE_DEBUG)
1395   if (pcbddc->benign_saddle_point) {
1396     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1397   }
1398 #endif
1399 
1400   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1401   if (computesolvers) {
1402     PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;
1403 
1404     if (computesubschurs && computetopography) {
1405       ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1406     }
1407     if (sub_schurs->use_mumps) {
1408       if (computesubschurs) {
1409         ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1410       }
1411       ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1412     } else {
1413       ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1414       if (computesubschurs) {
1415         ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1416       }
1417     }
1418     if (pcbddc->adaptive_selection) {
1419       ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1420       computeconstraintsmatrix = PETSC_TRUE;
1421     }
1422   }
1423 
1424   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1425   new_nearnullspace_provided = PETSC_FALSE;
1426   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1427   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1428     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1429       new_nearnullspace_provided = PETSC_TRUE;
1430     } else {
1431       /* determine if the two nullspaces are different (should be lightweight) */
1432       if (nearnullspace != pcbddc->onearnullspace) {
1433         new_nearnullspace_provided = PETSC_TRUE;
1434       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1435         PetscInt         i;
1436         const Vec        *nearnullvecs;
1437         PetscObjectState state;
1438         PetscInt         nnsp_size;
1439         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1440         for (i=0;i<nnsp_size;i++) {
1441           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1442           if (pcbddc->onearnullvecs_state[i] != state) {
1443             new_nearnullspace_provided = PETSC_TRUE;
1444             break;
1445           }
1446         }
1447       }
1448     }
1449   } else {
1450     if (!nearnullspace) { /* both nearnullspaces are null */
1451       new_nearnullspace_provided = PETSC_FALSE;
1452     } else { /* nearnullspace attached later */
1453       new_nearnullspace_provided = PETSC_TRUE;
1454     }
1455   }
1456 
1457   /* Setup constraints and related work vectors */
1458   /* reset primal space flags */
1459   pcbddc->new_primal_space = PETSC_FALSE;
1460   pcbddc->new_primal_space_local = PETSC_FALSE;
1461   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1462     /* It also sets the primal space flags */
1463     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1464     /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1465     ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1466   }
1467 
1468   if (computesolvers || pcbddc->new_primal_space) {
1469     if (pcbddc->use_change_of_basis) {
1470       PC_IS *pcis = (PC_IS*)(pc->data);
1471       Mat   temp_mat = NULL;
1472 
1473       if (zerodiag) {
1474         /* insert B0 in pcbddc->local_mat */
1475         ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_FALSE);CHKERRQ(ierr);
1476         /* swap local matrices */
1477         ierr = MatISGetLocalMat(pc->pmat,&temp_mat);CHKERRQ(ierr);
1478         ierr = PetscObjectReference((PetscObject)temp_mat);CHKERRQ(ierr);
1479         ierr = MatISSetLocalMat(pc->pmat,pcbddc->local_mat);CHKERRQ(ierr);
1480         ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1481       }
1482       ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1483       if (zerodiag) {
1484         /* restore original matrix */
1485         ierr = MatISSetLocalMat(pc->pmat,temp_mat);CHKERRQ(ierr);
1486         ierr = PetscObjectDereference((PetscObject)temp_mat);CHKERRQ(ierr);
1487         /* pop B0 from pcbddc->local_mat */
1488         ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1489       }
1490       /* get submatrices */
1491       ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1492       ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1493       ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1494       ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1495       ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1496       ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1497       /* set flag in pcis to not reuse submatrices during PCISCreate */
1498       pcis->reusesubmatrices = PETSC_FALSE;
1499     } else if (!pcbddc->user_ChangeOfBasisMatrix) {
1500       ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1501       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1502       pcbddc->local_mat = matis->A;
1503     }
1504     /* SetUp coarse and local Neumann solvers */
1505     ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1506     /* SetUp Scaling operator */
1507     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1508   }
1509   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1510 
1511   if (pcbddc->dbg_flag) {
1512     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1513   }
1514   PetscFunctionReturn(0);
1515 }
1516 
1517 /* -------------------------------------------------------------------------- */
1518 /*
1519    PCApply_BDDC - Applies the BDDC operator to a vector.
1520 
1521    Input Parameters:
1522 +  pc - the preconditioner context
1523 -  r - input vector (global)
1524 
1525    Output Parameter:
1526 .  z - output vector (global)
1527 
1528    Application Interface Routine: PCApply()
1529  */
1530 #undef __FUNCT__
1531 #define __FUNCT__ "PCApply_BDDC"
1532 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1533 {
1534   PC_IS             *pcis = (PC_IS*)(pc->data);
1535   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1536   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1537   PetscErrorCode    ierr;
1538   const PetscScalar one = 1.0;
1539   const PetscScalar m_one = -1.0;
1540   const PetscScalar zero = 0.0;
1541 
1542 /* This code is similar to that provided in nn.c for PCNN
1543    NN interface preconditioner changed to BDDC
1544    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1545 
1546   PetscFunctionBegin;
1547   if (pcbddc->benign_saddle_point) { /* get p0 from r */
1548     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1549   }
1550   if (!pcbddc->use_exact_dirichlet_trick) {
1551     ierr = VecCopy(r,z);CHKERRQ(ierr);
1552     /* First Dirichlet solve */
1553     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1554     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1555     /*
1556       Assembling right hand side for BDDC operator
1557       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1558       - pcis->vec1_B the interface part of the global vector z
1559     */
1560     if (n_D) {
1561       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1562       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1563       if (pcbddc->switch_static) { ierr = MatMultAdd(pcis->A_II,pcis->vec2_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1564       ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1565     } else {
1566       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1567     }
1568     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1569     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1570     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1571   } else {
1572     if (pcbddc->switch_static) {
1573       ierr = VecSet(pcis->vec1_D,zero);CHKERRQ(ierr);
1574     }
1575     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1576   }
1577 
1578   /* Apply interface preconditioner
1579      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1580   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1581 
1582   /* Apply transpose of partition of unity operator */
1583   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1584 
1585   /* Second Dirichlet solve and assembling of output */
1586   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1587   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1588   if (n_B) {
1589     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1590     if (pcbddc->switch_static) { ierr = MatMultAdd(pcis->A_II,pcis->vec1_D,pcis->vec3_D,pcis->vec3_D);CHKERRQ(ierr); }
1591   } else if (pcbddc->switch_static) {
1592     ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1593   }
1594   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1595 
1596   if (!pcbddc->use_exact_dirichlet_trick) {
1597     if (pcbddc->switch_static) {
1598       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1599     } else {
1600       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1601     }
1602     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1603     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1604   } else {
1605     if (pcbddc->switch_static) {
1606       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1607     } else {
1608       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1609     }
1610     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1611     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1612   }
1613 
1614   if (pcbddc->benign_saddle_point) { /* set p0 (computed in PCBDDCApplyInterface) */
1615     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1616   }
1617   PetscFunctionReturn(0);
1618 }
1619 
1620 /* -------------------------------------------------------------------------- */
1621 /*
1622    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1623 
1624    Input Parameters:
1625 +  pc - the preconditioner context
1626 -  r - input vector (global)
1627 
1628    Output Parameter:
1629 .  z - output vector (global)
1630 
1631    Application Interface Routine: PCApplyTranspose()
1632  */
1633 #undef __FUNCT__
1634 #define __FUNCT__ "PCApplyTranspose_BDDC"
1635 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1636 {
1637   PC_IS             *pcis = (PC_IS*)(pc->data);
1638   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1639   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1640   PetscErrorCode    ierr;
1641   const PetscScalar one = 1.0;
1642   const PetscScalar m_one = -1.0;
1643   const PetscScalar zero = 0.0;
1644 
1645   PetscFunctionBegin;
1646   if (pcbddc->benign_saddle_point) { /* get p0 from r */
1647     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1648   }
1649   if (!pcbddc->use_exact_dirichlet_trick) {
1650     ierr = VecCopy(r,z);CHKERRQ(ierr);
1651     /* First Dirichlet solve */
1652     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1653     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1654     /*
1655       Assembling right hand side for BDDC operator
1656       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1657       - pcis->vec1_B the interface part of the global vector z
1658     */
1659     if (n_D) {
1660       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1661       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1662       if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcis->A_II,pcis->vec2_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1663       ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1664     } else {
1665       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1666     }
1667     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1668     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1669     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1670   } else {
1671     if (pcbddc->switch_static) {
1672       ierr = VecSet(pcis->vec1_D,zero);CHKERRQ(ierr);
1673     }
1674     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1675   }
1676 
1677   /* Apply interface preconditioner
1678      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1679   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
1680 
1681   /* Apply transpose of partition of unity operator */
1682   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1683 
1684   /* Second Dirichlet solve and assembling of output */
1685   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1686   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1687   if (n_B) {
1688     ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1689     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcis->A_II,pcis->vec1_D,pcis->vec3_D,pcis->vec3_D);CHKERRQ(ierr); }
1690   } else if (pcbddc->switch_static) {
1691     ierr = MatMultTranspose(pcis->A_II,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1692   }
1693   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1694   if (!pcbddc->use_exact_dirichlet_trick) {
1695     if (pcbddc->switch_static) {
1696       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1697     } else {
1698       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1699     }
1700     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1701     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1702   } else {
1703     if (pcbddc->switch_static) {
1704       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1705     } else {
1706       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1707     }
1708     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1709     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1710   }
1711   if (pcbddc->benign_saddle_point) { /* set p0 (computed in PCBDDCApplyInterface) */
1712     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1713   }
1714   PetscFunctionReturn(0);
1715 }
1716 /* -------------------------------------------------------------------------- */
1717 
1718 #undef __FUNCT__
1719 #define __FUNCT__ "PCDestroy_BDDC"
1720 PetscErrorCode PCDestroy_BDDC(PC pc)
1721 {
1722   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1723   PetscErrorCode ierr;
1724 
1725   PetscFunctionBegin;
1726   /* free data created by PCIS */
1727   ierr = PCISDestroy(pc);CHKERRQ(ierr);
1728   /* free BDDC custom data  */
1729   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
1730   /* destroy objects related to topography */
1731   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
1732   /* free allocated graph structure */
1733   ierr = PetscFree(pcbddc->mat_graph);CHKERRQ(ierr);
1734   /* free allocated sub schurs structure */
1735   ierr = PetscFree(pcbddc->sub_schurs);CHKERRQ(ierr);
1736   /* destroy objects for scaling operator */
1737   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
1738   ierr = PetscFree(pcbddc->deluxe_ctx);CHKERRQ(ierr);
1739   /* free solvers stuff */
1740   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
1741   /* free global vectors needed in presolve */
1742   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
1743   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
1744   /* free stuff for change of basis hooks */
1745   if (pcbddc->new_global_mat) {
1746     PCBDDCChange_ctx change_ctx;
1747     ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
1748     ierr = MatDestroy(&change_ctx->original_mat);CHKERRQ(ierr);
1749     ierr = MatDestroy(&change_ctx->global_change);CHKERRQ(ierr);
1750     ierr = VecDestroyVecs(2,&change_ctx->work);CHKERRQ(ierr);
1751     ierr = PetscFree(change_ctx);CHKERRQ(ierr);
1752   }
1753   ierr = MatDestroy(&pcbddc->new_global_mat);CHKERRQ(ierr);
1754   /* remove functions */
1755   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
1756   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
1757   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
1758   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
1759   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
1760   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
1761   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNullSpace_C",NULL);CHKERRQ(ierr);
1762   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
1763   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
1764   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
1765   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
1766   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
1767   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
1768   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
1769   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
1770   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
1771   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
1772   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
1773   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
1774   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
1775   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
1776   /* Free the private data structure */
1777   ierr = PetscFree(pc->data);CHKERRQ(ierr);
1778   PetscFunctionReturn(0);
1779 }
1780 /* -------------------------------------------------------------------------- */
1781 
1782 #undef __FUNCT__
1783 #define __FUNCT__ "PCBDDCMatFETIDPGetRHS_BDDC"
1784 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
1785 {
1786   FETIDPMat_ctx  mat_ctx;
1787   Vec            copy_standard_rhs;
1788   PC_IS*         pcis;
1789   PC_BDDC*       pcbddc;
1790   PetscErrorCode ierr;
1791 
1792   PetscFunctionBegin;
1793   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
1794   pcis = (PC_IS*)mat_ctx->pc->data;
1795   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
1796 
1797   /*
1798      change of basis for physical rhs if needed
1799      It also changes the rhs in case of dirichlet boundaries
1800      TODO: better management when FETIDP will have its own class
1801   */
1802   ierr = VecDuplicate(standard_rhs,&copy_standard_rhs);CHKERRQ(ierr);
1803   ierr = VecCopy(standard_rhs,copy_standard_rhs);CHKERRQ(ierr);
1804   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,copy_standard_rhs,NULL);CHKERRQ(ierr);
1805   /* store vectors for computation of fetidp final solution */
1806   ierr = VecScatterBegin(pcis->global_to_D,copy_standard_rhs,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1807   ierr = VecScatterEnd(pcis->global_to_D,copy_standard_rhs,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1808   /* scale rhs since it should be unassembled */
1809   /* TODO use counter scaling? (also below) */
1810   ierr = VecScatterBegin(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1811   ierr = VecScatterEnd(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1812   /* Apply partition of unity */
1813   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
1814   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,copy_standard_rhs,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
1815   if (!pcbddc->switch_static) {
1816     /* compute partially subassembled Schur complement right-hand side */
1817     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
1818     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
1819     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
1820     ierr = VecSet(copy_standard_rhs,0.0);CHKERRQ(ierr);
1821     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,copy_standard_rhs,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1822     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,copy_standard_rhs,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1823     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,copy_standard_rhs,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
1824     ierr = VecScatterBegin(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1825     ierr = VecScatterEnd(pcis->global_to_B,copy_standard_rhs,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1826     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
1827   }
1828   ierr = VecDestroy(&copy_standard_rhs);CHKERRQ(ierr);
1829   /* BDDC rhs */
1830   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
1831   if (pcbddc->switch_static) {
1832     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
1833   }
1834   /* apply BDDC */
1835   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
1836   /* Application of B_delta and assembling of rhs for fetidp fluxes */
1837   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
1838   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
1839   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1840   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1841   PetscFunctionReturn(0);
1842 }
1843 
1844 #undef __FUNCT__
1845 #define __FUNCT__ "PCBDDCMatFETIDPGetRHS"
1846 /*@
1847  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
1848 
1849    Collective
1850 
1851    Input Parameters:
1852 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
1853 -  standard_rhs    - the right-hand side of the original linear system
1854 
1855    Output Parameters:
1856 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
1857 
1858    Level: developer
1859 
1860    Notes:
1861 
1862 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
1863 @*/
1864 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
1865 {
1866   FETIDPMat_ctx  mat_ctx;
1867   PetscErrorCode ierr;
1868 
1869   PetscFunctionBegin;
1870   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
1871   ierr = PetscTryMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
1872   PetscFunctionReturn(0);
1873 }
1874 /* -------------------------------------------------------------------------- */
1875 
1876 #undef __FUNCT__
1877 #define __FUNCT__ "PCBDDCMatFETIDPGetSolution_BDDC"
1878 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
1879 {
1880   FETIDPMat_ctx  mat_ctx;
1881   PC_IS*         pcis;
1882   PC_BDDC*       pcbddc;
1883   PetscErrorCode ierr;
1884 
1885   PetscFunctionBegin;
1886   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
1887   pcis = (PC_IS*)mat_ctx->pc->data;
1888   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
1889 
1890   /* apply B_delta^T */
1891   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1892   ierr = VecScatterEnd  (mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1893   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
1894   /* compute rhs for BDDC application */
1895   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
1896   if (pcbddc->switch_static) {
1897     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
1898   }
1899   /* apply BDDC */
1900   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
1901   /* put values into standard global vector */
1902   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1903   ierr = VecScatterEnd  (pcis->global_to_B,pcis->vec1_B,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1904   if (!pcbddc->switch_static) {
1905     /* compute values into the interior if solved for the partially subassembled Schur complement */
1906     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
1907     ierr = VecAXPY(mat_ctx->temp_solution_D,-1.0,pcis->vec1_D);CHKERRQ(ierr);
1908     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
1909   }
1910   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1911   ierr = VecScatterEnd  (pcis->global_to_D,pcis->vec1_D,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1912   /* final change of basis if needed
1913      Is also sums the dirichlet part removed during RHS assembling */
1914   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
1915   PetscFunctionReturn(0);
1916 }
1917 
1918 #undef __FUNCT__
1919 #define __FUNCT__ "PCBDDCMatFETIDPGetSolution"
1920 /*@
1921  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
1922 
1923    Collective
1924 
1925    Input Parameters:
1926 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
1927 -  fetidp_flux_sol - the solution of the FETI-DP linear system
1928 
1929    Output Parameters:
1930 .  standard_sol    - the solution defined on the physical domain
1931 
1932    Level: developer
1933 
1934    Notes:
1935 
1936 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
1937 @*/
1938 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
1939 {
1940   FETIDPMat_ctx  mat_ctx;
1941   PetscErrorCode ierr;
1942 
1943   PetscFunctionBegin;
1944   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
1945   ierr = PetscTryMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
1946   PetscFunctionReturn(0);
1947 }
1948 /* -------------------------------------------------------------------------- */
1949 
1950 extern PetscErrorCode FETIDPMatMult(Mat,Vec,Vec);
1951 extern PetscErrorCode FETIDPMatMultTranspose(Mat,Vec,Vec);
1952 extern PetscErrorCode PCBDDCDestroyFETIDPMat(Mat);
1953 extern PetscErrorCode FETIDPPCApply(PC,Vec,Vec);
1954 extern PetscErrorCode FETIDPPCApplyTranspose(PC,Vec,Vec);
1955 extern PetscErrorCode PCBDDCDestroyFETIDPPC(PC);
1956 
1957 #undef __FUNCT__
1958 #define __FUNCT__ "PCBDDCCreateFETIDPOperators_BDDC"
1959 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, Mat *fetidp_mat, PC *fetidp_pc)
1960 {
1961 
1962   FETIDPMat_ctx  fetidpmat_ctx;
1963   Mat            newmat;
1964   FETIDPPC_ctx   fetidppc_ctx;
1965   PC             newpc;
1966   MPI_Comm       comm;
1967   PetscErrorCode ierr;
1968 
1969   PetscFunctionBegin;
1970   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
1971   /* FETIDP linear matrix */
1972   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
1973   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
1974   ierr = MatCreateShell(comm,PETSC_DECIDE,PETSC_DECIDE,fetidpmat_ctx->n_lambda,fetidpmat_ctx->n_lambda,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
1975   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
1976   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
1977   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
1978   ierr = MatSetUp(newmat);CHKERRQ(ierr);
1979   /* FETIDP preconditioner */
1980   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
1981   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
1982   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
1983   ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
1984   ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
1985   ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
1986   ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
1987   ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
1988   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
1989   ierr = PCSetUp(newpc);CHKERRQ(ierr);
1990   /* return pointers for objects created */
1991   *fetidp_mat=newmat;
1992   *fetidp_pc=newpc;
1993   PetscFunctionReturn(0);
1994 }
1995 
1996 #undef __FUNCT__
1997 #define __FUNCT__ "PCBDDCCreateFETIDPOperators"
1998 /*@
1999  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2000 
2001    Collective
2002 
2003    Input Parameters:
2004 .  pc - the BDDC preconditioning context (setup should have been called before)
2005 
2006    Output Parameters:
2007 +  fetidp_mat - shell FETI-DP matrix object
2008 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2009 
2010    Options Database Keys:
2011 .    -fetidp_fullyredundant <false> - use or not a fully redundant set of Lagrange multipliers
2012 
2013    Level: developer
2014 
2015    Notes:
2016      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2017 
2018 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2019 @*/
2020 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, Mat *fetidp_mat, PC *fetidp_pc)
2021 {
2022   PetscErrorCode ierr;
2023 
2024   PetscFunctionBegin;
2025   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2026   if (pc->setupcalled) {
2027     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,Mat*,PC*),(pc,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2028   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2029   PetscFunctionReturn(0);
2030 }
2031 /* -------------------------------------------------------------------------- */
2032 /*MC
2033    PCBDDC - Balancing Domain Decomposition by Constraints.
2034 
2035    An implementation of the BDDC preconditioner based on
2036 
2037 .vb
2038    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2039    [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
2040    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2041    [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
2042 .ve
2043 
2044    The matrix to be preconditioned (Pmat) must be of type MATIS.
2045 
2046    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2047 
2048    It also works with unsymmetric and indefinite problems.
2049 
2050    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.
2051 
2052    Approximate local solvers are automatically adapted for singular linear problems (see [1]) if the user has provided the nullspace using PCBDDCSetNullSpace()
2053 
2054    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()
2055    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesLocalIS()
2056 
2057    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2058 
2059    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.
2060    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2061 
2062    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2063 
2064    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.
2065 
2066    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.
2067    Deluxe scaling is not supported yet for FETI-DP.
2068 
2069    Options Database Keys (some of them, run with -h for a complete list):
2070 
2071 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2072 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2073 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2074 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2075 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2076 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2077 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2078 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2079 .    -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)
2080 .    -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)
2081 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2082 .    -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)
2083 .    -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)
2084 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2085 
2086    Options for Dirichlet, Neumann or coarse solver can be set with
2087 .vb
2088       -pc_bddc_dirichlet_
2089       -pc_bddc_neumann_
2090       -pc_bddc_coarse_
2091 .ve
2092    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2093 
2094    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2095 .vb
2096       -pc_bddc_dirichlet_lN_
2097       -pc_bddc_neumann_lN_
2098       -pc_bddc_coarse_lN_
2099 .ve
2100    Note that level number ranges from the finest (0) to the coarsest (N).
2101    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.
2102 .vb
2103      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2104 .ve
2105    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
2106 
2107    Level: intermediate
2108 
2109    Developer notes:
2110 
2111    Contributed by Stefano Zampini
2112 
2113 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2114 M*/
2115 
2116 #undef __FUNCT__
2117 #define __FUNCT__ "PCCreate_BDDC"
2118 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2119 {
2120   PetscErrorCode      ierr;
2121   PC_BDDC             *pcbddc;
2122 
2123   PetscFunctionBegin;
2124   /* Creates the private data structure for this preconditioner and attach it to the PC object. */
2125   ierr      = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2126   pc->data  = (void*)pcbddc;
2127 
2128   /* create PCIS data structure */
2129   ierr = PCISCreate(pc);CHKERRQ(ierr);
2130 
2131   /* BDDC customization */
2132   pcbddc->use_local_adj       = PETSC_TRUE;
2133   pcbddc->use_vertices        = PETSC_TRUE;
2134   pcbddc->use_edges           = PETSC_TRUE;
2135   pcbddc->use_faces           = PETSC_FALSE;
2136   pcbddc->use_change_of_basis = PETSC_FALSE;
2137   pcbddc->use_change_on_faces = PETSC_FALSE;
2138   pcbddc->switch_static       = PETSC_FALSE;
2139   pcbddc->use_nnsp_true       = PETSC_FALSE;
2140   pcbddc->use_qr_single       = PETSC_FALSE;
2141   pcbddc->symmetric_primal    = PETSC_TRUE;
2142   pcbddc->benign_saddle_point = PETSC_FALSE;
2143   pcbddc->dbg_flag            = 0;
2144   /* private */
2145   pcbddc->local_primal_size          = 0;
2146   pcbddc->local_primal_size_cc       = 0;
2147   pcbddc->local_primal_ref_node      = 0;
2148   pcbddc->local_primal_ref_mult      = 0;
2149   pcbddc->n_vertices                 = 0;
2150   pcbddc->primal_indices_local_idxs  = 0;
2151   pcbddc->recompute_topography       = PETSC_FALSE;
2152   pcbddc->coarse_size                = -1;
2153   pcbddc->new_primal_space           = PETSC_FALSE;
2154   pcbddc->new_primal_space_local     = PETSC_FALSE;
2155   pcbddc->global_primal_indices      = 0;
2156   pcbddc->onearnullspace             = 0;
2157   pcbddc->onearnullvecs_state        = 0;
2158   pcbddc->user_primal_vertices       = 0;
2159   pcbddc->NullSpace                  = 0;
2160   pcbddc->temp_solution              = 0;
2161   pcbddc->original_rhs               = 0;
2162   pcbddc->local_mat                  = 0;
2163   pcbddc->ChangeOfBasisMatrix        = 0;
2164   pcbddc->user_ChangeOfBasisMatrix   = 0;
2165   pcbddc->new_global_mat             = 0;
2166   pcbddc->coarse_vec                 = 0;
2167   pcbddc->coarse_ksp                 = 0;
2168   pcbddc->coarse_phi_B               = 0;
2169   pcbddc->coarse_phi_D               = 0;
2170   pcbddc->coarse_psi_B               = 0;
2171   pcbddc->coarse_psi_D               = 0;
2172   pcbddc->vec1_P                     = 0;
2173   pcbddc->vec1_R                     = 0;
2174   pcbddc->vec2_R                     = 0;
2175   pcbddc->local_auxmat1              = 0;
2176   pcbddc->local_auxmat2              = 0;
2177   pcbddc->R_to_B                     = 0;
2178   pcbddc->R_to_D                     = 0;
2179   pcbddc->ksp_D                      = 0;
2180   pcbddc->ksp_R                      = 0;
2181   pcbddc->NeumannBoundaries          = 0;
2182   pcbddc->NeumannBoundariesLocal     = 0;
2183   pcbddc->DirichletBoundaries        = 0;
2184   pcbddc->DirichletBoundariesLocal   = 0;
2185   pcbddc->user_provided_isfordofs    = PETSC_FALSE;
2186   pcbddc->n_ISForDofs                = 0;
2187   pcbddc->n_ISForDofsLocal           = 0;
2188   pcbddc->ISForDofs                  = 0;
2189   pcbddc->ISForDofsLocal             = 0;
2190   pcbddc->ConstraintMatrix           = 0;
2191   pcbddc->use_exact_dirichlet_trick  = PETSC_TRUE;
2192   pcbddc->coarse_loc_to_glob         = 0;
2193   pcbddc->coarsening_ratio           = 8;
2194   pcbddc->coarse_adj_red             = 0;
2195   pcbddc->current_level              = 0;
2196   pcbddc->max_levels                 = 0;
2197   pcbddc->use_coarse_estimates       = PETSC_FALSE;
2198   pcbddc->redistribute_coarse        = 0;
2199   pcbddc->coarse_subassembling       = 0;
2200   pcbddc->coarse_subassembling_init  = 0;
2201 
2202   /* benign subspace trick */
2203   pcbddc->B0_ncol                    = 0;
2204   pcbddc->B0_cols                    = NULL;
2205   pcbddc->B0_vals                    = NULL;
2206   pcbddc->benign_change              = 0;
2207   pcbddc->benign_vec                 = 0;
2208   pcbddc->benign_original_mat        = 0;
2209   pcbddc->benign_sf                  = 0;
2210   pcbddc->benign_p0_lidx             = -1;
2211   pcbddc->benign_p0_gidx             = -1;
2212 
2213   /* create local graph structure */
2214   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2215 
2216   /* scaling */
2217   pcbddc->work_scaling          = 0;
2218   pcbddc->use_deluxe_scaling    = PETSC_FALSE;
2219   pcbddc->faster_deluxe         = PETSC_FALSE;
2220 
2221   /* create sub schurs structure */
2222   ierr = PCBDDCSubSchursCreate(&pcbddc->sub_schurs);CHKERRQ(ierr);
2223   pcbddc->sub_schurs_rebuild     = PETSC_FALSE;
2224   pcbddc->sub_schurs_layers      = -1;
2225   pcbddc->sub_schurs_use_useradj = PETSC_FALSE;
2226 
2227   pcbddc->computed_rowadj = PETSC_FALSE;
2228 
2229   /* adaptivity */
2230   pcbddc->adaptive_threshold      = 0.0;
2231   pcbddc->adaptive_nmax           = 0;
2232   pcbddc->adaptive_nmin           = 0;
2233 
2234   /* function pointers */
2235   pc->ops->apply               = PCApply_BDDC;
2236   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2237   pc->ops->setup               = PCSetUp_BDDC;
2238   pc->ops->destroy             = PCDestroy_BDDC;
2239   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2240   pc->ops->view                = 0;
2241   pc->ops->applyrichardson     = 0;
2242   pc->ops->applysymmetricleft  = 0;
2243   pc->ops->applysymmetricright = 0;
2244   pc->ops->presolve            = PCPreSolve_BDDC;
2245   pc->ops->postsolve           = PCPostSolve_BDDC;
2246 
2247   /* composing function */
2248   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2249   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2250   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2251   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2252   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2253   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2254   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNullSpace_C",PCBDDCSetNullSpace_BDDC);CHKERRQ(ierr);
2255   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2256   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2257   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2258   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2259   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2260   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2261   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2262   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2263   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2264   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2265   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2266   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2267   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2268   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2269   PetscFunctionReturn(0);
2270 }
2271 
2272