xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision e4c66b91ec5ecaeb63ae1fb42799e6dff316a2f4)
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    MATIS related operations contained in BDDC code
18    - Provide general case for subassembling
19 
20 */
21 
22 #include <../src/ksp/pc/impls/bddc/bddc.h> /*I "petscpc.h" I*/  /* includes for fortran wrappers */
23 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
24 #include <petscblaslapack.h>
25 
26 static PetscBool PCBDDCPackageInitialized = PETSC_FALSE;
27 
28 static PetscBool  cited = PETSC_FALSE;
29 static const char citation[] =
30 "@article{ZampiniPCBDDC,\n"
31 "author = {Stefano Zampini},\n"
32 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
33 "journal = {SIAM Journal on Scientific Computing},\n"
34 "volume = {38},\n"
35 "number = {5},\n"
36 "pages = {S282-S306},\n"
37 "year = {2016},\n"
38 "doi = {10.1137/15M1025785},\n"
39 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
40 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
41 "}\n";
42 
43 PetscLogEvent PC_BDDC_Topology[PETSC_PCBDDC_MAXLEVELS];
44 PetscLogEvent PC_BDDC_LocalSolvers[PETSC_PCBDDC_MAXLEVELS];
45 PetscLogEvent PC_BDDC_LocalWork[PETSC_PCBDDC_MAXLEVELS];
46 PetscLogEvent PC_BDDC_CorrectionSetUp[PETSC_PCBDDC_MAXLEVELS];
47 PetscLogEvent PC_BDDC_CoarseSetUp[PETSC_PCBDDC_MAXLEVELS];
48 PetscLogEvent PC_BDDC_CoarseSolver[PETSC_PCBDDC_MAXLEVELS];
49 PetscLogEvent PC_BDDC_AdaptiveSetUp[PETSC_PCBDDC_MAXLEVELS];
50 PetscLogEvent PC_BDDC_Scaling[PETSC_PCBDDC_MAXLEVELS];
51 PetscLogEvent PC_BDDC_Schurs[PETSC_PCBDDC_MAXLEVELS];
52 
53 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
54 
55 PetscErrorCode PCSetFromOptions_BDDC(PetscOptionItems *PetscOptionsObject,PC pc)
56 {
57   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
58   PetscInt       nt,i;
59   PetscErrorCode ierr;
60 
61   PetscFunctionBegin;
62   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
63   /* Verbose debugging */
64   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
65   /* Approximate solvers */
66   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate","Inform PCBDDC that we are using approximate Dirichlet solvers","none",pcbddc->NullSpace_corr[0],&pcbddc->NullSpace_corr[0],NULL);CHKERRQ(ierr);
67   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate_scale","Inform PCBDDC that we need to scale the Dirichlet solve","none",pcbddc->NullSpace_corr[1],&pcbddc->NullSpace_corr[1],NULL);CHKERRQ(ierr);
68   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate","Inform PCBDDC that we are using approximate Neumann solvers","none",pcbddc->NullSpace_corr[2],&pcbddc->NullSpace_corr[2],NULL);CHKERRQ(ierr);
69   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate_scale","Inform PCBDDC that we need to scale the Neumann solve","none",pcbddc->NullSpace_corr[3],&pcbddc->NullSpace_corr[3],NULL);CHKERRQ(ierr);
70   /* Primal space customization */
71   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);
72   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
73   ierr = PetscOptionsBool("-pc_bddc_corner_selection","Activates face-based corner selection","none",pcbddc->corner_selection,&pcbddc->corner_selection,NULL);CHKERRQ(ierr);
74   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
75   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
76   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
77   ierr = PetscOptionsInt("-pc_bddc_vertex_size","Connected components smaller or equal to vertex size will be considered as primal vertices","none",pcbddc->vertex_size,&pcbddc->vertex_size,NULL);CHKERRQ(ierr);
78   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);
79   ierr = PetscOptionsBool("-pc_bddc_use_qr_single","Use QR factorization for single constraints on cc (QR is always used when multiple constraints are present)","none",pcbddc->use_qr_single,&pcbddc->use_qr_single,NULL);CHKERRQ(ierr);
80   /* Change of basis */
81   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);
82   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);
83   if (!pcbddc->use_change_of_basis) {
84     pcbddc->use_change_on_faces = PETSC_FALSE;
85   }
86   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
87   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);
88   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_per_proc","Target number of equations per process for coarse problem redistribution (significant only at the coarsest level)","none",pcbddc->coarse_eqs_per_proc,&pcbddc->coarse_eqs_per_proc,NULL);CHKERRQ(ierr);
89   i    = pcbddc->coarsening_ratio;
90   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","PCBDDCSetCoarseningRatio",i,&i,NULL);CHKERRQ(ierr);
91   ierr = PCBDDCSetCoarseningRatio(pc,i);CHKERRQ(ierr);
92   i    = pcbddc->max_levels;
93   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","PCBDDCSetLevels",i,&i,NULL);CHKERRQ(ierr);
94   ierr = PCBDDCSetLevels(pc,i);CHKERRQ(ierr);
95   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_limit","Set maximum number of equations on coarsest grid to aim for","none",pcbddc->coarse_eqs_limit,&pcbddc->coarse_eqs_limit,NULL);CHKERRQ(ierr);
96   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);
97   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
98   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);
99   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);
100   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);
101   ierr = PetscOptionsBool("-pc_bddc_schur_exact","Whether or not to use the exact Schur complement instead of the reduced one (which excludes size 1 cc)","none",pcbddc->sub_schurs_exact_schur,&pcbddc->sub_schurs_exact_schur,NULL);CHKERRQ(ierr);
102   ierr = PetscOptionsBool("-pc_bddc_deluxe_zerorows","Zero rows and columns of deluxe operators associated with primal dofs","none",pcbddc->deluxe_zerorows,&pcbddc->deluxe_zerorows,NULL);CHKERRQ(ierr);
103   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
104   ierr = PetscOptionsBool("-pc_bddc_adaptive_userdefined","Use user-defined constraints (should be attached via MatSetNearNullSpace to pmat) in addition to those adaptively generated","none",pcbddc->adaptive_userdefined,&pcbddc->adaptive_userdefined,NULL);CHKERRQ(ierr);
105   nt   = 2;
106   ierr = PetscOptionsRealArray("-pc_bddc_adaptive_threshold","Thresholds to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&nt,NULL);CHKERRQ(ierr);
107   if (nt == 1) pcbddc->adaptive_threshold[1] = pcbddc->adaptive_threshold[0];
108   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
109   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
110   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
111   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);
112   ierr = PetscOptionsBool("-pc_bddc_benign_trick","Apply the benign subspace trick to saddle point problems with discontinuous pressures","none",pcbddc->benign_saddle_point,&pcbddc->benign_saddle_point,NULL);CHKERRQ(ierr);
113   ierr = PetscOptionsBool("-pc_bddc_benign_change","Compute the pressure change of basis explicitly","none",pcbddc->benign_change_explicit,&pcbddc->benign_change_explicit,NULL);CHKERRQ(ierr);
114   ierr = PetscOptionsBool("-pc_bddc_benign_compute_correction","Compute the benign correction during PreSolve","none",pcbddc->benign_compute_correction,&pcbddc->benign_compute_correction,NULL);CHKERRQ(ierr);
115   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
116   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
117   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected_filter","Filters out small entries in the local matrix when detecting disconnected subdomains","none",pcbddc->detect_disconnected_filter,&pcbddc->detect_disconnected_filter,NULL);CHKERRQ(ierr);
118   ierr = PetscOptionsBool("-pc_bddc_eliminate_dirichlet","Whether or not we want to eliminate dirichlet dofs during presolve","none",pcbddc->eliminate_dirdofs,&pcbddc->eliminate_dirdofs,NULL);CHKERRQ(ierr);
119   ierr = PetscOptionsTail();CHKERRQ(ierr);
120   PetscFunctionReturn(0);
121 }
122 
123 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
124 {
125   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
126   PC_IS                *pcis = (PC_IS*)pc->data;
127   PetscErrorCode       ierr;
128   PetscBool            isascii;
129   PetscSubcomm         subcomm;
130   PetscViewer          subviewer;
131 
132   PetscFunctionBegin;
133   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
134   /* ASCII viewer */
135   if (isascii) {
136     PetscMPIInt   color,rank,size;
137     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
138     PetscScalar   interface_size;
139     PetscReal     ratio1=0.,ratio2=0.;
140     Vec           counter;
141 
142     if (!pc->setupcalled) {
143       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
144     }
145     ierr = PetscViewerASCIIPrintf(viewer,"  Use verbose output: %D\n",pcbddc->dbg_flag);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  Use user-defined CSR: %d\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  Use local mat graph: %d\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
148     if (pcbddc->mat_graph->twodim) {
149       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
150     } else {
151       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
152     }
153     if (pcbddc->graphmaxcount != PETSC_MAX_INT) {
154       ierr = PetscViewerASCIIPrintf(viewer,"  Graph max count: %D\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
155     }
156     ierr = PetscViewerASCIIPrintf(viewer,"  Use vertices: %d (vertex size %D)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
160     ierr = PetscViewerASCIIPrintf(viewer,"  Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
161     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
162     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
163     ierr = PetscViewerASCIIPrintf(viewer,"  User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
164     ierr = PetscViewerASCIIPrintf(viewer,"  Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
165     ierr = PetscViewerASCIIPrintf(viewer,"  Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
167     ierr = PetscViewerASCIIPrintf(viewer,"  Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
168     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel max levels: %D\n",pcbddc->max_levels);CHKERRQ(ierr);
169     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel coarsening ratio: %D\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
170     ierr = PetscViewerASCIIPrintf(viewer,"  Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
171     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
172     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
173     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
174     ierr = PetscViewerASCIIPrintf(viewer,"  Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
175     ierr = PetscViewerASCIIPrintf(viewer,"  Number of dofs' layers for the computation of principal minors: %D\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
176     ierr = PetscViewerASCIIPrintf(viewer,"  Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
177     if (pcbddc->adaptive_threshold[1] != pcbddc->adaptive_threshold[0]) {
178       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection thresholds (active %d, userdefined %d): %g,%g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0],pcbddc->adaptive_threshold[1]);CHKERRQ(ierr);
179     } else {
180       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection threshold (active %d, userdefined %d): %g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0]);CHKERRQ(ierr);
181     }
182     ierr = PetscViewerASCIIPrintf(viewer,"  Min constraints / connected component: %D\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
183     ierr = PetscViewerASCIIPrintf(viewer,"  Max constraints / connected component: %D\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
184     ierr = PetscViewerASCIIPrintf(viewer,"  Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
185     ierr = PetscViewerASCIIPrintf(viewer,"  Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
186     ierr = PetscViewerASCIIPrintf(viewer,"  Num. Procs. to map coarse adjacency list: %D\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
187     ierr = PetscViewerASCIIPrintf(viewer,"  Coarse eqs per proc (significant at the coarsest level): %D\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
188     ierr = PetscViewerASCIIPrintf(viewer,"  Detect disconnected: %d (filter %d)\n",pcbddc->detect_disconnected,pcbddc->detect_disconnected_filter);CHKERRQ(ierr);
189     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
190     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
191     ierr = PetscViewerASCIIPrintf(viewer,"  Algebraic computation of no-net-flux: %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
192     if (!pc->setupcalled) PetscFunctionReturn(0);
193 
194     /* compute interface size */
195     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
196     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
197     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
198     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
199     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
200     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
201     ierr = VecDestroy(&counter);CHKERRQ(ierr);
202 
203     /* compute some statistics on the domain decomposition */
204     gsum[0] = 1;
205     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
206     loc[0]  = !!pcis->n;
207     loc[1]  = pcis->n - pcis->n_B;
208     loc[2]  = pcis->n_B;
209     loc[3]  = pcbddc->local_primal_size;
210     loc[4]  = pcis->n;
211     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
212     loc[6]  = pcbddc->benign_n;
213     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
214     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
215     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
216     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
217     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
218     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
219     if (pcbddc->coarse_size) {
220       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
221       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
222     }
223     ierr = PetscViewerASCIIPrintf(viewer,"********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
224     ierr = PetscViewerASCIIPrintf(viewer,"  Global dofs sizes: all %D interface %D coarse %D\n",pc->pmat->rmap->N,(PetscInt)PetscRealPart(interface_size),pcbddc->coarse_size);CHKERRQ(ierr);
225     ierr = PetscViewerASCIIPrintf(viewer,"  Coarsening ratios: all/coarse %D interface/coarse %D\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
226     ierr = PetscViewerASCIIPrintf(viewer,"  Active processes : %D\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
227     ierr = PetscViewerASCIIPrintf(viewer,"  Total subdomains : %D\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
228     if (pcbddc->benign_have_null) {
229       ierr = PetscViewerASCIIPrintf(viewer,"  Benign subs      : %D\n",(PetscInt)totbenign);CHKERRQ(ierr);
230     }
231     ierr = PetscViewerASCIIPrintf(viewer,"  Dofs type        :\tMIN\tMAX\tMEAN\n");CHKERRQ(ierr);
232     ierr = PetscViewerASCIIPrintf(viewer,"  Interior  dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
233     ierr = PetscViewerASCIIPrintf(viewer,"  Interface dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[2],(PetscInt)gmax[2],(PetscInt)(gsum[2]/gsum[0]));CHKERRQ(ierr);
234     ierr = PetscViewerASCIIPrintf(viewer,"  Primal    dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[3],(PetscInt)gmax[3],(PetscInt)(gsum[3]/gsum[0]));CHKERRQ(ierr);
235     ierr = PetscViewerASCIIPrintf(viewer,"  Local     dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[4],(PetscInt)gmax[4],(PetscInt)(gsum[4]/gsum[0]));CHKERRQ(ierr);
236     ierr = PetscViewerASCIIPrintf(viewer,"  Local     subs   :\t%D\t%D\n"    ,(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
237     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
238 
239     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
240 
241     /* local solvers */
242     ierr = PetscViewerGetSubViewer(viewer,PetscObjectComm((PetscObject)pcbddc->ksp_D),&subviewer);CHKERRQ(ierr);
243     if (!rank) {
244       ierr = PetscViewerASCIIPrintf(subviewer,"--- Interior solver (rank 0)\n");CHKERRQ(ierr);
245       ierr = PetscViewerASCIIPushTab(subviewer);CHKERRQ(ierr);
246       ierr = KSPView(pcbddc->ksp_D,subviewer);CHKERRQ(ierr);
247       ierr = PetscViewerASCIIPopTab(subviewer);CHKERRQ(ierr);
248       ierr = PetscViewerASCIIPrintf(subviewer,"--- Correction solver (rank 0)\n");CHKERRQ(ierr);
249       ierr = PetscViewerASCIIPushTab(subviewer);CHKERRQ(ierr);
250       ierr = KSPView(pcbddc->ksp_R,subviewer);CHKERRQ(ierr);
251       ierr = PetscViewerASCIIPopTab(subviewer);CHKERRQ(ierr);
252       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
253     }
254     ierr = PetscViewerRestoreSubViewer(viewer,PetscObjectComm((PetscObject)pcbddc->ksp_D),&subviewer);CHKERRQ(ierr);
255     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
256 
257     /* the coarse problem can be handled by a different communicator */
258     if (pcbddc->coarse_ksp) color = 1;
259     else color = 0;
260     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
261     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
262     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
263     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
264     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
265     if (color == 1) {
266       ierr = PetscViewerASCIIPrintf(subviewer,"--- Coarse solver\n");CHKERRQ(ierr);
267       ierr = PetscViewerASCIIPushTab(subviewer);CHKERRQ(ierr);
268       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
269       ierr = PetscViewerASCIIPopTab(subviewer);CHKERRQ(ierr);
270       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
271     }
272     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
273     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
274     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
275   }
276   PetscFunctionReturn(0);
277 }
278 
279 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
280 {
281   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
282   PetscErrorCode ierr;
283 
284   PetscFunctionBegin;
285   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
286   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
287   pcbddc->discretegradient = G;
288   pcbddc->nedorder         = order > 0 ? order : -order;
289   pcbddc->nedfield         = field;
290   pcbddc->nedglobal        = global;
291   pcbddc->conforming       = conforming;
292   PetscFunctionReturn(0);
293 }
294 
295 /*@
296  PCBDDCSetDiscreteGradient - Sets the discrete gradient
297 
298    Collective on PC
299 
300    Input Parameters:
301 +  pc         - the preconditioning context
302 .  G          - the discrete gradient matrix (should be in AIJ format)
303 .  order      - the order of the Nedelec space (1 for the lowest order)
304 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
305 .  global     - the type of global ordering for the rows of G
306 -  conforming - whether the mesh is conforming or not
307 
308    Level: advanced
309 
310    Notes:
311     The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
312           For variable order spaces, the order should be set to zero.
313           If global is true, the rows of G should be given in global ordering for the whole dofs;
314           if false, the ordering should be global for the Nedelec field.
315           In the latter case, it should hold gid[i] < gid[j] iff geid[i] < geid[j], with gid the global orderding for all the dofs
316           and geid the one for the Nedelec field.
317 
318 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
319 @*/
320 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
321 {
322   PetscErrorCode ierr;
323 
324   PetscFunctionBegin;
325   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
326   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
327   PetscValidLogicalCollectiveInt(pc,order,3);
328   PetscValidLogicalCollectiveInt(pc,field,4);
329   PetscValidLogicalCollectiveBool(pc,global,5);
330   PetscValidLogicalCollectiveBool(pc,conforming,6);
331   PetscCheckSameComm(pc,1,G,2);
332   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
333   PetscFunctionReturn(0);
334 }
335 
336 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
337 {
338   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
339   PetscErrorCode ierr;
340 
341   PetscFunctionBegin;
342   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
343   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
344   pcbddc->divudotp = divudotp;
345   pcbddc->divudotp_trans = trans;
346   pcbddc->compute_nonetflux = PETSC_TRUE;
347   if (vl2l) {
348     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
349     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
350     pcbddc->divudotp_vl2l = vl2l;
351   }
352   PetscFunctionReturn(0);
353 }
354 
355 /*@
356  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
357 
358    Collective on PC
359 
360    Input Parameters:
361 +  pc - the preconditioning context
362 .  divudotp - the matrix (must be of type MATIS)
363 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
364 -  vl2l - optional index set describing the local (wrt the local matrix in divudotp) to local (wrt the local matrix in the preconditioning matrix) map for the velocities
365 
366    Level: advanced
367 
368    Notes:
369     This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
370           If vl2l is NULL, the local ordering for velocities in divudotp should match that of the preconditioning matrix
371 
372 .seealso: PCBDDC
373 @*/
374 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
375 {
376   PetscBool      ismatis;
377   PetscErrorCode ierr;
378 
379   PetscFunctionBegin;
380   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
381   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
382   PetscCheckSameComm(pc,1,divudotp,2);
383   PetscValidLogicalCollectiveBool(pc,trans,3);
384   if (vl2l) PetscValidHeaderSpecific(vl2l,IS_CLASSID,4);
385   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
386   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
387   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
388   PetscFunctionReturn(0);
389 }
390 
391 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
392 {
393   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
394   PetscErrorCode ierr;
395 
396   PetscFunctionBegin;
397   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
398   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
399   pcbddc->user_ChangeOfBasisMatrix = change;
400   pcbddc->change_interior = interior;
401   PetscFunctionReturn(0);
402 }
403 /*@
404  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
405 
406    Collective on PC
407 
408    Input Parameters:
409 +  pc - the preconditioning context
410 .  change - the change of basis matrix
411 -  interior - whether or not the change of basis modifies interior dofs
412 
413    Level: intermediate
414 
415    Notes:
416 
417 .seealso: PCBDDC
418 @*/
419 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
420 {
421   PetscErrorCode ierr;
422 
423   PetscFunctionBegin;
424   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
425   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
426   PetscCheckSameComm(pc,1,change,2);
427   if (pc->mat) {
428     PetscInt rows_c,cols_c,rows,cols;
429     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
430     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
431     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of rows for change of basis matrix! %D != %D",rows_c,rows);
432     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of columns for change of basis matrix! %D != %D",cols_c,cols);
433     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
434     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
435     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local rows for change of basis matrix! %D != %D",rows_c,rows);
436     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local columns for change of basis matrix! %D != %D",cols_c,cols);
437   }
438   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
439   PetscFunctionReturn(0);
440 }
441 
442 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
443 {
444   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
445   PetscBool      isequal = PETSC_FALSE;
446   PetscErrorCode ierr;
447 
448   PetscFunctionBegin;
449   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
450   if (pcbddc->user_primal_vertices) {
451     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
452   }
453   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
454   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
455   pcbddc->user_primal_vertices = PrimalVertices;
456   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
457   PetscFunctionReturn(0);
458 }
459 
460 /*@
461  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
462 
463    Collective
464 
465    Input Parameters:
466 +  pc - the preconditioning context
467 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
468 
469    Level: intermediate
470 
471    Notes:
472      Any process can list any global node
473 
474 .seealso: PCBDDC, PCBDDCGetPrimalVerticesIS(), PCBDDCSetPrimalVerticesLocalIS(), PCBDDCGetPrimalVerticesLocalIS()
475 @*/
476 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
477 {
478   PetscErrorCode ierr;
479 
480   PetscFunctionBegin;
481   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
482   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
483   PetscCheckSameComm(pc,1,PrimalVertices,2);
484   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
485   PetscFunctionReturn(0);
486 }
487 
488 static PetscErrorCode PCBDDCGetPrimalVerticesIS_BDDC(PC pc, IS *is)
489 {
490   PC_BDDC *pcbddc = (PC_BDDC*)pc->data;
491 
492   PetscFunctionBegin;
493   *is = pcbddc->user_primal_vertices;
494   PetscFunctionReturn(0);
495 }
496 
497 /*@
498  PCBDDCGetPrimalVerticesIS - Get user defined primal vertices set with PCBDDCSetPrimalVerticesIS()
499 
500    Collective
501 
502    Input Parameters:
503 .  pc - the preconditioning context
504 
505    Output Parameters:
506 .  is - index set of primal vertices in global numbering (NULL if not set)
507 
508    Level: intermediate
509 
510    Notes:
511 
512 .seealso: PCBDDC, PCBDDCSetPrimalVerticesIS(), PCBDDCSetPrimalVerticesLocalIS(), PCBDDCGetPrimalVerticesLocalIS()
513 @*/
514 PetscErrorCode PCBDDCGetPrimalVerticesIS(PC pc, IS *is)
515 {
516   PetscErrorCode ierr;
517 
518   PetscFunctionBegin;
519   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
520   PetscValidPointer(is,2);
521   ierr = PetscUseMethod(pc,"PCBDDCGetPrimalVerticesIS_C",(PC,IS*),(pc,is));CHKERRQ(ierr);
522   PetscFunctionReturn(0);
523 }
524 
525 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
526 {
527   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
528   PetscBool      isequal = PETSC_FALSE;
529   PetscErrorCode ierr;
530 
531   PetscFunctionBegin;
532   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
533   if (pcbddc->user_primal_vertices_local) {
534     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
535   }
536   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
537   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
538   pcbddc->user_primal_vertices_local = PrimalVertices;
539   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
540   PetscFunctionReturn(0);
541 }
542 
543 /*@
544  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
545 
546    Collective
547 
548    Input Parameters:
549 +  pc - the preconditioning context
550 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
551 
552    Level: intermediate
553 
554    Notes:
555 
556 .seealso: PCBDDC, PCBDDCSetPrimalVerticesIS(), PCBDDCGetPrimalVerticesIS(), PCBDDCGetPrimalVerticesLocalIS()
557 @*/
558 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
559 {
560   PetscErrorCode ierr;
561 
562   PetscFunctionBegin;
563   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
564   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
565   PetscCheckSameComm(pc,1,PrimalVertices,2);
566   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
567   PetscFunctionReturn(0);
568 }
569 
570 static PetscErrorCode PCBDDCGetPrimalVerticesLocalIS_BDDC(PC pc, IS *is)
571 {
572   PC_BDDC *pcbddc = (PC_BDDC*)pc->data;
573 
574   PetscFunctionBegin;
575   *is = pcbddc->user_primal_vertices_local;
576   PetscFunctionReturn(0);
577 }
578 
579 /*@
580  PCBDDCGetPrimalVerticesLocalIS - Get user defined primal vertices set with PCBDDCSetPrimalVerticesLocalIS()
581 
582    Collective
583 
584    Input Parameters:
585 .  pc - the preconditioning context
586 
587    Output Parameters:
588 .  is - index set of primal vertices in local numbering (NULL if not set)
589 
590    Level: intermediate
591 
592    Notes:
593 
594 .seealso: PCBDDC, PCBDDCSetPrimalVerticesIS(), PCBDDCGetPrimalVerticesIS(), PCBDDCSetPrimalVerticesLocalIS()
595 @*/
596 PetscErrorCode PCBDDCGetPrimalVerticesLocalIS(PC pc, IS *is)
597 {
598   PetscErrorCode ierr;
599 
600   PetscFunctionBegin;
601   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
602   PetscValidPointer(is,2);
603   ierr = PetscUseMethod(pc,"PCBDDCGetPrimalVerticesLocalIS_C",(PC,IS*),(pc,is));CHKERRQ(ierr);
604   PetscFunctionReturn(0);
605 }
606 
607 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
608 {
609   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
610 
611   PetscFunctionBegin;
612   pcbddc->coarsening_ratio = k;
613   PetscFunctionReturn(0);
614 }
615 
616 /*@
617  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
618 
619    Logically collective on PC
620 
621    Input Parameters:
622 +  pc - the preconditioning context
623 -  k - coarsening ratio (H/h at the coarser level)
624 
625    Options Database Keys:
626 .    -pc_bddc_coarsening_ratio
627 
628    Level: intermediate
629 
630    Notes:
631      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
632 
633 .seealso: PCBDDC, PCBDDCSetLevels()
634 @*/
635 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
636 {
637   PetscErrorCode ierr;
638 
639   PetscFunctionBegin;
640   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
641   PetscValidLogicalCollectiveInt(pc,k,2);
642   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
643   PetscFunctionReturn(0);
644 }
645 
646 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
647 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
648 {
649   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
650 
651   PetscFunctionBegin;
652   pcbddc->use_exact_dirichlet_trick = flg;
653   PetscFunctionReturn(0);
654 }
655 
656 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
657 {
658   PetscErrorCode ierr;
659 
660   PetscFunctionBegin;
661   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
662   PetscValidLogicalCollectiveBool(pc,flg,2);
663   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
664   PetscFunctionReturn(0);
665 }
666 
667 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
668 {
669   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
670 
671   PetscFunctionBegin;
672   pcbddc->current_level = level;
673   PetscFunctionReturn(0);
674 }
675 
676 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
677 {
678   PetscErrorCode ierr;
679 
680   PetscFunctionBegin;
681   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
682   PetscValidLogicalCollectiveInt(pc,level,2);
683   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
684   PetscFunctionReturn(0);
685 }
686 
687 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
688 {
689   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
690 
691   PetscFunctionBegin;
692   if (levels > PETSC_PCBDDC_MAXLEVELS-1) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of additional levels for BDDC is %d",PETSC_PCBDDC_MAXLEVELS-1);
693   pcbddc->max_levels = levels;
694   PetscFunctionReturn(0);
695 }
696 
697 /*@
698  PCBDDCSetLevels - Sets the maximum number of additional levels allowed for multilevel BDDC
699 
700    Logically collective on PC
701 
702    Input Parameters:
703 +  pc - the preconditioning context
704 -  levels - the maximum number of levels
705 
706    Options Database Keys:
707 .    -pc_bddc_levels
708 
709    Level: intermediate
710 
711    Notes:
712      The default value is 0, that gives the classical two-levels BDDC
713 
714 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
715 @*/
716 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
717 {
718   PetscErrorCode ierr;
719 
720   PetscFunctionBegin;
721   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
722   PetscValidLogicalCollectiveInt(pc,levels,2);
723   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
724   PetscFunctionReturn(0);
725 }
726 
727 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
728 {
729   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
730   PetscBool      isequal = PETSC_FALSE;
731   PetscErrorCode ierr;
732 
733   PetscFunctionBegin;
734   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
735   if (pcbddc->DirichletBoundaries) {
736     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
737   }
738   /* last user setting takes precendence -> destroy any other customization */
739   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
740   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
741   pcbddc->DirichletBoundaries = DirichletBoundaries;
742   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
743   PetscFunctionReturn(0);
744 }
745 
746 /*@
747  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
748 
749    Collective
750 
751    Input Parameters:
752 +  pc - the preconditioning context
753 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
754 
755    Level: intermediate
756 
757    Notes:
758      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
759 
760 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
761 @*/
762 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
763 {
764   PetscErrorCode ierr;
765 
766   PetscFunctionBegin;
767   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
768   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
769   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
770   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
771   PetscFunctionReturn(0);
772 }
773 
774 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
775 {
776   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
777   PetscBool      isequal = PETSC_FALSE;
778   PetscErrorCode ierr;
779 
780   PetscFunctionBegin;
781   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
782   if (pcbddc->DirichletBoundariesLocal) {
783     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
784   }
785   /* last user setting takes precendence -> destroy any other customization */
786   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
787   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
788   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
789   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
790   PetscFunctionReturn(0);
791 }
792 
793 /*@
794  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
795 
796    Collective
797 
798    Input Parameters:
799 +  pc - the preconditioning context
800 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
801 
802    Level: intermediate
803 
804    Notes:
805 
806 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
807 @*/
808 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
809 {
810   PetscErrorCode ierr;
811 
812   PetscFunctionBegin;
813   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
814   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
815   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
816   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
817   PetscFunctionReturn(0);
818 }
819 
820 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
821 {
822   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
823   PetscBool      isequal = PETSC_FALSE;
824   PetscErrorCode ierr;
825 
826   PetscFunctionBegin;
827   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
828   if (pcbddc->NeumannBoundaries) {
829     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
830   }
831   /* last user setting takes precendence -> destroy any other customization */
832   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
833   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
834   pcbddc->NeumannBoundaries = NeumannBoundaries;
835   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
836   PetscFunctionReturn(0);
837 }
838 
839 /*@
840  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
841 
842    Collective
843 
844    Input Parameters:
845 +  pc - the preconditioning context
846 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
847 
848    Level: intermediate
849 
850    Notes:
851      Any process can list any global node
852 
853 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
854 @*/
855 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
856 {
857   PetscErrorCode ierr;
858 
859   PetscFunctionBegin;
860   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
861   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
862   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
863   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
864   PetscFunctionReturn(0);
865 }
866 
867 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
868 {
869   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
870   PetscBool      isequal = PETSC_FALSE;
871   PetscErrorCode ierr;
872 
873   PetscFunctionBegin;
874   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
875   if (pcbddc->NeumannBoundariesLocal) {
876     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
877   }
878   /* last user setting takes precendence -> destroy any other customization */
879   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
880   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
881   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
882   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
883   PetscFunctionReturn(0);
884 }
885 
886 /*@
887  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
888 
889    Collective
890 
891    Input Parameters:
892 +  pc - the preconditioning context
893 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
894 
895    Level: intermediate
896 
897    Notes:
898 
899 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
900 @*/
901 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
902 {
903   PetscErrorCode ierr;
904 
905   PetscFunctionBegin;
906   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
907   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
908   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
909   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
910   PetscFunctionReturn(0);
911 }
912 
913 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
914 {
915   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
916 
917   PetscFunctionBegin;
918   *DirichletBoundaries = pcbddc->DirichletBoundaries;
919   PetscFunctionReturn(0);
920 }
921 
922 /*@
923  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
924 
925    Collective
926 
927    Input Parameters:
928 .  pc - the preconditioning context
929 
930    Output Parameters:
931 .  DirichletBoundaries - index set defining the Dirichlet boundaries
932 
933    Level: intermediate
934 
935    Notes:
936      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
937 
938 .seealso: PCBDDC
939 @*/
940 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
941 {
942   PetscErrorCode ierr;
943 
944   PetscFunctionBegin;
945   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
946   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
947   PetscFunctionReturn(0);
948 }
949 
950 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
951 {
952   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
953 
954   PetscFunctionBegin;
955   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
956   PetscFunctionReturn(0);
957 }
958 
959 /*@
960  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
961 
962    Collective
963 
964    Input Parameters:
965 .  pc - the preconditioning context
966 
967    Output Parameters:
968 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
969 
970    Level: intermediate
971 
972    Notes:
973      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).
974           In the latter case, the IS will be available after PCSetUp.
975 
976 .seealso: PCBDDC
977 @*/
978 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
979 {
980   PetscErrorCode ierr;
981 
982   PetscFunctionBegin;
983   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
984   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
985   PetscFunctionReturn(0);
986 }
987 
988 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
989 {
990   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
991 
992   PetscFunctionBegin;
993   *NeumannBoundaries = pcbddc->NeumannBoundaries;
994   PetscFunctionReturn(0);
995 }
996 
997 /*@
998  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
999 
1000    Collective
1001 
1002    Input Parameters:
1003 .  pc - the preconditioning context
1004 
1005    Output Parameters:
1006 .  NeumannBoundaries - index set defining the Neumann boundaries
1007 
1008    Level: intermediate
1009 
1010    Notes:
1011      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
1012 
1013 .seealso: PCBDDC
1014 @*/
1015 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
1016 {
1017   PetscErrorCode ierr;
1018 
1019   PetscFunctionBegin;
1020   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1021   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
1022   PetscFunctionReturn(0);
1023 }
1024 
1025 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
1026 {
1027   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
1028 
1029   PetscFunctionBegin;
1030   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
1031   PetscFunctionReturn(0);
1032 }
1033 
1034 /*@
1035  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
1036 
1037    Collective
1038 
1039    Input Parameters:
1040 .  pc - the preconditioning context
1041 
1042    Output Parameters:
1043 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
1044 
1045    Level: intermediate
1046 
1047    Notes:
1048      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).
1049           In the latter case, the IS will be available after PCSetUp.
1050 
1051 .seealso: PCBDDC
1052 @*/
1053 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
1054 {
1055   PetscErrorCode ierr;
1056 
1057   PetscFunctionBegin;
1058   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1059   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
1060   PetscFunctionReturn(0);
1061 }
1062 
1063 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1064 {
1065   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1066   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
1067   PetscBool      same_data = PETSC_FALSE;
1068   PetscErrorCode ierr;
1069 
1070   PetscFunctionBegin;
1071   if (!nvtxs) {
1072     if (copymode == PETSC_OWN_POINTER) {
1073       ierr = PetscFree(xadj);CHKERRQ(ierr);
1074       ierr = PetscFree(adjncy);CHKERRQ(ierr);
1075     }
1076     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
1077     PetscFunctionReturn(0);
1078   }
1079   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
1080     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
1081     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
1082       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
1083       if (same_data) {
1084         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
1085       }
1086     }
1087   }
1088   if (!same_data) {
1089     /* free old CSR */
1090     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
1091     /* get CSR into graph structure */
1092     if (copymode == PETSC_COPY_VALUES) {
1093       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
1094       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
1095       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
1096       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
1097       mat_graph->freecsr = PETSC_TRUE;
1098     } else if (copymode == PETSC_OWN_POINTER) {
1099       mat_graph->xadj    = (PetscInt*)xadj;
1100       mat_graph->adjncy  = (PetscInt*)adjncy;
1101       mat_graph->freecsr = PETSC_TRUE;
1102     } else if (copymode == PETSC_USE_POINTER) {
1103       mat_graph->xadj    = (PetscInt*)xadj;
1104       mat_graph->adjncy  = (PetscInt*)adjncy;
1105       mat_graph->freecsr = PETSC_FALSE;
1106     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %D",copymode);
1107     mat_graph->nvtxs_csr = nvtxs;
1108     pcbddc->recompute_topography = PETSC_TRUE;
1109   }
1110   PetscFunctionReturn(0);
1111 }
1112 
1113 /*@
1114  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
1115 
1116    Not collective
1117 
1118    Input Parameters:
1119 +  pc - the preconditioning context.
1120 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
1121 .  xadj, adjncy - the connectivity of the dofs in CSR format.
1122 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1123 
1124    Level: intermediate
1125 
1126    Notes:
1127     A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1128 
1129 .seealso: PCBDDC,PetscCopyMode
1130 @*/
1131 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1132 {
1133   void (*f)(void) = 0;
1134   PetscErrorCode ierr;
1135 
1136   PetscFunctionBegin;
1137   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1138   if (nvtxs) {
1139     PetscValidIntPointer(xadj,3);
1140     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1141   }
1142   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1143   /* free arrays if PCBDDC is not the PC type */
1144   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1145   if (!f && copymode == PETSC_OWN_POINTER) {
1146     ierr = PetscFree(xadj);CHKERRQ(ierr);
1147     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1148   }
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1153 {
1154   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1155   PetscInt       i;
1156   PetscBool      isequal = PETSC_FALSE;
1157   PetscErrorCode ierr;
1158 
1159   PetscFunctionBegin;
1160   if (pcbddc->n_ISForDofsLocal == n_is) {
1161     for (i=0;i<n_is;i++) {
1162       PetscBool isequalt;
1163       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1164       if (!isequalt) break;
1165     }
1166     if (i == n_is) isequal = PETSC_TRUE;
1167   }
1168   for (i=0;i<n_is;i++) {
1169     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1170   }
1171   /* Destroy ISes if they were already set */
1172   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1173     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1174   }
1175   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1176   /* last user setting takes precendence -> destroy any other customization */
1177   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1178     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1179   }
1180   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1181   pcbddc->n_ISForDofs = 0;
1182   /* allocate space then set */
1183   if (n_is) {
1184     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1185   }
1186   for (i=0;i<n_is;i++) {
1187     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1188   }
1189   pcbddc->n_ISForDofsLocal = n_is;
1190   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1191   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1192   PetscFunctionReturn(0);
1193 }
1194 
1195 /*@
1196  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1197 
1198    Collective
1199 
1200    Input Parameters:
1201 +  pc - the preconditioning context
1202 .  n_is - number of index sets defining the fields
1203 -  ISForDofs - array of IS describing the fields in local ordering
1204 
1205    Level: intermediate
1206 
1207    Notes:
1208      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1209 
1210 .seealso: PCBDDC
1211 @*/
1212 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1213 {
1214   PetscInt       i;
1215   PetscErrorCode ierr;
1216 
1217   PetscFunctionBegin;
1218   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1219   PetscValidLogicalCollectiveInt(pc,n_is,2);
1220   for (i=0;i<n_is;i++) {
1221     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1222     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1223   }
1224   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1225   PetscFunctionReturn(0);
1226 }
1227 
1228 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1229 {
1230   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1231   PetscInt       i;
1232   PetscBool      isequal = PETSC_FALSE;
1233   PetscErrorCode ierr;
1234 
1235   PetscFunctionBegin;
1236   if (pcbddc->n_ISForDofs == n_is) {
1237     for (i=0;i<n_is;i++) {
1238       PetscBool isequalt;
1239       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1240       if (!isequalt) break;
1241     }
1242     if (i == n_is) isequal = PETSC_TRUE;
1243   }
1244   for (i=0;i<n_is;i++) {
1245     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1246   }
1247   /* Destroy ISes if they were already set */
1248   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1249     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1250   }
1251   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1252   /* last user setting takes precendence -> destroy any other customization */
1253   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1254     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1255   }
1256   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1257   pcbddc->n_ISForDofsLocal = 0;
1258   /* allocate space then set */
1259   if (n_is) {
1260     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1261   }
1262   for (i=0;i<n_is;i++) {
1263     pcbddc->ISForDofs[i] = ISForDofs[i];
1264   }
1265   pcbddc->n_ISForDofs = n_is;
1266   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1267   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1268   PetscFunctionReturn(0);
1269 }
1270 
1271 /*@
1272  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1273 
1274    Collective
1275 
1276    Input Parameters:
1277 +  pc - the preconditioning context
1278 .  n_is - number of index sets defining the fields
1279 -  ISForDofs - array of IS describing the fields in global ordering
1280 
1281    Level: intermediate
1282 
1283    Notes:
1284      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1285 
1286 .seealso: PCBDDC
1287 @*/
1288 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1289 {
1290   PetscInt       i;
1291   PetscErrorCode ierr;
1292 
1293   PetscFunctionBegin;
1294   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1295   PetscValidLogicalCollectiveInt(pc,n_is,2);
1296   for (i=0;i<n_is;i++) {
1297     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1298     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1299   }
1300   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1301   PetscFunctionReturn(0);
1302 }
1303 
1304 /*
1305    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1306                      guess if a transformation of basis approach has been selected.
1307 
1308    Input Parameter:
1309 +  pc - the preconditioner contex
1310 
1311    Application Interface Routine: PCPreSolve()
1312 
1313    Notes:
1314      The interface routine PCPreSolve() is not usually called directly by
1315    the user, but instead is called by KSPSolve().
1316 */
1317 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1318 {
1319   PetscErrorCode ierr;
1320   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1321   PC_IS          *pcis = (PC_IS*)(pc->data);
1322   Vec            used_vec;
1323   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1324 
1325   PetscFunctionBegin;
1326   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1327   if (ksp) {
1328     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1329     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1330     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1331     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1332     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1333     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1334       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1335     }
1336   }
1337   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1338     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1339   }
1340 
1341   /* Creates parallel work vectors used in presolve */
1342   if (!pcbddc->original_rhs) {
1343     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1344   }
1345   if (!pcbddc->temp_solution) {
1346     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1347   }
1348 
1349   pcbddc->temp_solution_used = PETSC_FALSE;
1350   if (x) {
1351     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1352     used_vec = x;
1353   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1354     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1355     used_vec = pcbddc->temp_solution;
1356     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1357     pcbddc->temp_solution_used = PETSC_TRUE;
1358     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1359     save_rhs = PETSC_FALSE;
1360     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1361   }
1362 
1363   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1364   if (ksp) {
1365     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1366     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1367     if (!pcbddc->ksp_guess_nonzero) {
1368       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1369     }
1370   }
1371 
1372   pcbddc->rhs_change = PETSC_FALSE;
1373   /* Take into account zeroed rows -> change rhs and store solution removed */
1374   if (rhs && pcbddc->eliminate_dirdofs) {
1375     IS dirIS = NULL;
1376 
1377     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1378     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1379     if (dirIS) {
1380       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1381       PetscInt          dirsize,i,*is_indices;
1382       PetscScalar       *array_x;
1383       const PetscScalar *array_diagonal;
1384 
1385       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1386       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1387       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1388       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1389       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1390       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1391       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1392       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1393       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1394       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1395       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1396       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1397       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1398       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1399       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1400       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1401       pcbddc->rhs_change = PETSC_TRUE;
1402       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1403     }
1404   }
1405 
1406   /* remove the computed solution or the initial guess from the rhs */
1407   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1408     /* save the original rhs */
1409     if (save_rhs) {
1410       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1411       save_rhs = PETSC_FALSE;
1412     }
1413     pcbddc->rhs_change = PETSC_TRUE;
1414     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1415     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1416     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1417     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1418     pcbddc->temp_solution_used = PETSC_TRUE;
1419     if (ksp) {
1420       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1421     }
1422   }
1423   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1424 
1425   /* compute initial vector in benign space if needed
1426      and remove non-benign solution from the rhs */
1427   benign_correction_computed = PETSC_FALSE;
1428   if (rhs && pcbddc->benign_compute_correction && (pcbddc->benign_have_null || pcbddc->benign_apply_coarse_only)) {
1429     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1430        Recursively apply BDDC in the multilevel case */
1431     if (!pcbddc->benign_vec) {
1432       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1433     }
1434     /* keep applying coarse solver unless we no longer have benign subdomains */
1435     pcbddc->benign_apply_coarse_only = pcbddc->benign_have_null ? PETSC_TRUE : PETSC_FALSE;
1436     if (!pcbddc->benign_skip_correction) {
1437       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1438       benign_correction_computed = PETSC_TRUE;
1439       if (pcbddc->temp_solution_used) {
1440         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1441       }
1442       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1443       /* store the original rhs if not done earlier */
1444       if (save_rhs) {
1445         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1446       }
1447       if (pcbddc->rhs_change) {
1448         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1449       } else {
1450         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1451       }
1452       pcbddc->rhs_change = PETSC_TRUE;
1453     }
1454     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1455   }
1456 
1457   /* dbg output */
1458   if (pcbddc->dbg_flag && benign_correction_computed) {
1459     Vec v;
1460 
1461     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1462     if (pcbddc->ChangeOfBasisMatrix) {
1463       ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1464     } else {
1465       ierr = VecCopy(rhs,v);CHKERRQ(ierr);
1466     }
1467     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1468     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1469     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,pcbddc->dbg_viewer);CHKERRQ(ierr);
1470     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1471     ierr = VecDestroy(&v);CHKERRQ(ierr);
1472   }
1473 
1474   /* set initial guess if using PCG */
1475   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1476   if (x && pcbddc->use_exact_dirichlet_trick) {
1477     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1478     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1479       if (benign_correction_computed) { /* we have already saved the changed rhs */
1480         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1481       } else {
1482         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1483       }
1484       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1485       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1486     } else {
1487       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1488       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1489     }
1490     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1491     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1492       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1493       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1494       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1495       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1496     } else {
1497       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1498       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1499     }
1500     if (ksp) {
1501       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1502     }
1503     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1504   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1505     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1506   }
1507   PetscFunctionReturn(0);
1508 }
1509 
1510 /*
1511    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1512                      approach has been selected. Also, restores rhs to its original state.
1513 
1514    Input Parameter:
1515 +  pc - the preconditioner contex
1516 
1517    Application Interface Routine: PCPostSolve()
1518 
1519    Notes:
1520      The interface routine PCPostSolve() is not usually called directly by
1521      the user, but instead is called by KSPSolve().
1522 */
1523 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1524 {
1525   PetscErrorCode ierr;
1526   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1527 
1528   PetscFunctionBegin;
1529   /* add solution removed in presolve */
1530   if (x && pcbddc->rhs_change) {
1531     if (pcbddc->temp_solution_used) {
1532       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1533     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1534       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1535     }
1536     /* restore to original state (not for FETI-DP) */
1537     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1538   }
1539 
1540   /* restore rhs to its original state (not needed for FETI-DP) */
1541   if (rhs && pcbddc->rhs_change) {
1542     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1543     pcbddc->rhs_change = PETSC_FALSE;
1544   }
1545   /* restore ksp guess state */
1546   if (ksp) {
1547     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1548     /* reset flag for exact dirichlet trick */
1549     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1550   }
1551   PetscFunctionReturn(0);
1552 }
1553 
1554 /*
1555    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1556                   by setting data structures and options.
1557 
1558    Input Parameter:
1559 +  pc - the preconditioner context
1560 
1561    Application Interface Routine: PCSetUp()
1562 
1563    Notes:
1564      The interface routine PCSetUp() is not usually called directly by
1565      the user, but instead is called by PCApply() if necessary.
1566 */
1567 PetscErrorCode PCSetUp_BDDC(PC pc)
1568 {
1569   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1570   PCBDDCSubSchurs sub_schurs;
1571   Mat_IS*         matis;
1572   MatNullSpace    nearnullspace;
1573   Mat             lA;
1574   IS              lP,zerodiag = NULL;
1575   PetscInt        nrows,ncols;
1576   PetscMPIInt     size;
1577   PetscBool       computesubschurs;
1578   PetscBool       computeconstraintsmatrix;
1579   PetscBool       new_nearnullspace_provided,ismatis;
1580   PetscErrorCode  ierr;
1581 
1582   PetscFunctionBegin;
1583   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1584   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1585   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1586   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1587   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
1588 
1589   matis = (Mat_IS*)pc->pmat->data;
1590   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1591   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1592      Also, BDDC builds its own KSP for the Dirichlet problem */
1593   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) pcbddc->recompute_topography = PETSC_TRUE;
1594   if (pcbddc->recompute_topography) {
1595     pcbddc->graphanalyzed    = PETSC_FALSE;
1596     computeconstraintsmatrix = PETSC_TRUE;
1597   } else {
1598     computeconstraintsmatrix = PETSC_FALSE;
1599   }
1600 
1601   /* check parameters' compatibility */
1602   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1603   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1604   pcbddc->use_deluxe_scaling   = (PetscBool)(pcbddc->use_deluxe_scaling && size > 1);
1605   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_selection && size > 1);
1606   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1607   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1608 
1609   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1610   if (pcbddc->switch_static) {
1611     PetscBool ismatis;
1612 
1613     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1614     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1615   }
1616 
1617   /* activate all connected components if the netflux has been requested */
1618   if (pcbddc->compute_nonetflux) {
1619     pcbddc->use_vertices = PETSC_TRUE;
1620     pcbddc->use_edges    = PETSC_TRUE;
1621     pcbddc->use_faces    = PETSC_TRUE;
1622   }
1623 
1624   /* Get stdout for dbg */
1625   if (pcbddc->dbg_flag) {
1626     if (!pcbddc->dbg_viewer) {
1627       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1628     }
1629     ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1630     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1631   }
1632 
1633   /* process topology information */
1634   ierr = PetscLogEventBegin(PC_BDDC_Topology[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1635   if (pcbddc->recompute_topography) {
1636     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1637     if (pcbddc->discretegradient) {
1638       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1639     }
1640   }
1641 
1642   /* change basis if requested by the user */
1643   if (pcbddc->user_ChangeOfBasisMatrix) {
1644     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1645     pcbddc->use_change_of_basis = PETSC_FALSE;
1646     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1647   } else {
1648     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1649     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1650     pcbddc->local_mat = matis->A;
1651   }
1652 
1653   /*
1654      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1655      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1656   */
1657   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1658   if (pcbddc->benign_saddle_point) {
1659     PC_IS* pcis = (PC_IS*)pc->data;
1660 
1661     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1662     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1663     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1664     /* pop B0 mat from local mat */
1665     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1666     /* give pcis a hint to not reuse submatrices during PCISCreate */
1667     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1668       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1669         pcis->reusesubmatrices = PETSC_FALSE;
1670       } else {
1671         pcis->reusesubmatrices = PETSC_TRUE;
1672       }
1673     } else {
1674       pcis->reusesubmatrices = PETSC_FALSE;
1675     }
1676   }
1677 
1678   /* propagate relevant information */
1679   if (matis->A->symmetric_set) {
1680     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1681   }
1682   if (matis->A->spd_set) {
1683     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1684   }
1685 
1686   /* Set up all the "iterative substructuring" common block without computing solvers */
1687   {
1688     Mat temp_mat;
1689 
1690     temp_mat = matis->A;
1691     matis->A = pcbddc->local_mat;
1692     ierr = PCISSetUp(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1693     pcbddc->local_mat = matis->A;
1694     matis->A = temp_mat;
1695   }
1696 
1697   /* Analyze interface */
1698   if (!pcbddc->graphanalyzed) {
1699     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1700     computeconstraintsmatrix = PETSC_TRUE;
1701     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1702       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1703     }
1704     if (pcbddc->compute_nonetflux) {
1705       MatNullSpace nnfnnsp;
1706 
1707       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1708       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1709       /* TODO what if a nearnullspace is already attached? */
1710       if (nnfnnsp) {
1711         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1712         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1713       }
1714     }
1715   }
1716   ierr = PetscLogEventEnd(PC_BDDC_Topology[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1717 
1718   /* check existence of a divergence free extension, i.e.
1719      b(v_I,p_0) = 0 for all v_I (raise error if not).
1720      Also, check that PCBDDCBenignGetOrSetP0 works */
1721   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1722     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1723   }
1724   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1725 
1726   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1727   if (computesubschurs && pcbddc->recompute_topography) {
1728     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1729   }
1730   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1731   if (!pcbddc->use_deluxe_scaling) {
1732     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1733   }
1734 
1735   /* finish setup solvers and do adaptive selection of constraints */
1736   sub_schurs = pcbddc->sub_schurs;
1737   if (sub_schurs && sub_schurs->schur_explicit) {
1738     if (computesubschurs) {
1739       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1740     }
1741     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1742   } else {
1743     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1744     if (computesubschurs) {
1745       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1746     }
1747   }
1748   if (pcbddc->adaptive_selection) {
1749     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1750     computeconstraintsmatrix = PETSC_TRUE;
1751   }
1752 
1753   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1754   new_nearnullspace_provided = PETSC_FALSE;
1755   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1756   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1757     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1758       new_nearnullspace_provided = PETSC_TRUE;
1759     } else {
1760       /* determine if the two nullspaces are different (should be lightweight) */
1761       if (nearnullspace != pcbddc->onearnullspace) {
1762         new_nearnullspace_provided = PETSC_TRUE;
1763       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1764         PetscInt         i;
1765         const Vec        *nearnullvecs;
1766         PetscObjectState state;
1767         PetscInt         nnsp_size;
1768         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1769         for (i=0;i<nnsp_size;i++) {
1770           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1771           if (pcbddc->onearnullvecs_state[i] != state) {
1772             new_nearnullspace_provided = PETSC_TRUE;
1773             break;
1774           }
1775         }
1776       }
1777     }
1778   } else {
1779     if (!nearnullspace) { /* both nearnullspaces are null */
1780       new_nearnullspace_provided = PETSC_FALSE;
1781     } else { /* nearnullspace attached later */
1782       new_nearnullspace_provided = PETSC_TRUE;
1783     }
1784   }
1785 
1786   /* Setup constraints and related work vectors */
1787   /* reset primal space flags */
1788   ierr = PetscLogEventBegin(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1789   pcbddc->new_primal_space = PETSC_FALSE;
1790   pcbddc->new_primal_space_local = PETSC_FALSE;
1791   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1792     /* It also sets the primal space flags */
1793     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1794   }
1795   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1796   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1797 
1798   if (pcbddc->use_change_of_basis) {
1799     PC_IS *pcis = (PC_IS*)(pc->data);
1800 
1801     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1802     if (pcbddc->benign_change) {
1803       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1804       /* pop B0 from pcbddc->local_mat */
1805       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1806     }
1807     /* get submatrices */
1808     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1809     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1810     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1811     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1812     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1813     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1814     /* set flag in pcis to not reuse submatrices during PCISCreate */
1815     pcis->reusesubmatrices = PETSC_FALSE;
1816   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1817     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1818     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1819     pcbddc->local_mat = matis->A;
1820   }
1821 
1822   /* interface pressure block row for B_C */
1823   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1824   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1825   if (lA && lP) {
1826     PC_IS*    pcis = (PC_IS*)pc->data;
1827     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1828     PetscBool issym;
1829     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1830     if (issym) {
1831       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1832       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1833       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1834       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1835     } else {
1836       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1837       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1838       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1839       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1840     }
1841     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1842     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1843     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1844     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1845     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1846     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1847     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1848     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1849   }
1850   ierr = PetscLogEventEnd(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1851 
1852   /* SetUp coarse and local Neumann solvers */
1853   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1854   /* SetUp Scaling operator */
1855   if (pcbddc->use_deluxe_scaling) {
1856     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1857   }
1858 
1859   /* mark topography as done */
1860   pcbddc->recompute_topography = PETSC_FALSE;
1861 
1862   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1863   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1864 
1865   if (pcbddc->dbg_flag) {
1866     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1867     ierr = PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1868   }
1869   PetscFunctionReturn(0);
1870 }
1871 
1872 /*
1873    PCApply_BDDC - Applies the BDDC operator to a vector.
1874 
1875    Input Parameters:
1876 +  pc - the preconditioner context
1877 -  r - input vector (global)
1878 
1879    Output Parameter:
1880 .  z - output vector (global)
1881 
1882    Application Interface Routine: PCApply()
1883  */
1884 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1885 {
1886   PC_IS             *pcis = (PC_IS*)(pc->data);
1887   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1888   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1889   PetscErrorCode    ierr;
1890   const PetscScalar one = 1.0;
1891   const PetscScalar m_one = -1.0;
1892   const PetscScalar zero = 0.0;
1893 
1894 /* This code is similar to that provided in nn.c for PCNN
1895    NN interface preconditioner changed to BDDC
1896    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1897 
1898   PetscFunctionBegin;
1899   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1900   if (pcbddc->ChangeOfBasisMatrix) {
1901     Vec swap;
1902 
1903     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1904     swap = pcbddc->work_change;
1905     pcbddc->work_change = r;
1906     r = swap;
1907     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1908     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1909       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1910       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1911     }
1912   }
1913   if (pcbddc->benign_have_null) { /* get p0 from r */
1914     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1915   }
1916   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1917     ierr = VecCopy(r,z);CHKERRQ(ierr);
1918     /* First Dirichlet solve */
1919     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1920     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1921     /*
1922       Assembling right hand side for BDDC operator
1923       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1924       - pcis->vec1_B the interface part of the global vector z
1925     */
1926     if (n_D) {
1927       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1928       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1929       if (pcbddc->switch_static) {
1930         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1931 
1932         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1933         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1934         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1935         if (!pcbddc->switch_static_change) {
1936           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1937         } else {
1938           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1939           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1940           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1941         }
1942         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1943         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1944         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1945         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1946       } else {
1947         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1948       }
1949     } else {
1950       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1951     }
1952     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1953     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1954     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1955   } else {
1956     if (!pcbddc->benign_apply_coarse_only) {
1957       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1958     }
1959   }
1960 
1961   /* Apply interface preconditioner
1962      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1963   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1964 
1965   /* Apply transpose of partition of unity operator */
1966   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1967 
1968   /* Second Dirichlet solve and assembling of output */
1969   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1970   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1971   if (n_B) {
1972     if (pcbddc->switch_static) {
1973       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1974 
1975       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1976       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1977       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1978       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1979       if (!pcbddc->switch_static_change) {
1980         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1981       } else {
1982         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1983         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1984         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1985       }
1986       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1987       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1988     } else {
1989       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1990     }
1991   } else if (pcbddc->switch_static) { /* n_B is zero */
1992     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1993 
1994     if (!pcbddc->switch_static_change) {
1995       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1996     } else {
1997       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1998       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1999       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2000     }
2001   }
2002   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2003 
2004   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2005     if (pcbddc->switch_static) {
2006       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2007     } else {
2008       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2009     }
2010     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2011     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2012   } else {
2013     if (pcbddc->switch_static) {
2014       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2015     } else {
2016       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2017     }
2018     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2019     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2020   }
2021   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2022     if (pcbddc->benign_apply_coarse_only) {
2023       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2024     }
2025     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2026   }
2027 
2028   if (pcbddc->ChangeOfBasisMatrix) {
2029     pcbddc->work_change = r;
2030     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2031     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2032   }
2033   PetscFunctionReturn(0);
2034 }
2035 
2036 /*
2037    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
2038 
2039    Input Parameters:
2040 +  pc - the preconditioner context
2041 -  r - input vector (global)
2042 
2043    Output Parameter:
2044 .  z - output vector (global)
2045 
2046    Application Interface Routine: PCApplyTranspose()
2047  */
2048 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
2049 {
2050   PC_IS             *pcis = (PC_IS*)(pc->data);
2051   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
2052   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
2053   PetscErrorCode    ierr;
2054   const PetscScalar one = 1.0;
2055   const PetscScalar m_one = -1.0;
2056   const PetscScalar zero = 0.0;
2057 
2058   PetscFunctionBegin;
2059   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
2060   if (pcbddc->ChangeOfBasisMatrix) {
2061     Vec swap;
2062 
2063     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
2064     swap = pcbddc->work_change;
2065     pcbddc->work_change = r;
2066     r = swap;
2067     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
2068     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
2069       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
2070       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
2071     }
2072   }
2073   if (pcbddc->benign_have_null) { /* get p0 from r */
2074     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
2075   }
2076   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2077     ierr = VecCopy(r,z);CHKERRQ(ierr);
2078     /* First Dirichlet solve */
2079     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2080     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2081     /*
2082       Assembling right hand side for BDDC operator
2083       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
2084       - pcis->vec1_B the interface part of the global vector z
2085     */
2086     if (n_D) {
2087       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
2088       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
2089       if (pcbddc->switch_static) {
2090         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2091 
2092         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
2093         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2094         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2095         if (!pcbddc->switch_static_change) {
2096           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2097         } else {
2098           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2099           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2100           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2101         }
2102         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2103         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2104         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2105         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2106       } else {
2107         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
2108       }
2109     } else {
2110       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
2111     }
2112     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2113     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2114     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
2115   } else {
2116     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
2117   }
2118 
2119   /* Apply interface preconditioner
2120      input/output vecs: pcis->vec1_B and pcis->vec1_D */
2121   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
2122 
2123   /* Apply transpose of partition of unity operator */
2124   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2125 
2126   /* Second Dirichlet solve and assembling of output */
2127   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2128   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2129   if (n_B) {
2130     if (pcbddc->switch_static) {
2131       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2132 
2133       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2134       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2135       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2136       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2137       if (!pcbddc->switch_static_change) {
2138         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2139       } else {
2140         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2141         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2142         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2143       }
2144       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2145       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2146     } else {
2147       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2148     }
2149   } else if (pcbddc->switch_static) { /* n_B is zero */
2150     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2151 
2152     if (!pcbddc->switch_static_change) {
2153       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2154     } else {
2155       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2156       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2157       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2158     }
2159   }
2160   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2161   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2162     if (pcbddc->switch_static) {
2163       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2164     } else {
2165       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2166     }
2167     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2168     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2169   } else {
2170     if (pcbddc->switch_static) {
2171       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2172     } else {
2173       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2174     }
2175     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2176     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2177   }
2178   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2179     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2180   }
2181   if (pcbddc->ChangeOfBasisMatrix) {
2182     pcbddc->work_change = r;
2183     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2184     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2185   }
2186   PetscFunctionReturn(0);
2187 }
2188 
2189 PetscErrorCode PCReset_BDDC(PC pc)
2190 {
2191   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2192   PC_IS          *pcis = (PC_IS*)pc->data;
2193   KSP            kspD,kspR,kspC;
2194   PetscErrorCode ierr;
2195 
2196   PetscFunctionBegin;
2197   /* free BDDC custom data  */
2198   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2199   /* destroy objects related to topography */
2200   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2201   /* destroy objects for scaling operator */
2202   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2203   /* free solvers stuff */
2204   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2205   /* free global vectors needed in presolve */
2206   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2207   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2208   /* free data created by PCIS */
2209   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2210 
2211   /* restore defaults */
2212   kspD = pcbddc->ksp_D;
2213   kspR = pcbddc->ksp_R;
2214   kspC = pcbddc->coarse_ksp;
2215   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2216   pcis->n_neigh                     = -1;
2217   pcis->scaling_factor              = 1.0;
2218   pcis->reusesubmatrices            = PETSC_TRUE;
2219   pcbddc->use_local_adj             = PETSC_TRUE;
2220   pcbddc->use_vertices              = PETSC_TRUE;
2221   pcbddc->use_edges                 = PETSC_TRUE;
2222   pcbddc->symmetric_primal          = PETSC_TRUE;
2223   pcbddc->vertex_size               = 1;
2224   pcbddc->recompute_topography      = PETSC_TRUE;
2225   pcbddc->coarse_size               = -1;
2226   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2227   pcbddc->coarsening_ratio          = 8;
2228   pcbddc->coarse_eqs_per_proc       = 1;
2229   pcbddc->benign_compute_correction = PETSC_TRUE;
2230   pcbddc->nedfield                  = -1;
2231   pcbddc->nedglobal                 = PETSC_TRUE;
2232   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2233   pcbddc->sub_schurs_layers         = -1;
2234   pcbddc->ksp_D                     = kspD;
2235   pcbddc->ksp_R                     = kspR;
2236   pcbddc->coarse_ksp                = kspC;
2237   PetscFunctionReturn(0);
2238 }
2239 
2240 PetscErrorCode PCDestroy_BDDC(PC pc)
2241 {
2242   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2243   PetscErrorCode ierr;
2244 
2245   PetscFunctionBegin;
2246   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2247   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2248   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2249   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2250   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2251   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2252   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2253   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2254   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2255   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2256   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2257   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2258   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2259   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2260   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2261   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2262   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2263   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2264   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2265   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2266   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2267   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2268   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2269   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2270   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2271   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2272   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2273   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2274   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2275   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2276   PetscFunctionReturn(0);
2277 }
2278 
2279 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2280 {
2281   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2282   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2283   PetscErrorCode ierr;
2284 
2285   PetscFunctionBegin;
2286   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2287   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2288   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2289   mat_graph->cnloc = nloc;
2290   mat_graph->cdim  = dim;
2291   mat_graph->cloc  = PETSC_FALSE;
2292   PetscFunctionReturn(0);
2293 }
2294 
2295 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2296 {
2297   PetscFunctionBegin;
2298   *change = PETSC_TRUE;
2299   PetscFunctionReturn(0);
2300 }
2301 
2302 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2303 {
2304   FETIDPMat_ctx  mat_ctx;
2305   Vec            work;
2306   PC_IS*         pcis;
2307   PC_BDDC*       pcbddc;
2308   PetscErrorCode ierr;
2309 
2310   PetscFunctionBegin;
2311   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2312   pcis = (PC_IS*)mat_ctx->pc->data;
2313   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2314 
2315   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2316   /* copy rhs since we may change it during PCPreSolve_BDDC */
2317   if (!pcbddc->original_rhs) {
2318     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2319   }
2320   if (mat_ctx->rhs_flip) {
2321     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2322   } else {
2323     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2324   }
2325   if (mat_ctx->g2g_p) {
2326     /* interface pressure rhs */
2327     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2328     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2329     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2330     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2331     if (!mat_ctx->rhs_flip) {
2332       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2333     }
2334   }
2335   /*
2336      change of basis for physical rhs if needed
2337      It also changes the rhs in case of dirichlet boundaries
2338   */
2339   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2340   if (pcbddc->ChangeOfBasisMatrix) {
2341     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2342     work = pcbddc->work_change;
2343    } else {
2344     work = pcbddc->original_rhs;
2345   }
2346   /* store vectors for computation of fetidp final solution */
2347   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2348   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2349   /* scale rhs since it should be unassembled */
2350   /* TODO use counter scaling? (also below) */
2351   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2352   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2353   /* Apply partition of unity */
2354   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2355   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2356   if (!pcbddc->switch_static) {
2357     /* compute partially subassembled Schur complement right-hand side */
2358     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2359     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2360     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2361     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2362     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2363     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2364     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2365     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2366     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2367     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2368   }
2369   /* BDDC rhs */
2370   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2371   if (pcbddc->switch_static) {
2372     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2373   }
2374   /* apply BDDC */
2375   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2376   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2377   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2378 
2379   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2380   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2381   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2382   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2383   /* Add contribution to interface pressures */
2384   if (mat_ctx->l2g_p) {
2385     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2386     if (pcbddc->switch_static) {
2387       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2388     }
2389     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2390     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2391   }
2392   PetscFunctionReturn(0);
2393 }
2394 
2395 /*@
2396  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2397 
2398    Collective
2399 
2400    Input Parameters:
2401 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2402 -  standard_rhs    - the right-hand side of the original linear system
2403 
2404    Output Parameters:
2405 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2406 
2407    Level: developer
2408 
2409    Notes:
2410 
2411 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2412 @*/
2413 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2414 {
2415   FETIDPMat_ctx  mat_ctx;
2416   PetscErrorCode ierr;
2417 
2418   PetscFunctionBegin;
2419   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2420   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2421   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2422   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2423   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2424   PetscFunctionReturn(0);
2425 }
2426 
2427 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2428 {
2429   FETIDPMat_ctx  mat_ctx;
2430   PC_IS*         pcis;
2431   PC_BDDC*       pcbddc;
2432   PetscErrorCode ierr;
2433   Vec            work;
2434 
2435   PetscFunctionBegin;
2436   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2437   pcis = (PC_IS*)mat_ctx->pc->data;
2438   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2439 
2440   /* apply B_delta^T */
2441   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2442   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2443   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2444   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2445   if (mat_ctx->l2g_p) {
2446     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2447     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2448     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2449   }
2450 
2451   /* compute rhs for BDDC application */
2452   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2453   if (pcbddc->switch_static) {
2454     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2455     if (mat_ctx->l2g_p) {
2456       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2457       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2458     }
2459   }
2460 
2461   /* apply BDDC */
2462   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2463   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2464 
2465   /* put values into global vector */
2466   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2467   else work = standard_sol;
2468   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2469   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2470   if (!pcbddc->switch_static) {
2471     /* compute values into the interior if solved for the partially subassembled Schur complement */
2472     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2473     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2474     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2475   }
2476 
2477   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2478   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2479   /* add p0 solution to final solution */
2480   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2481   if (pcbddc->ChangeOfBasisMatrix) {
2482     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2483   }
2484   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2485   if (mat_ctx->g2g_p) {
2486     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2487     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2488   }
2489   PetscFunctionReturn(0);
2490 }
2491 
2492 static PetscErrorCode PCView_BDDCIPC(PC pc, PetscViewer viewer)
2493 {
2494   PetscErrorCode ierr;
2495   BDDCIPC_ctx    bddcipc_ctx;
2496   PetscBool      isascii;
2497 
2498   PetscFunctionBegin;
2499   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2500   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
2501   if (isascii) {
2502     ierr = PetscViewerASCIIPrintf(viewer,"BDDC interface preconditioner\n");CHKERRQ(ierr);
2503   }
2504   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2505   ierr = PCView(bddcipc_ctx->bddc,viewer);CHKERRQ(ierr);
2506   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2507   PetscFunctionReturn(0);
2508 }
2509 
2510 static PetscErrorCode PCSetUp_BDDCIPC(PC pc)
2511 {
2512   PetscErrorCode ierr;
2513   BDDCIPC_ctx    bddcipc_ctx;
2514   PetscBool      isbddc;
2515   Vec            vv;
2516   IS             is;
2517   PC_IS          *pcis;
2518 
2519   PetscFunctionBegin;
2520   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2521   ierr = PetscObjectTypeCompare((PetscObject)bddcipc_ctx->bddc,PCBDDC,&isbddc);CHKERRQ(ierr);
2522   if (!isbddc) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid type %s. Must be of type bddc",((PetscObject)bddcipc_ctx->bddc)->type_name);
2523   ierr = PCSetUp(bddcipc_ctx->bddc);CHKERRQ(ierr);
2524 
2525   /* create interface scatter */
2526   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2527   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2528   ierr = MatCreateVecs(pc->pmat,&vv,NULL);CHKERRQ(ierr);
2529   ierr = ISRenumber(pcis->is_B_global,NULL,NULL,&is);CHKERRQ(ierr);
2530   ierr = VecScatterCreateWithData(vv,is,pcis->vec1_B,NULL,&bddcipc_ctx->g2l);CHKERRQ(ierr);
2531   ierr = ISDestroy(&is);CHKERRQ(ierr);
2532   ierr = VecDestroy(&vv);CHKERRQ(ierr);
2533   PetscFunctionReturn(0);
2534 }
2535 
2536 static PetscErrorCode PCApply_BDDCIPC(PC pc, Vec r, Vec x)
2537 {
2538   PetscErrorCode ierr;
2539   BDDCIPC_ctx    bddcipc_ctx;
2540   PC_IS          *pcis;
2541   VecScatter     tmps;
2542 
2543   PetscFunctionBegin;
2544   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2545   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2546   tmps = pcis->global_to_B;
2547   pcis->global_to_B = bddcipc_ctx->g2l;
2548   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2549   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_FALSE);CHKERRQ(ierr);
2550   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2551   pcis->global_to_B = tmps;
2552   PetscFunctionReturn(0);
2553 }
2554 
2555 static PetscErrorCode PCApplyTranspose_BDDCIPC(PC pc, Vec r, Vec x)
2556 {
2557   PetscErrorCode ierr;
2558   BDDCIPC_ctx    bddcipc_ctx;
2559   PC_IS          *pcis;
2560   VecScatter     tmps;
2561 
2562   PetscFunctionBegin;
2563   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2564   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2565   tmps = pcis->global_to_B;
2566   pcis->global_to_B = bddcipc_ctx->g2l;
2567   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2568   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_TRUE);CHKERRQ(ierr);
2569   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2570   pcis->global_to_B = tmps;
2571   PetscFunctionReturn(0);
2572 }
2573 
2574 static PetscErrorCode PCDestroy_BDDCIPC(PC pc)
2575 {
2576   PetscErrorCode ierr;
2577   BDDCIPC_ctx    bddcipc_ctx;
2578 
2579   PetscFunctionBegin;
2580   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2581   ierr = PCDestroy(&bddcipc_ctx->bddc);CHKERRQ(ierr);
2582   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2583   ierr = PetscFree(bddcipc_ctx);CHKERRQ(ierr);
2584   PetscFunctionReturn(0);
2585 }
2586 
2587 /*@
2588  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2589 
2590    Collective
2591 
2592    Input Parameters:
2593 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2594 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2595 
2596    Output Parameters:
2597 .  standard_sol    - the solution defined on the physical domain
2598 
2599    Level: developer
2600 
2601    Notes:
2602 
2603 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2604 @*/
2605 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2606 {
2607   FETIDPMat_ctx  mat_ctx;
2608   PetscErrorCode ierr;
2609 
2610   PetscFunctionBegin;
2611   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2612   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2613   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2614   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2615   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2616   PetscFunctionReturn(0);
2617 }
2618 
2619 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2620 {
2621 
2622   FETIDPMat_ctx  fetidpmat_ctx;
2623   Mat            newmat;
2624   FETIDPPC_ctx   fetidppc_ctx;
2625   PC             newpc;
2626   MPI_Comm       comm;
2627   PetscErrorCode ierr;
2628 
2629   PetscFunctionBegin;
2630   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2631   /* FETI-DP matrix */
2632   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2633   fetidpmat_ctx->fully_redundant = fully_redundant;
2634   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2635   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2636   ierr = PetscObjectSetName((PetscObject)newmat,!fetidpmat_ctx->l2g_lambda_only ? "F" : "G");CHKERRQ(ierr);
2637   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2638   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2639   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2640   /* propagate MatOptions */
2641   {
2642     PC_BDDC   *pcbddc = (PC_BDDC*)fetidpmat_ctx->pc->data;
2643     PetscBool issym;
2644 
2645     ierr = MatGetOption(pc->mat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2646     if (issym || pcbddc->symmetric_primal) {
2647       ierr = MatSetOption(newmat,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2648     }
2649   }
2650   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2651   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2652   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2653   /* FETI-DP preconditioner */
2654   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2655   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2656   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2657   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2658   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2659   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2660   ierr = PCSetErrorIfFailure(newpc,pc->erroriffailure);CHKERRQ(ierr);
2661   if (!fetidpmat_ctx->l2g_lambda_only) { /* standard FETI-DP */
2662     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2663     ierr = PCShellSetName(newpc,"FETI-DP multipliers");CHKERRQ(ierr);
2664     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2665     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2666     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2667     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2668     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2669   } else { /* saddle-point FETI-DP */
2670     Mat       M;
2671     PetscInt  psize;
2672     PetscBool fake = PETSC_FALSE, isfieldsplit;
2673 
2674     ierr = ISViewFromOptions(fetidpmat_ctx->lagrange,NULL,"-lag_view");CHKERRQ(ierr);
2675     ierr = ISViewFromOptions(fetidpmat_ctx->pressure,NULL,"-press_view");CHKERRQ(ierr);
2676     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2677     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2678     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2679     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2680     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2681     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2682     ierr = ISGetSize(fetidpmat_ctx->pressure,&psize);CHKERRQ(ierr);
2683     if (psize != M->rmap->N) {
2684       Mat      M2;
2685       PetscInt lpsize;
2686 
2687       fake = PETSC_TRUE;
2688       ierr = ISGetLocalSize(fetidpmat_ctx->pressure,&lpsize);CHKERRQ(ierr);
2689       ierr = MatCreate(comm,&M2);CHKERRQ(ierr);
2690       ierr = MatSetType(M2,MATAIJ);CHKERRQ(ierr);
2691       ierr = MatSetSizes(M2,lpsize,lpsize,psize,psize);CHKERRQ(ierr);
2692       ierr = MatSetUp(M2);CHKERRQ(ierr);
2693       ierr = MatAssemblyBegin(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2694       ierr = MatAssemblyEnd(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2695       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M2);CHKERRQ(ierr);
2696       ierr = MatDestroy(&M2);CHKERRQ(ierr);
2697     } else {
2698       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2699     }
2700     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2701 
2702     /* we need to setfromoptions and setup here to access the blocks */
2703     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2704     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2705 
2706     /* user may have changed the type (e.g. -fetidp_pc_type none) */
2707     ierr = PetscObjectTypeCompare((PetscObject)newpc,PCFIELDSPLIT,&isfieldsplit);CHKERRQ(ierr);
2708     if (isfieldsplit) {
2709       KSP       *ksps;
2710       PC        ppc,lagpc;
2711       PetscInt  nn;
2712       PetscBool ismatis,matisok = PETSC_FALSE,check = PETSC_FALSE;
2713 
2714       /* set the solver for the (0,0) block */
2715       ierr = PCFieldSplitSchurGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2716       if (!nn) { /* not of type PC_COMPOSITE_SCHUR */
2717         ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2718         if (!fake) { /* pass pmat to the pressure solver */
2719           Mat F;
2720 
2721           ierr = KSPGetOperators(ksps[1],&F,NULL);CHKERRQ(ierr);
2722           ierr = KSPSetOperators(ksps[1],F,M);CHKERRQ(ierr);
2723         }
2724       } else {
2725         PetscBool issym;
2726         Mat       S;
2727 
2728         ierr = PCFieldSplitSchurGetS(newpc,&S);CHKERRQ(ierr);
2729 
2730         ierr = MatGetOption(newmat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2731         if (issym) {
2732           ierr = MatSetOption(S,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2733         }
2734       }
2735       ierr = KSPGetPC(ksps[0],&lagpc);CHKERRQ(ierr);
2736       ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2737       ierr = PCShellSetName(lagpc,"FETI-DP multipliers");CHKERRQ(ierr);
2738       ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2739       ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2740       ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2741       ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2742       ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2743 
2744       /* Olof's idea: interface Schur complement preconditioner for the mass matrix */
2745       ierr = KSPGetPC(ksps[1],&ppc);CHKERRQ(ierr);
2746       if (fake) {
2747         BDDCIPC_ctx    bddcipc_ctx;
2748         PetscContainer c;
2749 
2750         matisok = PETSC_TRUE;
2751 
2752         /* create inner BDDC solver */
2753         ierr = PetscNew(&bddcipc_ctx);CHKERRQ(ierr);
2754         ierr = PCCreate(comm,&bddcipc_ctx->bddc);CHKERRQ(ierr);
2755         ierr = PCSetType(bddcipc_ctx->bddc,PCBDDC);CHKERRQ(ierr);
2756         ierr = PCSetOperators(bddcipc_ctx->bddc,M,M);CHKERRQ(ierr);
2757         ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_pCSR",(PetscObject*)&c);CHKERRQ(ierr);
2758         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2759         if (c && ismatis) {
2760           Mat      lM;
2761           PetscInt *csr,n;
2762 
2763           ierr = MatISGetLocalMat(M,&lM);CHKERRQ(ierr);
2764           ierr = MatGetSize(lM,&n,NULL);CHKERRQ(ierr);
2765           ierr = PetscContainerGetPointer(c,(void**)&csr);CHKERRQ(ierr);
2766           ierr = PCBDDCSetLocalAdjacencyGraph(bddcipc_ctx->bddc,n,csr,csr + (n + 1),PETSC_COPY_VALUES);CHKERRQ(ierr);
2767           ierr = MatISRestoreLocalMat(M,&lM);CHKERRQ(ierr);
2768         }
2769         ierr = PCSetOptionsPrefix(bddcipc_ctx->bddc,((PetscObject)ksps[1])->prefix);CHKERRQ(ierr);
2770         ierr = PCSetErrorIfFailure(bddcipc_ctx->bddc,pc->erroriffailure);CHKERRQ(ierr);
2771         ierr = PCSetFromOptions(bddcipc_ctx->bddc);CHKERRQ(ierr);
2772 
2773         /* wrap the interface application */
2774         ierr = PCSetType(ppc,PCSHELL);CHKERRQ(ierr);
2775         ierr = PCShellSetName(ppc,"FETI-DP pressure");CHKERRQ(ierr);
2776         ierr = PCShellSetContext(ppc,bddcipc_ctx);CHKERRQ(ierr);
2777         ierr = PCShellSetSetUp(ppc,PCSetUp_BDDCIPC);CHKERRQ(ierr);
2778         ierr = PCShellSetApply(ppc,PCApply_BDDCIPC);CHKERRQ(ierr);
2779         ierr = PCShellSetApplyTranspose(ppc,PCApplyTranspose_BDDCIPC);CHKERRQ(ierr);
2780         ierr = PCShellSetView(ppc,PCView_BDDCIPC);CHKERRQ(ierr);
2781         ierr = PCShellSetDestroy(ppc,PCDestroy_BDDCIPC);CHKERRQ(ierr);
2782       }
2783 
2784       /* determine if we need to assemble M to construct a preconditioner */
2785       if (!matisok) {
2786         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2787         ierr = PetscObjectTypeCompareAny((PetscObject)ppc,&matisok,PCBDDC,PCJACOBI,PCNONE,PCMG,"");CHKERRQ(ierr);
2788         if (ismatis && !matisok) {
2789           ierr = MatConvert(M,MATAIJ,MAT_INPLACE_MATRIX,&M);CHKERRQ(ierr);
2790         }
2791       }
2792 
2793       /* run the subproblems to check convergence */
2794       ierr = PetscOptionsGetBool(NULL,((PetscObject)newmat)->prefix,"-check_saddlepoint",&check,NULL);CHKERRQ(ierr);
2795       if (check) {
2796         PetscInt i;
2797 
2798         for (i=0;i<nn;i++) {
2799           KSP       kspC;
2800           PC        pc;
2801           Mat       F,pF;
2802           Vec       x,y;
2803           PetscBool isschur,prec = PETSC_TRUE;
2804 
2805           ierr = KSPCreate(PetscObjectComm((PetscObject)ksps[i]),&kspC);CHKERRQ(ierr);
2806           ierr = KSPSetOptionsPrefix(kspC,((PetscObject)ksps[i])->prefix);CHKERRQ(ierr);
2807           ierr = KSPAppendOptionsPrefix(kspC,"check_");CHKERRQ(ierr);
2808           ierr = KSPGetOperators(ksps[i],&F,&pF);CHKERRQ(ierr);
2809           ierr = PetscObjectTypeCompare((PetscObject)F,MATSCHURCOMPLEMENT,&isschur);CHKERRQ(ierr);
2810           if (isschur) {
2811             KSP  kspS,kspS2;
2812             Mat  A00,pA00,A10,A01,A11;
2813             char prefix[256];
2814 
2815             ierr = MatSchurComplementGetKSP(F,&kspS);CHKERRQ(ierr);
2816             ierr = MatSchurComplementGetSubMatrices(F,&A00,&pA00,&A01,&A10,&A11);CHKERRQ(ierr);
2817             ierr = MatCreateSchurComplement(A00,pA00,A01,A10,A11,&F);CHKERRQ(ierr);
2818             ierr = MatSchurComplementGetKSP(F,&kspS2);CHKERRQ(ierr);
2819             ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sschur_",((PetscObject)kspC)->prefix);CHKERRQ(ierr);
2820             ierr = KSPSetOptionsPrefix(kspS2,prefix);CHKERRQ(ierr);
2821             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2822             ierr = PCSetType(pc,PCKSP);CHKERRQ(ierr);
2823             ierr = PCKSPSetKSP(pc,kspS);CHKERRQ(ierr);
2824             ierr = KSPSetFromOptions(kspS2);CHKERRQ(ierr);
2825             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2826             ierr = PCSetUseAmat(pc,PETSC_TRUE);CHKERRQ(ierr);
2827           } else {
2828             ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
2829           }
2830           ierr = KSPSetFromOptions(kspC);CHKERRQ(ierr);
2831           ierr = PetscOptionsGetBool(NULL,((PetscObject)kspC)->prefix,"-preconditioned",&prec,NULL);CHKERRQ(ierr);
2832           if (prec)  {
2833             ierr = KSPGetPC(ksps[i],&pc);CHKERRQ(ierr);
2834             ierr = KSPSetPC(kspC,pc);CHKERRQ(ierr);
2835           }
2836           ierr = KSPSetOperators(kspC,F,pF);CHKERRQ(ierr);
2837           ierr = MatCreateVecs(F,&x,&y);CHKERRQ(ierr);
2838           ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2839           ierr = MatMult(F,x,y);CHKERRQ(ierr);
2840           ierr = KSPSolve(kspC,y,x);CHKERRQ(ierr);
2841           ierr = KSPDestroy(&kspC);CHKERRQ(ierr);
2842           ierr = MatDestroy(&F);CHKERRQ(ierr);
2843           ierr = VecDestroy(&x);CHKERRQ(ierr);
2844           ierr = VecDestroy(&y);CHKERRQ(ierr);
2845         }
2846       }
2847       ierr = PetscFree(ksps);CHKERRQ(ierr);
2848     }
2849   }
2850   /* return pointers for objects created */
2851   *fetidp_mat = newmat;
2852   *fetidp_pc  = newpc;
2853   PetscFunctionReturn(0);
2854 }
2855 
2856 /*@C
2857  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2858 
2859    Collective
2860 
2861    Input Parameters:
2862 +  pc - the BDDC preconditioning context (setup should have been called before)
2863 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2864 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2865 
2866    Output Parameters:
2867 +  fetidp_mat - shell FETI-DP matrix object
2868 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2869 
2870    Level: developer
2871 
2872    Notes:
2873      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2874 
2875 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2876 @*/
2877 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2878 {
2879   PetscErrorCode ierr;
2880 
2881   PetscFunctionBegin;
2882   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2883   if (pc->setupcalled) {
2884     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2885   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first");
2886   PetscFunctionReturn(0);
2887 }
2888 /* -------------------------------------------------------------------------- */
2889 /*MC
2890    PCBDDC - Balancing Domain Decomposition by Constraints.
2891 
2892    An implementation of the BDDC preconditioner based on
2893 
2894 .vb
2895    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2896    [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
2897    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2898    [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
2899 .ve
2900 
2901    The matrix to be preconditioned (Pmat) must be of type MATIS.
2902 
2903    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2904 
2905    It also works with unsymmetric and indefinite problems.
2906 
2907    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.
2908 
2909    Approximate local solvers are automatically adapted (see [1]) if the user has attached a nullspace object to the subdomain matrices, and informed BDDC of using approximate solvers (via the command line).
2910 
2911    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()
2912    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2913 
2914    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2915 
2916    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.
2917    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2918 
2919    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2920 
2921    Adaptive selection of primal constraints [4] is supported for SPD systems with high-contrast in the coefficients if MUMPS or MKL_PARDISO are present. Future versions of the code will also consider using PASTIX.
2922 
2923    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.
2924    Deluxe scaling is not supported yet for FETI-DP.
2925 
2926    Options Database Keys (some of them, run with -h for a complete list):
2927 
2928 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2929 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2930 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2931 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2932 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2933 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2934 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2935 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2936 .    -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)
2937 .    -pc_bddc_coarse_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)
2938 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2939 .    -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)
2940 .    -pc_bddc_adaptive_threshold <0.0> - when a value different than zero is specified, adaptive selection of constraints is performed on edges and faces (requires deluxe scaling and MUMPS or MKL_PARDISO installed)
2941 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2942 
2943    Options for Dirichlet, Neumann or coarse solver can be set with
2944 .vb
2945       -pc_bddc_dirichlet_
2946       -pc_bddc_neumann_
2947       -pc_bddc_coarse_
2948 .ve
2949    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2950 
2951    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2952 .vb
2953       -pc_bddc_dirichlet_lN_
2954       -pc_bddc_neumann_lN_
2955       -pc_bddc_coarse_lN_
2956 .ve
2957    Note that level number ranges from the finest (0) to the coarsest (N).
2958    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.
2959 .vb
2960      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2961 .ve
2962    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
2963 
2964    Level: intermediate
2965 
2966    Developer Notes:
2967 
2968    Contributed by Stefano Zampini
2969 
2970 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2971 M*/
2972 
2973 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2974 {
2975   PetscErrorCode      ierr;
2976   PC_BDDC             *pcbddc;
2977 
2978   PetscFunctionBegin;
2979   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2980   pc->data = (void*)pcbddc;
2981 
2982   /* create PCIS data structure */
2983   ierr = PCISCreate(pc);CHKERRQ(ierr);
2984 
2985   /* create local graph structure */
2986   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2987 
2988   /* BDDC nonzero defaults */
2989   pcbddc->use_local_adj             = PETSC_TRUE;
2990   pcbddc->use_vertices              = PETSC_TRUE;
2991   pcbddc->use_edges                 = PETSC_TRUE;
2992   pcbddc->symmetric_primal          = PETSC_TRUE;
2993   pcbddc->vertex_size               = 1;
2994   pcbddc->recompute_topography      = PETSC_TRUE;
2995   pcbddc->coarse_size               = -1;
2996   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2997   pcbddc->coarsening_ratio          = 8;
2998   pcbddc->coarse_eqs_per_proc       = 1;
2999   pcbddc->benign_compute_correction = PETSC_TRUE;
3000   pcbddc->nedfield                  = -1;
3001   pcbddc->nedglobal                 = PETSC_TRUE;
3002   pcbddc->graphmaxcount             = PETSC_MAX_INT;
3003   pcbddc->sub_schurs_layers         = -1;
3004   pcbddc->adaptive_threshold[0]     = 0.0;
3005   pcbddc->adaptive_threshold[1]     = 0.0;
3006 
3007   /* function pointers */
3008   pc->ops->apply               = PCApply_BDDC;
3009   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
3010   pc->ops->setup               = PCSetUp_BDDC;
3011   pc->ops->destroy             = PCDestroy_BDDC;
3012   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
3013   pc->ops->view                = PCView_BDDC;
3014   pc->ops->applyrichardson     = 0;
3015   pc->ops->applysymmetricleft  = 0;
3016   pc->ops->applysymmetricright = 0;
3017   pc->ops->presolve            = PCPreSolve_BDDC;
3018   pc->ops->postsolve           = PCPostSolve_BDDC;
3019   pc->ops->reset               = PCReset_BDDC;
3020 
3021   /* composing function */
3022   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
3023   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
3024   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
3025   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3026   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3027   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesLocalIS_C",PCBDDCGetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3028   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesIS_C",PCBDDCGetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3029   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
3030   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
3031   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
3032   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
3033   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3034   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3035   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3036   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3037   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3038   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3039   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3040   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3041   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
3042   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
3043   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
3044   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
3045   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
3046   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
3047   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
3048   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
3049   PetscFunctionReturn(0);
3050 }
3051 
3052 /*@C
3053  PCBDDCInitializePackage - This function initializes everything in the PCBDDC package. It is called
3054     from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to PCCreate_BDDC()
3055     when using static libraries.
3056 
3057  Level: developer
3058 
3059  .keywords: PC, PCBDDC, initialize, package
3060  .seealso: PetscInitialize()
3061 @*/
3062 PetscErrorCode PCBDDCInitializePackage(void)
3063 {
3064   PetscErrorCode ierr;
3065   int            i;
3066 
3067   PetscFunctionBegin;
3068   if (PCBDDCPackageInitialized) PetscFunctionReturn(0);
3069   PCBDDCPackageInitialized = PETSC_TRUE;
3070   ierr = PetscRegisterFinalize(PCBDDCFinalizePackage);CHKERRQ(ierr);
3071 
3072   /* general events */
3073   ierr = PetscLogEventRegister("PCBDDCTopo",PC_CLASSID,&PC_BDDC_Topology[0]);CHKERRQ(ierr);
3074   ierr = PetscLogEventRegister("PCBDDCLKSP",PC_CLASSID,&PC_BDDC_LocalSolvers[0]);CHKERRQ(ierr);
3075   ierr = PetscLogEventRegister("PCBDDCLWor",PC_CLASSID,&PC_BDDC_LocalWork[0]);CHKERRQ(ierr);
3076   ierr = PetscLogEventRegister("PCBDDCCorr",PC_CLASSID,&PC_BDDC_CorrectionSetUp[0]);CHKERRQ(ierr);
3077   ierr = PetscLogEventRegister("PCBDDCCSet",PC_CLASSID,&PC_BDDC_CoarseSetUp[0]);CHKERRQ(ierr);
3078   ierr = PetscLogEventRegister("PCBDDCCKSP",PC_CLASSID,&PC_BDDC_CoarseSolver[0]);CHKERRQ(ierr);
3079   ierr = PetscLogEventRegister("PCBDDCAdap",PC_CLASSID,&PC_BDDC_AdaptiveSetUp[0]);CHKERRQ(ierr);
3080   ierr = PetscLogEventRegister("PCBDDCScal",PC_CLASSID,&PC_BDDC_Scaling[0]);CHKERRQ(ierr);
3081   ierr = PetscLogEventRegister("PCBDDCSchr",PC_CLASSID,&PC_BDDC_Schurs[0]);CHKERRQ(ierr);
3082   for (i=1;i<PETSC_PCBDDC_MAXLEVELS;i++) {
3083     char ename[32];
3084 
3085     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCTopo l%02d",i);CHKERRQ(ierr);
3086     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Topology[i]);CHKERRQ(ierr);
3087     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLKSP l%02d",i);CHKERRQ(ierr);
3088     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalSolvers[i]);CHKERRQ(ierr);
3089     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLWor l%02d",i);CHKERRQ(ierr);
3090     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalWork[i]);CHKERRQ(ierr);
3091     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCorr l%02d",i);CHKERRQ(ierr);
3092     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CorrectionSetUp[i]);CHKERRQ(ierr);
3093     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCSet l%02d",i);CHKERRQ(ierr);
3094     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSetUp[i]);CHKERRQ(ierr);
3095     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCKSP l%02d",i);CHKERRQ(ierr);
3096     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSolver[i]);CHKERRQ(ierr);
3097     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCAdap l%02d",i);CHKERRQ(ierr);
3098     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_AdaptiveSetUp[i]);CHKERRQ(ierr);
3099     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCScal l%02d",i);CHKERRQ(ierr);
3100     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Scaling[i]);CHKERRQ(ierr);
3101     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCSchr l%02d",i);CHKERRQ(ierr);
3102     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Schurs[i]);CHKERRQ(ierr);
3103   }
3104   PetscFunctionReturn(0);
3105 }
3106 
3107 /*@C
3108  PCBDDCFinalizePackage - This function frees everything from the PCBDDC package. It is
3109     called from PetscFinalize() automatically.
3110 
3111  Level: developer
3112 
3113  .keywords: Petsc, destroy, package
3114  .seealso: PetscFinalize()
3115 @*/
3116 PetscErrorCode PCBDDCFinalizePackage(void)
3117 {
3118   PetscFunctionBegin;
3119   PCBDDCPackageInitialized = PETSC_FALSE;
3120   PetscFunctionReturn(0);
3121 }
3122