xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 5a856986583887c326abe5dfd149e8184a29cd80)
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 = PetscArraycmp(xadj,mat_graph->xadj,nvtxs+1,&same_data);CHKERRQ(ierr);
1083       if (same_data) {
1084         ierr = PetscArraycmp(adjncy,mat_graph->adjncy,xadj[nvtxs],&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 = PetscArraycpy(mat_graph->xadj,xadj,nvtxs+1);CHKERRQ(ierr);
1096       ierr = PetscArraycpy(mat_graph->adjncy,adjncy,xadj[nvtxs]);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      iscg = PETSC_FALSE, 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 isgroppcg, ispipecg, ispipelcg, ispipecgrr;
1329 
1330     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1331     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1332     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1333     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipelcg);CHKERRQ(ierr);
1334     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1335     iscg = (PetscBool)(iscg || isgroppcg || ispipecg || ispipelcg || ispipecgrr);
1336     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || !iscg || pc->mat != pc->pmat) {
1337       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1338     }
1339   }
1340   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || pc->mat != pc->pmat) {
1341     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1342   }
1343 
1344   /* Creates parallel work vectors used in presolve */
1345   if (!pcbddc->original_rhs) {
1346     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1347   }
1348   if (!pcbddc->temp_solution) {
1349     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1350   }
1351 
1352   pcbddc->temp_solution_used = PETSC_FALSE;
1353   if (x) {
1354     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1355     used_vec = x;
1356   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1357     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1358     used_vec = pcbddc->temp_solution;
1359     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1360     pcbddc->temp_solution_used = PETSC_TRUE;
1361     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1362     save_rhs = PETSC_FALSE;
1363     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1364   }
1365 
1366   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1367   if (ksp) {
1368     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1369     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1370     if (!pcbddc->ksp_guess_nonzero) {
1371       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1372     }
1373   }
1374 
1375   pcbddc->rhs_change = PETSC_FALSE;
1376   /* Take into account zeroed rows -> change rhs and store solution removed */
1377   if (rhs && pcbddc->eliminate_dirdofs) {
1378     IS dirIS = NULL;
1379 
1380     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1381     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1382     if (dirIS) {
1383       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1384       PetscInt          dirsize,i,*is_indices;
1385       PetscScalar       *array_x;
1386       const PetscScalar *array_diagonal;
1387 
1388       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1389       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1390       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1391       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1392       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1393       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1394       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1395       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1396       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1397       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1398       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1399       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1400       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1401       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1402       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1403       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1404       pcbddc->rhs_change = PETSC_TRUE;
1405       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1406     }
1407   }
1408 
1409   /* remove the computed solution or the initial guess from the rhs */
1410   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1411     /* save the original rhs */
1412     if (save_rhs) {
1413       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1414       save_rhs = PETSC_FALSE;
1415     }
1416     pcbddc->rhs_change = PETSC_TRUE;
1417     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1418     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1419     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1420     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1421     pcbddc->temp_solution_used = PETSC_TRUE;
1422     if (ksp) {
1423       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1424     }
1425   }
1426   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1427 
1428   /* compute initial vector in benign space if needed
1429      and remove non-benign solution from the rhs */
1430   benign_correction_computed = PETSC_FALSE;
1431   if (rhs && pcbddc->benign_compute_correction && (pcbddc->benign_have_null || pcbddc->benign_apply_coarse_only)) {
1432     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1433        Recursively apply BDDC in the multilevel case */
1434     if (!pcbddc->benign_vec) {
1435       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1436     }
1437     /* keep applying coarse solver unless we no longer have benign subdomains */
1438     pcbddc->benign_apply_coarse_only = pcbddc->benign_have_null ? PETSC_TRUE : PETSC_FALSE;
1439     if (!pcbddc->benign_skip_correction) {
1440       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1441       benign_correction_computed = PETSC_TRUE;
1442       if (pcbddc->temp_solution_used) {
1443         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1444       }
1445       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1446       /* store the original rhs if not done earlier */
1447       if (save_rhs) {
1448         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1449       }
1450       if (pcbddc->rhs_change) {
1451         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1452       } else {
1453         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1454       }
1455       pcbddc->rhs_change = PETSC_TRUE;
1456     }
1457     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1458   } else {
1459     ierr = VecDestroy(&pcbddc->benign_vec);CHKERRQ(ierr);
1460   }
1461 
1462   /* dbg output */
1463   if (pcbddc->dbg_flag && benign_correction_computed) {
1464     Vec v;
1465 
1466     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1467     if (pcbddc->ChangeOfBasisMatrix) {
1468       ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1469     } else {
1470       ierr = VecCopy(rhs,v);CHKERRQ(ierr);
1471     }
1472     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1473     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1474     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,pcbddc->dbg_viewer);CHKERRQ(ierr);
1475     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1476     ierr = VecDestroy(&v);CHKERRQ(ierr);
1477   }
1478 
1479   /* set initial guess if using PCG */
1480   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1481   if (x && pcbddc->use_exact_dirichlet_trick) {
1482     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1483     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1484       if (benign_correction_computed) { /* we have already saved the changed rhs */
1485         ierr = VecLockReadPop(pcis->vec1_global);CHKERRQ(ierr);
1486       } else {
1487         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1488       }
1489       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1490       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1491     } else {
1492       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1493       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1494     }
1495     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1496     ierr = KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);CHKERRQ(ierr);
1497     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1498       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1499       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1500       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1501       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1502     } else {
1503       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1504       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1505     }
1506     if (ksp) {
1507       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1508     }
1509     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1510   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1511     ierr = VecLockReadPop(pcis->vec1_global);CHKERRQ(ierr);
1512   }
1513   PetscFunctionReturn(0);
1514 }
1515 
1516 /*
1517    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1518                      approach has been selected. Also, restores rhs to its original state.
1519 
1520    Input Parameter:
1521 +  pc - the preconditioner contex
1522 
1523    Application Interface Routine: PCPostSolve()
1524 
1525    Notes:
1526      The interface routine PCPostSolve() is not usually called directly by
1527      the user, but instead is called by KSPSolve().
1528 */
1529 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1530 {
1531   PetscErrorCode ierr;
1532   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1533 
1534   PetscFunctionBegin;
1535   /* add solution removed in presolve */
1536   if (x && pcbddc->rhs_change) {
1537     if (pcbddc->temp_solution_used) {
1538       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1539     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1540       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1541     }
1542     /* restore to original state (not for FETI-DP) */
1543     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1544   }
1545 
1546   /* restore rhs to its original state (not needed for FETI-DP) */
1547   if (rhs && pcbddc->rhs_change) {
1548     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1549     pcbddc->rhs_change = PETSC_FALSE;
1550   }
1551   /* restore ksp guess state */
1552   if (ksp) {
1553     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1554     /* reset flag for exact dirichlet trick */
1555     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1556   }
1557   PetscFunctionReturn(0);
1558 }
1559 
1560 /*
1561    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1562                   by setting data structures and options.
1563 
1564    Input Parameter:
1565 +  pc - the preconditioner context
1566 
1567    Application Interface Routine: PCSetUp()
1568 
1569    Notes:
1570      The interface routine PCSetUp() is not usually called directly by
1571      the user, but instead is called by PCApply() if necessary.
1572 */
1573 PetscErrorCode PCSetUp_BDDC(PC pc)
1574 {
1575   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1576   PCBDDCSubSchurs sub_schurs;
1577   Mat_IS*         matis;
1578   MatNullSpace    nearnullspace;
1579   Mat             lA;
1580   IS              lP,zerodiag = NULL;
1581   PetscInt        nrows,ncols;
1582   PetscMPIInt     size;
1583   PetscBool       computesubschurs;
1584   PetscBool       computeconstraintsmatrix;
1585   PetscBool       new_nearnullspace_provided,ismatis,rl;
1586   PetscErrorCode  ierr;
1587 
1588   PetscFunctionBegin;
1589   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1590   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1591   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1592   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1593   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
1594 
1595   matis = (Mat_IS*)pc->pmat->data;
1596   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1597   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1598      Also, BDDC builds its own KSP for the Dirichlet problem */
1599   rl = pcbddc->recompute_topography;
1600   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) rl = PETSC_TRUE;
1601   ierr = MPIU_Allreduce(&rl,&pcbddc->recompute_topography,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1602   if (pcbddc->recompute_topography) {
1603     pcbddc->graphanalyzed    = PETSC_FALSE;
1604     computeconstraintsmatrix = PETSC_TRUE;
1605   } else {
1606     computeconstraintsmatrix = PETSC_FALSE;
1607   }
1608 
1609   /* check parameters' compatibility */
1610   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1611   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1612   pcbddc->use_deluxe_scaling   = (PetscBool)(pcbddc->use_deluxe_scaling && size > 1);
1613   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_selection && size > 1);
1614   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1615   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1616 
1617   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1618 
1619   /* activate all connected components if the netflux has been requested */
1620   if (pcbddc->compute_nonetflux) {
1621     pcbddc->use_vertices = PETSC_TRUE;
1622     pcbddc->use_edges    = PETSC_TRUE;
1623     pcbddc->use_faces    = PETSC_TRUE;
1624   }
1625 
1626   /* Get stdout for dbg */
1627   if (pcbddc->dbg_flag) {
1628     if (!pcbddc->dbg_viewer) {
1629       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1630     }
1631     ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1632     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1633   }
1634 
1635   /* process topology information */
1636   ierr = PetscLogEventBegin(PC_BDDC_Topology[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1637   if (pcbddc->recompute_topography) {
1638     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1639     if (pcbddc->discretegradient) {
1640       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1641     }
1642   }
1643   if (pcbddc->corner_selected) pcbddc->use_vertices = PETSC_TRUE;
1644 
1645   /* change basis if requested by the user */
1646   if (pcbddc->user_ChangeOfBasisMatrix) {
1647     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1648     pcbddc->use_change_of_basis = PETSC_FALSE;
1649     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1650   } else {
1651     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1652     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1653     pcbddc->local_mat = matis->A;
1654   }
1655 
1656   /*
1657      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1658      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1659   */
1660   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1661   if (pcbddc->benign_saddle_point) {
1662     PC_IS* pcis = (PC_IS*)pc->data;
1663 
1664     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1665     /* detect local saddle point and change the basis in pcbddc->local_mat */
1666     ierr = PCBDDCBenignDetectSaddlePoint(pc,(PetscBool)(!pcbddc->recompute_topography),&zerodiag);CHKERRQ(ierr);
1667     /* pop B0 mat from local mat */
1668     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1669     /* give pcis a hint to not reuse submatrices during PCISCreate */
1670     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1671       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1672         pcis->reusesubmatrices = PETSC_FALSE;
1673       } else {
1674         pcis->reusesubmatrices = PETSC_TRUE;
1675       }
1676     } else {
1677       pcis->reusesubmatrices = PETSC_FALSE;
1678     }
1679   }
1680 
1681   /* propagate relevant information */
1682   if (matis->A->symmetric_set) {
1683     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1684   }
1685   if (matis->A->spd_set) {
1686     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1687   }
1688 
1689   /* Set up all the "iterative substructuring" common block without computing solvers */
1690   {
1691     Mat temp_mat;
1692 
1693     temp_mat = matis->A;
1694     matis->A = pcbddc->local_mat;
1695     ierr = PCISSetUp(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1696     pcbddc->local_mat = matis->A;
1697     matis->A = temp_mat;
1698   }
1699 
1700   /* Analyze interface */
1701   if (!pcbddc->graphanalyzed) {
1702     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1703     computeconstraintsmatrix = PETSC_TRUE;
1704     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1705       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1706     }
1707     if (pcbddc->compute_nonetflux) {
1708       MatNullSpace nnfnnsp;
1709 
1710       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1711       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1712       /* TODO what if a nearnullspace is already attached? */
1713       if (nnfnnsp) {
1714         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1715         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1716       }
1717     }
1718   }
1719   ierr = PetscLogEventEnd(PC_BDDC_Topology[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1720 
1721   /* check existence of a divergence free extension, i.e.
1722      b(v_I,p_0) = 0 for all v_I (raise error if not).
1723      Also, check that PCBDDCBenignGetOrSetP0 works */
1724   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1725     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1726   }
1727   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1728 
1729   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1730   if (computesubschurs && pcbddc->recompute_topography) {
1731     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1732   }
1733   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1734   if (!pcbddc->use_deluxe_scaling) {
1735     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1736   }
1737 
1738   /* finish setup solvers and do adaptive selection of constraints */
1739   sub_schurs = pcbddc->sub_schurs;
1740   if (sub_schurs && sub_schurs->schur_explicit) {
1741     if (computesubschurs) {
1742       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1743     }
1744     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1745   } else {
1746     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1747     if (computesubschurs) {
1748       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1749     }
1750   }
1751   if (pcbddc->adaptive_selection) {
1752     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1753     computeconstraintsmatrix = PETSC_TRUE;
1754   }
1755 
1756   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1757   new_nearnullspace_provided = PETSC_FALSE;
1758   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1759   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1760     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1761       new_nearnullspace_provided = PETSC_TRUE;
1762     } else {
1763       /* determine if the two nullspaces are different (should be lightweight) */
1764       if (nearnullspace != pcbddc->onearnullspace) {
1765         new_nearnullspace_provided = PETSC_TRUE;
1766       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1767         PetscInt         i;
1768         const Vec        *nearnullvecs;
1769         PetscObjectState state;
1770         PetscInt         nnsp_size;
1771         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1772         for (i=0;i<nnsp_size;i++) {
1773           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1774           if (pcbddc->onearnullvecs_state[i] != state) {
1775             new_nearnullspace_provided = PETSC_TRUE;
1776             break;
1777           }
1778         }
1779       }
1780     }
1781   } else {
1782     if (!nearnullspace) { /* both nearnullspaces are null */
1783       new_nearnullspace_provided = PETSC_FALSE;
1784     } else { /* nearnullspace attached later */
1785       new_nearnullspace_provided = PETSC_TRUE;
1786     }
1787   }
1788 
1789   /* Setup constraints and related work vectors */
1790   /* reset primal space flags */
1791   ierr = PetscLogEventBegin(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1792   pcbddc->new_primal_space = PETSC_FALSE;
1793   pcbddc->new_primal_space_local = PETSC_FALSE;
1794   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1795     /* It also sets the primal space flags */
1796     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1797   }
1798   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1799   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1800 
1801   if (pcbddc->use_change_of_basis) {
1802     PC_IS *pcis = (PC_IS*)(pc->data);
1803 
1804     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1805     if (pcbddc->benign_change) {
1806       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1807       /* pop B0 from pcbddc->local_mat */
1808       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1809     }
1810     /* get submatrices */
1811     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1812     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1813     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1814     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1815     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1816     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1817     /* set flag in pcis to not reuse submatrices during PCISCreate */
1818     pcis->reusesubmatrices = PETSC_FALSE;
1819   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1820     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1821     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1822     pcbddc->local_mat = matis->A;
1823   }
1824 
1825   /* interface pressure block row for B_C */
1826   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1827   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1828   if (lA && lP) {
1829     PC_IS*    pcis = (PC_IS*)pc->data;
1830     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1831     PetscBool issym;
1832     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1833     if (issym) {
1834       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1835       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1836       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1837       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1838     } else {
1839       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1840       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1841       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1842       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1843     }
1844     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1845     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1846     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1847     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1848     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1849     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1850     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1851     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1852   }
1853   ierr = PetscLogEventEnd(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1854 
1855   /* SetUp coarse and local Neumann solvers */
1856   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1857   /* SetUp Scaling operator */
1858   if (pcbddc->use_deluxe_scaling) {
1859     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1860   }
1861 
1862   /* mark topography as done */
1863   pcbddc->recompute_topography = PETSC_FALSE;
1864 
1865   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1866   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1867 
1868   if (pcbddc->dbg_flag) {
1869     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1870     ierr = PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1871   }
1872   PetscFunctionReturn(0);
1873 }
1874 
1875 /*
1876    PCApply_BDDC - Applies the BDDC operator to a vector.
1877 
1878    Input Parameters:
1879 +  pc - the preconditioner context
1880 -  r - input vector (global)
1881 
1882    Output Parameter:
1883 .  z - output vector (global)
1884 
1885    Application Interface Routine: PCApply()
1886  */
1887 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1888 {
1889   PC_IS             *pcis = (PC_IS*)(pc->data);
1890   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1891   Mat               lA = NULL;
1892   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1893   PetscErrorCode    ierr;
1894   const PetscScalar one = 1.0;
1895   const PetscScalar m_one = -1.0;
1896   const PetscScalar zero = 0.0;
1897 /* This code is similar to that provided in nn.c for PCNN
1898    NN interface preconditioner changed to BDDC
1899    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1900 
1901   PetscFunctionBegin;
1902   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1903   if (pcbddc->switch_static) {
1904     ierr = MatISGetLocalMat(pc->useAmat ? pc->mat : pc->pmat,&lA);CHKERRQ(ierr);
1905   }
1906 
1907   if (pcbddc->ChangeOfBasisMatrix) {
1908     Vec swap;
1909 
1910     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1911     swap = pcbddc->work_change;
1912     pcbddc->work_change = r;
1913     r = swap;
1914     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1915     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1916       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1917       ierr = VecLockReadPush(pcis->vec1_global);CHKERRQ(ierr);
1918     }
1919   }
1920   if (pcbddc->benign_have_null) { /* get p0 from r */
1921     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1922   }
1923   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1924     ierr = VecCopy(r,z);CHKERRQ(ierr);
1925     /* First Dirichlet solve */
1926     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1927     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1928     /*
1929       Assembling right hand side for BDDC operator
1930       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1931       - pcis->vec1_B the interface part of the global vector z
1932     */
1933     if (n_D) {
1934       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1935       ierr = KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);CHKERRQ(ierr);
1936       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1937       if (pcbddc->switch_static) {
1938         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1939         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1940         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1941         if (!pcbddc->switch_static_change) {
1942           ierr = MatMult(lA,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1943         } else {
1944           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1945           ierr = MatMult(lA,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1946           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1947         }
1948         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1949         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1950         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1951         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1952       } else {
1953         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1954       }
1955     } else {
1956       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1957     }
1958     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1959     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1960     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1961   } else {
1962     if (!pcbddc->benign_apply_coarse_only) {
1963       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1964     }
1965   }
1966 
1967   /* Apply interface preconditioner
1968      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1969   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1970 
1971   /* Apply transpose of partition of unity operator */
1972   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1973 
1974   /* Second Dirichlet solve and assembling of output */
1975   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1976   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1977   if (n_B) {
1978     if (pcbddc->switch_static) {
1979       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1980       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1981       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1982       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1983       if (!pcbddc->switch_static_change) {
1984         ierr = MatMult(lA,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1985       } else {
1986         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1987         ierr = MatMult(lA,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1988         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1989       }
1990       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1991       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1992     } else {
1993       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1994     }
1995   } else if (pcbddc->switch_static) { /* n_B is zero */
1996     if (!pcbddc->switch_static_change) {
1997       ierr = MatMult(lA,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1998     } else {
1999       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2000       ierr = MatMult(lA,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2001       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2002     }
2003   }
2004   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2005   ierr = KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec4_D);CHKERRQ(ierr);
2006 
2007   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2008     if (pcbddc->switch_static) {
2009       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2010     } else {
2011       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2012     }
2013     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2014     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2015   } else {
2016     if (pcbddc->switch_static) {
2017       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2018     } else {
2019       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2020     }
2021     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2022     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2023   }
2024   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2025     if (pcbddc->benign_apply_coarse_only) {
2026       ierr = PetscArrayzero(pcbddc->benign_p0,pcbddc->benign_n);CHKERRQ(ierr);
2027     }
2028     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2029   }
2030 
2031   if (pcbddc->ChangeOfBasisMatrix) {
2032     pcbddc->work_change = r;
2033     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2034     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2035   }
2036   PetscFunctionReturn(0);
2037 }
2038 
2039 /*
2040    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
2041 
2042    Input Parameters:
2043 +  pc - the preconditioner context
2044 -  r - input vector (global)
2045 
2046    Output Parameter:
2047 .  z - output vector (global)
2048 
2049    Application Interface Routine: PCApplyTranspose()
2050  */
2051 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
2052 {
2053   PC_IS             *pcis = (PC_IS*)(pc->data);
2054   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
2055   Mat               lA = NULL;
2056   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
2057   PetscErrorCode    ierr;
2058   const PetscScalar one = 1.0;
2059   const PetscScalar m_one = -1.0;
2060   const PetscScalar zero = 0.0;
2061 
2062   PetscFunctionBegin;
2063   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
2064   if (pcbddc->switch_static) {
2065     ierr = MatISGetLocalMat(pc->useAmat ? pc->mat : pc->pmat,&lA);CHKERRQ(ierr);
2066   }
2067   if (pcbddc->ChangeOfBasisMatrix) {
2068     Vec swap;
2069 
2070     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
2071     swap = pcbddc->work_change;
2072     pcbddc->work_change = r;
2073     r = swap;
2074     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
2075     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
2076       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
2077       ierr = VecLockReadPush(pcis->vec1_global);CHKERRQ(ierr);
2078     }
2079   }
2080   if (pcbddc->benign_have_null) { /* get p0 from r */
2081     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
2082   }
2083   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2084     ierr = VecCopy(r,z);CHKERRQ(ierr);
2085     /* First Dirichlet solve */
2086     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2087     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2088     /*
2089       Assembling right hand side for BDDC operator
2090       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
2091       - pcis->vec1_B the interface part of the global vector z
2092     */
2093     if (n_D) {
2094       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
2095       ierr = KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);CHKERRQ(ierr);
2096       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
2097       if (pcbddc->switch_static) {
2098         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
2099         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2100         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2101         if (!pcbddc->switch_static_change) {
2102           ierr = MatMultTranspose(lA,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2103         } else {
2104           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2105           ierr = MatMultTranspose(lA,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2106           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2107         }
2108         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2109         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2110         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2111         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2112       } else {
2113         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
2114       }
2115     } else {
2116       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
2117     }
2118     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2119     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2120     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
2121   } else {
2122     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
2123   }
2124 
2125   /* Apply interface preconditioner
2126      input/output vecs: pcis->vec1_B and pcis->vec1_D */
2127   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
2128 
2129   /* Apply transpose of partition of unity operator */
2130   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2131 
2132   /* Second Dirichlet solve and assembling of output */
2133   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2134   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2135   if (n_B) {
2136     if (pcbddc->switch_static) {
2137       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2138       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2139       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2140       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2141       if (!pcbddc->switch_static_change) {
2142         ierr = MatMultTranspose(lA,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2143       } else {
2144         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2145         ierr = MatMultTranspose(lA,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2146         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2147       }
2148       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2149       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2150     } else {
2151       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2152     }
2153   } else if (pcbddc->switch_static) { /* n_B is zero */
2154     if (!pcbddc->switch_static_change) {
2155       ierr = MatMultTranspose(lA,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2156     } else {
2157       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2158       ierr = MatMultTranspose(lA,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2159       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2160     }
2161   }
2162   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2163   ierr = KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec4_D);CHKERRQ(ierr);
2164   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2165     if (pcbddc->switch_static) {
2166       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2167     } else {
2168       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2169     }
2170     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2171     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2172   } else {
2173     if (pcbddc->switch_static) {
2174       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2175     } else {
2176       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2177     }
2178     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2179     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2180   }
2181   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2182     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2183   }
2184   if (pcbddc->ChangeOfBasisMatrix) {
2185     pcbddc->work_change = r;
2186     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2187     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2188   }
2189   PetscFunctionReturn(0);
2190 }
2191 
2192 PetscErrorCode PCReset_BDDC(PC pc)
2193 {
2194   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2195   PC_IS          *pcis = (PC_IS*)pc->data;
2196   KSP            kspD,kspR,kspC;
2197   PetscErrorCode ierr;
2198 
2199   PetscFunctionBegin;
2200   /* free BDDC custom data  */
2201   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2202   /* destroy objects related to topography */
2203   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2204   /* destroy objects for scaling operator */
2205   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2206   /* free solvers stuff */
2207   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2208   /* free global vectors needed in presolve */
2209   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2210   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2211   /* free data created by PCIS */
2212   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2213 
2214   /* restore defaults */
2215   kspD = pcbddc->ksp_D;
2216   kspR = pcbddc->ksp_R;
2217   kspC = pcbddc->coarse_ksp;
2218   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2219   pcis->n_neigh                     = -1;
2220   pcis->scaling_factor              = 1.0;
2221   pcis->reusesubmatrices            = PETSC_TRUE;
2222   pcbddc->use_local_adj             = PETSC_TRUE;
2223   pcbddc->use_vertices              = PETSC_TRUE;
2224   pcbddc->use_edges                 = PETSC_TRUE;
2225   pcbddc->symmetric_primal          = PETSC_TRUE;
2226   pcbddc->vertex_size               = 1;
2227   pcbddc->recompute_topography      = PETSC_TRUE;
2228   pcbddc->coarse_size               = -1;
2229   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2230   pcbddc->coarsening_ratio          = 8;
2231   pcbddc->coarse_eqs_per_proc       = 1;
2232   pcbddc->benign_compute_correction = PETSC_TRUE;
2233   pcbddc->nedfield                  = -1;
2234   pcbddc->nedglobal                 = PETSC_TRUE;
2235   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2236   pcbddc->sub_schurs_layers         = -1;
2237   pcbddc->ksp_D                     = kspD;
2238   pcbddc->ksp_R                     = kspR;
2239   pcbddc->coarse_ksp                = kspC;
2240   PetscFunctionReturn(0);
2241 }
2242 
2243 PetscErrorCode PCDestroy_BDDC(PC pc)
2244 {
2245   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2246   PetscErrorCode ierr;
2247 
2248   PetscFunctionBegin;
2249   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2250   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2251   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2252   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2253   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2254   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2255   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2256   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2257   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2258   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2259   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2260   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2261   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2262   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2263   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2264   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2265   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2266   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2267   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2268   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2269   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2270   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2271   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2272   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2273   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2274   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2275   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2276   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2277   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2278   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2279   PetscFunctionReturn(0);
2280 }
2281 
2282 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2283 {
2284   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2285   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2286   PetscErrorCode ierr;
2287 
2288   PetscFunctionBegin;
2289   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2290   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2291   ierr = PetscArraycpy(mat_graph->coords,coords,nloc*dim);CHKERRQ(ierr);
2292   mat_graph->cnloc = nloc;
2293   mat_graph->cdim  = dim;
2294   mat_graph->cloc  = PETSC_FALSE;
2295   /* flg setup */
2296   pcbddc->recompute_topography = PETSC_TRUE;
2297   pcbddc->corner_selected = PETSC_FALSE;
2298   PetscFunctionReturn(0);
2299 }
2300 
2301 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2302 {
2303   PetscFunctionBegin;
2304   *change = PETSC_TRUE;
2305   PetscFunctionReturn(0);
2306 }
2307 
2308 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2309 {
2310   FETIDPMat_ctx  mat_ctx;
2311   Vec            work;
2312   PC_IS*         pcis;
2313   PC_BDDC*       pcbddc;
2314   PetscErrorCode ierr;
2315 
2316   PetscFunctionBegin;
2317   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2318   pcis = (PC_IS*)mat_ctx->pc->data;
2319   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2320 
2321   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2322   /* copy rhs since we may change it during PCPreSolve_BDDC */
2323   if (!pcbddc->original_rhs) {
2324     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2325   }
2326   if (mat_ctx->rhs_flip) {
2327     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2328   } else {
2329     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2330   }
2331   if (mat_ctx->g2g_p) {
2332     /* interface pressure rhs */
2333     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2334     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2335     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2336     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2337     if (!mat_ctx->rhs_flip) {
2338       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2339     }
2340   }
2341   /*
2342      change of basis for physical rhs if needed
2343      It also changes the rhs in case of dirichlet boundaries
2344   */
2345   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2346   if (pcbddc->ChangeOfBasisMatrix) {
2347     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2348     work = pcbddc->work_change;
2349    } else {
2350     work = pcbddc->original_rhs;
2351   }
2352   /* store vectors for computation of fetidp final solution */
2353   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2354   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2355   /* scale rhs since it should be unassembled */
2356   /* TODO use counter scaling? (also below) */
2357   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2358   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2359   /* Apply partition of unity */
2360   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2361   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2362   if (!pcbddc->switch_static) {
2363     /* compute partially subassembled Schur complement right-hand side */
2364     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2365     /* Cannot propagate up error in KSPSolve() because there is no access to the PC */
2366     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2367     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2368     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2369     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2370     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2371     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2372     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2373     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2374     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2375   }
2376   /* BDDC rhs */
2377   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2378   if (pcbddc->switch_static) {
2379     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2380   }
2381   /* apply BDDC */
2382   ierr = PetscArrayzero(pcbddc->benign_p0,pcbddc->benign_n);CHKERRQ(ierr);
2383   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2384   ierr = PetscArrayzero(pcbddc->benign_p0,pcbddc->benign_n);CHKERRQ(ierr);
2385 
2386   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2387   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2388   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2389   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2390   /* Add contribution to interface pressures */
2391   if (mat_ctx->l2g_p) {
2392     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2393     if (pcbddc->switch_static) {
2394       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2395     }
2396     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2397     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2398   }
2399   PetscFunctionReturn(0);
2400 }
2401 
2402 /*@
2403  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2404 
2405    Collective
2406 
2407    Input Parameters:
2408 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2409 -  standard_rhs    - the right-hand side of the original linear system
2410 
2411    Output Parameters:
2412 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2413 
2414    Level: developer
2415 
2416    Notes:
2417 
2418 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2419 @*/
2420 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2421 {
2422   FETIDPMat_ctx  mat_ctx;
2423   PetscErrorCode ierr;
2424 
2425   PetscFunctionBegin;
2426   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2427   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2428   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2429   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2430   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2431   PetscFunctionReturn(0);
2432 }
2433 
2434 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2435 {
2436   FETIDPMat_ctx  mat_ctx;
2437   PC_IS*         pcis;
2438   PC_BDDC*       pcbddc;
2439   PetscErrorCode ierr;
2440   Vec            work;
2441 
2442   PetscFunctionBegin;
2443   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2444   pcis = (PC_IS*)mat_ctx->pc->data;
2445   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2446 
2447   /* apply B_delta^T */
2448   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2449   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2450   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2451   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2452   if (mat_ctx->l2g_p) {
2453     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2454     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2455     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2456   }
2457 
2458   /* compute rhs for BDDC application */
2459   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2460   if (pcbddc->switch_static) {
2461     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2462     if (mat_ctx->l2g_p) {
2463       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2464       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2465     }
2466   }
2467 
2468   /* apply BDDC */
2469   ierr = PetscArrayzero(pcbddc->benign_p0,pcbddc->benign_n);CHKERRQ(ierr);
2470   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2471 
2472   /* put values into global vector */
2473   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2474   else work = standard_sol;
2475   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2476   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2477   if (!pcbddc->switch_static) {
2478     /* compute values into the interior if solved for the partially subassembled Schur complement */
2479     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2480     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2481     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2482     /* Cannot propagate up error in KSPSolve() because there is no access to the PC */
2483   }
2484 
2485   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2486   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2487   /* add p0 solution to final solution */
2488   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2489   if (pcbddc->ChangeOfBasisMatrix) {
2490     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2491   }
2492   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2493   if (mat_ctx->g2g_p) {
2494     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2495     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2496   }
2497   PetscFunctionReturn(0);
2498 }
2499 
2500 static PetscErrorCode PCView_BDDCIPC(PC pc, PetscViewer viewer)
2501 {
2502   PetscErrorCode ierr;
2503   BDDCIPC_ctx    bddcipc_ctx;
2504   PetscBool      isascii;
2505 
2506   PetscFunctionBegin;
2507   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2508   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
2509   if (isascii) {
2510     ierr = PetscViewerASCIIPrintf(viewer,"BDDC interface preconditioner\n");CHKERRQ(ierr);
2511   }
2512   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2513   ierr = PCView(bddcipc_ctx->bddc,viewer);CHKERRQ(ierr);
2514   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2515   PetscFunctionReturn(0);
2516 }
2517 
2518 static PetscErrorCode PCSetUp_BDDCIPC(PC pc)
2519 {
2520   PetscErrorCode ierr;
2521   BDDCIPC_ctx    bddcipc_ctx;
2522   PetscBool      isbddc;
2523   Vec            vv;
2524   IS             is;
2525   PC_IS          *pcis;
2526 
2527   PetscFunctionBegin;
2528   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2529   ierr = PetscObjectTypeCompare((PetscObject)bddcipc_ctx->bddc,PCBDDC,&isbddc);CHKERRQ(ierr);
2530   if (!isbddc) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid type %s. Must be of type bddc",((PetscObject)bddcipc_ctx->bddc)->type_name);
2531   ierr = PCSetUp(bddcipc_ctx->bddc);CHKERRQ(ierr);
2532 
2533   /* create interface scatter */
2534   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2535   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2536   ierr = MatCreateVecs(pc->pmat,&vv,NULL);CHKERRQ(ierr);
2537   ierr = ISRenumber(pcis->is_B_global,NULL,NULL,&is);CHKERRQ(ierr);
2538   ierr = VecScatterCreate(vv,is,pcis->vec1_B,NULL,&bddcipc_ctx->g2l);CHKERRQ(ierr);
2539   ierr = ISDestroy(&is);CHKERRQ(ierr);
2540   ierr = VecDestroy(&vv);CHKERRQ(ierr);
2541   PetscFunctionReturn(0);
2542 }
2543 
2544 static PetscErrorCode PCApply_BDDCIPC(PC pc, Vec r, Vec x)
2545 {
2546   PetscErrorCode ierr;
2547   BDDCIPC_ctx    bddcipc_ctx;
2548   PC_IS          *pcis;
2549   VecScatter     tmps;
2550 
2551   PetscFunctionBegin;
2552   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2553   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2554   tmps = pcis->global_to_B;
2555   pcis->global_to_B = bddcipc_ctx->g2l;
2556   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2557   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_FALSE);CHKERRQ(ierr);
2558   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2559   pcis->global_to_B = tmps;
2560   PetscFunctionReturn(0);
2561 }
2562 
2563 static PetscErrorCode PCApplyTranspose_BDDCIPC(PC pc, Vec r, Vec x)
2564 {
2565   PetscErrorCode ierr;
2566   BDDCIPC_ctx    bddcipc_ctx;
2567   PC_IS          *pcis;
2568   VecScatter     tmps;
2569 
2570   PetscFunctionBegin;
2571   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2572   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2573   tmps = pcis->global_to_B;
2574   pcis->global_to_B = bddcipc_ctx->g2l;
2575   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2576   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_TRUE);CHKERRQ(ierr);
2577   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2578   pcis->global_to_B = tmps;
2579   PetscFunctionReturn(0);
2580 }
2581 
2582 static PetscErrorCode PCDestroy_BDDCIPC(PC pc)
2583 {
2584   PetscErrorCode ierr;
2585   BDDCIPC_ctx    bddcipc_ctx;
2586 
2587   PetscFunctionBegin;
2588   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2589   ierr = PCDestroy(&bddcipc_ctx->bddc);CHKERRQ(ierr);
2590   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2591   ierr = PetscFree(bddcipc_ctx);CHKERRQ(ierr);
2592   PetscFunctionReturn(0);
2593 }
2594 
2595 /*@
2596  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2597 
2598    Collective
2599 
2600    Input Parameters:
2601 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2602 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2603 
2604    Output Parameters:
2605 .  standard_sol    - the solution defined on the physical domain
2606 
2607    Level: developer
2608 
2609    Notes:
2610 
2611 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2612 @*/
2613 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2614 {
2615   FETIDPMat_ctx  mat_ctx;
2616   PetscErrorCode ierr;
2617 
2618   PetscFunctionBegin;
2619   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2620   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2621   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2622   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2623   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2624   PetscFunctionReturn(0);
2625 }
2626 
2627 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2628 {
2629 
2630   FETIDPMat_ctx  fetidpmat_ctx;
2631   Mat            newmat;
2632   FETIDPPC_ctx   fetidppc_ctx;
2633   PC             newpc;
2634   MPI_Comm       comm;
2635   PetscErrorCode ierr;
2636 
2637   PetscFunctionBegin;
2638   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2639   /* FETI-DP matrix */
2640   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2641   fetidpmat_ctx->fully_redundant = fully_redundant;
2642   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2643   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2644   ierr = PetscObjectSetName((PetscObject)newmat,!fetidpmat_ctx->l2g_lambda_only ? "F" : "G");CHKERRQ(ierr);
2645   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2646   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2647   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2648   /* propagate MatOptions */
2649   {
2650     PC_BDDC   *pcbddc = (PC_BDDC*)fetidpmat_ctx->pc->data;
2651     PetscBool issym;
2652 
2653     ierr = MatGetOption(pc->mat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2654     if (issym || pcbddc->symmetric_primal) {
2655       ierr = MatSetOption(newmat,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2656     }
2657   }
2658   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2659   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2660   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2661   /* FETI-DP preconditioner */
2662   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2663   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2664   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2665   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2666   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2667   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2668   ierr = PCSetErrorIfFailure(newpc,pc->erroriffailure);CHKERRQ(ierr);
2669   if (!fetidpmat_ctx->l2g_lambda_only) { /* standard FETI-DP */
2670     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2671     ierr = PCShellSetName(newpc,"FETI-DP multipliers");CHKERRQ(ierr);
2672     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2673     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2674     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2675     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2676     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2677   } else { /* saddle-point FETI-DP */
2678     Mat       M;
2679     PetscInt  psize;
2680     PetscBool fake = PETSC_FALSE, isfieldsplit;
2681 
2682     ierr = ISViewFromOptions(fetidpmat_ctx->lagrange,NULL,"-lag_view");CHKERRQ(ierr);
2683     ierr = ISViewFromOptions(fetidpmat_ctx->pressure,NULL,"-press_view");CHKERRQ(ierr);
2684     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2685     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2686     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2687     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2688     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2689     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2690     ierr = ISGetSize(fetidpmat_ctx->pressure,&psize);CHKERRQ(ierr);
2691     if (psize != M->rmap->N) {
2692       Mat      M2;
2693       PetscInt lpsize;
2694 
2695       fake = PETSC_TRUE;
2696       ierr = ISGetLocalSize(fetidpmat_ctx->pressure,&lpsize);CHKERRQ(ierr);
2697       ierr = MatCreate(comm,&M2);CHKERRQ(ierr);
2698       ierr = MatSetType(M2,MATAIJ);CHKERRQ(ierr);
2699       ierr = MatSetSizes(M2,lpsize,lpsize,psize,psize);CHKERRQ(ierr);
2700       ierr = MatSetUp(M2);CHKERRQ(ierr);
2701       ierr = MatAssemblyBegin(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2702       ierr = MatAssemblyEnd(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2703       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M2);CHKERRQ(ierr);
2704       ierr = MatDestroy(&M2);CHKERRQ(ierr);
2705     } else {
2706       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2707     }
2708     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2709 
2710     /* we need to setfromoptions and setup here to access the blocks */
2711     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2712     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2713 
2714     /* user may have changed the type (e.g. -fetidp_pc_type none) */
2715     ierr = PetscObjectTypeCompare((PetscObject)newpc,PCFIELDSPLIT,&isfieldsplit);CHKERRQ(ierr);
2716     if (isfieldsplit) {
2717       KSP       *ksps;
2718       PC        ppc,lagpc;
2719       PetscInt  nn;
2720       PetscBool ismatis,matisok = PETSC_FALSE,check = PETSC_FALSE;
2721 
2722       /* set the solver for the (0,0) block */
2723       ierr = PCFieldSplitSchurGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2724       if (!nn) { /* not of type PC_COMPOSITE_SCHUR */
2725         ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2726         if (!fake) { /* pass pmat to the pressure solver */
2727           Mat F;
2728 
2729           ierr = KSPGetOperators(ksps[1],&F,NULL);CHKERRQ(ierr);
2730           ierr = KSPSetOperators(ksps[1],F,M);CHKERRQ(ierr);
2731         }
2732       } else {
2733         PetscBool issym;
2734         Mat       S;
2735 
2736         ierr = PCFieldSplitSchurGetS(newpc,&S);CHKERRQ(ierr);
2737 
2738         ierr = MatGetOption(newmat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2739         if (issym) {
2740           ierr = MatSetOption(S,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2741         }
2742       }
2743       ierr = KSPGetPC(ksps[0],&lagpc);CHKERRQ(ierr);
2744       ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2745       ierr = PCShellSetName(lagpc,"FETI-DP multipliers");CHKERRQ(ierr);
2746       ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2747       ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2748       ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2749       ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2750       ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2751 
2752       /* Olof's idea: interface Schur complement preconditioner for the mass matrix */
2753       ierr = KSPGetPC(ksps[1],&ppc);CHKERRQ(ierr);
2754       if (fake) {
2755         BDDCIPC_ctx    bddcipc_ctx;
2756         PetscContainer c;
2757 
2758         matisok = PETSC_TRUE;
2759 
2760         /* create inner BDDC solver */
2761         ierr = PetscNew(&bddcipc_ctx);CHKERRQ(ierr);
2762         ierr = PCCreate(comm,&bddcipc_ctx->bddc);CHKERRQ(ierr);
2763         ierr = PCSetType(bddcipc_ctx->bddc,PCBDDC);CHKERRQ(ierr);
2764         ierr = PCSetOperators(bddcipc_ctx->bddc,M,M);CHKERRQ(ierr);
2765         ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_pCSR",(PetscObject*)&c);CHKERRQ(ierr);
2766         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2767         if (c && ismatis) {
2768           Mat      lM;
2769           PetscInt *csr,n;
2770 
2771           ierr = MatISGetLocalMat(M,&lM);CHKERRQ(ierr);
2772           ierr = MatGetSize(lM,&n,NULL);CHKERRQ(ierr);
2773           ierr = PetscContainerGetPointer(c,(void**)&csr);CHKERRQ(ierr);
2774           ierr = PCBDDCSetLocalAdjacencyGraph(bddcipc_ctx->bddc,n,csr,csr + (n + 1),PETSC_COPY_VALUES);CHKERRQ(ierr);
2775           ierr = MatISRestoreLocalMat(M,&lM);CHKERRQ(ierr);
2776         }
2777         ierr = PCSetOptionsPrefix(bddcipc_ctx->bddc,((PetscObject)ksps[1])->prefix);CHKERRQ(ierr);
2778         ierr = PCSetErrorIfFailure(bddcipc_ctx->bddc,pc->erroriffailure);CHKERRQ(ierr);
2779         ierr = PCSetFromOptions(bddcipc_ctx->bddc);CHKERRQ(ierr);
2780 
2781         /* wrap the interface application */
2782         ierr = PCSetType(ppc,PCSHELL);CHKERRQ(ierr);
2783         ierr = PCShellSetName(ppc,"FETI-DP pressure");CHKERRQ(ierr);
2784         ierr = PCShellSetContext(ppc,bddcipc_ctx);CHKERRQ(ierr);
2785         ierr = PCShellSetSetUp(ppc,PCSetUp_BDDCIPC);CHKERRQ(ierr);
2786         ierr = PCShellSetApply(ppc,PCApply_BDDCIPC);CHKERRQ(ierr);
2787         ierr = PCShellSetApplyTranspose(ppc,PCApplyTranspose_BDDCIPC);CHKERRQ(ierr);
2788         ierr = PCShellSetView(ppc,PCView_BDDCIPC);CHKERRQ(ierr);
2789         ierr = PCShellSetDestroy(ppc,PCDestroy_BDDCIPC);CHKERRQ(ierr);
2790       }
2791 
2792       /* determine if we need to assemble M to construct a preconditioner */
2793       if (!matisok) {
2794         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2795         ierr = PetscObjectTypeCompareAny((PetscObject)ppc,&matisok,PCBDDC,PCJACOBI,PCNONE,PCMG,"");CHKERRQ(ierr);
2796         if (ismatis && !matisok) {
2797           ierr = MatConvert(M,MATAIJ,MAT_INPLACE_MATRIX,&M);CHKERRQ(ierr);
2798         }
2799       }
2800 
2801       /* run the subproblems to check convergence */
2802       ierr = PetscOptionsGetBool(NULL,((PetscObject)newmat)->prefix,"-check_saddlepoint",&check,NULL);CHKERRQ(ierr);
2803       if (check) {
2804         PetscInt i;
2805 
2806         for (i=0;i<nn;i++) {
2807           KSP       kspC;
2808           PC        pc;
2809           Mat       F,pF;
2810           Vec       x,y;
2811           PetscBool isschur,prec = PETSC_TRUE;
2812 
2813           ierr = KSPCreate(PetscObjectComm((PetscObject)ksps[i]),&kspC);CHKERRQ(ierr);
2814           ierr = KSPSetOptionsPrefix(kspC,((PetscObject)ksps[i])->prefix);CHKERRQ(ierr);
2815           ierr = KSPAppendOptionsPrefix(kspC,"check_");CHKERRQ(ierr);
2816           ierr = KSPGetOperators(ksps[i],&F,&pF);CHKERRQ(ierr);
2817           ierr = PetscObjectTypeCompare((PetscObject)F,MATSCHURCOMPLEMENT,&isschur);CHKERRQ(ierr);
2818           if (isschur) {
2819             KSP  kspS,kspS2;
2820             Mat  A00,pA00,A10,A01,A11;
2821             char prefix[256];
2822 
2823             ierr = MatSchurComplementGetKSP(F,&kspS);CHKERRQ(ierr);
2824             ierr = MatSchurComplementGetSubMatrices(F,&A00,&pA00,&A01,&A10,&A11);CHKERRQ(ierr);
2825             ierr = MatCreateSchurComplement(A00,pA00,A01,A10,A11,&F);CHKERRQ(ierr);
2826             ierr = MatSchurComplementGetKSP(F,&kspS2);CHKERRQ(ierr);
2827             ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sschur_",((PetscObject)kspC)->prefix);CHKERRQ(ierr);
2828             ierr = KSPSetOptionsPrefix(kspS2,prefix);CHKERRQ(ierr);
2829             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2830             ierr = PCSetType(pc,PCKSP);CHKERRQ(ierr);
2831             ierr = PCKSPSetKSP(pc,kspS);CHKERRQ(ierr);
2832             ierr = KSPSetFromOptions(kspS2);CHKERRQ(ierr);
2833             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2834             ierr = PCSetUseAmat(pc,PETSC_TRUE);CHKERRQ(ierr);
2835           } else {
2836             ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
2837           }
2838           ierr = KSPSetFromOptions(kspC);CHKERRQ(ierr);
2839           ierr = PetscOptionsGetBool(NULL,((PetscObject)kspC)->prefix,"-preconditioned",&prec,NULL);CHKERRQ(ierr);
2840           if (prec)  {
2841             ierr = KSPGetPC(ksps[i],&pc);CHKERRQ(ierr);
2842             ierr = KSPSetPC(kspC,pc);CHKERRQ(ierr);
2843           }
2844           ierr = KSPSetOperators(kspC,F,pF);CHKERRQ(ierr);
2845           ierr = MatCreateVecs(F,&x,&y);CHKERRQ(ierr);
2846           ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2847           ierr = MatMult(F,x,y);CHKERRQ(ierr);
2848           ierr = KSPSolve(kspC,y,x);CHKERRQ(ierr);
2849           ierr = KSPCheckSolve(kspC,pc,x);CHKERRQ(ierr);
2850           ierr = KSPDestroy(&kspC);CHKERRQ(ierr);
2851           ierr = MatDestroy(&F);CHKERRQ(ierr);
2852           ierr = VecDestroy(&x);CHKERRQ(ierr);
2853           ierr = VecDestroy(&y);CHKERRQ(ierr);
2854         }
2855       }
2856       ierr = PetscFree(ksps);CHKERRQ(ierr);
2857     }
2858   }
2859   /* return pointers for objects created */
2860   *fetidp_mat = newmat;
2861   *fetidp_pc  = newpc;
2862   PetscFunctionReturn(0);
2863 }
2864 
2865 /*@C
2866  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2867 
2868    Collective
2869 
2870    Input Parameters:
2871 +  pc - the BDDC preconditioning context (setup should have been called before)
2872 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2873 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2874 
2875    Output Parameters:
2876 +  fetidp_mat - shell FETI-DP matrix object
2877 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2878 
2879    Level: developer
2880 
2881    Notes:
2882      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2883 
2884 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2885 @*/
2886 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2887 {
2888   PetscErrorCode ierr;
2889 
2890   PetscFunctionBegin;
2891   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2892   if (pc->setupcalled) {
2893     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2894   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first");
2895   PetscFunctionReturn(0);
2896 }
2897 /* -------------------------------------------------------------------------- */
2898 /*MC
2899    PCBDDC - Balancing Domain Decomposition by Constraints.
2900 
2901    An implementation of the BDDC preconditioner based on
2902 
2903 .vb
2904    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2905    [2] A. Klawonn and O. B. Widlund. "Dual-Primal FETI Methods for Linear Elasticity", https://cs.nyu.edu/dynamic/reports/?year=all
2906    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", https://arxiv.org/abs/0712.3977
2907    [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
2908 .ve
2909 
2910    The matrix to be preconditioned (Pmat) must be of type MATIS.
2911 
2912    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2913 
2914    It also works with unsymmetric and indefinite problems.
2915 
2916    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.
2917 
2918    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).
2919 
2920    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()
2921    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2922 
2923    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2924 
2925    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.
2926    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2927 
2928    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2929 
2930    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.
2931 
2932    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.
2933    Deluxe scaling is not supported yet for FETI-DP.
2934 
2935    Options Database Keys (some of them, run with -h for a complete list):
2936 
2937 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2938 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2939 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2940 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2941 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2942 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2943 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2944 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2945 .    -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)
2946 .    -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)
2947 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2948 .    -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)
2949 .    -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)
2950 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2951 
2952    Options for Dirichlet, Neumann or coarse solver can be set with
2953 .vb
2954       -pc_bddc_dirichlet_
2955       -pc_bddc_neumann_
2956       -pc_bddc_coarse_
2957 .ve
2958    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2959 
2960    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2961 .vb
2962       -pc_bddc_dirichlet_lN_
2963       -pc_bddc_neumann_lN_
2964       -pc_bddc_coarse_lN_
2965 .ve
2966    Note that level number ranges from the finest (0) to the coarsest (N).
2967    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.
2968 .vb
2969      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2970 .ve
2971    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
2972 
2973    Level: intermediate
2974 
2975    Developer Notes:
2976 
2977    Contributed by Stefano Zampini
2978 
2979 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2980 M*/
2981 
2982 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2983 {
2984   PetscErrorCode      ierr;
2985   PC_BDDC             *pcbddc;
2986 
2987   PetscFunctionBegin;
2988   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2989   pc->data = (void*)pcbddc;
2990 
2991   /* create PCIS data structure */
2992   ierr = PCISCreate(pc);CHKERRQ(ierr);
2993 
2994   /* create local graph structure */
2995   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2996 
2997   /* BDDC nonzero defaults */
2998   pcbddc->use_local_adj             = PETSC_TRUE;
2999   pcbddc->use_vertices              = PETSC_TRUE;
3000   pcbddc->use_edges                 = PETSC_TRUE;
3001   pcbddc->symmetric_primal          = PETSC_TRUE;
3002   pcbddc->vertex_size               = 1;
3003   pcbddc->recompute_topography      = PETSC_TRUE;
3004   pcbddc->coarse_size               = -1;
3005   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
3006   pcbddc->coarsening_ratio          = 8;
3007   pcbddc->coarse_eqs_per_proc       = 1;
3008   pcbddc->benign_compute_correction = PETSC_TRUE;
3009   pcbddc->nedfield                  = -1;
3010   pcbddc->nedglobal                 = PETSC_TRUE;
3011   pcbddc->graphmaxcount             = PETSC_MAX_INT;
3012   pcbddc->sub_schurs_layers         = -1;
3013   pcbddc->adaptive_threshold[0]     = 0.0;
3014   pcbddc->adaptive_threshold[1]     = 0.0;
3015 
3016   /* function pointers */
3017   pc->ops->apply               = PCApply_BDDC;
3018   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
3019   pc->ops->setup               = PCSetUp_BDDC;
3020   pc->ops->destroy             = PCDestroy_BDDC;
3021   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
3022   pc->ops->view                = PCView_BDDC;
3023   pc->ops->applyrichardson     = 0;
3024   pc->ops->applysymmetricleft  = 0;
3025   pc->ops->applysymmetricright = 0;
3026   pc->ops->presolve            = PCPreSolve_BDDC;
3027   pc->ops->postsolve           = PCPostSolve_BDDC;
3028   pc->ops->reset               = PCReset_BDDC;
3029 
3030   /* composing function */
3031   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
3032   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
3033   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
3034   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3035   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3036   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesLocalIS_C",PCBDDCGetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3037   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesIS_C",PCBDDCGetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3038   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
3039   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
3040   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
3041   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
3042   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3043   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3044   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3045   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3046   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3047   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3048   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3049   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3050   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
3051   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
3052   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
3053   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
3054   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
3055   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
3056   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
3057   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
3058   PetscFunctionReturn(0);
3059 }
3060 
3061 /*@C
3062  PCBDDCInitializePackage - This function initializes everything in the PCBDDC package. It is called
3063     from PCInitializePackage().
3064 
3065  Level: developer
3066 
3067  .seealso: PetscInitialize()
3068 @*/
3069 PetscErrorCode PCBDDCInitializePackage(void)
3070 {
3071   PetscErrorCode ierr;
3072   int            i;
3073 
3074   PetscFunctionBegin;
3075   if (PCBDDCPackageInitialized) PetscFunctionReturn(0);
3076   PCBDDCPackageInitialized = PETSC_TRUE;
3077   ierr = PetscRegisterFinalize(PCBDDCFinalizePackage);CHKERRQ(ierr);
3078 
3079   /* general events */
3080   ierr = PetscLogEventRegister("PCBDDCTopo",PC_CLASSID,&PC_BDDC_Topology[0]);CHKERRQ(ierr);
3081   ierr = PetscLogEventRegister("PCBDDCLKSP",PC_CLASSID,&PC_BDDC_LocalSolvers[0]);CHKERRQ(ierr);
3082   ierr = PetscLogEventRegister("PCBDDCLWor",PC_CLASSID,&PC_BDDC_LocalWork[0]);CHKERRQ(ierr);
3083   ierr = PetscLogEventRegister("PCBDDCCorr",PC_CLASSID,&PC_BDDC_CorrectionSetUp[0]);CHKERRQ(ierr);
3084   ierr = PetscLogEventRegister("PCBDDCCSet",PC_CLASSID,&PC_BDDC_CoarseSetUp[0]);CHKERRQ(ierr);
3085   ierr = PetscLogEventRegister("PCBDDCCKSP",PC_CLASSID,&PC_BDDC_CoarseSolver[0]);CHKERRQ(ierr);
3086   ierr = PetscLogEventRegister("PCBDDCAdap",PC_CLASSID,&PC_BDDC_AdaptiveSetUp[0]);CHKERRQ(ierr);
3087   ierr = PetscLogEventRegister("PCBDDCScal",PC_CLASSID,&PC_BDDC_Scaling[0]);CHKERRQ(ierr);
3088   ierr = PetscLogEventRegister("PCBDDCSchr",PC_CLASSID,&PC_BDDC_Schurs[0]);CHKERRQ(ierr);
3089   for (i=1;i<PETSC_PCBDDC_MAXLEVELS;i++) {
3090     char ename[32];
3091 
3092     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCTopo l%02d",i);CHKERRQ(ierr);
3093     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Topology[i]);CHKERRQ(ierr);
3094     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLKSP l%02d",i);CHKERRQ(ierr);
3095     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalSolvers[i]);CHKERRQ(ierr);
3096     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLWor l%02d",i);CHKERRQ(ierr);
3097     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalWork[i]);CHKERRQ(ierr);
3098     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCorr l%02d",i);CHKERRQ(ierr);
3099     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CorrectionSetUp[i]);CHKERRQ(ierr);
3100     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCSet l%02d",i);CHKERRQ(ierr);
3101     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSetUp[i]);CHKERRQ(ierr);
3102     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCKSP l%02d",i);CHKERRQ(ierr);
3103     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSolver[i]);CHKERRQ(ierr);
3104     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCAdap l%02d",i);CHKERRQ(ierr);
3105     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_AdaptiveSetUp[i]);CHKERRQ(ierr);
3106     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCScal l%02d",i);CHKERRQ(ierr);
3107     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Scaling[i]);CHKERRQ(ierr);
3108     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCSchr l%02d",i);CHKERRQ(ierr);
3109     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Schurs[i]);CHKERRQ(ierr);
3110   }
3111   PetscFunctionReturn(0);
3112 }
3113 
3114 /*@C
3115  PCBDDCFinalizePackage - This function frees everything from the PCBDDC package. It is
3116     called from PetscFinalize() automatically.
3117 
3118  Level: developer
3119 
3120  .seealso: PetscFinalize()
3121 @*/
3122 PetscErrorCode PCBDDCFinalizePackage(void)
3123 {
3124   PetscFunctionBegin;
3125   PCBDDCPackageInitialized = PETSC_FALSE;
3126   PetscFunctionReturn(0);
3127 }
3128