xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 435bcee143ca6da6594e4782ceeaca4034d91c04)
1 /* TODOLIST
2 
3    Solvers
4    - Add support for cholesky for coarse solver (similar to local solvers)
5    - Propagate ksp prefixes for solvers to mat objects?
6 
7    User interface
8    - ** DM attached to pc?
9 
10    Debugging output
11    - * Better management of verbosity levels of debugging output
12 
13    Extra
14    - *** Is it possible to work with PCBDDCGraph on boundary indices only (less memory consumed)?
15    - BDDC with MG framework?
16 
17    MATIS related operations contained in BDDC code
18    - Provide general case for subassembling
19 
20 */
21 
22 #include <../src/ksp/pc/impls/bddc/bddc.h> /*I "petscpc.h" I*/  /* includes for fortran wrappers */
23 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
24 #include <petscblaslapack.h>
25 
26 static PetscBool PCBDDCPackageInitialized = PETSC_FALSE;
27 
28 static PetscBool  cited = PETSC_FALSE;
29 static const char citation[] =
30 "@article{ZampiniPCBDDC,\n"
31 "author = {Stefano Zampini},\n"
32 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
33 "journal = {SIAM Journal on Scientific Computing},\n"
34 "volume = {38},\n"
35 "number = {5},\n"
36 "pages = {S282-S306},\n"
37 "year = {2016},\n"
38 "doi = {10.1137/15M1025785},\n"
39 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
40 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
41 "}\n";
42 
43 PetscLogEvent PC_BDDC_Topology[PETSC_PCBDDC_MAXLEVELS];
44 PetscLogEvent PC_BDDC_LocalSolvers[PETSC_PCBDDC_MAXLEVELS];
45 PetscLogEvent PC_BDDC_LocalWork[PETSC_PCBDDC_MAXLEVELS];
46 PetscLogEvent PC_BDDC_CorrectionSetUp[PETSC_PCBDDC_MAXLEVELS];
47 PetscLogEvent PC_BDDC_CoarseSetUp[PETSC_PCBDDC_MAXLEVELS];
48 PetscLogEvent PC_BDDC_CoarseSolver[PETSC_PCBDDC_MAXLEVELS];
49 PetscLogEvent PC_BDDC_AdaptiveSetUp[PETSC_PCBDDC_MAXLEVELS];
50 PetscLogEvent PC_BDDC_Scaling[PETSC_PCBDDC_MAXLEVELS];
51 PetscLogEvent PC_BDDC_Schurs[PETSC_PCBDDC_MAXLEVELS];
52 
53 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
54 
55 PetscErrorCode PCSetFromOptions_BDDC(PetscOptionItems *PetscOptionsObject,PC pc)
56 {
57   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
58   PetscInt       nt,i;
59   PetscErrorCode ierr;
60 
61   PetscFunctionBegin;
62   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
63   /* Verbose debugging */
64   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
65   /* Approximate solvers */
66   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate","Inform PCBDDC that we are using approximate Dirichlet solvers","none",pcbddc->NullSpace_corr[0],&pcbddc->NullSpace_corr[0],NULL);CHKERRQ(ierr);
67   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate_scale","Inform PCBDDC that we need to scale the Dirichlet solve","none",pcbddc->NullSpace_corr[1],&pcbddc->NullSpace_corr[1],NULL);CHKERRQ(ierr);
68   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate","Inform PCBDDC that we are using approximate Neumann solvers","none",pcbddc->NullSpace_corr[2],&pcbddc->NullSpace_corr[2],NULL);CHKERRQ(ierr);
69   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate_scale","Inform PCBDDC that we need to scale the Neumann solve","none",pcbddc->NullSpace_corr[3],&pcbddc->NullSpace_corr[3],NULL);CHKERRQ(ierr);
70   /* Primal space customization */
71   ierr = PetscOptionsBool("-pc_bddc_use_local_mat_graph","Use or not adjacency graph of local mat for interface analysis","none",pcbddc->use_local_adj,&pcbddc->use_local_adj,NULL);CHKERRQ(ierr);
72   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
73   ierr = PetscOptionsBool("-pc_bddc_corner_selection","Activates face-based corner selection","none",pcbddc->corner_selection,&pcbddc->corner_selection,NULL);CHKERRQ(ierr);
74   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
75   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
76   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
77   ierr = PetscOptionsInt("-pc_bddc_vertex_size","Connected components smaller or equal to vertex size will be considered as primal vertices","none",pcbddc->vertex_size,&pcbddc->vertex_size,NULL);CHKERRQ(ierr);
78   ierr = PetscOptionsBool("-pc_bddc_use_true_nnsp","Use near null space attached to the matrix without modifications","none",pcbddc->use_nnsp_true,&pcbddc->use_nnsp_true,NULL);CHKERRQ(ierr);
79   ierr = PetscOptionsBool("-pc_bddc_use_qr_single","Use QR factorization for single constraints on cc (QR is always used when multiple constraints are present)","none",pcbddc->use_qr_single,&pcbddc->use_qr_single,NULL);CHKERRQ(ierr);
80   /* Change of basis */
81   ierr = PetscOptionsBool("-pc_bddc_use_change_of_basis","Use or not internal change of basis on local edge nodes","none",pcbddc->use_change_of_basis,&pcbddc->use_change_of_basis,NULL);CHKERRQ(ierr);
82   ierr = PetscOptionsBool("-pc_bddc_use_change_on_faces","Use or not internal change of basis on local face nodes","none",pcbddc->use_change_on_faces,&pcbddc->use_change_on_faces,NULL);CHKERRQ(ierr);
83   if (!pcbddc->use_change_of_basis) {
84     pcbddc->use_change_on_faces = PETSC_FALSE;
85   }
86   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
87   ierr = PetscOptionsBool("-pc_bddc_switch_static","Switch on static condensation ops around the interface preconditioner","none",pcbddc->switch_static,&pcbddc->switch_static,NULL);CHKERRQ(ierr);
88   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_per_proc","Target number of equations per process for coarse problem redistribution (significant only at the coarsest level)","none",pcbddc->coarse_eqs_per_proc,&pcbddc->coarse_eqs_per_proc,NULL);CHKERRQ(ierr);
89   i    = pcbddc->coarsening_ratio;
90   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","PCBDDCSetCoarseningRatio",i,&i,NULL);CHKERRQ(ierr);
91   ierr = PCBDDCSetCoarseningRatio(pc,i);CHKERRQ(ierr);
92   i    = pcbddc->max_levels;
93   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","PCBDDCSetLevels",i,&i,NULL);CHKERRQ(ierr);
94   ierr = PCBDDCSetLevels(pc,i);CHKERRQ(ierr);
95   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_limit","Set maximum number of equations on coarsest grid to aim for","none",pcbddc->coarse_eqs_limit,&pcbddc->coarse_eqs_limit,NULL);CHKERRQ(ierr);
96   ierr = PetscOptionsBool("-pc_bddc_use_coarse_estimates","Use estimated eigenvalues for coarse problem","none",pcbddc->use_coarse_estimates,&pcbddc->use_coarse_estimates,NULL);CHKERRQ(ierr);
97   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
98   ierr = PetscOptionsBool("-pc_bddc_schur_rebuild","Whether or not the interface graph for Schur principal minors has to be rebuilt (i.e. define the interface without any adjacency)","none",pcbddc->sub_schurs_rebuild,&pcbddc->sub_schurs_rebuild,NULL);CHKERRQ(ierr);
99   ierr = PetscOptionsInt("-pc_bddc_schur_layers","Number of dofs' layers for the computation of principal minors (i.e. -1 uses all dofs)","none",pcbddc->sub_schurs_layers,&pcbddc->sub_schurs_layers,NULL);CHKERRQ(ierr);
100   ierr = PetscOptionsBool("-pc_bddc_schur_use_useradj","Whether or not the CSR graph specified by the user should be used for computing successive layers (default is to use adj of local mat)","none",pcbddc->sub_schurs_use_useradj,&pcbddc->sub_schurs_use_useradj,NULL);CHKERRQ(ierr);
101   ierr = PetscOptionsBool("-pc_bddc_schur_exact","Whether or not to use the exact Schur complement instead of the reduced one (which excludes size 1 cc)","none",pcbddc->sub_schurs_exact_schur,&pcbddc->sub_schurs_exact_schur,NULL);CHKERRQ(ierr);
102   ierr = PetscOptionsBool("-pc_bddc_deluxe_zerorows","Zero rows and columns of deluxe operators associated with primal dofs","none",pcbddc->deluxe_zerorows,&pcbddc->deluxe_zerorows,NULL);CHKERRQ(ierr);
103   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
104   ierr = PetscOptionsBool("-pc_bddc_adaptive_userdefined","Use user-defined constraints (should be attached via MatSetNearNullSpace to pmat) in addition to those adaptively generated","none",pcbddc->adaptive_userdefined,&pcbddc->adaptive_userdefined,NULL);CHKERRQ(ierr);
105   nt   = 2;
106   ierr = PetscOptionsRealArray("-pc_bddc_adaptive_threshold","Thresholds to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&nt,NULL);CHKERRQ(ierr);
107   if (nt == 1) pcbddc->adaptive_threshold[1] = pcbddc->adaptive_threshold[0];
108   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
109   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
110   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
111   ierr = PetscOptionsInt("-pc_bddc_coarse_adj","Number of processors where to map the coarse adjacency list","none",pcbddc->coarse_adj_red,&pcbddc->coarse_adj_red,NULL);CHKERRQ(ierr);
112   ierr = PetscOptionsBool("-pc_bddc_benign_trick","Apply the benign subspace trick to saddle point problems with discontinuous pressures","none",pcbddc->benign_saddle_point,&pcbddc->benign_saddle_point,NULL);CHKERRQ(ierr);
113   ierr = PetscOptionsBool("-pc_bddc_benign_change","Compute the pressure change of basis explicitly","none",pcbddc->benign_change_explicit,&pcbddc->benign_change_explicit,NULL);CHKERRQ(ierr);
114   ierr = PetscOptionsBool("-pc_bddc_benign_compute_correction","Compute the benign correction during PreSolve","none",pcbddc->benign_compute_correction,&pcbddc->benign_compute_correction,NULL);CHKERRQ(ierr);
115   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
116   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
117   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected_filter","Filters out small entries in the local matrix when detecting disconnected subdomains","none",pcbddc->detect_disconnected_filter,&pcbddc->detect_disconnected_filter,NULL);CHKERRQ(ierr);
118   ierr = PetscOptionsBool("-pc_bddc_eliminate_dirichlet","Whether or not we want to eliminate dirichlet dofs during presolve","none",pcbddc->eliminate_dirdofs,&pcbddc->eliminate_dirdofs,NULL);CHKERRQ(ierr);
119   ierr = PetscOptionsTail();CHKERRQ(ierr);
120   PetscFunctionReturn(0);
121 }
122 
123 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
124 {
125   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
126   PC_IS                *pcis = (PC_IS*)pc->data;
127   PetscErrorCode       ierr;
128   PetscBool            isascii;
129   PetscSubcomm         subcomm;
130   PetscViewer          subviewer;
131 
132   PetscFunctionBegin;
133   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
134   /* ASCII viewer */
135   if (isascii) {
136     PetscMPIInt   color,rank,size;
137     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
138     PetscScalar   interface_size;
139     PetscReal     ratio1=0.,ratio2=0.;
140     Vec           counter;
141 
142     if (!pc->setupcalled) {
143       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
144     }
145     ierr = PetscViewerASCIIPrintf(viewer,"  Use verbose output: %D\n",pcbddc->dbg_flag);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  Use user-defined CSR: %d\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  Use local mat graph: %d\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
148     if (pcbddc->mat_graph->twodim) {
149       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
150     } else {
151       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
152     }
153     if (pcbddc->graphmaxcount != PETSC_MAX_INT) {
154       ierr = PetscViewerASCIIPrintf(viewer,"  Graph max count: %D\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
155     }
156     ierr = PetscViewerASCIIPrintf(viewer,"  Use vertices: %d (vertex size %D)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
160     ierr = PetscViewerASCIIPrintf(viewer,"  Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
161     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
162     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
163     ierr = PetscViewerASCIIPrintf(viewer,"  User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
164     ierr = PetscViewerASCIIPrintf(viewer,"  Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
165     ierr = PetscViewerASCIIPrintf(viewer,"  Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
167     ierr = PetscViewerASCIIPrintf(viewer,"  Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
168     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel max levels: %D\n",pcbddc->max_levels);CHKERRQ(ierr);
169     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel coarsening ratio: %D\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
170     ierr = PetscViewerASCIIPrintf(viewer,"  Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
171     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
172     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
173     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
174     ierr = PetscViewerASCIIPrintf(viewer,"  Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
175     ierr = PetscViewerASCIIPrintf(viewer,"  Number of dofs' layers for the computation of principal minors: %D\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
176     ierr = PetscViewerASCIIPrintf(viewer,"  Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
177     if (pcbddc->adaptive_threshold[1] != pcbddc->adaptive_threshold[0]) {
178       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection thresholds (active %d, userdefined %d): %g,%g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0],pcbddc->adaptive_threshold[1]);CHKERRQ(ierr);
179     } else {
180       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection threshold (active %d, userdefined %d): %g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0]);CHKERRQ(ierr);
181     }
182     ierr = PetscViewerASCIIPrintf(viewer,"  Min constraints / connected component: %D\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
183     ierr = PetscViewerASCIIPrintf(viewer,"  Max constraints / connected component: %D\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
184     ierr = PetscViewerASCIIPrintf(viewer,"  Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
185     ierr = PetscViewerASCIIPrintf(viewer,"  Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
186     ierr = PetscViewerASCIIPrintf(viewer,"  Num. Procs. to map coarse adjacency list: %D\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
187     ierr = PetscViewerASCIIPrintf(viewer,"  Coarse eqs per proc (significant at the coarsest level): %D\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
188     ierr = PetscViewerASCIIPrintf(viewer,"  Detect disconnected: %d (filter %d)\n",pcbddc->detect_disconnected,pcbddc->detect_disconnected_filter);CHKERRQ(ierr);
189     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
190     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
191     ierr = PetscViewerASCIIPrintf(viewer,"  Algebraic computation of no-net-flux: %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
192     if (!pc->setupcalled) PetscFunctionReturn(0);
193 
194     /* compute interface size */
195     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
196     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
197     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
198     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
199     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
200     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
201     ierr = VecDestroy(&counter);CHKERRQ(ierr);
202 
203     /* compute some statistics on the domain decomposition */
204     gsum[0] = 1;
205     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
206     loc[0]  = !!pcis->n;
207     loc[1]  = pcis->n - pcis->n_B;
208     loc[2]  = pcis->n_B;
209     loc[3]  = pcbddc->local_primal_size;
210     loc[4]  = pcis->n;
211     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
212     loc[6]  = pcbddc->benign_n;
213     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
214     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
215     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
216     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
217     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
218     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
219     if (pcbddc->coarse_size) {
220       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
221       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
222     }
223     ierr = PetscViewerASCIIPrintf(viewer,"********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
224     ierr = PetscViewerASCIIPrintf(viewer,"  Global dofs sizes: all %D interface %D coarse %D\n",pc->pmat->rmap->N,(PetscInt)PetscRealPart(interface_size),pcbddc->coarse_size);CHKERRQ(ierr);
225     ierr = PetscViewerASCIIPrintf(viewer,"  Coarsening ratios: all/coarse %D interface/coarse %D\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
226     ierr = PetscViewerASCIIPrintf(viewer,"  Active processes : %D\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
227     ierr = PetscViewerASCIIPrintf(viewer,"  Total subdomains : %D\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
228     if (pcbddc->benign_have_null) {
229       ierr = PetscViewerASCIIPrintf(viewer,"  Benign subs      : %D\n",(PetscInt)totbenign);CHKERRQ(ierr);
230     }
231     ierr = PetscViewerASCIIPrintf(viewer,"  Dofs type        :\tMIN\tMAX\tMEAN\n");CHKERRQ(ierr);
232     ierr = PetscViewerASCIIPrintf(viewer,"  Interior  dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
233     ierr = PetscViewerASCIIPrintf(viewer,"  Interface dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[2],(PetscInt)gmax[2],(PetscInt)(gsum[2]/gsum[0]));CHKERRQ(ierr);
234     ierr = PetscViewerASCIIPrintf(viewer,"  Primal    dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[3],(PetscInt)gmax[3],(PetscInt)(gsum[3]/gsum[0]));CHKERRQ(ierr);
235     ierr = PetscViewerASCIIPrintf(viewer,"  Local     dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[4],(PetscInt)gmax[4],(PetscInt)(gsum[4]/gsum[0]));CHKERRQ(ierr);
236     ierr = PetscViewerASCIIPrintf(viewer,"  Local     subs   :\t%D\t%D\n"    ,(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
237     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
238 
239     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
240 
241     /* local solvers */
242     ierr = PetscViewerGetSubViewer(viewer,PetscObjectComm((PetscObject)pcbddc->ksp_D),&subviewer);CHKERRQ(ierr);
243     if (!rank) {
244       ierr = PetscViewerASCIIPrintf(subviewer,"--- Interior solver (rank 0)\n");CHKERRQ(ierr);
245       ierr = PetscViewerASCIIPushTab(subviewer);CHKERRQ(ierr);
246       ierr = KSPView(pcbddc->ksp_D,subviewer);CHKERRQ(ierr);
247       ierr = PetscViewerASCIIPopTab(subviewer);CHKERRQ(ierr);
248       ierr = PetscViewerASCIIPrintf(subviewer,"--- Correction solver (rank 0)\n");CHKERRQ(ierr);
249       ierr = PetscViewerASCIIPushTab(subviewer);CHKERRQ(ierr);
250       ierr = KSPView(pcbddc->ksp_R,subviewer);CHKERRQ(ierr);
251       ierr = PetscViewerASCIIPopTab(subviewer);CHKERRQ(ierr);
252       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
253     }
254     ierr = PetscViewerRestoreSubViewer(viewer,PetscObjectComm((PetscObject)pcbddc->ksp_D),&subviewer);CHKERRQ(ierr);
255     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
256 
257     /* the coarse problem can be handled by a different communicator */
258     if (pcbddc->coarse_ksp) color = 1;
259     else color = 0;
260     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
261     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
262     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
263     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
264     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
265     if (color == 1) {
266       ierr = PetscViewerASCIIPrintf(subviewer,"--- Coarse solver\n");CHKERRQ(ierr);
267       ierr = PetscViewerASCIIPushTab(subviewer);CHKERRQ(ierr);
268       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
269       ierr = PetscViewerASCIIPopTab(subviewer);CHKERRQ(ierr);
270       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
271     }
272     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
273     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
274     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
275   }
276   PetscFunctionReturn(0);
277 }
278 
279 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
280 {
281   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
282   PetscErrorCode ierr;
283 
284   PetscFunctionBegin;
285   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
286   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
287   pcbddc->discretegradient = G;
288   pcbddc->nedorder         = order > 0 ? order : -order;
289   pcbddc->nedfield         = field;
290   pcbddc->nedglobal        = global;
291   pcbddc->conforming       = conforming;
292   PetscFunctionReturn(0);
293 }
294 
295 /*@
296  PCBDDCSetDiscreteGradient - Sets the discrete gradient
297 
298    Collective on PC
299 
300    Input Parameters:
301 +  pc         - the preconditioning context
302 .  G          - the discrete gradient matrix (should be in AIJ format)
303 .  order      - the order of the Nedelec space (1 for the lowest order)
304 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
305 .  global     - the type of global ordering for the rows of G
306 -  conforming - whether the mesh is conforming or not
307 
308    Level: advanced
309 
310    Notes:
311     The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
312           For variable order spaces, the order should be set to zero.
313           If global is true, the rows of G should be given in global ordering for the whole dofs;
314           if false, the ordering should be global for the Nedelec field.
315           In the latter case, it should hold gid[i] < gid[j] iff geid[i] < geid[j], with gid the global orderding for all the dofs
316           and geid the one for the Nedelec field.
317 
318 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
319 @*/
320 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
321 {
322   PetscErrorCode ierr;
323 
324   PetscFunctionBegin;
325   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
326   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
327   PetscValidLogicalCollectiveInt(pc,order,3);
328   PetscValidLogicalCollectiveInt(pc,field,4);
329   PetscValidLogicalCollectiveBool(pc,global,5);
330   PetscValidLogicalCollectiveBool(pc,conforming,6);
331   PetscCheckSameComm(pc,1,G,2);
332   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
333   PetscFunctionReturn(0);
334 }
335 
336 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
337 {
338   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
339   PetscErrorCode ierr;
340 
341   PetscFunctionBegin;
342   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
343   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
344   pcbddc->divudotp = divudotp;
345   pcbddc->divudotp_trans = trans;
346   pcbddc->compute_nonetflux = PETSC_TRUE;
347   if (vl2l) {
348     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
349     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
350     pcbddc->divudotp_vl2l = vl2l;
351   }
352   PetscFunctionReturn(0);
353 }
354 
355 /*@
356  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
357 
358    Collective on PC
359 
360    Input Parameters:
361 +  pc - the preconditioning context
362 .  divudotp - the matrix (must be of type MATIS)
363 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
364 -  vl2l - optional index set describing the local (wrt the local matrix in divudotp) to local (wrt the local matrix in the preconditioning matrix) map for the velocities
365 
366    Level: advanced
367 
368    Notes:
369     This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
370           If vl2l is NULL, the local ordering for velocities in divudotp should match that of the preconditioning matrix
371 
372 .seealso: PCBDDC
373 @*/
374 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
375 {
376   PetscBool      ismatis;
377   PetscErrorCode ierr;
378 
379   PetscFunctionBegin;
380   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
381   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
382   PetscCheckSameComm(pc,1,divudotp,2);
383   PetscValidLogicalCollectiveBool(pc,trans,3);
384   if (vl2l) PetscValidHeaderSpecific(vl2l,IS_CLASSID,4);
385   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
386   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
387   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
388   PetscFunctionReturn(0);
389 }
390 
391 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
392 {
393   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
394   PetscErrorCode ierr;
395 
396   PetscFunctionBegin;
397   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
398   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
399   pcbddc->user_ChangeOfBasisMatrix = change;
400   pcbddc->change_interior = interior;
401   PetscFunctionReturn(0);
402 }
403 /*@
404  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
405 
406    Collective on PC
407 
408    Input Parameters:
409 +  pc - the preconditioning context
410 .  change - the change of basis matrix
411 -  interior - whether or not the change of basis modifies interior dofs
412 
413    Level: intermediate
414 
415    Notes:
416 
417 .seealso: PCBDDC
418 @*/
419 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
420 {
421   PetscErrorCode ierr;
422 
423   PetscFunctionBegin;
424   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
425   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
426   PetscCheckSameComm(pc,1,change,2);
427   if (pc->mat) {
428     PetscInt rows_c,cols_c,rows,cols;
429     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
430     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
431     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of rows for change of basis matrix! %D != %D",rows_c,rows);
432     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of columns for change of basis matrix! %D != %D",cols_c,cols);
433     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
434     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
435     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local rows for change of basis matrix! %D != %D",rows_c,rows);
436     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local columns for change of basis matrix! %D != %D",cols_c,cols);
437   }
438   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
439   PetscFunctionReturn(0);
440 }
441 
442 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
443 {
444   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
445   PetscBool      isequal = PETSC_FALSE;
446   PetscErrorCode ierr;
447 
448   PetscFunctionBegin;
449   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
450   if (pcbddc->user_primal_vertices) {
451     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
452   }
453   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
454   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
455   pcbddc->user_primal_vertices = PrimalVertices;
456   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
457   PetscFunctionReturn(0);
458 }
459 
460 /*@
461  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
462 
463    Collective
464 
465    Input Parameters:
466 +  pc - the preconditioning context
467 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
468 
469    Level: intermediate
470 
471    Notes:
472      Any process can list any global node
473 
474 .seealso: PCBDDC, PCBDDCGetPrimalVerticesIS(), PCBDDCSetPrimalVerticesLocalIS(), PCBDDCGetPrimalVerticesLocalIS()
475 @*/
476 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
477 {
478   PetscErrorCode ierr;
479 
480   PetscFunctionBegin;
481   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
482   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
483   PetscCheckSameComm(pc,1,PrimalVertices,2);
484   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
485   PetscFunctionReturn(0);
486 }
487 
488 static PetscErrorCode PCBDDCGetPrimalVerticesIS_BDDC(PC pc, IS *is)
489 {
490   PC_BDDC *pcbddc = (PC_BDDC*)pc->data;
491 
492   PetscFunctionBegin;
493   *is = pcbddc->user_primal_vertices;
494   PetscFunctionReturn(0);
495 }
496 
497 /*@
498  PCBDDCGetPrimalVerticesIS - Get user defined primal vertices set with PCBDDCSetPrimalVerticesIS()
499 
500    Collective
501 
502    Input Parameters:
503 .  pc - the preconditioning context
504 
505    Output Parameters:
506 .  is - index set of primal vertices in global numbering (NULL if not set)
507 
508    Level: intermediate
509 
510    Notes:
511 
512 .seealso: PCBDDC, PCBDDCSetPrimalVerticesIS(), PCBDDCSetPrimalVerticesLocalIS(), PCBDDCGetPrimalVerticesLocalIS()
513 @*/
514 PetscErrorCode PCBDDCGetPrimalVerticesIS(PC pc, IS *is)
515 {
516   PetscErrorCode ierr;
517 
518   PetscFunctionBegin;
519   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
520   PetscValidPointer(is,2);
521   ierr = PetscUseMethod(pc,"PCBDDCGetPrimalVerticesIS_C",(PC,IS*),(pc,is));CHKERRQ(ierr);
522   PetscFunctionReturn(0);
523 }
524 
525 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
526 {
527   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
528   PetscBool      isequal = PETSC_FALSE;
529   PetscErrorCode ierr;
530 
531   PetscFunctionBegin;
532   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
533   if (pcbddc->user_primal_vertices_local) {
534     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
535   }
536   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
537   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
538   pcbddc->user_primal_vertices_local = PrimalVertices;
539   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
540   PetscFunctionReturn(0);
541 }
542 
543 /*@
544  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
545 
546    Collective
547 
548    Input Parameters:
549 +  pc - the preconditioning context
550 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
551 
552    Level: intermediate
553 
554    Notes:
555 
556 .seealso: PCBDDC, PCBDDCSetPrimalVerticesIS(), PCBDDCGetPrimalVerticesIS(), PCBDDCGetPrimalVerticesLocalIS()
557 @*/
558 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
559 {
560   PetscErrorCode ierr;
561 
562   PetscFunctionBegin;
563   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
564   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
565   PetscCheckSameComm(pc,1,PrimalVertices,2);
566   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
567   PetscFunctionReturn(0);
568 }
569 
570 static PetscErrorCode PCBDDCGetPrimalVerticesLocalIS_BDDC(PC pc, IS *is)
571 {
572   PC_BDDC *pcbddc = (PC_BDDC*)pc->data;
573 
574   PetscFunctionBegin;
575   *is = pcbddc->user_primal_vertices_local;
576   PetscFunctionReturn(0);
577 }
578 
579 /*@
580  PCBDDCGetPrimalVerticesLocalIS - Get user defined primal vertices set with PCBDDCSetPrimalVerticesLocalIS()
581 
582    Collective
583 
584    Input Parameters:
585 .  pc - the preconditioning context
586 
587    Output Parameters:
588 .  is - index set of primal vertices in local numbering (NULL if not set)
589 
590    Level: intermediate
591 
592    Notes:
593 
594 .seealso: PCBDDC, PCBDDCSetPrimalVerticesIS(), PCBDDCGetPrimalVerticesIS(), PCBDDCSetPrimalVerticesLocalIS()
595 @*/
596 PetscErrorCode PCBDDCGetPrimalVerticesLocalIS(PC pc, IS *is)
597 {
598   PetscErrorCode ierr;
599 
600   PetscFunctionBegin;
601   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
602   PetscValidPointer(is,2);
603   ierr = PetscUseMethod(pc,"PCBDDCGetPrimalVerticesLocalIS_C",(PC,IS*),(pc,is));CHKERRQ(ierr);
604   PetscFunctionReturn(0);
605 }
606 
607 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
608 {
609   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
610 
611   PetscFunctionBegin;
612   pcbddc->coarsening_ratio = k;
613   PetscFunctionReturn(0);
614 }
615 
616 /*@
617  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
618 
619    Logically collective on PC
620 
621    Input Parameters:
622 +  pc - the preconditioning context
623 -  k - coarsening ratio (H/h at the coarser level)
624 
625    Options Database Keys:
626 .    -pc_bddc_coarsening_ratio
627 
628    Level: intermediate
629 
630    Notes:
631      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
632 
633 .seealso: PCBDDC, PCBDDCSetLevels()
634 @*/
635 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
636 {
637   PetscErrorCode ierr;
638 
639   PetscFunctionBegin;
640   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
641   PetscValidLogicalCollectiveInt(pc,k,2);
642   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
643   PetscFunctionReturn(0);
644 }
645 
646 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
647 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
648 {
649   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
650 
651   PetscFunctionBegin;
652   pcbddc->use_exact_dirichlet_trick = flg;
653   PetscFunctionReturn(0);
654 }
655 
656 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
657 {
658   PetscErrorCode ierr;
659 
660   PetscFunctionBegin;
661   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
662   PetscValidLogicalCollectiveBool(pc,flg,2);
663   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
664   PetscFunctionReturn(0);
665 }
666 
667 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
668 {
669   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
670 
671   PetscFunctionBegin;
672   pcbddc->current_level = level;
673   PetscFunctionReturn(0);
674 }
675 
676 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
677 {
678   PetscErrorCode ierr;
679 
680   PetscFunctionBegin;
681   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
682   PetscValidLogicalCollectiveInt(pc,level,2);
683   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
684   PetscFunctionReturn(0);
685 }
686 
687 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
688 {
689   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
690 
691   PetscFunctionBegin;
692   if (levels > PETSC_PCBDDC_MAXLEVELS-1) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of additional levels for BDDC is %d",PETSC_PCBDDC_MAXLEVELS-1);
693   pcbddc->max_levels = levels;
694   PetscFunctionReturn(0);
695 }
696 
697 /*@
698  PCBDDCSetLevels - Sets the maximum number of additional levels allowed for multilevel BDDC
699 
700    Logically collective on PC
701 
702    Input Parameters:
703 +  pc - the preconditioning context
704 -  levels - the maximum number of levels
705 
706    Options Database Keys:
707 .    -pc_bddc_levels
708 
709    Level: intermediate
710 
711    Notes:
712      The default value is 0, that gives the classical two-levels BDDC
713 
714 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
715 @*/
716 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
717 {
718   PetscErrorCode ierr;
719 
720   PetscFunctionBegin;
721   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
722   PetscValidLogicalCollectiveInt(pc,levels,2);
723   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
724   PetscFunctionReturn(0);
725 }
726 
727 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
728 {
729   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
730   PetscBool      isequal = PETSC_FALSE;
731   PetscErrorCode ierr;
732 
733   PetscFunctionBegin;
734   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
735   if (pcbddc->DirichletBoundaries) {
736     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
737   }
738   /* last user setting takes precendence -> destroy any other customization */
739   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
740   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
741   pcbddc->DirichletBoundaries = DirichletBoundaries;
742   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
743   PetscFunctionReturn(0);
744 }
745 
746 /*@
747  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
748 
749    Collective
750 
751    Input Parameters:
752 +  pc - the preconditioning context
753 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
754 
755    Level: intermediate
756 
757    Notes:
758      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
759 
760 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
761 @*/
762 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
763 {
764   PetscErrorCode ierr;
765 
766   PetscFunctionBegin;
767   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
768   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
769   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
770   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
771   PetscFunctionReturn(0);
772 }
773 
774 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
775 {
776   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
777   PetscBool      isequal = PETSC_FALSE;
778   PetscErrorCode ierr;
779 
780   PetscFunctionBegin;
781   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
782   if (pcbddc->DirichletBoundariesLocal) {
783     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
784   }
785   /* last user setting takes precendence -> destroy any other customization */
786   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
787   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
788   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
789   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
790   PetscFunctionReturn(0);
791 }
792 
793 /*@
794  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
795 
796    Collective
797 
798    Input Parameters:
799 +  pc - the preconditioning context
800 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
801 
802    Level: intermediate
803 
804    Notes:
805 
806 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
807 @*/
808 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
809 {
810   PetscErrorCode ierr;
811 
812   PetscFunctionBegin;
813   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
814   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
815   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
816   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
817   PetscFunctionReturn(0);
818 }
819 
820 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
821 {
822   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
823   PetscBool      isequal = PETSC_FALSE;
824   PetscErrorCode ierr;
825 
826   PetscFunctionBegin;
827   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
828   if (pcbddc->NeumannBoundaries) {
829     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
830   }
831   /* last user setting takes precendence -> destroy any other customization */
832   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
833   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
834   pcbddc->NeumannBoundaries = NeumannBoundaries;
835   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
836   PetscFunctionReturn(0);
837 }
838 
839 /*@
840  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
841 
842    Collective
843 
844    Input Parameters:
845 +  pc - the preconditioning context
846 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
847 
848    Level: intermediate
849 
850    Notes:
851      Any process can list any global node
852 
853 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
854 @*/
855 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
856 {
857   PetscErrorCode ierr;
858 
859   PetscFunctionBegin;
860   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
861   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
862   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
863   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
864   PetscFunctionReturn(0);
865 }
866 
867 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
868 {
869   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
870   PetscBool      isequal = PETSC_FALSE;
871   PetscErrorCode ierr;
872 
873   PetscFunctionBegin;
874   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
875   if (pcbddc->NeumannBoundariesLocal) {
876     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
877   }
878   /* last user setting takes precendence -> destroy any other customization */
879   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
880   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
881   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
882   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
883   PetscFunctionReturn(0);
884 }
885 
886 /*@
887  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
888 
889    Collective
890 
891    Input Parameters:
892 +  pc - the preconditioning context
893 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
894 
895    Level: intermediate
896 
897    Notes:
898 
899 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
900 @*/
901 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
902 {
903   PetscErrorCode ierr;
904 
905   PetscFunctionBegin;
906   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
907   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
908   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
909   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
910   PetscFunctionReturn(0);
911 }
912 
913 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
914 {
915   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
916 
917   PetscFunctionBegin;
918   *DirichletBoundaries = pcbddc->DirichletBoundaries;
919   PetscFunctionReturn(0);
920 }
921 
922 /*@
923  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
924 
925    Collective
926 
927    Input Parameters:
928 .  pc - the preconditioning context
929 
930    Output Parameters:
931 .  DirichletBoundaries - index set defining the Dirichlet boundaries
932 
933    Level: intermediate
934 
935    Notes:
936      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
937 
938 .seealso: PCBDDC
939 @*/
940 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
941 {
942   PetscErrorCode ierr;
943 
944   PetscFunctionBegin;
945   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
946   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
947   PetscFunctionReturn(0);
948 }
949 
950 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
951 {
952   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
953 
954   PetscFunctionBegin;
955   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
956   PetscFunctionReturn(0);
957 }
958 
959 /*@
960  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
961 
962    Collective
963 
964    Input Parameters:
965 .  pc - the preconditioning context
966 
967    Output Parameters:
968 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
969 
970    Level: intermediate
971 
972    Notes:
973      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetDirichletBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetDirichletBoundaries).
974           In the latter case, the IS will be available after PCSetUp.
975 
976 .seealso: PCBDDC
977 @*/
978 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
979 {
980   PetscErrorCode ierr;
981 
982   PetscFunctionBegin;
983   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
984   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
985   PetscFunctionReturn(0);
986 }
987 
988 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
989 {
990   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
991 
992   PetscFunctionBegin;
993   *NeumannBoundaries = pcbddc->NeumannBoundaries;
994   PetscFunctionReturn(0);
995 }
996 
997 /*@
998  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
999 
1000    Collective
1001 
1002    Input Parameters:
1003 .  pc - the preconditioning context
1004 
1005    Output Parameters:
1006 .  NeumannBoundaries - index set defining the Neumann boundaries
1007 
1008    Level: intermediate
1009 
1010    Notes:
1011      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
1012 
1013 .seealso: PCBDDC
1014 @*/
1015 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
1016 {
1017   PetscErrorCode ierr;
1018 
1019   PetscFunctionBegin;
1020   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1021   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
1022   PetscFunctionReturn(0);
1023 }
1024 
1025 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
1026 {
1027   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
1028 
1029   PetscFunctionBegin;
1030   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
1031   PetscFunctionReturn(0);
1032 }
1033 
1034 /*@
1035  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
1036 
1037    Collective
1038 
1039    Input Parameters:
1040 .  pc - the preconditioning context
1041 
1042    Output Parameters:
1043 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
1044 
1045    Level: intermediate
1046 
1047    Notes:
1048      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetNeumannBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetNeumannBoundaries).
1049           In the latter case, the IS will be available after PCSetUp.
1050 
1051 .seealso: PCBDDC
1052 @*/
1053 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
1054 {
1055   PetscErrorCode ierr;
1056 
1057   PetscFunctionBegin;
1058   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1059   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
1060   PetscFunctionReturn(0);
1061 }
1062 
1063 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1064 {
1065   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1066   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
1067   PetscBool      same_data = PETSC_FALSE;
1068   PetscErrorCode ierr;
1069 
1070   PetscFunctionBegin;
1071   if (!nvtxs) {
1072     if (copymode == PETSC_OWN_POINTER) {
1073       ierr = PetscFree(xadj);CHKERRQ(ierr);
1074       ierr = PetscFree(adjncy);CHKERRQ(ierr);
1075     }
1076     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
1077     PetscFunctionReturn(0);
1078   }
1079   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
1080     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
1081     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
1082       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
1083       if (same_data) {
1084         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
1085       }
1086     }
1087   }
1088   if (!same_data) {
1089     /* free old CSR */
1090     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
1091     /* get CSR into graph structure */
1092     if (copymode == PETSC_COPY_VALUES) {
1093       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
1094       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
1095       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
1096       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
1097       mat_graph->freecsr = PETSC_TRUE;
1098     } else if (copymode == PETSC_OWN_POINTER) {
1099       mat_graph->xadj    = (PetscInt*)xadj;
1100       mat_graph->adjncy  = (PetscInt*)adjncy;
1101       mat_graph->freecsr = PETSC_TRUE;
1102     } else if (copymode == PETSC_USE_POINTER) {
1103       mat_graph->xadj    = (PetscInt*)xadj;
1104       mat_graph->adjncy  = (PetscInt*)adjncy;
1105       mat_graph->freecsr = PETSC_FALSE;
1106     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %D",copymode);
1107     mat_graph->nvtxs_csr = nvtxs;
1108     pcbddc->recompute_topography = PETSC_TRUE;
1109   }
1110   PetscFunctionReturn(0);
1111 }
1112 
1113 /*@
1114  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
1115 
1116    Not collective
1117 
1118    Input Parameters:
1119 +  pc - the preconditioning context.
1120 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
1121 .  xadj, adjncy - the connectivity of the dofs in CSR format.
1122 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1123 
1124    Level: intermediate
1125 
1126    Notes:
1127     A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1128 
1129 .seealso: PCBDDC,PetscCopyMode
1130 @*/
1131 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1132 {
1133   void (*f)(void) = 0;
1134   PetscErrorCode ierr;
1135 
1136   PetscFunctionBegin;
1137   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1138   if (nvtxs) {
1139     PetscValidIntPointer(xadj,3);
1140     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1141   }
1142   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1143   /* free arrays if PCBDDC is not the PC type */
1144   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1145   if (!f && copymode == PETSC_OWN_POINTER) {
1146     ierr = PetscFree(xadj);CHKERRQ(ierr);
1147     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1148   }
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1153 {
1154   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1155   PetscInt       i;
1156   PetscBool      isequal = PETSC_FALSE;
1157   PetscErrorCode ierr;
1158 
1159   PetscFunctionBegin;
1160   if (pcbddc->n_ISForDofsLocal == n_is) {
1161     for (i=0;i<n_is;i++) {
1162       PetscBool isequalt;
1163       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1164       if (!isequalt) break;
1165     }
1166     if (i == n_is) isequal = PETSC_TRUE;
1167   }
1168   for (i=0;i<n_is;i++) {
1169     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1170   }
1171   /* Destroy ISes if they were already set */
1172   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1173     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1174   }
1175   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1176   /* last user setting takes precendence -> destroy any other customization */
1177   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1178     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1179   }
1180   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1181   pcbddc->n_ISForDofs = 0;
1182   /* allocate space then set */
1183   if (n_is) {
1184     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1185   }
1186   for (i=0;i<n_is;i++) {
1187     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1188   }
1189   pcbddc->n_ISForDofsLocal = n_is;
1190   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1191   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1192   PetscFunctionReturn(0);
1193 }
1194 
1195 /*@
1196  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1197 
1198    Collective
1199 
1200    Input Parameters:
1201 +  pc - the preconditioning context
1202 .  n_is - number of index sets defining the fields
1203 -  ISForDofs - array of IS describing the fields in local ordering
1204 
1205    Level: intermediate
1206 
1207    Notes:
1208      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1209 
1210 .seealso: PCBDDC
1211 @*/
1212 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1213 {
1214   PetscInt       i;
1215   PetscErrorCode ierr;
1216 
1217   PetscFunctionBegin;
1218   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1219   PetscValidLogicalCollectiveInt(pc,n_is,2);
1220   for (i=0;i<n_is;i++) {
1221     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1222     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1223   }
1224   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1225   PetscFunctionReturn(0);
1226 }
1227 
1228 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1229 {
1230   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1231   PetscInt       i;
1232   PetscBool      isequal = PETSC_FALSE;
1233   PetscErrorCode ierr;
1234 
1235   PetscFunctionBegin;
1236   if (pcbddc->n_ISForDofs == n_is) {
1237     for (i=0;i<n_is;i++) {
1238       PetscBool isequalt;
1239       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1240       if (!isequalt) break;
1241     }
1242     if (i == n_is) isequal = PETSC_TRUE;
1243   }
1244   for (i=0;i<n_is;i++) {
1245     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1246   }
1247   /* Destroy ISes if they were already set */
1248   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1249     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1250   }
1251   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1252   /* last user setting takes precendence -> destroy any other customization */
1253   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1254     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1255   }
1256   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1257   pcbddc->n_ISForDofsLocal = 0;
1258   /* allocate space then set */
1259   if (n_is) {
1260     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1261   }
1262   for (i=0;i<n_is;i++) {
1263     pcbddc->ISForDofs[i] = ISForDofs[i];
1264   }
1265   pcbddc->n_ISForDofs = n_is;
1266   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1267   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1268   PetscFunctionReturn(0);
1269 }
1270 
1271 /*@
1272  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1273 
1274    Collective
1275 
1276    Input Parameters:
1277 +  pc - the preconditioning context
1278 .  n_is - number of index sets defining the fields
1279 -  ISForDofs - array of IS describing the fields in global ordering
1280 
1281    Level: intermediate
1282 
1283    Notes:
1284      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1285 
1286 .seealso: PCBDDC
1287 @*/
1288 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1289 {
1290   PetscInt       i;
1291   PetscErrorCode ierr;
1292 
1293   PetscFunctionBegin;
1294   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1295   PetscValidLogicalCollectiveInt(pc,n_is,2);
1296   for (i=0;i<n_is;i++) {
1297     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1298     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1299   }
1300   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1301   PetscFunctionReturn(0);
1302 }
1303 
1304 /*
1305    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1306                      guess if a transformation of basis approach has been selected.
1307 
1308    Input Parameter:
1309 +  pc - the preconditioner contex
1310 
1311    Application Interface Routine: PCPreSolve()
1312 
1313    Notes:
1314      The interface routine PCPreSolve() is not usually called directly by
1315    the user, but instead is called by KSPSolve().
1316 */
1317 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1318 {
1319   PetscErrorCode ierr;
1320   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1321   PC_IS          *pcis = (PC_IS*)(pc->data);
1322   Vec            used_vec;
1323   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1324 
1325   PetscFunctionBegin;
1326   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1327   if (ksp) {
1328     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1329     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1330     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1331     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1332     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1333     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1334       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1335     }
1336   }
1337   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1338     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1339   }
1340 
1341   /* Creates parallel work vectors used in presolve */
1342   if (!pcbddc->original_rhs) {
1343     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1344   }
1345   if (!pcbddc->temp_solution) {
1346     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1347   }
1348 
1349   pcbddc->temp_solution_used = PETSC_FALSE;
1350   if (x) {
1351     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1352     used_vec = x;
1353   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1354     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1355     used_vec = pcbddc->temp_solution;
1356     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1357     pcbddc->temp_solution_used = PETSC_TRUE;
1358     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1359     save_rhs = PETSC_FALSE;
1360     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1361   }
1362 
1363   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1364   if (ksp) {
1365     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1366     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1367     if (!pcbddc->ksp_guess_nonzero) {
1368       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1369     }
1370   }
1371 
1372   pcbddc->rhs_change = PETSC_FALSE;
1373   /* Take into account zeroed rows -> change rhs and store solution removed */
1374   if (rhs && pcbddc->eliminate_dirdofs) {
1375     IS dirIS = NULL;
1376 
1377     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1378     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1379     if (dirIS) {
1380       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1381       PetscInt          dirsize,i,*is_indices;
1382       PetscScalar       *array_x;
1383       const PetscScalar *array_diagonal;
1384 
1385       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1386       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1387       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1388       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1389       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1390       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1391       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1392       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1393       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1394       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1395       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1396       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1397       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1398       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1399       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1400       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1401       pcbddc->rhs_change = PETSC_TRUE;
1402       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1403     }
1404   }
1405 
1406   /* remove the computed solution or the initial guess from the rhs */
1407   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1408     /* save the original rhs */
1409     if (save_rhs) {
1410       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1411       save_rhs = PETSC_FALSE;
1412     }
1413     pcbddc->rhs_change = PETSC_TRUE;
1414     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1415     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1416     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1417     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1418     pcbddc->temp_solution_used = PETSC_TRUE;
1419     if (ksp) {
1420       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1421     }
1422   }
1423   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1424 
1425   /* compute initial vector in benign space if needed
1426      and remove non-benign solution from the rhs */
1427   benign_correction_computed = PETSC_FALSE;
1428   if (rhs && pcbddc->benign_compute_correction && (pcbddc->benign_have_null || pcbddc->benign_apply_coarse_only)) {
1429     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1430        Recursively apply BDDC in the multilevel case */
1431     if (!pcbddc->benign_vec) {
1432       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1433     }
1434     /* keep applying coarse solver unless we no longer have benign subdomains */
1435     pcbddc->benign_apply_coarse_only = pcbddc->benign_have_null ? PETSC_TRUE : PETSC_FALSE;
1436     if (!pcbddc->benign_skip_correction) {
1437       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1438       benign_correction_computed = PETSC_TRUE;
1439       if (pcbddc->temp_solution_used) {
1440         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1441       }
1442       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1443       /* store the original rhs if not done earlier */
1444       if (save_rhs) {
1445         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1446       }
1447       if (pcbddc->rhs_change) {
1448         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1449       } else {
1450         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1451       }
1452       pcbddc->rhs_change = PETSC_TRUE;
1453     }
1454     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1455   }
1456 
1457   /* dbg output */
1458   if (pcbddc->dbg_flag && benign_correction_computed) {
1459     Vec v;
1460 
1461     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1462     if (pcbddc->ChangeOfBasisMatrix) {
1463       ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1464     } else {
1465       ierr = VecCopy(rhs,v);CHKERRQ(ierr);
1466     }
1467     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1468     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1469     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,pcbddc->dbg_viewer);CHKERRQ(ierr);
1470     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1471     ierr = VecDestroy(&v);CHKERRQ(ierr);
1472   }
1473 
1474   /* set initial guess if using PCG */
1475   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1476   if (x && pcbddc->use_exact_dirichlet_trick) {
1477     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1478     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1479       if (benign_correction_computed) { /* we have already saved the changed rhs */
1480         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1481       } else {
1482         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1483       }
1484       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1485       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1486     } else {
1487       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1488       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1489     }
1490     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1491     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1492       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1493       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1494       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1495       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1496     } else {
1497       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1498       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1499     }
1500     if (ksp) {
1501       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1502     }
1503     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1504   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1505     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1506   }
1507   PetscFunctionReturn(0);
1508 }
1509 
1510 /*
1511    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1512                      approach has been selected. Also, restores rhs to its original state.
1513 
1514    Input Parameter:
1515 +  pc - the preconditioner contex
1516 
1517    Application Interface Routine: PCPostSolve()
1518 
1519    Notes:
1520      The interface routine PCPostSolve() is not usually called directly by
1521      the user, but instead is called by KSPSolve().
1522 */
1523 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1524 {
1525   PetscErrorCode ierr;
1526   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1527 
1528   PetscFunctionBegin;
1529   /* add solution removed in presolve */
1530   if (x && pcbddc->rhs_change) {
1531     if (pcbddc->temp_solution_used) {
1532       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1533     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1534       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1535     }
1536     /* restore to original state (not for FETI-DP) */
1537     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1538   }
1539 
1540   /* restore rhs to its original state (not needed for FETI-DP) */
1541   if (rhs && pcbddc->rhs_change) {
1542     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1543     pcbddc->rhs_change = PETSC_FALSE;
1544   }
1545   /* restore ksp guess state */
1546   if (ksp) {
1547     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1548     /* reset flag for exact dirichlet trick */
1549     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1550   }
1551   PetscFunctionReturn(0);
1552 }
1553 
1554 /*
1555    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1556                   by setting data structures and options.
1557 
1558    Input Parameter:
1559 +  pc - the preconditioner context
1560 
1561    Application Interface Routine: PCSetUp()
1562 
1563    Notes:
1564      The interface routine PCSetUp() is not usually called directly by
1565      the user, but instead is called by PCApply() if necessary.
1566 */
1567 PetscErrorCode PCSetUp_BDDC(PC pc)
1568 {
1569   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1570   PCBDDCSubSchurs sub_schurs;
1571   Mat_IS*         matis;
1572   MatNullSpace    nearnullspace;
1573   Mat             lA;
1574   IS              lP,zerodiag = NULL;
1575   PetscInt        nrows,ncols;
1576   PetscMPIInt     size;
1577   PetscBool       computesubschurs;
1578   PetscBool       computeconstraintsmatrix;
1579   PetscBool       new_nearnullspace_provided,ismatis,rl;
1580   PetscErrorCode  ierr;
1581 
1582   PetscFunctionBegin;
1583   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1584   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1585   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1586   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1587   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
1588 
1589   matis = (Mat_IS*)pc->pmat->data;
1590   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1591   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1592      Also, BDDC builds its own KSP for the Dirichlet problem */
1593   rl = pcbddc->recompute_topography;
1594   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) rl = PETSC_TRUE;
1595   ierr = MPIU_Allreduce(&rl,&pcbddc->recompute_topography,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1596   if (pcbddc->recompute_topography) {
1597     pcbddc->graphanalyzed    = PETSC_FALSE;
1598     computeconstraintsmatrix = PETSC_TRUE;
1599   } else {
1600     computeconstraintsmatrix = PETSC_FALSE;
1601   }
1602 
1603   /* check parameters' compatibility */
1604   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1605   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1606   pcbddc->use_deluxe_scaling   = (PetscBool)(pcbddc->use_deluxe_scaling && size > 1);
1607   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_selection && size > 1);
1608   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1609   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1610 
1611   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1612   if (pcbddc->switch_static) {
1613     PetscBool ismatis;
1614 
1615     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1616     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1617   }
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 
1644   /* change basis if requested by the user */
1645   if (pcbddc->user_ChangeOfBasisMatrix) {
1646     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1647     pcbddc->use_change_of_basis = PETSC_FALSE;
1648     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1649   } else {
1650     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1651     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1652     pcbddc->local_mat = matis->A;
1653   }
1654 
1655   /*
1656      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1657      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1658   */
1659   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1660   if (pcbddc->benign_saddle_point) {
1661     PC_IS* pcis = (PC_IS*)pc->data;
1662 
1663     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1664     /* detect local saddle point and change the basis in pcbddc->local_mat */
1665     ierr = PCBDDCBenignDetectSaddlePoint(pc,(PetscBool)(!pcbddc->recompute_topography),&zerodiag);CHKERRQ(ierr);
1666     /* pop B0 mat from local mat */
1667     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1668     /* give pcis a hint to not reuse submatrices during PCISCreate */
1669     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1670       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1671         pcis->reusesubmatrices = PETSC_FALSE;
1672       } else {
1673         pcis->reusesubmatrices = PETSC_TRUE;
1674       }
1675     } else {
1676       pcis->reusesubmatrices = PETSC_FALSE;
1677     }
1678   }
1679 
1680   /* propagate relevant information */
1681   if (matis->A->symmetric_set) {
1682     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1683   }
1684   if (matis->A->spd_set) {
1685     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1686   }
1687 
1688   /* Set up all the "iterative substructuring" common block without computing solvers */
1689   {
1690     Mat temp_mat;
1691 
1692     temp_mat = matis->A;
1693     matis->A = pcbddc->local_mat;
1694     ierr = PCISSetUp(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1695     pcbddc->local_mat = matis->A;
1696     matis->A = temp_mat;
1697   }
1698 
1699   /* Analyze interface */
1700   if (!pcbddc->graphanalyzed) {
1701     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1702     computeconstraintsmatrix = PETSC_TRUE;
1703     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1704       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1705     }
1706     if (pcbddc->compute_nonetflux) {
1707       MatNullSpace nnfnnsp;
1708 
1709       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1710       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1711       /* TODO what if a nearnullspace is already attached? */
1712       if (nnfnnsp) {
1713         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1714         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1715       }
1716     }
1717   }
1718   ierr = PetscLogEventEnd(PC_BDDC_Topology[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1719 
1720   /* check existence of a divergence free extension, i.e.
1721      b(v_I,p_0) = 0 for all v_I (raise error if not).
1722      Also, check that PCBDDCBenignGetOrSetP0 works */
1723   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1724     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1725   }
1726   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1727 
1728   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1729   if (computesubschurs && pcbddc->recompute_topography) {
1730     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1731   }
1732   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1733   if (!pcbddc->use_deluxe_scaling) {
1734     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1735   }
1736 
1737   /* finish setup solvers and do adaptive selection of constraints */
1738   sub_schurs = pcbddc->sub_schurs;
1739   if (sub_schurs && sub_schurs->schur_explicit) {
1740     if (computesubschurs) {
1741       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1742     }
1743     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1744   } else {
1745     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1746     if (computesubschurs) {
1747       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1748     }
1749   }
1750   if (pcbddc->adaptive_selection) {
1751     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1752     computeconstraintsmatrix = PETSC_TRUE;
1753   }
1754 
1755   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1756   new_nearnullspace_provided = PETSC_FALSE;
1757   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1758   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1759     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1760       new_nearnullspace_provided = PETSC_TRUE;
1761     } else {
1762       /* determine if the two nullspaces are different (should be lightweight) */
1763       if (nearnullspace != pcbddc->onearnullspace) {
1764         new_nearnullspace_provided = PETSC_TRUE;
1765       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1766         PetscInt         i;
1767         const Vec        *nearnullvecs;
1768         PetscObjectState state;
1769         PetscInt         nnsp_size;
1770         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1771         for (i=0;i<nnsp_size;i++) {
1772           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1773           if (pcbddc->onearnullvecs_state[i] != state) {
1774             new_nearnullspace_provided = PETSC_TRUE;
1775             break;
1776           }
1777         }
1778       }
1779     }
1780   } else {
1781     if (!nearnullspace) { /* both nearnullspaces are null */
1782       new_nearnullspace_provided = PETSC_FALSE;
1783     } else { /* nearnullspace attached later */
1784       new_nearnullspace_provided = PETSC_TRUE;
1785     }
1786   }
1787 
1788   /* Setup constraints and related work vectors */
1789   /* reset primal space flags */
1790   ierr = PetscLogEventBegin(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1791   pcbddc->new_primal_space = PETSC_FALSE;
1792   pcbddc->new_primal_space_local = PETSC_FALSE;
1793   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1794     /* It also sets the primal space flags */
1795     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1796   }
1797   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1798   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1799 
1800   if (pcbddc->use_change_of_basis) {
1801     PC_IS *pcis = (PC_IS*)(pc->data);
1802 
1803     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1804     if (pcbddc->benign_change) {
1805       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1806       /* pop B0 from pcbddc->local_mat */
1807       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1808     }
1809     /* get submatrices */
1810     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1811     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1812     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1813     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1814     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1815     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1816     /* set flag in pcis to not reuse submatrices during PCISCreate */
1817     pcis->reusesubmatrices = PETSC_FALSE;
1818   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1819     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1820     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1821     pcbddc->local_mat = matis->A;
1822   }
1823 
1824   /* interface pressure block row for B_C */
1825   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1826   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1827   if (lA && lP) {
1828     PC_IS*    pcis = (PC_IS*)pc->data;
1829     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1830     PetscBool issym;
1831     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1832     if (issym) {
1833       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1834       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1835       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1836       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1837     } else {
1838       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1839       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1840       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1841       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1842     }
1843     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1844     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1845     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1846     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1847     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1848     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1849     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1850     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1851   }
1852   ierr = PetscLogEventEnd(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1853 
1854   /* SetUp coarse and local Neumann solvers */
1855   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1856   /* SetUp Scaling operator */
1857   if (pcbddc->use_deluxe_scaling) {
1858     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1859   }
1860 
1861   /* mark topography as done */
1862   pcbddc->recompute_topography = PETSC_FALSE;
1863 
1864   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1865   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1866 
1867   if (pcbddc->dbg_flag) {
1868     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1869     ierr = PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1870   }
1871   PetscFunctionReturn(0);
1872 }
1873 
1874 /*
1875    PCApply_BDDC - Applies the BDDC operator to a vector.
1876 
1877    Input Parameters:
1878 +  pc - the preconditioner context
1879 -  r - input vector (global)
1880 
1881    Output Parameter:
1882 .  z - output vector (global)
1883 
1884    Application Interface Routine: PCApply()
1885  */
1886 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1887 {
1888   PC_IS             *pcis = (PC_IS*)(pc->data);
1889   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1890   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1891   PetscErrorCode    ierr;
1892   const PetscScalar one = 1.0;
1893   const PetscScalar m_one = -1.0;
1894   const PetscScalar zero = 0.0;
1895 
1896 /* This code is similar to that provided in nn.c for PCNN
1897    NN interface preconditioner changed to BDDC
1898    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1899 
1900   PetscFunctionBegin;
1901   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1902   if (pcbddc->ChangeOfBasisMatrix) {
1903     Vec swap;
1904 
1905     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1906     swap = pcbddc->work_change;
1907     pcbddc->work_change = r;
1908     r = swap;
1909     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1910     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1911       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1912       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1913     }
1914   }
1915   if (pcbddc->benign_have_null) { /* get p0 from r */
1916     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1917   }
1918   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1919     ierr = VecCopy(r,z);CHKERRQ(ierr);
1920     /* First Dirichlet solve */
1921     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1922     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1923     /*
1924       Assembling right hand side for BDDC operator
1925       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1926       - pcis->vec1_B the interface part of the global vector z
1927     */
1928     if (n_D) {
1929       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1930       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1931       if (pcbddc->switch_static) {
1932         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1933 
1934         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1935         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1936         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1937         if (!pcbddc->switch_static_change) {
1938           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1939         } else {
1940           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1941           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1942           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1943         }
1944         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1945         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1946         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1947         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1948       } else {
1949         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1950       }
1951     } else {
1952       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1953     }
1954     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1955     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1956     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1957   } else {
1958     if (!pcbddc->benign_apply_coarse_only) {
1959       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1960     }
1961   }
1962 
1963   /* Apply interface preconditioner
1964      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1965   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1966 
1967   /* Apply transpose of partition of unity operator */
1968   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1969 
1970   /* Second Dirichlet solve and assembling of output */
1971   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1972   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1973   if (n_B) {
1974     if (pcbddc->switch_static) {
1975       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1976 
1977       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1978       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1979       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1980       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1981       if (!pcbddc->switch_static_change) {
1982         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1983       } else {
1984         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1985         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1986         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1987       }
1988       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1989       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1990     } else {
1991       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1992     }
1993   } else if (pcbddc->switch_static) { /* n_B is zero */
1994     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1995 
1996     if (!pcbddc->switch_static_change) {
1997       ierr = MatMult(matis->A,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(matis->A,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 
2006   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2007     if (pcbddc->switch_static) {
2008       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2009     } else {
2010       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2011     }
2012     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2013     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2014   } else {
2015     if (pcbddc->switch_static) {
2016       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2017     } else {
2018       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2019     }
2020     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2021     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2022   }
2023   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2024     if (pcbddc->benign_apply_coarse_only) {
2025       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2026     }
2027     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2028   }
2029 
2030   if (pcbddc->ChangeOfBasisMatrix) {
2031     pcbddc->work_change = r;
2032     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2033     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2034   }
2035   PetscFunctionReturn(0);
2036 }
2037 
2038 /*
2039    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
2040 
2041    Input Parameters:
2042 +  pc - the preconditioner context
2043 -  r - input vector (global)
2044 
2045    Output Parameter:
2046 .  z - output vector (global)
2047 
2048    Application Interface Routine: PCApplyTranspose()
2049  */
2050 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
2051 {
2052   PC_IS             *pcis = (PC_IS*)(pc->data);
2053   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
2054   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
2055   PetscErrorCode    ierr;
2056   const PetscScalar one = 1.0;
2057   const PetscScalar m_one = -1.0;
2058   const PetscScalar zero = 0.0;
2059 
2060   PetscFunctionBegin;
2061   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
2062   if (pcbddc->ChangeOfBasisMatrix) {
2063     Vec swap;
2064 
2065     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
2066     swap = pcbddc->work_change;
2067     pcbddc->work_change = r;
2068     r = swap;
2069     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
2070     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
2071       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
2072       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
2073     }
2074   }
2075   if (pcbddc->benign_have_null) { /* get p0 from r */
2076     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
2077   }
2078   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2079     ierr = VecCopy(r,z);CHKERRQ(ierr);
2080     /* First Dirichlet solve */
2081     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2082     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2083     /*
2084       Assembling right hand side for BDDC operator
2085       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
2086       - pcis->vec1_B the interface part of the global vector z
2087     */
2088     if (n_D) {
2089       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
2090       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
2091       if (pcbddc->switch_static) {
2092         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2093 
2094         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
2095         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2096         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2097         if (!pcbddc->switch_static_change) {
2098           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2099         } else {
2100           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2101           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2102           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2103         }
2104         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2105         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2106         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2107         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2108       } else {
2109         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
2110       }
2111     } else {
2112       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
2113     }
2114     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2115     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2116     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
2117   } else {
2118     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
2119   }
2120 
2121   /* Apply interface preconditioner
2122      input/output vecs: pcis->vec1_B and pcis->vec1_D */
2123   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
2124 
2125   /* Apply transpose of partition of unity operator */
2126   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2127 
2128   /* Second Dirichlet solve and assembling of output */
2129   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2130   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2131   if (n_B) {
2132     if (pcbddc->switch_static) {
2133       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2134 
2135       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2136       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2137       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2138       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2139       if (!pcbddc->switch_static_change) {
2140         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2141       } else {
2142         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2143         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2144         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2145       }
2146       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2147       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2148     } else {
2149       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2150     }
2151   } else if (pcbddc->switch_static) { /* n_B is zero */
2152     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2153 
2154     if (!pcbddc->switch_static_change) {
2155       ierr = MatMultTranspose(matis->A,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(matis->A,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   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2164     if (pcbddc->switch_static) {
2165       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2166     } else {
2167       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2168     }
2169     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2170     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2171   } else {
2172     if (pcbddc->switch_static) {
2173       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2174     } else {
2175       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2176     }
2177     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2178     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2179   }
2180   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2181     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2182   }
2183   if (pcbddc->ChangeOfBasisMatrix) {
2184     pcbddc->work_change = r;
2185     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2186     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2187   }
2188   PetscFunctionReturn(0);
2189 }
2190 
2191 PetscErrorCode PCReset_BDDC(PC pc)
2192 {
2193   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2194   PC_IS          *pcis = (PC_IS*)pc->data;
2195   KSP            kspD,kspR,kspC;
2196   PetscErrorCode ierr;
2197 
2198   PetscFunctionBegin;
2199   /* free BDDC custom data  */
2200   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2201   /* destroy objects related to topography */
2202   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2203   /* destroy objects for scaling operator */
2204   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2205   /* free solvers stuff */
2206   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2207   /* free global vectors needed in presolve */
2208   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2209   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2210   /* free data created by PCIS */
2211   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2212 
2213   /* restore defaults */
2214   kspD = pcbddc->ksp_D;
2215   kspR = pcbddc->ksp_R;
2216   kspC = pcbddc->coarse_ksp;
2217   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2218   pcis->n_neigh                     = -1;
2219   pcis->scaling_factor              = 1.0;
2220   pcis->reusesubmatrices            = PETSC_TRUE;
2221   pcbddc->use_local_adj             = PETSC_TRUE;
2222   pcbddc->use_vertices              = PETSC_TRUE;
2223   pcbddc->use_edges                 = PETSC_TRUE;
2224   pcbddc->symmetric_primal          = PETSC_TRUE;
2225   pcbddc->vertex_size               = 1;
2226   pcbddc->recompute_topography      = PETSC_TRUE;
2227   pcbddc->coarse_size               = -1;
2228   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2229   pcbddc->coarsening_ratio          = 8;
2230   pcbddc->coarse_eqs_per_proc       = 1;
2231   pcbddc->benign_compute_correction = PETSC_TRUE;
2232   pcbddc->nedfield                  = -1;
2233   pcbddc->nedglobal                 = PETSC_TRUE;
2234   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2235   pcbddc->sub_schurs_layers         = -1;
2236   pcbddc->ksp_D                     = kspD;
2237   pcbddc->ksp_R                     = kspR;
2238   pcbddc->coarse_ksp                = kspC;
2239   PetscFunctionReturn(0);
2240 }
2241 
2242 PetscErrorCode PCDestroy_BDDC(PC pc)
2243 {
2244   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2245   PetscErrorCode ierr;
2246 
2247   PetscFunctionBegin;
2248   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2249   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2250   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2251   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2252   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2253   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2254   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2255   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2256   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2257   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2258   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2259   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2260   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2261   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2262   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2263   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2264   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2265   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2266   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2267   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2268   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2269   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2270   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2271   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2272   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2273   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2274   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2275   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2276   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2277   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2278   PetscFunctionReturn(0);
2279 }
2280 
2281 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2282 {
2283   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2284   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2285   PetscErrorCode ierr;
2286 
2287   PetscFunctionBegin;
2288   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2289   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2290   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2291   mat_graph->cnloc = nloc;
2292   mat_graph->cdim  = dim;
2293   mat_graph->cloc  = PETSC_FALSE;
2294   PetscFunctionReturn(0);
2295 }
2296 
2297 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2298 {
2299   PetscFunctionBegin;
2300   *change = PETSC_TRUE;
2301   PetscFunctionReturn(0);
2302 }
2303 
2304 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2305 {
2306   FETIDPMat_ctx  mat_ctx;
2307   Vec            work;
2308   PC_IS*         pcis;
2309   PC_BDDC*       pcbddc;
2310   PetscErrorCode ierr;
2311 
2312   PetscFunctionBegin;
2313   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2314   pcis = (PC_IS*)mat_ctx->pc->data;
2315   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2316 
2317   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2318   /* copy rhs since we may change it during PCPreSolve_BDDC */
2319   if (!pcbddc->original_rhs) {
2320     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2321   }
2322   if (mat_ctx->rhs_flip) {
2323     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2324   } else {
2325     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2326   }
2327   if (mat_ctx->g2g_p) {
2328     /* interface pressure rhs */
2329     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2330     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2331     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2332     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2333     if (!mat_ctx->rhs_flip) {
2334       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2335     }
2336   }
2337   /*
2338      change of basis for physical rhs if needed
2339      It also changes the rhs in case of dirichlet boundaries
2340   */
2341   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2342   if (pcbddc->ChangeOfBasisMatrix) {
2343     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2344     work = pcbddc->work_change;
2345    } else {
2346     work = pcbddc->original_rhs;
2347   }
2348   /* store vectors for computation of fetidp final solution */
2349   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2350   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2351   /* scale rhs since it should be unassembled */
2352   /* TODO use counter scaling? (also below) */
2353   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2354   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2355   /* Apply partition of unity */
2356   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2357   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2358   if (!pcbddc->switch_static) {
2359     /* compute partially subassembled Schur complement right-hand side */
2360     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2361     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2362     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2363     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2364     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2365     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2366     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2367     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2368     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2369     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2370   }
2371   /* BDDC rhs */
2372   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2373   if (pcbddc->switch_static) {
2374     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2375   }
2376   /* apply BDDC */
2377   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2378   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2379   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2380 
2381   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2382   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2383   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2384   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2385   /* Add contribution to interface pressures */
2386   if (mat_ctx->l2g_p) {
2387     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2388     if (pcbddc->switch_static) {
2389       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2390     }
2391     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2392     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2393   }
2394   PetscFunctionReturn(0);
2395 }
2396 
2397 /*@
2398  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2399 
2400    Collective
2401 
2402    Input Parameters:
2403 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2404 -  standard_rhs    - the right-hand side of the original linear system
2405 
2406    Output Parameters:
2407 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2408 
2409    Level: developer
2410 
2411    Notes:
2412 
2413 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2414 @*/
2415 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2416 {
2417   FETIDPMat_ctx  mat_ctx;
2418   PetscErrorCode ierr;
2419 
2420   PetscFunctionBegin;
2421   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2422   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2423   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2424   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2425   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2426   PetscFunctionReturn(0);
2427 }
2428 
2429 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2430 {
2431   FETIDPMat_ctx  mat_ctx;
2432   PC_IS*         pcis;
2433   PC_BDDC*       pcbddc;
2434   PetscErrorCode ierr;
2435   Vec            work;
2436 
2437   PetscFunctionBegin;
2438   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2439   pcis = (PC_IS*)mat_ctx->pc->data;
2440   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2441 
2442   /* apply B_delta^T */
2443   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2444   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2445   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2446   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2447   if (mat_ctx->l2g_p) {
2448     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2449     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2450     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2451   }
2452 
2453   /* compute rhs for BDDC application */
2454   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2455   if (pcbddc->switch_static) {
2456     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2457     if (mat_ctx->l2g_p) {
2458       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2459       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2460     }
2461   }
2462 
2463   /* apply BDDC */
2464   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2465   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2466 
2467   /* put values into global vector */
2468   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2469   else work = standard_sol;
2470   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2471   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2472   if (!pcbddc->switch_static) {
2473     /* compute values into the interior if solved for the partially subassembled Schur complement */
2474     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2475     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2476     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2477   }
2478 
2479   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2480   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2481   /* add p0 solution to final solution */
2482   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2483   if (pcbddc->ChangeOfBasisMatrix) {
2484     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2485   }
2486   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2487   if (mat_ctx->g2g_p) {
2488     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2489     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2490   }
2491   PetscFunctionReturn(0);
2492 }
2493 
2494 static PetscErrorCode PCView_BDDCIPC(PC pc, PetscViewer viewer)
2495 {
2496   PetscErrorCode ierr;
2497   BDDCIPC_ctx    bddcipc_ctx;
2498   PetscBool      isascii;
2499 
2500   PetscFunctionBegin;
2501   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2502   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
2503   if (isascii) {
2504     ierr = PetscViewerASCIIPrintf(viewer,"BDDC interface preconditioner\n");CHKERRQ(ierr);
2505   }
2506   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2507   ierr = PCView(bddcipc_ctx->bddc,viewer);CHKERRQ(ierr);
2508   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2509   PetscFunctionReturn(0);
2510 }
2511 
2512 static PetscErrorCode PCSetUp_BDDCIPC(PC pc)
2513 {
2514   PetscErrorCode ierr;
2515   BDDCIPC_ctx    bddcipc_ctx;
2516   PetscBool      isbddc;
2517   Vec            vv;
2518   IS             is;
2519   PC_IS          *pcis;
2520 
2521   PetscFunctionBegin;
2522   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2523   ierr = PetscObjectTypeCompare((PetscObject)bddcipc_ctx->bddc,PCBDDC,&isbddc);CHKERRQ(ierr);
2524   if (!isbddc) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid type %s. Must be of type bddc",((PetscObject)bddcipc_ctx->bddc)->type_name);
2525   ierr = PCSetUp(bddcipc_ctx->bddc);CHKERRQ(ierr);
2526 
2527   /* create interface scatter */
2528   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2529   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2530   ierr = MatCreateVecs(pc->pmat,&vv,NULL);CHKERRQ(ierr);
2531   ierr = ISRenumber(pcis->is_B_global,NULL,NULL,&is);CHKERRQ(ierr);
2532   ierr = VecScatterCreateWithData(vv,is,pcis->vec1_B,NULL,&bddcipc_ctx->g2l);CHKERRQ(ierr);
2533   ierr = ISDestroy(&is);CHKERRQ(ierr);
2534   ierr = VecDestroy(&vv);CHKERRQ(ierr);
2535   PetscFunctionReturn(0);
2536 }
2537 
2538 static PetscErrorCode PCApply_BDDCIPC(PC pc, Vec r, Vec x)
2539 {
2540   PetscErrorCode ierr;
2541   BDDCIPC_ctx    bddcipc_ctx;
2542   PC_IS          *pcis;
2543   VecScatter     tmps;
2544 
2545   PetscFunctionBegin;
2546   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2547   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2548   tmps = pcis->global_to_B;
2549   pcis->global_to_B = bddcipc_ctx->g2l;
2550   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2551   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_FALSE);CHKERRQ(ierr);
2552   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2553   pcis->global_to_B = tmps;
2554   PetscFunctionReturn(0);
2555 }
2556 
2557 static PetscErrorCode PCApplyTranspose_BDDCIPC(PC pc, Vec r, Vec x)
2558 {
2559   PetscErrorCode ierr;
2560   BDDCIPC_ctx    bddcipc_ctx;
2561   PC_IS          *pcis;
2562   VecScatter     tmps;
2563 
2564   PetscFunctionBegin;
2565   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2566   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2567   tmps = pcis->global_to_B;
2568   pcis->global_to_B = bddcipc_ctx->g2l;
2569   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2570   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_TRUE);CHKERRQ(ierr);
2571   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2572   pcis->global_to_B = tmps;
2573   PetscFunctionReturn(0);
2574 }
2575 
2576 static PetscErrorCode PCDestroy_BDDCIPC(PC pc)
2577 {
2578   PetscErrorCode ierr;
2579   BDDCIPC_ctx    bddcipc_ctx;
2580 
2581   PetscFunctionBegin;
2582   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2583   ierr = PCDestroy(&bddcipc_ctx->bddc);CHKERRQ(ierr);
2584   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2585   ierr = PetscFree(bddcipc_ctx);CHKERRQ(ierr);
2586   PetscFunctionReturn(0);
2587 }
2588 
2589 /*@
2590  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2591 
2592    Collective
2593 
2594    Input Parameters:
2595 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2596 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2597 
2598    Output Parameters:
2599 .  standard_sol    - the solution defined on the physical domain
2600 
2601    Level: developer
2602 
2603    Notes:
2604 
2605 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2606 @*/
2607 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2608 {
2609   FETIDPMat_ctx  mat_ctx;
2610   PetscErrorCode ierr;
2611 
2612   PetscFunctionBegin;
2613   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2614   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2615   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2616   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2617   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2618   PetscFunctionReturn(0);
2619 }
2620 
2621 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2622 {
2623 
2624   FETIDPMat_ctx  fetidpmat_ctx;
2625   Mat            newmat;
2626   FETIDPPC_ctx   fetidppc_ctx;
2627   PC             newpc;
2628   MPI_Comm       comm;
2629   PetscErrorCode ierr;
2630 
2631   PetscFunctionBegin;
2632   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2633   /* FETI-DP matrix */
2634   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2635   fetidpmat_ctx->fully_redundant = fully_redundant;
2636   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2637   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2638   ierr = PetscObjectSetName((PetscObject)newmat,!fetidpmat_ctx->l2g_lambda_only ? "F" : "G");CHKERRQ(ierr);
2639   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2640   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2641   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2642   /* propagate MatOptions */
2643   {
2644     PC_BDDC   *pcbddc = (PC_BDDC*)fetidpmat_ctx->pc->data;
2645     PetscBool issym;
2646 
2647     ierr = MatGetOption(pc->mat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2648     if (issym || pcbddc->symmetric_primal) {
2649       ierr = MatSetOption(newmat,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2650     }
2651   }
2652   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2653   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2654   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2655   /* FETI-DP preconditioner */
2656   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2657   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2658   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2659   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2660   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2661   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2662   ierr = PCSetErrorIfFailure(newpc,pc->erroriffailure);CHKERRQ(ierr);
2663   if (!fetidpmat_ctx->l2g_lambda_only) { /* standard FETI-DP */
2664     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2665     ierr = PCShellSetName(newpc,"FETI-DP multipliers");CHKERRQ(ierr);
2666     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2667     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2668     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2669     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2670     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2671   } else { /* saddle-point FETI-DP */
2672     Mat       M;
2673     PetscInt  psize;
2674     PetscBool fake = PETSC_FALSE, isfieldsplit;
2675 
2676     ierr = ISViewFromOptions(fetidpmat_ctx->lagrange,NULL,"-lag_view");CHKERRQ(ierr);
2677     ierr = ISViewFromOptions(fetidpmat_ctx->pressure,NULL,"-press_view");CHKERRQ(ierr);
2678     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2679     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2680     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2681     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2682     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2683     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2684     ierr = ISGetSize(fetidpmat_ctx->pressure,&psize);CHKERRQ(ierr);
2685     if (psize != M->rmap->N) {
2686       Mat      M2;
2687       PetscInt lpsize;
2688 
2689       fake = PETSC_TRUE;
2690       ierr = ISGetLocalSize(fetidpmat_ctx->pressure,&lpsize);CHKERRQ(ierr);
2691       ierr = MatCreate(comm,&M2);CHKERRQ(ierr);
2692       ierr = MatSetType(M2,MATAIJ);CHKERRQ(ierr);
2693       ierr = MatSetSizes(M2,lpsize,lpsize,psize,psize);CHKERRQ(ierr);
2694       ierr = MatSetUp(M2);CHKERRQ(ierr);
2695       ierr = MatAssemblyBegin(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2696       ierr = MatAssemblyEnd(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2697       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M2);CHKERRQ(ierr);
2698       ierr = MatDestroy(&M2);CHKERRQ(ierr);
2699     } else {
2700       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2701     }
2702     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2703 
2704     /* we need to setfromoptions and setup here to access the blocks */
2705     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2706     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2707 
2708     /* user may have changed the type (e.g. -fetidp_pc_type none) */
2709     ierr = PetscObjectTypeCompare((PetscObject)newpc,PCFIELDSPLIT,&isfieldsplit);CHKERRQ(ierr);
2710     if (isfieldsplit) {
2711       KSP       *ksps;
2712       PC        ppc,lagpc;
2713       PetscInt  nn;
2714       PetscBool ismatis,matisok = PETSC_FALSE,check = PETSC_FALSE;
2715 
2716       /* set the solver for the (0,0) block */
2717       ierr = PCFieldSplitSchurGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2718       if (!nn) { /* not of type PC_COMPOSITE_SCHUR */
2719         ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2720         if (!fake) { /* pass pmat to the pressure solver */
2721           Mat F;
2722 
2723           ierr = KSPGetOperators(ksps[1],&F,NULL);CHKERRQ(ierr);
2724           ierr = KSPSetOperators(ksps[1],F,M);CHKERRQ(ierr);
2725         }
2726       } else {
2727         PetscBool issym;
2728         Mat       S;
2729 
2730         ierr = PCFieldSplitSchurGetS(newpc,&S);CHKERRQ(ierr);
2731 
2732         ierr = MatGetOption(newmat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2733         if (issym) {
2734           ierr = MatSetOption(S,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2735         }
2736       }
2737       ierr = KSPGetPC(ksps[0],&lagpc);CHKERRQ(ierr);
2738       ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2739       ierr = PCShellSetName(lagpc,"FETI-DP multipliers");CHKERRQ(ierr);
2740       ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2741       ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2742       ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2743       ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2744       ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2745 
2746       /* Olof's idea: interface Schur complement preconditioner for the mass matrix */
2747       ierr = KSPGetPC(ksps[1],&ppc);CHKERRQ(ierr);
2748       if (fake) {
2749         BDDCIPC_ctx    bddcipc_ctx;
2750         PetscContainer c;
2751 
2752         matisok = PETSC_TRUE;
2753 
2754         /* create inner BDDC solver */
2755         ierr = PetscNew(&bddcipc_ctx);CHKERRQ(ierr);
2756         ierr = PCCreate(comm,&bddcipc_ctx->bddc);CHKERRQ(ierr);
2757         ierr = PCSetType(bddcipc_ctx->bddc,PCBDDC);CHKERRQ(ierr);
2758         ierr = PCSetOperators(bddcipc_ctx->bddc,M,M);CHKERRQ(ierr);
2759         ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_pCSR",(PetscObject*)&c);CHKERRQ(ierr);
2760         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2761         if (c && ismatis) {
2762           Mat      lM;
2763           PetscInt *csr,n;
2764 
2765           ierr = MatISGetLocalMat(M,&lM);CHKERRQ(ierr);
2766           ierr = MatGetSize(lM,&n,NULL);CHKERRQ(ierr);
2767           ierr = PetscContainerGetPointer(c,(void**)&csr);CHKERRQ(ierr);
2768           ierr = PCBDDCSetLocalAdjacencyGraph(bddcipc_ctx->bddc,n,csr,csr + (n + 1),PETSC_COPY_VALUES);CHKERRQ(ierr);
2769           ierr = MatISRestoreLocalMat(M,&lM);CHKERRQ(ierr);
2770         }
2771         ierr = PCSetOptionsPrefix(bddcipc_ctx->bddc,((PetscObject)ksps[1])->prefix);CHKERRQ(ierr);
2772         ierr = PCSetErrorIfFailure(bddcipc_ctx->bddc,pc->erroriffailure);CHKERRQ(ierr);
2773         ierr = PCSetFromOptions(bddcipc_ctx->bddc);CHKERRQ(ierr);
2774 
2775         /* wrap the interface application */
2776         ierr = PCSetType(ppc,PCSHELL);CHKERRQ(ierr);
2777         ierr = PCShellSetName(ppc,"FETI-DP pressure");CHKERRQ(ierr);
2778         ierr = PCShellSetContext(ppc,bddcipc_ctx);CHKERRQ(ierr);
2779         ierr = PCShellSetSetUp(ppc,PCSetUp_BDDCIPC);CHKERRQ(ierr);
2780         ierr = PCShellSetApply(ppc,PCApply_BDDCIPC);CHKERRQ(ierr);
2781         ierr = PCShellSetApplyTranspose(ppc,PCApplyTranspose_BDDCIPC);CHKERRQ(ierr);
2782         ierr = PCShellSetView(ppc,PCView_BDDCIPC);CHKERRQ(ierr);
2783         ierr = PCShellSetDestroy(ppc,PCDestroy_BDDCIPC);CHKERRQ(ierr);
2784       }
2785 
2786       /* determine if we need to assemble M to construct a preconditioner */
2787       if (!matisok) {
2788         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2789         ierr = PetscObjectTypeCompareAny((PetscObject)ppc,&matisok,PCBDDC,PCJACOBI,PCNONE,PCMG,"");CHKERRQ(ierr);
2790         if (ismatis && !matisok) {
2791           ierr = MatConvert(M,MATAIJ,MAT_INPLACE_MATRIX,&M);CHKERRQ(ierr);
2792         }
2793       }
2794 
2795       /* run the subproblems to check convergence */
2796       ierr = PetscOptionsGetBool(NULL,((PetscObject)newmat)->prefix,"-check_saddlepoint",&check,NULL);CHKERRQ(ierr);
2797       if (check) {
2798         PetscInt i;
2799 
2800         for (i=0;i<nn;i++) {
2801           KSP       kspC;
2802           PC        pc;
2803           Mat       F,pF;
2804           Vec       x,y;
2805           PetscBool isschur,prec = PETSC_TRUE;
2806 
2807           ierr = KSPCreate(PetscObjectComm((PetscObject)ksps[i]),&kspC);CHKERRQ(ierr);
2808           ierr = KSPSetOptionsPrefix(kspC,((PetscObject)ksps[i])->prefix);CHKERRQ(ierr);
2809           ierr = KSPAppendOptionsPrefix(kspC,"check_");CHKERRQ(ierr);
2810           ierr = KSPGetOperators(ksps[i],&F,&pF);CHKERRQ(ierr);
2811           ierr = PetscObjectTypeCompare((PetscObject)F,MATSCHURCOMPLEMENT,&isschur);CHKERRQ(ierr);
2812           if (isschur) {
2813             KSP  kspS,kspS2;
2814             Mat  A00,pA00,A10,A01,A11;
2815             char prefix[256];
2816 
2817             ierr = MatSchurComplementGetKSP(F,&kspS);CHKERRQ(ierr);
2818             ierr = MatSchurComplementGetSubMatrices(F,&A00,&pA00,&A01,&A10,&A11);CHKERRQ(ierr);
2819             ierr = MatCreateSchurComplement(A00,pA00,A01,A10,A11,&F);CHKERRQ(ierr);
2820             ierr = MatSchurComplementGetKSP(F,&kspS2);CHKERRQ(ierr);
2821             ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sschur_",((PetscObject)kspC)->prefix);CHKERRQ(ierr);
2822             ierr = KSPSetOptionsPrefix(kspS2,prefix);CHKERRQ(ierr);
2823             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2824             ierr = PCSetType(pc,PCKSP);CHKERRQ(ierr);
2825             ierr = PCKSPSetKSP(pc,kspS);CHKERRQ(ierr);
2826             ierr = KSPSetFromOptions(kspS2);CHKERRQ(ierr);
2827             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2828             ierr = PCSetUseAmat(pc,PETSC_TRUE);CHKERRQ(ierr);
2829           } else {
2830             ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
2831           }
2832           ierr = KSPSetFromOptions(kspC);CHKERRQ(ierr);
2833           ierr = PetscOptionsGetBool(NULL,((PetscObject)kspC)->prefix,"-preconditioned",&prec,NULL);CHKERRQ(ierr);
2834           if (prec)  {
2835             ierr = KSPGetPC(ksps[i],&pc);CHKERRQ(ierr);
2836             ierr = KSPSetPC(kspC,pc);CHKERRQ(ierr);
2837           }
2838           ierr = KSPSetOperators(kspC,F,pF);CHKERRQ(ierr);
2839           ierr = MatCreateVecs(F,&x,&y);CHKERRQ(ierr);
2840           ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2841           ierr = MatMult(F,x,y);CHKERRQ(ierr);
2842           ierr = KSPSolve(kspC,y,x);CHKERRQ(ierr);
2843           ierr = KSPDestroy(&kspC);CHKERRQ(ierr);
2844           ierr = MatDestroy(&F);CHKERRQ(ierr);
2845           ierr = VecDestroy(&x);CHKERRQ(ierr);
2846           ierr = VecDestroy(&y);CHKERRQ(ierr);
2847         }
2848       }
2849       ierr = PetscFree(ksps);CHKERRQ(ierr);
2850     }
2851   }
2852   /* return pointers for objects created */
2853   *fetidp_mat = newmat;
2854   *fetidp_pc  = newpc;
2855   PetscFunctionReturn(0);
2856 }
2857 
2858 /*@C
2859  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2860 
2861    Collective
2862 
2863    Input Parameters:
2864 +  pc - the BDDC preconditioning context (setup should have been called before)
2865 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2866 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2867 
2868    Output Parameters:
2869 +  fetidp_mat - shell FETI-DP matrix object
2870 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2871 
2872    Level: developer
2873 
2874    Notes:
2875      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2876 
2877 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2878 @*/
2879 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2880 {
2881   PetscErrorCode ierr;
2882 
2883   PetscFunctionBegin;
2884   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2885   if (pc->setupcalled) {
2886     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2887   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first");
2888   PetscFunctionReturn(0);
2889 }
2890 /* -------------------------------------------------------------------------- */
2891 /*MC
2892    PCBDDC - Balancing Domain Decomposition by Constraints.
2893 
2894    An implementation of the BDDC preconditioner based on
2895 
2896 .vb
2897    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2898    [2] A. Klawonn and O. B. Widlund. "Dual-Primal FETI Methods for Linear Elasticity", http://cs.nyu.edu/csweb/Research/TechReports/TR2004-855/TR2004-855.pdf
2899    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2900    [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
2901 .ve
2902 
2903    The matrix to be preconditioned (Pmat) must be of type MATIS.
2904 
2905    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2906 
2907    It also works with unsymmetric and indefinite problems.
2908 
2909    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.
2910 
2911    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).
2912 
2913    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()
2914    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2915 
2916    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2917 
2918    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.
2919    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2920 
2921    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2922 
2923    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.
2924 
2925    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.
2926    Deluxe scaling is not supported yet for FETI-DP.
2927 
2928    Options Database Keys (some of them, run with -h for a complete list):
2929 
2930 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2931 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2932 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2933 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2934 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2935 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2936 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2937 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2938 .    -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)
2939 .    -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)
2940 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2941 .    -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)
2942 .    -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)
2943 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2944 
2945    Options for Dirichlet, Neumann or coarse solver can be set with
2946 .vb
2947       -pc_bddc_dirichlet_
2948       -pc_bddc_neumann_
2949       -pc_bddc_coarse_
2950 .ve
2951    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2952 
2953    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2954 .vb
2955       -pc_bddc_dirichlet_lN_
2956       -pc_bddc_neumann_lN_
2957       -pc_bddc_coarse_lN_
2958 .ve
2959    Note that level number ranges from the finest (0) to the coarsest (N).
2960    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.
2961 .vb
2962      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2963 .ve
2964    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
2965 
2966    Level: intermediate
2967 
2968    Developer Notes:
2969 
2970    Contributed by Stefano Zampini
2971 
2972 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2973 M*/
2974 
2975 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2976 {
2977   PetscErrorCode      ierr;
2978   PC_BDDC             *pcbddc;
2979 
2980   PetscFunctionBegin;
2981   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2982   pc->data = (void*)pcbddc;
2983 
2984   /* create PCIS data structure */
2985   ierr = PCISCreate(pc);CHKERRQ(ierr);
2986 
2987   /* create local graph structure */
2988   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2989 
2990   /* BDDC nonzero defaults */
2991   pcbddc->use_local_adj             = PETSC_TRUE;
2992   pcbddc->use_vertices              = PETSC_TRUE;
2993   pcbddc->use_edges                 = PETSC_TRUE;
2994   pcbddc->symmetric_primal          = PETSC_TRUE;
2995   pcbddc->vertex_size               = 1;
2996   pcbddc->recompute_topography      = PETSC_TRUE;
2997   pcbddc->coarse_size               = -1;
2998   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2999   pcbddc->coarsening_ratio          = 8;
3000   pcbddc->coarse_eqs_per_proc       = 1;
3001   pcbddc->benign_compute_correction = PETSC_TRUE;
3002   pcbddc->nedfield                  = -1;
3003   pcbddc->nedglobal                 = PETSC_TRUE;
3004   pcbddc->graphmaxcount             = PETSC_MAX_INT;
3005   pcbddc->sub_schurs_layers         = -1;
3006   pcbddc->adaptive_threshold[0]     = 0.0;
3007   pcbddc->adaptive_threshold[1]     = 0.0;
3008 
3009   /* function pointers */
3010   pc->ops->apply               = PCApply_BDDC;
3011   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
3012   pc->ops->setup               = PCSetUp_BDDC;
3013   pc->ops->destroy             = PCDestroy_BDDC;
3014   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
3015   pc->ops->view                = PCView_BDDC;
3016   pc->ops->applyrichardson     = 0;
3017   pc->ops->applysymmetricleft  = 0;
3018   pc->ops->applysymmetricright = 0;
3019   pc->ops->presolve            = PCPreSolve_BDDC;
3020   pc->ops->postsolve           = PCPostSolve_BDDC;
3021   pc->ops->reset               = PCReset_BDDC;
3022 
3023   /* composing function */
3024   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
3025   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
3026   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
3027   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3028   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3029   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesLocalIS_C",PCBDDCGetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3030   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesIS_C",PCBDDCGetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3031   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
3032   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
3033   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
3034   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
3035   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3036   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3037   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3038   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3039   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3040   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3041   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3042   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3043   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
3044   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
3045   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
3046   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
3047   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
3048   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
3049   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
3050   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
3051   PetscFunctionReturn(0);
3052 }
3053 
3054 /*@C
3055  PCBDDCInitializePackage - This function initializes everything in the PCBDDC package. It is called
3056     from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to PCCreate_BDDC()
3057     when using static libraries.
3058 
3059  Level: developer
3060 
3061  .keywords: PC, PCBDDC, initialize, package
3062  .seealso: PetscInitialize()
3063 @*/
3064 PetscErrorCode PCBDDCInitializePackage(void)
3065 {
3066   PetscErrorCode ierr;
3067   int            i;
3068 
3069   PetscFunctionBegin;
3070   if (PCBDDCPackageInitialized) PetscFunctionReturn(0);
3071   PCBDDCPackageInitialized = PETSC_TRUE;
3072   ierr = PetscRegisterFinalize(PCBDDCFinalizePackage);CHKERRQ(ierr);
3073 
3074   /* general events */
3075   ierr = PetscLogEventRegister("PCBDDCTopo",PC_CLASSID,&PC_BDDC_Topology[0]);CHKERRQ(ierr);
3076   ierr = PetscLogEventRegister("PCBDDCLKSP",PC_CLASSID,&PC_BDDC_LocalSolvers[0]);CHKERRQ(ierr);
3077   ierr = PetscLogEventRegister("PCBDDCLWor",PC_CLASSID,&PC_BDDC_LocalWork[0]);CHKERRQ(ierr);
3078   ierr = PetscLogEventRegister("PCBDDCCorr",PC_CLASSID,&PC_BDDC_CorrectionSetUp[0]);CHKERRQ(ierr);
3079   ierr = PetscLogEventRegister("PCBDDCCSet",PC_CLASSID,&PC_BDDC_CoarseSetUp[0]);CHKERRQ(ierr);
3080   ierr = PetscLogEventRegister("PCBDDCCKSP",PC_CLASSID,&PC_BDDC_CoarseSolver[0]);CHKERRQ(ierr);
3081   ierr = PetscLogEventRegister("PCBDDCAdap",PC_CLASSID,&PC_BDDC_AdaptiveSetUp[0]);CHKERRQ(ierr);
3082   ierr = PetscLogEventRegister("PCBDDCScal",PC_CLASSID,&PC_BDDC_Scaling[0]);CHKERRQ(ierr);
3083   ierr = PetscLogEventRegister("PCBDDCSchr",PC_CLASSID,&PC_BDDC_Schurs[0]);CHKERRQ(ierr);
3084   for (i=1;i<PETSC_PCBDDC_MAXLEVELS;i++) {
3085     char ename[32];
3086 
3087     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCTopo l%02d",i);CHKERRQ(ierr);
3088     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Topology[i]);CHKERRQ(ierr);
3089     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLKSP l%02d",i);CHKERRQ(ierr);
3090     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalSolvers[i]);CHKERRQ(ierr);
3091     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLWor l%02d",i);CHKERRQ(ierr);
3092     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalWork[i]);CHKERRQ(ierr);
3093     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCorr l%02d",i);CHKERRQ(ierr);
3094     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CorrectionSetUp[i]);CHKERRQ(ierr);
3095     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCSet l%02d",i);CHKERRQ(ierr);
3096     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSetUp[i]);CHKERRQ(ierr);
3097     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCKSP l%02d",i);CHKERRQ(ierr);
3098     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSolver[i]);CHKERRQ(ierr);
3099     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCAdap l%02d",i);CHKERRQ(ierr);
3100     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_AdaptiveSetUp[i]);CHKERRQ(ierr);
3101     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCScal l%02d",i);CHKERRQ(ierr);
3102     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Scaling[i]);CHKERRQ(ierr);
3103     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCSchr l%02d",i);CHKERRQ(ierr);
3104     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Schurs[i]);CHKERRQ(ierr);
3105   }
3106   PetscFunctionReturn(0);
3107 }
3108 
3109 /*@C
3110  PCBDDCFinalizePackage - This function frees everything from the PCBDDC package. It is
3111     called from PetscFinalize() automatically.
3112 
3113  Level: developer
3114 
3115  .keywords: Petsc, destroy, package
3116  .seealso: PetscFinalize()
3117 @*/
3118 PetscErrorCode PCBDDCFinalizePackage(void)
3119 {
3120   PetscFunctionBegin;
3121   PCBDDCPackageInitialized = PETSC_FALSE;
3122   PetscFunctionReturn(0);
3123 }
3124