xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 55e7fe800d976e85ed2b5cd8bfdef564daa37bd9)
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      iscg = PETSC_FALSE, save_rhs = PETSC_TRUE, benign_correction_computed;
1324 
1325   PetscFunctionBegin;
1326   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1327   if (ksp) {
1328     PetscBool isgroppcg, ispipecg, ispipelcg, ispipecgrr;
1329 
1330     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1331     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1332     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1333     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipelcg);CHKERRQ(ierr);
1334     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1335     iscg = (PetscBool)(iscg || isgroppcg || ispipecg || ispipelcg || ispipecgrr);
1336     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || !iscg) {
1337       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1338     }
1339   }
1340   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1341     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1342   }
1343 
1344   /* Creates parallel work vectors used in presolve */
1345   if (!pcbddc->original_rhs) {
1346     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1347   }
1348   if (!pcbddc->temp_solution) {
1349     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1350   }
1351 
1352   pcbddc->temp_solution_used = PETSC_FALSE;
1353   if (x) {
1354     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1355     used_vec = x;
1356   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1357     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1358     used_vec = pcbddc->temp_solution;
1359     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1360     pcbddc->temp_solution_used = PETSC_TRUE;
1361     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1362     save_rhs = PETSC_FALSE;
1363     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1364   }
1365 
1366   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1367   if (ksp) {
1368     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1369     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1370     if (!pcbddc->ksp_guess_nonzero) {
1371       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1372     }
1373   }
1374 
1375   pcbddc->rhs_change = PETSC_FALSE;
1376   /* Take into account zeroed rows -> change rhs and store solution removed */
1377   if (rhs && pcbddc->eliminate_dirdofs) {
1378     IS dirIS = NULL;
1379 
1380     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1381     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1382     if (dirIS) {
1383       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1384       PetscInt          dirsize,i,*is_indices;
1385       PetscScalar       *array_x;
1386       const PetscScalar *array_diagonal;
1387 
1388       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1389       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1390       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1391       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1392       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1393       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1394       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1395       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1396       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1397       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1398       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1399       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1400       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1401       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1402       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1403       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1404       pcbddc->rhs_change = PETSC_TRUE;
1405       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1406     }
1407   }
1408 
1409   /* remove the computed solution or the initial guess from the rhs */
1410   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1411     /* save the original rhs */
1412     if (save_rhs) {
1413       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1414       save_rhs = PETSC_FALSE;
1415     }
1416     pcbddc->rhs_change = PETSC_TRUE;
1417     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1418     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1419     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1420     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1421     pcbddc->temp_solution_used = PETSC_TRUE;
1422     if (ksp) {
1423       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1424     }
1425   }
1426   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1427 
1428   /* compute initial vector in benign space if needed
1429      and remove non-benign solution from the rhs */
1430   benign_correction_computed = PETSC_FALSE;
1431   if (rhs && pcbddc->benign_compute_correction && (pcbddc->benign_have_null || pcbddc->benign_apply_coarse_only)) {
1432     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1433        Recursively apply BDDC in the multilevel case */
1434     if (!pcbddc->benign_vec) {
1435       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1436     }
1437     /* keep applying coarse solver unless we no longer have benign subdomains */
1438     pcbddc->benign_apply_coarse_only = pcbddc->benign_have_null ? PETSC_TRUE : PETSC_FALSE;
1439     if (!pcbddc->benign_skip_correction) {
1440       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1441       benign_correction_computed = PETSC_TRUE;
1442       if (pcbddc->temp_solution_used) {
1443         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1444       }
1445       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1446       /* store the original rhs if not done earlier */
1447       if (save_rhs) {
1448         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1449       }
1450       if (pcbddc->rhs_change) {
1451         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1452       } else {
1453         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1454       }
1455       pcbddc->rhs_change = PETSC_TRUE;
1456     }
1457     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1458   } else {
1459     ierr = VecDestroy(&pcbddc->benign_vec);CHKERRQ(ierr);
1460   }
1461 
1462   /* dbg output */
1463   if (pcbddc->dbg_flag && benign_correction_computed) {
1464     Vec v;
1465 
1466     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1467     if (pcbddc->ChangeOfBasisMatrix) {
1468       ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1469     } else {
1470       ierr = VecCopy(rhs,v);CHKERRQ(ierr);
1471     }
1472     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1473     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1474     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,pcbddc->dbg_viewer);CHKERRQ(ierr);
1475     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1476     ierr = VecDestroy(&v);CHKERRQ(ierr);
1477   }
1478 
1479   /* set initial guess if using PCG */
1480   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1481   if (x && pcbddc->use_exact_dirichlet_trick) {
1482     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1483     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1484       if (benign_correction_computed) { /* we have already saved the changed rhs */
1485         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1486       } else {
1487         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1488       }
1489       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1490       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1491     } else {
1492       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1493       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1494     }
1495     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1496     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1497       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1498       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1499       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1500       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1501     } else {
1502       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1503       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1504     }
1505     if (ksp) {
1506       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1507     }
1508     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1509   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1510     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1511   }
1512   PetscFunctionReturn(0);
1513 }
1514 
1515 /*
1516    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1517                      approach has been selected. Also, restores rhs to its original state.
1518 
1519    Input Parameter:
1520 +  pc - the preconditioner contex
1521 
1522    Application Interface Routine: PCPostSolve()
1523 
1524    Notes:
1525      The interface routine PCPostSolve() is not usually called directly by
1526      the user, but instead is called by KSPSolve().
1527 */
1528 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1529 {
1530   PetscErrorCode ierr;
1531   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1532 
1533   PetscFunctionBegin;
1534   /* add solution removed in presolve */
1535   if (x && pcbddc->rhs_change) {
1536     if (pcbddc->temp_solution_used) {
1537       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1538     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1539       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1540     }
1541     /* restore to original state (not for FETI-DP) */
1542     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1543   }
1544 
1545   /* restore rhs to its original state (not needed for FETI-DP) */
1546   if (rhs && pcbddc->rhs_change) {
1547     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1548     pcbddc->rhs_change = PETSC_FALSE;
1549   }
1550   /* restore ksp guess state */
1551   if (ksp) {
1552     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1553     /* reset flag for exact dirichlet trick */
1554     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1555   }
1556   PetscFunctionReturn(0);
1557 }
1558 
1559 /*
1560    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1561                   by setting data structures and options.
1562 
1563    Input Parameter:
1564 +  pc - the preconditioner context
1565 
1566    Application Interface Routine: PCSetUp()
1567 
1568    Notes:
1569      The interface routine PCSetUp() is not usually called directly by
1570      the user, but instead is called by PCApply() if necessary.
1571 */
1572 PetscErrorCode PCSetUp_BDDC(PC pc)
1573 {
1574   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1575   PCBDDCSubSchurs sub_schurs;
1576   Mat_IS*         matis;
1577   MatNullSpace    nearnullspace;
1578   Mat             lA;
1579   IS              lP,zerodiag = NULL;
1580   PetscInt        nrows,ncols;
1581   PetscMPIInt     size;
1582   PetscBool       computesubschurs;
1583   PetscBool       computeconstraintsmatrix;
1584   PetscBool       new_nearnullspace_provided,ismatis,rl;
1585   PetscErrorCode  ierr;
1586 
1587   PetscFunctionBegin;
1588   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1589   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1590   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1591   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1592   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
1593 
1594   matis = (Mat_IS*)pc->pmat->data;
1595   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1596   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1597      Also, BDDC builds its own KSP for the Dirichlet problem */
1598   rl = pcbddc->recompute_topography;
1599   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) rl = PETSC_TRUE;
1600   ierr = MPIU_Allreduce(&rl,&pcbddc->recompute_topography,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1601   if (pcbddc->recompute_topography) {
1602     pcbddc->graphanalyzed    = PETSC_FALSE;
1603     computeconstraintsmatrix = PETSC_TRUE;
1604   } else {
1605     computeconstraintsmatrix = PETSC_FALSE;
1606   }
1607 
1608   /* check parameters' compatibility */
1609   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1610   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1611   pcbddc->use_deluxe_scaling   = (PetscBool)(pcbddc->use_deluxe_scaling && size > 1);
1612   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_selection && size > 1);
1613   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1614   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1615 
1616   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1617   if (pcbddc->switch_static) {
1618     PetscBool ismatis;
1619 
1620     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1621     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1622   }
1623 
1624   /* activate all connected components if the netflux has been requested */
1625   if (pcbddc->compute_nonetflux) {
1626     pcbddc->use_vertices = PETSC_TRUE;
1627     pcbddc->use_edges    = PETSC_TRUE;
1628     pcbddc->use_faces    = PETSC_TRUE;
1629   }
1630 
1631   /* Get stdout for dbg */
1632   if (pcbddc->dbg_flag) {
1633     if (!pcbddc->dbg_viewer) {
1634       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1635     }
1636     ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1637     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1638   }
1639 
1640   /* process topology information */
1641   ierr = PetscLogEventBegin(PC_BDDC_Topology[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1642   if (pcbddc->recompute_topography) {
1643     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1644     if (pcbddc->discretegradient) {
1645       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1646     }
1647   }
1648 
1649   /* change basis if requested by the user */
1650   if (pcbddc->user_ChangeOfBasisMatrix) {
1651     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1652     pcbddc->use_change_of_basis = PETSC_FALSE;
1653     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1654   } else {
1655     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1656     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1657     pcbddc->local_mat = matis->A;
1658   }
1659 
1660   /*
1661      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1662      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1663   */
1664   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1665   if (pcbddc->benign_saddle_point) {
1666     PC_IS* pcis = (PC_IS*)pc->data;
1667 
1668     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1669     /* detect local saddle point and change the basis in pcbddc->local_mat */
1670     ierr = PCBDDCBenignDetectSaddlePoint(pc,(PetscBool)(!pcbddc->recompute_topography),&zerodiag);CHKERRQ(ierr);
1671     /* pop B0 mat from local mat */
1672     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1673     /* give pcis a hint to not reuse submatrices during PCISCreate */
1674     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1675       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1676         pcis->reusesubmatrices = PETSC_FALSE;
1677       } else {
1678         pcis->reusesubmatrices = PETSC_TRUE;
1679       }
1680     } else {
1681       pcis->reusesubmatrices = PETSC_FALSE;
1682     }
1683   }
1684 
1685   /* propagate relevant information */
1686   if (matis->A->symmetric_set) {
1687     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1688   }
1689   if (matis->A->spd_set) {
1690     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1691   }
1692 
1693   /* Set up all the "iterative substructuring" common block without computing solvers */
1694   {
1695     Mat temp_mat;
1696 
1697     temp_mat = matis->A;
1698     matis->A = pcbddc->local_mat;
1699     ierr = PCISSetUp(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1700     pcbddc->local_mat = matis->A;
1701     matis->A = temp_mat;
1702   }
1703 
1704   /* Analyze interface */
1705   if (!pcbddc->graphanalyzed) {
1706     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1707     computeconstraintsmatrix = PETSC_TRUE;
1708     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1709       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1710     }
1711     if (pcbddc->compute_nonetflux) {
1712       MatNullSpace nnfnnsp;
1713 
1714       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1715       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1716       /* TODO what if a nearnullspace is already attached? */
1717       if (nnfnnsp) {
1718         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1719         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1720       }
1721     }
1722   }
1723   ierr = PetscLogEventEnd(PC_BDDC_Topology[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1724 
1725   /* check existence of a divergence free extension, i.e.
1726      b(v_I,p_0) = 0 for all v_I (raise error if not).
1727      Also, check that PCBDDCBenignGetOrSetP0 works */
1728   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1729     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1730   }
1731   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1732 
1733   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1734   if (computesubschurs && pcbddc->recompute_topography) {
1735     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1736   }
1737   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1738   if (!pcbddc->use_deluxe_scaling) {
1739     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1740   }
1741 
1742   /* finish setup solvers and do adaptive selection of constraints */
1743   sub_schurs = pcbddc->sub_schurs;
1744   if (sub_schurs && sub_schurs->schur_explicit) {
1745     if (computesubschurs) {
1746       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1747     }
1748     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1749   } else {
1750     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1751     if (computesubschurs) {
1752       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1753     }
1754   }
1755   if (pcbddc->adaptive_selection) {
1756     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1757     computeconstraintsmatrix = PETSC_TRUE;
1758   }
1759 
1760   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1761   new_nearnullspace_provided = PETSC_FALSE;
1762   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1763   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1764     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1765       new_nearnullspace_provided = PETSC_TRUE;
1766     } else {
1767       /* determine if the two nullspaces are different (should be lightweight) */
1768       if (nearnullspace != pcbddc->onearnullspace) {
1769         new_nearnullspace_provided = PETSC_TRUE;
1770       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1771         PetscInt         i;
1772         const Vec        *nearnullvecs;
1773         PetscObjectState state;
1774         PetscInt         nnsp_size;
1775         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1776         for (i=0;i<nnsp_size;i++) {
1777           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1778           if (pcbddc->onearnullvecs_state[i] != state) {
1779             new_nearnullspace_provided = PETSC_TRUE;
1780             break;
1781           }
1782         }
1783       }
1784     }
1785   } else {
1786     if (!nearnullspace) { /* both nearnullspaces are null */
1787       new_nearnullspace_provided = PETSC_FALSE;
1788     } else { /* nearnullspace attached later */
1789       new_nearnullspace_provided = PETSC_TRUE;
1790     }
1791   }
1792 
1793   /* Setup constraints and related work vectors */
1794   /* reset primal space flags */
1795   ierr = PetscLogEventBegin(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1796   pcbddc->new_primal_space = PETSC_FALSE;
1797   pcbddc->new_primal_space_local = PETSC_FALSE;
1798   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1799     /* It also sets the primal space flags */
1800     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1801   }
1802   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1803   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1804 
1805   if (pcbddc->use_change_of_basis) {
1806     PC_IS *pcis = (PC_IS*)(pc->data);
1807 
1808     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1809     if (pcbddc->benign_change) {
1810       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1811       /* pop B0 from pcbddc->local_mat */
1812       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1813     }
1814     /* get submatrices */
1815     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1816     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1817     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1818     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1819     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1820     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1821     /* set flag in pcis to not reuse submatrices during PCISCreate */
1822     pcis->reusesubmatrices = PETSC_FALSE;
1823   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1824     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1825     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1826     pcbddc->local_mat = matis->A;
1827   }
1828 
1829   /* interface pressure block row for B_C */
1830   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1831   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1832   if (lA && lP) {
1833     PC_IS*    pcis = (PC_IS*)pc->data;
1834     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1835     PetscBool issym;
1836     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1837     if (issym) {
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 = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1841       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1842     } else {
1843       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1844       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1845       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1846       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1847     }
1848     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1849     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1850     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1851     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1852     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1853     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1854     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1855     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1856   }
1857   ierr = PetscLogEventEnd(PC_BDDC_LocalWork[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
1858 
1859   /* SetUp coarse and local Neumann solvers */
1860   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1861   /* SetUp Scaling operator */
1862   if (pcbddc->use_deluxe_scaling) {
1863     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1864   }
1865 
1866   /* mark topography as done */
1867   pcbddc->recompute_topography = PETSC_FALSE;
1868 
1869   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1870   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1871 
1872   if (pcbddc->dbg_flag) {
1873     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1874     ierr = PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1875   }
1876   PetscFunctionReturn(0);
1877 }
1878 
1879 /*
1880    PCApply_BDDC - Applies the BDDC operator to a vector.
1881 
1882    Input Parameters:
1883 +  pc - the preconditioner context
1884 -  r - input vector (global)
1885 
1886    Output Parameter:
1887 .  z - output vector (global)
1888 
1889    Application Interface Routine: PCApply()
1890  */
1891 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1892 {
1893   PC_IS             *pcis = (PC_IS*)(pc->data);
1894   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1895   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1896   PetscErrorCode    ierr;
1897   const PetscScalar one = 1.0;
1898   const PetscScalar m_one = -1.0;
1899   const PetscScalar zero = 0.0;
1900 
1901 /* This code is similar to that provided in nn.c for PCNN
1902    NN interface preconditioner changed to BDDC
1903    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1904 
1905   PetscFunctionBegin;
1906   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1907   if (pcbddc->ChangeOfBasisMatrix) {
1908     Vec swap;
1909 
1910     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1911     swap = pcbddc->work_change;
1912     pcbddc->work_change = r;
1913     r = swap;
1914     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1915     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1916       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1917       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1918     }
1919   }
1920   if (pcbddc->benign_have_null) { /* get p0 from r */
1921     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1922   }
1923   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1924     ierr = VecCopy(r,z);CHKERRQ(ierr);
1925     /* First Dirichlet solve */
1926     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1927     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1928     /*
1929       Assembling right hand side for BDDC operator
1930       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1931       - pcis->vec1_B the interface part of the global vector z
1932     */
1933     if (n_D) {
1934       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1935       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1936       if (pcbddc->switch_static) {
1937         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1938 
1939         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1940         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1941         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1942         if (!pcbddc->switch_static_change) {
1943           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1944         } else {
1945           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1946           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1947           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1948         }
1949         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1950         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1951         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1952         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1953       } else {
1954         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1955       }
1956     } else {
1957       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1958     }
1959     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1960     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1961     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1962   } else {
1963     if (!pcbddc->benign_apply_coarse_only) {
1964       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1965     }
1966   }
1967 
1968   /* Apply interface preconditioner
1969      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1970   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1971 
1972   /* Apply transpose of partition of unity operator */
1973   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1974 
1975   /* Second Dirichlet solve and assembling of output */
1976   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1977   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1978   if (n_B) {
1979     if (pcbddc->switch_static) {
1980       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1981 
1982       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1983       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1984       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1985       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1986       if (!pcbddc->switch_static_change) {
1987         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1988       } else {
1989         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1990         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1991         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1992       }
1993       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1994       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1995     } else {
1996       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1997     }
1998   } else if (pcbddc->switch_static) { /* n_B is zero */
1999     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2000 
2001     if (!pcbddc->switch_static_change) {
2002       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2003     } else {
2004       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2005       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2006       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2007     }
2008   }
2009   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2010 
2011   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2012     if (pcbddc->switch_static) {
2013       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2014     } else {
2015       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2016     }
2017     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2018     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2019   } else {
2020     if (pcbddc->switch_static) {
2021       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2022     } else {
2023       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2024     }
2025     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2026     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2027   }
2028   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2029     if (pcbddc->benign_apply_coarse_only) {
2030       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2031     }
2032     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2033   }
2034 
2035   if (pcbddc->ChangeOfBasisMatrix) {
2036     pcbddc->work_change = r;
2037     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2038     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2039   }
2040   PetscFunctionReturn(0);
2041 }
2042 
2043 /*
2044    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
2045 
2046    Input Parameters:
2047 +  pc - the preconditioner context
2048 -  r - input vector (global)
2049 
2050    Output Parameter:
2051 .  z - output vector (global)
2052 
2053    Application Interface Routine: PCApplyTranspose()
2054  */
2055 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
2056 {
2057   PC_IS             *pcis = (PC_IS*)(pc->data);
2058   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
2059   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
2060   PetscErrorCode    ierr;
2061   const PetscScalar one = 1.0;
2062   const PetscScalar m_one = -1.0;
2063   const PetscScalar zero = 0.0;
2064 
2065   PetscFunctionBegin;
2066   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
2067   if (pcbddc->ChangeOfBasisMatrix) {
2068     Vec swap;
2069 
2070     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
2071     swap = pcbddc->work_change;
2072     pcbddc->work_change = r;
2073     r = swap;
2074     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
2075     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
2076       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
2077       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
2078     }
2079   }
2080   if (pcbddc->benign_have_null) { /* get p0 from r */
2081     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
2082   }
2083   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2084     ierr = VecCopy(r,z);CHKERRQ(ierr);
2085     /* First Dirichlet solve */
2086     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2087     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2088     /*
2089       Assembling right hand side for BDDC operator
2090       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
2091       - pcis->vec1_B the interface part of the global vector z
2092     */
2093     if (n_D) {
2094       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
2095       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
2096       if (pcbddc->switch_static) {
2097         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2098 
2099         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
2100         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2101         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2102         if (!pcbddc->switch_static_change) {
2103           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2104         } else {
2105           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2106           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2107           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2108         }
2109         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2110         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2111         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2112         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2113       } else {
2114         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
2115       }
2116     } else {
2117       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
2118     }
2119     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2120     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2121     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
2122   } else {
2123     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
2124   }
2125 
2126   /* Apply interface preconditioner
2127      input/output vecs: pcis->vec1_B and pcis->vec1_D */
2128   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
2129 
2130   /* Apply transpose of partition of unity operator */
2131   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2132 
2133   /* Second Dirichlet solve and assembling of output */
2134   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2135   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2136   if (n_B) {
2137     if (pcbddc->switch_static) {
2138       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2139 
2140       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2141       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2142       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2143       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2144       if (!pcbddc->switch_static_change) {
2145         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2146       } else {
2147         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2148         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2149         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2150       }
2151       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2152       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2153     } else {
2154       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2155     }
2156   } else if (pcbddc->switch_static) { /* n_B is zero */
2157     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2158 
2159     if (!pcbddc->switch_static_change) {
2160       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2161     } else {
2162       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2163       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2164       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2165     }
2166   }
2167   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2168   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2169     if (pcbddc->switch_static) {
2170       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2171     } else {
2172       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2173     }
2174     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2175     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2176   } else {
2177     if (pcbddc->switch_static) {
2178       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2179     } else {
2180       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2181     }
2182     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2183     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2184   }
2185   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2186     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2187   }
2188   if (pcbddc->ChangeOfBasisMatrix) {
2189     pcbddc->work_change = r;
2190     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2191     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2192   }
2193   PetscFunctionReturn(0);
2194 }
2195 
2196 PetscErrorCode PCReset_BDDC(PC pc)
2197 {
2198   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2199   PC_IS          *pcis = (PC_IS*)pc->data;
2200   KSP            kspD,kspR,kspC;
2201   PetscErrorCode ierr;
2202 
2203   PetscFunctionBegin;
2204   /* free BDDC custom data  */
2205   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2206   /* destroy objects related to topography */
2207   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2208   /* destroy objects for scaling operator */
2209   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2210   /* free solvers stuff */
2211   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2212   /* free global vectors needed in presolve */
2213   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2214   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2215   /* free data created by PCIS */
2216   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2217 
2218   /* restore defaults */
2219   kspD = pcbddc->ksp_D;
2220   kspR = pcbddc->ksp_R;
2221   kspC = pcbddc->coarse_ksp;
2222   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2223   pcis->n_neigh                     = -1;
2224   pcis->scaling_factor              = 1.0;
2225   pcis->reusesubmatrices            = PETSC_TRUE;
2226   pcbddc->use_local_adj             = PETSC_TRUE;
2227   pcbddc->use_vertices              = PETSC_TRUE;
2228   pcbddc->use_edges                 = PETSC_TRUE;
2229   pcbddc->symmetric_primal          = PETSC_TRUE;
2230   pcbddc->vertex_size               = 1;
2231   pcbddc->recompute_topography      = PETSC_TRUE;
2232   pcbddc->coarse_size               = -1;
2233   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2234   pcbddc->coarsening_ratio          = 8;
2235   pcbddc->coarse_eqs_per_proc       = 1;
2236   pcbddc->benign_compute_correction = PETSC_TRUE;
2237   pcbddc->nedfield                  = -1;
2238   pcbddc->nedglobal                 = PETSC_TRUE;
2239   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2240   pcbddc->sub_schurs_layers         = -1;
2241   pcbddc->ksp_D                     = kspD;
2242   pcbddc->ksp_R                     = kspR;
2243   pcbddc->coarse_ksp                = kspC;
2244   PetscFunctionReturn(0);
2245 }
2246 
2247 PetscErrorCode PCDestroy_BDDC(PC pc)
2248 {
2249   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2250   PetscErrorCode ierr;
2251 
2252   PetscFunctionBegin;
2253   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2254   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2255   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2256   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2257   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2258   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2259   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2260   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2261   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2262   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2263   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2264   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2265   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2266   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2267   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2268   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2269   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2270   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2271   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2272   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2273   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2274   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2275   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2276   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2277   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2278   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2279   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2280   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2281   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2282   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2283   PetscFunctionReturn(0);
2284 }
2285 
2286 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2287 {
2288   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2289   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2290   PetscErrorCode ierr;
2291 
2292   PetscFunctionBegin;
2293   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2294   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2295   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2296   mat_graph->cnloc = nloc;
2297   mat_graph->cdim  = dim;
2298   mat_graph->cloc  = PETSC_FALSE;
2299   PetscFunctionReturn(0);
2300 }
2301 
2302 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2303 {
2304   PetscFunctionBegin;
2305   *change = PETSC_TRUE;
2306   PetscFunctionReturn(0);
2307 }
2308 
2309 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2310 {
2311   FETIDPMat_ctx  mat_ctx;
2312   Vec            work;
2313   PC_IS*         pcis;
2314   PC_BDDC*       pcbddc;
2315   PetscErrorCode ierr;
2316 
2317   PetscFunctionBegin;
2318   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2319   pcis = (PC_IS*)mat_ctx->pc->data;
2320   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2321 
2322   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2323   /* copy rhs since we may change it during PCPreSolve_BDDC */
2324   if (!pcbddc->original_rhs) {
2325     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2326   }
2327   if (mat_ctx->rhs_flip) {
2328     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2329   } else {
2330     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2331   }
2332   if (mat_ctx->g2g_p) {
2333     /* interface pressure rhs */
2334     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2335     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2336     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2337     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2338     if (!mat_ctx->rhs_flip) {
2339       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2340     }
2341   }
2342   /*
2343      change of basis for physical rhs if needed
2344      It also changes the rhs in case of dirichlet boundaries
2345   */
2346   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2347   if (pcbddc->ChangeOfBasisMatrix) {
2348     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2349     work = pcbddc->work_change;
2350    } else {
2351     work = pcbddc->original_rhs;
2352   }
2353   /* store vectors for computation of fetidp final solution */
2354   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2355   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2356   /* scale rhs since it should be unassembled */
2357   /* TODO use counter scaling? (also below) */
2358   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2359   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2360   /* Apply partition of unity */
2361   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2362   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2363   if (!pcbddc->switch_static) {
2364     /* compute partially subassembled Schur complement right-hand side */
2365     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2366     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2367     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2368     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2369     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2370     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2371     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2372     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2373     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2374     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2375   }
2376   /* BDDC rhs */
2377   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2378   if (pcbddc->switch_static) {
2379     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2380   }
2381   /* apply BDDC */
2382   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2383   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2384   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2385 
2386   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2387   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2388   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2389   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2390   /* Add contribution to interface pressures */
2391   if (mat_ctx->l2g_p) {
2392     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2393     if (pcbddc->switch_static) {
2394       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2395     }
2396     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2397     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2398   }
2399   PetscFunctionReturn(0);
2400 }
2401 
2402 /*@
2403  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2404 
2405    Collective
2406 
2407    Input Parameters:
2408 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2409 -  standard_rhs    - the right-hand side of the original linear system
2410 
2411    Output Parameters:
2412 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2413 
2414    Level: developer
2415 
2416    Notes:
2417 
2418 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2419 @*/
2420 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2421 {
2422   FETIDPMat_ctx  mat_ctx;
2423   PetscErrorCode ierr;
2424 
2425   PetscFunctionBegin;
2426   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2427   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2428   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2429   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2430   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2431   PetscFunctionReturn(0);
2432 }
2433 
2434 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2435 {
2436   FETIDPMat_ctx  mat_ctx;
2437   PC_IS*         pcis;
2438   PC_BDDC*       pcbddc;
2439   PetscErrorCode ierr;
2440   Vec            work;
2441 
2442   PetscFunctionBegin;
2443   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2444   pcis = (PC_IS*)mat_ctx->pc->data;
2445   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2446 
2447   /* apply B_delta^T */
2448   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2449   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2450   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2451   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2452   if (mat_ctx->l2g_p) {
2453     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2454     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2455     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2456   }
2457 
2458   /* compute rhs for BDDC application */
2459   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2460   if (pcbddc->switch_static) {
2461     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2462     if (mat_ctx->l2g_p) {
2463       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2464       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2465     }
2466   }
2467 
2468   /* apply BDDC */
2469   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2470   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2471 
2472   /* put values into global vector */
2473   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2474   else work = standard_sol;
2475   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2476   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2477   if (!pcbddc->switch_static) {
2478     /* compute values into the interior if solved for the partially subassembled Schur complement */
2479     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2480     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2481     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2482   }
2483 
2484   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2485   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2486   /* add p0 solution to final solution */
2487   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2488   if (pcbddc->ChangeOfBasisMatrix) {
2489     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2490   }
2491   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2492   if (mat_ctx->g2g_p) {
2493     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2494     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2495   }
2496   PetscFunctionReturn(0);
2497 }
2498 
2499 static PetscErrorCode PCView_BDDCIPC(PC pc, PetscViewer viewer)
2500 {
2501   PetscErrorCode ierr;
2502   BDDCIPC_ctx    bddcipc_ctx;
2503   PetscBool      isascii;
2504 
2505   PetscFunctionBegin;
2506   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2507   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
2508   if (isascii) {
2509     ierr = PetscViewerASCIIPrintf(viewer,"BDDC interface preconditioner\n");CHKERRQ(ierr);
2510   }
2511   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2512   ierr = PCView(bddcipc_ctx->bddc,viewer);CHKERRQ(ierr);
2513   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2514   PetscFunctionReturn(0);
2515 }
2516 
2517 static PetscErrorCode PCSetUp_BDDCIPC(PC pc)
2518 {
2519   PetscErrorCode ierr;
2520   BDDCIPC_ctx    bddcipc_ctx;
2521   PetscBool      isbddc;
2522   Vec            vv;
2523   IS             is;
2524   PC_IS          *pcis;
2525 
2526   PetscFunctionBegin;
2527   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2528   ierr = PetscObjectTypeCompare((PetscObject)bddcipc_ctx->bddc,PCBDDC,&isbddc);CHKERRQ(ierr);
2529   if (!isbddc) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid type %s. Must be of type bddc",((PetscObject)bddcipc_ctx->bddc)->type_name);
2530   ierr = PCSetUp(bddcipc_ctx->bddc);CHKERRQ(ierr);
2531 
2532   /* create interface scatter */
2533   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2534   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2535   ierr = MatCreateVecs(pc->pmat,&vv,NULL);CHKERRQ(ierr);
2536   ierr = ISRenumber(pcis->is_B_global,NULL,NULL,&is);CHKERRQ(ierr);
2537   ierr = VecScatterCreateWithData(vv,is,pcis->vec1_B,NULL,&bddcipc_ctx->g2l);CHKERRQ(ierr);
2538   ierr = ISDestroy(&is);CHKERRQ(ierr);
2539   ierr = VecDestroy(&vv);CHKERRQ(ierr);
2540   PetscFunctionReturn(0);
2541 }
2542 
2543 static PetscErrorCode PCApply_BDDCIPC(PC pc, Vec r, Vec x)
2544 {
2545   PetscErrorCode ierr;
2546   BDDCIPC_ctx    bddcipc_ctx;
2547   PC_IS          *pcis;
2548   VecScatter     tmps;
2549 
2550   PetscFunctionBegin;
2551   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2552   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2553   tmps = pcis->global_to_B;
2554   pcis->global_to_B = bddcipc_ctx->g2l;
2555   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2556   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_FALSE);CHKERRQ(ierr);
2557   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2558   pcis->global_to_B = tmps;
2559   PetscFunctionReturn(0);
2560 }
2561 
2562 static PetscErrorCode PCApplyTranspose_BDDCIPC(PC pc, Vec r, Vec x)
2563 {
2564   PetscErrorCode ierr;
2565   BDDCIPC_ctx    bddcipc_ctx;
2566   PC_IS          *pcis;
2567   VecScatter     tmps;
2568 
2569   PetscFunctionBegin;
2570   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2571   pcis = (PC_IS*)(bddcipc_ctx->bddc->data);
2572   tmps = pcis->global_to_B;
2573   pcis->global_to_B = bddcipc_ctx->g2l;
2574   ierr = PCBDDCScalingRestriction(bddcipc_ctx->bddc,r,pcis->vec1_B);CHKERRQ(ierr);
2575   ierr = PCBDDCApplyInterfacePreconditioner(bddcipc_ctx->bddc,PETSC_TRUE);CHKERRQ(ierr);
2576   ierr = PCBDDCScalingExtension(bddcipc_ctx->bddc,pcis->vec1_B,x);CHKERRQ(ierr);
2577   pcis->global_to_B = tmps;
2578   PetscFunctionReturn(0);
2579 }
2580 
2581 static PetscErrorCode PCDestroy_BDDCIPC(PC pc)
2582 {
2583   PetscErrorCode ierr;
2584   BDDCIPC_ctx    bddcipc_ctx;
2585 
2586   PetscFunctionBegin;
2587   ierr = PCShellGetContext(pc,(void **)&bddcipc_ctx);CHKERRQ(ierr);
2588   ierr = PCDestroy(&bddcipc_ctx->bddc);CHKERRQ(ierr);
2589   ierr = VecScatterDestroy(&bddcipc_ctx->g2l);CHKERRQ(ierr);
2590   ierr = PetscFree(bddcipc_ctx);CHKERRQ(ierr);
2591   PetscFunctionReturn(0);
2592 }
2593 
2594 /*@
2595  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2596 
2597    Collective
2598 
2599    Input Parameters:
2600 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2601 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2602 
2603    Output Parameters:
2604 .  standard_sol    - the solution defined on the physical domain
2605 
2606    Level: developer
2607 
2608    Notes:
2609 
2610 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2611 @*/
2612 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2613 {
2614   FETIDPMat_ctx  mat_ctx;
2615   PetscErrorCode ierr;
2616 
2617   PetscFunctionBegin;
2618   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2619   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2620   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2621   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2622   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2623   PetscFunctionReturn(0);
2624 }
2625 
2626 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2627 {
2628 
2629   FETIDPMat_ctx  fetidpmat_ctx;
2630   Mat            newmat;
2631   FETIDPPC_ctx   fetidppc_ctx;
2632   PC             newpc;
2633   MPI_Comm       comm;
2634   PetscErrorCode ierr;
2635 
2636   PetscFunctionBegin;
2637   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2638   /* FETI-DP matrix */
2639   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2640   fetidpmat_ctx->fully_redundant = fully_redundant;
2641   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2642   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2643   ierr = PetscObjectSetName((PetscObject)newmat,!fetidpmat_ctx->l2g_lambda_only ? "F" : "G");CHKERRQ(ierr);
2644   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2645   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2646   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2647   /* propagate MatOptions */
2648   {
2649     PC_BDDC   *pcbddc = (PC_BDDC*)fetidpmat_ctx->pc->data;
2650     PetscBool issym;
2651 
2652     ierr = MatGetOption(pc->mat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2653     if (issym || pcbddc->symmetric_primal) {
2654       ierr = MatSetOption(newmat,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2655     }
2656   }
2657   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2658   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2659   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2660   /* FETI-DP preconditioner */
2661   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2662   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2663   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2664   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2665   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2666   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2667   ierr = PCSetErrorIfFailure(newpc,pc->erroriffailure);CHKERRQ(ierr);
2668   if (!fetidpmat_ctx->l2g_lambda_only) { /* standard FETI-DP */
2669     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2670     ierr = PCShellSetName(newpc,"FETI-DP multipliers");CHKERRQ(ierr);
2671     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2672     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2673     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2674     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2675     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2676   } else { /* saddle-point FETI-DP */
2677     Mat       M;
2678     PetscInt  psize;
2679     PetscBool fake = PETSC_FALSE, isfieldsplit;
2680 
2681     ierr = ISViewFromOptions(fetidpmat_ctx->lagrange,NULL,"-lag_view");CHKERRQ(ierr);
2682     ierr = ISViewFromOptions(fetidpmat_ctx->pressure,NULL,"-press_view");CHKERRQ(ierr);
2683     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2684     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2685     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2686     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2687     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2688     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2689     ierr = ISGetSize(fetidpmat_ctx->pressure,&psize);CHKERRQ(ierr);
2690     if (psize != M->rmap->N) {
2691       Mat      M2;
2692       PetscInt lpsize;
2693 
2694       fake = PETSC_TRUE;
2695       ierr = ISGetLocalSize(fetidpmat_ctx->pressure,&lpsize);CHKERRQ(ierr);
2696       ierr = MatCreate(comm,&M2);CHKERRQ(ierr);
2697       ierr = MatSetType(M2,MATAIJ);CHKERRQ(ierr);
2698       ierr = MatSetSizes(M2,lpsize,lpsize,psize,psize);CHKERRQ(ierr);
2699       ierr = MatSetUp(M2);CHKERRQ(ierr);
2700       ierr = MatAssemblyBegin(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2701       ierr = MatAssemblyEnd(M2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2702       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M2);CHKERRQ(ierr);
2703       ierr = MatDestroy(&M2);CHKERRQ(ierr);
2704     } else {
2705       ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2706     }
2707     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2708 
2709     /* we need to setfromoptions and setup here to access the blocks */
2710     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2711     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2712 
2713     /* user may have changed the type (e.g. -fetidp_pc_type none) */
2714     ierr = PetscObjectTypeCompare((PetscObject)newpc,PCFIELDSPLIT,&isfieldsplit);CHKERRQ(ierr);
2715     if (isfieldsplit) {
2716       KSP       *ksps;
2717       PC        ppc,lagpc;
2718       PetscInt  nn;
2719       PetscBool ismatis,matisok = PETSC_FALSE,check = PETSC_FALSE;
2720 
2721       /* set the solver for the (0,0) block */
2722       ierr = PCFieldSplitSchurGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2723       if (!nn) { /* not of type PC_COMPOSITE_SCHUR */
2724         ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2725         if (!fake) { /* pass pmat to the pressure solver */
2726           Mat F;
2727 
2728           ierr = KSPGetOperators(ksps[1],&F,NULL);CHKERRQ(ierr);
2729           ierr = KSPSetOperators(ksps[1],F,M);CHKERRQ(ierr);
2730         }
2731       } else {
2732         PetscBool issym;
2733         Mat       S;
2734 
2735         ierr = PCFieldSplitSchurGetS(newpc,&S);CHKERRQ(ierr);
2736 
2737         ierr = MatGetOption(newmat,MAT_SYMMETRIC,&issym);CHKERRQ(ierr);
2738         if (issym) {
2739           ierr = MatSetOption(S,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2740         }
2741       }
2742       ierr = KSPGetPC(ksps[0],&lagpc);CHKERRQ(ierr);
2743       ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2744       ierr = PCShellSetName(lagpc,"FETI-DP multipliers");CHKERRQ(ierr);
2745       ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2746       ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2747       ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2748       ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2749       ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2750 
2751       /* Olof's idea: interface Schur complement preconditioner for the mass matrix */
2752       ierr = KSPGetPC(ksps[1],&ppc);CHKERRQ(ierr);
2753       if (fake) {
2754         BDDCIPC_ctx    bddcipc_ctx;
2755         PetscContainer c;
2756 
2757         matisok = PETSC_TRUE;
2758 
2759         /* create inner BDDC solver */
2760         ierr = PetscNew(&bddcipc_ctx);CHKERRQ(ierr);
2761         ierr = PCCreate(comm,&bddcipc_ctx->bddc);CHKERRQ(ierr);
2762         ierr = PCSetType(bddcipc_ctx->bddc,PCBDDC);CHKERRQ(ierr);
2763         ierr = PCSetOperators(bddcipc_ctx->bddc,M,M);CHKERRQ(ierr);
2764         ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_pCSR",(PetscObject*)&c);CHKERRQ(ierr);
2765         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2766         if (c && ismatis) {
2767           Mat      lM;
2768           PetscInt *csr,n;
2769 
2770           ierr = MatISGetLocalMat(M,&lM);CHKERRQ(ierr);
2771           ierr = MatGetSize(lM,&n,NULL);CHKERRQ(ierr);
2772           ierr = PetscContainerGetPointer(c,(void**)&csr);CHKERRQ(ierr);
2773           ierr = PCBDDCSetLocalAdjacencyGraph(bddcipc_ctx->bddc,n,csr,csr + (n + 1),PETSC_COPY_VALUES);CHKERRQ(ierr);
2774           ierr = MatISRestoreLocalMat(M,&lM);CHKERRQ(ierr);
2775         }
2776         ierr = PCSetOptionsPrefix(bddcipc_ctx->bddc,((PetscObject)ksps[1])->prefix);CHKERRQ(ierr);
2777         ierr = PCSetErrorIfFailure(bddcipc_ctx->bddc,pc->erroriffailure);CHKERRQ(ierr);
2778         ierr = PCSetFromOptions(bddcipc_ctx->bddc);CHKERRQ(ierr);
2779 
2780         /* wrap the interface application */
2781         ierr = PCSetType(ppc,PCSHELL);CHKERRQ(ierr);
2782         ierr = PCShellSetName(ppc,"FETI-DP pressure");CHKERRQ(ierr);
2783         ierr = PCShellSetContext(ppc,bddcipc_ctx);CHKERRQ(ierr);
2784         ierr = PCShellSetSetUp(ppc,PCSetUp_BDDCIPC);CHKERRQ(ierr);
2785         ierr = PCShellSetApply(ppc,PCApply_BDDCIPC);CHKERRQ(ierr);
2786         ierr = PCShellSetApplyTranspose(ppc,PCApplyTranspose_BDDCIPC);CHKERRQ(ierr);
2787         ierr = PCShellSetView(ppc,PCView_BDDCIPC);CHKERRQ(ierr);
2788         ierr = PCShellSetDestroy(ppc,PCDestroy_BDDCIPC);CHKERRQ(ierr);
2789       }
2790 
2791       /* determine if we need to assemble M to construct a preconditioner */
2792       if (!matisok) {
2793         ierr = PetscObjectTypeCompare((PetscObject)M,MATIS,&ismatis);CHKERRQ(ierr);
2794         ierr = PetscObjectTypeCompareAny((PetscObject)ppc,&matisok,PCBDDC,PCJACOBI,PCNONE,PCMG,"");CHKERRQ(ierr);
2795         if (ismatis && !matisok) {
2796           ierr = MatConvert(M,MATAIJ,MAT_INPLACE_MATRIX,&M);CHKERRQ(ierr);
2797         }
2798       }
2799 
2800       /* run the subproblems to check convergence */
2801       ierr = PetscOptionsGetBool(NULL,((PetscObject)newmat)->prefix,"-check_saddlepoint",&check,NULL);CHKERRQ(ierr);
2802       if (check) {
2803         PetscInt i;
2804 
2805         for (i=0;i<nn;i++) {
2806           KSP       kspC;
2807           PC        pc;
2808           Mat       F,pF;
2809           Vec       x,y;
2810           PetscBool isschur,prec = PETSC_TRUE;
2811 
2812           ierr = KSPCreate(PetscObjectComm((PetscObject)ksps[i]),&kspC);CHKERRQ(ierr);
2813           ierr = KSPSetOptionsPrefix(kspC,((PetscObject)ksps[i])->prefix);CHKERRQ(ierr);
2814           ierr = KSPAppendOptionsPrefix(kspC,"check_");CHKERRQ(ierr);
2815           ierr = KSPGetOperators(ksps[i],&F,&pF);CHKERRQ(ierr);
2816           ierr = PetscObjectTypeCompare((PetscObject)F,MATSCHURCOMPLEMENT,&isschur);CHKERRQ(ierr);
2817           if (isschur) {
2818             KSP  kspS,kspS2;
2819             Mat  A00,pA00,A10,A01,A11;
2820             char prefix[256];
2821 
2822             ierr = MatSchurComplementGetKSP(F,&kspS);CHKERRQ(ierr);
2823             ierr = MatSchurComplementGetSubMatrices(F,&A00,&pA00,&A01,&A10,&A11);CHKERRQ(ierr);
2824             ierr = MatCreateSchurComplement(A00,pA00,A01,A10,A11,&F);CHKERRQ(ierr);
2825             ierr = MatSchurComplementGetKSP(F,&kspS2);CHKERRQ(ierr);
2826             ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sschur_",((PetscObject)kspC)->prefix);CHKERRQ(ierr);
2827             ierr = KSPSetOptionsPrefix(kspS2,prefix);CHKERRQ(ierr);
2828             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2829             ierr = PCSetType(pc,PCKSP);CHKERRQ(ierr);
2830             ierr = PCKSPSetKSP(pc,kspS);CHKERRQ(ierr);
2831             ierr = KSPSetFromOptions(kspS2);CHKERRQ(ierr);
2832             ierr = KSPGetPC(kspS2,&pc);CHKERRQ(ierr);
2833             ierr = PCSetUseAmat(pc,PETSC_TRUE);CHKERRQ(ierr);
2834           } else {
2835             ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
2836           }
2837           ierr = KSPSetFromOptions(kspC);CHKERRQ(ierr);
2838           ierr = PetscOptionsGetBool(NULL,((PetscObject)kspC)->prefix,"-preconditioned",&prec,NULL);CHKERRQ(ierr);
2839           if (prec)  {
2840             ierr = KSPGetPC(ksps[i],&pc);CHKERRQ(ierr);
2841             ierr = KSPSetPC(kspC,pc);CHKERRQ(ierr);
2842           }
2843           ierr = KSPSetOperators(kspC,F,pF);CHKERRQ(ierr);
2844           ierr = MatCreateVecs(F,&x,&y);CHKERRQ(ierr);
2845           ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2846           ierr = MatMult(F,x,y);CHKERRQ(ierr);
2847           ierr = KSPSolve(kspC,y,x);CHKERRQ(ierr);
2848           ierr = KSPDestroy(&kspC);CHKERRQ(ierr);
2849           ierr = MatDestroy(&F);CHKERRQ(ierr);
2850           ierr = VecDestroy(&x);CHKERRQ(ierr);
2851           ierr = VecDestroy(&y);CHKERRQ(ierr);
2852         }
2853       }
2854       ierr = PetscFree(ksps);CHKERRQ(ierr);
2855     }
2856   }
2857   /* return pointers for objects created */
2858   *fetidp_mat = newmat;
2859   *fetidp_pc  = newpc;
2860   PetscFunctionReturn(0);
2861 }
2862 
2863 /*@C
2864  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2865 
2866    Collective
2867 
2868    Input Parameters:
2869 +  pc - the BDDC preconditioning context (setup should have been called before)
2870 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2871 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2872 
2873    Output Parameters:
2874 +  fetidp_mat - shell FETI-DP matrix object
2875 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2876 
2877    Level: developer
2878 
2879    Notes:
2880      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2881 
2882 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2883 @*/
2884 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2885 {
2886   PetscErrorCode ierr;
2887 
2888   PetscFunctionBegin;
2889   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2890   if (pc->setupcalled) {
2891     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2892   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first");
2893   PetscFunctionReturn(0);
2894 }
2895 /* -------------------------------------------------------------------------- */
2896 /*MC
2897    PCBDDC - Balancing Domain Decomposition by Constraints.
2898 
2899    An implementation of the BDDC preconditioner based on
2900 
2901 .vb
2902    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2903    [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
2904    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2905    [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
2906 .ve
2907 
2908    The matrix to be preconditioned (Pmat) must be of type MATIS.
2909 
2910    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2911 
2912    It also works with unsymmetric and indefinite problems.
2913 
2914    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.
2915 
2916    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).
2917 
2918    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()
2919    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2920 
2921    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2922 
2923    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.
2924    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2925 
2926    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2927 
2928    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.
2929 
2930    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.
2931    Deluxe scaling is not supported yet for FETI-DP.
2932 
2933    Options Database Keys (some of them, run with -h for a complete list):
2934 
2935 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2936 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2937 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2938 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2939 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2940 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2941 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2942 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2943 .    -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)
2944 .    -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)
2945 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2946 .    -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)
2947 .    -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)
2948 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2949 
2950    Options for Dirichlet, Neumann or coarse solver can be set with
2951 .vb
2952       -pc_bddc_dirichlet_
2953       -pc_bddc_neumann_
2954       -pc_bddc_coarse_
2955 .ve
2956    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2957 
2958    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2959 .vb
2960       -pc_bddc_dirichlet_lN_
2961       -pc_bddc_neumann_lN_
2962       -pc_bddc_coarse_lN_
2963 .ve
2964    Note that level number ranges from the finest (0) to the coarsest (N).
2965    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.
2966 .vb
2967      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2968 .ve
2969    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
2970 
2971    Level: intermediate
2972 
2973    Developer Notes:
2974 
2975    Contributed by Stefano Zampini
2976 
2977 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2978 M*/
2979 
2980 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2981 {
2982   PetscErrorCode      ierr;
2983   PC_BDDC             *pcbddc;
2984 
2985   PetscFunctionBegin;
2986   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2987   pc->data = (void*)pcbddc;
2988 
2989   /* create PCIS data structure */
2990   ierr = PCISCreate(pc);CHKERRQ(ierr);
2991 
2992   /* create local graph structure */
2993   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2994 
2995   /* BDDC nonzero defaults */
2996   pcbddc->use_local_adj             = PETSC_TRUE;
2997   pcbddc->use_vertices              = PETSC_TRUE;
2998   pcbddc->use_edges                 = PETSC_TRUE;
2999   pcbddc->symmetric_primal          = PETSC_TRUE;
3000   pcbddc->vertex_size               = 1;
3001   pcbddc->recompute_topography      = PETSC_TRUE;
3002   pcbddc->coarse_size               = -1;
3003   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
3004   pcbddc->coarsening_ratio          = 8;
3005   pcbddc->coarse_eqs_per_proc       = 1;
3006   pcbddc->benign_compute_correction = PETSC_TRUE;
3007   pcbddc->nedfield                  = -1;
3008   pcbddc->nedglobal                 = PETSC_TRUE;
3009   pcbddc->graphmaxcount             = PETSC_MAX_INT;
3010   pcbddc->sub_schurs_layers         = -1;
3011   pcbddc->adaptive_threshold[0]     = 0.0;
3012   pcbddc->adaptive_threshold[1]     = 0.0;
3013 
3014   /* function pointers */
3015   pc->ops->apply               = PCApply_BDDC;
3016   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
3017   pc->ops->setup               = PCSetUp_BDDC;
3018   pc->ops->destroy             = PCDestroy_BDDC;
3019   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
3020   pc->ops->view                = PCView_BDDC;
3021   pc->ops->applyrichardson     = 0;
3022   pc->ops->applysymmetricleft  = 0;
3023   pc->ops->applysymmetricright = 0;
3024   pc->ops->presolve            = PCPreSolve_BDDC;
3025   pc->ops->postsolve           = PCPostSolve_BDDC;
3026   pc->ops->reset               = PCReset_BDDC;
3027 
3028   /* composing function */
3029   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
3030   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
3031   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
3032   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3033   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3034   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesLocalIS_C",PCBDDCGetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
3035   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetPrimalVerticesIS_C",PCBDDCGetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
3036   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
3037   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
3038   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
3039   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
3040   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3041   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3042   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3043   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3044   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
3045   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
3046   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
3047   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
3048   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
3049   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
3050   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
3051   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
3052   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
3053   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
3054   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
3055   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
3056   PetscFunctionReturn(0);
3057 }
3058 
3059 /*@C
3060  PCBDDCInitializePackage - This function initializes everything in the PCBDDC package. It is called
3061     from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to PCCreate_BDDC()
3062     when using static libraries.
3063 
3064  Level: developer
3065 
3066  .keywords: PC, PCBDDC, initialize, package
3067  .seealso: PetscInitialize()
3068 @*/
3069 PetscErrorCode PCBDDCInitializePackage(void)
3070 {
3071   PetscErrorCode ierr;
3072   int            i;
3073 
3074   PetscFunctionBegin;
3075   if (PCBDDCPackageInitialized) PetscFunctionReturn(0);
3076   PCBDDCPackageInitialized = PETSC_TRUE;
3077   ierr = PetscRegisterFinalize(PCBDDCFinalizePackage);CHKERRQ(ierr);
3078 
3079   /* general events */
3080   ierr = PetscLogEventRegister("PCBDDCTopo",PC_CLASSID,&PC_BDDC_Topology[0]);CHKERRQ(ierr);
3081   ierr = PetscLogEventRegister("PCBDDCLKSP",PC_CLASSID,&PC_BDDC_LocalSolvers[0]);CHKERRQ(ierr);
3082   ierr = PetscLogEventRegister("PCBDDCLWor",PC_CLASSID,&PC_BDDC_LocalWork[0]);CHKERRQ(ierr);
3083   ierr = PetscLogEventRegister("PCBDDCCorr",PC_CLASSID,&PC_BDDC_CorrectionSetUp[0]);CHKERRQ(ierr);
3084   ierr = PetscLogEventRegister("PCBDDCCSet",PC_CLASSID,&PC_BDDC_CoarseSetUp[0]);CHKERRQ(ierr);
3085   ierr = PetscLogEventRegister("PCBDDCCKSP",PC_CLASSID,&PC_BDDC_CoarseSolver[0]);CHKERRQ(ierr);
3086   ierr = PetscLogEventRegister("PCBDDCAdap",PC_CLASSID,&PC_BDDC_AdaptiveSetUp[0]);CHKERRQ(ierr);
3087   ierr = PetscLogEventRegister("PCBDDCScal",PC_CLASSID,&PC_BDDC_Scaling[0]);CHKERRQ(ierr);
3088   ierr = PetscLogEventRegister("PCBDDCSchr",PC_CLASSID,&PC_BDDC_Schurs[0]);CHKERRQ(ierr);
3089   for (i=1;i<PETSC_PCBDDC_MAXLEVELS;i++) {
3090     char ename[32];
3091 
3092     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCTopo l%02d",i);CHKERRQ(ierr);
3093     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Topology[i]);CHKERRQ(ierr);
3094     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLKSP l%02d",i);CHKERRQ(ierr);
3095     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalSolvers[i]);CHKERRQ(ierr);
3096     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCLWor l%02d",i);CHKERRQ(ierr);
3097     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_LocalWork[i]);CHKERRQ(ierr);
3098     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCorr l%02d",i);CHKERRQ(ierr);
3099     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CorrectionSetUp[i]);CHKERRQ(ierr);
3100     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCSet l%02d",i);CHKERRQ(ierr);
3101     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSetUp[i]);CHKERRQ(ierr);
3102     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCCKSP l%02d",i);CHKERRQ(ierr);
3103     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_CoarseSolver[i]);CHKERRQ(ierr);
3104     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCAdap l%02d",i);CHKERRQ(ierr);
3105     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_AdaptiveSetUp[i]);CHKERRQ(ierr);
3106     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCScal l%02d",i);CHKERRQ(ierr);
3107     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Scaling[i]);CHKERRQ(ierr);
3108     ierr = PetscSNPrintf(ename,sizeof(ename),"PCBDDCSchr l%02d",i);CHKERRQ(ierr);
3109     ierr = PetscLogEventRegister(ename,PC_CLASSID,&PC_BDDC_Schurs[i]);CHKERRQ(ierr);
3110   }
3111   PetscFunctionReturn(0);
3112 }
3113 
3114 /*@C
3115  PCBDDCFinalizePackage - This function frees everything from the PCBDDC package. It is
3116     called from PetscFinalize() automatically.
3117 
3118  Level: developer
3119 
3120  .keywords: Petsc, destroy, package
3121  .seealso: PetscFinalize()
3122 @*/
3123 PetscErrorCode PCBDDCFinalizePackage(void)
3124 {
3125   PetscFunctionBegin;
3126   PCBDDCPackageInitialized = PETSC_FALSE;
3127   PetscFunctionReturn(0);
3128 }
3129