xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 715b75585fd277b048903486c3bbde8d0b0c8e8b)
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  cited = PETSC_FALSE;
27 static const char citation[] =
28 "@article{ZampiniPCBDDC,\n"
29 "author = {Stefano Zampini},\n"
30 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
31 "journal = {SIAM Journal on Scientific Computing},\n"
32 "volume = {38},\n"
33 "number = {5},\n"
34 "pages = {S282-S306},\n"
35 "year = {2016},\n"
36 "doi = {10.1137/15M1025785},\n"
37 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
38 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
39 "}\n";
40 
41 /* temporarily declare it */
42 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
43 
44 PetscErrorCode PCSetFromOptions_BDDC(PetscOptionItems *PetscOptionsObject,PC pc)
45 {
46   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
47   PetscInt       nt;
48   PetscErrorCode ierr;
49 
50   PetscFunctionBegin;
51   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
52   /* Verbose debugging */
53   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
54   /* Approximate solvers */
55   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);
56   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);
57   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);
58   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);
59   /* Primal space customization */
60   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);
61   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
62   ierr = PetscOptionsBool("-pc_bddc_corner_selection","Activates face-based corner selection","none",pcbddc->corner_selection,&pcbddc->corner_selection,NULL);CHKERRQ(ierr);
63   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
64   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
65   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
66   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);
67   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);
68   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);
69   /* Change of basis */
70   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);
71   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);
72   if (!pcbddc->use_change_of_basis) {
73     pcbddc->use_change_on_faces = PETSC_FALSE;
74   }
75   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
76   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);
77   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_per_proc","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);
78   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,NULL);CHKERRQ(ierr);
79   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","none",pcbddc->max_levels,&pcbddc->max_levels,NULL);CHKERRQ(ierr);
80   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);
81   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
82   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);
83   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);
84   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);
85   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);
86   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);
87   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
88   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);
89   nt   = 2;
90   ierr = PetscOptionsRealArray("-pc_bddc_adaptive_threshold","Thresholds to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&nt,NULL);CHKERRQ(ierr);
91   if (nt == 1) pcbddc->adaptive_threshold[1] = pcbddc->adaptive_threshold[0];
92   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
93   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
94   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
95   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);
96   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);
97   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);
98   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);
99   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
100   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
101   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);
102   ierr = PetscOptionsTail();CHKERRQ(ierr);
103   PetscFunctionReturn(0);
104 }
105 
106 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
107 {
108   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
109   PC_IS                *pcis = (PC_IS*)pc->data;
110   PetscErrorCode       ierr;
111   PetscBool            isascii;
112   PetscSubcomm         subcomm;
113   PetscViewer          subviewer;
114 
115   PetscFunctionBegin;
116   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
117   /* ASCII viewer */
118   if (isascii) {
119     PetscMPIInt   color,rank,size;
120     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
121     PetscScalar   interface_size;
122     PetscReal     ratio1=0.,ratio2=0.;
123     Vec           counter;
124 
125     if (!pc->setupcalled) {
126       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
127     }
128     ierr = PetscViewerASCIIPrintf(viewer,"  Use verbose output: %D\n",pcbddc->dbg_flag);CHKERRQ(ierr);
129     ierr = PetscViewerASCIIPrintf(viewer,"  Use user-defined CSR: %d\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
130     ierr = PetscViewerASCIIPrintf(viewer,"  Use local mat graph: %d\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
131     if (pcbddc->mat_graph->twodim) {
132       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
133     } else {
134       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
135     }
136     if (pcbddc->graphmaxcount != PETSC_MAX_INT) {
137       ierr = PetscViewerASCIIPrintf(viewer,"  Graph max count: %D\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
138     }
139     ierr = PetscViewerASCIIPrintf(viewer,"  Use vertices: %d (vertex size %D)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
140     ierr = PetscViewerASCIIPrintf(viewer,"  Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
141     ierr = PetscViewerASCIIPrintf(viewer,"  Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
142     ierr = PetscViewerASCIIPrintf(viewer,"  Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
143     ierr = PetscViewerASCIIPrintf(viewer,"  Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
144     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
145     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
148     ierr = PetscViewerASCIIPrintf(viewer,"  Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
149     ierr = PetscViewerASCIIPrintf(viewer,"  Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
150     ierr = PetscViewerASCIIPrintf(viewer,"  Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
151     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel max levels: %D\n",pcbddc->max_levels);CHKERRQ(ierr);
152     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel coarsening ratio: %D\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
153     ierr = PetscViewerASCIIPrintf(viewer,"  Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
154     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
155     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
156     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  Number of dofs' layers for the computation of principal minors: %D\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
160     if (pcbddc->adaptive_threshold[1] != pcbddc->adaptive_threshold[0]) {
161       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);
162     } else {
163       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);
164     }
165     ierr = PetscViewerASCIIPrintf(viewer,"  Min constraints / connected component: %D\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  Max constraints / connected component: %D\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
167     ierr = PetscViewerASCIIPrintf(viewer,"  Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
168     ierr = PetscViewerASCIIPrintf(viewer,"  Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
169     ierr = PetscViewerASCIIPrintf(viewer,"  Num. Procs. to map coarse adjacency list: %D\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
170     ierr = PetscViewerASCIIPrintf(viewer,"  Coarse eqs per proc (significant at the coarsest level): %D\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
171     ierr = PetscViewerASCIIPrintf(viewer,"  Detect disconnected: %d\n",pcbddc->detect_disconnected);CHKERRQ(ierr);
172     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
173     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
174     ierr = PetscViewerASCIIPrintf(viewer,"  Algebraic computation of no-net-flux %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
175     if (!pc->setupcalled) PetscFunctionReturn(0);
176 
177     /* compute interface size */
178     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
179     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
180     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
181     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
182     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
183     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
184     ierr = VecDestroy(&counter);CHKERRQ(ierr);
185 
186     /* compute some statistics on the domain decomposition */
187     gsum[0] = 1;
188     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
189     loc[0]  = !!pcis->n;
190     loc[1]  = pcis->n - pcis->n_B;
191     loc[2]  = pcis->n_B;
192     loc[3]  = pcbddc->local_primal_size;
193     loc[4]  = pcis->n;
194     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
195     loc[6]  = pcbddc->benign_n;
196     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
197     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
198     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
199     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
200     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
201     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
202     if (pcbddc->coarse_size) {
203       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
204       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
205     }
206     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
207     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);
208     ierr = PetscViewerASCIIPrintf(viewer,"  Coarsening ratios: all/coarse %D interface/coarse %D\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
209     ierr = PetscViewerASCIIPrintf(viewer,"  Active processes : %D\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
210     ierr = PetscViewerASCIIPrintf(viewer,"  Total subdomains : %D\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
211     if (pcbddc->benign_have_null) {
212       ierr = PetscViewerASCIIPrintf(viewer,"  Benign subs      : %D\n",(PetscInt)totbenign);CHKERRQ(ierr);
213     }
214     ierr = PetscViewerASCIIPrintf(viewer,"  Dofs type        :\tMIN\tMAX\tMEAN\n");CHKERRQ(ierr);
215     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);
216     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);
217     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);
218     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);
219     ierr = PetscViewerASCIIPrintf(viewer,"  Local     subs   :\t%D\t%D\n"    ,(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
220     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** COARSE PROBLEM DETAILS *********************************\n");CHKERRQ(ierr);
221     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
222 
223     /* the coarse problem can be handled by a different communicator */
224     if (pcbddc->coarse_ksp) color = 1;
225     else color = 0;
226     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
227     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
228     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
229     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
230     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
231     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
232     if (color == 1) {
233       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
234       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
235     }
236     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
237     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
238     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
239   }
240   PetscFunctionReturn(0);
241 }
242 
243 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
244 {
245   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
246   PetscErrorCode ierr;
247 
248   PetscFunctionBegin;
249   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
250   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
251   pcbddc->discretegradient = G;
252   pcbddc->nedorder         = order > 0 ? order : -order;
253   pcbddc->nedfield         = field;
254   pcbddc->nedglobal        = global;
255   pcbddc->conforming       = conforming;
256   PetscFunctionReturn(0);
257 }
258 
259 /*@
260  PCBDDCSetDiscreteGradient - Sets the discrete gradient
261 
262    Collective on PC
263 
264    Input Parameters:
265 +  pc         - the preconditioning context
266 .  G          - the discrete gradient matrix (should be in AIJ format)
267 .  order      - the order of the Nedelec space (1 for the lowest order)
268 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
269 .  global     - the type of global ordering for the rows of G
270 -  conforming - whether the mesh is conforming or not
271 
272    Level: advanced
273 
274    Notes: The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
275           For variable order spaces, the order should be set to zero.
276           If global is true, the rows of G should be given in global ordering for the whole dofs;
277           if false, the ordering should be global for the Nedelec field.
278           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
279           and geid the one for the Nedelec field.
280 
281 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
282 @*/
283 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
284 {
285   PetscErrorCode ierr;
286 
287   PetscFunctionBegin;
288   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
289   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
290   PetscValidLogicalCollectiveInt(pc,order,3);
291   PetscValidLogicalCollectiveInt(pc,field,4);
292   PetscValidLogicalCollectiveBool(pc,global,5);
293   PetscValidLogicalCollectiveBool(pc,conforming,6);
294   PetscCheckSameComm(pc,1,G,2);
295   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
296   PetscFunctionReturn(0);
297 }
298 
299 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
300 {
301   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
302   PetscErrorCode ierr;
303 
304   PetscFunctionBegin;
305   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
306   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
307   pcbddc->divudotp = divudotp;
308   pcbddc->divudotp_trans = trans;
309   pcbddc->compute_nonetflux = PETSC_TRUE;
310   if (vl2l) {
311     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
312     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
313     pcbddc->divudotp_vl2l = vl2l;
314   }
315   PetscFunctionReturn(0);
316 }
317 
318 /*@
319  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
320 
321    Collective on PC
322 
323    Input Parameters:
324 +  pc - the preconditioning context
325 .  divudotp - the matrix (must be of type MATIS)
326 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
327 -  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
328 
329    Level: advanced
330 
331    Notes: This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
332           If vl2l is NULL, the local ordering for velocities in divudotp should match that of the preconditioning matrix
333 
334 .seealso: PCBDDC
335 @*/
336 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
337 {
338   PetscBool      ismatis;
339   PetscErrorCode ierr;
340 
341   PetscFunctionBegin;
342   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
343   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
344   PetscCheckSameComm(pc,1,divudotp,2);
345   PetscValidLogicalCollectiveBool(pc,trans,3);
346   if (vl2l) PetscValidHeaderSpecific(divudotp,IS_CLASSID,4);
347   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
348   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
349   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
350   PetscFunctionReturn(0);
351 }
352 
353 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
354 {
355   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
356   PetscErrorCode ierr;
357 
358   PetscFunctionBegin;
359   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
360   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
361   pcbddc->user_ChangeOfBasisMatrix = change;
362   pcbddc->change_interior = interior;
363   PetscFunctionReturn(0);
364 }
365 /*@
366  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
367 
368    Collective on PC
369 
370    Input Parameters:
371 +  pc - the preconditioning context
372 .  change - the change of basis matrix
373 -  interior - whether or not the change of basis modifies interior dofs
374 
375    Level: intermediate
376 
377    Notes:
378 
379 .seealso: PCBDDC
380 @*/
381 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
382 {
383   PetscErrorCode ierr;
384 
385   PetscFunctionBegin;
386   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
387   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
388   PetscCheckSameComm(pc,1,change,2);
389   if (pc->mat) {
390     PetscInt rows_c,cols_c,rows,cols;
391     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
392     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
393     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);
394     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);
395     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
396     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
397     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);
398     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);
399   }
400   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
401   PetscFunctionReturn(0);
402 }
403 
404 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
405 {
406   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
407   PetscBool      isequal = PETSC_FALSE;
408   PetscErrorCode ierr;
409 
410   PetscFunctionBegin;
411   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
412   if (pcbddc->user_primal_vertices) {
413     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
414   }
415   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
416   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
417   pcbddc->user_primal_vertices = PrimalVertices;
418   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
419   PetscFunctionReturn(0);
420 }
421 
422 /*@
423  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
424 
425    Collective
426 
427    Input Parameters:
428 +  pc - the preconditioning context
429 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
430 
431    Level: intermediate
432 
433    Notes:
434      Any process can list any global node
435 
436 .seealso: PCBDDC
437 @*/
438 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
439 {
440   PetscErrorCode ierr;
441 
442   PetscFunctionBegin;
443   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
444   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
445   PetscCheckSameComm(pc,1,PrimalVertices,2);
446   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
447   PetscFunctionReturn(0);
448 }
449 
450 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
451 {
452   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
453   PetscBool      isequal = PETSC_FALSE;
454   PetscErrorCode ierr;
455 
456   PetscFunctionBegin;
457   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
458   if (pcbddc->user_primal_vertices_local) {
459     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
460   }
461   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
462   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
463   pcbddc->user_primal_vertices_local = PrimalVertices;
464   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
465   PetscFunctionReturn(0);
466 }
467 /*@
468  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
469 
470    Collective
471 
472    Input Parameters:
473 +  pc - the preconditioning context
474 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
475 
476    Level: intermediate
477 
478    Notes:
479 
480 .seealso: PCBDDC
481 @*/
482 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
483 {
484   PetscErrorCode ierr;
485 
486   PetscFunctionBegin;
487   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
488   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
489   PetscCheckSameComm(pc,1,PrimalVertices,2);
490   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
491   PetscFunctionReturn(0);
492 }
493 
494 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
495 {
496   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
497 
498   PetscFunctionBegin;
499   pcbddc->coarsening_ratio = k;
500   PetscFunctionReturn(0);
501 }
502 
503 /*@
504  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
505 
506    Logically collective on PC
507 
508    Input Parameters:
509 +  pc - the preconditioning context
510 -  k - coarsening ratio (H/h at the coarser level)
511 
512    Options Database Keys:
513 .    -pc_bddc_coarsening_ratio
514 
515    Level: intermediate
516 
517    Notes:
518      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
519 
520 .seealso: PCBDDC, PCBDDCSetLevels()
521 @*/
522 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
523 {
524   PetscErrorCode ierr;
525 
526   PetscFunctionBegin;
527   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
528   PetscValidLogicalCollectiveInt(pc,k,2);
529   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
530   PetscFunctionReturn(0);
531 }
532 
533 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
534 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
535 {
536   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
537 
538   PetscFunctionBegin;
539   pcbddc->use_exact_dirichlet_trick = flg;
540   PetscFunctionReturn(0);
541 }
542 
543 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
544 {
545   PetscErrorCode ierr;
546 
547   PetscFunctionBegin;
548   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
549   PetscValidLogicalCollectiveBool(pc,flg,2);
550   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
551   PetscFunctionReturn(0);
552 }
553 
554 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
555 {
556   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
557 
558   PetscFunctionBegin;
559   pcbddc->current_level = level;
560   PetscFunctionReturn(0);
561 }
562 
563 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
564 {
565   PetscErrorCode ierr;
566 
567   PetscFunctionBegin;
568   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
569   PetscValidLogicalCollectiveInt(pc,level,2);
570   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
571   PetscFunctionReturn(0);
572 }
573 
574 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
575 {
576   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
577 
578   PetscFunctionBegin;
579   pcbddc->max_levels = levels;
580   PetscFunctionReturn(0);
581 }
582 
583 /*@
584  PCBDDCSetLevels - Sets the maximum number of levels for multilevel
585 
586    Logically collective on PC
587 
588    Input Parameters:
589 +  pc - the preconditioning context
590 -  levels - the maximum number of levels (max 9)
591 
592    Options Database Keys:
593 .    -pc_bddc_levels
594 
595    Level: intermediate
596 
597    Notes:
598      Default value is 0, i.e. traditional one-level BDDC
599 
600 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
601 @*/
602 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
603 {
604   PetscErrorCode ierr;
605 
606   PetscFunctionBegin;
607   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
608   PetscValidLogicalCollectiveInt(pc,levels,2);
609   if (levels > 99) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of levels for bddc is 99\n");
610   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
611   PetscFunctionReturn(0);
612 }
613 
614 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
615 {
616   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
617   PetscBool      isequal = PETSC_FALSE;
618   PetscErrorCode ierr;
619 
620   PetscFunctionBegin;
621   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
622   if (pcbddc->DirichletBoundaries) {
623     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
624   }
625   /* last user setting takes precendence -> destroy any other customization */
626   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
627   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
628   pcbddc->DirichletBoundaries = DirichletBoundaries;
629   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
630   PetscFunctionReturn(0);
631 }
632 
633 /*@
634  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
635 
636    Collective
637 
638    Input Parameters:
639 +  pc - the preconditioning context
640 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
641 
642    Level: intermediate
643 
644    Notes:
645      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
646 
647 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
648 @*/
649 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
650 {
651   PetscErrorCode ierr;
652 
653   PetscFunctionBegin;
654   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
655   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
656   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
657   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
658   PetscFunctionReturn(0);
659 }
660 
661 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
662 {
663   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
664   PetscBool      isequal = PETSC_FALSE;
665   PetscErrorCode ierr;
666 
667   PetscFunctionBegin;
668   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
669   if (pcbddc->DirichletBoundariesLocal) {
670     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
671   }
672   /* last user setting takes precendence -> destroy any other customization */
673   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
674   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
675   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
676   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
677   PetscFunctionReturn(0);
678 }
679 
680 /*@
681  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
682 
683    Collective
684 
685    Input Parameters:
686 +  pc - the preconditioning context
687 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
688 
689    Level: intermediate
690 
691    Notes:
692 
693 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
694 @*/
695 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
696 {
697   PetscErrorCode ierr;
698 
699   PetscFunctionBegin;
700   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
701   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
702   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
703   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
704   PetscFunctionReturn(0);
705 }
706 
707 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
708 {
709   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
710   PetscBool      isequal = PETSC_FALSE;
711   PetscErrorCode ierr;
712 
713   PetscFunctionBegin;
714   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
715   if (pcbddc->NeumannBoundaries) {
716     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
717   }
718   /* last user setting takes precendence -> destroy any other customization */
719   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
720   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
721   pcbddc->NeumannBoundaries = NeumannBoundaries;
722   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
723   PetscFunctionReturn(0);
724 }
725 
726 /*@
727  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
728 
729    Collective
730 
731    Input Parameters:
732 +  pc - the preconditioning context
733 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
734 
735    Level: intermediate
736 
737    Notes:
738      Any process can list any global node
739 
740 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
741 @*/
742 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
743 {
744   PetscErrorCode ierr;
745 
746   PetscFunctionBegin;
747   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
748   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
749   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
750   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
751   PetscFunctionReturn(0);
752 }
753 
754 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
755 {
756   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
757   PetscBool      isequal = PETSC_FALSE;
758   PetscErrorCode ierr;
759 
760   PetscFunctionBegin;
761   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
762   if (pcbddc->NeumannBoundariesLocal) {
763     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
764   }
765   /* last user setting takes precendence -> destroy any other customization */
766   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
767   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
768   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
769   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
770   PetscFunctionReturn(0);
771 }
772 
773 /*@
774  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
775 
776    Collective
777 
778    Input Parameters:
779 +  pc - the preconditioning context
780 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
781 
782    Level: intermediate
783 
784    Notes:
785 
786 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
787 @*/
788 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
789 {
790   PetscErrorCode ierr;
791 
792   PetscFunctionBegin;
793   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
794   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
795   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
796   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
797   PetscFunctionReturn(0);
798 }
799 
800 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
801 {
802   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
803 
804   PetscFunctionBegin;
805   *DirichletBoundaries = pcbddc->DirichletBoundaries;
806   PetscFunctionReturn(0);
807 }
808 
809 /*@
810  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
811 
812    Collective
813 
814    Input Parameters:
815 .  pc - the preconditioning context
816 
817    Output Parameters:
818 .  DirichletBoundaries - index set defining the Dirichlet boundaries
819 
820    Level: intermediate
821 
822    Notes:
823      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
824 
825 .seealso: PCBDDC
826 @*/
827 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
828 {
829   PetscErrorCode ierr;
830 
831   PetscFunctionBegin;
832   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
833   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
834   PetscFunctionReturn(0);
835 }
836 
837 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
838 {
839   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
840 
841   PetscFunctionBegin;
842   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
843   PetscFunctionReturn(0);
844 }
845 
846 /*@
847  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
848 
849    Collective
850 
851    Input Parameters:
852 .  pc - the preconditioning context
853 
854    Output Parameters:
855 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
856 
857    Level: intermediate
858 
859    Notes:
860      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).
861           In the latter case, the IS will be available after PCSetUp.
862 
863 .seealso: PCBDDC
864 @*/
865 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
866 {
867   PetscErrorCode ierr;
868 
869   PetscFunctionBegin;
870   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
871   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
872   PetscFunctionReturn(0);
873 }
874 
875 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
876 {
877   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
878 
879   PetscFunctionBegin;
880   *NeumannBoundaries = pcbddc->NeumannBoundaries;
881   PetscFunctionReturn(0);
882 }
883 
884 /*@
885  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
886 
887    Collective
888 
889    Input Parameters:
890 .  pc - the preconditioning context
891 
892    Output Parameters:
893 .  NeumannBoundaries - index set defining the Neumann boundaries
894 
895    Level: intermediate
896 
897    Notes:
898      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
899 
900 .seealso: PCBDDC
901 @*/
902 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
903 {
904   PetscErrorCode ierr;
905 
906   PetscFunctionBegin;
907   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
908   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
909   PetscFunctionReturn(0);
910 }
911 
912 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
913 {
914   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
915 
916   PetscFunctionBegin;
917   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
918   PetscFunctionReturn(0);
919 }
920 
921 /*@
922  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
923 
924    Collective
925 
926    Input Parameters:
927 .  pc - the preconditioning context
928 
929    Output Parameters:
930 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
931 
932    Level: intermediate
933 
934    Notes:
935      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).
936           In the latter case, the IS will be available after PCSetUp.
937 
938 .seealso: PCBDDC
939 @*/
940 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
941 {
942   PetscErrorCode ierr;
943 
944   PetscFunctionBegin;
945   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
946   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
947   PetscFunctionReturn(0);
948 }
949 
950 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
951 {
952   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
953   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
954   PetscBool      same_data = PETSC_FALSE;
955   PetscErrorCode ierr;
956 
957   PetscFunctionBegin;
958   if (!nvtxs) {
959     if (copymode == PETSC_OWN_POINTER) {
960       ierr = PetscFree(xadj);CHKERRQ(ierr);
961       ierr = PetscFree(adjncy);CHKERRQ(ierr);
962     }
963     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
964     PetscFunctionReturn(0);
965   }
966   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
967     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
968     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
969       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
970       if (same_data) {
971         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
972       }
973     }
974   }
975   if (!same_data) {
976     /* free old CSR */
977     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
978     /* get CSR into graph structure */
979     if (copymode == PETSC_COPY_VALUES) {
980       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
981       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
982       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
983       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
984       mat_graph->freecsr = PETSC_TRUE;
985     } else if (copymode == PETSC_OWN_POINTER) {
986       mat_graph->xadj    = (PetscInt*)xadj;
987       mat_graph->adjncy  = (PetscInt*)adjncy;
988       mat_graph->freecsr = PETSC_TRUE;
989     } else if (copymode == PETSC_USE_POINTER) {
990       mat_graph->xadj    = (PetscInt*)xadj;
991       mat_graph->adjncy  = (PetscInt*)adjncy;
992       mat_graph->freecsr = PETSC_FALSE;
993     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %D",copymode);
994     mat_graph->nvtxs_csr = nvtxs;
995     pcbddc->recompute_topography = PETSC_TRUE;
996   }
997   PetscFunctionReturn(0);
998 }
999 
1000 /*@
1001  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
1002 
1003    Not collective
1004 
1005    Input Parameters:
1006 +  pc - the preconditioning context.
1007 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
1008 .  xadj, adjncy - the connectivity of the dofs in CSR format.
1009 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1010 
1011    Level: intermediate
1012 
1013    Notes: A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1014 
1015 .seealso: PCBDDC,PetscCopyMode
1016 @*/
1017 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1018 {
1019   void (*f)(void) = 0;
1020   PetscErrorCode ierr;
1021 
1022   PetscFunctionBegin;
1023   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1024   if (nvtxs) {
1025     PetscValidIntPointer(xadj,3);
1026     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1027   }
1028   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1029   /* free arrays if PCBDDC is not the PC type */
1030   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1031   if (!f && copymode == PETSC_OWN_POINTER) {
1032     ierr = PetscFree(xadj);CHKERRQ(ierr);
1033     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1034   }
1035   PetscFunctionReturn(0);
1036 }
1037 
1038 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1039 {
1040   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1041   PetscInt       i;
1042   PetscBool      isequal = PETSC_FALSE;
1043   PetscErrorCode ierr;
1044 
1045   PetscFunctionBegin;
1046   if (pcbddc->n_ISForDofsLocal == n_is) {
1047     for (i=0;i<n_is;i++) {
1048       PetscBool isequalt;
1049       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1050       if (!isequalt) break;
1051     }
1052     if (i == n_is) isequal = PETSC_TRUE;
1053   }
1054   for (i=0;i<n_is;i++) {
1055     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1056   }
1057   /* Destroy ISes if they were already set */
1058   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1059     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1060   }
1061   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1062   /* last user setting takes precendence -> destroy any other customization */
1063   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1064     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1065   }
1066   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1067   pcbddc->n_ISForDofs = 0;
1068   /* allocate space then set */
1069   if (n_is) {
1070     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1071   }
1072   for (i=0;i<n_is;i++) {
1073     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1074   }
1075   pcbddc->n_ISForDofsLocal = n_is;
1076   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1077   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1078   PetscFunctionReturn(0);
1079 }
1080 
1081 /*@
1082  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1083 
1084    Collective
1085 
1086    Input Parameters:
1087 +  pc - the preconditioning context
1088 .  n_is - number of index sets defining the fields
1089 -  ISForDofs - array of IS describing the fields in local ordering
1090 
1091    Level: intermediate
1092 
1093    Notes:
1094      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1095 
1096 .seealso: PCBDDC
1097 @*/
1098 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1099 {
1100   PetscInt       i;
1101   PetscErrorCode ierr;
1102 
1103   PetscFunctionBegin;
1104   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1105   PetscValidLogicalCollectiveInt(pc,n_is,2);
1106   for (i=0;i<n_is;i++) {
1107     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1108     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1109   }
1110   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1111   PetscFunctionReturn(0);
1112 }
1113 
1114 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1115 {
1116   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1117   PetscInt       i;
1118   PetscBool      isequal = PETSC_FALSE;
1119   PetscErrorCode ierr;
1120 
1121   PetscFunctionBegin;
1122   if (pcbddc->n_ISForDofs == n_is) {
1123     for (i=0;i<n_is;i++) {
1124       PetscBool isequalt;
1125       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1126       if (!isequalt) break;
1127     }
1128     if (i == n_is) isequal = PETSC_TRUE;
1129   }
1130   for (i=0;i<n_is;i++) {
1131     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1132   }
1133   /* Destroy ISes if they were already set */
1134   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1135     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1136   }
1137   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1138   /* last user setting takes precendence -> destroy any other customization */
1139   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1140     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1141   }
1142   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1143   pcbddc->n_ISForDofsLocal = 0;
1144   /* allocate space then set */
1145   if (n_is) {
1146     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1147   }
1148   for (i=0;i<n_is;i++) {
1149     pcbddc->ISForDofs[i] = ISForDofs[i];
1150   }
1151   pcbddc->n_ISForDofs = n_is;
1152   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1153   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1154   PetscFunctionReturn(0);
1155 }
1156 
1157 /*@
1158  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1159 
1160    Collective
1161 
1162    Input Parameters:
1163 +  pc - the preconditioning context
1164 .  n_is - number of index sets defining the fields
1165 -  ISForDofs - array of IS describing the fields in global ordering
1166 
1167    Level: intermediate
1168 
1169    Notes:
1170      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1171 
1172 .seealso: PCBDDC
1173 @*/
1174 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1175 {
1176   PetscInt       i;
1177   PetscErrorCode ierr;
1178 
1179   PetscFunctionBegin;
1180   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1181   PetscValidLogicalCollectiveInt(pc,n_is,2);
1182   for (i=0;i<n_is;i++) {
1183     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1184     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1185   }
1186   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1187   PetscFunctionReturn(0);
1188 }
1189 
1190 /*
1191    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1192                      guess if a transformation of basis approach has been selected.
1193 
1194    Input Parameter:
1195 +  pc - the preconditioner contex
1196 
1197    Application Interface Routine: PCPreSolve()
1198 
1199    Notes:
1200      The interface routine PCPreSolve() is not usually called directly by
1201    the user, but instead is called by KSPSolve().
1202 */
1203 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1204 {
1205   PetscErrorCode ierr;
1206   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1207   PC_IS          *pcis = (PC_IS*)(pc->data);
1208   Vec            used_vec;
1209   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1210 
1211   PetscFunctionBegin;
1212   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1213   if (ksp) {
1214     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1215     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1216     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1217     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1218     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1219     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1220       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1221     }
1222   }
1223   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1224     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1225   }
1226 
1227   /* Creates parallel work vectors used in presolve */
1228   if (!pcbddc->original_rhs) {
1229     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1230   }
1231   if (!pcbddc->temp_solution) {
1232     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1233   }
1234 
1235   pcbddc->temp_solution_used = PETSC_FALSE;
1236   if (x) {
1237     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1238     used_vec = x;
1239   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1240     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1241     used_vec = pcbddc->temp_solution;
1242     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1243     pcbddc->temp_solution_used = PETSC_TRUE;
1244     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1245     save_rhs = PETSC_FALSE;
1246     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1247   }
1248 
1249   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1250   if (ksp) {
1251     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1252     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1253     if (!pcbddc->ksp_guess_nonzero) {
1254       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1255     }
1256   }
1257 
1258   pcbddc->rhs_change = PETSC_FALSE;
1259   /* Take into account zeroed rows -> change rhs and store solution removed */
1260   if (rhs && pcbddc->eliminate_dirdofs) {
1261     IS dirIS = NULL;
1262 
1263     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1264     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1265     if (dirIS) {
1266       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1267       PetscInt          dirsize,i,*is_indices;
1268       PetscScalar       *array_x;
1269       const PetscScalar *array_diagonal;
1270 
1271       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1272       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1273       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1274       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1275       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1276       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1277       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1278       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1279       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1280       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1281       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1282       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1283       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1284       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1285       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1286       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1287       pcbddc->rhs_change = PETSC_TRUE;
1288       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1289     }
1290   }
1291 
1292   /* remove the computed solution or the initial guess from the rhs */
1293   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1294     /* save the original rhs */
1295     if (save_rhs) {
1296       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1297       save_rhs = PETSC_FALSE;
1298     }
1299     pcbddc->rhs_change = PETSC_TRUE;
1300     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1301     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1302     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1303     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1304     pcbddc->temp_solution_used = PETSC_TRUE;
1305     if (ksp) {
1306       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1307     }
1308   }
1309   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1310 
1311   /* compute initial vector in benign space if needed
1312      and remove non-benign solution from the rhs */
1313   benign_correction_computed = PETSC_FALSE;
1314   if (rhs && pcbddc->benign_compute_correction && (pcbddc->benign_have_null || pcbddc->benign_apply_coarse_only)) {
1315     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1316        Recursively apply BDDC in the multilevel case */
1317     if (!pcbddc->benign_vec) {
1318       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1319     }
1320     /* keep applying coarse solver unless we no longer have benign subdomains */
1321     pcbddc->benign_apply_coarse_only = pcbddc->benign_have_null ? PETSC_TRUE : PETSC_FALSE;
1322     if (!pcbddc->benign_skip_correction) {
1323       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1324       benign_correction_computed = PETSC_TRUE;
1325       if (pcbddc->temp_solution_used) {
1326         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1327       }
1328       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1329       /* store the original rhs if not done earlier */
1330       if (save_rhs) {
1331         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1332       }
1333       if (pcbddc->rhs_change) {
1334         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1335       } else {
1336         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1337       }
1338       pcbddc->rhs_change = PETSC_TRUE;
1339     }
1340     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1341   }
1342 
1343   /* dbg output */
1344   if (pcbddc->dbg_flag && benign_correction_computed) {
1345     Vec v;
1346 
1347     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1348     if (pcbddc->ChangeOfBasisMatrix) {
1349       ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1350     } else {
1351       ierr = VecCopy(rhs,v);CHKERRQ(ierr);
1352     }
1353     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1354     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1355     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,pcbddc->dbg_viewer);CHKERRQ(ierr);
1356     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1357     ierr = VecDestroy(&v);CHKERRQ(ierr);
1358   }
1359 
1360   /* set initial guess if using PCG */
1361   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1362   if (x && pcbddc->use_exact_dirichlet_trick) {
1363     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1364     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1365       if (benign_correction_computed) { /* we have already saved the changed rhs */
1366         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1367       } else {
1368         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1369       }
1370       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1371       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1372     } else {
1373       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1374       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1375     }
1376     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1377     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1378       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1379       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1380       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1381       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1382     } else {
1383       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1384       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1385     }
1386     if (ksp) {
1387       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1388     }
1389     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1390   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1391     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1392   }
1393   PetscFunctionReturn(0);
1394 }
1395 
1396 /*
1397    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1398                      approach has been selected. Also, restores rhs to its original state.
1399 
1400    Input Parameter:
1401 +  pc - the preconditioner contex
1402 
1403    Application Interface Routine: PCPostSolve()
1404 
1405    Notes:
1406      The interface routine PCPostSolve() is not usually called directly by
1407      the user, but instead is called by KSPSolve().
1408 */
1409 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1410 {
1411   PetscErrorCode ierr;
1412   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1413 
1414   PetscFunctionBegin;
1415   /* add solution removed in presolve */
1416   if (x && pcbddc->rhs_change) {
1417     if (pcbddc->temp_solution_used) {
1418       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1419     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1420       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1421     }
1422     /* restore to original state (not for FETI-DP) */
1423     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1424   }
1425 
1426   /* restore rhs to its original state (not needed for FETI-DP) */
1427   if (rhs && pcbddc->rhs_change) {
1428     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1429     pcbddc->rhs_change = PETSC_FALSE;
1430   }
1431   /* restore ksp guess state */
1432   if (ksp) {
1433     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1434     /* reset flag for exact dirichlet trick */
1435     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1436   }
1437   PetscFunctionReturn(0);
1438 }
1439 
1440 /*
1441    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1442                   by setting data structures and options.
1443 
1444    Input Parameter:
1445 +  pc - the preconditioner context
1446 
1447    Application Interface Routine: PCSetUp()
1448 
1449    Notes:
1450      The interface routine PCSetUp() is not usually called directly by
1451      the user, but instead is called by PCApply() if necessary.
1452 */
1453 PetscErrorCode PCSetUp_BDDC(PC pc)
1454 {
1455   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1456   PCBDDCSubSchurs sub_schurs;
1457   Mat_IS*         matis;
1458   MatNullSpace    nearnullspace;
1459   Mat             lA;
1460   IS              lP,zerodiag = NULL;
1461   PetscInt        nrows,ncols;
1462   PetscMPIInt     size;
1463   PetscBool       computesubschurs;
1464   PetscBool       computeconstraintsmatrix;
1465   PetscBool       new_nearnullspace_provided,ismatis;
1466   PetscErrorCode  ierr;
1467 
1468   PetscFunctionBegin;
1469   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1470   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1471   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1472   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1473   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
1474 
1475   matis = (Mat_IS*)pc->pmat->data;
1476   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1477   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1478      Also, BDDC builds its own KSP for the Dirichlet problem */
1479   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) pcbddc->recompute_topography = PETSC_TRUE;
1480   if (pcbddc->recompute_topography) {
1481     pcbddc->graphanalyzed    = PETSC_FALSE;
1482     computeconstraintsmatrix = PETSC_TRUE;
1483   } else {
1484     computeconstraintsmatrix = PETSC_FALSE;
1485   }
1486 
1487   /* check parameters' compatibility */
1488   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1489   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1490   pcbddc->use_deluxe_scaling   = (PetscBool)(pcbddc->use_deluxe_scaling && size > 1);
1491   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_selection && size > 1);
1492   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1493   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1494 
1495   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1496   if (pcbddc->switch_static) {
1497     PetscBool ismatis;
1498     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1499     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1500   }
1501 
1502   /* activate all connected components if the netflux has been requested */
1503   if (pcbddc->compute_nonetflux) {
1504     pcbddc->use_vertices = PETSC_TRUE;
1505     pcbddc->use_edges = PETSC_TRUE;
1506     pcbddc->use_faces = PETSC_TRUE;
1507   }
1508 
1509   /* Get stdout for dbg */
1510   if (pcbddc->dbg_flag) {
1511     if (!pcbddc->dbg_viewer) {
1512       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1513       ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1514     }
1515     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1516   }
1517 
1518   /* process topology information */
1519   if (pcbddc->recompute_topography) {
1520     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1521     if (pcbddc->discretegradient) {
1522       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1523     }
1524   }
1525 
1526   /* change basis if requested by the user */
1527   if (pcbddc->user_ChangeOfBasisMatrix) {
1528     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1529     pcbddc->use_change_of_basis = PETSC_FALSE;
1530     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1531   } else {
1532     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1533     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1534     pcbddc->local_mat = matis->A;
1535   }
1536 
1537   /*
1538      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1539      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1540   */
1541   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1542   if (pcbddc->benign_saddle_point) {
1543     PC_IS* pcis = (PC_IS*)pc->data;
1544 
1545     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1546     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1547     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1548     /* pop B0 mat from local mat */
1549     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1550     /* give pcis a hint to not reuse submatrices during PCISCreate */
1551     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1552       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1553         pcis->reusesubmatrices = PETSC_FALSE;
1554       } else {
1555         pcis->reusesubmatrices = PETSC_TRUE;
1556       }
1557     } else {
1558       pcis->reusesubmatrices = PETSC_FALSE;
1559     }
1560   }
1561 
1562   /* propagate relevant information */
1563   if (matis->A->symmetric_set) {
1564     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1565   }
1566   if (matis->A->spd_set) {
1567     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1568   }
1569 
1570   /* Set up all the "iterative substructuring" common block without computing solvers */
1571   {
1572     Mat temp_mat;
1573 
1574     temp_mat = matis->A;
1575     matis->A = pcbddc->local_mat;
1576     ierr = PCISSetUp(pc,PETSC_FALSE);CHKERRQ(ierr);
1577     pcbddc->local_mat = matis->A;
1578     matis->A = temp_mat;
1579   }
1580 
1581   /* Analyze interface */
1582   if (!pcbddc->graphanalyzed) {
1583     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1584     computeconstraintsmatrix = PETSC_TRUE;
1585     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1586       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1587     }
1588     if (pcbddc->compute_nonetflux) {
1589       MatNullSpace nnfnnsp;
1590 
1591       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1592       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1593       /* TODO what if a nearnullspace is already attached? */
1594       if (nnfnnsp) {
1595         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1596         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1597       }
1598     }
1599   }
1600 
1601   /* check existence of a divergence free extension, i.e.
1602      b(v_I,p_0) = 0 for all v_I (raise error if not).
1603      Also, check that PCBDDCBenignGetOrSetP0 works */
1604   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1605     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1606   }
1607   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1608 
1609   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1610   if (computesubschurs && pcbddc->recompute_topography) {
1611     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1612   }
1613   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1614   if (!pcbddc->use_deluxe_scaling) {
1615     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1616   }
1617 
1618   /* finish setup solvers and do adaptive selection of constraints */
1619   sub_schurs = pcbddc->sub_schurs;
1620   if (sub_schurs && sub_schurs->schur_explicit) {
1621     if (computesubschurs) {
1622       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1623     }
1624     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1625   } else {
1626     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1627     if (computesubschurs) {
1628       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1629     }
1630   }
1631   if (pcbddc->adaptive_selection) {
1632     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1633     computeconstraintsmatrix = PETSC_TRUE;
1634   }
1635 
1636   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1637   new_nearnullspace_provided = PETSC_FALSE;
1638   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1639   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1640     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1641       new_nearnullspace_provided = PETSC_TRUE;
1642     } else {
1643       /* determine if the two nullspaces are different (should be lightweight) */
1644       if (nearnullspace != pcbddc->onearnullspace) {
1645         new_nearnullspace_provided = PETSC_TRUE;
1646       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1647         PetscInt         i;
1648         const Vec        *nearnullvecs;
1649         PetscObjectState state;
1650         PetscInt         nnsp_size;
1651         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1652         for (i=0;i<nnsp_size;i++) {
1653           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1654           if (pcbddc->onearnullvecs_state[i] != state) {
1655             new_nearnullspace_provided = PETSC_TRUE;
1656             break;
1657           }
1658         }
1659       }
1660     }
1661   } else {
1662     if (!nearnullspace) { /* both nearnullspaces are null */
1663       new_nearnullspace_provided = PETSC_FALSE;
1664     } else { /* nearnullspace attached later */
1665       new_nearnullspace_provided = PETSC_TRUE;
1666     }
1667   }
1668 
1669   /* Setup constraints and related work vectors */
1670   /* reset primal space flags */
1671   pcbddc->new_primal_space = PETSC_FALSE;
1672   pcbddc->new_primal_space_local = PETSC_FALSE;
1673   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1674     /* It also sets the primal space flags */
1675     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1676   }
1677   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1678   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1679 
1680   if (pcbddc->use_change_of_basis) {
1681     PC_IS *pcis = (PC_IS*)(pc->data);
1682 
1683     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1684     if (pcbddc->benign_change) {
1685       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1686       /* pop B0 from pcbddc->local_mat */
1687       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1688     }
1689     /* get submatrices */
1690     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1691     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1692     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1693     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1694     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1695     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1696     /* set flag in pcis to not reuse submatrices during PCISCreate */
1697     pcis->reusesubmatrices = PETSC_FALSE;
1698   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1699     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1700     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1701     pcbddc->local_mat = matis->A;
1702   }
1703 
1704   /* interface pressure block row for B_C */
1705   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1706   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1707   if (lA && lP) {
1708     PC_IS*    pcis = (PC_IS*)pc->data;
1709     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1710     PetscBool issym;
1711     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1712     if (issym) {
1713       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1714       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1715       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1716       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1717     } else {
1718       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1719       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1720       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1721       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1722     }
1723     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1724     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1725     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1726     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1727     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1728     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1729     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1730     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1731   }
1732 
1733   /* SetUp coarse and local Neumann solvers */
1734   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1735   /* SetUp Scaling operator */
1736   if (pcbddc->use_deluxe_scaling) {
1737     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1738   }
1739 
1740   /* mark topography as done */
1741   pcbddc->recompute_topography = PETSC_FALSE;
1742 
1743   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1744   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1745 
1746   if (pcbddc->dbg_flag) {
1747     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1748   }
1749   PetscFunctionReturn(0);
1750 }
1751 
1752 /*
1753    PCApply_BDDC - Applies the BDDC operator to a vector.
1754 
1755    Input Parameters:
1756 +  pc - the preconditioner context
1757 -  r - input vector (global)
1758 
1759    Output Parameter:
1760 .  z - output vector (global)
1761 
1762    Application Interface Routine: PCApply()
1763  */
1764 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1765 {
1766   PC_IS             *pcis = (PC_IS*)(pc->data);
1767   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1768   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1769   PetscErrorCode    ierr;
1770   const PetscScalar one = 1.0;
1771   const PetscScalar m_one = -1.0;
1772   const PetscScalar zero = 0.0;
1773 
1774 /* This code is similar to that provided in nn.c for PCNN
1775    NN interface preconditioner changed to BDDC
1776    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1777 
1778   PetscFunctionBegin;
1779   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1780   if (pcbddc->ChangeOfBasisMatrix) {
1781     Vec swap;
1782 
1783     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1784     swap = pcbddc->work_change;
1785     pcbddc->work_change = r;
1786     r = swap;
1787     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1788     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1789       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1790       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1791     }
1792   }
1793   if (pcbddc->benign_have_null) { /* get p0 from r */
1794     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1795   }
1796   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1797     ierr = VecCopy(r,z);CHKERRQ(ierr);
1798     /* First Dirichlet solve */
1799     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1800     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1801     /*
1802       Assembling right hand side for BDDC operator
1803       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1804       - pcis->vec1_B the interface part of the global vector z
1805     */
1806     if (n_D) {
1807       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1808       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1809       if (pcbddc->switch_static) {
1810         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1811 
1812         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1813         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1814         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1815         if (!pcbddc->switch_static_change) {
1816           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1817         } else {
1818           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1819           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1820           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1821         }
1822         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1823         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1824         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1825         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1826       } else {
1827         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1828       }
1829     } else {
1830       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1831     }
1832     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1833     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1834     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1835   } else {
1836     if (!pcbddc->benign_apply_coarse_only) {
1837       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1838     }
1839   }
1840 
1841   /* Apply interface preconditioner
1842      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1843   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1844 
1845   /* Apply transpose of partition of unity operator */
1846   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1847 
1848   /* Second Dirichlet solve and assembling of output */
1849   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1850   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1851   if (n_B) {
1852     if (pcbddc->switch_static) {
1853       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1854 
1855       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1856       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1857       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1858       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1859       if (!pcbddc->switch_static_change) {
1860         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1861       } else {
1862         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1863         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1864         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1865       }
1866       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1867       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1868     } else {
1869       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1870     }
1871   } else if (pcbddc->switch_static) { /* n_B is zero */
1872     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1873 
1874     if (!pcbddc->switch_static_change) {
1875       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1876     } else {
1877       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1878       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1879       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
1880     }
1881   }
1882   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1883 
1884   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1885     if (pcbddc->switch_static) {
1886       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1887     } else {
1888       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1889     }
1890     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1891     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1892   } else {
1893     if (pcbddc->switch_static) {
1894       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1895     } else {
1896       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1897     }
1898     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1899     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1900   }
1901   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
1902     if (pcbddc->benign_apply_coarse_only) {
1903       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
1904     }
1905     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1906   }
1907 
1908   if (pcbddc->ChangeOfBasisMatrix) {
1909     pcbddc->work_change = r;
1910     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
1911     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
1912   }
1913   PetscFunctionReturn(0);
1914 }
1915 
1916 /*
1917    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1918 
1919    Input Parameters:
1920 +  pc - the preconditioner context
1921 -  r - input vector (global)
1922 
1923    Output Parameter:
1924 .  z - output vector (global)
1925 
1926    Application Interface Routine: PCApplyTranspose()
1927  */
1928 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1929 {
1930   PC_IS             *pcis = (PC_IS*)(pc->data);
1931   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1932   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1933   PetscErrorCode    ierr;
1934   const PetscScalar one = 1.0;
1935   const PetscScalar m_one = -1.0;
1936   const PetscScalar zero = 0.0;
1937 
1938   PetscFunctionBegin;
1939   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1940   if (pcbddc->ChangeOfBasisMatrix) {
1941     Vec swap;
1942 
1943     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1944     swap = pcbddc->work_change;
1945     pcbddc->work_change = r;
1946     r = swap;
1947     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1948     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
1949       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1950       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1951     }
1952   }
1953   if (pcbddc->benign_have_null) { /* get p0 from r */
1954     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1955   }
1956   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1957     ierr = VecCopy(r,z);CHKERRQ(ierr);
1958     /* First Dirichlet solve */
1959     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1960     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1961     /*
1962       Assembling right hand side for BDDC operator
1963       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1964       - pcis->vec1_B the interface part of the global vector z
1965     */
1966     if (n_D) {
1967       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1968       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1969       if (pcbddc->switch_static) {
1970         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1971 
1972         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1973         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1974         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1975         if (!pcbddc->switch_static_change) {
1976           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1977         } else {
1978           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1979           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1980           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1981         }
1982         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1983         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1984         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1985         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1986       } else {
1987         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1988       }
1989     } else {
1990       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1991     }
1992     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1993     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1994     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1995   } else {
1996     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1997   }
1998 
1999   /* Apply interface preconditioner
2000      input/output vecs: pcis->vec1_B and pcis->vec1_D */
2001   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
2002 
2003   /* Apply transpose of partition of unity operator */
2004   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2005 
2006   /* Second Dirichlet solve and assembling of output */
2007   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2008   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2009   if (n_B) {
2010     if (pcbddc->switch_static) {
2011       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2012 
2013       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2014       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2015       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2016       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2017       if (!pcbddc->switch_static_change) {
2018         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2019       } else {
2020         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2021         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2022         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2023       }
2024       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2025       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2026     } else {
2027       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2028     }
2029   } else if (pcbddc->switch_static) { /* n_B is zero */
2030     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2031 
2032     if (!pcbddc->switch_static_change) {
2033       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2034     } else {
2035       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2036       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2037       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2038     }
2039   }
2040   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2041   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2042     if (pcbddc->switch_static) {
2043       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2044     } else {
2045       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2046     }
2047     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2048     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2049   } else {
2050     if (pcbddc->switch_static) {
2051       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2052     } else {
2053       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2054     }
2055     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2056     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2057   }
2058   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2059     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2060   }
2061   if (pcbddc->ChangeOfBasisMatrix) {
2062     pcbddc->work_change = r;
2063     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2064     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2065   }
2066   PetscFunctionReturn(0);
2067 }
2068 
2069 PetscErrorCode PCReset_BDDC(PC pc)
2070 {
2071   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2072   PC_IS          *pcis = (PC_IS*)pc->data;
2073   KSP            kspD,kspR,kspC;
2074   PetscErrorCode ierr;
2075 
2076   PetscFunctionBegin;
2077   /* free BDDC custom data  */
2078   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2079   /* destroy objects related to topography */
2080   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2081   /* destroy objects for scaling operator */
2082   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2083   /* free solvers stuff */
2084   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2085   /* free global vectors needed in presolve */
2086   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2087   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2088   /* free data created by PCIS */
2089   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2090 
2091   /* restore defaults */
2092   kspD = pcbddc->ksp_D;
2093   kspR = pcbddc->ksp_R;
2094   kspC = pcbddc->coarse_ksp;
2095   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2096   pcis->n_neigh                     = -1;
2097   pcis->scaling_factor              = 1.0;
2098   pcis->reusesubmatrices            = PETSC_TRUE;
2099   pcbddc->use_local_adj             = PETSC_TRUE;
2100   pcbddc->use_vertices              = PETSC_TRUE;
2101   pcbddc->use_edges                 = PETSC_TRUE;
2102   pcbddc->symmetric_primal          = PETSC_TRUE;
2103   pcbddc->vertex_size               = 1;
2104   pcbddc->recompute_topography      = PETSC_TRUE;
2105   pcbddc->coarse_size               = -1;
2106   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2107   pcbddc->coarsening_ratio          = 8;
2108   pcbddc->coarse_eqs_per_proc       = 1;
2109   pcbddc->benign_compute_correction = PETSC_TRUE;
2110   pcbddc->nedfield                  = -1;
2111   pcbddc->nedglobal                 = PETSC_TRUE;
2112   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2113   pcbddc->sub_schurs_layers         = -1;
2114   pcbddc->ksp_D                     = kspD;
2115   pcbddc->ksp_R                     = kspR;
2116   pcbddc->coarse_ksp                = kspC;
2117   PetscFunctionReturn(0);
2118 }
2119 
2120 PetscErrorCode PCDestroy_BDDC(PC pc)
2121 {
2122   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2123   PetscErrorCode ierr;
2124 
2125   PetscFunctionBegin;
2126   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2127   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2128   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2129   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2130   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2131   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2132   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2133   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2134   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2135   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2136   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2137   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2138   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2139   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2140   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2141   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2142   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2143   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2144   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2145   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2146   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2147   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2148   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2149   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2150   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2151   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2152   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2153   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2154   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2155   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2156   PetscFunctionReturn(0);
2157 }
2158 
2159 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2160 {
2161   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2162   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2163   PetscErrorCode ierr;
2164 
2165   PetscFunctionBegin;
2166   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2167   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2168   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2169   mat_graph->cnloc = nloc;
2170   mat_graph->cdim  = dim;
2171   mat_graph->cloc  = PETSC_FALSE;
2172   PetscFunctionReturn(0);
2173 }
2174 
2175 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2176 {
2177   PetscFunctionBegin;
2178   *change = PETSC_TRUE;
2179   PetscFunctionReturn(0);
2180 }
2181 
2182 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2183 {
2184   FETIDPMat_ctx  mat_ctx;
2185   Vec            work;
2186   PC_IS*         pcis;
2187   PC_BDDC*       pcbddc;
2188   PetscErrorCode ierr;
2189 
2190   PetscFunctionBegin;
2191   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2192   pcis = (PC_IS*)mat_ctx->pc->data;
2193   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2194 
2195   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2196   /* copy rhs since we may change it during PCPreSolve_BDDC */
2197   if (!pcbddc->original_rhs) {
2198     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2199   }
2200   if (mat_ctx->rhs_flip) {
2201     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2202   } else {
2203     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2204   }
2205   if (mat_ctx->g2g_p) {
2206     /* interface pressure rhs */
2207     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2208     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2209     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2210     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2211     if (!mat_ctx->rhs_flip) {
2212       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2213     }
2214   }
2215   /*
2216      change of basis for physical rhs if needed
2217      It also changes the rhs in case of dirichlet boundaries
2218   */
2219   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2220   if (pcbddc->ChangeOfBasisMatrix) {
2221     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2222     work = pcbddc->work_change;
2223    } else {
2224     work = pcbddc->original_rhs;
2225   }
2226   /* store vectors for computation of fetidp final solution */
2227   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2228   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2229   /* scale rhs since it should be unassembled */
2230   /* TODO use counter scaling? (also below) */
2231   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2232   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2233   /* Apply partition of unity */
2234   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2235   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2236   if (!pcbddc->switch_static) {
2237     /* compute partially subassembled Schur complement right-hand side */
2238     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2239     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2240     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2241     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2242     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2243     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2244     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2245     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2246     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2247     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2248   }
2249   /* BDDC rhs */
2250   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2251   if (pcbddc->switch_static) {
2252     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2253   }
2254   /* apply BDDC */
2255   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2256   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2257   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2258 
2259   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2260   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2261   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2262   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2263   /* Add contribution to interface pressures */
2264   if (mat_ctx->l2g_p) {
2265     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2266     if (pcbddc->switch_static) {
2267       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2268     }
2269     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2270     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2271   }
2272   PetscFunctionReturn(0);
2273 }
2274 
2275 /*@
2276  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2277 
2278    Collective
2279 
2280    Input Parameters:
2281 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2282 -  standard_rhs    - the right-hand side of the original linear system
2283 
2284    Output Parameters:
2285 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2286 
2287    Level: developer
2288 
2289    Notes:
2290 
2291 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2292 @*/
2293 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2294 {
2295   FETIDPMat_ctx  mat_ctx;
2296   PetscErrorCode ierr;
2297 
2298   PetscFunctionBegin;
2299   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2300   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2301   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2302   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2303   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2304   PetscFunctionReturn(0);
2305 }
2306 
2307 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2308 {
2309   FETIDPMat_ctx  mat_ctx;
2310   PC_IS*         pcis;
2311   PC_BDDC*       pcbddc;
2312   PetscErrorCode ierr;
2313   Vec            work;
2314 
2315   PetscFunctionBegin;
2316   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2317   pcis = (PC_IS*)mat_ctx->pc->data;
2318   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2319 
2320   /* apply B_delta^T */
2321   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2322   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2323   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2324   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2325   if (mat_ctx->l2g_p) {
2326     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2327     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2328     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2329   }
2330 
2331   /* compute rhs for BDDC application */
2332   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2333   if (pcbddc->switch_static) {
2334     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2335     if (mat_ctx->l2g_p) {
2336       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2337       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2338     }
2339   }
2340 
2341   /* apply BDDC */
2342   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2343   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2344 
2345   /* put values into global vector */
2346   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2347   else work = standard_sol;
2348   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2349   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2350   if (!pcbddc->switch_static) {
2351     /* compute values into the interior if solved for the partially subassembled Schur complement */
2352     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2353     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2354     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2355   }
2356 
2357   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2358   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2359   /* add p0 solution to final solution */
2360   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2361   if (pcbddc->ChangeOfBasisMatrix) {
2362     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2363   }
2364   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2365   if (mat_ctx->g2g_p) {
2366     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2367     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2368   }
2369   PetscFunctionReturn(0);
2370 }
2371 
2372 /*@
2373  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2374 
2375    Collective
2376 
2377    Input Parameters:
2378 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2379 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2380 
2381    Output Parameters:
2382 .  standard_sol    - the solution defined on the physical domain
2383 
2384    Level: developer
2385 
2386    Notes:
2387 
2388 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2389 @*/
2390 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2391 {
2392   FETIDPMat_ctx  mat_ctx;
2393   PetscErrorCode ierr;
2394 
2395   PetscFunctionBegin;
2396   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2397   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2398   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2399   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2400   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2401   PetscFunctionReturn(0);
2402 }
2403 
2404 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2405 {
2406 
2407   FETIDPMat_ctx  fetidpmat_ctx;
2408   Mat            newmat;
2409   FETIDPPC_ctx   fetidppc_ctx;
2410   PC             newpc;
2411   MPI_Comm       comm;
2412   PetscErrorCode ierr;
2413 
2414   PetscFunctionBegin;
2415   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2416   /* FETIDP linear matrix */
2417   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2418   fetidpmat_ctx->fully_redundant = fully_redundant;
2419   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2420   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2421   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2422   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2423   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2424   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2425   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2426   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2427   /* FETIDP preconditioner */
2428   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2429   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2430   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2431   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2432   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2433   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2434   if (!fetidpmat_ctx->l2g_lambda_only) {
2435     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2436     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2437     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2438     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2439     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2440     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2441   } else {
2442     KSP      *ksps;
2443     PC       lagpc;
2444     Mat      M,AM,PM;
2445     PetscInt nn;
2446 
2447     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2448     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2449     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2450     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2451     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2452     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2453     ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2454     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2455     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2456     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2457 
2458     /* set the solver for the (0,0) block */
2459     ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2460     ierr = PCCreate(comm,&lagpc);CHKERRQ(ierr);
2461     ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2462     ierr = KSPGetOperators(ksps[0],&AM,&PM);CHKERRQ(ierr);
2463     ierr = PCSetOperators(lagpc,AM,PM);CHKERRQ(ierr);
2464     ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2465     ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2466     ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2467     ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2468     ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2469     ierr = KSPSetPC(ksps[0],lagpc);CHKERRQ(ierr);
2470     ierr = PCDestroy(&lagpc);CHKERRQ(ierr);
2471     ierr = PetscFree(ksps);CHKERRQ(ierr);
2472   }
2473   /* return pointers for objects created */
2474   *fetidp_mat = newmat;
2475   *fetidp_pc = newpc;
2476   PetscFunctionReturn(0);
2477 }
2478 
2479 /*@C
2480  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2481 
2482    Collective
2483 
2484    Input Parameters:
2485 +  pc - the BDDC preconditioning context (setup should have been called before)
2486 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2487 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2488 
2489    Output Parameters:
2490 +  fetidp_mat - shell FETI-DP matrix object
2491 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2492 
2493    Level: developer
2494 
2495    Notes:
2496      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2497 
2498 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2499 @*/
2500 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2501 {
2502   PetscErrorCode ierr;
2503 
2504   PetscFunctionBegin;
2505   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2506   if (pc->setupcalled) {
2507     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2508   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2509   PetscFunctionReturn(0);
2510 }
2511 /* -------------------------------------------------------------------------- */
2512 /*MC
2513    PCBDDC - Balancing Domain Decomposition by Constraints.
2514 
2515    An implementation of the BDDC preconditioner based on
2516 
2517 .vb
2518    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2519    [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
2520    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2521    [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
2522 .ve
2523 
2524    The matrix to be preconditioned (Pmat) must be of type MATIS.
2525 
2526    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2527 
2528    It also works with unsymmetric and indefinite problems.
2529 
2530    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.
2531 
2532    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).
2533 
2534    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()
2535    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2536 
2537    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2538 
2539    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.
2540    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2541 
2542    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2543 
2544    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.
2545 
2546    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.
2547    Deluxe scaling is not supported yet for FETI-DP.
2548 
2549    Options Database Keys (some of them, run with -h for a complete list):
2550 
2551 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2552 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2553 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2554 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2555 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2556 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2557 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2558 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2559 .    -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)
2560 .    -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)
2561 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2562 .    -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)
2563 .    -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)
2564 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2565 
2566    Options for Dirichlet, Neumann or coarse solver can be set with
2567 .vb
2568       -pc_bddc_dirichlet_
2569       -pc_bddc_neumann_
2570       -pc_bddc_coarse_
2571 .ve
2572    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2573 
2574    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2575 .vb
2576       -pc_bddc_dirichlet_lN_
2577       -pc_bddc_neumann_lN_
2578       -pc_bddc_coarse_lN_
2579 .ve
2580    Note that level number ranges from the finest (0) to the coarsest (N).
2581    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.
2582 .vb
2583      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2584 .ve
2585    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
2586 
2587    Level: intermediate
2588 
2589    Developer notes:
2590 
2591    Contributed by Stefano Zampini
2592 
2593 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2594 M*/
2595 
2596 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2597 {
2598   PetscErrorCode      ierr;
2599   PC_BDDC             *pcbddc;
2600 
2601   PetscFunctionBegin;
2602   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2603   pc->data = (void*)pcbddc;
2604 
2605   /* create PCIS data structure */
2606   ierr = PCISCreate(pc);CHKERRQ(ierr);
2607 
2608   /* create local graph structure */
2609   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2610 
2611   /* BDDC nonzero defaults */
2612   pcbddc->use_local_adj             = PETSC_TRUE;
2613   pcbddc->use_vertices              = PETSC_TRUE;
2614   pcbddc->use_edges                 = PETSC_TRUE;
2615   pcbddc->symmetric_primal          = PETSC_TRUE;
2616   pcbddc->vertex_size               = 1;
2617   pcbddc->recompute_topography      = PETSC_TRUE;
2618   pcbddc->coarse_size               = -1;
2619   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2620   pcbddc->coarsening_ratio          = 8;
2621   pcbddc->coarse_eqs_per_proc       = 1;
2622   pcbddc->benign_compute_correction = PETSC_TRUE;
2623   pcbddc->nedfield                  = -1;
2624   pcbddc->nedglobal                 = PETSC_TRUE;
2625   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2626   pcbddc->sub_schurs_layers         = -1;
2627   pcbddc->adaptive_threshold[0]     = 0.0;
2628   pcbddc->adaptive_threshold[1]     = 0.0;
2629 
2630   /* function pointers */
2631   pc->ops->apply               = PCApply_BDDC;
2632   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2633   pc->ops->setup               = PCSetUp_BDDC;
2634   pc->ops->destroy             = PCDestroy_BDDC;
2635   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2636   pc->ops->view                = PCView_BDDC;
2637   pc->ops->applyrichardson     = 0;
2638   pc->ops->applysymmetricleft  = 0;
2639   pc->ops->applysymmetricright = 0;
2640   pc->ops->presolve            = PCPreSolve_BDDC;
2641   pc->ops->postsolve           = PCPostSolve_BDDC;
2642   pc->ops->reset               = PCReset_BDDC;
2643 
2644   /* composing function */
2645   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
2646   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
2647   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2648   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2649   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
2650   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2651   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2652   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2653   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2654   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2655   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2656   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2657   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2658   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2659   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2660   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2661   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2662   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2663   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2664   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2665   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2666   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2667   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2668   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
2669   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
2670   PetscFunctionReturn(0);
2671 }
2672