xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 94ef8dde638caef1d0cd84a7dc8a2db65fcda8b6)
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   PetscErrorCode ierr;
48 
49   PetscFunctionBegin;
50   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
51   /* Verbose debugging */
52   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
53   /* Approximate solvers */
54   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);
55   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);
56   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);
57   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);
58   /* Primal space customization */
59   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);
60   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
61   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
62   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
63   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
64   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);
65   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);
66   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);
67   /* Change of basis */
68   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);
69   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);
70   if (!pcbddc->use_change_of_basis) {
71     pcbddc->use_change_on_faces = PETSC_FALSE;
72   }
73   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
74   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);
75   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);
76   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,NULL);CHKERRQ(ierr);
77   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","none",pcbddc->max_levels,&pcbddc->max_levels,NULL);CHKERRQ(ierr);
78   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);
79   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
80   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);
81   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);
82   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);
83   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);
84   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);
85   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
86   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);
87   ierr = PetscOptionsReal("-pc_bddc_adaptive_threshold","Threshold to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&pcbddc->adaptive_threshold,NULL);CHKERRQ(ierr);
88   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
89   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
90   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
91   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);
92   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);
93   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);
94   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);
95   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
96   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
97   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);
98   ierr = PetscOptionsTail();CHKERRQ(ierr);
99   PetscFunctionReturn(0);
100 }
101 
102 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
103 {
104   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
105   PC_IS                *pcis = (PC_IS*)pc->data;
106   PetscErrorCode       ierr;
107   PetscBool            isascii,isstring;
108   PetscSubcomm         subcomm;
109   PetscViewer          subviewer;
110 
111   PetscFunctionBegin;
112   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
113   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);
114   /* Nothing printed for the String viewer */
115   /* ASCII viewer */
116   if (isascii) {
117     PetscMPIInt   color,rank,size;
118     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
119     PetscScalar   interface_size;
120     PetscReal     ratio1=0.,ratio2=0.;
121     Vec           counter;
122 
123     if (!pc->setupcalled) {
124       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
125     }
126     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use verbose output: %d\n",pcbddc->dbg_flag);CHKERRQ(ierr);
127     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use user-defined CSR: %d\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
128     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use local mat graph: %d\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
129     if (pcbddc->mat_graph->twodim) {
130       ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
131     } else {
132       ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
133     }
134     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Graph max count: %d\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
135     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use vertices: %d (vertex size %d)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
136     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
137     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
138     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
139     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
140     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
141     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
142     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
143     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
144     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
145     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Multilevel max levels: %d\n",pcbddc->max_levels);CHKERRQ(ierr);
148     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Multilevel coarsening ratio: %d\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
149     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
150     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
151     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
152     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
153     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
154     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Number of dofs' layers for the computation of principal minors: %d\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
155     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
156     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Adaptive constraint selection threshold (active %d, userdefined %d): %g\n",pcbddc->adaptive_threshold,pcbddc->adaptive_selection,pcbddc->adaptive_userdefined);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Min constraints / connected component: %d\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Max constraints / connected component: %d\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
160     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
161     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Num. Procs. to map coarse adjacency list: %d\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
162     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Coarse eqs per proc (significant at the coarsest level): %d\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
163     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Detect disconnected: %d\n",pcbddc->detect_disconnected);CHKERRQ(ierr);
164     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
165     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Algebraic computation of no-net-flux %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
167     if (!pc->setupcalled) PetscFunctionReturn(0);
168 
169     /* compute interface size */
170     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
171     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
172     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
173     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
174     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
175     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
176     ierr = VecDestroy(&counter);CHKERRQ(ierr);
177 
178     /* compute some statistics on the domain decomposition */
179     gsum[0] = 1;
180     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
181     loc[0]  = !!pcis->n;
182     loc[1]  = pcis->n - pcis->n_B;
183     loc[2]  = pcis->n_B;
184     loc[3]  = pcbddc->local_primal_size;
185     loc[4]  = pcis->n;
186     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
187     loc[6]  = pcbddc->benign_n;
188     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
189     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
190     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
191     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
192     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
193     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
194     if (pcbddc->coarse_size) {
195       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
196       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
197     }
198     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: ********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
199     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Global dofs sizes: all %d interface %d coarse %d\n",pc->pmat->rmap->N,(PetscInt)PetscRealPart(interface_size),pcbddc->coarse_size);CHKERRQ(ierr);
200     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Coarsening ratios: all/coarse %d interface/coarse %d\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
201     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Active processes : %d\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
202     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Total subdomains : %d\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
203     if (pcbddc->benign_have_null) {
204       ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Benign subs      : %d\n",(PetscInt)totbenign);CHKERRQ(ierr);
205     }
206     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Dofs type        :\tMIN\tMAX\tMEAN\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
207     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Interior  dofs   :\t%d\t%d\t%d\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
208     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Interface dofs   :\t%d\t%d\t%d\n",(PetscInt)gmin[2],(PetscInt)gmax[2],(PetscInt)(gsum[2]/gsum[0]));CHKERRQ(ierr);
209     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Primal    dofs   :\t%d\t%d\t%d\n",(PetscInt)gmin[3],(PetscInt)gmax[3],(PetscInt)(gsum[3]/gsum[0]));CHKERRQ(ierr);
210     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Local     dofs   :\t%d\t%d\t%d\n",(PetscInt)gmin[4],(PetscInt)gmax[4],(PetscInt)(gsum[4]/gsum[0]));CHKERRQ(ierr);
211     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: Local     subs   :\t%d\t%d\n",(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
212     ierr = PetscViewerASCIIPrintf(viewer,"  BDDC: ********************************** COARSE PROBLEM DETAILS *********************************\n",pcbddc->current_level);CHKERRQ(ierr);
213     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
214 
215     /* the coarse problem can be handled by a different communicator */
216     if (pcbddc->coarse_ksp) color = 1;
217     else color = 0;
218     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
219     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
220     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
221     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
222     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
223     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
224     if (color == 1) {
225       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
226       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
227     }
228     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
229     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
230     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
231   }
232   PetscFunctionReturn(0);
233 }
234 
235 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
236 {
237   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
238   PetscErrorCode ierr;
239 
240   PetscFunctionBegin;
241   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
242   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
243   pcbddc->discretegradient = G;
244   pcbddc->nedorder         = order > 0 ? order : -order;
245   pcbddc->nedfield         = field;
246   pcbddc->nedglobal        = global;
247   pcbddc->conforming       = conforming;
248   PetscFunctionReturn(0);
249 }
250 
251 /*@
252  PCBDDCSetDiscreteGradient - Sets the discrete gradient
253 
254    Collective on PC
255 
256    Input Parameters:
257 +  pc         - the preconditioning context
258 .  G          - the discrete gradient matrix (should be in AIJ format)
259 .  order      - the order of the Nedelec space (1 for the lowest order)
260 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
261 .  global     - the type of global ordering for the rows of G
262 -  conforming - whether the mesh is conforming or not
263 
264    Level: advanced
265 
266    Notes: The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
267           For variable order spaces, the order should be set to zero.
268           If global is true, the rows of G should be given in global ordering for the whole dofs;
269           if false, the ordering should be global for the Nedelec field.
270           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
271           and geid the one for the Nedelec field.
272 
273 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
274 @*/
275 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
276 {
277   PetscErrorCode ierr;
278 
279   PetscFunctionBegin;
280   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
281   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
282   PetscValidLogicalCollectiveInt(pc,order,3);
283   PetscValidLogicalCollectiveInt(pc,field,4);
284   PetscValidLogicalCollectiveBool(pc,global,5);
285   PetscValidLogicalCollectiveBool(pc,conforming,6);
286   PetscCheckSameComm(pc,1,G,2);
287   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
288   PetscFunctionReturn(0);
289 }
290 
291 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
292 {
293   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
294   PetscErrorCode ierr;
295 
296   PetscFunctionBegin;
297   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
298   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
299   pcbddc->divudotp = divudotp;
300   pcbddc->divudotp_trans = trans;
301   pcbddc->compute_nonetflux = PETSC_TRUE;
302   if (vl2l) {
303     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
304     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
305     pcbddc->divudotp_vl2l = vl2l;
306   }
307   PetscFunctionReturn(0);
308 }
309 
310 /*@
311  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
312 
313    Collective on PC
314 
315    Input Parameters:
316 +  pc - the preconditioning context
317 .  divudotp - the matrix (must be of type MATIS)
318 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
319 -  vl2l - optional IS describing the local (wrt the local mat in divudotp) to local (wrt the local mat in pc->pmat) map for the velocities
320 
321    Level: advanced
322 
323    Notes: This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
324 
325 .seealso: PCBDDC
326 @*/
327 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
328 {
329   PetscBool      ismatis;
330   PetscErrorCode ierr;
331 
332   PetscFunctionBegin;
333   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
334   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
335   PetscCheckSameComm(pc,1,divudotp,2);
336   PetscValidLogicalCollectiveBool(pc,trans,3);
337   if (vl2l) PetscValidHeaderSpecific(divudotp,IS_CLASSID,4);
338   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
339   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
340   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
341   PetscFunctionReturn(0);
342 }
343 
344 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
345 {
346   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
347   PetscErrorCode ierr;
348 
349   PetscFunctionBegin;
350   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
351   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
352   pcbddc->user_ChangeOfBasisMatrix = change;
353   pcbddc->change_interior = interior;
354   PetscFunctionReturn(0);
355 }
356 /*@
357  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
358 
359    Collective on PC
360 
361    Input Parameters:
362 +  pc - the preconditioning context
363 .  change - the change of basis matrix
364 -  interior - whether or not the change of basis modifies interior dofs
365 
366    Level: intermediate
367 
368    Notes:
369 
370 .seealso: PCBDDC
371 @*/
372 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
373 {
374   PetscErrorCode ierr;
375 
376   PetscFunctionBegin;
377   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
378   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
379   PetscCheckSameComm(pc,1,change,2);
380   if (pc->mat) {
381     PetscInt rows_c,cols_c,rows,cols;
382     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
383     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
384     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);
385     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);
386     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
387     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
388     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);
389     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);
390   }
391   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
392   PetscFunctionReturn(0);
393 }
394 
395 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
396 {
397   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
398   PetscBool      isequal = PETSC_FALSE;
399   PetscErrorCode ierr;
400 
401   PetscFunctionBegin;
402   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
403   if (pcbddc->user_primal_vertices) {
404     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
405   }
406   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
407   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
408   pcbddc->user_primal_vertices = PrimalVertices;
409   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
410   PetscFunctionReturn(0);
411 }
412 /*@
413  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
414 
415    Collective
416 
417    Input Parameters:
418 +  pc - the preconditioning context
419 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
420 
421    Level: intermediate
422 
423    Notes:
424      Any process can list any global node
425 
426 .seealso: PCBDDC
427 @*/
428 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
429 {
430   PetscErrorCode ierr;
431 
432   PetscFunctionBegin;
433   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
434   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
435   PetscCheckSameComm(pc,1,PrimalVertices,2);
436   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
437   PetscFunctionReturn(0);
438 }
439 
440 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
441 {
442   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
443   PetscBool      isequal = PETSC_FALSE;
444   PetscErrorCode ierr;
445 
446   PetscFunctionBegin;
447   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
448   if (pcbddc->user_primal_vertices_local) {
449     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
450   }
451   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
452   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
453   pcbddc->user_primal_vertices_local = PrimalVertices;
454   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
455   PetscFunctionReturn(0);
456 }
457 /*@
458  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
459 
460    Collective
461 
462    Input Parameters:
463 +  pc - the preconditioning context
464 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
465 
466    Level: intermediate
467 
468    Notes:
469 
470 .seealso: PCBDDC
471 @*/
472 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
473 {
474   PetscErrorCode ierr;
475 
476   PetscFunctionBegin;
477   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
478   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
479   PetscCheckSameComm(pc,1,PrimalVertices,2);
480   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
481   PetscFunctionReturn(0);
482 }
483 
484 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
485 {
486   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
487 
488   PetscFunctionBegin;
489   pcbddc->coarsening_ratio = k;
490   PetscFunctionReturn(0);
491 }
492 
493 /*@
494  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
495 
496    Logically collective on PC
497 
498    Input Parameters:
499 +  pc - the preconditioning context
500 -  k - coarsening ratio (H/h at the coarser level)
501 
502    Options Database Keys:
503 .    -pc_bddc_coarsening_ratio
504 
505    Level: intermediate
506 
507    Notes:
508      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
509 
510 .seealso: PCBDDC, PCBDDCSetLevels()
511 @*/
512 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
513 {
514   PetscErrorCode ierr;
515 
516   PetscFunctionBegin;
517   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
518   PetscValidLogicalCollectiveInt(pc,k,2);
519   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
520   PetscFunctionReturn(0);
521 }
522 
523 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
524 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
525 {
526   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
527 
528   PetscFunctionBegin;
529   pcbddc->use_exact_dirichlet_trick = flg;
530   PetscFunctionReturn(0);
531 }
532 
533 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
534 {
535   PetscErrorCode ierr;
536 
537   PetscFunctionBegin;
538   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
539   PetscValidLogicalCollectiveBool(pc,flg,2);
540   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
541   PetscFunctionReturn(0);
542 }
543 
544 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
545 {
546   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
547 
548   PetscFunctionBegin;
549   pcbddc->current_level = level;
550   PetscFunctionReturn(0);
551 }
552 
553 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
554 {
555   PetscErrorCode ierr;
556 
557   PetscFunctionBegin;
558   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
559   PetscValidLogicalCollectiveInt(pc,level,2);
560   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
561   PetscFunctionReturn(0);
562 }
563 
564 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
565 {
566   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
567 
568   PetscFunctionBegin;
569   pcbddc->max_levels = levels;
570   PetscFunctionReturn(0);
571 }
572 
573 /*@
574  PCBDDCSetLevels - Sets the maximum number of levels for multilevel
575 
576    Logically collective on PC
577 
578    Input Parameters:
579 +  pc - the preconditioning context
580 -  levels - the maximum number of levels (max 9)
581 
582    Options Database Keys:
583 .    -pc_bddc_levels
584 
585    Level: intermediate
586 
587    Notes:
588      Default value is 0, i.e. traditional one-level BDDC
589 
590 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
591 @*/
592 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
593 {
594   PetscErrorCode ierr;
595 
596   PetscFunctionBegin;
597   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
598   PetscValidLogicalCollectiveInt(pc,levels,2);
599   if (levels > 99) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of levels for bddc is 99\n");
600   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
601   PetscFunctionReturn(0);
602 }
603 
604 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
605 {
606   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
607   PetscBool      isequal = PETSC_FALSE;
608   PetscErrorCode ierr;
609 
610   PetscFunctionBegin;
611   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
612   if (pcbddc->DirichletBoundaries) {
613     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
614   }
615   /* last user setting takes precendence -> destroy any other customization */
616   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
617   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
618   pcbddc->DirichletBoundaries = DirichletBoundaries;
619   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
620   PetscFunctionReturn(0);
621 }
622 
623 /*@
624  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
625 
626    Collective
627 
628    Input Parameters:
629 +  pc - the preconditioning context
630 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
631 
632    Level: intermediate
633 
634    Notes:
635      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
636 
637 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
638 @*/
639 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
640 {
641   PetscErrorCode ierr;
642 
643   PetscFunctionBegin;
644   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
645   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
646   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
647   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
648   PetscFunctionReturn(0);
649 }
650 
651 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
652 {
653   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
654   PetscBool      isequal = PETSC_FALSE;
655   PetscErrorCode ierr;
656 
657   PetscFunctionBegin;
658   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
659   if (pcbddc->DirichletBoundariesLocal) {
660     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
661   }
662   /* last user setting takes precendence -> destroy any other customization */
663   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
664   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
665   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
666   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
667   PetscFunctionReturn(0);
668 }
669 
670 /*@
671  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
672 
673    Collective
674 
675    Input Parameters:
676 +  pc - the preconditioning context
677 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
678 
679    Level: intermediate
680 
681    Notes:
682 
683 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
684 @*/
685 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
686 {
687   PetscErrorCode ierr;
688 
689   PetscFunctionBegin;
690   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
691   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
692   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
693   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
694   PetscFunctionReturn(0);
695 }
696 
697 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
698 {
699   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
700   PetscBool      isequal = PETSC_FALSE;
701   PetscErrorCode ierr;
702 
703   PetscFunctionBegin;
704   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
705   if (pcbddc->NeumannBoundaries) {
706     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
707   }
708   /* last user setting takes precendence -> destroy any other customization */
709   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
710   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
711   pcbddc->NeumannBoundaries = NeumannBoundaries;
712   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
713   PetscFunctionReturn(0);
714 }
715 
716 /*@
717  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
718 
719    Collective
720 
721    Input Parameters:
722 +  pc - the preconditioning context
723 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
724 
725    Level: intermediate
726 
727    Notes:
728      Any process can list any global node
729 
730 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
731 @*/
732 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
733 {
734   PetscErrorCode ierr;
735 
736   PetscFunctionBegin;
737   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
738   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
739   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
740   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
741   PetscFunctionReturn(0);
742 }
743 
744 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
745 {
746   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
747   PetscBool      isequal = PETSC_FALSE;
748   PetscErrorCode ierr;
749 
750   PetscFunctionBegin;
751   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
752   if (pcbddc->NeumannBoundariesLocal) {
753     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
754   }
755   /* last user setting takes precendence -> destroy any other customization */
756   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
757   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
758   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
759   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
760   PetscFunctionReturn(0);
761 }
762 
763 /*@
764  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
765 
766    Collective
767 
768    Input Parameters:
769 +  pc - the preconditioning context
770 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
771 
772    Level: intermediate
773 
774    Notes:
775 
776 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
777 @*/
778 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
779 {
780   PetscErrorCode ierr;
781 
782   PetscFunctionBegin;
783   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
784   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
785   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
786   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
787   PetscFunctionReturn(0);
788 }
789 
790 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
791 {
792   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
793 
794   PetscFunctionBegin;
795   *DirichletBoundaries = pcbddc->DirichletBoundaries;
796   PetscFunctionReturn(0);
797 }
798 
799 /*@
800  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
801 
802    Collective
803 
804    Input Parameters:
805 .  pc - the preconditioning context
806 
807    Output Parameters:
808 .  DirichletBoundaries - index set defining the Dirichlet boundaries
809 
810    Level: intermediate
811 
812    Notes:
813      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
814 
815 .seealso: PCBDDC
816 @*/
817 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
818 {
819   PetscErrorCode ierr;
820 
821   PetscFunctionBegin;
822   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
823   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
824   PetscFunctionReturn(0);
825 }
826 
827 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
828 {
829   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
830 
831   PetscFunctionBegin;
832   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
833   PetscFunctionReturn(0);
834 }
835 
836 /*@
837  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
838 
839    Collective
840 
841    Input Parameters:
842 .  pc - the preconditioning context
843 
844    Output Parameters:
845 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
846 
847    Level: intermediate
848 
849    Notes:
850      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).
851           In the latter case, the IS will be available after PCSetUp.
852 
853 .seealso: PCBDDC
854 @*/
855 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
856 {
857   PetscErrorCode ierr;
858 
859   PetscFunctionBegin;
860   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
861   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
862   PetscFunctionReturn(0);
863 }
864 
865 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
866 {
867   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
868 
869   PetscFunctionBegin;
870   *NeumannBoundaries = pcbddc->NeumannBoundaries;
871   PetscFunctionReturn(0);
872 }
873 
874 /*@
875  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
876 
877    Collective
878 
879    Input Parameters:
880 .  pc - the preconditioning context
881 
882    Output Parameters:
883 .  NeumannBoundaries - index set defining the Neumann boundaries
884 
885    Level: intermediate
886 
887    Notes:
888      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
889 
890 .seealso: PCBDDC
891 @*/
892 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
893 {
894   PetscErrorCode ierr;
895 
896   PetscFunctionBegin;
897   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
898   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
899   PetscFunctionReturn(0);
900 }
901 
902 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
903 {
904   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
905 
906   PetscFunctionBegin;
907   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
908   PetscFunctionReturn(0);
909 }
910 
911 /*@
912  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
913 
914    Collective
915 
916    Input Parameters:
917 .  pc - the preconditioning context
918 
919    Output Parameters:
920 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
921 
922    Level: intermediate
923 
924    Notes:
925      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).
926           In the latter case, the IS will be available after PCSetUp.
927 
928 .seealso: PCBDDC
929 @*/
930 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
931 {
932   PetscErrorCode ierr;
933 
934   PetscFunctionBegin;
935   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
936   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
937   PetscFunctionReturn(0);
938 }
939 
940 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
941 {
942   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
943   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
944   PetscBool      same_data = PETSC_FALSE;
945   PetscErrorCode ierr;
946 
947   PetscFunctionBegin;
948   if (!nvtxs) {
949     if (copymode == PETSC_OWN_POINTER) {
950       ierr = PetscFree(xadj);CHKERRQ(ierr);
951       ierr = PetscFree(adjncy);CHKERRQ(ierr);
952     }
953     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
954     PetscFunctionReturn(0);
955   }
956   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
957     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
958     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
959       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
960       if (same_data) {
961         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
962       }
963     }
964   }
965   if (!same_data) {
966     /* free old CSR */
967     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
968     /* get CSR into graph structure */
969     if (copymode == PETSC_COPY_VALUES) {
970       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
971       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
972       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
973       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
974       mat_graph->freecsr = PETSC_TRUE;
975     } else if (copymode == PETSC_OWN_POINTER) {
976       mat_graph->xadj    = (PetscInt*)xadj;
977       mat_graph->adjncy  = (PetscInt*)adjncy;
978       mat_graph->freecsr = PETSC_TRUE;
979     } else if (copymode == PETSC_USE_POINTER) {
980       mat_graph->xadj    = (PetscInt*)xadj;
981       mat_graph->adjncy  = (PetscInt*)adjncy;
982       mat_graph->freecsr = PETSC_FALSE;
983     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %d",copymode);
984     mat_graph->nvtxs_csr = nvtxs;
985     pcbddc->recompute_topography = PETSC_TRUE;
986   }
987   PetscFunctionReturn(0);
988 }
989 
990 /*@
991  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
992 
993    Not collective
994 
995    Input Parameters:
996 +  pc - the preconditioning context.
997 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
998 .  xadj, adjncy - the connectivity of the dofs in CSR format.
999 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1000 
1001    Level: intermediate
1002 
1003    Notes: A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1004 
1005 .seealso: PCBDDC,PetscCopyMode
1006 @*/
1007 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1008 {
1009   void (*f)(void) = 0;
1010   PetscErrorCode ierr;
1011 
1012   PetscFunctionBegin;
1013   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1014   if (nvtxs) {
1015     PetscValidIntPointer(xadj,3);
1016     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1017   }
1018   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1019   /* free arrays if PCBDDC is not the PC type */
1020   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1021   if (!f && copymode == PETSC_OWN_POINTER) {
1022     ierr = PetscFree(xadj);CHKERRQ(ierr);
1023     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1024   }
1025   PetscFunctionReturn(0);
1026 }
1027 
1028 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1029 {
1030   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1031   PetscInt       i;
1032   PetscBool      isequal = PETSC_FALSE;
1033   PetscErrorCode ierr;
1034 
1035   PetscFunctionBegin;
1036   if (pcbddc->n_ISForDofsLocal == n_is) {
1037     for (i=0;i<n_is;i++) {
1038       PetscBool isequalt;
1039       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1040       if (!isequalt) break;
1041     }
1042     if (i == n_is) isequal = PETSC_TRUE;
1043   }
1044   for (i=0;i<n_is;i++) {
1045     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1046   }
1047   /* Destroy ISes if they were already set */
1048   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1049     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1050   }
1051   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1052   /* last user setting takes precendence -> destroy any other customization */
1053   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1054     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1055   }
1056   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1057   pcbddc->n_ISForDofs = 0;
1058   /* allocate space then set */
1059   if (n_is) {
1060     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1061   }
1062   for (i=0;i<n_is;i++) {
1063     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1064   }
1065   pcbddc->n_ISForDofsLocal = n_is;
1066   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1067   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1068   PetscFunctionReturn(0);
1069 }
1070 
1071 /*@
1072  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1073 
1074    Collective
1075 
1076    Input Parameters:
1077 +  pc - the preconditioning context
1078 .  n_is - number of index sets defining the fields
1079 -  ISForDofs - array of IS describing the fields in local ordering
1080 
1081    Level: intermediate
1082 
1083    Notes:
1084      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1085 
1086 .seealso: PCBDDC
1087 @*/
1088 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1089 {
1090   PetscInt       i;
1091   PetscErrorCode ierr;
1092 
1093   PetscFunctionBegin;
1094   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1095   PetscValidLogicalCollectiveInt(pc,n_is,2);
1096   for (i=0;i<n_is;i++) {
1097     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1098     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1099   }
1100   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1101   PetscFunctionReturn(0);
1102 }
1103 
1104 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1105 {
1106   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1107   PetscInt       i;
1108   PetscBool      isequal = PETSC_FALSE;
1109   PetscErrorCode ierr;
1110 
1111   PetscFunctionBegin;
1112   if (pcbddc->n_ISForDofs == n_is) {
1113     for (i=0;i<n_is;i++) {
1114       PetscBool isequalt;
1115       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1116       if (!isequalt) break;
1117     }
1118     if (i == n_is) isequal = PETSC_TRUE;
1119   }
1120   for (i=0;i<n_is;i++) {
1121     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1122   }
1123   /* Destroy ISes if they were already set */
1124   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1125     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1126   }
1127   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1128   /* last user setting takes precendence -> destroy any other customization */
1129   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1130     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1131   }
1132   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1133   pcbddc->n_ISForDofsLocal = 0;
1134   /* allocate space then set */
1135   if (n_is) {
1136     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1137   }
1138   for (i=0;i<n_is;i++) {
1139     pcbddc->ISForDofs[i] = ISForDofs[i];
1140   }
1141   pcbddc->n_ISForDofs = n_is;
1142   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1143   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1144   PetscFunctionReturn(0);
1145 }
1146 
1147 /*@
1148  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1149 
1150    Collective
1151 
1152    Input Parameters:
1153 +  pc - the preconditioning context
1154 .  n_is - number of index sets defining the fields
1155 -  ISForDofs - array of IS describing the fields in global ordering
1156 
1157    Level: intermediate
1158 
1159    Notes:
1160      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1161 
1162 .seealso: PCBDDC
1163 @*/
1164 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1165 {
1166   PetscInt       i;
1167   PetscErrorCode ierr;
1168 
1169   PetscFunctionBegin;
1170   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1171   PetscValidLogicalCollectiveInt(pc,n_is,2);
1172   for (i=0;i<n_is;i++) {
1173     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1174     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1175   }
1176   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 /*
1181    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1182                      guess if a transformation of basis approach has been selected.
1183 
1184    Input Parameter:
1185 +  pc - the preconditioner contex
1186 
1187    Application Interface Routine: PCPreSolve()
1188 
1189    Notes:
1190      The interface routine PCPreSolve() is not usually called directly by
1191    the user, but instead is called by KSPSolve().
1192 */
1193 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1194 {
1195   PetscErrorCode ierr;
1196   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1197   PC_IS          *pcis = (PC_IS*)(pc->data);
1198   Vec            used_vec;
1199   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1200 
1201   PetscFunctionBegin;
1202   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1203   if (ksp) {
1204     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1205     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1206     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1207     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1208     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1209     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1210       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1211     }
1212   }
1213   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1214     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1215   }
1216 
1217   /* Creates parallel work vectors used in presolve */
1218   if (!pcbddc->original_rhs) {
1219     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1220   }
1221   if (!pcbddc->temp_solution) {
1222     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1223   }
1224 
1225   pcbddc->temp_solution_used = PETSC_FALSE;
1226   if (x) {
1227     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1228     used_vec = x;
1229   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1230     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1231     used_vec = pcbddc->temp_solution;
1232     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1233     pcbddc->temp_solution_used = PETSC_TRUE;
1234     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1235     save_rhs = PETSC_FALSE;
1236     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1237   }
1238 
1239   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1240   if (ksp) {
1241     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1242     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1243     if (!pcbddc->ksp_guess_nonzero) {
1244       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1245     }
1246   }
1247 
1248   pcbddc->rhs_change = PETSC_FALSE;
1249   /* Take into account zeroed rows -> change rhs and store solution removed */
1250   if (rhs && pcbddc->eliminate_dirdofs) {
1251     IS dirIS = NULL;
1252 
1253     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1254     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1255     if (dirIS) {
1256       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1257       PetscInt          dirsize,i,*is_indices;
1258       PetscScalar       *array_x;
1259       const PetscScalar *array_diagonal;
1260 
1261       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1262       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1263       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1264       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1265       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1266       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1267       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1268       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1269       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1270       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1271       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1272       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1273       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1274       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1275       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1276       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1277       pcbddc->rhs_change = PETSC_TRUE;
1278       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1279     }
1280   }
1281 
1282   /* remove the computed solution or the initial guess from the rhs */
1283   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1284     /* save the original rhs */
1285     if (save_rhs) {
1286       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1287       save_rhs = PETSC_FALSE;
1288     }
1289     pcbddc->rhs_change = PETSC_TRUE;
1290     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1291     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1292     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1293     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1294     pcbddc->temp_solution_used = PETSC_TRUE;
1295     if (ksp) {
1296       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1297     }
1298   }
1299   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1300 
1301   /* compute initial vector in benign space if needed
1302      and remove non-benign solution from the rhs */
1303   benign_correction_computed = PETSC_FALSE;
1304   if (rhs && pcbddc->benign_compute_correction && pcbddc->benign_have_null) {
1305     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1306        Recursively apply BDDC in the multilevel case */
1307     if (!pcbddc->benign_vec) {
1308       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1309     }
1310     pcbddc->benign_apply_coarse_only = PETSC_TRUE;
1311     if (!pcbddc->benign_skip_correction) {
1312       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1313       benign_correction_computed = PETSC_TRUE;
1314       if (pcbddc->temp_solution_used) {
1315         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1316       }
1317       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1318       /* store the original rhs if not done earlier */
1319       if (save_rhs) {
1320         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1321       }
1322       if (pcbddc->rhs_change) {
1323         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1324       } else {
1325         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1326       }
1327       pcbddc->rhs_change = PETSC_TRUE;
1328     }
1329     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1330   }
1331 
1332   /* dbg output */
1333   if (pcbddc->dbg_flag && benign_correction_computed) {
1334     Vec v;
1335     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1336     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1337     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1338     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %d: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1339     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc)));CHKERRQ(ierr);
1340     ierr = VecDestroy(&v);CHKERRQ(ierr);
1341   }
1342 
1343   /* set initial guess if using PCG */
1344   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1345   if (x && pcbddc->use_exact_dirichlet_trick) {
1346     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1347     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1348       if (benign_correction_computed) { /* we have already saved the changed rhs */
1349         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1350       } else {
1351         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1352       }
1353       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1354       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1355     } else {
1356       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1357       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1358     }
1359     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1360     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1361       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1362       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1363       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1364       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1365     } else {
1366       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1367       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1368     }
1369     if (ksp) {
1370       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1371     }
1372     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1373   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1374     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1375   }
1376   PetscFunctionReturn(0);
1377 }
1378 
1379 /*
1380    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1381                      approach has been selected. Also, restores rhs to its original state.
1382 
1383    Input Parameter:
1384 +  pc - the preconditioner contex
1385 
1386    Application Interface Routine: PCPostSolve()
1387 
1388    Notes:
1389      The interface routine PCPostSolve() is not usually called directly by
1390      the user, but instead is called by KSPSolve().
1391 */
1392 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1393 {
1394   PetscErrorCode ierr;
1395   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1396 
1397   PetscFunctionBegin;
1398   /* add solution removed in presolve */
1399   if (x && pcbddc->rhs_change) {
1400     if (pcbddc->temp_solution_used) {
1401       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1402     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1403       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1404     }
1405     /* restore to original state (not for FETI-DP) */
1406     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1407   }
1408 
1409   /* restore rhs to its original state (not needed for FETI-DP) */
1410   if (rhs && pcbddc->rhs_change) {
1411     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1412     pcbddc->rhs_change = PETSC_FALSE;
1413   }
1414   /* restore ksp guess state */
1415   if (ksp) {
1416     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1417     /* reset flag for exact dirichlet trick */
1418     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1419   }
1420   PetscFunctionReturn(0);
1421 }
1422 
1423 /*
1424    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1425                   by setting data structures and options.
1426 
1427    Input Parameter:
1428 +  pc - the preconditioner context
1429 
1430    Application Interface Routine: PCSetUp()
1431 
1432    Notes:
1433      The interface routine PCSetUp() is not usually called directly by
1434      the user, but instead is called by PCApply() if necessary.
1435 */
1436 PetscErrorCode PCSetUp_BDDC(PC pc)
1437 {
1438   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1439   PCBDDCSubSchurs sub_schurs;
1440   Mat_IS*         matis;
1441   MatNullSpace    nearnullspace;
1442   Mat             lA;
1443   IS              lP,zerodiag = NULL;
1444   PetscInt        nrows,ncols;
1445   PetscBool       computesubschurs;
1446   PetscBool       computeconstraintsmatrix;
1447   PetscBool       new_nearnullspace_provided,ismatis;
1448   PetscErrorCode  ierr;
1449 
1450   PetscFunctionBegin;
1451   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1452   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1453   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1454   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1455   matis = (Mat_IS*)pc->pmat->data;
1456   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1457   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1458      Also, BDDC builds its own KSP for the Dirichlet problem */
1459   if (pc->setupcalled && pc->flag != SAME_NONZERO_PATTERN) pcbddc->recompute_topography = PETSC_TRUE;
1460   if (pcbddc->recompute_topography) {
1461     pcbddc->graphanalyzed    = PETSC_FALSE;
1462     computeconstraintsmatrix = PETSC_TRUE;
1463   } else {
1464     computeconstraintsmatrix = PETSC_FALSE;
1465   }
1466 
1467   /* check parameters' compatibility */
1468   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1469   pcbddc->adaptive_selection = (PetscBool)(pcbddc->adaptive_threshold > 0.0);
1470   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1471   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1472 
1473   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1474   if (pcbddc->switch_static) {
1475     PetscBool ismatis;
1476     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1477     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1478   }
1479 
1480   /* activate all connected components if the netflux has been requested */
1481   if (pcbddc->compute_nonetflux) {
1482     pcbddc->use_vertices = PETSC_TRUE;
1483     pcbddc->use_edges = PETSC_TRUE;
1484     pcbddc->use_faces = PETSC_TRUE;
1485   }
1486 
1487   /* Get stdout for dbg */
1488   if (pcbddc->dbg_flag) {
1489     if (!pcbddc->dbg_viewer) {
1490       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1491       ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1492     }
1493     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1494   }
1495 
1496   /* process topology information */
1497   if (pcbddc->recompute_topography) {
1498     PetscContainer   c;
1499 
1500     ierr = PetscObjectQuery((PetscObject)pc->pmat,"_convert_nest_lfields",(PetscObject*)&c);CHKERRQ(ierr);
1501     if (c) {
1502       MatISLocalFields lf;
1503       ierr = PetscContainerGetPointer(c,(void**)&lf);CHKERRQ(ierr);
1504       ierr = PCBDDCSetDofsSplittingLocal(pc,lf->nr,lf->rf);CHKERRQ(ierr);
1505     }
1506     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1507     /* detect local disconnected subdomains if requested (use matis->A) */
1508     if (pcbddc->detect_disconnected) {
1509       PetscInt i;
1510       for (i=0;i<pcbddc->n_local_subs;i++) {
1511         ierr = ISDestroy(&pcbddc->local_subs[i]);CHKERRQ(ierr);
1512       }
1513       ierr = PetscFree(pcbddc->local_subs);CHKERRQ(ierr);
1514       ierr = MatDetectDisconnectedComponents(matis->A,PETSC_FALSE,&pcbddc->n_local_subs,&pcbddc->local_subs);CHKERRQ(ierr);
1515     }
1516     if (pcbddc->discretegradient) {
1517       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1518     }
1519   }
1520 
1521   /* change basis if requested by the user */
1522   if (pcbddc->user_ChangeOfBasisMatrix) {
1523     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1524     pcbddc->use_change_of_basis = PETSC_FALSE;
1525     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1526   } else {
1527     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1528     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1529     pcbddc->local_mat = matis->A;
1530   }
1531 
1532   /*
1533      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1534      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1535   */
1536   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1537   if (pcbddc->benign_saddle_point) {
1538     PC_IS* pcis = (PC_IS*)pc->data;
1539 
1540     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1541     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1542     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1543     /* pop B0 mat from local mat */
1544     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1545     /* give pcis a hint to not reuse submatrices during PCISCreate */
1546     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1547       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1548         pcis->reusesubmatrices = PETSC_FALSE;
1549       } else {
1550         pcis->reusesubmatrices = PETSC_TRUE;
1551       }
1552     } else {
1553       pcis->reusesubmatrices = PETSC_FALSE;
1554     }
1555   }
1556 
1557   /* propagate relevant information -> TODO remove*/
1558 #if !defined(PETSC_USE_COMPLEX) /* workaround for reals */
1559   if (matis->A->symmetric_set) {
1560     ierr = MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);CHKERRQ(ierr);
1561   }
1562 #endif
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(PETSC_COMM_SELF,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       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1592       /* TODO what if a nearnullspace is already attached? */
1593       ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1594       ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1595     }
1596   }
1597 
1598   /* check existence of a divergence free extension, i.e.
1599      b(v_I,p_0) = 0 for all v_I (raise error if not).
1600      Also, check that PCBDDCBenignGetOrSetP0 works */
1601   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1602     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1603   }
1604   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1605 
1606   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1607   if (computesubschurs && pcbddc->recompute_topography) {
1608     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1609   }
1610   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1611   if (!pcbddc->use_deluxe_scaling) {
1612     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1613   }
1614 
1615   /* finish setup solvers and do adaptive selection of constraints */
1616   sub_schurs = pcbddc->sub_schurs;
1617   if (sub_schurs && sub_schurs->schur_explicit) {
1618     if (computesubschurs) {
1619       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1620     }
1621     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1622   } else {
1623     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1624     if (computesubschurs) {
1625       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1626     }
1627   }
1628   if (pcbddc->adaptive_selection) {
1629     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1630     computeconstraintsmatrix = PETSC_TRUE;
1631   }
1632 
1633   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1634   new_nearnullspace_provided = PETSC_FALSE;
1635   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1636   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1637     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1638       new_nearnullspace_provided = PETSC_TRUE;
1639     } else {
1640       /* determine if the two nullspaces are different (should be lightweight) */
1641       if (nearnullspace != pcbddc->onearnullspace) {
1642         new_nearnullspace_provided = PETSC_TRUE;
1643       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1644         PetscInt         i;
1645         const Vec        *nearnullvecs;
1646         PetscObjectState state;
1647         PetscInt         nnsp_size;
1648         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1649         for (i=0;i<nnsp_size;i++) {
1650           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1651           if (pcbddc->onearnullvecs_state[i] != state) {
1652             new_nearnullspace_provided = PETSC_TRUE;
1653             break;
1654           }
1655         }
1656       }
1657     }
1658   } else {
1659     if (!nearnullspace) { /* both nearnullspaces are null */
1660       new_nearnullspace_provided = PETSC_FALSE;
1661     } else { /* nearnullspace attached later */
1662       new_nearnullspace_provided = PETSC_TRUE;
1663     }
1664   }
1665 
1666   /* Setup constraints and related work vectors */
1667   /* reset primal space flags */
1668   pcbddc->new_primal_space = PETSC_FALSE;
1669   pcbddc->new_primal_space_local = PETSC_FALSE;
1670   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1671     /* It also sets the primal space flags */
1672     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1673   }
1674   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1675   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1676 
1677   if (pcbddc->use_change_of_basis) {
1678     PC_IS *pcis = (PC_IS*)(pc->data);
1679 
1680     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1681     if (pcbddc->benign_change) {
1682       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1683       /* pop B0 from pcbddc->local_mat */
1684       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1685     }
1686     /* get submatrices */
1687     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1688     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1689     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1690     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1691     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1692     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1693     /* set flag in pcis to not reuse submatrices during PCISCreate */
1694     pcis->reusesubmatrices = PETSC_FALSE;
1695   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1696     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1697     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1698     pcbddc->local_mat = matis->A;
1699   }
1700 
1701   /* interface pressure block row for B_C */
1702   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1703   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1704   if (lA && lP) {
1705     PC_IS*    pcis = (PC_IS*)pc->data;
1706     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1707     PetscBool issym;
1708     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1709     if (issym) {
1710       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1711       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1712       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1713       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1714     } else {
1715       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1716       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1717       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1718       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1719     }
1720     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1721     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1722     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1723     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1724     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1725     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1726     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1727     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1728   }
1729 
1730   /* SetUp coarse and local Neumann solvers */
1731   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1732   /* SetUp Scaling operator */
1733   if (pcbddc->use_deluxe_scaling) {
1734     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1735   }
1736 
1737   /* mark topography as done */
1738   pcbddc->recompute_topography = PETSC_FALSE;
1739 
1740   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1741   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1742 
1743   if (pcbddc->dbg_flag) {
1744     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1745   }
1746   PetscFunctionReturn(0);
1747 }
1748 
1749 /*
1750    PCApply_BDDC - Applies the BDDC operator to a vector.
1751 
1752    Input Parameters:
1753 +  pc - the preconditioner context
1754 -  r - input vector (global)
1755 
1756    Output Parameter:
1757 .  z - output vector (global)
1758 
1759    Application Interface Routine: PCApply()
1760  */
1761 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1762 {
1763   PC_IS             *pcis = (PC_IS*)(pc->data);
1764   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1765   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1766   PetscErrorCode    ierr;
1767   const PetscScalar one = 1.0;
1768   const PetscScalar m_one = -1.0;
1769   const PetscScalar zero = 0.0;
1770 
1771 /* This code is similar to that provided in nn.c for PCNN
1772    NN interface preconditioner changed to BDDC
1773    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1774 
1775   PetscFunctionBegin;
1776   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1777   if (pcbddc->ChangeOfBasisMatrix) {
1778     Vec swap;
1779 
1780     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1781     swap = pcbddc->work_change;
1782     pcbddc->work_change = r;
1783     r = swap;
1784     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1785     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1786       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1787       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1788     }
1789   }
1790   if (pcbddc->benign_have_null) { /* get p0 from r */
1791     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1792   }
1793   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1794     ierr = VecCopy(r,z);CHKERRQ(ierr);
1795     /* First Dirichlet solve */
1796     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1797     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1798     /*
1799       Assembling right hand side for BDDC operator
1800       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1801       - pcis->vec1_B the interface part of the global vector z
1802     */
1803     if (n_D) {
1804       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1805       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1806       if (pcbddc->switch_static) {
1807         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1808 
1809         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1810         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1811         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1812         if (!pcbddc->switch_static_change) {
1813           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1814         } else {
1815           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1816           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1817           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1818         }
1819         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1820         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1821         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1822         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1823       } else {
1824         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1825       }
1826     } else {
1827       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1828     }
1829     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1830     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1831     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1832   } else {
1833     if (!pcbddc->benign_apply_coarse_only) {
1834       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1835     }
1836   }
1837 
1838   /* Apply interface preconditioner
1839      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1840   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1841 
1842   /* Apply transpose of partition of unity operator */
1843   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1844 
1845   /* Second Dirichlet solve and assembling of output */
1846   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1847   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1848   if (n_B) {
1849     if (pcbddc->switch_static) {
1850       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1851 
1852       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1853       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1854       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1855       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1856       if (!pcbddc->switch_static_change) {
1857         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1858       } else {
1859         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1860         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1861         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1862       }
1863       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1864       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1865     } else {
1866       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1867     }
1868   } else if (pcbddc->switch_static) { /* n_B is zero */
1869     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1870 
1871     if (!pcbddc->switch_static_change) {
1872       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1873     } else {
1874       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1875       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1876       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
1877     }
1878   }
1879   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1880 
1881   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1882     if (pcbddc->switch_static) {
1883       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1884     } else {
1885       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1886     }
1887     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1888     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1889   } else {
1890     if (pcbddc->switch_static) {
1891       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1892     } else {
1893       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1894     }
1895     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1896     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1897   }
1898   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
1899     if (pcbddc->benign_apply_coarse_only) {
1900       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
1901     }
1902     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1903   }
1904 
1905   if (pcbddc->ChangeOfBasisMatrix) {
1906     pcbddc->work_change = r;
1907     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
1908     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
1909   }
1910   PetscFunctionReturn(0);
1911 }
1912 
1913 /*
1914    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1915 
1916    Input Parameters:
1917 +  pc - the preconditioner context
1918 -  r - input vector (global)
1919 
1920    Output Parameter:
1921 .  z - output vector (global)
1922 
1923    Application Interface Routine: PCApplyTranspose()
1924  */
1925 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1926 {
1927   PC_IS             *pcis = (PC_IS*)(pc->data);
1928   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1929   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1930   PetscErrorCode    ierr;
1931   const PetscScalar one = 1.0;
1932   const PetscScalar m_one = -1.0;
1933   const PetscScalar zero = 0.0;
1934 
1935   PetscFunctionBegin;
1936   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1937   if (pcbddc->ChangeOfBasisMatrix) {
1938     Vec swap;
1939 
1940     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1941     swap = pcbddc->work_change;
1942     pcbddc->work_change = r;
1943     r = swap;
1944     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1945     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
1946       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1947       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1948     }
1949   }
1950   if (pcbddc->benign_have_null) { /* get p0 from r */
1951     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1952   }
1953   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1954     ierr = VecCopy(r,z);CHKERRQ(ierr);
1955     /* First Dirichlet solve */
1956     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1957     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1958     /*
1959       Assembling right hand side for BDDC operator
1960       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1961       - pcis->vec1_B the interface part of the global vector z
1962     */
1963     if (n_D) {
1964       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1965       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1966       if (pcbddc->switch_static) {
1967         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1968 
1969         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1970         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1971         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1972         if (!pcbddc->switch_static_change) {
1973           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1974         } else {
1975           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1976           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1977           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1978         }
1979         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1980         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1981         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1982         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1983       } else {
1984         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1985       }
1986     } else {
1987       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1988     }
1989     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1990     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1991     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1992   } else {
1993     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1994   }
1995 
1996   /* Apply interface preconditioner
1997      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1998   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
1999 
2000   /* Apply transpose of partition of unity operator */
2001   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2002 
2003   /* Second Dirichlet solve and assembling of output */
2004   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2005   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2006   if (n_B) {
2007     if (pcbddc->switch_static) {
2008       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2009 
2010       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2011       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2012       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2013       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2014       if (!pcbddc->switch_static_change) {
2015         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2016       } else {
2017         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2018         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2019         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2020       }
2021       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2022       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2023     } else {
2024       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2025     }
2026   } else if (pcbddc->switch_static) { /* n_B is zero */
2027     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2028 
2029     if (!pcbddc->switch_static_change) {
2030       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2031     } else {
2032       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2033       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2034       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2035     }
2036   }
2037   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2038   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2039     if (pcbddc->switch_static) {
2040       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2041     } else {
2042       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2043     }
2044     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2045     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2046   } else {
2047     if (pcbddc->switch_static) {
2048       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2049     } else {
2050       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2051     }
2052     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2053     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2054   }
2055   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2056     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2057   }
2058   if (pcbddc->ChangeOfBasisMatrix) {
2059     pcbddc->work_change = r;
2060     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2061     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2062   }
2063   PetscFunctionReturn(0);
2064 }
2065 
2066 PetscErrorCode PCReset_BDDC(PC pc)
2067 {
2068   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2069   PC_IS          *pcis = (PC_IS*)pc->data;
2070   KSP            kspD,kspR,kspC;
2071   PetscErrorCode ierr;
2072 
2073   PetscFunctionBegin;
2074   /* free BDDC custom data  */
2075   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2076   /* destroy objects related to topography */
2077   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2078   /* destroy objects for scaling operator */
2079   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2080   /* free solvers stuff */
2081   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2082   /* free global vectors needed in presolve */
2083   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2084   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2085   /* free data created by PCIS */
2086   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2087 
2088   /* restore defaults */
2089   kspD = pcbddc->ksp_D;
2090   kspR = pcbddc->ksp_R;
2091   kspC = pcbddc->coarse_ksp;
2092   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2093   pcis->n_neigh                     = -1;
2094   pcis->scaling_factor              = 1.0;
2095   pcis->reusesubmatrices            = PETSC_TRUE;
2096   pcbddc->use_local_adj             = PETSC_TRUE;
2097   pcbddc->use_vertices              = PETSC_TRUE;
2098   pcbddc->use_edges                 = PETSC_TRUE;
2099   pcbddc->symmetric_primal          = PETSC_TRUE;
2100   pcbddc->vertex_size               = 1;
2101   pcbddc->recompute_topography      = PETSC_TRUE;
2102   pcbddc->coarse_size               = -1;
2103   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2104   pcbddc->coarsening_ratio          = 8;
2105   pcbddc->coarse_eqs_per_proc       = 1;
2106   pcbddc->benign_compute_correction = PETSC_TRUE;
2107   pcbddc->nedfield                  = -1;
2108   pcbddc->nedglobal                 = PETSC_TRUE;
2109   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2110   pcbddc->sub_schurs_layers         = -1;
2111   pcbddc->ksp_D                     = kspD;
2112   pcbddc->ksp_R                     = kspR;
2113   pcbddc->coarse_ksp                = kspC;
2114   PetscFunctionReturn(0);
2115 }
2116 
2117 PetscErrorCode PCDestroy_BDDC(PC pc)
2118 {
2119   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2120   PetscErrorCode ierr;
2121 
2122   PetscFunctionBegin;
2123   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2124   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2125   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2126   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2127   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2128   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2129   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2130   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2131   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2132   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2133   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2134   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2135   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2136   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2137   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2138   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2139   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2140   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2141   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2142   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2143   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2144   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2145   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2146   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2147   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2148   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2149   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2150   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2151   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2152   PetscFunctionReturn(0);
2153 }
2154 
2155 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2156 {
2157   PetscFunctionBegin;
2158   *change = PETSC_TRUE;
2159   PetscFunctionReturn(0);
2160 }
2161 
2162 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2163 {
2164   FETIDPMat_ctx  mat_ctx;
2165   Vec            work;
2166   PC_IS*         pcis;
2167   PC_BDDC*       pcbddc;
2168   PetscErrorCode ierr;
2169 
2170   PetscFunctionBegin;
2171   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2172   pcis = (PC_IS*)mat_ctx->pc->data;
2173   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2174 
2175   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2176   /* copy rhs since we may change it during PCPreSolve_BDDC */
2177   if (!pcbddc->original_rhs) {
2178     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2179   }
2180   if (mat_ctx->rhs_flip) {
2181     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2182   } else {
2183     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2184   }
2185   if (mat_ctx->g2g_p) {
2186     /* interface pressure rhs */
2187     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2188     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2189     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2190     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2191     if (!mat_ctx->rhs_flip) {
2192       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2193     }
2194   }
2195   /*
2196      change of basis for physical rhs if needed
2197      It also changes the rhs in case of dirichlet boundaries
2198   */
2199   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2200   if (pcbddc->ChangeOfBasisMatrix) {
2201     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2202     work = pcbddc->work_change;
2203    } else {
2204     work = pcbddc->original_rhs;
2205   }
2206   /* store vectors for computation of fetidp final solution */
2207   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2208   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2209   /* scale rhs since it should be unassembled */
2210   /* TODO use counter scaling? (also below) */
2211   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2212   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2213   /* Apply partition of unity */
2214   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2215   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2216   if (!pcbddc->switch_static) {
2217     /* compute partially subassembled Schur complement right-hand side */
2218     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2219     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2220     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2221     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2222     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2223     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2224     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2225     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2226     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2227     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2228   }
2229   /* BDDC rhs */
2230   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2231   if (pcbddc->switch_static) {
2232     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2233   }
2234   /* apply BDDC */
2235   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2236   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2237   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2238 
2239   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2240   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2241   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2242   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2243   /* Add contribution to interface pressures */
2244   if (mat_ctx->l2g_p) {
2245     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2246     if (pcbddc->switch_static) {
2247       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2248     }
2249     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2250     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2251   }
2252   PetscFunctionReturn(0);
2253 }
2254 
2255 /*@
2256  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2257 
2258    Collective
2259 
2260    Input Parameters:
2261 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2262 -  standard_rhs    - the right-hand side of the original linear system
2263 
2264    Output Parameters:
2265 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2266 
2267    Level: developer
2268 
2269    Notes:
2270 
2271 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2272 @*/
2273 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2274 {
2275   FETIDPMat_ctx  mat_ctx;
2276   PetscErrorCode ierr;
2277 
2278   PetscFunctionBegin;
2279   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2280   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2281   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2282   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2283   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2284   PetscFunctionReturn(0);
2285 }
2286 
2287 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2288 {
2289   FETIDPMat_ctx  mat_ctx;
2290   PC_IS*         pcis;
2291   PC_BDDC*       pcbddc;
2292   PetscErrorCode ierr;
2293   Vec            work;
2294 
2295   PetscFunctionBegin;
2296   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2297   pcis = (PC_IS*)mat_ctx->pc->data;
2298   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2299 
2300   /* apply B_delta^T */
2301   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2302   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2303   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2304   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2305   if (mat_ctx->l2g_p) {
2306     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2307     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2308     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2309   }
2310 
2311   /* compute rhs for BDDC application */
2312   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2313   if (pcbddc->switch_static) {
2314     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2315     if (mat_ctx->l2g_p) {
2316       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2317       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2318     }
2319   }
2320 
2321   /* apply BDDC */
2322   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2323   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2324 
2325   /* put values into global vector */
2326   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2327   else work = standard_sol;
2328   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2329   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2330   if (!pcbddc->switch_static) {
2331     /* compute values into the interior if solved for the partially subassembled Schur complement */
2332     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2333     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2334     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2335   }
2336 
2337   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2338   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2339   /* add p0 solution to final solution */
2340   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2341   if (pcbddc->ChangeOfBasisMatrix) {
2342     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2343   }
2344   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2345   if (mat_ctx->g2g_p) {
2346     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2347     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2348   }
2349   PetscFunctionReturn(0);
2350 }
2351 
2352 /*@
2353  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2354 
2355    Collective
2356 
2357    Input Parameters:
2358 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2359 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2360 
2361    Output Parameters:
2362 .  standard_sol    - the solution defined on the physical domain
2363 
2364    Level: developer
2365 
2366    Notes:
2367 
2368 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2369 @*/
2370 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2371 {
2372   FETIDPMat_ctx  mat_ctx;
2373   PetscErrorCode ierr;
2374 
2375   PetscFunctionBegin;
2376   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2377   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2378   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2379   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2380   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2381   PetscFunctionReturn(0);
2382 }
2383 
2384 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2385 {
2386 
2387   FETIDPMat_ctx  fetidpmat_ctx;
2388   Mat            newmat;
2389   FETIDPPC_ctx   fetidppc_ctx;
2390   PC             newpc;
2391   MPI_Comm       comm;
2392   PetscErrorCode ierr;
2393 
2394   PetscFunctionBegin;
2395   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2396   /* FETIDP linear matrix */
2397   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2398   fetidpmat_ctx->fully_redundant = fully_redundant;
2399   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2400   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2401   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2402   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2403   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2404   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2405   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2406   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2407   /* FETIDP preconditioner */
2408   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2409   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2410   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2411   ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2412   ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2413   ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2414   ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2415   ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2416   ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2417   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2418   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2419   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2420   /* return pointers for objects created */
2421   *fetidp_mat = newmat;
2422   *fetidp_pc = newpc;
2423   PetscFunctionReturn(0);
2424 }
2425 
2426 /*@C
2427  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2428 
2429    Collective
2430 
2431    Input Parameters:
2432 +  pc - the BDDC preconditioning context (setup should have been called before)
2433 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2434 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2435 
2436    Output Parameters:
2437 +  fetidp_mat - shell FETI-DP matrix object
2438 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2439 
2440    Level: developer
2441 
2442    Notes:
2443      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2444 
2445 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2446 @*/
2447 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2448 {
2449   PetscErrorCode ierr;
2450 
2451   PetscFunctionBegin;
2452   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2453   if (pc->setupcalled) {
2454     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2455   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2456   PetscFunctionReturn(0);
2457 }
2458 /* -------------------------------------------------------------------------- */
2459 /*MC
2460    PCBDDC - Balancing Domain Decomposition by Constraints.
2461 
2462    An implementation of the BDDC preconditioner based on
2463 
2464 .vb
2465    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2466    [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
2467    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2468    [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
2469 .ve
2470 
2471    The matrix to be preconditioned (Pmat) must be of type MATIS.
2472 
2473    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2474 
2475    It also works with unsymmetric and indefinite problems.
2476 
2477    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.
2478 
2479    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).
2480 
2481    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()
2482    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2483 
2484    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2485 
2486    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.
2487    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2488 
2489    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2490 
2491    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.
2492 
2493    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.
2494    Deluxe scaling is not supported yet for FETI-DP.
2495 
2496    Options Database Keys (some of them, run with -h for a complete list):
2497 
2498 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2499 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2500 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2501 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2502 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2503 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2504 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2505 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2506 .    -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)
2507 .    -pc_bddc_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)
2508 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2509 .    -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)
2510 .    -pc_bddc_adaptive_threshold <0.0> - when a value greater than one is specified, adaptive selection of constraints is performed on edges and faces (requires deluxe scaling and MUMPS or MKL_PARDISO installed)
2511 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2512 
2513    Options for Dirichlet, Neumann or coarse solver can be set with
2514 .vb
2515       -pc_bddc_dirichlet_
2516       -pc_bddc_neumann_
2517       -pc_bddc_coarse_
2518 .ve
2519    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2520 
2521    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2522 .vb
2523       -pc_bddc_dirichlet_lN_
2524       -pc_bddc_neumann_lN_
2525       -pc_bddc_coarse_lN_
2526 .ve
2527    Note that level number ranges from the finest (0) to the coarsest (N).
2528    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.
2529 .vb
2530      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2531 .ve
2532    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
2533 
2534    Level: intermediate
2535 
2536    Developer notes:
2537 
2538    Contributed by Stefano Zampini
2539 
2540 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2541 M*/
2542 
2543 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2544 {
2545   PetscErrorCode      ierr;
2546   PC_BDDC             *pcbddc;
2547 
2548   PetscFunctionBegin;
2549   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2550   pc->data = (void*)pcbddc;
2551 
2552   /* create PCIS data structure */
2553   ierr = PCISCreate(pc);CHKERRQ(ierr);
2554 
2555   /* create local graph structure */
2556   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2557 
2558   /* BDDC nonzero defaults */
2559   pcbddc->use_local_adj             = PETSC_TRUE;
2560   pcbddc->use_vertices              = PETSC_TRUE;
2561   pcbddc->use_edges                 = PETSC_TRUE;
2562   pcbddc->symmetric_primal          = PETSC_TRUE;
2563   pcbddc->vertex_size               = 1;
2564   pcbddc->recompute_topography      = PETSC_TRUE;
2565   pcbddc->coarse_size               = -1;
2566   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2567   pcbddc->coarsening_ratio          = 8;
2568   pcbddc->coarse_eqs_per_proc       = 1;
2569   pcbddc->benign_compute_correction = PETSC_TRUE;
2570   pcbddc->nedfield                  = -1;
2571   pcbddc->nedglobal                 = PETSC_TRUE;
2572   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2573   pcbddc->sub_schurs_layers         = -1;
2574 
2575   /* function pointers */
2576   pc->ops->apply               = PCApply_BDDC;
2577   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2578   pc->ops->setup               = PCSetUp_BDDC;
2579   pc->ops->destroy             = PCDestroy_BDDC;
2580   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2581   pc->ops->view                = PCView_BDDC;
2582   pc->ops->applyrichardson     = 0;
2583   pc->ops->applysymmetricleft  = 0;
2584   pc->ops->applysymmetricright = 0;
2585   pc->ops->presolve            = PCPreSolve_BDDC;
2586   pc->ops->postsolve           = PCPostSolve_BDDC;
2587   pc->ops->reset               = PCReset_BDDC;
2588 
2589   /* composing function */
2590   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
2591   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
2592   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2593   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2594   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
2595   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2596   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2597   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2598   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2599   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2600   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2601   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2602   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2603   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2604   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2605   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2606   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2607   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2608   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2609   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2610   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2611   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2612   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2613   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
2614   PetscFunctionReturn(0);
2615 }
2616 
2617