xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision d2fc88d660d899f5d302fca28cab2ba057217d62)
1 /* TODOLIST
2 
3    Solvers
4    - Add support for cholesky for coarse solver (similar to local solvers)
5    - Propagate ksp prefixes for solvers to mat objects?
6 
7    User interface
8    - ** DM attached to pc?
9 
10    Debugging output
11    - * Better management of verbosity levels of debugging output
12 
13    Extra
14    - *** Is it possible to work with PCBDDCGraph on boundary indices only (less memory consumed)?
15    - BDDC with MG framework?
16 
17    MATIS related operations contained in BDDC code
18    - Provide general case for subassembling
19 
20 */
21 
22 #include <../src/ksp/pc/impls/bddc/bddc.h> /*I "petscpc.h" I*/  /* includes for fortran wrappers */
23 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
24 #include <petscblaslapack.h>
25 
26 static PetscBool  cited = PETSC_FALSE;
27 static const char citation[] =
28 "@article{ZampiniPCBDDC,\n"
29 "author = {Stefano Zampini},\n"
30 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
31 "journal = {SIAM Journal on Scientific Computing},\n"
32 "volume = {38},\n"
33 "number = {5},\n"
34 "pages = {S282-S306},\n"
35 "year = {2016},\n"
36 "doi = {10.1137/15M1025785},\n"
37 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
38 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
39 "}\n";
40 
41 /* temporarily declare it */
42 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
43 
44 PetscErrorCode PCSetFromOptions_BDDC(PetscOptionItems *PetscOptionsObject,PC pc)
45 {
46   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
47   PetscInt       nt;
48   PetscErrorCode ierr;
49 
50   PetscFunctionBegin;
51   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
52   /* Verbose debugging */
53   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
54   /* Approximate solvers */
55   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate","Inform PCBDDC that we are using approximate Dirichlet solvers","none",pcbddc->NullSpace_corr[0],&pcbddc->NullSpace_corr[0],NULL);CHKERRQ(ierr);
56   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate_scale","Inform PCBDDC that we need to scale the Dirichlet solve","none",pcbddc->NullSpace_corr[1],&pcbddc->NullSpace_corr[1],NULL);CHKERRQ(ierr);
57   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate","Inform PCBDDC that we are using approximate Neumann solvers","none",pcbddc->NullSpace_corr[2],&pcbddc->NullSpace_corr[2],NULL);CHKERRQ(ierr);
58   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate_scale","Inform PCBDDC that we need to scale the Neumann solve","none",pcbddc->NullSpace_corr[3],&pcbddc->NullSpace_corr[3],NULL);CHKERRQ(ierr);
59   /* Primal space customization */
60   ierr = PetscOptionsBool("-pc_bddc_use_local_mat_graph","Use or not adjacency graph of local mat for interface analysis","none",pcbddc->use_local_adj,&pcbddc->use_local_adj,NULL);CHKERRQ(ierr);
61   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
62   ierr = PetscOptionsBool("-pc_bddc_corner_selection","Activates face-based corner selection","none",pcbddc->corner_selection,&pcbddc->corner_selection,NULL);CHKERRQ(ierr);
63   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
64   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
65   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
66   ierr = PetscOptionsInt("-pc_bddc_vertex_size","Connected components smaller or equal to vertex size will be considered as primal vertices","none",pcbddc->vertex_size,&pcbddc->vertex_size,NULL);CHKERRQ(ierr);
67   ierr = PetscOptionsBool("-pc_bddc_use_true_nnsp","Use near null space attached to the matrix without modifications","none",pcbddc->use_nnsp_true,&pcbddc->use_nnsp_true,NULL);CHKERRQ(ierr);
68   ierr = PetscOptionsBool("-pc_bddc_use_qr_single","Use QR factorization for single constraints on cc (QR is always used when multiple constraints are present)","none",pcbddc->use_qr_single,&pcbddc->use_qr_single,NULL);CHKERRQ(ierr);
69   /* Change of basis */
70   ierr = PetscOptionsBool("-pc_bddc_use_change_of_basis","Use or not internal change of basis on local edge nodes","none",pcbddc->use_change_of_basis,&pcbddc->use_change_of_basis,NULL);CHKERRQ(ierr);
71   ierr = PetscOptionsBool("-pc_bddc_use_change_on_faces","Use or not internal change of basis on local face nodes","none",pcbddc->use_change_on_faces,&pcbddc->use_change_on_faces,NULL);CHKERRQ(ierr);
72   if (!pcbddc->use_change_of_basis) {
73     pcbddc->use_change_on_faces = PETSC_FALSE;
74   }
75   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
76   ierr = PetscOptionsBool("-pc_bddc_switch_static","Switch on static condensation ops around the interface preconditioner","none",pcbddc->switch_static,&pcbddc->switch_static,NULL);CHKERRQ(ierr);
77   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_per_proc","Number of equations per process for coarse problem redistribution (significant only at the coarsest level)","none",pcbddc->coarse_eqs_per_proc,&pcbddc->coarse_eqs_per_proc,NULL);CHKERRQ(ierr);
78   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,NULL);CHKERRQ(ierr);
79   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","none",pcbddc->max_levels,&pcbddc->max_levels,NULL);CHKERRQ(ierr);
80   ierr = PetscOptionsBool("-pc_bddc_use_coarse_estimates","Use estimated eigenvalues for coarse problem","none",pcbddc->use_coarse_estimates,&pcbddc->use_coarse_estimates,NULL);CHKERRQ(ierr);
81   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
82   ierr = PetscOptionsBool("-pc_bddc_schur_rebuild","Whether or not the interface graph for Schur principal minors has to be rebuilt (i.e. define the interface without any adjacency)","none",pcbddc->sub_schurs_rebuild,&pcbddc->sub_schurs_rebuild,NULL);CHKERRQ(ierr);
83   ierr = PetscOptionsInt("-pc_bddc_schur_layers","Number of dofs' layers for the computation of principal minors (i.e. -1 uses all dofs)","none",pcbddc->sub_schurs_layers,&pcbddc->sub_schurs_layers,NULL);CHKERRQ(ierr);
84   ierr = PetscOptionsBool("-pc_bddc_schur_use_useradj","Whether or not the CSR graph specified by the user should be used for computing successive layers (default is to use adj of local mat)","none",pcbddc->sub_schurs_use_useradj,&pcbddc->sub_schurs_use_useradj,NULL);CHKERRQ(ierr);
85   ierr = PetscOptionsBool("-pc_bddc_schur_exact","Whether or not to use the exact Schur complement instead of the reduced one (which excludes size 1 cc)","none",pcbddc->sub_schurs_exact_schur,&pcbddc->sub_schurs_exact_schur,NULL);CHKERRQ(ierr);
86   ierr = PetscOptionsBool("-pc_bddc_deluxe_zerorows","Zero rows and columns of deluxe operators associated with primal dofs","none",pcbddc->deluxe_zerorows,&pcbddc->deluxe_zerorows,NULL);CHKERRQ(ierr);
87   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
88   ierr = PetscOptionsBool("-pc_bddc_adaptive_userdefined","Use user-defined constraints (should be attached via MatSetNearNullSpace to pmat) in addition to those adaptively generated","none",pcbddc->adaptive_userdefined,&pcbddc->adaptive_userdefined,NULL);CHKERRQ(ierr);
89   nt   = 2;
90   ierr = PetscOptionsRealArray("-pc_bddc_adaptive_threshold","Thresholds to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&nt,NULL);CHKERRQ(ierr);
91   if (nt == 1) pcbddc->adaptive_threshold[1] = pcbddc->adaptive_threshold[0];
92   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
93   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
94   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
95   ierr = PetscOptionsInt("-pc_bddc_coarse_adj","Number of processors where to map the coarse adjacency list","none",pcbddc->coarse_adj_red,&pcbddc->coarse_adj_red,NULL);CHKERRQ(ierr);
96   ierr = PetscOptionsBool("-pc_bddc_benign_trick","Apply the benign subspace trick to saddle point problems with discontinuous pressures","none",pcbddc->benign_saddle_point,&pcbddc->benign_saddle_point,NULL);CHKERRQ(ierr);
97   ierr = PetscOptionsBool("-pc_bddc_benign_change","Compute the pressure change of basis explicitly","none",pcbddc->benign_change_explicit,&pcbddc->benign_change_explicit,NULL);CHKERRQ(ierr);
98   ierr = PetscOptionsBool("-pc_bddc_benign_compute_correction","Compute the benign correction during PreSolve","none",pcbddc->benign_compute_correction,&pcbddc->benign_compute_correction,NULL);CHKERRQ(ierr);
99   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
100   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
101   ierr = PetscOptionsBool("-pc_bddc_eliminate_dirichlet","Whether or not we want to eliminate dirichlet dofs during presolve","none",pcbddc->eliminate_dirdofs,&pcbddc->eliminate_dirdofs,NULL);CHKERRQ(ierr);
102   ierr = PetscOptionsTail();CHKERRQ(ierr);
103   PetscFunctionReturn(0);
104 }
105 
106 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
107 {
108   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
109   PC_IS                *pcis = (PC_IS*)pc->data;
110   PetscErrorCode       ierr;
111   PetscBool            isascii;
112   PetscSubcomm         subcomm;
113   PetscViewer          subviewer;
114 
115   PetscFunctionBegin;
116   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
117   /* ASCII viewer */
118   if (isascii) {
119     PetscMPIInt   color,rank,size;
120     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
121     PetscScalar   interface_size;
122     PetscReal     ratio1=0.,ratio2=0.;
123     Vec           counter;
124 
125     if (!pc->setupcalled) {
126       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
127     }
128     ierr = PetscViewerASCIIPrintf(viewer,"  Use verbose output: %D\n",pcbddc->dbg_flag);CHKERRQ(ierr);
129     ierr = PetscViewerASCIIPrintf(viewer,"  Use user-defined CSR: %d\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
130     ierr = PetscViewerASCIIPrintf(viewer,"  Use local mat graph: %d\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
131     if (pcbddc->mat_graph->twodim) {
132       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
133     } else {
134       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
135     }
136     if (pcbddc->graphmaxcount != PETSC_MAX_INT) {
137       ierr = PetscViewerASCIIPrintf(viewer,"  Graph max count: %D\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
138     }
139     ierr = PetscViewerASCIIPrintf(viewer,"  Use vertices: %d (vertex size %D)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
140     ierr = PetscViewerASCIIPrintf(viewer,"  Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
141     ierr = PetscViewerASCIIPrintf(viewer,"  Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
142     ierr = PetscViewerASCIIPrintf(viewer,"  Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
143     ierr = PetscViewerASCIIPrintf(viewer,"  Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
144     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
145     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
148     ierr = PetscViewerASCIIPrintf(viewer,"  Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
149     ierr = PetscViewerASCIIPrintf(viewer,"  Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
150     ierr = PetscViewerASCIIPrintf(viewer,"  Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
151     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel max levels: %D\n",pcbddc->max_levels);CHKERRQ(ierr);
152     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel coarsening ratio: %D\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
153     ierr = PetscViewerASCIIPrintf(viewer,"  Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
154     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
155     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
156     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  Number of dofs' layers for the computation of principal minors: %D\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
160     if (pcbddc->adaptive_threshold[1] != pcbddc->adaptive_threshold[0]) {
161       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection thresholds (active %d, userdefined %d): %g,%g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0],pcbddc->adaptive_threshold[1]);CHKERRQ(ierr);
162     } else {
163       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection threshold (active %d, userdefined %d): %g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0]);CHKERRQ(ierr);
164     }
165     ierr = PetscViewerASCIIPrintf(viewer,"  Min constraints / connected component: %D\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  Max constraints / connected component: %D\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
167     ierr = PetscViewerASCIIPrintf(viewer,"  Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
168     ierr = PetscViewerASCIIPrintf(viewer,"  Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
169     ierr = PetscViewerASCIIPrintf(viewer,"  Num. Procs. to map coarse adjacency list: %D\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
170     ierr = PetscViewerASCIIPrintf(viewer,"  Coarse eqs per proc (significant at the coarsest level): %D\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
171     ierr = PetscViewerASCIIPrintf(viewer,"  Detect disconnected: %d\n",pcbddc->detect_disconnected);CHKERRQ(ierr);
172     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
173     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
174     ierr = PetscViewerASCIIPrintf(viewer,"  Algebraic computation of no-net-flux %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
175     if (!pc->setupcalled) PetscFunctionReturn(0);
176 
177     /* compute interface size */
178     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
179     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
180     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
181     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
182     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
183     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
184     ierr = VecDestroy(&counter);CHKERRQ(ierr);
185 
186     /* compute some statistics on the domain decomposition */
187     gsum[0] = 1;
188     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
189     loc[0]  = !!pcis->n;
190     loc[1]  = pcis->n - pcis->n_B;
191     loc[2]  = pcis->n_B;
192     loc[3]  = pcbddc->local_primal_size;
193     loc[4]  = pcis->n;
194     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
195     loc[6]  = pcbddc->benign_n;
196     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
197     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
198     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
199     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
200     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
201     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
202     if (pcbddc->coarse_size) {
203       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
204       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
205     }
206     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
207     ierr = PetscViewerASCIIPrintf(viewer,"  Global dofs sizes: all %D interface %D coarse %D\n",pc->pmat->rmap->N,(PetscInt)PetscRealPart(interface_size),pcbddc->coarse_size);CHKERRQ(ierr);
208     ierr = PetscViewerASCIIPrintf(viewer,"  Coarsening ratios: all/coarse %D interface/coarse %D\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
209     ierr = PetscViewerASCIIPrintf(viewer,"  Active processes : %D\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
210     ierr = PetscViewerASCIIPrintf(viewer,"  Total subdomains : %D\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
211     if (pcbddc->benign_have_null) {
212       ierr = PetscViewerASCIIPrintf(viewer,"  Benign subs      : %D\n",(PetscInt)totbenign);CHKERRQ(ierr);
213     }
214     ierr = PetscViewerASCIIPrintf(viewer,"  Dofs type        :\tMIN\tMAX\tMEAN\n");CHKERRQ(ierr);
215     ierr = PetscViewerASCIIPrintf(viewer,"  Interior  dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
216     ierr = PetscViewerASCIIPrintf(viewer,"  Interface dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[2],(PetscInt)gmax[2],(PetscInt)(gsum[2]/gsum[0]));CHKERRQ(ierr);
217     ierr = PetscViewerASCIIPrintf(viewer,"  Primal    dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[3],(PetscInt)gmax[3],(PetscInt)(gsum[3]/gsum[0]));CHKERRQ(ierr);
218     ierr = PetscViewerASCIIPrintf(viewer,"  Local     dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[4],(PetscInt)gmax[4],(PetscInt)(gsum[4]/gsum[0]));CHKERRQ(ierr);
219     ierr = PetscViewerASCIIPrintf(viewer,"  Local     subs   :\t%D\t%D\n"    ,(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
220     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** COARSE PROBLEM DETAILS *********************************\n");CHKERRQ(ierr);
221     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
222 
223     /* the coarse problem can be handled by a different communicator */
224     if (pcbddc->coarse_ksp) color = 1;
225     else color = 0;
226     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
227     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
228     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
229     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
230     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
231     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
232     if (color == 1) {
233       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
234       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
235     }
236     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
237     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
238     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
239   }
240   PetscFunctionReturn(0);
241 }
242 
243 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
244 {
245   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
246   PetscErrorCode ierr;
247 
248   PetscFunctionBegin;
249   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
250   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
251   pcbddc->discretegradient = G;
252   pcbddc->nedorder         = order > 0 ? order : -order;
253   pcbddc->nedfield         = field;
254   pcbddc->nedglobal        = global;
255   pcbddc->conforming       = conforming;
256   PetscFunctionReturn(0);
257 }
258 
259 /*@
260  PCBDDCSetDiscreteGradient - Sets the discrete gradient
261 
262    Collective on PC
263 
264    Input Parameters:
265 +  pc         - the preconditioning context
266 .  G          - the discrete gradient matrix (should be in AIJ format)
267 .  order      - the order of the Nedelec space (1 for the lowest order)
268 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
269 .  global     - the type of global ordering for the rows of G
270 -  conforming - whether the mesh is conforming or not
271 
272    Level: advanced
273 
274    Notes:
275     The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
276           For variable order spaces, the order should be set to zero.
277           If global is true, the rows of G should be given in global ordering for the whole dofs;
278           if false, the ordering should be global for the Nedelec field.
279           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
280           and geid the one for the Nedelec field.
281 
282 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
283 @*/
284 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
285 {
286   PetscErrorCode ierr;
287 
288   PetscFunctionBegin;
289   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
290   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
291   PetscValidLogicalCollectiveInt(pc,order,3);
292   PetscValidLogicalCollectiveInt(pc,field,4);
293   PetscValidLogicalCollectiveBool(pc,global,5);
294   PetscValidLogicalCollectiveBool(pc,conforming,6);
295   PetscCheckSameComm(pc,1,G,2);
296   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
297   PetscFunctionReturn(0);
298 }
299 
300 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
301 {
302   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
303   PetscErrorCode ierr;
304 
305   PetscFunctionBegin;
306   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
307   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
308   pcbddc->divudotp = divudotp;
309   pcbddc->divudotp_trans = trans;
310   pcbddc->compute_nonetflux = PETSC_TRUE;
311   if (vl2l) {
312     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
313     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
314     pcbddc->divudotp_vl2l = vl2l;
315   }
316   PetscFunctionReturn(0);
317 }
318 
319 /*@
320  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
321 
322    Collective on PC
323 
324    Input Parameters:
325 +  pc - the preconditioning context
326 .  divudotp - the matrix (must be of type MATIS)
327 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
328 -  vl2l - optional index set describing the local (wrt the local matrix in divudotp) to local (wrt the local matrix in the preconditioning matrix) map for the velocities
329 
330    Level: advanced
331 
332    Notes:
333     This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
334           If vl2l is NULL, the local ordering for velocities in divudotp should match that of the preconditioning matrix
335 
336 .seealso: PCBDDC
337 @*/
338 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
339 {
340   PetscBool      ismatis;
341   PetscErrorCode ierr;
342 
343   PetscFunctionBegin;
344   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
345   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
346   PetscCheckSameComm(pc,1,divudotp,2);
347   PetscValidLogicalCollectiveBool(pc,trans,3);
348   if (vl2l) PetscValidHeaderSpecific(divudotp,IS_CLASSID,4);
349   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
350   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
351   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
352   PetscFunctionReturn(0);
353 }
354 
355 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
356 {
357   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
358   PetscErrorCode ierr;
359 
360   PetscFunctionBegin;
361   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
362   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
363   pcbddc->user_ChangeOfBasisMatrix = change;
364   pcbddc->change_interior = interior;
365   PetscFunctionReturn(0);
366 }
367 /*@
368  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
369 
370    Collective on PC
371 
372    Input Parameters:
373 +  pc - the preconditioning context
374 .  change - the change of basis matrix
375 -  interior - whether or not the change of basis modifies interior dofs
376 
377    Level: intermediate
378 
379    Notes:
380 
381 .seealso: PCBDDC
382 @*/
383 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
384 {
385   PetscErrorCode ierr;
386 
387   PetscFunctionBegin;
388   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
389   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
390   PetscCheckSameComm(pc,1,change,2);
391   if (pc->mat) {
392     PetscInt rows_c,cols_c,rows,cols;
393     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
394     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
395     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);
396     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);
397     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
398     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
399     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);
400     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);
401   }
402   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
403   PetscFunctionReturn(0);
404 }
405 
406 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
407 {
408   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
409   PetscBool      isequal = PETSC_FALSE;
410   PetscErrorCode ierr;
411 
412   PetscFunctionBegin;
413   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
414   if (pcbddc->user_primal_vertices) {
415     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
416   }
417   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
418   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
419   pcbddc->user_primal_vertices = PrimalVertices;
420   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
421   PetscFunctionReturn(0);
422 }
423 
424 /*@
425  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
426 
427    Collective
428 
429    Input Parameters:
430 +  pc - the preconditioning context
431 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
432 
433    Level: intermediate
434 
435    Notes:
436      Any process can list any global node
437 
438 .seealso: PCBDDC
439 @*/
440 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
441 {
442   PetscErrorCode ierr;
443 
444   PetscFunctionBegin;
445   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
446   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
447   PetscCheckSameComm(pc,1,PrimalVertices,2);
448   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
449   PetscFunctionReturn(0);
450 }
451 
452 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
453 {
454   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
455   PetscBool      isequal = PETSC_FALSE;
456   PetscErrorCode ierr;
457 
458   PetscFunctionBegin;
459   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
460   if (pcbddc->user_primal_vertices_local) {
461     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
462   }
463   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
464   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
465   pcbddc->user_primal_vertices_local = PrimalVertices;
466   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
467   PetscFunctionReturn(0);
468 }
469 /*@
470  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
471 
472    Collective
473 
474    Input Parameters:
475 +  pc - the preconditioning context
476 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
477 
478    Level: intermediate
479 
480    Notes:
481 
482 .seealso: PCBDDC
483 @*/
484 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
485 {
486   PetscErrorCode ierr;
487 
488   PetscFunctionBegin;
489   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
490   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
491   PetscCheckSameComm(pc,1,PrimalVertices,2);
492   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
493   PetscFunctionReturn(0);
494 }
495 
496 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
497 {
498   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
499 
500   PetscFunctionBegin;
501   pcbddc->coarsening_ratio = k;
502   PetscFunctionReturn(0);
503 }
504 
505 /*@
506  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
507 
508    Logically collective on PC
509 
510    Input Parameters:
511 +  pc - the preconditioning context
512 -  k - coarsening ratio (H/h at the coarser level)
513 
514    Options Database Keys:
515 .    -pc_bddc_coarsening_ratio
516 
517    Level: intermediate
518 
519    Notes:
520      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
521 
522 .seealso: PCBDDC, PCBDDCSetLevels()
523 @*/
524 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
525 {
526   PetscErrorCode ierr;
527 
528   PetscFunctionBegin;
529   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
530   PetscValidLogicalCollectiveInt(pc,k,2);
531   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
532   PetscFunctionReturn(0);
533 }
534 
535 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
536 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
537 {
538   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
539 
540   PetscFunctionBegin;
541   pcbddc->use_exact_dirichlet_trick = flg;
542   PetscFunctionReturn(0);
543 }
544 
545 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
546 {
547   PetscErrorCode ierr;
548 
549   PetscFunctionBegin;
550   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
551   PetscValidLogicalCollectiveBool(pc,flg,2);
552   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
553   PetscFunctionReturn(0);
554 }
555 
556 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
557 {
558   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
559 
560   PetscFunctionBegin;
561   pcbddc->current_level = level;
562   PetscFunctionReturn(0);
563 }
564 
565 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
566 {
567   PetscErrorCode ierr;
568 
569   PetscFunctionBegin;
570   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
571   PetscValidLogicalCollectiveInt(pc,level,2);
572   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
573   PetscFunctionReturn(0);
574 }
575 
576 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
577 {
578   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
579 
580   PetscFunctionBegin;
581   pcbddc->max_levels = levels;
582   PetscFunctionReturn(0);
583 }
584 
585 /*@
586  PCBDDCSetLevels - Sets the maximum number of levels for multilevel
587 
588    Logically collective on PC
589 
590    Input Parameters:
591 +  pc - the preconditioning context
592 -  levels - the maximum number of levels (max 9)
593 
594    Options Database Keys:
595 .    -pc_bddc_levels
596 
597    Level: intermediate
598 
599    Notes:
600      Default value is 0, i.e. traditional one-level BDDC
601 
602 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
603 @*/
604 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
605 {
606   PetscErrorCode ierr;
607 
608   PetscFunctionBegin;
609   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
610   PetscValidLogicalCollectiveInt(pc,levels,2);
611   if (levels > 99) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of levels for bddc is 99\n");
612   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
613   PetscFunctionReturn(0);
614 }
615 
616 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
617 {
618   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
619   PetscBool      isequal = PETSC_FALSE;
620   PetscErrorCode ierr;
621 
622   PetscFunctionBegin;
623   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
624   if (pcbddc->DirichletBoundaries) {
625     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
626   }
627   /* last user setting takes precendence -> destroy any other customization */
628   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
629   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
630   pcbddc->DirichletBoundaries = DirichletBoundaries;
631   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
632   PetscFunctionReturn(0);
633 }
634 
635 /*@
636  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
637 
638    Collective
639 
640    Input Parameters:
641 +  pc - the preconditioning context
642 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
643 
644    Level: intermediate
645 
646    Notes:
647      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
648 
649 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
650 @*/
651 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
652 {
653   PetscErrorCode ierr;
654 
655   PetscFunctionBegin;
656   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
657   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
658   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
659   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
660   PetscFunctionReturn(0);
661 }
662 
663 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
664 {
665   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
666   PetscBool      isequal = PETSC_FALSE;
667   PetscErrorCode ierr;
668 
669   PetscFunctionBegin;
670   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
671   if (pcbddc->DirichletBoundariesLocal) {
672     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
673   }
674   /* last user setting takes precendence -> destroy any other customization */
675   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
676   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
677   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
678   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
679   PetscFunctionReturn(0);
680 }
681 
682 /*@
683  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
684 
685    Collective
686 
687    Input Parameters:
688 +  pc - the preconditioning context
689 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
690 
691    Level: intermediate
692 
693    Notes:
694 
695 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
696 @*/
697 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
698 {
699   PetscErrorCode ierr;
700 
701   PetscFunctionBegin;
702   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
703   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
704   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
705   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
706   PetscFunctionReturn(0);
707 }
708 
709 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
710 {
711   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
712   PetscBool      isequal = PETSC_FALSE;
713   PetscErrorCode ierr;
714 
715   PetscFunctionBegin;
716   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
717   if (pcbddc->NeumannBoundaries) {
718     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
719   }
720   /* last user setting takes precendence -> destroy any other customization */
721   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
722   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
723   pcbddc->NeumannBoundaries = NeumannBoundaries;
724   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
725   PetscFunctionReturn(0);
726 }
727 
728 /*@
729  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
730 
731    Collective
732 
733    Input Parameters:
734 +  pc - the preconditioning context
735 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
736 
737    Level: intermediate
738 
739    Notes:
740      Any process can list any global node
741 
742 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
743 @*/
744 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
745 {
746   PetscErrorCode ierr;
747 
748   PetscFunctionBegin;
749   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
750   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
751   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
752   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
753   PetscFunctionReturn(0);
754 }
755 
756 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
757 {
758   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
759   PetscBool      isequal = PETSC_FALSE;
760   PetscErrorCode ierr;
761 
762   PetscFunctionBegin;
763   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
764   if (pcbddc->NeumannBoundariesLocal) {
765     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
766   }
767   /* last user setting takes precendence -> destroy any other customization */
768   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
769   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
770   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
771   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
772   PetscFunctionReturn(0);
773 }
774 
775 /*@
776  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
777 
778    Collective
779 
780    Input Parameters:
781 +  pc - the preconditioning context
782 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
783 
784    Level: intermediate
785 
786    Notes:
787 
788 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
789 @*/
790 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
791 {
792   PetscErrorCode ierr;
793 
794   PetscFunctionBegin;
795   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
796   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
797   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
798   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
799   PetscFunctionReturn(0);
800 }
801 
802 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
803 {
804   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
805 
806   PetscFunctionBegin;
807   *DirichletBoundaries = pcbddc->DirichletBoundaries;
808   PetscFunctionReturn(0);
809 }
810 
811 /*@
812  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
813 
814    Collective
815 
816    Input Parameters:
817 .  pc - the preconditioning context
818 
819    Output Parameters:
820 .  DirichletBoundaries - index set defining the Dirichlet boundaries
821 
822    Level: intermediate
823 
824    Notes:
825      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
826 
827 .seealso: PCBDDC
828 @*/
829 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
830 {
831   PetscErrorCode ierr;
832 
833   PetscFunctionBegin;
834   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
835   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
836   PetscFunctionReturn(0);
837 }
838 
839 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
840 {
841   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
842 
843   PetscFunctionBegin;
844   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
845   PetscFunctionReturn(0);
846 }
847 
848 /*@
849  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
850 
851    Collective
852 
853    Input Parameters:
854 .  pc - the preconditioning context
855 
856    Output Parameters:
857 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
858 
859    Level: intermediate
860 
861    Notes:
862      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).
863           In the latter case, the IS will be available after PCSetUp.
864 
865 .seealso: PCBDDC
866 @*/
867 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
868 {
869   PetscErrorCode ierr;
870 
871   PetscFunctionBegin;
872   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
873   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
874   PetscFunctionReturn(0);
875 }
876 
877 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
878 {
879   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
880 
881   PetscFunctionBegin;
882   *NeumannBoundaries = pcbddc->NeumannBoundaries;
883   PetscFunctionReturn(0);
884 }
885 
886 /*@
887  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
888 
889    Collective
890 
891    Input Parameters:
892 .  pc - the preconditioning context
893 
894    Output Parameters:
895 .  NeumannBoundaries - index set defining the Neumann boundaries
896 
897    Level: intermediate
898 
899    Notes:
900      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
901 
902 .seealso: PCBDDC
903 @*/
904 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
905 {
906   PetscErrorCode ierr;
907 
908   PetscFunctionBegin;
909   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
910   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
911   PetscFunctionReturn(0);
912 }
913 
914 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
915 {
916   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
917 
918   PetscFunctionBegin;
919   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
920   PetscFunctionReturn(0);
921 }
922 
923 /*@
924  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
925 
926    Collective
927 
928    Input Parameters:
929 .  pc - the preconditioning context
930 
931    Output Parameters:
932 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
933 
934    Level: intermediate
935 
936    Notes:
937      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).
938           In the latter case, the IS will be available after PCSetUp.
939 
940 .seealso: PCBDDC
941 @*/
942 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
943 {
944   PetscErrorCode ierr;
945 
946   PetscFunctionBegin;
947   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
948   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
949   PetscFunctionReturn(0);
950 }
951 
952 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
953 {
954   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
955   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
956   PetscBool      same_data = PETSC_FALSE;
957   PetscErrorCode ierr;
958 
959   PetscFunctionBegin;
960   if (!nvtxs) {
961     if (copymode == PETSC_OWN_POINTER) {
962       ierr = PetscFree(xadj);CHKERRQ(ierr);
963       ierr = PetscFree(adjncy);CHKERRQ(ierr);
964     }
965     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
966     PetscFunctionReturn(0);
967   }
968   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
969     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
970     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
971       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
972       if (same_data) {
973         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
974       }
975     }
976   }
977   if (!same_data) {
978     /* free old CSR */
979     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
980     /* get CSR into graph structure */
981     if (copymode == PETSC_COPY_VALUES) {
982       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
983       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
984       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
985       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
986       mat_graph->freecsr = PETSC_TRUE;
987     } else if (copymode == PETSC_OWN_POINTER) {
988       mat_graph->xadj    = (PetscInt*)xadj;
989       mat_graph->adjncy  = (PetscInt*)adjncy;
990       mat_graph->freecsr = PETSC_TRUE;
991     } else if (copymode == PETSC_USE_POINTER) {
992       mat_graph->xadj    = (PetscInt*)xadj;
993       mat_graph->adjncy  = (PetscInt*)adjncy;
994       mat_graph->freecsr = PETSC_FALSE;
995     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %D",copymode);
996     mat_graph->nvtxs_csr = nvtxs;
997     pcbddc->recompute_topography = PETSC_TRUE;
998   }
999   PetscFunctionReturn(0);
1000 }
1001 
1002 /*@
1003  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
1004 
1005    Not collective
1006 
1007    Input Parameters:
1008 +  pc - the preconditioning context.
1009 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
1010 .  xadj, adjncy - the connectivity of the dofs in CSR format.
1011 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1012 
1013    Level: intermediate
1014 
1015    Notes:
1016     A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1017 
1018 .seealso: PCBDDC,PetscCopyMode
1019 @*/
1020 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1021 {
1022   void (*f)(void) = 0;
1023   PetscErrorCode ierr;
1024 
1025   PetscFunctionBegin;
1026   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1027   if (nvtxs) {
1028     PetscValidIntPointer(xadj,3);
1029     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1030   }
1031   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1032   /* free arrays if PCBDDC is not the PC type */
1033   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1034   if (!f && copymode == PETSC_OWN_POINTER) {
1035     ierr = PetscFree(xadj);CHKERRQ(ierr);
1036     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1037   }
1038   PetscFunctionReturn(0);
1039 }
1040 
1041 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1042 {
1043   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1044   PetscInt       i;
1045   PetscBool      isequal = PETSC_FALSE;
1046   PetscErrorCode ierr;
1047 
1048   PetscFunctionBegin;
1049   if (pcbddc->n_ISForDofsLocal == n_is) {
1050     for (i=0;i<n_is;i++) {
1051       PetscBool isequalt;
1052       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1053       if (!isequalt) break;
1054     }
1055     if (i == n_is) isequal = PETSC_TRUE;
1056   }
1057   for (i=0;i<n_is;i++) {
1058     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1059   }
1060   /* Destroy ISes if they were already set */
1061   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1062     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1063   }
1064   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1065   /* last user setting takes precendence -> destroy any other customization */
1066   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1067     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1068   }
1069   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1070   pcbddc->n_ISForDofs = 0;
1071   /* allocate space then set */
1072   if (n_is) {
1073     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1074   }
1075   for (i=0;i<n_is;i++) {
1076     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1077   }
1078   pcbddc->n_ISForDofsLocal = n_is;
1079   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1080   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1081   PetscFunctionReturn(0);
1082 }
1083 
1084 /*@
1085  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1086 
1087    Collective
1088 
1089    Input Parameters:
1090 +  pc - the preconditioning context
1091 .  n_is - number of index sets defining the fields
1092 -  ISForDofs - array of IS describing the fields in local ordering
1093 
1094    Level: intermediate
1095 
1096    Notes:
1097      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1098 
1099 .seealso: PCBDDC
1100 @*/
1101 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1102 {
1103   PetscInt       i;
1104   PetscErrorCode ierr;
1105 
1106   PetscFunctionBegin;
1107   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1108   PetscValidLogicalCollectiveInt(pc,n_is,2);
1109   for (i=0;i<n_is;i++) {
1110     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1111     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1112   }
1113   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1114   PetscFunctionReturn(0);
1115 }
1116 
1117 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1118 {
1119   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1120   PetscInt       i;
1121   PetscBool      isequal = PETSC_FALSE;
1122   PetscErrorCode ierr;
1123 
1124   PetscFunctionBegin;
1125   if (pcbddc->n_ISForDofs == n_is) {
1126     for (i=0;i<n_is;i++) {
1127       PetscBool isequalt;
1128       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1129       if (!isequalt) break;
1130     }
1131     if (i == n_is) isequal = PETSC_TRUE;
1132   }
1133   for (i=0;i<n_is;i++) {
1134     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1135   }
1136   /* Destroy ISes if they were already set */
1137   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1138     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1139   }
1140   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1141   /* last user setting takes precendence -> destroy any other customization */
1142   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1143     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1144   }
1145   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1146   pcbddc->n_ISForDofsLocal = 0;
1147   /* allocate space then set */
1148   if (n_is) {
1149     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1150   }
1151   for (i=0;i<n_is;i++) {
1152     pcbddc->ISForDofs[i] = ISForDofs[i];
1153   }
1154   pcbddc->n_ISForDofs = n_is;
1155   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1156   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1157   PetscFunctionReturn(0);
1158 }
1159 
1160 /*@
1161  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1162 
1163    Collective
1164 
1165    Input Parameters:
1166 +  pc - the preconditioning context
1167 .  n_is - number of index sets defining the fields
1168 -  ISForDofs - array of IS describing the fields in global ordering
1169 
1170    Level: intermediate
1171 
1172    Notes:
1173      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1174 
1175 .seealso: PCBDDC
1176 @*/
1177 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1178 {
1179   PetscInt       i;
1180   PetscErrorCode ierr;
1181 
1182   PetscFunctionBegin;
1183   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1184   PetscValidLogicalCollectiveInt(pc,n_is,2);
1185   for (i=0;i<n_is;i++) {
1186     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1187     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1188   }
1189   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1190   PetscFunctionReturn(0);
1191 }
1192 
1193 /*
1194    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1195                      guess if a transformation of basis approach has been selected.
1196 
1197    Input Parameter:
1198 +  pc - the preconditioner contex
1199 
1200    Application Interface Routine: PCPreSolve()
1201 
1202    Notes:
1203      The interface routine PCPreSolve() is not usually called directly by
1204    the user, but instead is called by KSPSolve().
1205 */
1206 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1207 {
1208   PetscErrorCode ierr;
1209   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1210   PC_IS          *pcis = (PC_IS*)(pc->data);
1211   Vec            used_vec;
1212   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1213 
1214   PetscFunctionBegin;
1215   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1216   if (ksp) {
1217     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1218     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1219     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1220     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1221     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1222     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1223       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1224     }
1225   }
1226   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1227     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1228   }
1229 
1230   /* Creates parallel work vectors used in presolve */
1231   if (!pcbddc->original_rhs) {
1232     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1233   }
1234   if (!pcbddc->temp_solution) {
1235     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1236   }
1237 
1238   pcbddc->temp_solution_used = PETSC_FALSE;
1239   if (x) {
1240     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1241     used_vec = x;
1242   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1243     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1244     used_vec = pcbddc->temp_solution;
1245     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1246     pcbddc->temp_solution_used = PETSC_TRUE;
1247     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1248     save_rhs = PETSC_FALSE;
1249     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1250   }
1251 
1252   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1253   if (ksp) {
1254     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1255     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1256     if (!pcbddc->ksp_guess_nonzero) {
1257       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1258     }
1259   }
1260 
1261   pcbddc->rhs_change = PETSC_FALSE;
1262   /* Take into account zeroed rows -> change rhs and store solution removed */
1263   if (rhs && pcbddc->eliminate_dirdofs) {
1264     IS dirIS = NULL;
1265 
1266     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1267     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1268     if (dirIS) {
1269       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1270       PetscInt          dirsize,i,*is_indices;
1271       PetscScalar       *array_x;
1272       const PetscScalar *array_diagonal;
1273 
1274       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1275       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1276       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1277       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1278       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1279       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1280       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1281       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1282       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1283       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1284       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1285       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1286       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1287       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1288       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1289       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1290       pcbddc->rhs_change = PETSC_TRUE;
1291       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1292     }
1293   }
1294 
1295   /* remove the computed solution or the initial guess from the rhs */
1296   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1297     /* save the original rhs */
1298     if (save_rhs) {
1299       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1300       save_rhs = PETSC_FALSE;
1301     }
1302     pcbddc->rhs_change = PETSC_TRUE;
1303     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1304     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1305     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1306     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1307     pcbddc->temp_solution_used = PETSC_TRUE;
1308     if (ksp) {
1309       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1310     }
1311   }
1312   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1313 
1314   /* compute initial vector in benign space if needed
1315      and remove non-benign solution from the rhs */
1316   benign_correction_computed = PETSC_FALSE;
1317   if (rhs && pcbddc->benign_compute_correction && pcbddc->benign_have_null) {
1318     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1319        Recursively apply BDDC in the multilevel case */
1320     if (!pcbddc->benign_vec) {
1321       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1322     }
1323     pcbddc->benign_apply_coarse_only = PETSC_TRUE;
1324     if (!pcbddc->benign_skip_correction) {
1325       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1326       benign_correction_computed = PETSC_TRUE;
1327       if (pcbddc->temp_solution_used) {
1328         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1329       }
1330       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1331       /* store the original rhs if not done earlier */
1332       if (save_rhs) {
1333         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1334       }
1335       if (pcbddc->rhs_change) {
1336         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1337       } else {
1338         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1339       }
1340       pcbddc->rhs_change = PETSC_TRUE;
1341     }
1342     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1343   }
1344 
1345   /* dbg output */
1346   if (pcbddc->dbg_flag && benign_correction_computed) {
1347     Vec v;
1348     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1349     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1350     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1351     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1352     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc)));CHKERRQ(ierr);
1353     ierr = VecDestroy(&v);CHKERRQ(ierr);
1354   }
1355 
1356   /* set initial guess if using PCG */
1357   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1358   if (x && pcbddc->use_exact_dirichlet_trick) {
1359     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1360     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1361       if (benign_correction_computed) { /* we have already saved the changed rhs */
1362         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1363       } else {
1364         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1365       }
1366       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1367       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1368     } else {
1369       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1370       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1371     }
1372     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1373     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1374       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1375       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1376       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1377       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1378     } else {
1379       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1380       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1381     }
1382     if (ksp) {
1383       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1384     }
1385     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1386   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1387     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1388   }
1389   PetscFunctionReturn(0);
1390 }
1391 
1392 /*
1393    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1394                      approach has been selected. Also, restores rhs to its original state.
1395 
1396    Input Parameter:
1397 +  pc - the preconditioner contex
1398 
1399    Application Interface Routine: PCPostSolve()
1400 
1401    Notes:
1402      The interface routine PCPostSolve() is not usually called directly by
1403      the user, but instead is called by KSPSolve().
1404 */
1405 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1406 {
1407   PetscErrorCode ierr;
1408   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1409 
1410   PetscFunctionBegin;
1411   /* add solution removed in presolve */
1412   if (x && pcbddc->rhs_change) {
1413     if (pcbddc->temp_solution_used) {
1414       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1415     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1416       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1417     }
1418     /* restore to original state (not for FETI-DP) */
1419     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1420   }
1421 
1422   /* restore rhs to its original state (not needed for FETI-DP) */
1423   if (rhs && pcbddc->rhs_change) {
1424     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1425     pcbddc->rhs_change = PETSC_FALSE;
1426   }
1427   /* restore ksp guess state */
1428   if (ksp) {
1429     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1430     /* reset flag for exact dirichlet trick */
1431     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1432   }
1433   PetscFunctionReturn(0);
1434 }
1435 
1436 /*
1437    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1438                   by setting data structures and options.
1439 
1440    Input Parameter:
1441 +  pc - the preconditioner context
1442 
1443    Application Interface Routine: PCSetUp()
1444 
1445    Notes:
1446      The interface routine PCSetUp() is not usually called directly by
1447      the user, but instead is called by PCApply() if necessary.
1448 */
1449 PetscErrorCode PCSetUp_BDDC(PC pc)
1450 {
1451   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1452   PCBDDCSubSchurs sub_schurs;
1453   Mat_IS*         matis;
1454   MatNullSpace    nearnullspace;
1455   Mat             lA;
1456   IS              lP,zerodiag = NULL;
1457   PetscInt        nrows,ncols;
1458   PetscBool       computesubschurs;
1459   PetscBool       computeconstraintsmatrix;
1460   PetscBool       new_nearnullspace_provided,ismatis;
1461   PetscErrorCode  ierr;
1462 
1463   PetscFunctionBegin;
1464   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1465   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1466   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1467   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1468   matis = (Mat_IS*)pc->pmat->data;
1469   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1470   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1471      Also, BDDC builds its own KSP for the Dirichlet problem */
1472   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) pcbddc->recompute_topography = PETSC_TRUE;
1473   if (pcbddc->recompute_topography) {
1474     pcbddc->graphanalyzed    = PETSC_FALSE;
1475     computeconstraintsmatrix = PETSC_TRUE;
1476   } else {
1477     computeconstraintsmatrix = PETSC_FALSE;
1478   }
1479 
1480   /* check parameters' compatibility */
1481   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1482   pcbddc->adaptive_selection = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1483   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1484   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1485 
1486   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1487   if (pcbddc->switch_static) {
1488     PetscBool ismatis;
1489     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1490     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1491   }
1492 
1493   /* activate all connected components if the netflux has been requested */
1494   if (pcbddc->compute_nonetflux) {
1495     pcbddc->use_vertices = PETSC_TRUE;
1496     pcbddc->use_edges = PETSC_TRUE;
1497     pcbddc->use_faces = PETSC_TRUE;
1498   }
1499 
1500   /* Get stdout for dbg */
1501   if (pcbddc->dbg_flag) {
1502     if (!pcbddc->dbg_viewer) {
1503       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1504       ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1505     }
1506     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1507   }
1508 
1509   /* process topology information */
1510   if (pcbddc->recompute_topography) {
1511     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1512     if (pcbddc->discretegradient) {
1513       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1514     }
1515   }
1516 
1517   /* change basis if requested by the user */
1518   if (pcbddc->user_ChangeOfBasisMatrix) {
1519     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1520     pcbddc->use_change_of_basis = PETSC_FALSE;
1521     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1522   } else {
1523     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1524     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1525     pcbddc->local_mat = matis->A;
1526   }
1527 
1528   /*
1529      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1530      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1531   */
1532   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1533   if (pcbddc->benign_saddle_point) {
1534     PC_IS* pcis = (PC_IS*)pc->data;
1535 
1536     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1537     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1538     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1539     /* pop B0 mat from local mat */
1540     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1541     /* give pcis a hint to not reuse submatrices during PCISCreate */
1542     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1543       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1544         pcis->reusesubmatrices = PETSC_FALSE;
1545       } else {
1546         pcis->reusesubmatrices = PETSC_TRUE;
1547       }
1548     } else {
1549       pcis->reusesubmatrices = PETSC_FALSE;
1550     }
1551   }
1552 
1553   /* propagate relevant information */
1554   if (matis->A->symmetric_set) {
1555     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1556   }
1557   if (matis->A->spd_set) {
1558     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1559   }
1560 
1561   /* Set up all the "iterative substructuring" common block without computing solvers */
1562   {
1563     Mat temp_mat;
1564 
1565     temp_mat = matis->A;
1566     matis->A = pcbddc->local_mat;
1567     ierr = PCISSetUp(pc,PETSC_FALSE);CHKERRQ(ierr);
1568     pcbddc->local_mat = matis->A;
1569     matis->A = temp_mat;
1570   }
1571 
1572   /* Analyze interface */
1573   if (!pcbddc->graphanalyzed) {
1574     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1575     computeconstraintsmatrix = PETSC_TRUE;
1576     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1577       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1578     }
1579     if (pcbddc->compute_nonetflux) {
1580       MatNullSpace nnfnnsp;
1581 
1582       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1583       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1584       /* TODO what if a nearnullspace is already attached? */
1585       if (nnfnnsp) {
1586         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1587         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1588       }
1589     }
1590   }
1591 
1592   /* check existence of a divergence free extension, i.e.
1593      b(v_I,p_0) = 0 for all v_I (raise error if not).
1594      Also, check that PCBDDCBenignGetOrSetP0 works */
1595   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1596     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1597   }
1598   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1599 
1600   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1601   if (computesubschurs && pcbddc->recompute_topography) {
1602     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1603   }
1604   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1605   if (!pcbddc->use_deluxe_scaling) {
1606     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1607   }
1608 
1609   /* finish setup solvers and do adaptive selection of constraints */
1610   sub_schurs = pcbddc->sub_schurs;
1611   if (sub_schurs && sub_schurs->schur_explicit) {
1612     if (computesubschurs) {
1613       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1614     }
1615     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1616   } else {
1617     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1618     if (computesubschurs) {
1619       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1620     }
1621   }
1622   if (pcbddc->adaptive_selection) {
1623     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1624     computeconstraintsmatrix = PETSC_TRUE;
1625   }
1626 
1627   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1628   new_nearnullspace_provided = PETSC_FALSE;
1629   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1630   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1631     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1632       new_nearnullspace_provided = PETSC_TRUE;
1633     } else {
1634       /* determine if the two nullspaces are different (should be lightweight) */
1635       if (nearnullspace != pcbddc->onearnullspace) {
1636         new_nearnullspace_provided = PETSC_TRUE;
1637       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1638         PetscInt         i;
1639         const Vec        *nearnullvecs;
1640         PetscObjectState state;
1641         PetscInt         nnsp_size;
1642         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1643         for (i=0;i<nnsp_size;i++) {
1644           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1645           if (pcbddc->onearnullvecs_state[i] != state) {
1646             new_nearnullspace_provided = PETSC_TRUE;
1647             break;
1648           }
1649         }
1650       }
1651     }
1652   } else {
1653     if (!nearnullspace) { /* both nearnullspaces are null */
1654       new_nearnullspace_provided = PETSC_FALSE;
1655     } else { /* nearnullspace attached later */
1656       new_nearnullspace_provided = PETSC_TRUE;
1657     }
1658   }
1659 
1660   /* Setup constraints and related work vectors */
1661   /* reset primal space flags */
1662   pcbddc->new_primal_space = PETSC_FALSE;
1663   pcbddc->new_primal_space_local = PETSC_FALSE;
1664   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1665     /* It also sets the primal space flags */
1666     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1667   }
1668   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1669   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1670 
1671   if (pcbddc->use_change_of_basis) {
1672     PC_IS *pcis = (PC_IS*)(pc->data);
1673 
1674     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1675     if (pcbddc->benign_change) {
1676       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1677       /* pop B0 from pcbddc->local_mat */
1678       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1679     }
1680     /* get submatrices */
1681     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1682     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1683     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1684     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1685     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1686     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1687     /* set flag in pcis to not reuse submatrices during PCISCreate */
1688     pcis->reusesubmatrices = PETSC_FALSE;
1689   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1690     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1691     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1692     pcbddc->local_mat = matis->A;
1693   }
1694 
1695   /* interface pressure block row for B_C */
1696   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1697   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1698   if (lA && lP) {
1699     PC_IS*    pcis = (PC_IS*)pc->data;
1700     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1701     PetscBool issym;
1702     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1703     if (issym) {
1704       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1705       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1706       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1707       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1708     } else {
1709       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1710       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1711       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1712       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1713     }
1714     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1715     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1716     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1717     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1718     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1719     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1720     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1721     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1722   }
1723 
1724   /* SetUp coarse and local Neumann solvers */
1725   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1726   /* SetUp Scaling operator */
1727   if (pcbddc->use_deluxe_scaling) {
1728     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1729   }
1730 
1731   /* mark topography as done */
1732   pcbddc->recompute_topography = PETSC_FALSE;
1733 
1734   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1735   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1736 
1737   if (pcbddc->dbg_flag) {
1738     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1739   }
1740   PetscFunctionReturn(0);
1741 }
1742 
1743 /*
1744    PCApply_BDDC - Applies the BDDC operator to a vector.
1745 
1746    Input Parameters:
1747 +  pc - the preconditioner context
1748 -  r - input vector (global)
1749 
1750    Output Parameter:
1751 .  z - output vector (global)
1752 
1753    Application Interface Routine: PCApply()
1754  */
1755 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1756 {
1757   PC_IS             *pcis = (PC_IS*)(pc->data);
1758   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1759   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1760   PetscErrorCode    ierr;
1761   const PetscScalar one = 1.0;
1762   const PetscScalar m_one = -1.0;
1763   const PetscScalar zero = 0.0;
1764 
1765 /* This code is similar to that provided in nn.c for PCNN
1766    NN interface preconditioner changed to BDDC
1767    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1768 
1769   PetscFunctionBegin;
1770   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1771   if (pcbddc->ChangeOfBasisMatrix) {
1772     Vec swap;
1773 
1774     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1775     swap = pcbddc->work_change;
1776     pcbddc->work_change = r;
1777     r = swap;
1778     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1779     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1780       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1781       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1782     }
1783   }
1784   if (pcbddc->benign_have_null) { /* get p0 from r */
1785     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1786   }
1787   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1788     ierr = VecCopy(r,z);CHKERRQ(ierr);
1789     /* First Dirichlet solve */
1790     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1791     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1792     /*
1793       Assembling right hand side for BDDC operator
1794       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1795       - pcis->vec1_B the interface part of the global vector z
1796     */
1797     if (n_D) {
1798       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1799       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1800       if (pcbddc->switch_static) {
1801         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1802 
1803         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1804         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1805         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1806         if (!pcbddc->switch_static_change) {
1807           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1808         } else {
1809           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1810           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1811           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1812         }
1813         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1814         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1815         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1816         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1817       } else {
1818         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1819       }
1820     } else {
1821       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1822     }
1823     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1824     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1825     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1826   } else {
1827     if (!pcbddc->benign_apply_coarse_only) {
1828       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1829     }
1830   }
1831 
1832   /* Apply interface preconditioner
1833      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1834   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1835 
1836   /* Apply transpose of partition of unity operator */
1837   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1838 
1839   /* Second Dirichlet solve and assembling of output */
1840   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1841   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1842   if (n_B) {
1843     if (pcbddc->switch_static) {
1844       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1845 
1846       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1847       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1848       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1849       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1850       if (!pcbddc->switch_static_change) {
1851         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1852       } else {
1853         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1854         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1855         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1856       }
1857       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1858       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1859     } else {
1860       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1861     }
1862   } else if (pcbddc->switch_static) { /* n_B is zero */
1863     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1864 
1865     if (!pcbddc->switch_static_change) {
1866       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1867     } else {
1868       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1869       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1870       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
1871     }
1872   }
1873   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1874 
1875   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1876     if (pcbddc->switch_static) {
1877       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1878     } else {
1879       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1880     }
1881     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1882     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1883   } else {
1884     if (pcbddc->switch_static) {
1885       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1886     } else {
1887       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1888     }
1889     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1890     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1891   }
1892   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
1893     if (pcbddc->benign_apply_coarse_only) {
1894       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
1895     }
1896     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1897   }
1898 
1899   if (pcbddc->ChangeOfBasisMatrix) {
1900     pcbddc->work_change = r;
1901     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
1902     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
1903   }
1904   PetscFunctionReturn(0);
1905 }
1906 
1907 /*
1908    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1909 
1910    Input Parameters:
1911 +  pc - the preconditioner context
1912 -  r - input vector (global)
1913 
1914    Output Parameter:
1915 .  z - output vector (global)
1916 
1917    Application Interface Routine: PCApplyTranspose()
1918  */
1919 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1920 {
1921   PC_IS             *pcis = (PC_IS*)(pc->data);
1922   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1923   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1924   PetscErrorCode    ierr;
1925   const PetscScalar one = 1.0;
1926   const PetscScalar m_one = -1.0;
1927   const PetscScalar zero = 0.0;
1928 
1929   PetscFunctionBegin;
1930   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1931   if (pcbddc->ChangeOfBasisMatrix) {
1932     Vec swap;
1933 
1934     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1935     swap = pcbddc->work_change;
1936     pcbddc->work_change = r;
1937     r = swap;
1938     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1939     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
1940       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1941       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1942     }
1943   }
1944   if (pcbddc->benign_have_null) { /* get p0 from r */
1945     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1946   }
1947   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1948     ierr = VecCopy(r,z);CHKERRQ(ierr);
1949     /* First Dirichlet solve */
1950     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1951     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1952     /*
1953       Assembling right hand side for BDDC operator
1954       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1955       - pcis->vec1_B the interface part of the global vector z
1956     */
1957     if (n_D) {
1958       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1959       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1960       if (pcbddc->switch_static) {
1961         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1962 
1963         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1964         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1965         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1966         if (!pcbddc->switch_static_change) {
1967           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1968         } else {
1969           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1970           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1971           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1972         }
1973         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1974         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1975         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1976         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1977       } else {
1978         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1979       }
1980     } else {
1981       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1982     }
1983     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1984     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1985     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1986   } else {
1987     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1988   }
1989 
1990   /* Apply interface preconditioner
1991      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1992   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
1993 
1994   /* Apply transpose of partition of unity operator */
1995   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1996 
1997   /* Second Dirichlet solve and assembling of output */
1998   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1999   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2000   if (n_B) {
2001     if (pcbddc->switch_static) {
2002       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2003 
2004       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2005       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2006       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2007       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2008       if (!pcbddc->switch_static_change) {
2009         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2010       } else {
2011         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2012         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2013         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2014       }
2015       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2016       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2017     } else {
2018       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2019     }
2020   } else if (pcbddc->switch_static) { /* n_B is zero */
2021     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2022 
2023     if (!pcbddc->switch_static_change) {
2024       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2025     } else {
2026       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2027       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2028       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2029     }
2030   }
2031   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2032   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2033     if (pcbddc->switch_static) {
2034       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2035     } else {
2036       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2037     }
2038     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2039     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2040   } else {
2041     if (pcbddc->switch_static) {
2042       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2043     } else {
2044       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2045     }
2046     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2047     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2048   }
2049   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2050     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2051   }
2052   if (pcbddc->ChangeOfBasisMatrix) {
2053     pcbddc->work_change = r;
2054     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2055     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2056   }
2057   PetscFunctionReturn(0);
2058 }
2059 
2060 PetscErrorCode PCReset_BDDC(PC pc)
2061 {
2062   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2063   PC_IS          *pcis = (PC_IS*)pc->data;
2064   KSP            kspD,kspR,kspC;
2065   PetscErrorCode ierr;
2066 
2067   PetscFunctionBegin;
2068   /* free BDDC custom data  */
2069   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2070   /* destroy objects related to topography */
2071   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2072   /* destroy objects for scaling operator */
2073   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2074   /* free solvers stuff */
2075   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2076   /* free global vectors needed in presolve */
2077   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2078   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2079   /* free data created by PCIS */
2080   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2081 
2082   /* restore defaults */
2083   kspD = pcbddc->ksp_D;
2084   kspR = pcbddc->ksp_R;
2085   kspC = pcbddc->coarse_ksp;
2086   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2087   pcis->n_neigh                     = -1;
2088   pcis->scaling_factor              = 1.0;
2089   pcis->reusesubmatrices            = PETSC_TRUE;
2090   pcbddc->use_local_adj             = PETSC_TRUE;
2091   pcbddc->use_vertices              = PETSC_TRUE;
2092   pcbddc->use_edges                 = PETSC_TRUE;
2093   pcbddc->symmetric_primal          = PETSC_TRUE;
2094   pcbddc->vertex_size               = 1;
2095   pcbddc->recompute_topography      = PETSC_TRUE;
2096   pcbddc->coarse_size               = -1;
2097   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2098   pcbddc->coarsening_ratio          = 8;
2099   pcbddc->coarse_eqs_per_proc       = 1;
2100   pcbddc->benign_compute_correction = PETSC_TRUE;
2101   pcbddc->nedfield                  = -1;
2102   pcbddc->nedglobal                 = PETSC_TRUE;
2103   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2104   pcbddc->sub_schurs_layers         = -1;
2105   pcbddc->ksp_D                     = kspD;
2106   pcbddc->ksp_R                     = kspR;
2107   pcbddc->coarse_ksp                = kspC;
2108   PetscFunctionReturn(0);
2109 }
2110 
2111 PetscErrorCode PCDestroy_BDDC(PC pc)
2112 {
2113   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2114   PetscErrorCode ierr;
2115 
2116   PetscFunctionBegin;
2117   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2118   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2119   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2120   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2121   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2122   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2123   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2124   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2125   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2126   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2127   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2128   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2129   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2130   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2131   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2132   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2133   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2134   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2135   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2136   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2137   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2138   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2139   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2140   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2141   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2142   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2143   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2144   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2145   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2146   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2147   PetscFunctionReturn(0);
2148 }
2149 
2150 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2151 {
2152   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2153   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2154   PetscErrorCode ierr;
2155 
2156   PetscFunctionBegin;
2157   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2158   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2159   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2160   mat_graph->cnloc = nloc;
2161   mat_graph->cdim  = dim;
2162   mat_graph->cloc  = PETSC_FALSE;
2163   PetscFunctionReturn(0);
2164 }
2165 
2166 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2167 {
2168   PetscFunctionBegin;
2169   *change = PETSC_TRUE;
2170   PetscFunctionReturn(0);
2171 }
2172 
2173 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2174 {
2175   FETIDPMat_ctx  mat_ctx;
2176   Vec            work;
2177   PC_IS*         pcis;
2178   PC_BDDC*       pcbddc;
2179   PetscErrorCode ierr;
2180 
2181   PetscFunctionBegin;
2182   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2183   pcis = (PC_IS*)mat_ctx->pc->data;
2184   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2185 
2186   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2187   /* copy rhs since we may change it during PCPreSolve_BDDC */
2188   if (!pcbddc->original_rhs) {
2189     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2190   }
2191   if (mat_ctx->rhs_flip) {
2192     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2193   } else {
2194     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2195   }
2196   if (mat_ctx->g2g_p) {
2197     /* interface pressure rhs */
2198     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2199     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2200     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2201     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2202     if (!mat_ctx->rhs_flip) {
2203       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2204     }
2205   }
2206   /*
2207      change of basis for physical rhs if needed
2208      It also changes the rhs in case of dirichlet boundaries
2209   */
2210   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2211   if (pcbddc->ChangeOfBasisMatrix) {
2212     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2213     work = pcbddc->work_change;
2214    } else {
2215     work = pcbddc->original_rhs;
2216   }
2217   /* store vectors for computation of fetidp final solution */
2218   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2219   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2220   /* scale rhs since it should be unassembled */
2221   /* TODO use counter scaling? (also below) */
2222   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2223   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2224   /* Apply partition of unity */
2225   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2226   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2227   if (!pcbddc->switch_static) {
2228     /* compute partially subassembled Schur complement right-hand side */
2229     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2230     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2231     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2232     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2233     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2234     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2235     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2236     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2237     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2238     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2239   }
2240   /* BDDC rhs */
2241   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2242   if (pcbddc->switch_static) {
2243     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2244   }
2245   /* apply BDDC */
2246   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2247   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2248   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2249 
2250   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2251   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2252   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2253   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2254   /* Add contribution to interface pressures */
2255   if (mat_ctx->l2g_p) {
2256     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2257     if (pcbddc->switch_static) {
2258       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2259     }
2260     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2261     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2262   }
2263   PetscFunctionReturn(0);
2264 }
2265 
2266 /*@
2267  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2268 
2269    Collective
2270 
2271    Input Parameters:
2272 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2273 -  standard_rhs    - the right-hand side of the original linear system
2274 
2275    Output Parameters:
2276 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2277 
2278    Level: developer
2279 
2280    Notes:
2281 
2282 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2283 @*/
2284 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2285 {
2286   FETIDPMat_ctx  mat_ctx;
2287   PetscErrorCode ierr;
2288 
2289   PetscFunctionBegin;
2290   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2291   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2292   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2293   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2294   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2295   PetscFunctionReturn(0);
2296 }
2297 
2298 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2299 {
2300   FETIDPMat_ctx  mat_ctx;
2301   PC_IS*         pcis;
2302   PC_BDDC*       pcbddc;
2303   PetscErrorCode ierr;
2304   Vec            work;
2305 
2306   PetscFunctionBegin;
2307   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2308   pcis = (PC_IS*)mat_ctx->pc->data;
2309   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2310 
2311   /* apply B_delta^T */
2312   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2313   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2314   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2315   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2316   if (mat_ctx->l2g_p) {
2317     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2318     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2319     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2320   }
2321 
2322   /* compute rhs for BDDC application */
2323   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2324   if (pcbddc->switch_static) {
2325     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2326     if (mat_ctx->l2g_p) {
2327       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2328       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2329     }
2330   }
2331 
2332   /* apply BDDC */
2333   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2334   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2335 
2336   /* put values into global vector */
2337   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2338   else work = standard_sol;
2339   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2340   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2341   if (!pcbddc->switch_static) {
2342     /* compute values into the interior if solved for the partially subassembled Schur complement */
2343     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2344     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2345     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2346   }
2347 
2348   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2349   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2350   /* add p0 solution to final solution */
2351   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2352   if (pcbddc->ChangeOfBasisMatrix) {
2353     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2354   }
2355   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2356   if (mat_ctx->g2g_p) {
2357     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2358     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2359   }
2360   PetscFunctionReturn(0);
2361 }
2362 
2363 /*@
2364  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2365 
2366    Collective
2367 
2368    Input Parameters:
2369 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2370 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2371 
2372    Output Parameters:
2373 .  standard_sol    - the solution defined on the physical domain
2374 
2375    Level: developer
2376 
2377    Notes:
2378 
2379 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2380 @*/
2381 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2382 {
2383   FETIDPMat_ctx  mat_ctx;
2384   PetscErrorCode ierr;
2385 
2386   PetscFunctionBegin;
2387   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2388   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2389   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2390   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2391   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2392   PetscFunctionReturn(0);
2393 }
2394 
2395 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2396 {
2397 
2398   FETIDPMat_ctx  fetidpmat_ctx;
2399   Mat            newmat;
2400   FETIDPPC_ctx   fetidppc_ctx;
2401   PC             newpc;
2402   MPI_Comm       comm;
2403   PetscErrorCode ierr;
2404 
2405   PetscFunctionBegin;
2406   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2407   /* FETIDP linear matrix */
2408   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2409   fetidpmat_ctx->fully_redundant = fully_redundant;
2410   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2411   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2412   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2413   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2414   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2415   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2416   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2417   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2418   /* FETIDP preconditioner */
2419   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2420   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2421   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2422   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2423   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2424   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2425   if (!fetidpmat_ctx->l2g_lambda_only) {
2426     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2427     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2428     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2429     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2430     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2431     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2432   } else {
2433     KSP      *ksps;
2434     PC       lagpc;
2435     Mat      M,AM,PM;
2436     PetscInt nn;
2437 
2438     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2439     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2440     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2441     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2442     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2443     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2444     ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2445     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2446     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2447     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2448 
2449     /* set the solver for the (0,0) block */
2450     ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2451     ierr = PCCreate(comm,&lagpc);CHKERRQ(ierr);
2452     ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2453     ierr = KSPGetOperators(ksps[0],&AM,&PM);CHKERRQ(ierr);
2454     ierr = PCSetOperators(lagpc,AM,PM);CHKERRQ(ierr);
2455     ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2456     ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2457     ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2458     ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2459     ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2460     ierr = KSPSetPC(ksps[0],lagpc);CHKERRQ(ierr);
2461     ierr = PCDestroy(&lagpc);CHKERRQ(ierr);
2462     ierr = PetscFree(ksps);CHKERRQ(ierr);
2463   }
2464   /* return pointers for objects created */
2465   *fetidp_mat = newmat;
2466   *fetidp_pc = newpc;
2467   PetscFunctionReturn(0);
2468 }
2469 
2470 /*@C
2471  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2472 
2473    Collective
2474 
2475    Input Parameters:
2476 +  pc - the BDDC preconditioning context (setup should have been called before)
2477 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2478 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2479 
2480    Output Parameters:
2481 +  fetidp_mat - shell FETI-DP matrix object
2482 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2483 
2484    Level: developer
2485 
2486    Notes:
2487      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2488 
2489 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2490 @*/
2491 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2492 {
2493   PetscErrorCode ierr;
2494 
2495   PetscFunctionBegin;
2496   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2497   if (pc->setupcalled) {
2498     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2499   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2500   PetscFunctionReturn(0);
2501 }
2502 /* -------------------------------------------------------------------------- */
2503 /*MC
2504    PCBDDC - Balancing Domain Decomposition by Constraints.
2505 
2506    An implementation of the BDDC preconditioner based on
2507 
2508 .vb
2509    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2510    [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
2511    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2512    [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
2513 .ve
2514 
2515    The matrix to be preconditioned (Pmat) must be of type MATIS.
2516 
2517    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2518 
2519    It also works with unsymmetric and indefinite problems.
2520 
2521    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.
2522 
2523    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).
2524 
2525    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()
2526    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2527 
2528    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2529 
2530    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.
2531    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2532 
2533    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2534 
2535    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.
2536 
2537    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.
2538    Deluxe scaling is not supported yet for FETI-DP.
2539 
2540    Options Database Keys (some of them, run with -h for a complete list):
2541 
2542 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2543 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2544 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2545 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2546 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2547 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2548 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2549 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2550 .    -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)
2551 .    -pc_bddc_coarse_redistribute <0> - size of a subset of processors where the coarse problem will be remapped (the value is ignored if not at the coarsest level)
2552 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2553 .    -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)
2554 .    -pc_bddc_adaptive_threshold <0.0> - when a value different than zero is specified, adaptive selection of constraints is performed on edges and faces (requires deluxe scaling and MUMPS or MKL_PARDISO installed)
2555 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2556 
2557    Options for Dirichlet, Neumann or coarse solver can be set with
2558 .vb
2559       -pc_bddc_dirichlet_
2560       -pc_bddc_neumann_
2561       -pc_bddc_coarse_
2562 .ve
2563    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2564 
2565    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2566 .vb
2567       -pc_bddc_dirichlet_lN_
2568       -pc_bddc_neumann_lN_
2569       -pc_bddc_coarse_lN_
2570 .ve
2571    Note that level number ranges from the finest (0) to the coarsest (N).
2572    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.
2573 .vb
2574      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2575 .ve
2576    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
2577 
2578    Level: intermediate
2579 
2580    Developer Notes:
2581 
2582    Contributed by Stefano Zampini
2583 
2584 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2585 M*/
2586 
2587 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2588 {
2589   PetscErrorCode      ierr;
2590   PC_BDDC             *pcbddc;
2591 
2592   PetscFunctionBegin;
2593   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2594   pc->data = (void*)pcbddc;
2595 
2596   /* create PCIS data structure */
2597   ierr = PCISCreate(pc);CHKERRQ(ierr);
2598 
2599   /* create local graph structure */
2600   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2601 
2602   /* BDDC nonzero defaults */
2603   pcbddc->use_local_adj             = PETSC_TRUE;
2604   pcbddc->use_vertices              = PETSC_TRUE;
2605   pcbddc->use_edges                 = PETSC_TRUE;
2606   pcbddc->symmetric_primal          = PETSC_TRUE;
2607   pcbddc->vertex_size               = 1;
2608   pcbddc->recompute_topography      = PETSC_TRUE;
2609   pcbddc->coarse_size               = -1;
2610   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2611   pcbddc->coarsening_ratio          = 8;
2612   pcbddc->coarse_eqs_per_proc       = 1;
2613   pcbddc->benign_compute_correction = PETSC_TRUE;
2614   pcbddc->nedfield                  = -1;
2615   pcbddc->nedglobal                 = PETSC_TRUE;
2616   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2617   pcbddc->sub_schurs_layers         = -1;
2618   pcbddc->adaptive_threshold[0]     = 0.0;
2619   pcbddc->adaptive_threshold[1]     = 0.0;
2620 
2621   /* function pointers */
2622   pc->ops->apply               = PCApply_BDDC;
2623   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2624   pc->ops->setup               = PCSetUp_BDDC;
2625   pc->ops->destroy             = PCDestroy_BDDC;
2626   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2627   pc->ops->view                = PCView_BDDC;
2628   pc->ops->applyrichardson     = 0;
2629   pc->ops->applysymmetricleft  = 0;
2630   pc->ops->applysymmetricright = 0;
2631   pc->ops->presolve            = PCPreSolve_BDDC;
2632   pc->ops->postsolve           = PCPostSolve_BDDC;
2633   pc->ops->reset               = PCReset_BDDC;
2634 
2635   /* composing function */
2636   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
2637   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
2638   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2639   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2640   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
2641   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2642   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2643   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2644   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2645   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2646   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2647   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2648   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2649   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2650   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2651   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2652   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2653   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2654   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2655   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2656   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2657   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2658   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2659   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
2660   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
2661   PetscFunctionReturn(0);
2662 }
2663