xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision fa2f3a98544cffa8147e57031dd6780dd55215d2)
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 
1490     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1491     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1492   }
1493 
1494   /* activate all connected components if the netflux has been requested */
1495   if (pcbddc->compute_nonetflux) {
1496     pcbddc->use_vertices = PETSC_TRUE;
1497     pcbddc->use_edges    = PETSC_TRUE;
1498     pcbddc->use_faces    = PETSC_TRUE;
1499   }
1500 
1501   /* Get stdout for dbg */
1502   if (pcbddc->dbg_flag) {
1503     if (!pcbddc->dbg_viewer) {
1504       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1505     }
1506     ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1507     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1508   }
1509 
1510   /* process topology information */
1511   if (pcbddc->recompute_topography) {
1512     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1513     if (pcbddc->discretegradient) {
1514       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1515     }
1516   }
1517 
1518   /* change basis if requested by the user */
1519   if (pcbddc->user_ChangeOfBasisMatrix) {
1520     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1521     pcbddc->use_change_of_basis = PETSC_FALSE;
1522     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1523   } else {
1524     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1525     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1526     pcbddc->local_mat = matis->A;
1527   }
1528 
1529   /*
1530      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1531      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1532   */
1533   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1534   if (pcbddc->benign_saddle_point) {
1535     PC_IS* pcis = (PC_IS*)pc->data;
1536 
1537     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1538     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1539     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1540     /* pop B0 mat from local mat */
1541     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1542     /* give pcis a hint to not reuse submatrices during PCISCreate */
1543     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1544       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1545         pcis->reusesubmatrices = PETSC_FALSE;
1546       } else {
1547         pcis->reusesubmatrices = PETSC_TRUE;
1548       }
1549     } else {
1550       pcis->reusesubmatrices = PETSC_FALSE;
1551     }
1552   }
1553 
1554   /* propagate relevant information */
1555   if (matis->A->symmetric_set) {
1556     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1557   }
1558   if (matis->A->spd_set) {
1559     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1560   }
1561 
1562   /* Set up all the "iterative substructuring" common block without computing solvers */
1563   {
1564     Mat temp_mat;
1565 
1566     temp_mat = matis->A;
1567     matis->A = pcbddc->local_mat;
1568     ierr = PCISSetUp(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1569     pcbddc->local_mat = matis->A;
1570     matis->A = temp_mat;
1571   }
1572 
1573   /* Analyze interface */
1574   if (!pcbddc->graphanalyzed) {
1575     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1576     computeconstraintsmatrix = PETSC_TRUE;
1577     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1578       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1579     }
1580     if (pcbddc->compute_nonetflux) {
1581       MatNullSpace nnfnnsp;
1582 
1583       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1584       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1585       /* TODO what if a nearnullspace is already attached? */
1586       if (nnfnnsp) {
1587         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1588         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1589       }
1590     }
1591   }
1592 
1593   /* check existence of a divergence free extension, i.e.
1594      b(v_I,p_0) = 0 for all v_I (raise error if not).
1595      Also, check that PCBDDCBenignGetOrSetP0 works */
1596   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1597     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1598   }
1599   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1600 
1601   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1602   if (computesubschurs && pcbddc->recompute_topography) {
1603     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1604   }
1605   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1606   if (!pcbddc->use_deluxe_scaling) {
1607     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1608   }
1609 
1610   /* finish setup solvers and do adaptive selection of constraints */
1611   sub_schurs = pcbddc->sub_schurs;
1612   if (sub_schurs && sub_schurs->schur_explicit) {
1613     if (computesubschurs) {
1614       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1615     }
1616     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1617   } else {
1618     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1619     if (computesubschurs) {
1620       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1621     }
1622   }
1623   if (pcbddc->adaptive_selection) {
1624     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1625     computeconstraintsmatrix = PETSC_TRUE;
1626   }
1627 
1628   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1629   new_nearnullspace_provided = PETSC_FALSE;
1630   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1631   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1632     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1633       new_nearnullspace_provided = PETSC_TRUE;
1634     } else {
1635       /* determine if the two nullspaces are different (should be lightweight) */
1636       if (nearnullspace != pcbddc->onearnullspace) {
1637         new_nearnullspace_provided = PETSC_TRUE;
1638       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1639         PetscInt         i;
1640         const Vec        *nearnullvecs;
1641         PetscObjectState state;
1642         PetscInt         nnsp_size;
1643         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1644         for (i=0;i<nnsp_size;i++) {
1645           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1646           if (pcbddc->onearnullvecs_state[i] != state) {
1647             new_nearnullspace_provided = PETSC_TRUE;
1648             break;
1649           }
1650         }
1651       }
1652     }
1653   } else {
1654     if (!nearnullspace) { /* both nearnullspaces are null */
1655       new_nearnullspace_provided = PETSC_FALSE;
1656     } else { /* nearnullspace attached later */
1657       new_nearnullspace_provided = PETSC_TRUE;
1658     }
1659   }
1660 
1661   /* Setup constraints and related work vectors */
1662   /* reset primal space flags */
1663   pcbddc->new_primal_space = PETSC_FALSE;
1664   pcbddc->new_primal_space_local = PETSC_FALSE;
1665   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1666     /* It also sets the primal space flags */
1667     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1668   }
1669   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1670   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1671 
1672   if (pcbddc->use_change_of_basis) {
1673     PC_IS *pcis = (PC_IS*)(pc->data);
1674 
1675     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1676     if (pcbddc->benign_change) {
1677       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1678       /* pop B0 from pcbddc->local_mat */
1679       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1680     }
1681     /* get submatrices */
1682     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1683     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1684     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1685     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1686     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1687     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1688     /* set flag in pcis to not reuse submatrices during PCISCreate */
1689     pcis->reusesubmatrices = PETSC_FALSE;
1690   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1691     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1692     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1693     pcbddc->local_mat = matis->A;
1694   }
1695 
1696   /* interface pressure block row for B_C */
1697   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1698   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1699   if (lA && lP) {
1700     PC_IS*    pcis = (PC_IS*)pc->data;
1701     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1702     PetscBool issym;
1703     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1704     if (issym) {
1705       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1706       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1707       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1708       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1709     } else {
1710       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1711       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1712       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1713       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1714     }
1715     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1716     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1717     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1718     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1719     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1720     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1721     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1722     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1723   }
1724 
1725   /* SetUp coarse and local Neumann solvers */
1726   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1727   /* SetUp Scaling operator */
1728   if (pcbddc->use_deluxe_scaling) {
1729     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1730   }
1731 
1732   /* mark topography as done */
1733   pcbddc->recompute_topography = PETSC_FALSE;
1734 
1735   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1736   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1737 
1738   if (pcbddc->dbg_flag) {
1739     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1740     ierr = PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1741   }
1742   PetscFunctionReturn(0);
1743 }
1744 
1745 /*
1746    PCApply_BDDC - Applies the BDDC operator to a vector.
1747 
1748    Input Parameters:
1749 +  pc - the preconditioner context
1750 -  r - input vector (global)
1751 
1752    Output Parameter:
1753 .  z - output vector (global)
1754 
1755    Application Interface Routine: PCApply()
1756  */
1757 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1758 {
1759   PC_IS             *pcis = (PC_IS*)(pc->data);
1760   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1761   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1762   PetscErrorCode    ierr;
1763   const PetscScalar one = 1.0;
1764   const PetscScalar m_one = -1.0;
1765   const PetscScalar zero = 0.0;
1766 
1767 /* This code is similar to that provided in nn.c for PCNN
1768    NN interface preconditioner changed to BDDC
1769    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1770 
1771   PetscFunctionBegin;
1772   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1773   if (pcbddc->ChangeOfBasisMatrix) {
1774     Vec swap;
1775 
1776     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1777     swap = pcbddc->work_change;
1778     pcbddc->work_change = r;
1779     r = swap;
1780     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1781     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1782       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1783       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1784     }
1785   }
1786   if (pcbddc->benign_have_null) { /* get p0 from r */
1787     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1788   }
1789   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1790     ierr = VecCopy(r,z);CHKERRQ(ierr);
1791     /* First Dirichlet solve */
1792     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1793     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1794     /*
1795       Assembling right hand side for BDDC operator
1796       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1797       - pcis->vec1_B the interface part of the global vector z
1798     */
1799     if (n_D) {
1800       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1801       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1802       if (pcbddc->switch_static) {
1803         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1804 
1805         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1806         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1807         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1808         if (!pcbddc->switch_static_change) {
1809           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1810         } else {
1811           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1812           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1813           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1814         }
1815         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1816         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1817         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1818         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1819       } else {
1820         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1821       }
1822     } else {
1823       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1824     }
1825     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1826     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1827     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1828   } else {
1829     if (!pcbddc->benign_apply_coarse_only) {
1830       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1831     }
1832   }
1833 
1834   /* Apply interface preconditioner
1835      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1836   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1837 
1838   /* Apply transpose of partition of unity operator */
1839   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1840 
1841   /* Second Dirichlet solve and assembling of output */
1842   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1843   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1844   if (n_B) {
1845     if (pcbddc->switch_static) {
1846       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1847 
1848       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1849       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1850       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1851       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1852       if (!pcbddc->switch_static_change) {
1853         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1854       } else {
1855         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1856         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1857         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1858       }
1859       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1860       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1861     } else {
1862       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1863     }
1864   } else if (pcbddc->switch_static) { /* n_B is zero */
1865     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1866 
1867     if (!pcbddc->switch_static_change) {
1868       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1869     } else {
1870       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1871       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1872       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
1873     }
1874   }
1875   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1876 
1877   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1878     if (pcbddc->switch_static) {
1879       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1880     } else {
1881       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1882     }
1883     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1884     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1885   } else {
1886     if (pcbddc->switch_static) {
1887       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1888     } else {
1889       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1890     }
1891     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1892     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1893   }
1894   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
1895     if (pcbddc->benign_apply_coarse_only) {
1896       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
1897     }
1898     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1899   }
1900 
1901   if (pcbddc->ChangeOfBasisMatrix) {
1902     pcbddc->work_change = r;
1903     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
1904     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
1905   }
1906   PetscFunctionReturn(0);
1907 }
1908 
1909 /*
1910    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1911 
1912    Input Parameters:
1913 +  pc - the preconditioner context
1914 -  r - input vector (global)
1915 
1916    Output Parameter:
1917 .  z - output vector (global)
1918 
1919    Application Interface Routine: PCApplyTranspose()
1920  */
1921 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1922 {
1923   PC_IS             *pcis = (PC_IS*)(pc->data);
1924   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1925   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1926   PetscErrorCode    ierr;
1927   const PetscScalar one = 1.0;
1928   const PetscScalar m_one = -1.0;
1929   const PetscScalar zero = 0.0;
1930 
1931   PetscFunctionBegin;
1932   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1933   if (pcbddc->ChangeOfBasisMatrix) {
1934     Vec swap;
1935 
1936     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1937     swap = pcbddc->work_change;
1938     pcbddc->work_change = r;
1939     r = swap;
1940     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1941     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
1942       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1943       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1944     }
1945   }
1946   if (pcbddc->benign_have_null) { /* get p0 from r */
1947     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1948   }
1949   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1950     ierr = VecCopy(r,z);CHKERRQ(ierr);
1951     /* First Dirichlet solve */
1952     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1953     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1954     /*
1955       Assembling right hand side for BDDC operator
1956       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1957       - pcis->vec1_B the interface part of the global vector z
1958     */
1959     if (n_D) {
1960       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1961       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1962       if (pcbddc->switch_static) {
1963         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1964 
1965         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1966         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1967         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1968         if (!pcbddc->switch_static_change) {
1969           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1970         } else {
1971           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1972           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1973           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1974         }
1975         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1976         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1977         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1978         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1979       } else {
1980         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1981       }
1982     } else {
1983       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1984     }
1985     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1986     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1987     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1988   } else {
1989     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1990   }
1991 
1992   /* Apply interface preconditioner
1993      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1994   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
1995 
1996   /* Apply transpose of partition of unity operator */
1997   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1998 
1999   /* Second Dirichlet solve and assembling of output */
2000   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2001   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2002   if (n_B) {
2003     if (pcbddc->switch_static) {
2004       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2005 
2006       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2007       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2008       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2009       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2010       if (!pcbddc->switch_static_change) {
2011         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2012       } else {
2013         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2014         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2015         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2016       }
2017       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2018       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2019     } else {
2020       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2021     }
2022   } else if (pcbddc->switch_static) { /* n_B is zero */
2023     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2024 
2025     if (!pcbddc->switch_static_change) {
2026       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2027     } else {
2028       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2029       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2030       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2031     }
2032   }
2033   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2034   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2035     if (pcbddc->switch_static) {
2036       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2037     } else {
2038       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2039     }
2040     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2041     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2042   } else {
2043     if (pcbddc->switch_static) {
2044       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2045     } else {
2046       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2047     }
2048     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2049     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2050   }
2051   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2052     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2053   }
2054   if (pcbddc->ChangeOfBasisMatrix) {
2055     pcbddc->work_change = r;
2056     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2057     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2058   }
2059   PetscFunctionReturn(0);
2060 }
2061 
2062 PetscErrorCode PCReset_BDDC(PC pc)
2063 {
2064   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2065   PC_IS          *pcis = (PC_IS*)pc->data;
2066   KSP            kspD,kspR,kspC;
2067   PetscErrorCode ierr;
2068 
2069   PetscFunctionBegin;
2070   /* free BDDC custom data  */
2071   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2072   /* destroy objects related to topography */
2073   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2074   /* destroy objects for scaling operator */
2075   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2076   /* free solvers stuff */
2077   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2078   /* free global vectors needed in presolve */
2079   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2080   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2081   /* free data created by PCIS */
2082   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2083 
2084   /* restore defaults */
2085   kspD = pcbddc->ksp_D;
2086   kspR = pcbddc->ksp_R;
2087   kspC = pcbddc->coarse_ksp;
2088   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2089   pcis->n_neigh                     = -1;
2090   pcis->scaling_factor              = 1.0;
2091   pcis->reusesubmatrices            = PETSC_TRUE;
2092   pcbddc->use_local_adj             = PETSC_TRUE;
2093   pcbddc->use_vertices              = PETSC_TRUE;
2094   pcbddc->use_edges                 = PETSC_TRUE;
2095   pcbddc->symmetric_primal          = PETSC_TRUE;
2096   pcbddc->vertex_size               = 1;
2097   pcbddc->recompute_topography      = PETSC_TRUE;
2098   pcbddc->coarse_size               = -1;
2099   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2100   pcbddc->coarsening_ratio          = 8;
2101   pcbddc->coarse_eqs_per_proc       = 1;
2102   pcbddc->benign_compute_correction = PETSC_TRUE;
2103   pcbddc->nedfield                  = -1;
2104   pcbddc->nedglobal                 = PETSC_TRUE;
2105   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2106   pcbddc->sub_schurs_layers         = -1;
2107   pcbddc->ksp_D                     = kspD;
2108   pcbddc->ksp_R                     = kspR;
2109   pcbddc->coarse_ksp                = kspC;
2110   PetscFunctionReturn(0);
2111 }
2112 
2113 PetscErrorCode PCDestroy_BDDC(PC pc)
2114 {
2115   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2116   PetscErrorCode ierr;
2117 
2118   PetscFunctionBegin;
2119   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2120   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2121   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2122   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2123   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2124   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2125   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2126   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2127   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2128   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2129   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2130   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2131   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2132   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2133   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2134   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2135   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2136   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2137   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2138   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2139   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2140   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2141   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2142   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2143   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2144   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2145   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2146   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2147   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2148   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2149   PetscFunctionReturn(0);
2150 }
2151 
2152 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2153 {
2154   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2155   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2156   PetscErrorCode ierr;
2157 
2158   PetscFunctionBegin;
2159   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2160   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2161   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2162   mat_graph->cnloc = nloc;
2163   mat_graph->cdim  = dim;
2164   mat_graph->cloc  = PETSC_FALSE;
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2169 {
2170   PetscFunctionBegin;
2171   *change = PETSC_TRUE;
2172   PetscFunctionReturn(0);
2173 }
2174 
2175 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2176 {
2177   FETIDPMat_ctx  mat_ctx;
2178   Vec            work;
2179   PC_IS*         pcis;
2180   PC_BDDC*       pcbddc;
2181   PetscErrorCode ierr;
2182 
2183   PetscFunctionBegin;
2184   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2185   pcis = (PC_IS*)mat_ctx->pc->data;
2186   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2187 
2188   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2189   /* copy rhs since we may change it during PCPreSolve_BDDC */
2190   if (!pcbddc->original_rhs) {
2191     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2192   }
2193   if (mat_ctx->rhs_flip) {
2194     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2195   } else {
2196     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2197   }
2198   if (mat_ctx->g2g_p) {
2199     /* interface pressure rhs */
2200     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2201     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2202     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2203     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2204     if (!mat_ctx->rhs_flip) {
2205       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2206     }
2207   }
2208   /*
2209      change of basis for physical rhs if needed
2210      It also changes the rhs in case of dirichlet boundaries
2211   */
2212   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2213   if (pcbddc->ChangeOfBasisMatrix) {
2214     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2215     work = pcbddc->work_change;
2216    } else {
2217     work = pcbddc->original_rhs;
2218   }
2219   /* store vectors for computation of fetidp final solution */
2220   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2221   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2222   /* scale rhs since it should be unassembled */
2223   /* TODO use counter scaling? (also below) */
2224   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2225   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2226   /* Apply partition of unity */
2227   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2228   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2229   if (!pcbddc->switch_static) {
2230     /* compute partially subassembled Schur complement right-hand side */
2231     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2232     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2233     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2234     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2235     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2236     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2237     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2238     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2239     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2240     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2241   }
2242   /* BDDC rhs */
2243   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2244   if (pcbddc->switch_static) {
2245     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2246   }
2247   /* apply BDDC */
2248   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2249   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2250   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2251 
2252   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2253   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2254   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2255   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2256   /* Add contribution to interface pressures */
2257   if (mat_ctx->l2g_p) {
2258     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2259     if (pcbddc->switch_static) {
2260       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2261     }
2262     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2263     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2264   }
2265   PetscFunctionReturn(0);
2266 }
2267 
2268 /*@
2269  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2270 
2271    Collective
2272 
2273    Input Parameters:
2274 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2275 -  standard_rhs    - the right-hand side of the original linear system
2276 
2277    Output Parameters:
2278 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2279 
2280    Level: developer
2281 
2282    Notes:
2283 
2284 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2285 @*/
2286 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2287 {
2288   FETIDPMat_ctx  mat_ctx;
2289   PetscErrorCode ierr;
2290 
2291   PetscFunctionBegin;
2292   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2293   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2294   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2295   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2296   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2297   PetscFunctionReturn(0);
2298 }
2299 
2300 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2301 {
2302   FETIDPMat_ctx  mat_ctx;
2303   PC_IS*         pcis;
2304   PC_BDDC*       pcbddc;
2305   PetscErrorCode ierr;
2306   Vec            work;
2307 
2308   PetscFunctionBegin;
2309   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2310   pcis = (PC_IS*)mat_ctx->pc->data;
2311   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2312 
2313   /* apply B_delta^T */
2314   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2315   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2316   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2317   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2318   if (mat_ctx->l2g_p) {
2319     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2320     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2321     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2322   }
2323 
2324   /* compute rhs for BDDC application */
2325   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2326   if (pcbddc->switch_static) {
2327     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2328     if (mat_ctx->l2g_p) {
2329       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2330       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2331     }
2332   }
2333 
2334   /* apply BDDC */
2335   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2336   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2337 
2338   /* put values into global vector */
2339   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2340   else work = standard_sol;
2341   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2342   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2343   if (!pcbddc->switch_static) {
2344     /* compute values into the interior if solved for the partially subassembled Schur complement */
2345     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2346     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2347     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2348   }
2349 
2350   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2351   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2352   /* add p0 solution to final solution */
2353   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2354   if (pcbddc->ChangeOfBasisMatrix) {
2355     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2356   }
2357   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2358   if (mat_ctx->g2g_p) {
2359     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2360     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2361   }
2362   PetscFunctionReturn(0);
2363 }
2364 
2365 /*@
2366  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2367 
2368    Collective
2369 
2370    Input Parameters:
2371 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2372 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2373 
2374    Output Parameters:
2375 .  standard_sol    - the solution defined on the physical domain
2376 
2377    Level: developer
2378 
2379    Notes:
2380 
2381 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2382 @*/
2383 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2384 {
2385   FETIDPMat_ctx  mat_ctx;
2386   PetscErrorCode ierr;
2387 
2388   PetscFunctionBegin;
2389   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2390   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2391   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2392   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2393   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2394   PetscFunctionReturn(0);
2395 }
2396 
2397 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2398 {
2399 
2400   FETIDPMat_ctx  fetidpmat_ctx;
2401   Mat            newmat;
2402   FETIDPPC_ctx   fetidppc_ctx;
2403   PC             newpc;
2404   MPI_Comm       comm;
2405   PetscErrorCode ierr;
2406 
2407   PetscFunctionBegin;
2408   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2409   /* FETIDP linear matrix */
2410   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2411   fetidpmat_ctx->fully_redundant = fully_redundant;
2412   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2413   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2414   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2415   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2416   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2417   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2418   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2419   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2420   /* FETIDP preconditioner */
2421   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2422   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2423   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2424   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2425   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2426   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2427   if (!fetidpmat_ctx->l2g_lambda_only) {
2428     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2429     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2430     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2431     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2432     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2433     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2434   } else {
2435     KSP      *ksps;
2436     PC       lagpc;
2437     Mat      M,AM,PM;
2438     PetscInt nn;
2439 
2440     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2441     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2442     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2443     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2444     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2445     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2446     ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2447     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2448     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2449     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2450 
2451     /* set the solver for the (0,0) block */
2452     ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2453     ierr = PCCreate(comm,&lagpc);CHKERRQ(ierr);
2454     ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2455     ierr = KSPGetOperators(ksps[0],&AM,&PM);CHKERRQ(ierr);
2456     ierr = PCSetOperators(lagpc,AM,PM);CHKERRQ(ierr);
2457     ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2458     ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2459     ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2460     ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2461     ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2462     ierr = KSPSetPC(ksps[0],lagpc);CHKERRQ(ierr);
2463     ierr = PCDestroy(&lagpc);CHKERRQ(ierr);
2464     ierr = PetscFree(ksps);CHKERRQ(ierr);
2465   }
2466   /* return pointers for objects created */
2467   *fetidp_mat = newmat;
2468   *fetidp_pc = newpc;
2469   PetscFunctionReturn(0);
2470 }
2471 
2472 /*@C
2473  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2474 
2475    Collective
2476 
2477    Input Parameters:
2478 +  pc - the BDDC preconditioning context (setup should have been called before)
2479 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2480 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2481 
2482    Output Parameters:
2483 +  fetidp_mat - shell FETI-DP matrix object
2484 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2485 
2486    Level: developer
2487 
2488    Notes:
2489      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2490 
2491 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2492 @*/
2493 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2494 {
2495   PetscErrorCode ierr;
2496 
2497   PetscFunctionBegin;
2498   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2499   if (pc->setupcalled) {
2500     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2501   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2502   PetscFunctionReturn(0);
2503 }
2504 /* -------------------------------------------------------------------------- */
2505 /*MC
2506    PCBDDC - Balancing Domain Decomposition by Constraints.
2507 
2508    An implementation of the BDDC preconditioner based on
2509 
2510 .vb
2511    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2512    [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
2513    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2514    [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
2515 .ve
2516 
2517    The matrix to be preconditioned (Pmat) must be of type MATIS.
2518 
2519    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2520 
2521    It also works with unsymmetric and indefinite problems.
2522 
2523    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.
2524 
2525    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).
2526 
2527    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()
2528    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2529 
2530    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2531 
2532    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.
2533    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2534 
2535    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2536 
2537    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.
2538 
2539    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.
2540    Deluxe scaling is not supported yet for FETI-DP.
2541 
2542    Options Database Keys (some of them, run with -h for a complete list):
2543 
2544 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2545 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2546 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2547 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2548 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2549 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2550 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2551 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2552 .    -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)
2553 .    -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)
2554 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2555 .    -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)
2556 .    -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)
2557 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2558 
2559    Options for Dirichlet, Neumann or coarse solver can be set with
2560 .vb
2561       -pc_bddc_dirichlet_
2562       -pc_bddc_neumann_
2563       -pc_bddc_coarse_
2564 .ve
2565    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2566 
2567    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2568 .vb
2569       -pc_bddc_dirichlet_lN_
2570       -pc_bddc_neumann_lN_
2571       -pc_bddc_coarse_lN_
2572 .ve
2573    Note that level number ranges from the finest (0) to the coarsest (N).
2574    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.
2575 .vb
2576      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2577 .ve
2578    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
2579 
2580    Level: intermediate
2581 
2582    Developer Notes:
2583 
2584    Contributed by Stefano Zampini
2585 
2586 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2587 M*/
2588 
2589 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2590 {
2591   PetscErrorCode      ierr;
2592   PC_BDDC             *pcbddc;
2593 
2594   PetscFunctionBegin;
2595   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2596   pc->data = (void*)pcbddc;
2597 
2598   /* create PCIS data structure */
2599   ierr = PCISCreate(pc);CHKERRQ(ierr);
2600 
2601   /* create local graph structure */
2602   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2603 
2604   /* BDDC nonzero defaults */
2605   pcbddc->use_local_adj             = PETSC_TRUE;
2606   pcbddc->use_vertices              = PETSC_TRUE;
2607   pcbddc->use_edges                 = PETSC_TRUE;
2608   pcbddc->symmetric_primal          = PETSC_TRUE;
2609   pcbddc->vertex_size               = 1;
2610   pcbddc->recompute_topography      = PETSC_TRUE;
2611   pcbddc->coarse_size               = -1;
2612   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2613   pcbddc->coarsening_ratio          = 8;
2614   pcbddc->coarse_eqs_per_proc       = 1;
2615   pcbddc->benign_compute_correction = PETSC_TRUE;
2616   pcbddc->nedfield                  = -1;
2617   pcbddc->nedglobal                 = PETSC_TRUE;
2618   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2619   pcbddc->sub_schurs_layers         = -1;
2620   pcbddc->adaptive_threshold[0]     = 0.0;
2621   pcbddc->adaptive_threshold[1]     = 0.0;
2622 
2623   /* function pointers */
2624   pc->ops->apply               = PCApply_BDDC;
2625   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2626   pc->ops->setup               = PCSetUp_BDDC;
2627   pc->ops->destroy             = PCDestroy_BDDC;
2628   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2629   pc->ops->view                = PCView_BDDC;
2630   pc->ops->applyrichardson     = 0;
2631   pc->ops->applysymmetricleft  = 0;
2632   pc->ops->applysymmetricright = 0;
2633   pc->ops->presolve            = PCPreSolve_BDDC;
2634   pc->ops->postsolve           = PCPostSolve_BDDC;
2635   pc->ops->reset               = PCReset_BDDC;
2636 
2637   /* composing function */
2638   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
2639   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
2640   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2641   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2642   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
2643   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2644   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2645   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2646   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2647   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2648   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2649   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2650   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2651   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2652   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2653   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2654   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2655   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2656   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2657   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2658   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2659   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2660   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2661   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
2662   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
2663   PetscFunctionReturn(0);
2664 }
2665