xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 1c7a958b905b87bd3b0c48d575407f05fa79ac30)
1 /* TODOLIST
2 
3    Solvers
4    - Add support for cholesky for coarse solver (similar to local solvers)
5    - Propagate ksp prefixes for solvers to mat objects?
6 
7    User interface
8    - ** DM attached to pc?
9 
10    Debugging output
11    - * Better management of verbosity levels of debugging output
12 
13    Extra
14    - *** Is it possible to work with PCBDDCGraph on boundary indices only (less memory consumed)?
15    - BDDC with MG framework?
16 
17    MATIS related operations contained in BDDC code
18    - Provide general case for subassembling
19 
20 */
21 
22 #include <../src/ksp/pc/impls/bddc/bddc.h> /*I "petscpc.h" I*/  /* includes for fortran wrappers */
23 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
24 #include <petscblaslapack.h>
25 
26 static PetscBool  cited = PETSC_FALSE;
27 static const char citation[] =
28 "@article{ZampiniPCBDDC,\n"
29 "author = {Stefano Zampini},\n"
30 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
31 "journal = {SIAM Journal on Scientific Computing},\n"
32 "volume = {38},\n"
33 "number = {5},\n"
34 "pages = {S282-S306},\n"
35 "year = {2016},\n"
36 "doi = {10.1137/15M1025785},\n"
37 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
38 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
39 "}\n";
40 
41 /* temporarily declare it */
42 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
43 
44 PetscErrorCode PCSetFromOptions_BDDC(PetscOptionItems *PetscOptionsObject,PC pc)
45 {
46   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
47   PetscInt       nt;
48   PetscErrorCode ierr;
49 
50   PetscFunctionBegin;
51   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
52   /* Verbose debugging */
53   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
54   /* Approximate solvers */
55   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate","Inform PCBDDC that we are using approximate Dirichlet solvers","none",pcbddc->NullSpace_corr[0],&pcbddc->NullSpace_corr[0],NULL);CHKERRQ(ierr);
56   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate_scale","Inform PCBDDC that we need to scale the Dirichlet solve","none",pcbddc->NullSpace_corr[1],&pcbddc->NullSpace_corr[1],NULL);CHKERRQ(ierr);
57   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate","Inform PCBDDC that we are using approximate Neumann solvers","none",pcbddc->NullSpace_corr[2],&pcbddc->NullSpace_corr[2],NULL);CHKERRQ(ierr);
58   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate_scale","Inform PCBDDC that we need to scale the Neumann solve","none",pcbddc->NullSpace_corr[3],&pcbddc->NullSpace_corr[3],NULL);CHKERRQ(ierr);
59   /* Primal space customization */
60   ierr = PetscOptionsBool("-pc_bddc_use_local_mat_graph","Use or not adjacency graph of local mat for interface analysis","none",pcbddc->use_local_adj,&pcbddc->use_local_adj,NULL);CHKERRQ(ierr);
61   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
62   ierr = PetscOptionsBool("-pc_bddc_corner_selection","Activates face-based corner selection","none",pcbddc->corner_selection,&pcbddc->corner_selection,NULL);CHKERRQ(ierr);
63   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
64   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
65   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
66   ierr = PetscOptionsInt("-pc_bddc_vertex_size","Connected components smaller or equal to vertex size will be considered as primal vertices","none",pcbddc->vertex_size,&pcbddc->vertex_size,NULL);CHKERRQ(ierr);
67   ierr = PetscOptionsBool("-pc_bddc_use_true_nnsp","Use near null space attached to the matrix without modifications","none",pcbddc->use_nnsp_true,&pcbddc->use_nnsp_true,NULL);CHKERRQ(ierr);
68   ierr = PetscOptionsBool("-pc_bddc_use_qr_single","Use QR factorization for single constraints on cc (QR is always used when multiple constraints are present)","none",pcbddc->use_qr_single,&pcbddc->use_qr_single,NULL);CHKERRQ(ierr);
69   /* Change of basis */
70   ierr = PetscOptionsBool("-pc_bddc_use_change_of_basis","Use or not internal change of basis on local edge nodes","none",pcbddc->use_change_of_basis,&pcbddc->use_change_of_basis,NULL);CHKERRQ(ierr);
71   ierr = PetscOptionsBool("-pc_bddc_use_change_on_faces","Use or not internal change of basis on local face nodes","none",pcbddc->use_change_on_faces,&pcbddc->use_change_on_faces,NULL);CHKERRQ(ierr);
72   if (!pcbddc->use_change_of_basis) {
73     pcbddc->use_change_on_faces = PETSC_FALSE;
74   }
75   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
76   ierr = PetscOptionsBool("-pc_bddc_switch_static","Switch on static condensation ops around the interface preconditioner","none",pcbddc->switch_static,&pcbddc->switch_static,NULL);CHKERRQ(ierr);
77   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_per_proc","Number of equations per process for coarse problem redistribution (significant only at the coarsest level)","none",pcbddc->coarse_eqs_per_proc,&pcbddc->coarse_eqs_per_proc,NULL);CHKERRQ(ierr);
78   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,NULL);CHKERRQ(ierr);
79   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","none",pcbddc->max_levels,&pcbddc->max_levels,NULL);CHKERRQ(ierr);
80   ierr = PetscOptionsBool("-pc_bddc_use_coarse_estimates","Use estimated eigenvalues for coarse problem","none",pcbddc->use_coarse_estimates,&pcbddc->use_coarse_estimates,NULL);CHKERRQ(ierr);
81   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
82   ierr = PetscOptionsBool("-pc_bddc_schur_rebuild","Whether or not the interface graph for Schur principal minors has to be rebuilt (i.e. define the interface without any adjacency)","none",pcbddc->sub_schurs_rebuild,&pcbddc->sub_schurs_rebuild,NULL);CHKERRQ(ierr);
83   ierr = PetscOptionsInt("-pc_bddc_schur_layers","Number of dofs' layers for the computation of principal minors (i.e. -1 uses all dofs)","none",pcbddc->sub_schurs_layers,&pcbddc->sub_schurs_layers,NULL);CHKERRQ(ierr);
84   ierr = PetscOptionsBool("-pc_bddc_schur_use_useradj","Whether or not the CSR graph specified by the user should be used for computing successive layers (default is to use adj of local mat)","none",pcbddc->sub_schurs_use_useradj,&pcbddc->sub_schurs_use_useradj,NULL);CHKERRQ(ierr);
85   ierr = PetscOptionsBool("-pc_bddc_schur_exact","Whether or not to use the exact Schur complement instead of the reduced one (which excludes size 1 cc)","none",pcbddc->sub_schurs_exact_schur,&pcbddc->sub_schurs_exact_schur,NULL);CHKERRQ(ierr);
86   ierr = PetscOptionsBool("-pc_bddc_deluxe_zerorows","Zero rows and columns of deluxe operators associated with primal dofs","none",pcbddc->deluxe_zerorows,&pcbddc->deluxe_zerorows,NULL);CHKERRQ(ierr);
87   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
88   ierr = PetscOptionsBool("-pc_bddc_adaptive_userdefined","Use user-defined constraints (should be attached via MatSetNearNullSpace to pmat) in addition to those adaptively generated","none",pcbddc->adaptive_userdefined,&pcbddc->adaptive_userdefined,NULL);CHKERRQ(ierr);
89   nt   = 2;
90   ierr = PetscOptionsRealArray("-pc_bddc_adaptive_threshold","Thresholds to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&nt,NULL);CHKERRQ(ierr);
91   if (nt == 1) pcbddc->adaptive_threshold[1] = pcbddc->adaptive_threshold[0];
92   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
93   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
94   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
95   ierr = PetscOptionsInt("-pc_bddc_coarse_adj","Number of processors where to map the coarse adjacency list","none",pcbddc->coarse_adj_red,&pcbddc->coarse_adj_red,NULL);CHKERRQ(ierr);
96   ierr = PetscOptionsBool("-pc_bddc_benign_trick","Apply the benign subspace trick to saddle point problems with discontinuous pressures","none",pcbddc->benign_saddle_point,&pcbddc->benign_saddle_point,NULL);CHKERRQ(ierr);
97   ierr = PetscOptionsBool("-pc_bddc_benign_change","Compute the pressure change of basis explicitly","none",pcbddc->benign_change_explicit,&pcbddc->benign_change_explicit,NULL);CHKERRQ(ierr);
98   ierr = PetscOptionsBool("-pc_bddc_benign_compute_correction","Compute the benign correction during PreSolve","none",pcbddc->benign_compute_correction,&pcbddc->benign_compute_correction,NULL);CHKERRQ(ierr);
99   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
100   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
101   ierr = PetscOptionsBool("-pc_bddc_eliminate_dirichlet","Whether or not we want to eliminate dirichlet dofs during presolve","none",pcbddc->eliminate_dirdofs,&pcbddc->eliminate_dirdofs,NULL);CHKERRQ(ierr);
102   ierr = PetscOptionsTail();CHKERRQ(ierr);
103   PetscFunctionReturn(0);
104 }
105 
106 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
107 {
108   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
109   PC_IS                *pcis = (PC_IS*)pc->data;
110   PetscErrorCode       ierr;
111   PetscBool            isascii;
112   PetscSubcomm         subcomm;
113   PetscViewer          subviewer;
114 
115   PetscFunctionBegin;
116   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
117   /* ASCII viewer */
118   if (isascii) {
119     PetscMPIInt   color,rank,size;
120     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
121     PetscScalar   interface_size;
122     PetscReal     ratio1=0.,ratio2=0.;
123     Vec           counter;
124 
125     if (!pc->setupcalled) {
126       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
127     }
128     ierr = PetscViewerASCIIPrintf(viewer,"  Use verbose output: %D\n",pcbddc->dbg_flag);CHKERRQ(ierr);
129     ierr = PetscViewerASCIIPrintf(viewer,"  Use user-defined CSR: %d\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
130     ierr = PetscViewerASCIIPrintf(viewer,"  Use local mat graph: %d\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
131     if (pcbddc->mat_graph->twodim) {
132       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
133     } else {
134       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
135     }
136     if (pcbddc->graphmaxcount != PETSC_MAX_INT) {
137       ierr = PetscViewerASCIIPrintf(viewer,"  Graph max count: %D\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
138     }
139     ierr = PetscViewerASCIIPrintf(viewer,"  Use vertices: %d (vertex size %D)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
140     ierr = PetscViewerASCIIPrintf(viewer,"  Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
141     ierr = PetscViewerASCIIPrintf(viewer,"  Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
142     ierr = PetscViewerASCIIPrintf(viewer,"  Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
143     ierr = PetscViewerASCIIPrintf(viewer,"  Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
144     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
145     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
148     ierr = PetscViewerASCIIPrintf(viewer,"  Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
149     ierr = PetscViewerASCIIPrintf(viewer,"  Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
150     ierr = PetscViewerASCIIPrintf(viewer,"  Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
151     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel max levels: %D\n",pcbddc->max_levels);CHKERRQ(ierr);
152     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel coarsening ratio: %D\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
153     ierr = PetscViewerASCIIPrintf(viewer,"  Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
154     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
155     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
156     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  Number of dofs' layers for the computation of principal minors: %D\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
160     if (pcbddc->adaptive_threshold[1] != pcbddc->adaptive_threshold[0]) {
161       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection thresholds (active %d, userdefined %d): %g,%g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0],pcbddc->adaptive_threshold[1]);CHKERRQ(ierr);
162     } else {
163       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection threshold (active %d, userdefined %d): %g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0]);CHKERRQ(ierr);
164     }
165     ierr = PetscViewerASCIIPrintf(viewer,"  Min constraints / connected component: %D\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  Max constraints / connected component: %D\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
167     ierr = PetscViewerASCIIPrintf(viewer,"  Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
168     ierr = PetscViewerASCIIPrintf(viewer,"  Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
169     ierr = PetscViewerASCIIPrintf(viewer,"  Num. Procs. to map coarse adjacency list: %D\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
170     ierr = PetscViewerASCIIPrintf(viewer,"  Coarse eqs per proc (significant at the coarsest level): %D\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
171     ierr = PetscViewerASCIIPrintf(viewer,"  Detect disconnected: %d\n",pcbddc->detect_disconnected);CHKERRQ(ierr);
172     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
173     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
174     ierr = PetscViewerASCIIPrintf(viewer,"  Algebraic computation of no-net-flux %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
175     if (!pc->setupcalled) PetscFunctionReturn(0);
176 
177     /* compute interface size */
178     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
179     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
180     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
181     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
182     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
183     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
184     ierr = VecDestroy(&counter);CHKERRQ(ierr);
185 
186     /* compute some statistics on the domain decomposition */
187     gsum[0] = 1;
188     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
189     loc[0]  = !!pcis->n;
190     loc[1]  = pcis->n - pcis->n_B;
191     loc[2]  = pcis->n_B;
192     loc[3]  = pcbddc->local_primal_size;
193     loc[4]  = pcis->n;
194     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
195     loc[6]  = pcbddc->benign_n;
196     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
197     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
198     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
199     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
200     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
201     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
202     if (pcbddc->coarse_size) {
203       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
204       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
205     }
206     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
207     ierr = PetscViewerASCIIPrintf(viewer,"  Global dofs sizes: all %D interface %D coarse %D\n",pc->pmat->rmap->N,(PetscInt)PetscRealPart(interface_size),pcbddc->coarse_size);CHKERRQ(ierr);
208     ierr = PetscViewerASCIIPrintf(viewer,"  Coarsening ratios: all/coarse %D interface/coarse %D\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
209     ierr = PetscViewerASCIIPrintf(viewer,"  Active processes : %D\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
210     ierr = PetscViewerASCIIPrintf(viewer,"  Total subdomains : %D\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
211     if (pcbddc->benign_have_null) {
212       ierr = PetscViewerASCIIPrintf(viewer,"  Benign subs      : %D\n",(PetscInt)totbenign);CHKERRQ(ierr);
213     }
214     ierr = PetscViewerASCIIPrintf(viewer,"  Dofs type        :\tMIN\tMAX\tMEAN\n");CHKERRQ(ierr);
215     ierr = PetscViewerASCIIPrintf(viewer,"  Interior  dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
216     ierr = PetscViewerASCIIPrintf(viewer,"  Interface dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[2],(PetscInt)gmax[2],(PetscInt)(gsum[2]/gsum[0]));CHKERRQ(ierr);
217     ierr = PetscViewerASCIIPrintf(viewer,"  Primal    dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[3],(PetscInt)gmax[3],(PetscInt)(gsum[3]/gsum[0]));CHKERRQ(ierr);
218     ierr = PetscViewerASCIIPrintf(viewer,"  Local     dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[4],(PetscInt)gmax[4],(PetscInt)(gsum[4]/gsum[0]));CHKERRQ(ierr);
219     ierr = PetscViewerASCIIPrintf(viewer,"  Local     subs   :\t%D\t%D\n"    ,(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
220     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** COARSE PROBLEM DETAILS *********************************\n");CHKERRQ(ierr);
221     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
222 
223     /* the coarse problem can be handled by a different communicator */
224     if (pcbddc->coarse_ksp) color = 1;
225     else color = 0;
226     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
227     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
228     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
229     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
230     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
231     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
232     if (color == 1) {
233       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
234       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
235     }
236     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
237     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
238     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
239   }
240   PetscFunctionReturn(0);
241 }
242 
243 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
244 {
245   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
246   PetscErrorCode ierr;
247 
248   PetscFunctionBegin;
249   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
250   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
251   pcbddc->discretegradient = G;
252   pcbddc->nedorder         = order > 0 ? order : -order;
253   pcbddc->nedfield         = field;
254   pcbddc->nedglobal        = global;
255   pcbddc->conforming       = conforming;
256   PetscFunctionReturn(0);
257 }
258 
259 /*@
260  PCBDDCSetDiscreteGradient - Sets the discrete gradient
261 
262    Collective on PC
263 
264    Input Parameters:
265 +  pc         - the preconditioning context
266 .  G          - the discrete gradient matrix (should be in AIJ format)
267 .  order      - the order of the Nedelec space (1 for the lowest order)
268 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
269 .  global     - the type of global ordering for the rows of G
270 -  conforming - whether the mesh is conforming or not
271 
272    Level: advanced
273 
274    Notes: The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
275           For variable order spaces, the order should be set to zero.
276           If global is true, the rows of G should be given in global ordering for the whole dofs;
277           if false, the ordering should be global for the Nedelec field.
278           In the latter case, it should hold gid[i] < gid[j] iff geid[i] < geid[j], with gid the global orderding for all the dofs
279           and geid the one for the Nedelec field.
280 
281 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
282 @*/
283 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
284 {
285   PetscErrorCode ierr;
286 
287   PetscFunctionBegin;
288   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
289   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
290   PetscValidLogicalCollectiveInt(pc,order,3);
291   PetscValidLogicalCollectiveInt(pc,field,4);
292   PetscValidLogicalCollectiveBool(pc,global,5);
293   PetscValidLogicalCollectiveBool(pc,conforming,6);
294   PetscCheckSameComm(pc,1,G,2);
295   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
296   PetscFunctionReturn(0);
297 }
298 
299 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
300 {
301   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
302   PetscErrorCode ierr;
303 
304   PetscFunctionBegin;
305   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
306   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
307   pcbddc->divudotp = divudotp;
308   pcbddc->divudotp_trans = trans;
309   pcbddc->compute_nonetflux = PETSC_TRUE;
310   if (vl2l) {
311     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
312     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
313     pcbddc->divudotp_vl2l = vl2l;
314   }
315   PetscFunctionReturn(0);
316 }
317 
318 /*@
319  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
320 
321    Collective on PC
322 
323    Input Parameters:
324 +  pc - the preconditioning context
325 .  divudotp - the matrix (must be of type MATIS)
326 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
327 -  vl2l - optional index set describing the local (wrt the local matrix in divudotp) to local (wrt the local matrix in the preconditioning matrix) map for the velocities
328 
329    Level: advanced
330 
331    Notes: This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
332           If vl2l is NULL, the local ordering for velocities in divudotp should match that of the preconditioning matrix
333 
334 .seealso: PCBDDC
335 @*/
336 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
337 {
338   PetscBool      ismatis;
339   PetscErrorCode ierr;
340 
341   PetscFunctionBegin;
342   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
343   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
344   PetscCheckSameComm(pc,1,divudotp,2);
345   PetscValidLogicalCollectiveBool(pc,trans,3);
346   if (vl2l) PetscValidHeaderSpecific(divudotp,IS_CLASSID,4);
347   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
348   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
349   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
350   PetscFunctionReturn(0);
351 }
352 
353 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
354 {
355   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
356   PetscErrorCode ierr;
357 
358   PetscFunctionBegin;
359   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
360   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
361   pcbddc->user_ChangeOfBasisMatrix = change;
362   pcbddc->change_interior = interior;
363   PetscFunctionReturn(0);
364 }
365 /*@
366  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
367 
368    Collective on PC
369 
370    Input Parameters:
371 +  pc - the preconditioning context
372 .  change - the change of basis matrix
373 -  interior - whether or not the change of basis modifies interior dofs
374 
375    Level: intermediate
376 
377    Notes:
378 
379 .seealso: PCBDDC
380 @*/
381 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
382 {
383   PetscErrorCode ierr;
384 
385   PetscFunctionBegin;
386   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
387   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
388   PetscCheckSameComm(pc,1,change,2);
389   if (pc->mat) {
390     PetscInt rows_c,cols_c,rows,cols;
391     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
392     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
393     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of rows for change of basis matrix! %D != %D",rows_c,rows);
394     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of columns for change of basis matrix! %D != %D",cols_c,cols);
395     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
396     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
397     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local rows for change of basis matrix! %D != %D",rows_c,rows);
398     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local columns for change of basis matrix! %D != %D",cols_c,cols);
399   }
400   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
401   PetscFunctionReturn(0);
402 }
403 
404 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
405 {
406   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
407   PetscBool      isequal = PETSC_FALSE;
408   PetscErrorCode ierr;
409 
410   PetscFunctionBegin;
411   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
412   if (pcbddc->user_primal_vertices) {
413     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
414   }
415   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
416   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
417   pcbddc->user_primal_vertices = PrimalVertices;
418   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
419   PetscFunctionReturn(0);
420 }
421 
422 /*@
423  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
424 
425    Collective
426 
427    Input Parameters:
428 +  pc - the preconditioning context
429 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
430 
431    Level: intermediate
432 
433    Notes:
434      Any process can list any global node
435 
436 .seealso: PCBDDC
437 @*/
438 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
439 {
440   PetscErrorCode ierr;
441 
442   PetscFunctionBegin;
443   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
444   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
445   PetscCheckSameComm(pc,1,PrimalVertices,2);
446   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
447   PetscFunctionReturn(0);
448 }
449 
450 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
451 {
452   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
453   PetscBool      isequal = PETSC_FALSE;
454   PetscErrorCode ierr;
455 
456   PetscFunctionBegin;
457   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
458   if (pcbddc->user_primal_vertices_local) {
459     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
460   }
461   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
462   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
463   pcbddc->user_primal_vertices_local = PrimalVertices;
464   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
465   PetscFunctionReturn(0);
466 }
467 /*@
468  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
469 
470    Collective
471 
472    Input Parameters:
473 +  pc - the preconditioning context
474 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
475 
476    Level: intermediate
477 
478    Notes:
479 
480 .seealso: PCBDDC
481 @*/
482 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
483 {
484   PetscErrorCode ierr;
485 
486   PetscFunctionBegin;
487   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
488   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
489   PetscCheckSameComm(pc,1,PrimalVertices,2);
490   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
491   PetscFunctionReturn(0);
492 }
493 
494 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
495 {
496   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
497 
498   PetscFunctionBegin;
499   pcbddc->coarsening_ratio = k;
500   PetscFunctionReturn(0);
501 }
502 
503 /*@
504  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
505 
506    Logically collective on PC
507 
508    Input Parameters:
509 +  pc - the preconditioning context
510 -  k - coarsening ratio (H/h at the coarser level)
511 
512    Options Database Keys:
513 .    -pc_bddc_coarsening_ratio
514 
515    Level: intermediate
516 
517    Notes:
518      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
519 
520 .seealso: PCBDDC, PCBDDCSetLevels()
521 @*/
522 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
523 {
524   PetscErrorCode ierr;
525 
526   PetscFunctionBegin;
527   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
528   PetscValidLogicalCollectiveInt(pc,k,2);
529   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
530   PetscFunctionReturn(0);
531 }
532 
533 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
534 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
535 {
536   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
537 
538   PetscFunctionBegin;
539   pcbddc->use_exact_dirichlet_trick = flg;
540   PetscFunctionReturn(0);
541 }
542 
543 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
544 {
545   PetscErrorCode ierr;
546 
547   PetscFunctionBegin;
548   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
549   PetscValidLogicalCollectiveBool(pc,flg,2);
550   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
551   PetscFunctionReturn(0);
552 }
553 
554 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
555 {
556   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
557 
558   PetscFunctionBegin;
559   pcbddc->current_level = level;
560   PetscFunctionReturn(0);
561 }
562 
563 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
564 {
565   PetscErrorCode ierr;
566 
567   PetscFunctionBegin;
568   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
569   PetscValidLogicalCollectiveInt(pc,level,2);
570   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
571   PetscFunctionReturn(0);
572 }
573 
574 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
575 {
576   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
577 
578   PetscFunctionBegin;
579   pcbddc->max_levels = levels;
580   PetscFunctionReturn(0);
581 }
582 
583 /*@
584  PCBDDCSetLevels - Sets the maximum number of levels for multilevel
585 
586    Logically collective on PC
587 
588    Input Parameters:
589 +  pc - the preconditioning context
590 -  levels - the maximum number of levels (max 9)
591 
592    Options Database Keys:
593 .    -pc_bddc_levels
594 
595    Level: intermediate
596 
597    Notes:
598      Default value is 0, i.e. traditional one-level BDDC
599 
600 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
601 @*/
602 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
603 {
604   PetscErrorCode ierr;
605 
606   PetscFunctionBegin;
607   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
608   PetscValidLogicalCollectiveInt(pc,levels,2);
609   if (levels > 99) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of levels for bddc is 99\n");
610   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
611   PetscFunctionReturn(0);
612 }
613 
614 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
615 {
616   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
617   PetscBool      isequal = PETSC_FALSE;
618   PetscErrorCode ierr;
619 
620   PetscFunctionBegin;
621   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
622   if (pcbddc->DirichletBoundaries) {
623     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
624   }
625   /* last user setting takes precendence -> destroy any other customization */
626   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
627   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
628   pcbddc->DirichletBoundaries = DirichletBoundaries;
629   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
630   PetscFunctionReturn(0);
631 }
632 
633 /*@
634  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
635 
636    Collective
637 
638    Input Parameters:
639 +  pc - the preconditioning context
640 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
641 
642    Level: intermediate
643 
644    Notes:
645      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
646 
647 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
648 @*/
649 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
650 {
651   PetscErrorCode ierr;
652 
653   PetscFunctionBegin;
654   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
655   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
656   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
657   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
658   PetscFunctionReturn(0);
659 }
660 
661 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
662 {
663   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
664   PetscBool      isequal = PETSC_FALSE;
665   PetscErrorCode ierr;
666 
667   PetscFunctionBegin;
668   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
669   if (pcbddc->DirichletBoundariesLocal) {
670     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
671   }
672   /* last user setting takes precendence -> destroy any other customization */
673   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
674   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
675   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
676   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
677   PetscFunctionReturn(0);
678 }
679 
680 /*@
681  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
682 
683    Collective
684 
685    Input Parameters:
686 +  pc - the preconditioning context
687 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
688 
689    Level: intermediate
690 
691    Notes:
692 
693 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
694 @*/
695 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
696 {
697   PetscErrorCode ierr;
698 
699   PetscFunctionBegin;
700   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
701   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
702   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
703   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
704   PetscFunctionReturn(0);
705 }
706 
707 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
708 {
709   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
710   PetscBool      isequal = PETSC_FALSE;
711   PetscErrorCode ierr;
712 
713   PetscFunctionBegin;
714   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
715   if (pcbddc->NeumannBoundaries) {
716     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
717   }
718   /* last user setting takes precendence -> destroy any other customization */
719   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
720   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
721   pcbddc->NeumannBoundaries = NeumannBoundaries;
722   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
723   PetscFunctionReturn(0);
724 }
725 
726 /*@
727  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
728 
729    Collective
730 
731    Input Parameters:
732 +  pc - the preconditioning context
733 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
734 
735    Level: intermediate
736 
737    Notes:
738      Any process can list any global node
739 
740 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
741 @*/
742 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
743 {
744   PetscErrorCode ierr;
745 
746   PetscFunctionBegin;
747   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
748   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
749   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
750   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
751   PetscFunctionReturn(0);
752 }
753 
754 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
755 {
756   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
757   PetscBool      isequal = PETSC_FALSE;
758   PetscErrorCode ierr;
759 
760   PetscFunctionBegin;
761   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
762   if (pcbddc->NeumannBoundariesLocal) {
763     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
764   }
765   /* last user setting takes precendence -> destroy any other customization */
766   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
767   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
768   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
769   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
770   PetscFunctionReturn(0);
771 }
772 
773 /*@
774  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
775 
776    Collective
777 
778    Input Parameters:
779 +  pc - the preconditioning context
780 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
781 
782    Level: intermediate
783 
784    Notes:
785 
786 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
787 @*/
788 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
789 {
790   PetscErrorCode ierr;
791 
792   PetscFunctionBegin;
793   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
794   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
795   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
796   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
797   PetscFunctionReturn(0);
798 }
799 
800 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
801 {
802   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
803 
804   PetscFunctionBegin;
805   *DirichletBoundaries = pcbddc->DirichletBoundaries;
806   PetscFunctionReturn(0);
807 }
808 
809 /*@
810  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
811 
812    Collective
813 
814    Input Parameters:
815 .  pc - the preconditioning context
816 
817    Output Parameters:
818 .  DirichletBoundaries - index set defining the Dirichlet boundaries
819 
820    Level: intermediate
821 
822    Notes:
823      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
824 
825 .seealso: PCBDDC
826 @*/
827 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
828 {
829   PetscErrorCode ierr;
830 
831   PetscFunctionBegin;
832   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
833   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
834   PetscFunctionReturn(0);
835 }
836 
837 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
838 {
839   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
840 
841   PetscFunctionBegin;
842   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
843   PetscFunctionReturn(0);
844 }
845 
846 /*@
847  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
848 
849    Collective
850 
851    Input Parameters:
852 .  pc - the preconditioning context
853 
854    Output Parameters:
855 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
856 
857    Level: intermediate
858 
859    Notes:
860      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetDirichletBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetDirichletBoundaries).
861           In the latter case, the IS will be available after PCSetUp.
862 
863 .seealso: PCBDDC
864 @*/
865 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
866 {
867   PetscErrorCode ierr;
868 
869   PetscFunctionBegin;
870   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
871   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
872   PetscFunctionReturn(0);
873 }
874 
875 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
876 {
877   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
878 
879   PetscFunctionBegin;
880   *NeumannBoundaries = pcbddc->NeumannBoundaries;
881   PetscFunctionReturn(0);
882 }
883 
884 /*@
885  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
886 
887    Collective
888 
889    Input Parameters:
890 .  pc - the preconditioning context
891 
892    Output Parameters:
893 .  NeumannBoundaries - index set defining the Neumann boundaries
894 
895    Level: intermediate
896 
897    Notes:
898      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
899 
900 .seealso: PCBDDC
901 @*/
902 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
903 {
904   PetscErrorCode ierr;
905 
906   PetscFunctionBegin;
907   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
908   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
909   PetscFunctionReturn(0);
910 }
911 
912 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
913 {
914   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
915 
916   PetscFunctionBegin;
917   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
918   PetscFunctionReturn(0);
919 }
920 
921 /*@
922  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
923 
924    Collective
925 
926    Input Parameters:
927 .  pc - the preconditioning context
928 
929    Output Parameters:
930 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
931 
932    Level: intermediate
933 
934    Notes:
935      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetNeumannBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetNeumannBoundaries).
936           In the latter case, the IS will be available after PCSetUp.
937 
938 .seealso: PCBDDC
939 @*/
940 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
941 {
942   PetscErrorCode ierr;
943 
944   PetscFunctionBegin;
945   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
946   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
947   PetscFunctionReturn(0);
948 }
949 
950 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
951 {
952   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
953   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
954   PetscBool      same_data = PETSC_FALSE;
955   PetscErrorCode ierr;
956 
957   PetscFunctionBegin;
958   if (!nvtxs) {
959     if (copymode == PETSC_OWN_POINTER) {
960       ierr = PetscFree(xadj);CHKERRQ(ierr);
961       ierr = PetscFree(adjncy);CHKERRQ(ierr);
962     }
963     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
964     PetscFunctionReturn(0);
965   }
966   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
967     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
968     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
969       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
970       if (same_data) {
971         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
972       }
973     }
974   }
975   if (!same_data) {
976     /* free old CSR */
977     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
978     /* get CSR into graph structure */
979     if (copymode == PETSC_COPY_VALUES) {
980       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
981       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
982       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
983       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
984       mat_graph->freecsr = PETSC_TRUE;
985     } else if (copymode == PETSC_OWN_POINTER) {
986       mat_graph->xadj    = (PetscInt*)xadj;
987       mat_graph->adjncy  = (PetscInt*)adjncy;
988       mat_graph->freecsr = PETSC_TRUE;
989     } else if (copymode == PETSC_USE_POINTER) {
990       mat_graph->xadj    = (PetscInt*)xadj;
991       mat_graph->adjncy  = (PetscInt*)adjncy;
992       mat_graph->freecsr = PETSC_FALSE;
993     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %D",copymode);
994     mat_graph->nvtxs_csr = nvtxs;
995     pcbddc->recompute_topography = PETSC_TRUE;
996   }
997   PetscFunctionReturn(0);
998 }
999 
1000 /*@
1001  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
1002 
1003    Not collective
1004 
1005    Input Parameters:
1006 +  pc - the preconditioning context.
1007 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
1008 .  xadj, adjncy - the connectivity of the dofs in CSR format.
1009 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1010 
1011    Level: intermediate
1012 
1013    Notes: A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1014 
1015 .seealso: PCBDDC,PetscCopyMode
1016 @*/
1017 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1018 {
1019   void (*f)(void) = 0;
1020   PetscErrorCode ierr;
1021 
1022   PetscFunctionBegin;
1023   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1024   if (nvtxs) {
1025     PetscValidIntPointer(xadj,3);
1026     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1027   }
1028   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1029   /* free arrays if PCBDDC is not the PC type */
1030   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1031   if (!f && copymode == PETSC_OWN_POINTER) {
1032     ierr = PetscFree(xadj);CHKERRQ(ierr);
1033     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1034   }
1035   PetscFunctionReturn(0);
1036 }
1037 
1038 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1039 {
1040   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1041   PetscInt       i;
1042   PetscBool      isequal = PETSC_FALSE;
1043   PetscErrorCode ierr;
1044 
1045   PetscFunctionBegin;
1046   if (pcbddc->n_ISForDofsLocal == n_is) {
1047     for (i=0;i<n_is;i++) {
1048       PetscBool isequalt;
1049       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1050       if (!isequalt) break;
1051     }
1052     if (i == n_is) isequal = PETSC_TRUE;
1053   }
1054   for (i=0;i<n_is;i++) {
1055     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1056   }
1057   /* Destroy ISes if they were already set */
1058   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1059     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1060   }
1061   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1062   /* last user setting takes precendence -> destroy any other customization */
1063   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1064     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1065   }
1066   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1067   pcbddc->n_ISForDofs = 0;
1068   /* allocate space then set */
1069   if (n_is) {
1070     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1071   }
1072   for (i=0;i<n_is;i++) {
1073     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1074   }
1075   pcbddc->n_ISForDofsLocal = n_is;
1076   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1077   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1078   PetscFunctionReturn(0);
1079 }
1080 
1081 /*@
1082  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1083 
1084    Collective
1085 
1086    Input Parameters:
1087 +  pc - the preconditioning context
1088 .  n_is - number of index sets defining the fields
1089 -  ISForDofs - array of IS describing the fields in local ordering
1090 
1091    Level: intermediate
1092 
1093    Notes:
1094      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1095 
1096 .seealso: PCBDDC
1097 @*/
1098 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1099 {
1100   PetscInt       i;
1101   PetscErrorCode ierr;
1102 
1103   PetscFunctionBegin;
1104   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1105   PetscValidLogicalCollectiveInt(pc,n_is,2);
1106   for (i=0;i<n_is;i++) {
1107     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1108     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1109   }
1110   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1111   PetscFunctionReturn(0);
1112 }
1113 
1114 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1115 {
1116   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1117   PetscInt       i;
1118   PetscBool      isequal = PETSC_FALSE;
1119   PetscErrorCode ierr;
1120 
1121   PetscFunctionBegin;
1122   if (pcbddc->n_ISForDofs == n_is) {
1123     for (i=0;i<n_is;i++) {
1124       PetscBool isequalt;
1125       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1126       if (!isequalt) break;
1127     }
1128     if (i == n_is) isequal = PETSC_TRUE;
1129   }
1130   for (i=0;i<n_is;i++) {
1131     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1132   }
1133   /* Destroy ISes if they were already set */
1134   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1135     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1136   }
1137   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1138   /* last user setting takes precendence -> destroy any other customization */
1139   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1140     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1141   }
1142   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1143   pcbddc->n_ISForDofsLocal = 0;
1144   /* allocate space then set */
1145   if (n_is) {
1146     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1147   }
1148   for (i=0;i<n_is;i++) {
1149     pcbddc->ISForDofs[i] = ISForDofs[i];
1150   }
1151   pcbddc->n_ISForDofs = n_is;
1152   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1153   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1154   PetscFunctionReturn(0);
1155 }
1156 
1157 /*@
1158  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1159 
1160    Collective
1161 
1162    Input Parameters:
1163 +  pc - the preconditioning context
1164 .  n_is - number of index sets defining the fields
1165 -  ISForDofs - array of IS describing the fields in global ordering
1166 
1167    Level: intermediate
1168 
1169    Notes:
1170      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1171 
1172 .seealso: PCBDDC
1173 @*/
1174 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1175 {
1176   PetscInt       i;
1177   PetscErrorCode ierr;
1178 
1179   PetscFunctionBegin;
1180   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1181   PetscValidLogicalCollectiveInt(pc,n_is,2);
1182   for (i=0;i<n_is;i++) {
1183     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1184     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1185   }
1186   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1187   PetscFunctionReturn(0);
1188 }
1189 
1190 /*
1191    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1192                      guess if a transformation of basis approach has been selected.
1193 
1194    Input Parameter:
1195 +  pc - the preconditioner contex
1196 
1197    Application Interface Routine: PCPreSolve()
1198 
1199    Notes:
1200      The interface routine PCPreSolve() is not usually called directly by
1201    the user, but instead is called by KSPSolve().
1202 */
1203 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1204 {
1205   PetscErrorCode ierr;
1206   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1207   PC_IS          *pcis = (PC_IS*)(pc->data);
1208   Vec            used_vec;
1209   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1210 
1211   PetscFunctionBegin;
1212   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1213   if (ksp) {
1214     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1215     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1216     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1217     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1218     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1219     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1220       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1221     }
1222   }
1223   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1224     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1225   }
1226 
1227   /* Creates parallel work vectors used in presolve */
1228   if (!pcbddc->original_rhs) {
1229     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1230   }
1231   if (!pcbddc->temp_solution) {
1232     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1233   }
1234 
1235   pcbddc->temp_solution_used = PETSC_FALSE;
1236   if (x) {
1237     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1238     used_vec = x;
1239   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1240     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1241     used_vec = pcbddc->temp_solution;
1242     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1243     pcbddc->temp_solution_used = PETSC_TRUE;
1244     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1245     save_rhs = PETSC_FALSE;
1246     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1247   }
1248 
1249   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1250   if (ksp) {
1251     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1252     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1253     if (!pcbddc->ksp_guess_nonzero) {
1254       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1255     }
1256   }
1257 
1258   pcbddc->rhs_change = PETSC_FALSE;
1259   /* Take into account zeroed rows -> change rhs and store solution removed */
1260   if (rhs && pcbddc->eliminate_dirdofs) {
1261     IS dirIS = NULL;
1262 
1263     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1264     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1265     if (dirIS) {
1266       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1267       PetscInt          dirsize,i,*is_indices;
1268       PetscScalar       *array_x;
1269       const PetscScalar *array_diagonal;
1270 
1271       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1272       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1273       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1274       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1275       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1276       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1277       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1278       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1279       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1280       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1281       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1282       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1283       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1284       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1285       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1286       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1287       pcbddc->rhs_change = PETSC_TRUE;
1288       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1289     }
1290   }
1291 
1292   /* remove the computed solution or the initial guess from the rhs */
1293   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1294     /* save the original rhs */
1295     if (save_rhs) {
1296       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1297       save_rhs = PETSC_FALSE;
1298     }
1299     pcbddc->rhs_change = PETSC_TRUE;
1300     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1301     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1302     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1303     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1304     pcbddc->temp_solution_used = PETSC_TRUE;
1305     if (ksp) {
1306       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1307     }
1308   }
1309   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1310 
1311   /* compute initial vector in benign space if needed
1312      and remove non-benign solution from the rhs */
1313   benign_correction_computed = PETSC_FALSE;
1314   if (rhs && pcbddc->benign_compute_correction && pcbddc->benign_have_null) {
1315     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1316        Recursively apply BDDC in the multilevel case */
1317     if (!pcbddc->benign_vec) {
1318       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1319     }
1320     pcbddc->benign_apply_coarse_only = PETSC_TRUE;
1321     if (!pcbddc->benign_skip_correction) {
1322       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1323       benign_correction_computed = PETSC_TRUE;
1324       if (pcbddc->temp_solution_used) {
1325         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1326       }
1327       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1328       /* store the original rhs if not done earlier */
1329       if (save_rhs) {
1330         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1331       }
1332       if (pcbddc->rhs_change) {
1333         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1334       } else {
1335         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1336       }
1337       pcbddc->rhs_change = PETSC_TRUE;
1338     }
1339     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1340   }
1341 
1342   /* dbg output */
1343   if (pcbddc->dbg_flag && benign_correction_computed) {
1344     Vec v;
1345     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1346     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1347     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1348     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1349     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc)));CHKERRQ(ierr);
1350     ierr = VecDestroy(&v);CHKERRQ(ierr);
1351   }
1352 
1353   /* set initial guess if using PCG */
1354   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1355   if (x && pcbddc->use_exact_dirichlet_trick) {
1356     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1357     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1358       if (benign_correction_computed) { /* we have already saved the changed rhs */
1359         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1360       } else {
1361         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1362       }
1363       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1364       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1365     } else {
1366       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1367       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1368     }
1369     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1370     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1371       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1372       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1373       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1374       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1375     } else {
1376       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1377       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1378     }
1379     if (ksp) {
1380       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1381     }
1382     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1383   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1384     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1385   }
1386   PetscFunctionReturn(0);
1387 }
1388 
1389 /*
1390    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1391                      approach has been selected. Also, restores rhs to its original state.
1392 
1393    Input Parameter:
1394 +  pc - the preconditioner contex
1395 
1396    Application Interface Routine: PCPostSolve()
1397 
1398    Notes:
1399      The interface routine PCPostSolve() is not usually called directly by
1400      the user, but instead is called by KSPSolve().
1401 */
1402 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1403 {
1404   PetscErrorCode ierr;
1405   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1406 
1407   PetscFunctionBegin;
1408   /* add solution removed in presolve */
1409   if (x && pcbddc->rhs_change) {
1410     if (pcbddc->temp_solution_used) {
1411       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1412     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1413       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1414     }
1415     /* restore to original state (not for FETI-DP) */
1416     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1417   }
1418 
1419   /* restore rhs to its original state (not needed for FETI-DP) */
1420   if (rhs && pcbddc->rhs_change) {
1421     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1422     pcbddc->rhs_change = PETSC_FALSE;
1423   }
1424   /* restore ksp guess state */
1425   if (ksp) {
1426     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1427     /* reset flag for exact dirichlet trick */
1428     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1429   }
1430   PetscFunctionReturn(0);
1431 }
1432 
1433 /*
1434    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1435                   by setting data structures and options.
1436 
1437    Input Parameter:
1438 +  pc - the preconditioner context
1439 
1440    Application Interface Routine: PCSetUp()
1441 
1442    Notes:
1443      The interface routine PCSetUp() is not usually called directly by
1444      the user, but instead is called by PCApply() if necessary.
1445 */
1446 PetscErrorCode PCSetUp_BDDC(PC pc)
1447 {
1448   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1449   PCBDDCSubSchurs sub_schurs;
1450   Mat_IS*         matis;
1451   MatNullSpace    nearnullspace;
1452   Mat             lA;
1453   IS              lP,zerodiag = NULL;
1454   PetscInt        nrows,ncols;
1455   PetscBool       computesubschurs;
1456   PetscBool       computeconstraintsmatrix;
1457   PetscBool       new_nearnullspace_provided,ismatis;
1458   PetscErrorCode  ierr;
1459 
1460   PetscFunctionBegin;
1461   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1462   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1463   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1464   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1465   matis = (Mat_IS*)pc->pmat->data;
1466   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1467   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1468      Also, BDDC builds its own KSP for the Dirichlet problem */
1469   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) pcbddc->recompute_topography = PETSC_TRUE;
1470   if (pcbddc->recompute_topography) {
1471     pcbddc->graphanalyzed    = PETSC_FALSE;
1472     computeconstraintsmatrix = PETSC_TRUE;
1473   } else {
1474     computeconstraintsmatrix = PETSC_FALSE;
1475   }
1476 
1477   /* check parameters' compatibility */
1478   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1479   pcbddc->adaptive_selection = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1480   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1481   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1482 
1483   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1484   if (pcbddc->switch_static) {
1485     PetscBool ismatis;
1486     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1487     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1488   }
1489 
1490   /* activate all connected components if the netflux has been requested */
1491   if (pcbddc->compute_nonetflux) {
1492     pcbddc->use_vertices = PETSC_TRUE;
1493     pcbddc->use_edges = PETSC_TRUE;
1494     pcbddc->use_faces = PETSC_TRUE;
1495   }
1496 
1497   /* Get stdout for dbg */
1498   if (pcbddc->dbg_flag) {
1499     if (!pcbddc->dbg_viewer) {
1500       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1501       ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1502     }
1503     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1504   }
1505 
1506   /* process topology information */
1507   if (pcbddc->recompute_topography) {
1508     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1509     if (pcbddc->discretegradient) {
1510       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1511     }
1512   }
1513 
1514   /* change basis if requested by the user */
1515   if (pcbddc->user_ChangeOfBasisMatrix) {
1516     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1517     pcbddc->use_change_of_basis = PETSC_FALSE;
1518     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1519   } else {
1520     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1521     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1522     pcbddc->local_mat = matis->A;
1523   }
1524 
1525   /*
1526      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1527      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1528   */
1529   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1530   if (pcbddc->benign_saddle_point) {
1531     PC_IS* pcis = (PC_IS*)pc->data;
1532 
1533     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1534     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1535     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1536     /* pop B0 mat from local mat */
1537     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1538     /* give pcis a hint to not reuse submatrices during PCISCreate */
1539     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1540       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1541         pcis->reusesubmatrices = PETSC_FALSE;
1542       } else {
1543         pcis->reusesubmatrices = PETSC_TRUE;
1544       }
1545     } else {
1546       pcis->reusesubmatrices = PETSC_FALSE;
1547     }
1548   }
1549 
1550   /* propagate relevant information -> TODO remove*/
1551 #if !defined(PETSC_USE_COMPLEX) /* workaround for reals */
1552   if (matis->A->symmetric_set) {
1553     ierr = MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);CHKERRQ(ierr);
1554   }
1555 #endif
1556   if (matis->A->symmetric_set) {
1557     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1558   }
1559   if (matis->A->spd_set) {
1560     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1561   }
1562 
1563   /* Set up all the "iterative substructuring" common block without computing solvers */
1564   {
1565     Mat temp_mat;
1566 
1567     temp_mat = matis->A;
1568     matis->A = pcbddc->local_mat;
1569     ierr = PCISSetUp(pc,PETSC_FALSE);CHKERRQ(ierr);
1570     pcbddc->local_mat = matis->A;
1571     matis->A = temp_mat;
1572   }
1573 
1574   /* Analyze interface */
1575   if (!pcbddc->graphanalyzed) {
1576     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1577     computeconstraintsmatrix = PETSC_TRUE;
1578     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1579       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1580     }
1581     if (pcbddc->compute_nonetflux) {
1582       MatNullSpace nnfnnsp;
1583 
1584       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1585       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1586       /* TODO what if a nearnullspace is already attached? */
1587       ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1588       ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1589     }
1590   }
1591 
1592   /* check existence of a divergence free extension, i.e.
1593      b(v_I,p_0) = 0 for all v_I (raise error if not).
1594      Also, check that PCBDDCBenignGetOrSetP0 works */
1595   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1596     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1597   }
1598   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1599 
1600   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1601   if (computesubschurs && pcbddc->recompute_topography) {
1602     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1603   }
1604   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1605   if (!pcbddc->use_deluxe_scaling) {
1606     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1607   }
1608 
1609   /* finish setup solvers and do adaptive selection of constraints */
1610   sub_schurs = pcbddc->sub_schurs;
1611   if (sub_schurs && sub_schurs->schur_explicit) {
1612     if (computesubschurs) {
1613       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1614     }
1615     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1616   } else {
1617     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1618     if (computesubschurs) {
1619       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1620     }
1621   }
1622   if (pcbddc->adaptive_selection) {
1623     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1624     computeconstraintsmatrix = PETSC_TRUE;
1625   }
1626 
1627   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1628   new_nearnullspace_provided = PETSC_FALSE;
1629   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1630   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1631     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1632       new_nearnullspace_provided = PETSC_TRUE;
1633     } else {
1634       /* determine if the two nullspaces are different (should be lightweight) */
1635       if (nearnullspace != pcbddc->onearnullspace) {
1636         new_nearnullspace_provided = PETSC_TRUE;
1637       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1638         PetscInt         i;
1639         const Vec        *nearnullvecs;
1640         PetscObjectState state;
1641         PetscInt         nnsp_size;
1642         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1643         for (i=0;i<nnsp_size;i++) {
1644           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1645           if (pcbddc->onearnullvecs_state[i] != state) {
1646             new_nearnullspace_provided = PETSC_TRUE;
1647             break;
1648           }
1649         }
1650       }
1651     }
1652   } else {
1653     if (!nearnullspace) { /* both nearnullspaces are null */
1654       new_nearnullspace_provided = PETSC_FALSE;
1655     } else { /* nearnullspace attached later */
1656       new_nearnullspace_provided = PETSC_TRUE;
1657     }
1658   }
1659 
1660   /* Setup constraints and related work vectors */
1661   /* reset primal space flags */
1662   pcbddc->new_primal_space = PETSC_FALSE;
1663   pcbddc->new_primal_space_local = PETSC_FALSE;
1664   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1665     /* It also sets the primal space flags */
1666     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1667   }
1668   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1669   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1670 
1671   if (pcbddc->use_change_of_basis) {
1672     PC_IS *pcis = (PC_IS*)(pc->data);
1673 
1674     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1675     if (pcbddc->benign_change) {
1676       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1677       /* pop B0 from pcbddc->local_mat */
1678       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1679     }
1680     /* get submatrices */
1681     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1682     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1683     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1684     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1685     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1686     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1687     /* set flag in pcis to not reuse submatrices during PCISCreate */
1688     pcis->reusesubmatrices = PETSC_FALSE;
1689   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1690     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1691     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1692     pcbddc->local_mat = matis->A;
1693   }
1694 
1695   /* interface pressure block row for B_C */
1696   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1697   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1698   if (lA && lP) {
1699     PC_IS*    pcis = (PC_IS*)pc->data;
1700     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1701     PetscBool issym;
1702     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1703     if (issym) {
1704       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1705       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1706       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1707       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1708     } else {
1709       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1710       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1711       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1712       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1713     }
1714     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1715     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1716     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1717     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1718     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1719     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1720     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1721     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1722   }
1723 
1724   /* SetUp coarse and local Neumann solvers */
1725   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1726   /* SetUp Scaling operator */
1727   if (pcbddc->use_deluxe_scaling) {
1728     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1729   }
1730 
1731   /* mark topography as done */
1732   pcbddc->recompute_topography = PETSC_FALSE;
1733 
1734   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1735   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1736 
1737   if (pcbddc->dbg_flag) {
1738     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1739   }
1740   PetscFunctionReturn(0);
1741 }
1742 
1743 /*
1744    PCApply_BDDC - Applies the BDDC operator to a vector.
1745 
1746    Input Parameters:
1747 +  pc - the preconditioner context
1748 -  r - input vector (global)
1749 
1750    Output Parameter:
1751 .  z - output vector (global)
1752 
1753    Application Interface Routine: PCApply()
1754  */
1755 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1756 {
1757   PC_IS             *pcis = (PC_IS*)(pc->data);
1758   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1759   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1760   PetscErrorCode    ierr;
1761   const PetscScalar one = 1.0;
1762   const PetscScalar m_one = -1.0;
1763   const PetscScalar zero = 0.0;
1764 
1765 /* This code is similar to that provided in nn.c for PCNN
1766    NN interface preconditioner changed to BDDC
1767    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1768 
1769   PetscFunctionBegin;
1770   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1771   if (pcbddc->ChangeOfBasisMatrix) {
1772     Vec swap;
1773 
1774     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1775     swap = pcbddc->work_change;
1776     pcbddc->work_change = r;
1777     r = swap;
1778     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1779     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1780       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1781       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1782     }
1783   }
1784   if (pcbddc->benign_have_null) { /* get p0 from r */
1785     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1786   }
1787   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1788     ierr = VecCopy(r,z);CHKERRQ(ierr);
1789     /* First Dirichlet solve */
1790     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1791     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1792     /*
1793       Assembling right hand side for BDDC operator
1794       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1795       - pcis->vec1_B the interface part of the global vector z
1796     */
1797     if (n_D) {
1798       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1799       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1800       if (pcbddc->switch_static) {
1801         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1802 
1803         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1804         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1805         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1806         if (!pcbddc->switch_static_change) {
1807           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1808         } else {
1809           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1810           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1811           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1812         }
1813         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1814         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1815         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1816         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1817       } else {
1818         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1819       }
1820     } else {
1821       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1822     }
1823     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1824     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1825     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1826   } else {
1827     if (!pcbddc->benign_apply_coarse_only) {
1828       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1829     }
1830   }
1831 
1832   /* Apply interface preconditioner
1833      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1834   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1835 
1836   /* Apply transpose of partition of unity operator */
1837   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1838 
1839   /* Second Dirichlet solve and assembling of output */
1840   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1841   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1842   if (n_B) {
1843     if (pcbddc->switch_static) {
1844       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1845 
1846       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1847       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1848       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1849       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1850       if (!pcbddc->switch_static_change) {
1851         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1852       } else {
1853         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1854         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1855         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1856       }
1857       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1858       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1859     } else {
1860       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1861     }
1862   } else if (pcbddc->switch_static) { /* n_B is zero */
1863     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1864 
1865     if (!pcbddc->switch_static_change) {
1866       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1867     } else {
1868       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1869       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1870       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
1871     }
1872   }
1873   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1874 
1875   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1876     if (pcbddc->switch_static) {
1877       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1878     } else {
1879       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1880     }
1881     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1882     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1883   } else {
1884     if (pcbddc->switch_static) {
1885       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1886     } else {
1887       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1888     }
1889     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1890     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1891   }
1892   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
1893     if (pcbddc->benign_apply_coarse_only) {
1894       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
1895     }
1896     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1897   }
1898 
1899   if (pcbddc->ChangeOfBasisMatrix) {
1900     pcbddc->work_change = r;
1901     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
1902     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
1903   }
1904   PetscFunctionReturn(0);
1905 }
1906 
1907 /*
1908    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1909 
1910    Input Parameters:
1911 +  pc - the preconditioner context
1912 -  r - input vector (global)
1913 
1914    Output Parameter:
1915 .  z - output vector (global)
1916 
1917    Application Interface Routine: PCApplyTranspose()
1918  */
1919 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1920 {
1921   PC_IS             *pcis = (PC_IS*)(pc->data);
1922   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1923   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1924   PetscErrorCode    ierr;
1925   const PetscScalar one = 1.0;
1926   const PetscScalar m_one = -1.0;
1927   const PetscScalar zero = 0.0;
1928 
1929   PetscFunctionBegin;
1930   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1931   if (pcbddc->ChangeOfBasisMatrix) {
1932     Vec swap;
1933 
1934     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1935     swap = pcbddc->work_change;
1936     pcbddc->work_change = r;
1937     r = swap;
1938     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1939     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
1940       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1941       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1942     }
1943   }
1944   if (pcbddc->benign_have_null) { /* get p0 from r */
1945     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1946   }
1947   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1948     ierr = VecCopy(r,z);CHKERRQ(ierr);
1949     /* First Dirichlet solve */
1950     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1951     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1952     /*
1953       Assembling right hand side for BDDC operator
1954       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1955       - pcis->vec1_B the interface part of the global vector z
1956     */
1957     if (n_D) {
1958       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1959       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1960       if (pcbddc->switch_static) {
1961         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1962 
1963         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1964         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1965         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1966         if (!pcbddc->switch_static_change) {
1967           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1968         } else {
1969           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1970           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1971           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1972         }
1973         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1974         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1975         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1976         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1977       } else {
1978         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1979       }
1980     } else {
1981       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1982     }
1983     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1984     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1985     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1986   } else {
1987     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1988   }
1989 
1990   /* Apply interface preconditioner
1991      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1992   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
1993 
1994   /* Apply transpose of partition of unity operator */
1995   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1996 
1997   /* Second Dirichlet solve and assembling of output */
1998   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1999   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2000   if (n_B) {
2001     if (pcbddc->switch_static) {
2002       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2003 
2004       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2005       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2006       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2007       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2008       if (!pcbddc->switch_static_change) {
2009         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2010       } else {
2011         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2012         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2013         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2014       }
2015       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2016       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2017     } else {
2018       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2019     }
2020   } else if (pcbddc->switch_static) { /* n_B is zero */
2021     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2022 
2023     if (!pcbddc->switch_static_change) {
2024       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2025     } else {
2026       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2027       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2028       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2029     }
2030   }
2031   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2032   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2033     if (pcbddc->switch_static) {
2034       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2035     } else {
2036       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2037     }
2038     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2039     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2040   } else {
2041     if (pcbddc->switch_static) {
2042       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2043     } else {
2044       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2045     }
2046     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2047     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2048   }
2049   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2050     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2051   }
2052   if (pcbddc->ChangeOfBasisMatrix) {
2053     pcbddc->work_change = r;
2054     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2055     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2056   }
2057   PetscFunctionReturn(0);
2058 }
2059 
2060 PetscErrorCode PCReset_BDDC(PC pc)
2061 {
2062   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2063   PC_IS          *pcis = (PC_IS*)pc->data;
2064   KSP            kspD,kspR,kspC;
2065   PetscErrorCode ierr;
2066 
2067   PetscFunctionBegin;
2068   /* free BDDC custom data  */
2069   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2070   /* destroy objects related to topography */
2071   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2072   /* destroy objects for scaling operator */
2073   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2074   /* free solvers stuff */
2075   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2076   /* free global vectors needed in presolve */
2077   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2078   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2079   /* free data created by PCIS */
2080   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2081 
2082   /* restore defaults */
2083   kspD = pcbddc->ksp_D;
2084   kspR = pcbddc->ksp_R;
2085   kspC = pcbddc->coarse_ksp;
2086   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2087   pcis->n_neigh                     = -1;
2088   pcis->scaling_factor              = 1.0;
2089   pcis->reusesubmatrices            = PETSC_TRUE;
2090   pcbddc->use_local_adj             = PETSC_TRUE;
2091   pcbddc->use_vertices              = PETSC_TRUE;
2092   pcbddc->use_edges                 = PETSC_TRUE;
2093   pcbddc->symmetric_primal          = PETSC_TRUE;
2094   pcbddc->vertex_size               = 1;
2095   pcbddc->recompute_topography      = PETSC_TRUE;
2096   pcbddc->coarse_size               = -1;
2097   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2098   pcbddc->coarsening_ratio          = 8;
2099   pcbddc->coarse_eqs_per_proc       = 1;
2100   pcbddc->benign_compute_correction = PETSC_TRUE;
2101   pcbddc->nedfield                  = -1;
2102   pcbddc->nedglobal                 = PETSC_TRUE;
2103   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2104   pcbddc->sub_schurs_layers         = -1;
2105   pcbddc->ksp_D                     = kspD;
2106   pcbddc->ksp_R                     = kspR;
2107   pcbddc->coarse_ksp                = kspC;
2108   PetscFunctionReturn(0);
2109 }
2110 
2111 PetscErrorCode PCDestroy_BDDC(PC pc)
2112 {
2113   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2114   PetscErrorCode ierr;
2115 
2116   PetscFunctionBegin;
2117   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2118   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2119   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2120   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2121   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2122   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2123   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2124   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2125   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2126   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2127   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2128   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2129   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2130   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2131   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2132   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2133   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2134   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2135   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2136   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2137   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2138   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2139   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2140   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2141   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2142   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2143   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2144   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2145   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2146   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2147   PetscFunctionReturn(0);
2148 }
2149 
2150 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2151 {
2152   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2153   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2154   PetscErrorCode ierr;
2155 
2156   PetscFunctionBegin;
2157   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2158   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2159   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2160   mat_graph->cnloc = nloc;
2161   mat_graph->cdim  = dim;
2162   mat_graph->cloc  = PETSC_FALSE;
2163   PetscFunctionReturn(0);
2164 }
2165 
2166 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2167 {
2168   PetscFunctionBegin;
2169   *change = PETSC_TRUE;
2170   PetscFunctionReturn(0);
2171 }
2172 
2173 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2174 {
2175   FETIDPMat_ctx  mat_ctx;
2176   Vec            work;
2177   PC_IS*         pcis;
2178   PC_BDDC*       pcbddc;
2179   PetscErrorCode ierr;
2180 
2181   PetscFunctionBegin;
2182   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2183   pcis = (PC_IS*)mat_ctx->pc->data;
2184   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2185 
2186   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2187   /* copy rhs since we may change it during PCPreSolve_BDDC */
2188   if (!pcbddc->original_rhs) {
2189     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2190   }
2191   if (mat_ctx->rhs_flip) {
2192     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2193   } else {
2194     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2195   }
2196   if (mat_ctx->g2g_p) {
2197     /* interface pressure rhs */
2198     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2199     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2200     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2201     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2202     if (!mat_ctx->rhs_flip) {
2203       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2204     }
2205   }
2206   /*
2207      change of basis for physical rhs if needed
2208      It also changes the rhs in case of dirichlet boundaries
2209   */
2210   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2211   if (pcbddc->ChangeOfBasisMatrix) {
2212     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2213     work = pcbddc->work_change;
2214    } else {
2215     work = pcbddc->original_rhs;
2216   }
2217   /* store vectors for computation of fetidp final solution */
2218   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2219   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2220   /* scale rhs since it should be unassembled */
2221   /* TODO use counter scaling? (also below) */
2222   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2223   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2224   /* Apply partition of unity */
2225   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2226   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2227   if (!pcbddc->switch_static) {
2228     /* compute partially subassembled Schur complement right-hand side */
2229     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2230     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2231     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2232     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2233     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2234     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2235     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2236     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2237     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2238     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2239   }
2240   /* BDDC rhs */
2241   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2242   if (pcbddc->switch_static) {
2243     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2244   }
2245   /* apply BDDC */
2246   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2247   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2248   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2249 
2250   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2251   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2252   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2253   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2254   /* Add contribution to interface pressures */
2255   if (mat_ctx->l2g_p) {
2256     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2257     if (pcbddc->switch_static) {
2258       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2259     }
2260     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2261     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2262   }
2263   PetscFunctionReturn(0);
2264 }
2265 
2266 /*@
2267  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2268 
2269    Collective
2270 
2271    Input Parameters:
2272 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2273 -  standard_rhs    - the right-hand side of the original linear system
2274 
2275    Output Parameters:
2276 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2277 
2278    Level: developer
2279 
2280    Notes:
2281 
2282 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2283 @*/
2284 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2285 {
2286   FETIDPMat_ctx  mat_ctx;
2287   PetscErrorCode ierr;
2288 
2289   PetscFunctionBegin;
2290   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2291   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2292   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2293   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2294   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2295   PetscFunctionReturn(0);
2296 }
2297 
2298 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2299 {
2300   FETIDPMat_ctx  mat_ctx;
2301   PC_IS*         pcis;
2302   PC_BDDC*       pcbddc;
2303   PetscErrorCode ierr;
2304   Vec            work;
2305 
2306   PetscFunctionBegin;
2307   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2308   pcis = (PC_IS*)mat_ctx->pc->data;
2309   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2310 
2311   /* apply B_delta^T */
2312   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2313   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2314   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2315   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2316   if (mat_ctx->l2g_p) {
2317     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2318     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2319     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2320   }
2321 
2322   /* compute rhs for BDDC application */
2323   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2324   if (pcbddc->switch_static) {
2325     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2326     if (mat_ctx->l2g_p) {
2327       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2328       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2329     }
2330   }
2331 
2332   /* apply BDDC */
2333   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2334   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2335 
2336   /* put values into global vector */
2337   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2338   else work = standard_sol;
2339   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2340   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2341   if (!pcbddc->switch_static) {
2342     /* compute values into the interior if solved for the partially subassembled Schur complement */
2343     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2344     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2345     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2346   }
2347 
2348   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2349   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2350   /* add p0 solution to final solution */
2351   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2352   if (pcbddc->ChangeOfBasisMatrix) {
2353     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2354   }
2355   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2356   if (mat_ctx->g2g_p) {
2357     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2358     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2359   }
2360   PetscFunctionReturn(0);
2361 }
2362 
2363 /*@
2364  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2365 
2366    Collective
2367 
2368    Input Parameters:
2369 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2370 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2371 
2372    Output Parameters:
2373 .  standard_sol    - the solution defined on the physical domain
2374 
2375    Level: developer
2376 
2377    Notes:
2378 
2379 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2380 @*/
2381 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2382 {
2383   FETIDPMat_ctx  mat_ctx;
2384   PetscErrorCode ierr;
2385 
2386   PetscFunctionBegin;
2387   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2388   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2389   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2390   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2391   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2392   PetscFunctionReturn(0);
2393 }
2394 
2395 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2396 {
2397 
2398   FETIDPMat_ctx  fetidpmat_ctx;
2399   Mat            newmat;
2400   FETIDPPC_ctx   fetidppc_ctx;
2401   PC             newpc;
2402   MPI_Comm       comm;
2403   PetscErrorCode ierr;
2404 
2405   PetscFunctionBegin;
2406   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2407   /* FETIDP linear matrix */
2408   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2409   fetidpmat_ctx->fully_redundant = fully_redundant;
2410   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2411   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2412   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2413   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2414   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2415   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2416   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2417   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2418   /* FETIDP preconditioner */
2419   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2420   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2421   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2422   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2423   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2424   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2425   if (!fetidpmat_ctx->l2g_lambda_only) {
2426     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2427     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2428     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2429     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2430     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2431     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2432   } else {
2433     KSP      *ksps;
2434     PC       lagpc;
2435     Mat      M,AM,PM;
2436     PetscInt nn;
2437 
2438     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2439     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2440     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2441     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2442     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2443     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2444     ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2445     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2446     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2447     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2448 
2449     /* set the solver for the (0,0) block */
2450     ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2451     ierr = PCCreate(comm,&lagpc);CHKERRQ(ierr);
2452     ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2453     ierr = KSPGetOperators(ksps[0],&AM,&PM);CHKERRQ(ierr);
2454     ierr = PCSetOperators(lagpc,AM,PM);CHKERRQ(ierr);
2455     ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2456     ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2457     ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2458     ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2459     ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2460     ierr = KSPSetPC(ksps[0],lagpc);CHKERRQ(ierr);
2461     ierr = PCDestroy(&lagpc);CHKERRQ(ierr);
2462     ierr = PetscFree(ksps);CHKERRQ(ierr);
2463   }
2464   /* return pointers for objects created */
2465   *fetidp_mat = newmat;
2466   *fetidp_pc = newpc;
2467   PetscFunctionReturn(0);
2468 }
2469 
2470 /*@C
2471  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2472 
2473    Collective
2474 
2475    Input Parameters:
2476 +  pc - the BDDC preconditioning context (setup should have been called before)
2477 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2478 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2479 
2480    Output Parameters:
2481 +  fetidp_mat - shell FETI-DP matrix object
2482 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2483 
2484    Level: developer
2485 
2486    Notes:
2487      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2488 
2489 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2490 @*/
2491 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2492 {
2493   PetscErrorCode ierr;
2494 
2495   PetscFunctionBegin;
2496   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2497   if (pc->setupcalled) {
2498     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2499   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2500   PetscFunctionReturn(0);
2501 }
2502 /* -------------------------------------------------------------------------- */
2503 /*MC
2504    PCBDDC - Balancing Domain Decomposition by Constraints.
2505 
2506    An implementation of the BDDC preconditioner based on
2507 
2508 .vb
2509    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2510    [2] A. Klawonn and O. B. Widlund. "Dual-Primal FETI Methods for Linear Elasticity", http://cs.nyu.edu/csweb/Research/TechReports/TR2004-855/TR2004-855.pdf
2511    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2512    [4] C. Pechstein and C. R. Dohrmann. "Modern domain decomposition methods BDDC, deluxe scaling, and an algebraic approach", Seminar talk, Linz, December 2013, http://people.ricam.oeaw.ac.at/c.pechstein/pechstein-bddc2013.pdf
2513 .ve
2514 
2515    The matrix to be preconditioned (Pmat) must be of type MATIS.
2516 
2517    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2518 
2519    It also works with unsymmetric and indefinite problems.
2520 
2521    Unlike 'conventional' interface preconditioners, PCBDDC iterates over all degrees of freedom, not just those on the interface. This allows the use of approximate solvers on the subdomains.
2522 
2523    Approximate local solvers are automatically adapted (see [1]) if the user has attached a nullspace object to the subdomain matrices, and informed BDDC of using approximate solvers (via the command line).
2524 
2525    Boundary nodes are split in vertices, edges and faces classes using information from the local to global mapping of dofs and the local connectivity graph of nodes. The latter can be customized by using PCBDDCSetLocalAdjacencyGraph()
2526    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2527 
2528    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2529 
2530    Change of basis is performed similarly to [2] when requested. When more than one constraint is present on a single connected component (i.e. an edge or a face), a robust method based on local QR factorizations is used.
2531    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2532 
2533    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2534 
2535    Adaptive selection of primal constraints [4] is supported for SPD systems with high-contrast in the coefficients if MUMPS or MKL_PARDISO are present. Future versions of the code will also consider using PASTIX.
2536 
2537    An experimental interface to the FETI-DP method is available. FETI-DP operators could be created using PCBDDCCreateFETIDPOperators(). A stand-alone class for the FETI-DP method will be provided in the next releases.
2538    Deluxe scaling is not supported yet for FETI-DP.
2539 
2540    Options Database Keys (some of them, run with -h for a complete list):
2541 
2542 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2543 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2544 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2545 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2546 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2547 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2548 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2549 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2550 .    -pc_bddc_coarsening_ratio <8> - number of subdomains which will be aggregated together at the coarser level (e.g. H/h ratio at the coarser level, significative only in the multilevel case)
2551 .    -pc_bddc_coarse_redistribute <0> - size of a subset of processors where the coarse problem will be remapped (the value is ignored if not at the coarsest level)
2552 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2553 .    -pc_bddc_schur_layers <-1> - select the economic version of deluxe scaling by specifying the number of layers (-1 corresponds to the original deluxe scaling)
2554 .    -pc_bddc_adaptive_threshold <0.0> - when a value different than zero is specified, adaptive selection of constraints is performed on edges and faces (requires deluxe scaling and MUMPS or MKL_PARDISO installed)
2555 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2556 
2557    Options for Dirichlet, Neumann or coarse solver can be set with
2558 .vb
2559       -pc_bddc_dirichlet_
2560       -pc_bddc_neumann_
2561       -pc_bddc_coarse_
2562 .ve
2563    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2564 
2565    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2566 .vb
2567       -pc_bddc_dirichlet_lN_
2568       -pc_bddc_neumann_lN_
2569       -pc_bddc_coarse_lN_
2570 .ve
2571    Note that level number ranges from the finest (0) to the coarsest (N).
2572    In order to specify options for the BDDC operators at the coarser levels (and not for the solvers), prepend -pc_bddc_coarse_ or -pc_bddc_coarse_l to the option, e.g.
2573 .vb
2574      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2575 .ve
2576    will use a threshold of 5 for constraints' selection at the first coarse level and will redistribute the coarse problem of the first coarse level on 3 processors
2577 
2578    Level: intermediate
2579 
2580    Developer notes:
2581 
2582    Contributed by Stefano Zampini
2583 
2584 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2585 M*/
2586 
2587 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2588 {
2589   PetscErrorCode      ierr;
2590   PC_BDDC             *pcbddc;
2591 
2592   PetscFunctionBegin;
2593   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2594   pc->data = (void*)pcbddc;
2595 
2596   /* create PCIS data structure */
2597   ierr = PCISCreate(pc);CHKERRQ(ierr);
2598 
2599   /* create local graph structure */
2600   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2601 
2602   /* BDDC nonzero defaults */
2603   pcbddc->use_local_adj             = PETSC_TRUE;
2604   pcbddc->use_vertices              = PETSC_TRUE;
2605   pcbddc->use_edges                 = PETSC_TRUE;
2606   pcbddc->symmetric_primal          = PETSC_TRUE;
2607   pcbddc->vertex_size               = 1;
2608   pcbddc->recompute_topography      = PETSC_TRUE;
2609   pcbddc->coarse_size               = -1;
2610   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2611   pcbddc->coarsening_ratio          = 8;
2612   pcbddc->coarse_eqs_per_proc       = 1;
2613   pcbddc->benign_compute_correction = PETSC_TRUE;
2614   pcbddc->nedfield                  = -1;
2615   pcbddc->nedglobal                 = PETSC_TRUE;
2616   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2617   pcbddc->sub_schurs_layers         = -1;
2618   pcbddc->adaptive_threshold[0]     = 0.0;
2619   pcbddc->adaptive_threshold[1]     = 0.0;
2620 
2621   /* function pointers */
2622   pc->ops->apply               = PCApply_BDDC;
2623   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2624   pc->ops->setup               = PCSetUp_BDDC;
2625   pc->ops->destroy             = PCDestroy_BDDC;
2626   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2627   pc->ops->view                = PCView_BDDC;
2628   pc->ops->applyrichardson     = 0;
2629   pc->ops->applysymmetricleft  = 0;
2630   pc->ops->applysymmetricright = 0;
2631   pc->ops->presolve            = PCPreSolve_BDDC;
2632   pc->ops->postsolve           = PCPostSolve_BDDC;
2633   pc->ops->reset               = PCReset_BDDC;
2634 
2635   /* composing function */
2636   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
2637   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
2638   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2639   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2640   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
2641   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2642   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2643   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2644   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2645   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2646   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2647   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2648   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2649   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2650   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2651   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2652   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2653   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2654   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2655   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2656   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2657   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2658   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2659   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
2660   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
2661   PetscFunctionReturn(0);
2662 }
2663