xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision efd4aadf157bf1ba2d80c2be092fcf4247860003)
1 /* TODOLIST
2 
3    Solvers
4    - Add support for cholesky for coarse solver (similar to local solvers)
5    - Propagate ksp prefixes for solvers to mat objects?
6 
7    User interface
8    - ** DM attached to pc?
9 
10    Debugging output
11    - * Better management of verbosity levels of debugging output
12 
13    Extra
14    - *** Is it possible to work with PCBDDCGraph on boundary indices only (less memory consumed)?
15    - BDDC with MG framework?
16 
17    MATIS related operations contained in BDDC code
18    - Provide general case for subassembling
19 
20 */
21 
22 #include <../src/ksp/pc/impls/bddc/bddc.h> /*I "petscpc.h" I*/  /* includes for fortran wrappers */
23 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
24 #include <petscblaslapack.h>
25 
26 static PetscBool  cited = PETSC_FALSE;
27 static const char citation[] =
28 "@article{ZampiniPCBDDC,\n"
29 "author = {Stefano Zampini},\n"
30 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
31 "journal = {SIAM Journal on Scientific Computing},\n"
32 "volume = {38},\n"
33 "number = {5},\n"
34 "pages = {S282-S306},\n"
35 "year = {2016},\n"
36 "doi = {10.1137/15M1025785},\n"
37 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
38 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
39 "}\n";
40 
41 /* temporarily declare it */
42 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
43 
44 PetscErrorCode PCSetFromOptions_BDDC(PetscOptionItems *PetscOptionsObject,PC pc)
45 {
46   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
47   PetscErrorCode ierr;
48 
49   PetscFunctionBegin;
50   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
51   /* Verbose debugging */
52   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
53   /* Approximate solvers */
54   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate","Inform PCBDDC that we are using approximate Dirichlet solvers","none",pcbddc->NullSpace_corr[0],&pcbddc->NullSpace_corr[0],NULL);CHKERRQ(ierr);
55   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate_scale","Inform PCBDDC that we need to scale the Dirichlet solve","none",pcbddc->NullSpace_corr[1],&pcbddc->NullSpace_corr[1],NULL);CHKERRQ(ierr);
56   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate","Inform PCBDDC that we are using approximate Neumann solvers","none",pcbddc->NullSpace_corr[2],&pcbddc->NullSpace_corr[2],NULL);CHKERRQ(ierr);
57   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate_scale","Inform PCBDDC that we need to scale the Neumann solve","none",pcbddc->NullSpace_corr[3],&pcbddc->NullSpace_corr[3],NULL);CHKERRQ(ierr);
58   /* Primal space customization */
59   ierr = PetscOptionsBool("-pc_bddc_use_local_mat_graph","Use or not adjacency graph of local mat for interface analysis","none",pcbddc->use_local_adj,&pcbddc->use_local_adj,NULL);CHKERRQ(ierr);
60   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
61   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
62   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
63   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
64   ierr = PetscOptionsInt("-pc_bddc_vertex_size","Connected components smaller or equal to vertex size will be considered as primal vertices","none",pcbddc->vertex_size,&pcbddc->vertex_size,NULL);CHKERRQ(ierr);
65   ierr = PetscOptionsBool("-pc_bddc_use_true_nnsp","Use near null space attached to the matrix without modifications","none",pcbddc->use_nnsp_true,&pcbddc->use_nnsp_true,NULL);CHKERRQ(ierr);
66   ierr = PetscOptionsBool("-pc_bddc_use_qr_single","Use QR factorization for single constraints on cc (QR is always used when multiple constraints are present)","none",pcbddc->use_qr_single,&pcbddc->use_qr_single,NULL);CHKERRQ(ierr);
67   /* Change of basis */
68   ierr = PetscOptionsBool("-pc_bddc_use_change_of_basis","Use or not internal change of basis on local edge nodes","none",pcbddc->use_change_of_basis,&pcbddc->use_change_of_basis,NULL);CHKERRQ(ierr);
69   ierr = PetscOptionsBool("-pc_bddc_use_change_on_faces","Use or not internal change of basis on local face nodes","none",pcbddc->use_change_on_faces,&pcbddc->use_change_on_faces,NULL);CHKERRQ(ierr);
70   if (!pcbddc->use_change_of_basis) {
71     pcbddc->use_change_on_faces = PETSC_FALSE;
72   }
73   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
74   ierr = PetscOptionsBool("-pc_bddc_switch_static","Switch on static condensation ops around the interface preconditioner","none",pcbddc->switch_static,&pcbddc->switch_static,NULL);CHKERRQ(ierr);
75   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_per_proc","Number of equations per process for coarse problem redistribution (significant only at the coarsest level)","none",pcbddc->coarse_eqs_per_proc,&pcbddc->coarse_eqs_per_proc,NULL);CHKERRQ(ierr);
76   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,NULL);CHKERRQ(ierr);
77   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","none",pcbddc->max_levels,&pcbddc->max_levels,NULL);CHKERRQ(ierr);
78   ierr = PetscOptionsBool("-pc_bddc_use_coarse_estimates","Use estimated eigenvalues for coarse problem","none",pcbddc->use_coarse_estimates,&pcbddc->use_coarse_estimates,NULL);CHKERRQ(ierr);
79   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
80   ierr = PetscOptionsBool("-pc_bddc_schur_rebuild","Whether or not the interface graph for Schur principal minors has to be rebuilt (i.e. define the interface without any adjacency)","none",pcbddc->sub_schurs_rebuild,&pcbddc->sub_schurs_rebuild,NULL);CHKERRQ(ierr);
81   ierr = PetscOptionsInt("-pc_bddc_schur_layers","Number of dofs' layers for the computation of principal minors (i.e. -1 uses all dofs)","none",pcbddc->sub_schurs_layers,&pcbddc->sub_schurs_layers,NULL);CHKERRQ(ierr);
82   ierr = PetscOptionsBool("-pc_bddc_schur_use_useradj","Whether or not the CSR graph specified by the user should be used for computing successive layers (default is to use adj of local mat)","none",pcbddc->sub_schurs_use_useradj,&pcbddc->sub_schurs_use_useradj,NULL);CHKERRQ(ierr);
83   ierr = PetscOptionsBool("-pc_bddc_schur_exact","Whether or not to use the exact Schur complement instead of the reduced one (which excludes size 1 cc)","none",pcbddc->sub_schurs_exact_schur,&pcbddc->sub_schurs_exact_schur,NULL);CHKERRQ(ierr);
84   ierr = PetscOptionsBool("-pc_bddc_deluxe_zerorows","Zero rows and columns of deluxe operators associated with primal dofs","none",pcbddc->deluxe_zerorows,&pcbddc->deluxe_zerorows,NULL);CHKERRQ(ierr);
85   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
86   ierr = PetscOptionsBool("-pc_bddc_adaptive_userdefined","Use user-defined constraints (should be attached via MatSetNearNullSpace to pmat) in addition to those adaptively generated","none",pcbddc->adaptive_userdefined,&pcbddc->adaptive_userdefined,NULL);CHKERRQ(ierr);
87   ierr = PetscOptionsReal("-pc_bddc_adaptive_threshold","Threshold to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&pcbddc->adaptive_threshold,NULL);CHKERRQ(ierr);
88   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
89   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
90   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
91   ierr = PetscOptionsInt("-pc_bddc_coarse_adj","Number of processors where to map the coarse adjacency list","none",pcbddc->coarse_adj_red,&pcbddc->coarse_adj_red,NULL);CHKERRQ(ierr);
92   ierr = PetscOptionsBool("-pc_bddc_benign_trick","Apply the benign subspace trick to saddle point problems with discontinuous pressures","none",pcbddc->benign_saddle_point,&pcbddc->benign_saddle_point,NULL);CHKERRQ(ierr);
93   ierr = PetscOptionsBool("-pc_bddc_benign_change","Compute the pressure change of basis explicitly","none",pcbddc->benign_change_explicit,&pcbddc->benign_change_explicit,NULL);CHKERRQ(ierr);
94   ierr = PetscOptionsBool("-pc_bddc_benign_compute_correction","Compute the benign correction during PreSolve","none",pcbddc->benign_compute_correction,&pcbddc->benign_compute_correction,NULL);CHKERRQ(ierr);
95   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
96   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
97   ierr = PetscOptionsBool("-pc_bddc_eliminate_dirichlet","Whether or not we want to eliminate dirichlet dofs during presolve","none",pcbddc->eliminate_dirdofs,&pcbddc->eliminate_dirdofs,NULL);CHKERRQ(ierr);
98   ierr = PetscOptionsTail();CHKERRQ(ierr);
99   PetscFunctionReturn(0);
100 }
101 
102 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
103 {
104   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
105   PC_IS                *pcis = (PC_IS*)pc->data;
106   PetscErrorCode       ierr;
107   PetscBool            isascii,isstring;
108   PetscSubcomm         subcomm;
109   PetscViewer          subviewer;
110 
111   PetscFunctionBegin;
112   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
113   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);
114   /* Nothing printed for the String viewer */
115   /* ASCII viewer */
116   if (isascii) {
117     PetscMPIInt   color,rank,size;
118     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
119     PetscScalar   interface_size;
120     PetscReal     ratio1=0.,ratio2=0.;
121     Vec           counter;
122 
123     if (!pc->setupcalled) {
124       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
125     }
126     ierr = PetscViewerASCIIPrintf(viewer,"  Use verbose output: %D\n",pcbddc->dbg_flag);CHKERRQ(ierr);
127     ierr = PetscViewerASCIIPrintf(viewer,"  Use user-defined CSR: %D\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
128     ierr = PetscViewerASCIIPrintf(viewer,"  Use local mat graph: %D\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
129     if (pcbddc->mat_graph->twodim) {
130       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
131     } else {
132       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
133     }
134     ierr = PetscViewerASCIIPrintf(viewer,"  Graph max count: %D\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
135     ierr = PetscViewerASCIIPrintf(viewer,"  Use vertices: %d (vertex size %d)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
136     ierr = PetscViewerASCIIPrintf(viewer,"  Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
137     ierr = PetscViewerASCIIPrintf(viewer,"  Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
138     ierr = PetscViewerASCIIPrintf(viewer,"  Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
139     ierr = PetscViewerASCIIPrintf(viewer,"  Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
140     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
141     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
142     ierr = PetscViewerASCIIPrintf(viewer,"  User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
143     ierr = PetscViewerASCIIPrintf(viewer,"  Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
144     ierr = PetscViewerASCIIPrintf(viewer,"  Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
145     ierr = PetscViewerASCIIPrintf(viewer,"  Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel max levels: %d\n",pcbddc->max_levels);CHKERRQ(ierr);
148     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel coarsening ratio: %d\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
149     ierr = PetscViewerASCIIPrintf(viewer,"  Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
150     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
151     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
152     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
153     ierr = PetscViewerASCIIPrintf(viewer,"  Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
154     ierr = PetscViewerASCIIPrintf(viewer,"  Number of dofs' layers for the computation of principal minors: %d\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
155     ierr = PetscViewerASCIIPrintf(viewer,"  Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
156     ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection threshold (active %d, userdefined %d): %g\n",pcbddc->adaptive_threshold,pcbddc->adaptive_selection,pcbddc->adaptive_userdefined);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  Min constraints / connected component: %d\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  Max constraints / connected component: %d\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
160     ierr = PetscViewerASCIIPrintf(viewer,"  Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
161     ierr = PetscViewerASCIIPrintf(viewer,"  Num. Procs. to map coarse adjacency list: %d\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
162     ierr = PetscViewerASCIIPrintf(viewer,"  Coarse eqs per proc (significant at the coarsest level): %d\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
163     ierr = PetscViewerASCIIPrintf(viewer,"  Detect disconnected: %d\n",pcbddc->detect_disconnected);CHKERRQ(ierr);
164     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
165     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  Algebraic computation of no-net-flux %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
167     if (!pc->setupcalled) PetscFunctionReturn(0);
168 
169     /* compute interface size */
170     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
171     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
172     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
173     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
174     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
175     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
176     ierr = VecDestroy(&counter);CHKERRQ(ierr);
177 
178     /* compute some statistics on the domain decomposition */
179     gsum[0] = 1;
180     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
181     loc[0]  = !!pcis->n;
182     loc[1]  = pcis->n - pcis->n_B;
183     loc[2]  = pcis->n_B;
184     loc[3]  = pcbddc->local_primal_size;
185     loc[4]  = pcis->n;
186     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
187     loc[6]  = pcbddc->benign_n;
188     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
189     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
190     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
191     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
192     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
193     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
194     if (pcbddc->coarse_size) {
195       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
196       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
197     }
198     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
199     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);
200     ierr = PetscViewerASCIIPrintf(viewer,"  Coarsening ratios: all/coarse %d interface/coarse %d\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
201     ierr = PetscViewerASCIIPrintf(viewer,"  Active processes : %d\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
202     ierr = PetscViewerASCIIPrintf(viewer,"  Total subdomains : %d\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
203     if (pcbddc->benign_have_null) {
204       ierr = PetscViewerASCIIPrintf(viewer,"  Benign subs      : %d\n",(PetscInt)totbenign);CHKERRQ(ierr);
205     }
206     ierr = PetscViewerASCIIPrintf(viewer,"  Dofs type        :\tMIN\tMAX\tMEAN\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
207     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);
208     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);
209     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);
210     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);
211     ierr = PetscViewerASCIIPrintf(viewer,"  Local     subs   :\t%d\t%d\n",(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
212     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** COARSE PROBLEM DETAILS *********************************\n",pcbddc->current_level);CHKERRQ(ierr);
213     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
214 
215     /* the coarse problem can be handled by a different communicator */
216     if (pcbddc->coarse_ksp) color = 1;
217     else color = 0;
218     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
219     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
220     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
221     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
222     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
223     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
224     if (color == 1) {
225       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
226       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
227     }
228     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
229     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
230     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
231   }
232   PetscFunctionReturn(0);
233 }
234 
235 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
236 {
237   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
238   PetscErrorCode ierr;
239 
240   PetscFunctionBegin;
241   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
242   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
243   pcbddc->discretegradient = G;
244   pcbddc->nedorder         = order > 0 ? order : -order;
245   pcbddc->nedfield         = field;
246   pcbddc->nedglobal        = global;
247   pcbddc->conforming       = conforming;
248   PetscFunctionReturn(0);
249 }
250 
251 /*@
252  PCBDDCSetDiscreteGradient - Sets the discrete gradient
253 
254    Collective on PC
255 
256    Input Parameters:
257 +  pc         - the preconditioning context
258 .  G          - the discrete gradient matrix (should be in AIJ format)
259 .  order      - the order of the Nedelec space (1 for the lowest order)
260 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
261 .  global     - the type of global ordering for the rows of G
262 -  conforming - whether the mesh is conforming or not
263 
264    Level: advanced
265 
266    Notes: The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
267           For variable order spaces, the order should be set to zero.
268           If global is true, the rows of G should be given in global ordering for the whole dofs;
269           if false, the ordering should be global for the Nedelec field.
270           In the latter case, it should hold gid[i] < gid[j] iff geid[i] < geid[j], with gid the global orderding for all the dofs
271           and geid the one for the Nedelec field.
272 
273 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
274 @*/
275 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
276 {
277   PetscErrorCode ierr;
278 
279   PetscFunctionBegin;
280   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
281   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
282   PetscValidLogicalCollectiveInt(pc,order,3);
283   PetscValidLogicalCollectiveInt(pc,field,4);
284   PetscValidLogicalCollectiveBool(pc,global,5);
285   PetscValidLogicalCollectiveBool(pc,conforming,6);
286   PetscCheckSameComm(pc,1,G,2);
287   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
288   PetscFunctionReturn(0);
289 }
290 
291 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
292 {
293   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
294   PetscErrorCode ierr;
295 
296   PetscFunctionBegin;
297   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
298   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
299   pcbddc->divudotp = divudotp;
300   pcbddc->divudotp_trans = trans;
301   pcbddc->compute_nonetflux = PETSC_TRUE;
302   if (vl2l) {
303     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
304     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
305     pcbddc->divudotp_vl2l = vl2l;
306   }
307   PetscFunctionReturn(0);
308 }
309 
310 /*@
311  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
312 
313    Collective on PC
314 
315    Input Parameters:
316 +  pc - the preconditioning context
317 .  divudotp - the matrix (must be of type MATIS)
318 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
319 -  vl2l - optional IS describing the local (wrt the local mat in divudotp) to local (wrt the local mat in pc->pmat) map for the velocities
320 
321    Level: advanced
322 
323    Notes: This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
324 
325 .seealso: PCBDDC
326 @*/
327 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
328 {
329   PetscBool      ismatis;
330   PetscErrorCode ierr;
331 
332   PetscFunctionBegin;
333   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
334   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
335   PetscCheckSameComm(pc,1,divudotp,2);
336   PetscValidLogicalCollectiveBool(pc,trans,3);
337   if (vl2l) PetscValidHeaderSpecific(divudotp,IS_CLASSID,4);
338   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
339   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
340   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
341   PetscFunctionReturn(0);
342 }
343 
344 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
345 {
346   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
347   PetscErrorCode ierr;
348 
349   PetscFunctionBegin;
350   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
351   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
352   pcbddc->user_ChangeOfBasisMatrix = change;
353   pcbddc->change_interior = interior;
354   PetscFunctionReturn(0);
355 }
356 /*@
357  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
358 
359    Collective on PC
360 
361    Input Parameters:
362 +  pc - the preconditioning context
363 .  change - the change of basis matrix
364 -  interior - whether or not the change of basis modifies interior dofs
365 
366    Level: intermediate
367 
368    Notes:
369 
370 .seealso: PCBDDC
371 @*/
372 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
373 {
374   PetscErrorCode ierr;
375 
376   PetscFunctionBegin;
377   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
378   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
379   PetscCheckSameComm(pc,1,change,2);
380   if (pc->mat) {
381     PetscInt rows_c,cols_c,rows,cols;
382     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
383     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
384     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of rows for change of basis matrix! %D != %D",rows_c,rows);
385     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of columns for change of basis matrix! %D != %D",cols_c,cols);
386     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
387     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
388     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local rows for change of basis matrix! %D != %D",rows_c,rows);
389     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local columns for change of basis matrix! %D != %D",cols_c,cols);
390   }
391   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
392   PetscFunctionReturn(0);
393 }
394 
395 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
396 {
397   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
398   PetscBool      isequal = PETSC_FALSE;
399   PetscErrorCode ierr;
400 
401   PetscFunctionBegin;
402   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
403   if (pcbddc->user_primal_vertices) {
404     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
405   }
406   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
407   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
408   pcbddc->user_primal_vertices = PrimalVertices;
409   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
410   PetscFunctionReturn(0);
411 }
412 /*@
413  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
414 
415    Collective
416 
417    Input Parameters:
418 +  pc - the preconditioning context
419 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
420 
421    Level: intermediate
422 
423    Notes:
424      Any process can list any global node
425 
426 .seealso: PCBDDC
427 @*/
428 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
429 {
430   PetscErrorCode ierr;
431 
432   PetscFunctionBegin;
433   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
434   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
435   PetscCheckSameComm(pc,1,PrimalVertices,2);
436   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
437   PetscFunctionReturn(0);
438 }
439 
440 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
441 {
442   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
443   PetscBool      isequal = PETSC_FALSE;
444   PetscErrorCode ierr;
445 
446   PetscFunctionBegin;
447   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
448   if (pcbddc->user_primal_vertices_local) {
449     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
450   }
451   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
452   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
453   pcbddc->user_primal_vertices_local = PrimalVertices;
454   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
455   PetscFunctionReturn(0);
456 }
457 /*@
458  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
459 
460    Collective
461 
462    Input Parameters:
463 +  pc - the preconditioning context
464 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
465 
466    Level: intermediate
467 
468    Notes:
469 
470 .seealso: PCBDDC
471 @*/
472 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
473 {
474   PetscErrorCode ierr;
475 
476   PetscFunctionBegin;
477   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
478   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
479   PetscCheckSameComm(pc,1,PrimalVertices,2);
480   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
481   PetscFunctionReturn(0);
482 }
483 
484 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
485 {
486   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
487 
488   PetscFunctionBegin;
489   pcbddc->coarsening_ratio = k;
490   PetscFunctionReturn(0);
491 }
492 
493 /*@
494  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
495 
496    Logically collective on PC
497 
498    Input Parameters:
499 +  pc - the preconditioning context
500 -  k - coarsening ratio (H/h at the coarser level)
501 
502    Options Database Keys:
503 .    -pc_bddc_coarsening_ratio
504 
505    Level: intermediate
506 
507    Notes:
508      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
509 
510 .seealso: PCBDDC, PCBDDCSetLevels()
511 @*/
512 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
513 {
514   PetscErrorCode ierr;
515 
516   PetscFunctionBegin;
517   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
518   PetscValidLogicalCollectiveInt(pc,k,2);
519   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
520   PetscFunctionReturn(0);
521 }
522 
523 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
524 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
525 {
526   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
527 
528   PetscFunctionBegin;
529   pcbddc->use_exact_dirichlet_trick = flg;
530   PetscFunctionReturn(0);
531 }
532 
533 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
534 {
535   PetscErrorCode ierr;
536 
537   PetscFunctionBegin;
538   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
539   PetscValidLogicalCollectiveBool(pc,flg,2);
540   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
541   PetscFunctionReturn(0);
542 }
543 
544 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
545 {
546   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
547 
548   PetscFunctionBegin;
549   pcbddc->current_level = level;
550   PetscFunctionReturn(0);
551 }
552 
553 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
554 {
555   PetscErrorCode ierr;
556 
557   PetscFunctionBegin;
558   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
559   PetscValidLogicalCollectiveInt(pc,level,2);
560   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
561   PetscFunctionReturn(0);
562 }
563 
564 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
565 {
566   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
567 
568   PetscFunctionBegin;
569   pcbddc->max_levels = levels;
570   PetscFunctionReturn(0);
571 }
572 
573 /*@
574  PCBDDCSetLevels - Sets the maximum number of levels for multilevel
575 
576    Logically collective on PC
577 
578    Input Parameters:
579 +  pc - the preconditioning context
580 -  levels - the maximum number of levels (max 9)
581 
582    Options Database Keys:
583 .    -pc_bddc_levels
584 
585    Level: intermediate
586 
587    Notes:
588      Default value is 0, i.e. traditional one-level BDDC
589 
590 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
591 @*/
592 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
593 {
594   PetscErrorCode ierr;
595 
596   PetscFunctionBegin;
597   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
598   PetscValidLogicalCollectiveInt(pc,levels,2);
599   if (levels > 99) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of levels for bddc is 99\n");
600   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
601   PetscFunctionReturn(0);
602 }
603 
604 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
605 {
606   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
607   PetscBool      isequal = PETSC_FALSE;
608   PetscErrorCode ierr;
609 
610   PetscFunctionBegin;
611   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
612   if (pcbddc->DirichletBoundaries) {
613     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
614   }
615   /* last user setting takes precendence -> destroy any other customization */
616   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
617   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
618   pcbddc->DirichletBoundaries = DirichletBoundaries;
619   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
620   PetscFunctionReturn(0);
621 }
622 
623 /*@
624  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
625 
626    Collective
627 
628    Input Parameters:
629 +  pc - the preconditioning context
630 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
631 
632    Level: intermediate
633 
634    Notes:
635      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
636 
637 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
638 @*/
639 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
640 {
641   PetscErrorCode ierr;
642 
643   PetscFunctionBegin;
644   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
645   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
646   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
647   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
648   PetscFunctionReturn(0);
649 }
650 
651 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
652 {
653   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
654   PetscBool      isequal = PETSC_FALSE;
655   PetscErrorCode ierr;
656 
657   PetscFunctionBegin;
658   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
659   if (pcbddc->DirichletBoundariesLocal) {
660     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
661   }
662   /* last user setting takes precendence -> destroy any other customization */
663   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
664   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
665   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
666   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
667   PetscFunctionReturn(0);
668 }
669 
670 /*@
671  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
672 
673    Collective
674 
675    Input Parameters:
676 +  pc - the preconditioning context
677 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
678 
679    Level: intermediate
680 
681    Notes:
682 
683 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
684 @*/
685 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
686 {
687   PetscErrorCode ierr;
688 
689   PetscFunctionBegin;
690   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
691   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
692   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
693   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
694   PetscFunctionReturn(0);
695 }
696 
697 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
698 {
699   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
700   PetscBool      isequal = PETSC_FALSE;
701   PetscErrorCode ierr;
702 
703   PetscFunctionBegin;
704   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
705   if (pcbddc->NeumannBoundaries) {
706     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
707   }
708   /* last user setting takes precendence -> destroy any other customization */
709   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
710   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
711   pcbddc->NeumannBoundaries = NeumannBoundaries;
712   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
713   PetscFunctionReturn(0);
714 }
715 
716 /*@
717  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
718 
719    Collective
720 
721    Input Parameters:
722 +  pc - the preconditioning context
723 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
724 
725    Level: intermediate
726 
727    Notes:
728      Any process can list any global node
729 
730 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
731 @*/
732 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
733 {
734   PetscErrorCode ierr;
735 
736   PetscFunctionBegin;
737   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
738   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
739   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
740   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
741   PetscFunctionReturn(0);
742 }
743 
744 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
745 {
746   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
747   PetscBool      isequal = PETSC_FALSE;
748   PetscErrorCode ierr;
749 
750   PetscFunctionBegin;
751   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
752   if (pcbddc->NeumannBoundariesLocal) {
753     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
754   }
755   /* last user setting takes precendence -> destroy any other customization */
756   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
757   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
758   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
759   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
760   PetscFunctionReturn(0);
761 }
762 
763 /*@
764  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
765 
766    Collective
767 
768    Input Parameters:
769 +  pc - the preconditioning context
770 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
771 
772    Level: intermediate
773 
774    Notes:
775 
776 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
777 @*/
778 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
779 {
780   PetscErrorCode ierr;
781 
782   PetscFunctionBegin;
783   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
784   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
785   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
786   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
787   PetscFunctionReturn(0);
788 }
789 
790 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
791 {
792   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
793 
794   PetscFunctionBegin;
795   *DirichletBoundaries = pcbddc->DirichletBoundaries;
796   PetscFunctionReturn(0);
797 }
798 
799 /*@
800  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
801 
802    Collective
803 
804    Input Parameters:
805 .  pc - the preconditioning context
806 
807    Output Parameters:
808 .  DirichletBoundaries - index set defining the Dirichlet boundaries
809 
810    Level: intermediate
811 
812    Notes:
813      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
814 
815 .seealso: PCBDDC
816 @*/
817 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
818 {
819   PetscErrorCode ierr;
820 
821   PetscFunctionBegin;
822   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
823   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
824   PetscFunctionReturn(0);
825 }
826 
827 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
828 {
829   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
830 
831   PetscFunctionBegin;
832   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
833   PetscFunctionReturn(0);
834 }
835 
836 /*@
837  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
838 
839    Collective
840 
841    Input Parameters:
842 .  pc - the preconditioning context
843 
844    Output Parameters:
845 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
846 
847    Level: intermediate
848 
849    Notes:
850      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetDirichletBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetDirichletBoundaries).
851           In the latter case, the IS will be available after PCSetUp.
852 
853 .seealso: PCBDDC
854 @*/
855 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
856 {
857   PetscErrorCode ierr;
858 
859   PetscFunctionBegin;
860   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
861   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
862   PetscFunctionReturn(0);
863 }
864 
865 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
866 {
867   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
868 
869   PetscFunctionBegin;
870   *NeumannBoundaries = pcbddc->NeumannBoundaries;
871   PetscFunctionReturn(0);
872 }
873 
874 /*@
875  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
876 
877    Collective
878 
879    Input Parameters:
880 .  pc - the preconditioning context
881 
882    Output Parameters:
883 .  NeumannBoundaries - index set defining the Neumann boundaries
884 
885    Level: intermediate
886 
887    Notes:
888      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
889 
890 .seealso: PCBDDC
891 @*/
892 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
893 {
894   PetscErrorCode ierr;
895 
896   PetscFunctionBegin;
897   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
898   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
899   PetscFunctionReturn(0);
900 }
901 
902 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
903 {
904   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
905 
906   PetscFunctionBegin;
907   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
908   PetscFunctionReturn(0);
909 }
910 
911 /*@
912  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
913 
914    Collective
915 
916    Input Parameters:
917 .  pc - the preconditioning context
918 
919    Output Parameters:
920 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
921 
922    Level: intermediate
923 
924    Notes:
925      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetNeumannBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetNeumannBoundaries).
926           In the latter case, the IS will be available after PCSetUp.
927 
928 .seealso: PCBDDC
929 @*/
930 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
931 {
932   PetscErrorCode ierr;
933 
934   PetscFunctionBegin;
935   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
936   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
937   PetscFunctionReturn(0);
938 }
939 
940 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
941 {
942   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
943   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
944   PetscBool      same_data = PETSC_FALSE;
945   PetscErrorCode ierr;
946 
947   PetscFunctionBegin;
948   if (!nvtxs) {
949     if (copymode == PETSC_OWN_POINTER) {
950       ierr = PetscFree(xadj);CHKERRQ(ierr);
951       ierr = PetscFree(adjncy);CHKERRQ(ierr);
952     }
953     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
954     PetscFunctionReturn(0);
955   }
956   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
957     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
958     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
959       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
960       if (same_data) {
961         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
962       }
963     }
964   }
965   if (!same_data) {
966     /* free old CSR */
967     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
968     /* get CSR into graph structure */
969     if (copymode == PETSC_COPY_VALUES) {
970       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
971       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
972       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
973       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
974       mat_graph->freecsr = PETSC_TRUE;
975     } else if (copymode == PETSC_OWN_POINTER) {
976       mat_graph->xadj    = (PetscInt*)xadj;
977       mat_graph->adjncy  = (PetscInt*)adjncy;
978       mat_graph->freecsr = PETSC_TRUE;
979     } else if (copymode == PETSC_USE_POINTER) {
980       mat_graph->xadj    = (PetscInt*)xadj;
981       mat_graph->adjncy  = (PetscInt*)adjncy;
982       mat_graph->freecsr = PETSC_FALSE;
983     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %D",copymode);
984     mat_graph->nvtxs_csr = nvtxs;
985     pcbddc->recompute_topography = PETSC_TRUE;
986   }
987   PetscFunctionReturn(0);
988 }
989 
990 /*@
991  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
992 
993    Not collective
994 
995    Input Parameters:
996 +  pc - the preconditioning context.
997 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
998 .  xadj, adjncy - the connectivity of the dofs in CSR format.
999 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1000 
1001    Level: intermediate
1002 
1003    Notes: A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1004 
1005 .seealso: PCBDDC,PetscCopyMode
1006 @*/
1007 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1008 {
1009   void (*f)(void) = 0;
1010   PetscErrorCode ierr;
1011 
1012   PetscFunctionBegin;
1013   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1014   if (nvtxs) {
1015     PetscValidIntPointer(xadj,3);
1016     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1017   }
1018   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1019   /* free arrays if PCBDDC is not the PC type */
1020   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1021   if (!f && copymode == PETSC_OWN_POINTER) {
1022     ierr = PetscFree(xadj);CHKERRQ(ierr);
1023     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1024   }
1025   PetscFunctionReturn(0);
1026 }
1027 
1028 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1029 {
1030   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1031   PetscInt       i;
1032   PetscBool      isequal = PETSC_FALSE;
1033   PetscErrorCode ierr;
1034 
1035   PetscFunctionBegin;
1036   if (pcbddc->n_ISForDofsLocal == n_is) {
1037     for (i=0;i<n_is;i++) {
1038       PetscBool isequalt;
1039       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1040       if (!isequalt) break;
1041     }
1042     if (i == n_is) isequal = PETSC_TRUE;
1043   }
1044   for (i=0;i<n_is;i++) {
1045     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1046   }
1047   /* Destroy ISes if they were already set */
1048   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1049     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1050   }
1051   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1052   /* last user setting takes precendence -> destroy any other customization */
1053   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1054     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1055   }
1056   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1057   pcbddc->n_ISForDofs = 0;
1058   /* allocate space then set */
1059   if (n_is) {
1060     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1061   }
1062   for (i=0;i<n_is;i++) {
1063     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1064   }
1065   pcbddc->n_ISForDofsLocal = n_is;
1066   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1067   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1068   PetscFunctionReturn(0);
1069 }
1070 
1071 /*@
1072  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1073 
1074    Collective
1075 
1076    Input Parameters:
1077 +  pc - the preconditioning context
1078 .  n_is - number of index sets defining the fields
1079 -  ISForDofs - array of IS describing the fields in local ordering
1080 
1081    Level: intermediate
1082 
1083    Notes:
1084      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1085 
1086 .seealso: PCBDDC
1087 @*/
1088 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1089 {
1090   PetscInt       i;
1091   PetscErrorCode ierr;
1092 
1093   PetscFunctionBegin;
1094   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1095   PetscValidLogicalCollectiveInt(pc,n_is,2);
1096   for (i=0;i<n_is;i++) {
1097     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1098     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1099   }
1100   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1101   PetscFunctionReturn(0);
1102 }
1103 
1104 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1105 {
1106   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1107   PetscInt       i;
1108   PetscBool      isequal = PETSC_FALSE;
1109   PetscErrorCode ierr;
1110 
1111   PetscFunctionBegin;
1112   if (pcbddc->n_ISForDofs == n_is) {
1113     for (i=0;i<n_is;i++) {
1114       PetscBool isequalt;
1115       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1116       if (!isequalt) break;
1117     }
1118     if (i == n_is) isequal = PETSC_TRUE;
1119   }
1120   for (i=0;i<n_is;i++) {
1121     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1122   }
1123   /* Destroy ISes if they were already set */
1124   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1125     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1126   }
1127   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1128   /* last user setting takes precendence -> destroy any other customization */
1129   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1130     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1131   }
1132   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1133   pcbddc->n_ISForDofsLocal = 0;
1134   /* allocate space then set */
1135   if (n_is) {
1136     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1137   }
1138   for (i=0;i<n_is;i++) {
1139     pcbddc->ISForDofs[i] = ISForDofs[i];
1140   }
1141   pcbddc->n_ISForDofs = n_is;
1142   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1143   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1144   PetscFunctionReturn(0);
1145 }
1146 
1147 /*@
1148  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1149 
1150    Collective
1151 
1152    Input Parameters:
1153 +  pc - the preconditioning context
1154 .  n_is - number of index sets defining the fields
1155 -  ISForDofs - array of IS describing the fields in global ordering
1156 
1157    Level: intermediate
1158 
1159    Notes:
1160      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1161 
1162 .seealso: PCBDDC
1163 @*/
1164 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1165 {
1166   PetscInt       i;
1167   PetscErrorCode ierr;
1168 
1169   PetscFunctionBegin;
1170   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1171   PetscValidLogicalCollectiveInt(pc,n_is,2);
1172   for (i=0;i<n_is;i++) {
1173     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1174     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1175   }
1176   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 /*
1181    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1182                      guess if a transformation of basis approach has been selected.
1183 
1184    Input Parameter:
1185 +  pc - the preconditioner contex
1186 
1187    Application Interface Routine: PCPreSolve()
1188 
1189    Notes:
1190      The interface routine PCPreSolve() is not usually called directly by
1191    the user, but instead is called by KSPSolve().
1192 */
1193 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1194 {
1195   PetscErrorCode ierr;
1196   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1197   PC_IS          *pcis = (PC_IS*)(pc->data);
1198   Vec            used_vec;
1199   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1200 
1201   PetscFunctionBegin;
1202   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1203   if (ksp) {
1204     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1205     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1206     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1207     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1208     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1209     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1210       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1211     }
1212   }
1213   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1214     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1215   }
1216 
1217   /* Creates parallel work vectors used in presolve */
1218   if (!pcbddc->original_rhs) {
1219     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1220   }
1221   if (!pcbddc->temp_solution) {
1222     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1223   }
1224 
1225   pcbddc->temp_solution_used = PETSC_FALSE;
1226   if (x) {
1227     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1228     used_vec = x;
1229   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1230     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1231     used_vec = pcbddc->temp_solution;
1232     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1233     pcbddc->temp_solution_used = PETSC_TRUE;
1234     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1235     save_rhs = PETSC_FALSE;
1236     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1237   }
1238 
1239   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1240   if (ksp) {
1241     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1242     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1243     if (!pcbddc->ksp_guess_nonzero) {
1244       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1245     }
1246   }
1247 
1248   pcbddc->rhs_change = PETSC_FALSE;
1249   /* Take into account zeroed rows -> change rhs and store solution removed */
1250   if (rhs && pcbddc->eliminate_dirdofs) {
1251     IS dirIS = NULL;
1252 
1253     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1254     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1255     if (dirIS) {
1256       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1257       PetscInt          dirsize,i,*is_indices;
1258       PetscScalar       *array_x;
1259       const PetscScalar *array_diagonal;
1260 
1261       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1262       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1263       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1264       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1265       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1266       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1267       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1268       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1269       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1270       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1271       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1272       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1273       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1274       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1275       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1276       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1277       pcbddc->rhs_change = PETSC_TRUE;
1278       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1279     }
1280   }
1281 
1282   /* remove the computed solution or the initial guess from the rhs */
1283   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1284     /* save the original rhs */
1285     if (save_rhs) {
1286       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1287       save_rhs = PETSC_FALSE;
1288     }
1289     pcbddc->rhs_change = PETSC_TRUE;
1290     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1291     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1292     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1293     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1294     pcbddc->temp_solution_used = PETSC_TRUE;
1295     if (ksp) {
1296       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1297     }
1298   }
1299   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1300 
1301   /* compute initial vector in benign space if needed
1302      and remove non-benign solution from the rhs */
1303   benign_correction_computed = PETSC_FALSE;
1304   if (rhs && pcbddc->benign_compute_correction && pcbddc->benign_have_null) {
1305     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1306        Recursively apply BDDC in the multilevel case */
1307     if (!pcbddc->benign_vec) {
1308       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1309     }
1310     pcbddc->benign_apply_coarse_only = PETSC_TRUE;
1311     if (!pcbddc->benign_skip_correction) {
1312       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1313       benign_correction_computed = PETSC_TRUE;
1314       if (pcbddc->temp_solution_used) {
1315         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1316       }
1317       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1318       /* store the original rhs if not done earlier */
1319       if (save_rhs) {
1320         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1321       }
1322       if (pcbddc->rhs_change) {
1323         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1324       } else {
1325         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1326       }
1327       pcbddc->rhs_change = PETSC_TRUE;
1328     }
1329     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1330   }
1331 
1332   /* dbg output */
1333   if (pcbddc->dbg_flag && benign_correction_computed) {
1334     Vec v;
1335     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1336     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1337     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1338     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1339     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc)));CHKERRQ(ierr);
1340     ierr = VecDestroy(&v);CHKERRQ(ierr);
1341   }
1342 
1343   /* set initial guess if using PCG */
1344   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1345   if (x && pcbddc->use_exact_dirichlet_trick) {
1346     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1347     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1348       if (benign_correction_computed) { /* we have already saved the changed rhs */
1349         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1350       } else {
1351         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1352       }
1353       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1354       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1355     } else {
1356       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1357       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1358     }
1359     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1360     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1361       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1362       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1363       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1364       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1365     } else {
1366       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1367       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1368     }
1369     if (ksp) {
1370       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1371     }
1372     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1373   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1374     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1375   }
1376   PetscFunctionReturn(0);
1377 }
1378 
1379 /*
1380    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1381                      approach has been selected. Also, restores rhs to its original state.
1382 
1383    Input Parameter:
1384 +  pc - the preconditioner contex
1385 
1386    Application Interface Routine: PCPostSolve()
1387 
1388    Notes:
1389      The interface routine PCPostSolve() is not usually called directly by
1390      the user, but instead is called by KSPSolve().
1391 */
1392 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1393 {
1394   PetscErrorCode ierr;
1395   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1396 
1397   PetscFunctionBegin;
1398   /* add solution removed in presolve */
1399   if (x && pcbddc->rhs_change) {
1400     if (pcbddc->temp_solution_used) {
1401       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1402     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1403       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1404     }
1405     /* restore to original state (not for FETI-DP) */
1406     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1407   }
1408 
1409   /* restore rhs to its original state (not needed for FETI-DP) */
1410   if (rhs && pcbddc->rhs_change) {
1411     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1412     pcbddc->rhs_change = PETSC_FALSE;
1413   }
1414   /* restore ksp guess state */
1415   if (ksp) {
1416     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1417     /* reset flag for exact dirichlet trick */
1418     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1419   }
1420   PetscFunctionReturn(0);
1421 }
1422 
1423 /*
1424    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1425                   by setting data structures and options.
1426 
1427    Input Parameter:
1428 +  pc - the preconditioner context
1429 
1430    Application Interface Routine: PCSetUp()
1431 
1432    Notes:
1433      The interface routine PCSetUp() is not usually called directly by
1434      the user, but instead is called by PCApply() if necessary.
1435 */
1436 PetscErrorCode PCSetUp_BDDC(PC pc)
1437 {
1438   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1439   PCBDDCSubSchurs sub_schurs;
1440   Mat_IS*         matis;
1441   MatNullSpace    nearnullspace;
1442   Mat             lA;
1443   IS              lP,zerodiag = NULL;
1444   PetscInt        nrows,ncols;
1445   PetscBool       computesubschurs;
1446   PetscBool       computeconstraintsmatrix;
1447   PetscBool       new_nearnullspace_provided,ismatis;
1448   PetscErrorCode  ierr;
1449 
1450   PetscFunctionBegin;
1451   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1452   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1453   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1454   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1455   matis = (Mat_IS*)pc->pmat->data;
1456   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1457   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1458      Also, BDDC builds its own KSP for the Dirichlet problem */
1459   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) pcbddc->recompute_topography = PETSC_TRUE;
1460   if (pcbddc->recompute_topography) {
1461     pcbddc->graphanalyzed    = PETSC_FALSE;
1462     computeconstraintsmatrix = PETSC_TRUE;
1463   } else {
1464     computeconstraintsmatrix = PETSC_FALSE;
1465   }
1466 
1467   /* check parameters' compatibility */
1468   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1469   pcbddc->adaptive_selection = (PetscBool)(pcbddc->adaptive_threshold > 0.0);
1470   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1471   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1472 
1473   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1474   if (pcbddc->switch_static) {
1475     PetscBool ismatis;
1476     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1477     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1478   }
1479 
1480   /* activate all connected components if the netflux has been requested */
1481   if (pcbddc->compute_nonetflux) {
1482     pcbddc->use_vertices = PETSC_TRUE;
1483     pcbddc->use_edges = PETSC_TRUE;
1484     pcbddc->use_faces = PETSC_TRUE;
1485   }
1486 
1487   /* Get stdout for dbg */
1488   if (pcbddc->dbg_flag) {
1489     if (!pcbddc->dbg_viewer) {
1490       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1491       ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1492     }
1493     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1494   }
1495 
1496   /* process topology information */
1497   if (pcbddc->recompute_topography) {
1498     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1499     /* detect local disconnected subdomains if requested (use matis->A) */
1500     if (pcbddc->detect_disconnected) {
1501       IS       primalv;
1502       PetscInt i;
1503 
1504       for (i=0;i<pcbddc->n_local_subs;i++) {
1505         ierr = ISDestroy(&pcbddc->local_subs[i]);CHKERRQ(ierr);
1506       }
1507       ierr = PetscFree(pcbddc->local_subs);CHKERRQ(ierr);
1508       ierr = PCBDDCDetectDisconnectedComponents(pc,&pcbddc->n_local_subs,&pcbddc->local_subs,&primalv);CHKERRQ(ierr);
1509       if (primalv) {
1510         if (pcbddc->user_primal_vertices_local) {
1511           IS list[2] = {primalv, pcbddc->user_primal_vertices_local}, newp;
1512 
1513           ierr = ISConcatenate(PetscObjectComm((PetscObject)pc),2,list,&newp);CHKERRQ(ierr);
1514           ierr = ISDestroy(&list[0]);CHKERRQ(ierr);
1515           ierr = ISDestroy(&list[1]);CHKERRQ(ierr);
1516           pcbddc->user_primal_vertices_local = newp;
1517         } else {
1518           pcbddc->user_primal_vertices_local = primalv;
1519         }
1520       }
1521     }
1522     if (pcbddc->discretegradient) {
1523       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1524     }
1525   }
1526 
1527   /* change basis if requested by the user */
1528   if (pcbddc->user_ChangeOfBasisMatrix) {
1529     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1530     pcbddc->use_change_of_basis = PETSC_FALSE;
1531     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1532   } else {
1533     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1534     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1535     pcbddc->local_mat = matis->A;
1536   }
1537 
1538   /*
1539      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1540      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1541   */
1542   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1543   if (pcbddc->benign_saddle_point) {
1544     PC_IS* pcis = (PC_IS*)pc->data;
1545 
1546     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1547     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1548     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1549     /* pop B0 mat from local mat */
1550     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1551     /* give pcis a hint to not reuse submatrices during PCISCreate */
1552     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1553       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1554         pcis->reusesubmatrices = PETSC_FALSE;
1555       } else {
1556         pcis->reusesubmatrices = PETSC_TRUE;
1557       }
1558     } else {
1559       pcis->reusesubmatrices = PETSC_FALSE;
1560     }
1561   }
1562 
1563   /* propagate relevant information -> TODO remove*/
1564 #if !defined(PETSC_USE_COMPLEX) /* workaround for reals */
1565   if (matis->A->symmetric_set) {
1566     ierr = MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);CHKERRQ(ierr);
1567   }
1568 #endif
1569   if (matis->A->symmetric_set) {
1570     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1571   }
1572   if (matis->A->spd_set) {
1573     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1574   }
1575 
1576   /* Set up all the "iterative substructuring" common block without computing solvers */
1577   {
1578     Mat temp_mat;
1579 
1580     temp_mat = matis->A;
1581     matis->A = pcbddc->local_mat;
1582     ierr = PCISSetUp(pc,PETSC_FALSE);CHKERRQ(ierr);
1583     pcbddc->local_mat = matis->A;
1584     matis->A = temp_mat;
1585   }
1586 
1587   /* Analyze interface */
1588   if (!pcbddc->graphanalyzed) {
1589     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1590     computeconstraintsmatrix = PETSC_TRUE;
1591     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1592       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1593     }
1594     if (pcbddc->compute_nonetflux) {
1595       MatNullSpace nnfnnsp;
1596 
1597       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1598       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1599       /* TODO what if a nearnullspace is already attached? */
1600       ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1601       ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1602     }
1603   }
1604 
1605   /* check existence of a divergence free extension, i.e.
1606      b(v_I,p_0) = 0 for all v_I (raise error if not).
1607      Also, check that PCBDDCBenignGetOrSetP0 works */
1608   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1609     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1610   }
1611   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1612 
1613   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1614   if (computesubschurs && pcbddc->recompute_topography) {
1615     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1616   }
1617   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1618   if (!pcbddc->use_deluxe_scaling) {
1619     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1620   }
1621 
1622   /* finish setup solvers and do adaptive selection of constraints */
1623   sub_schurs = pcbddc->sub_schurs;
1624   if (sub_schurs && sub_schurs->schur_explicit) {
1625     if (computesubschurs) {
1626       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1627     }
1628     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1629   } else {
1630     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1631     if (computesubschurs) {
1632       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1633     }
1634   }
1635   if (pcbddc->adaptive_selection) {
1636     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1637     computeconstraintsmatrix = PETSC_TRUE;
1638   }
1639 
1640   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1641   new_nearnullspace_provided = PETSC_FALSE;
1642   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1643   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1644     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1645       new_nearnullspace_provided = PETSC_TRUE;
1646     } else {
1647       /* determine if the two nullspaces are different (should be lightweight) */
1648       if (nearnullspace != pcbddc->onearnullspace) {
1649         new_nearnullspace_provided = PETSC_TRUE;
1650       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1651         PetscInt         i;
1652         const Vec        *nearnullvecs;
1653         PetscObjectState state;
1654         PetscInt         nnsp_size;
1655         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1656         for (i=0;i<nnsp_size;i++) {
1657           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1658           if (pcbddc->onearnullvecs_state[i] != state) {
1659             new_nearnullspace_provided = PETSC_TRUE;
1660             break;
1661           }
1662         }
1663       }
1664     }
1665   } else {
1666     if (!nearnullspace) { /* both nearnullspaces are null */
1667       new_nearnullspace_provided = PETSC_FALSE;
1668     } else { /* nearnullspace attached later */
1669       new_nearnullspace_provided = PETSC_TRUE;
1670     }
1671   }
1672 
1673   /* Setup constraints and related work vectors */
1674   /* reset primal space flags */
1675   pcbddc->new_primal_space = PETSC_FALSE;
1676   pcbddc->new_primal_space_local = PETSC_FALSE;
1677   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1678     /* It also sets the primal space flags */
1679     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1680   }
1681   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1682   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1683 
1684   if (pcbddc->use_change_of_basis) {
1685     PC_IS *pcis = (PC_IS*)(pc->data);
1686 
1687     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1688     if (pcbddc->benign_change) {
1689       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1690       /* pop B0 from pcbddc->local_mat */
1691       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1692     }
1693     /* get submatrices */
1694     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1695     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1696     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1697     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1698     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1699     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1700     /* set flag in pcis to not reuse submatrices during PCISCreate */
1701     pcis->reusesubmatrices = PETSC_FALSE;
1702   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1703     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1704     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1705     pcbddc->local_mat = matis->A;
1706   }
1707 
1708   /* interface pressure block row for B_C */
1709   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1710   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1711   if (lA && lP) {
1712     PC_IS*    pcis = (PC_IS*)pc->data;
1713     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1714     PetscBool issym;
1715     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1716     if (issym) {
1717       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1718       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1719       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1720       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1721     } else {
1722       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1723       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1724       ierr = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1725       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1726     }
1727     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1728     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1729     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1730     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1731     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1732     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1733     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1734     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1735   }
1736 
1737   /* SetUp coarse and local Neumann solvers */
1738   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1739   /* SetUp Scaling operator */
1740   if (pcbddc->use_deluxe_scaling) {
1741     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1742   }
1743 
1744   /* mark topography as done */
1745   pcbddc->recompute_topography = PETSC_FALSE;
1746 
1747   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1748   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1749 
1750   if (pcbddc->dbg_flag) {
1751     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1752   }
1753   PetscFunctionReturn(0);
1754 }
1755 
1756 /*
1757    PCApply_BDDC - Applies the BDDC operator to a vector.
1758 
1759    Input Parameters:
1760 +  pc - the preconditioner context
1761 -  r - input vector (global)
1762 
1763    Output Parameter:
1764 .  z - output vector (global)
1765 
1766    Application Interface Routine: PCApply()
1767  */
1768 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1769 {
1770   PC_IS             *pcis = (PC_IS*)(pc->data);
1771   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1772   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1773   PetscErrorCode    ierr;
1774   const PetscScalar one = 1.0;
1775   const PetscScalar m_one = -1.0;
1776   const PetscScalar zero = 0.0;
1777 
1778 /* This code is similar to that provided in nn.c for PCNN
1779    NN interface preconditioner changed to BDDC
1780    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1781 
1782   PetscFunctionBegin;
1783   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1784   if (pcbddc->ChangeOfBasisMatrix) {
1785     Vec swap;
1786 
1787     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1788     swap = pcbddc->work_change;
1789     pcbddc->work_change = r;
1790     r = swap;
1791     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1792     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1793       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1794       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1795     }
1796   }
1797   if (pcbddc->benign_have_null) { /* get p0 from r */
1798     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1799   }
1800   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1801     ierr = VecCopy(r,z);CHKERRQ(ierr);
1802     /* First Dirichlet solve */
1803     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1804     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1805     /*
1806       Assembling right hand side for BDDC operator
1807       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1808       - pcis->vec1_B the interface part of the global vector z
1809     */
1810     if (n_D) {
1811       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1812       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1813       if (pcbddc->switch_static) {
1814         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1815 
1816         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1817         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1818         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1819         if (!pcbddc->switch_static_change) {
1820           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1821         } else {
1822           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1823           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1824           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1825         }
1826         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1827         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1828         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1829         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1830       } else {
1831         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1832       }
1833     } else {
1834       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1835     }
1836     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1837     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1838     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1839   } else {
1840     if (!pcbddc->benign_apply_coarse_only) {
1841       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1842     }
1843   }
1844 
1845   /* Apply interface preconditioner
1846      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1847   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1848 
1849   /* Apply transpose of partition of unity operator */
1850   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1851 
1852   /* Second Dirichlet solve and assembling of output */
1853   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1854   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1855   if (n_B) {
1856     if (pcbddc->switch_static) {
1857       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1858 
1859       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1860       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1861       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1862       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1863       if (!pcbddc->switch_static_change) {
1864         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1865       } else {
1866         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1867         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1868         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1869       }
1870       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1871       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1872     } else {
1873       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1874     }
1875   } else if (pcbddc->switch_static) { /* n_B is zero */
1876     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1877 
1878     if (!pcbddc->switch_static_change) {
1879       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1880     } else {
1881       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1882       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1883       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
1884     }
1885   }
1886   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1887 
1888   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1889     if (pcbddc->switch_static) {
1890       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1891     } else {
1892       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1893     }
1894     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1895     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1896   } else {
1897     if (pcbddc->switch_static) {
1898       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1899     } else {
1900       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1901     }
1902     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1903     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1904   }
1905   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
1906     if (pcbddc->benign_apply_coarse_only) {
1907       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
1908     }
1909     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1910   }
1911 
1912   if (pcbddc->ChangeOfBasisMatrix) {
1913     pcbddc->work_change = r;
1914     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
1915     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
1916   }
1917   PetscFunctionReturn(0);
1918 }
1919 
1920 /*
1921    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1922 
1923    Input Parameters:
1924 +  pc - the preconditioner context
1925 -  r - input vector (global)
1926 
1927    Output Parameter:
1928 .  z - output vector (global)
1929 
1930    Application Interface Routine: PCApplyTranspose()
1931  */
1932 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1933 {
1934   PC_IS             *pcis = (PC_IS*)(pc->data);
1935   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1936   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1937   PetscErrorCode    ierr;
1938   const PetscScalar one = 1.0;
1939   const PetscScalar m_one = -1.0;
1940   const PetscScalar zero = 0.0;
1941 
1942   PetscFunctionBegin;
1943   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1944   if (pcbddc->ChangeOfBasisMatrix) {
1945     Vec swap;
1946 
1947     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1948     swap = pcbddc->work_change;
1949     pcbddc->work_change = r;
1950     r = swap;
1951     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1952     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
1953       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1954       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1955     }
1956   }
1957   if (pcbddc->benign_have_null) { /* get p0 from r */
1958     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1959   }
1960   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1961     ierr = VecCopy(r,z);CHKERRQ(ierr);
1962     /* First Dirichlet solve */
1963     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1964     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1965     /*
1966       Assembling right hand side for BDDC operator
1967       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1968       - pcis->vec1_B the interface part of the global vector z
1969     */
1970     if (n_D) {
1971       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1972       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1973       if (pcbddc->switch_static) {
1974         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1975 
1976         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1977         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1978         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1979         if (!pcbddc->switch_static_change) {
1980           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1981         } else {
1982           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1983           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1984           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1985         }
1986         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1987         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1988         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1989         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1990       } else {
1991         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1992       }
1993     } else {
1994       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1995     }
1996     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1997     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1998     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1999   } else {
2000     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
2001   }
2002 
2003   /* Apply interface preconditioner
2004      input/output vecs: pcis->vec1_B and pcis->vec1_D */
2005   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
2006 
2007   /* Apply transpose of partition of unity operator */
2008   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2009 
2010   /* Second Dirichlet solve and assembling of output */
2011   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2012   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2013   if (n_B) {
2014     if (pcbddc->switch_static) {
2015       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2016 
2017       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2018       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2019       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2020       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2021       if (!pcbddc->switch_static_change) {
2022         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2023       } else {
2024         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2025         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2026         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2027       }
2028       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2029       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2030     } else {
2031       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2032     }
2033   } else if (pcbddc->switch_static) { /* n_B is zero */
2034     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2035 
2036     if (!pcbddc->switch_static_change) {
2037       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2038     } else {
2039       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2040       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2041       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2042     }
2043   }
2044   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2045   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2046     if (pcbddc->switch_static) {
2047       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2048     } else {
2049       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2050     }
2051     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2052     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2053   } else {
2054     if (pcbddc->switch_static) {
2055       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2056     } else {
2057       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2058     }
2059     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2060     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2061   }
2062   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2063     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2064   }
2065   if (pcbddc->ChangeOfBasisMatrix) {
2066     pcbddc->work_change = r;
2067     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2068     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2069   }
2070   PetscFunctionReturn(0);
2071 }
2072 
2073 PetscErrorCode PCReset_BDDC(PC pc)
2074 {
2075   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2076   PC_IS          *pcis = (PC_IS*)pc->data;
2077   KSP            kspD,kspR,kspC;
2078   PetscErrorCode ierr;
2079 
2080   PetscFunctionBegin;
2081   /* free BDDC custom data  */
2082   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2083   /* destroy objects related to topography */
2084   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2085   /* destroy objects for scaling operator */
2086   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2087   /* free solvers stuff */
2088   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2089   /* free global vectors needed in presolve */
2090   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2091   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2092   /* free data created by PCIS */
2093   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2094 
2095   /* restore defaults */
2096   kspD = pcbddc->ksp_D;
2097   kspR = pcbddc->ksp_R;
2098   kspC = pcbddc->coarse_ksp;
2099   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2100   pcis->n_neigh                     = -1;
2101   pcis->scaling_factor              = 1.0;
2102   pcis->reusesubmatrices            = PETSC_TRUE;
2103   pcbddc->use_local_adj             = PETSC_TRUE;
2104   pcbddc->use_vertices              = PETSC_TRUE;
2105   pcbddc->use_edges                 = PETSC_TRUE;
2106   pcbddc->symmetric_primal          = PETSC_TRUE;
2107   pcbddc->vertex_size               = 1;
2108   pcbddc->recompute_topography      = PETSC_TRUE;
2109   pcbddc->coarse_size               = -1;
2110   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2111   pcbddc->coarsening_ratio          = 8;
2112   pcbddc->coarse_eqs_per_proc       = 1;
2113   pcbddc->benign_compute_correction = PETSC_TRUE;
2114   pcbddc->nedfield                  = -1;
2115   pcbddc->nedglobal                 = PETSC_TRUE;
2116   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2117   pcbddc->sub_schurs_layers         = -1;
2118   pcbddc->ksp_D                     = kspD;
2119   pcbddc->ksp_R                     = kspR;
2120   pcbddc->coarse_ksp                = kspC;
2121   PetscFunctionReturn(0);
2122 }
2123 
2124 PetscErrorCode PCDestroy_BDDC(PC pc)
2125 {
2126   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2127   PetscErrorCode ierr;
2128 
2129   PetscFunctionBegin;
2130   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2131   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2132   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2133   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2134   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2135   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2136   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2137   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2138   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2139   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2140   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2141   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2142   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2143   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2144   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2145   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2146   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2147   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2148   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2149   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2150   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2151   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2152   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2153   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2154   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2155   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2156   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2157   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2158   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2159   PetscFunctionReturn(0);
2160 }
2161 
2162 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2163 {
2164   PetscFunctionBegin;
2165   *change = PETSC_TRUE;
2166   PetscFunctionReturn(0);
2167 }
2168 
2169 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2170 {
2171   FETIDPMat_ctx  mat_ctx;
2172   Vec            work;
2173   PC_IS*         pcis;
2174   PC_BDDC*       pcbddc;
2175   PetscErrorCode ierr;
2176 
2177   PetscFunctionBegin;
2178   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2179   pcis = (PC_IS*)mat_ctx->pc->data;
2180   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2181 
2182   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2183   /* copy rhs since we may change it during PCPreSolve_BDDC */
2184   if (!pcbddc->original_rhs) {
2185     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2186   }
2187   if (mat_ctx->rhs_flip) {
2188     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2189   } else {
2190     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2191   }
2192   if (mat_ctx->g2g_p) {
2193     /* interface pressure rhs */
2194     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2195     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2196     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2197     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2198     if (!mat_ctx->rhs_flip) {
2199       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2200     }
2201   }
2202   /*
2203      change of basis for physical rhs if needed
2204      It also changes the rhs in case of dirichlet boundaries
2205   */
2206   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2207   if (pcbddc->ChangeOfBasisMatrix) {
2208     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2209     work = pcbddc->work_change;
2210    } else {
2211     work = pcbddc->original_rhs;
2212   }
2213   /* store vectors for computation of fetidp final solution */
2214   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2215   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2216   /* scale rhs since it should be unassembled */
2217   /* TODO use counter scaling? (also below) */
2218   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2219   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2220   /* Apply partition of unity */
2221   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2222   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2223   if (!pcbddc->switch_static) {
2224     /* compute partially subassembled Schur complement right-hand side */
2225     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2226     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2227     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2228     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2229     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2230     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2231     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2232     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2233     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2234     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2235   }
2236   /* BDDC rhs */
2237   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2238   if (pcbddc->switch_static) {
2239     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2240   }
2241   /* apply BDDC */
2242   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2243   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2244   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2245 
2246   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2247   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2248   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2249   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2250   /* Add contribution to interface pressures */
2251   if (mat_ctx->l2g_p) {
2252     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2253     if (pcbddc->switch_static) {
2254       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2255     }
2256     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2257     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2258   }
2259   PetscFunctionReturn(0);
2260 }
2261 
2262 /*@
2263  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2264 
2265    Collective
2266 
2267    Input Parameters:
2268 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2269 -  standard_rhs    - the right-hand side of the original linear system
2270 
2271    Output Parameters:
2272 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2273 
2274    Level: developer
2275 
2276    Notes:
2277 
2278 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2279 @*/
2280 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2281 {
2282   FETIDPMat_ctx  mat_ctx;
2283   PetscErrorCode ierr;
2284 
2285   PetscFunctionBegin;
2286   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2287   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2288   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2289   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2290   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2291   PetscFunctionReturn(0);
2292 }
2293 
2294 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2295 {
2296   FETIDPMat_ctx  mat_ctx;
2297   PC_IS*         pcis;
2298   PC_BDDC*       pcbddc;
2299   PetscErrorCode ierr;
2300   Vec            work;
2301 
2302   PetscFunctionBegin;
2303   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2304   pcis = (PC_IS*)mat_ctx->pc->data;
2305   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2306 
2307   /* apply B_delta^T */
2308   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2309   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2310   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2311   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2312   if (mat_ctx->l2g_p) {
2313     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2314     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2315     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2316   }
2317 
2318   /* compute rhs for BDDC application */
2319   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2320   if (pcbddc->switch_static) {
2321     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2322     if (mat_ctx->l2g_p) {
2323       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2324       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2325     }
2326   }
2327 
2328   /* apply BDDC */
2329   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2330   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2331 
2332   /* put values into global vector */
2333   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2334   else work = standard_sol;
2335   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2336   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2337   if (!pcbddc->switch_static) {
2338     /* compute values into the interior if solved for the partially subassembled Schur complement */
2339     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2340     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2341     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2342   }
2343 
2344   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2345   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2346   /* add p0 solution to final solution */
2347   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2348   if (pcbddc->ChangeOfBasisMatrix) {
2349     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2350   }
2351   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2352   if (mat_ctx->g2g_p) {
2353     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2354     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2355   }
2356   PetscFunctionReturn(0);
2357 }
2358 
2359 /*@
2360  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2361 
2362    Collective
2363 
2364    Input Parameters:
2365 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2366 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2367 
2368    Output Parameters:
2369 .  standard_sol    - the solution defined on the physical domain
2370 
2371    Level: developer
2372 
2373    Notes:
2374 
2375 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2376 @*/
2377 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2378 {
2379   FETIDPMat_ctx  mat_ctx;
2380   PetscErrorCode ierr;
2381 
2382   PetscFunctionBegin;
2383   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2384   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2385   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2386   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2387   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2388   PetscFunctionReturn(0);
2389 }
2390 
2391 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2392 {
2393 
2394   FETIDPMat_ctx  fetidpmat_ctx;
2395   Mat            newmat;
2396   FETIDPPC_ctx   fetidppc_ctx;
2397   PC             newpc;
2398   MPI_Comm       comm;
2399   PetscErrorCode ierr;
2400 
2401   PetscFunctionBegin;
2402   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2403   /* FETIDP linear matrix */
2404   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2405   fetidpmat_ctx->fully_redundant = fully_redundant;
2406   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2407   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2408   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2409   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2410   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2411   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2412   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2413   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2414   /* FETIDP preconditioner */
2415   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2416   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2417   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2418   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2419   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2420   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2421   if (!fetidpmat_ctx->l2g_lambda_only) {
2422     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2423     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2424     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2425     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2426     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2427     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2428   } else {
2429     KSP      *ksps;
2430     PC       lagpc;
2431     Mat      M,AM,PM;
2432     PetscInt nn;
2433 
2434     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2435     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2436     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2437     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2438     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2439     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2440     ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2441     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2442     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2443     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2444 
2445     /* set the solver for the (0,0) block */
2446     ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2447     ierr = PCCreate(comm,&lagpc);CHKERRQ(ierr);
2448     ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2449     ierr = KSPGetOperators(ksps[0],&AM,&PM);CHKERRQ(ierr);
2450     ierr = PCSetOperators(lagpc,AM,PM);CHKERRQ(ierr);
2451     ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2452     ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2453     ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2454     ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2455     ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2456     ierr = KSPSetPC(ksps[0],lagpc);CHKERRQ(ierr);
2457     ierr = PCDestroy(&lagpc);CHKERRQ(ierr);
2458     ierr = PetscFree(ksps);CHKERRQ(ierr);
2459   }
2460   /* return pointers for objects created */
2461   *fetidp_mat = newmat;
2462   *fetidp_pc = newpc;
2463   PetscFunctionReturn(0);
2464 }
2465 
2466 /*@C
2467  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2468 
2469    Collective
2470 
2471    Input Parameters:
2472 +  pc - the BDDC preconditioning context (setup should have been called before)
2473 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2474 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2475 
2476    Output Parameters:
2477 +  fetidp_mat - shell FETI-DP matrix object
2478 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2479 
2480    Level: developer
2481 
2482    Notes:
2483      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2484 
2485 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2486 @*/
2487 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2488 {
2489   PetscErrorCode ierr;
2490 
2491   PetscFunctionBegin;
2492   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2493   if (pc->setupcalled) {
2494     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2495   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2496   PetscFunctionReturn(0);
2497 }
2498 /* -------------------------------------------------------------------------- */
2499 /*MC
2500    PCBDDC - Balancing Domain Decomposition by Constraints.
2501 
2502    An implementation of the BDDC preconditioner based on
2503 
2504 .vb
2505    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2506    [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
2507    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2508    [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
2509 .ve
2510 
2511    The matrix to be preconditioned (Pmat) must be of type MATIS.
2512 
2513    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2514 
2515    It also works with unsymmetric and indefinite problems.
2516 
2517    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.
2518 
2519    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).
2520 
2521    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()
2522    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2523 
2524    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2525 
2526    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.
2527    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2528 
2529    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2530 
2531    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.
2532 
2533    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.
2534    Deluxe scaling is not supported yet for FETI-DP.
2535 
2536    Options Database Keys (some of them, run with -h for a complete list):
2537 
2538 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2539 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2540 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2541 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2542 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2543 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2544 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2545 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2546 .    -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)
2547 .    -pc_bddc_redistribute <0> - size of a subset of processors where the coarse problem will be remapped (the value is ignored if not at the coarsest level)
2548 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2549 .    -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)
2550 .    -pc_bddc_adaptive_threshold <0.0> - when a value greater than one is specified, adaptive selection of constraints is performed on edges and faces (requires deluxe scaling and MUMPS or MKL_PARDISO installed)
2551 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2552 
2553    Options for Dirichlet, Neumann or coarse solver can be set with
2554 .vb
2555       -pc_bddc_dirichlet_
2556       -pc_bddc_neumann_
2557       -pc_bddc_coarse_
2558 .ve
2559    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2560 
2561    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2562 .vb
2563       -pc_bddc_dirichlet_lN_
2564       -pc_bddc_neumann_lN_
2565       -pc_bddc_coarse_lN_
2566 .ve
2567    Note that level number ranges from the finest (0) to the coarsest (N).
2568    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.
2569 .vb
2570      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2571 .ve
2572    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
2573 
2574    Level: intermediate
2575 
2576    Developer notes:
2577 
2578    Contributed by Stefano Zampini
2579 
2580 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2581 M*/
2582 
2583 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2584 {
2585   PetscErrorCode      ierr;
2586   PC_BDDC             *pcbddc;
2587 
2588   PetscFunctionBegin;
2589   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2590   pc->data = (void*)pcbddc;
2591 
2592   /* create PCIS data structure */
2593   ierr = PCISCreate(pc);CHKERRQ(ierr);
2594 
2595   /* create local graph structure */
2596   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2597 
2598   /* BDDC nonzero defaults */
2599   pcbddc->use_local_adj             = PETSC_TRUE;
2600   pcbddc->use_vertices              = PETSC_TRUE;
2601   pcbddc->use_edges                 = PETSC_TRUE;
2602   pcbddc->symmetric_primal          = PETSC_TRUE;
2603   pcbddc->vertex_size               = 1;
2604   pcbddc->recompute_topography      = PETSC_TRUE;
2605   pcbddc->coarse_size               = -1;
2606   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2607   pcbddc->coarsening_ratio          = 8;
2608   pcbddc->coarse_eqs_per_proc       = 1;
2609   pcbddc->benign_compute_correction = PETSC_TRUE;
2610   pcbddc->nedfield                  = -1;
2611   pcbddc->nedglobal                 = PETSC_TRUE;
2612   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2613   pcbddc->sub_schurs_layers         = -1;
2614 
2615   /* function pointers */
2616   pc->ops->apply               = PCApply_BDDC;
2617   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2618   pc->ops->setup               = PCSetUp_BDDC;
2619   pc->ops->destroy             = PCDestroy_BDDC;
2620   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2621   pc->ops->view                = PCView_BDDC;
2622   pc->ops->applyrichardson     = 0;
2623   pc->ops->applysymmetricleft  = 0;
2624   pc->ops->applysymmetricright = 0;
2625   pc->ops->presolve            = PCPreSolve_BDDC;
2626   pc->ops->postsolve           = PCPostSolve_BDDC;
2627   pc->ops->reset               = PCReset_BDDC;
2628 
2629   /* composing function */
2630   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
2631   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
2632   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2633   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2634   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
2635   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2636   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2637   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2638   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2639   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2640   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2641   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2642   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2643   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2644   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2645   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2646   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2647   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2648   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2649   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2650   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2651   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2652   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2653   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
2654   PetscFunctionReturn(0);
2655 }
2656 
2657