xref: /petsc/src/ksp/pc/impls/bddc/bddc.c (revision 285fb4e2b69b3de46a0633bd0adc6a7f684caa1e)
1 /* TODOLIST
2 
3    Solvers
4    - Add support for cholesky for coarse solver (similar to local solvers)
5    - Propagate ksp prefixes for solvers to mat objects?
6 
7    User interface
8    - ** DM attached to pc?
9 
10    Debugging output
11    - * Better management of verbosity levels of debugging output
12 
13    Extra
14    - *** Is it possible to work with PCBDDCGraph on boundary indices only (less memory consumed)?
15    - BDDC with MG framework?
16 
17    MATIS related operations contained in BDDC code
18    - Provide general case for subassembling
19 
20 */
21 
22 #include <../src/ksp/pc/impls/bddc/bddc.h> /*I "petscpc.h" I*/  /* includes for fortran wrappers */
23 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
24 #include <petscblaslapack.h>
25 
26 static PetscBool  cited = PETSC_FALSE;
27 static const char citation[] =
28 "@article{ZampiniPCBDDC,\n"
29 "author = {Stefano Zampini},\n"
30 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
31 "journal = {SIAM Journal on Scientific Computing},\n"
32 "volume = {38},\n"
33 "number = {5},\n"
34 "pages = {S282-S306},\n"
35 "year = {2016},\n"
36 "doi = {10.1137/15M1025785},\n"
37 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
38 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
39 "}\n";
40 
41 /* temporarily declare it */
42 PetscErrorCode PCApply_BDDC(PC,Vec,Vec);
43 
44 PetscErrorCode PCSetFromOptions_BDDC(PetscOptionItems *PetscOptionsObject,PC pc)
45 {
46   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
47   PetscInt       nt;
48   PetscErrorCode ierr;
49 
50   PetscFunctionBegin;
51   ierr = PetscOptionsHead(PetscOptionsObject,"BDDC options");CHKERRQ(ierr);
52   /* Verbose debugging */
53   ierr = PetscOptionsInt("-pc_bddc_check_level","Verbose output for PCBDDC (intended for debug)","none",pcbddc->dbg_flag,&pcbddc->dbg_flag,NULL);CHKERRQ(ierr);
54   /* Approximate solvers */
55   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate","Inform PCBDDC that we are using approximate Dirichlet solvers","none",pcbddc->NullSpace_corr[0],&pcbddc->NullSpace_corr[0],NULL);CHKERRQ(ierr);
56   ierr = PetscOptionsBool("-pc_bddc_dirichlet_approximate_scale","Inform PCBDDC that we need to scale the Dirichlet solve","none",pcbddc->NullSpace_corr[1],&pcbddc->NullSpace_corr[1],NULL);CHKERRQ(ierr);
57   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate","Inform PCBDDC that we are using approximate Neumann solvers","none",pcbddc->NullSpace_corr[2],&pcbddc->NullSpace_corr[2],NULL);CHKERRQ(ierr);
58   ierr = PetscOptionsBool("-pc_bddc_neumann_approximate_scale","Inform PCBDDC that we need to scale the Neumann solve","none",pcbddc->NullSpace_corr[3],&pcbddc->NullSpace_corr[3],NULL);CHKERRQ(ierr);
59   /* Primal space customization */
60   ierr = PetscOptionsBool("-pc_bddc_use_local_mat_graph","Use or not adjacency graph of local mat for interface analysis","none",pcbddc->use_local_adj,&pcbddc->use_local_adj,NULL);CHKERRQ(ierr);
61   ierr = PetscOptionsInt("-pc_bddc_graph_maxcount","Maximum number of shared subdomains for a connected component","none",pcbddc->graphmaxcount,&pcbddc->graphmaxcount,NULL);CHKERRQ(ierr);
62   ierr = PetscOptionsBool("-pc_bddc_corner_selection","Activates face-based corner selection","none",pcbddc->corner_selection,&pcbddc->corner_selection,NULL);CHKERRQ(ierr);
63   ierr = PetscOptionsBool("-pc_bddc_use_vertices","Use or not corner dofs in coarse space","none",pcbddc->use_vertices,&pcbddc->use_vertices,NULL);CHKERRQ(ierr);
64   ierr = PetscOptionsBool("-pc_bddc_use_edges","Use or not edge constraints in coarse space","none",pcbddc->use_edges,&pcbddc->use_edges,NULL);CHKERRQ(ierr);
65   ierr = PetscOptionsBool("-pc_bddc_use_faces","Use or not face constraints in coarse space","none",pcbddc->use_faces,&pcbddc->use_faces,NULL);CHKERRQ(ierr);
66   ierr = PetscOptionsInt("-pc_bddc_vertex_size","Connected components smaller or equal to vertex size will be considered as primal vertices","none",pcbddc->vertex_size,&pcbddc->vertex_size,NULL);CHKERRQ(ierr);
67   ierr = PetscOptionsBool("-pc_bddc_use_true_nnsp","Use near null space attached to the matrix without modifications","none",pcbddc->use_nnsp_true,&pcbddc->use_nnsp_true,NULL);CHKERRQ(ierr);
68   ierr = PetscOptionsBool("-pc_bddc_use_qr_single","Use QR factorization for single constraints on cc (QR is always used when multiple constraints are present)","none",pcbddc->use_qr_single,&pcbddc->use_qr_single,NULL);CHKERRQ(ierr);
69   /* Change of basis */
70   ierr = PetscOptionsBool("-pc_bddc_use_change_of_basis","Use or not internal change of basis on local edge nodes","none",pcbddc->use_change_of_basis,&pcbddc->use_change_of_basis,NULL);CHKERRQ(ierr);
71   ierr = PetscOptionsBool("-pc_bddc_use_change_on_faces","Use or not internal change of basis on local face nodes","none",pcbddc->use_change_on_faces,&pcbddc->use_change_on_faces,NULL);CHKERRQ(ierr);
72   if (!pcbddc->use_change_of_basis) {
73     pcbddc->use_change_on_faces = PETSC_FALSE;
74   }
75   /* Switch between M_2 (default) and M_3 preconditioners (as defined by C. Dohrmann in the ref. article) */
76   ierr = PetscOptionsBool("-pc_bddc_switch_static","Switch on static condensation ops around the interface preconditioner","none",pcbddc->switch_static,&pcbddc->switch_static,NULL);CHKERRQ(ierr);
77   ierr = PetscOptionsInt("-pc_bddc_coarse_eqs_per_proc","Number of equations per process for coarse problem redistribution (significant only at the coarsest level)","none",pcbddc->coarse_eqs_per_proc,&pcbddc->coarse_eqs_per_proc,NULL);CHKERRQ(ierr);
78   ierr = PetscOptionsInt("-pc_bddc_coarsening_ratio","Set coarsening ratio used in multilevel coarsening","none",pcbddc->coarsening_ratio,&pcbddc->coarsening_ratio,NULL);CHKERRQ(ierr);
79   ierr = PetscOptionsInt("-pc_bddc_levels","Set maximum number of levels for multilevel","none",pcbddc->max_levels,&pcbddc->max_levels,NULL);CHKERRQ(ierr);
80   ierr = PetscOptionsBool("-pc_bddc_use_coarse_estimates","Use estimated eigenvalues for coarse problem","none",pcbddc->use_coarse_estimates,&pcbddc->use_coarse_estimates,NULL);CHKERRQ(ierr);
81   ierr = PetscOptionsBool("-pc_bddc_use_deluxe_scaling","Use deluxe scaling for BDDC","none",pcbddc->use_deluxe_scaling,&pcbddc->use_deluxe_scaling,NULL);CHKERRQ(ierr);
82   ierr = PetscOptionsBool("-pc_bddc_schur_rebuild","Whether or not the interface graph for Schur principal minors has to be rebuilt (i.e. define the interface without any adjacency)","none",pcbddc->sub_schurs_rebuild,&pcbddc->sub_schurs_rebuild,NULL);CHKERRQ(ierr);
83   ierr = PetscOptionsInt("-pc_bddc_schur_layers","Number of dofs' layers for the computation of principal minors (i.e. -1 uses all dofs)","none",pcbddc->sub_schurs_layers,&pcbddc->sub_schurs_layers,NULL);CHKERRQ(ierr);
84   ierr = PetscOptionsBool("-pc_bddc_schur_use_useradj","Whether or not the CSR graph specified by the user should be used for computing successive layers (default is to use adj of local mat)","none",pcbddc->sub_schurs_use_useradj,&pcbddc->sub_schurs_use_useradj,NULL);CHKERRQ(ierr);
85   ierr = PetscOptionsBool("-pc_bddc_schur_exact","Whether or not to use the exact Schur complement instead of the reduced one (which excludes size 1 cc)","none",pcbddc->sub_schurs_exact_schur,&pcbddc->sub_schurs_exact_schur,NULL);CHKERRQ(ierr);
86   ierr = PetscOptionsBool("-pc_bddc_deluxe_zerorows","Zero rows and columns of deluxe operators associated with primal dofs","none",pcbddc->deluxe_zerorows,&pcbddc->deluxe_zerorows,NULL);CHKERRQ(ierr);
87   ierr = PetscOptionsBool("-pc_bddc_deluxe_singlemat","Collapse deluxe operators","none",pcbddc->deluxe_singlemat,&pcbddc->deluxe_singlemat,NULL);CHKERRQ(ierr);
88   ierr = PetscOptionsBool("-pc_bddc_adaptive_userdefined","Use user-defined constraints (should be attached via MatSetNearNullSpace to pmat) in addition to those adaptively generated","none",pcbddc->adaptive_userdefined,&pcbddc->adaptive_userdefined,NULL);CHKERRQ(ierr);
89   nt   = 2;
90   ierr = PetscOptionsRealArray("-pc_bddc_adaptive_threshold","Thresholds to be used for adaptive selection of constraints","none",pcbddc->adaptive_threshold,&nt,NULL);CHKERRQ(ierr);
91   if (nt == 1) pcbddc->adaptive_threshold[1] = pcbddc->adaptive_threshold[0];
92   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmin","Minimum number of constraints per connected components","none",pcbddc->adaptive_nmin,&pcbddc->adaptive_nmin,NULL);CHKERRQ(ierr);
93   ierr = PetscOptionsInt("-pc_bddc_adaptive_nmax","Maximum number of constraints per connected components","none",pcbddc->adaptive_nmax,&pcbddc->adaptive_nmax,NULL);CHKERRQ(ierr);
94   ierr = PetscOptionsBool("-pc_bddc_symmetric","Symmetric computation of primal basis functions","none",pcbddc->symmetric_primal,&pcbddc->symmetric_primal,NULL);CHKERRQ(ierr);
95   ierr = PetscOptionsInt("-pc_bddc_coarse_adj","Number of processors where to map the coarse adjacency list","none",pcbddc->coarse_adj_red,&pcbddc->coarse_adj_red,NULL);CHKERRQ(ierr);
96   ierr = PetscOptionsBool("-pc_bddc_benign_trick","Apply the benign subspace trick to saddle point problems with discontinuous pressures","none",pcbddc->benign_saddle_point,&pcbddc->benign_saddle_point,NULL);CHKERRQ(ierr);
97   ierr = PetscOptionsBool("-pc_bddc_benign_change","Compute the pressure change of basis explicitly","none",pcbddc->benign_change_explicit,&pcbddc->benign_change_explicit,NULL);CHKERRQ(ierr);
98   ierr = PetscOptionsBool("-pc_bddc_benign_compute_correction","Compute the benign correction during PreSolve","none",pcbddc->benign_compute_correction,&pcbddc->benign_compute_correction,NULL);CHKERRQ(ierr);
99   ierr = PetscOptionsBool("-pc_bddc_nonetflux","Automatic computation of no-net-flux quadrature weights","none",pcbddc->compute_nonetflux,&pcbddc->compute_nonetflux,NULL);CHKERRQ(ierr);
100   ierr = PetscOptionsBool("-pc_bddc_detect_disconnected","Detects disconnected subdomains","none",pcbddc->detect_disconnected,&pcbddc->detect_disconnected,NULL);CHKERRQ(ierr);
101   ierr = PetscOptionsBool("-pc_bddc_eliminate_dirichlet","Whether or not we want to eliminate dirichlet dofs during presolve","none",pcbddc->eliminate_dirdofs,&pcbddc->eliminate_dirdofs,NULL);CHKERRQ(ierr);
102   ierr = PetscOptionsTail();CHKERRQ(ierr);
103   PetscFunctionReturn(0);
104 }
105 
106 static PetscErrorCode PCView_BDDC(PC pc,PetscViewer viewer)
107 {
108   PC_BDDC              *pcbddc = (PC_BDDC*)pc->data;
109   PC_IS                *pcis = (PC_IS*)pc->data;
110   PetscErrorCode       ierr;
111   PetscBool            isascii;
112   PetscSubcomm         subcomm;
113   PetscViewer          subviewer;
114 
115   PetscFunctionBegin;
116   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
117   /* ASCII viewer */
118   if (isascii) {
119     PetscMPIInt   color,rank,size;
120     PetscInt64    loc[7],gsum[6],gmax[6],gmin[6],totbenign;
121     PetscScalar   interface_size;
122     PetscReal     ratio1=0.,ratio2=0.;
123     Vec           counter;
124 
125     if (!pc->setupcalled) {
126       ierr = PetscViewerASCIIPrintf(viewer,"  Partial information available: preconditioner has not been setup yet\n");CHKERRQ(ierr);
127     }
128     ierr = PetscViewerASCIIPrintf(viewer,"  Use verbose output: %D\n",pcbddc->dbg_flag);CHKERRQ(ierr);
129     ierr = PetscViewerASCIIPrintf(viewer,"  Use user-defined CSR: %d\n",!!pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
130     ierr = PetscViewerASCIIPrintf(viewer,"  Use local mat graph: %d\n",pcbddc->use_local_adj && !pcbddc->mat_graph->nvtxs_csr);CHKERRQ(ierr);
131     if (pcbddc->mat_graph->twodim) {
132       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 2\n");CHKERRQ(ierr);
133     } else {
134       ierr = PetscViewerASCIIPrintf(viewer,"  Connectivity graph topological dimension: 3\n");CHKERRQ(ierr);
135     }
136     if (pcbddc->graphmaxcount != PETSC_MAX_INT) {
137       ierr = PetscViewerASCIIPrintf(viewer,"  Graph max count: %D\n",pcbddc->graphmaxcount);CHKERRQ(ierr);
138     }
139     ierr = PetscViewerASCIIPrintf(viewer,"  Use vertices: %d (vertex size %D)\n",pcbddc->use_vertices,pcbddc->vertex_size);CHKERRQ(ierr);
140     ierr = PetscViewerASCIIPrintf(viewer,"  Use edges: %d\n",pcbddc->use_edges);CHKERRQ(ierr);
141     ierr = PetscViewerASCIIPrintf(viewer,"  Use faces: %d\n",pcbddc->use_faces);CHKERRQ(ierr);
142     ierr = PetscViewerASCIIPrintf(viewer,"  Use true near null space: %d\n",pcbddc->use_nnsp_true);CHKERRQ(ierr);
143     ierr = PetscViewerASCIIPrintf(viewer,"  Use QR for single constraints on cc: %d\n",pcbddc->use_qr_single);CHKERRQ(ierr);
144     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local edge nodes: %d\n",pcbddc->use_change_of_basis);CHKERRQ(ierr);
145     ierr = PetscViewerASCIIPrintf(viewer,"  Use change of basis on local face nodes: %d\n",pcbddc->use_change_on_faces);CHKERRQ(ierr);
146     ierr = PetscViewerASCIIPrintf(viewer,"  User defined change of basis matrix: %d\n",!!pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
147     ierr = PetscViewerASCIIPrintf(viewer,"  Has change of basis matrix: %d\n",!!pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
148     ierr = PetscViewerASCIIPrintf(viewer,"  Eliminate dirichlet boundary dofs: %d\n",pcbddc->eliminate_dirdofs);CHKERRQ(ierr);
149     ierr = PetscViewerASCIIPrintf(viewer,"  Switch on static condensation ops around the interface preconditioner: %d\n",pcbddc->switch_static);CHKERRQ(ierr);
150     ierr = PetscViewerASCIIPrintf(viewer,"  Use exact dirichlet trick: %d\n",pcbddc->use_exact_dirichlet_trick);CHKERRQ(ierr);
151     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel max levels: %D\n",pcbddc->max_levels);CHKERRQ(ierr);
152     ierr = PetscViewerASCIIPrintf(viewer,"  Multilevel coarsening ratio: %D\n",pcbddc->coarsening_ratio);CHKERRQ(ierr);
153     ierr = PetscViewerASCIIPrintf(viewer,"  Use estimated eigs for coarse problem: %d\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
154     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe scaling: %d\n",pcbddc->use_deluxe_scaling);CHKERRQ(ierr);
155     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe zerorows: %d\n",pcbddc->deluxe_zerorows);CHKERRQ(ierr);
156     ierr = PetscViewerASCIIPrintf(viewer,"  Use deluxe singlemat: %d\n",pcbddc->deluxe_singlemat);CHKERRQ(ierr);
157     ierr = PetscViewerASCIIPrintf(viewer,"  Rebuild interface graph for Schur principal minors: %d\n",pcbddc->sub_schurs_rebuild);CHKERRQ(ierr);
158     ierr = PetscViewerASCIIPrintf(viewer,"  Number of dofs' layers for the computation of principal minors: %D\n",pcbddc->sub_schurs_layers);CHKERRQ(ierr);
159     ierr = PetscViewerASCIIPrintf(viewer,"  Use user CSR graph to compute successive layers: %d\n",pcbddc->sub_schurs_use_useradj);CHKERRQ(ierr);
160     if (pcbddc->adaptive_threshold[1] != pcbddc->adaptive_threshold[0]) {
161       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection thresholds (active %d, userdefined %d): %g,%g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0],pcbddc->adaptive_threshold[1]);CHKERRQ(ierr);
162     } else {
163       ierr = PetscViewerASCIIPrintf(viewer,"  Adaptive constraint selection threshold (active %d, userdefined %d): %g\n",pcbddc->adaptive_selection,pcbddc->adaptive_userdefined,pcbddc->adaptive_threshold[0]);CHKERRQ(ierr);
164     }
165     ierr = PetscViewerASCIIPrintf(viewer,"  Min constraints / connected component: %D\n",pcbddc->adaptive_nmin);CHKERRQ(ierr);
166     ierr = PetscViewerASCIIPrintf(viewer,"  Max constraints / connected component: %D\n",pcbddc->adaptive_nmax);CHKERRQ(ierr);
167     ierr = PetscViewerASCIIPrintf(viewer,"  Invert exact Schur complement for adaptive selection: %d\n",pcbddc->sub_schurs_exact_schur);CHKERRQ(ierr);
168     ierr = PetscViewerASCIIPrintf(viewer,"  Symmetric computation of primal basis functions: %d\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
169     ierr = PetscViewerASCIIPrintf(viewer,"  Num. Procs. to map coarse adjacency list: %D\n",pcbddc->coarse_adj_red);CHKERRQ(ierr);
170     ierr = PetscViewerASCIIPrintf(viewer,"  Coarse eqs per proc (significant at the coarsest level): %D\n",pcbddc->coarse_eqs_per_proc);CHKERRQ(ierr);
171     ierr = PetscViewerASCIIPrintf(viewer,"  Detect disconnected: %d\n",pcbddc->detect_disconnected);CHKERRQ(ierr);
172     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick: %d (change explicit %d)\n",pcbddc->benign_saddle_point,pcbddc->benign_change_explicit);CHKERRQ(ierr);
173     ierr = PetscViewerASCIIPrintf(viewer,"  Benign subspace trick is active: %d\n",pcbddc->benign_have_null);CHKERRQ(ierr);
174     ierr = PetscViewerASCIIPrintf(viewer,"  Algebraic computation of no-net-flux %d\n",pcbddc->compute_nonetflux);CHKERRQ(ierr);
175     if (!pc->setupcalled) PetscFunctionReturn(0);
176 
177     /* compute interface size */
178     ierr = VecSet(pcis->vec1_B,1.0);CHKERRQ(ierr);
179     ierr = MatCreateVecs(pc->pmat,&counter,0);CHKERRQ(ierr);
180     ierr = VecSet(counter,0.0);CHKERRQ(ierr);
181     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
182     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,counter,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
183     ierr = VecSum(counter,&interface_size);CHKERRQ(ierr);
184     ierr = VecDestroy(&counter);CHKERRQ(ierr);
185 
186     /* compute some statistics on the domain decomposition */
187     gsum[0] = 1;
188     gsum[1] = gsum[2] = gsum[3] = gsum[4] = gsum[5] = 0;
189     loc[0]  = !!pcis->n;
190     loc[1]  = pcis->n - pcis->n_B;
191     loc[2]  = pcis->n_B;
192     loc[3]  = pcbddc->local_primal_size;
193     loc[4]  = pcis->n;
194     loc[5]  = pcbddc->n_local_subs > 0 ? pcbddc->n_local_subs : (pcis->n ? 1 : 0);
195     loc[6]  = pcbddc->benign_n;
196     ierr = MPI_Reduce(loc,gsum,6,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
197     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = -1;
198     ierr = MPI_Reduce(loc,gmax,6,MPIU_INT64,MPI_MAX,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
199     if (!loc[0]) loc[1] = loc[2] = loc[3] = loc[4] = loc[5] = PETSC_MAX_INT;
200     ierr = MPI_Reduce(loc,gmin,6,MPIU_INT64,MPI_MIN,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
201     ierr = MPI_Reduce(&loc[6],&totbenign,1,MPIU_INT64,MPI_SUM,0,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
202     if (pcbddc->coarse_size) {
203       ratio1 = pc->pmat->rmap->N/(1.*pcbddc->coarse_size);
204       ratio2 = PetscRealPart(interface_size)/pcbddc->coarse_size;
205     }
206     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** STATISTICS AT LEVEL %d **********************************\n",pcbddc->current_level);CHKERRQ(ierr);
207     ierr = PetscViewerASCIIPrintf(viewer,"  Global dofs sizes: all %D interface %D coarse %D\n",pc->pmat->rmap->N,(PetscInt)PetscRealPart(interface_size),pcbddc->coarse_size);CHKERRQ(ierr);
208     ierr = PetscViewerASCIIPrintf(viewer,"  Coarsening ratios: all/coarse %D interface/coarse %D\n",(PetscInt)ratio1,(PetscInt)ratio2);CHKERRQ(ierr);
209     ierr = PetscViewerASCIIPrintf(viewer,"  Active processes : %D\n",(PetscInt)gsum[0]);CHKERRQ(ierr);
210     ierr = PetscViewerASCIIPrintf(viewer,"  Total subdomains : %D\n",(PetscInt)gsum[5]);CHKERRQ(ierr);
211     if (pcbddc->benign_have_null) {
212       ierr = PetscViewerASCIIPrintf(viewer,"  Benign subs      : %D\n",(PetscInt)totbenign);CHKERRQ(ierr);
213     }
214     ierr = PetscViewerASCIIPrintf(viewer,"  Dofs type        :\tMIN\tMAX\tMEAN\n");CHKERRQ(ierr);
215     ierr = PetscViewerASCIIPrintf(viewer,"  Interior  dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[1],(PetscInt)gmax[1],(PetscInt)(gsum[1]/gsum[0]));CHKERRQ(ierr);
216     ierr = PetscViewerASCIIPrintf(viewer,"  Interface dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[2],(PetscInt)gmax[2],(PetscInt)(gsum[2]/gsum[0]));CHKERRQ(ierr);
217     ierr = PetscViewerASCIIPrintf(viewer,"  Primal    dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[3],(PetscInt)gmax[3],(PetscInt)(gsum[3]/gsum[0]));CHKERRQ(ierr);
218     ierr = PetscViewerASCIIPrintf(viewer,"  Local     dofs   :\t%D\t%D\t%D\n",(PetscInt)gmin[4],(PetscInt)gmax[4],(PetscInt)(gsum[4]/gsum[0]));CHKERRQ(ierr);
219     ierr = PetscViewerASCIIPrintf(viewer,"  Local     subs   :\t%D\t%D\n"    ,(PetscInt)gmin[5],(PetscInt)gmax[5]);CHKERRQ(ierr);
220     ierr = PetscViewerASCIIPrintf(viewer,"  ********************************** COARSE PROBLEM DETAILS *********************************\n");CHKERRQ(ierr);
221     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
222 
223     /* the coarse problem can be handled by a different communicator */
224     if (pcbddc->coarse_ksp) color = 1;
225     else color = 0;
226     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
227     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);CHKERRQ(ierr);
228     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)pc),&subcomm);CHKERRQ(ierr);
229     ierr = PetscSubcommSetNumber(subcomm,PetscMin(size,2));CHKERRQ(ierr);
230     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
231     ierr = PetscViewerGetSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
232     if (color == 1) {
233       ierr = KSPView(pcbddc->coarse_ksp,subviewer);CHKERRQ(ierr);
234       ierr = PetscViewerFlush(subviewer);CHKERRQ(ierr);
235     }
236     ierr = PetscViewerRestoreSubViewer(viewer,PetscSubcommChild(subcomm),&subviewer);CHKERRQ(ierr);
237     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
238     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
239   }
240   PetscFunctionReturn(0);
241 }
242 
243 static PetscErrorCode PCBDDCSetDiscreteGradient_BDDC(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
244 {
245   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
246   PetscErrorCode ierr;
247 
248   PetscFunctionBegin;
249   ierr = PetscObjectReference((PetscObject)G);CHKERRQ(ierr);
250   ierr = MatDestroy(&pcbddc->discretegradient);CHKERRQ(ierr);
251   pcbddc->discretegradient = G;
252   pcbddc->nedorder         = order > 0 ? order : -order;
253   pcbddc->nedfield         = field;
254   pcbddc->nedglobal        = global;
255   pcbddc->conforming       = conforming;
256   PetscFunctionReturn(0);
257 }
258 
259 /*@
260  PCBDDCSetDiscreteGradient - Sets the discrete gradient
261 
262    Collective on PC
263 
264    Input Parameters:
265 +  pc         - the preconditioning context
266 .  G          - the discrete gradient matrix (should be in AIJ format)
267 .  order      - the order of the Nedelec space (1 for the lowest order)
268 .  field      - the field id of the Nedelec dofs (not used if the fields have not been specified)
269 .  global     - the type of global ordering for the rows of G
270 -  conforming - whether the mesh is conforming or not
271 
272    Level: advanced
273 
274    Notes:
275     The discrete gradient matrix G is used to analyze the subdomain edges, and it should not contain any zero entry.
276           For variable order spaces, the order should be set to zero.
277           If global is true, the rows of G should be given in global ordering for the whole dofs;
278           if false, the ordering should be global for the Nedelec field.
279           In the latter case, it should hold gid[i] < gid[j] iff geid[i] < geid[j], with gid the global orderding for all the dofs
280           and geid the one for the Nedelec field.
281 
282 .seealso: PCBDDC,PCBDDCSetDofsSplitting(),PCBDDCSetDofsSplittingLocal()
283 @*/
284 PetscErrorCode PCBDDCSetDiscreteGradient(PC pc, Mat G, PetscInt order, PetscInt field, PetscBool global, PetscBool conforming)
285 {
286   PetscErrorCode ierr;
287 
288   PetscFunctionBegin;
289   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
290   PetscValidHeaderSpecific(G,MAT_CLASSID,2);
291   PetscValidLogicalCollectiveInt(pc,order,3);
292   PetscValidLogicalCollectiveInt(pc,field,4);
293   PetscValidLogicalCollectiveBool(pc,global,5);
294   PetscValidLogicalCollectiveBool(pc,conforming,6);
295   PetscCheckSameComm(pc,1,G,2);
296   ierr = PetscTryMethod(pc,"PCBDDCSetDiscreteGradient_C",(PC,Mat,PetscInt,PetscInt,PetscBool,PetscBool),(pc,G,order,field,global,conforming));CHKERRQ(ierr);
297   PetscFunctionReturn(0);
298 }
299 
300 static PetscErrorCode PCBDDCSetDivergenceMat_BDDC(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
301 {
302   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
303   PetscErrorCode ierr;
304 
305   PetscFunctionBegin;
306   ierr = PetscObjectReference((PetscObject)divudotp);CHKERRQ(ierr);
307   ierr = MatDestroy(&pcbddc->divudotp);CHKERRQ(ierr);
308   pcbddc->divudotp = divudotp;
309   pcbddc->divudotp_trans = trans;
310   pcbddc->compute_nonetflux = PETSC_TRUE;
311   if (vl2l) {
312     ierr = PetscObjectReference((PetscObject)vl2l);CHKERRQ(ierr);
313     ierr = ISDestroy(&pcbddc->divudotp_vl2l);CHKERRQ(ierr);
314     pcbddc->divudotp_vl2l = vl2l;
315   }
316   PetscFunctionReturn(0);
317 }
318 
319 /*@
320  PCBDDCSetDivergenceMat - Sets the linear operator representing \int_\Omega \div {\bf u} \cdot p dx
321 
322    Collective on PC
323 
324    Input Parameters:
325 +  pc - the preconditioning context
326 .  divudotp - the matrix (must be of type MATIS)
327 .  trans - if trans if false (resp. true), then pressures are in the test (trial) space and velocities are in the trial (test) space.
328 -  vl2l - optional index set describing the local (wrt the local matrix in divudotp) to local (wrt the local matrix in the preconditioning matrix) map for the velocities
329 
330    Level: advanced
331 
332    Notes:
333     This auxiliary matrix is used to compute quadrature weights representing the net-flux across subdomain boundaries
334           If vl2l is NULL, the local ordering for velocities in divudotp should match that of the preconditioning matrix
335 
336 .seealso: PCBDDC
337 @*/
338 PetscErrorCode PCBDDCSetDivergenceMat(PC pc, Mat divudotp, PetscBool trans, IS vl2l)
339 {
340   PetscBool      ismatis;
341   PetscErrorCode ierr;
342 
343   PetscFunctionBegin;
344   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
345   PetscValidHeaderSpecific(divudotp,MAT_CLASSID,2);
346   PetscCheckSameComm(pc,1,divudotp,2);
347   PetscValidLogicalCollectiveBool(pc,trans,3);
348   if (vl2l) PetscValidHeaderSpecific(divudotp,IS_CLASSID,4);
349   ierr = PetscObjectTypeCompare((PetscObject)divudotp,MATIS,&ismatis);CHKERRQ(ierr);
350   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Divergence matrix needs to be of type MATIS");
351   ierr = PetscTryMethod(pc,"PCBDDCSetDivergenceMat_C",(PC,Mat,PetscBool,IS),(pc,divudotp,trans,vl2l));CHKERRQ(ierr);
352   PetscFunctionReturn(0);
353 }
354 
355 static PetscErrorCode PCBDDCSetChangeOfBasisMat_BDDC(PC pc, Mat change, PetscBool interior)
356 {
357   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
358   PetscErrorCode ierr;
359 
360   PetscFunctionBegin;
361   ierr = PetscObjectReference((PetscObject)change);CHKERRQ(ierr);
362   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
363   pcbddc->user_ChangeOfBasisMatrix = change;
364   pcbddc->change_interior = interior;
365   PetscFunctionReturn(0);
366 }
367 /*@
368  PCBDDCSetChangeOfBasisMat - Set user defined change of basis for dofs
369 
370    Collective on PC
371 
372    Input Parameters:
373 +  pc - the preconditioning context
374 .  change - the change of basis matrix
375 -  interior - whether or not the change of basis modifies interior dofs
376 
377    Level: intermediate
378 
379    Notes:
380 
381 .seealso: PCBDDC
382 @*/
383 PetscErrorCode PCBDDCSetChangeOfBasisMat(PC pc, Mat change, PetscBool interior)
384 {
385   PetscErrorCode ierr;
386 
387   PetscFunctionBegin;
388   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
389   PetscValidHeaderSpecific(change,MAT_CLASSID,2);
390   PetscCheckSameComm(pc,1,change,2);
391   if (pc->mat) {
392     PetscInt rows_c,cols_c,rows,cols;
393     ierr = MatGetSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
394     ierr = MatGetSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
395     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of rows for change of basis matrix! %D != %D",rows_c,rows);
396     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of columns for change of basis matrix! %D != %D",cols_c,cols);
397     ierr = MatGetLocalSize(pc->mat,&rows,&cols);CHKERRQ(ierr);
398     ierr = MatGetLocalSize(change,&rows_c,&cols_c);CHKERRQ(ierr);
399     if (rows_c != rows) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local rows for change of basis matrix! %D != %D",rows_c,rows);
400     if (cols_c != cols) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Invalid number of local columns for change of basis matrix! %D != %D",cols_c,cols);
401   }
402   ierr = PetscTryMethod(pc,"PCBDDCSetChangeOfBasisMat_C",(PC,Mat,PetscBool),(pc,change,interior));CHKERRQ(ierr);
403   PetscFunctionReturn(0);
404 }
405 
406 static PetscErrorCode PCBDDCSetPrimalVerticesIS_BDDC(PC pc, IS PrimalVertices)
407 {
408   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
409   PetscBool      isequal = PETSC_FALSE;
410   PetscErrorCode ierr;
411 
412   PetscFunctionBegin;
413   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
414   if (pcbddc->user_primal_vertices) {
415     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices,&isequal);CHKERRQ(ierr);
416   }
417   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
418   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
419   pcbddc->user_primal_vertices = PrimalVertices;
420   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
421   PetscFunctionReturn(0);
422 }
423 
424 /*@
425  PCBDDCSetPrimalVerticesIS - Set additional user defined primal vertices in PCBDDC
426 
427    Collective
428 
429    Input Parameters:
430 +  pc - the preconditioning context
431 -  PrimalVertices - index set of primal vertices in global numbering (can be empty)
432 
433    Level: intermediate
434 
435    Notes:
436      Any process can list any global node
437 
438 .seealso: PCBDDC
439 @*/
440 PetscErrorCode PCBDDCSetPrimalVerticesIS(PC pc, IS PrimalVertices)
441 {
442   PetscErrorCode ierr;
443 
444   PetscFunctionBegin;
445   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
446   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
447   PetscCheckSameComm(pc,1,PrimalVertices,2);
448   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
449   PetscFunctionReturn(0);
450 }
451 
452 static PetscErrorCode PCBDDCSetPrimalVerticesLocalIS_BDDC(PC pc, IS PrimalVertices)
453 {
454   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
455   PetscBool      isequal = PETSC_FALSE;
456   PetscErrorCode ierr;
457 
458   PetscFunctionBegin;
459   ierr = PetscObjectReference((PetscObject)PrimalVertices);CHKERRQ(ierr);
460   if (pcbddc->user_primal_vertices_local) {
461     ierr = ISEqual(PrimalVertices,pcbddc->user_primal_vertices_local,&isequal);CHKERRQ(ierr);
462   }
463   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
464   ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
465   pcbddc->user_primal_vertices_local = PrimalVertices;
466   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
467   PetscFunctionReturn(0);
468 }
469 /*@
470  PCBDDCSetPrimalVerticesLocalIS - Set additional user defined primal vertices in PCBDDC
471 
472    Collective
473 
474    Input Parameters:
475 +  pc - the preconditioning context
476 -  PrimalVertices - index set of primal vertices in local numbering (can be empty)
477 
478    Level: intermediate
479 
480    Notes:
481 
482 .seealso: PCBDDC
483 @*/
484 PetscErrorCode PCBDDCSetPrimalVerticesLocalIS(PC pc, IS PrimalVertices)
485 {
486   PetscErrorCode ierr;
487 
488   PetscFunctionBegin;
489   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
490   PetscValidHeaderSpecific(PrimalVertices,IS_CLASSID,2);
491   PetscCheckSameComm(pc,1,PrimalVertices,2);
492   ierr = PetscTryMethod(pc,"PCBDDCSetPrimalVerticesLocalIS_C",(PC,IS),(pc,PrimalVertices));CHKERRQ(ierr);
493   PetscFunctionReturn(0);
494 }
495 
496 static PetscErrorCode PCBDDCSetCoarseningRatio_BDDC(PC pc,PetscInt k)
497 {
498   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
499 
500   PetscFunctionBegin;
501   pcbddc->coarsening_ratio = k;
502   PetscFunctionReturn(0);
503 }
504 
505 /*@
506  PCBDDCSetCoarseningRatio - Set coarsening ratio used in multilevel
507 
508    Logically collective on PC
509 
510    Input Parameters:
511 +  pc - the preconditioning context
512 -  k - coarsening ratio (H/h at the coarser level)
513 
514    Options Database Keys:
515 .    -pc_bddc_coarsening_ratio
516 
517    Level: intermediate
518 
519    Notes:
520      Approximatively k subdomains at the finer level will be aggregated into a single subdomain at the coarser level
521 
522 .seealso: PCBDDC, PCBDDCSetLevels()
523 @*/
524 PetscErrorCode PCBDDCSetCoarseningRatio(PC pc,PetscInt k)
525 {
526   PetscErrorCode ierr;
527 
528   PetscFunctionBegin;
529   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
530   PetscValidLogicalCollectiveInt(pc,k,2);
531   ierr = PetscTryMethod(pc,"PCBDDCSetCoarseningRatio_C",(PC,PetscInt),(pc,k));CHKERRQ(ierr);
532   PetscFunctionReturn(0);
533 }
534 
535 /* The following functions (PCBDDCSetUseExactDirichlet PCBDDCSetLevel) are not public */
536 static PetscErrorCode PCBDDCSetUseExactDirichlet_BDDC(PC pc,PetscBool flg)
537 {
538   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
539 
540   PetscFunctionBegin;
541   pcbddc->use_exact_dirichlet_trick = flg;
542   PetscFunctionReturn(0);
543 }
544 
545 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool flg)
546 {
547   PetscErrorCode ierr;
548 
549   PetscFunctionBegin;
550   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
551   PetscValidLogicalCollectiveBool(pc,flg,2);
552   ierr = PetscTryMethod(pc,"PCBDDCSetUseExactDirichlet_C",(PC,PetscBool),(pc,flg));CHKERRQ(ierr);
553   PetscFunctionReturn(0);
554 }
555 
556 static PetscErrorCode PCBDDCSetLevel_BDDC(PC pc,PetscInt level)
557 {
558   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
559 
560   PetscFunctionBegin;
561   pcbddc->current_level = level;
562   PetscFunctionReturn(0);
563 }
564 
565 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
566 {
567   PetscErrorCode ierr;
568 
569   PetscFunctionBegin;
570   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
571   PetscValidLogicalCollectiveInt(pc,level,2);
572   ierr = PetscTryMethod(pc,"PCBDDCSetLevel_C",(PC,PetscInt),(pc,level));CHKERRQ(ierr);
573   PetscFunctionReturn(0);
574 }
575 
576 static PetscErrorCode PCBDDCSetLevels_BDDC(PC pc,PetscInt levels)
577 {
578   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
579 
580   PetscFunctionBegin;
581   pcbddc->max_levels = levels;
582   PetscFunctionReturn(0);
583 }
584 
585 /*@
586  PCBDDCSetLevels - Sets the maximum number of levels for multilevel
587 
588    Logically collective on PC
589 
590    Input Parameters:
591 +  pc - the preconditioning context
592 -  levels - the maximum number of levels (max 9)
593 
594    Options Database Keys:
595 .    -pc_bddc_levels
596 
597    Level: intermediate
598 
599    Notes:
600      Default value is 0, i.e. traditional one-level BDDC
601 
602 .seealso: PCBDDC, PCBDDCSetCoarseningRatio()
603 @*/
604 PetscErrorCode PCBDDCSetLevels(PC pc,PetscInt levels)
605 {
606   PetscErrorCode ierr;
607 
608   PetscFunctionBegin;
609   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
610   PetscValidLogicalCollectiveInt(pc,levels,2);
611   if (levels > 99) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Maximum number of levels for bddc is 99\n");
612   ierr = PetscTryMethod(pc,"PCBDDCSetLevels_C",(PC,PetscInt),(pc,levels));CHKERRQ(ierr);
613   PetscFunctionReturn(0);
614 }
615 
616 static PetscErrorCode PCBDDCSetDirichletBoundaries_BDDC(PC pc,IS DirichletBoundaries)
617 {
618   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
619   PetscBool      isequal = PETSC_FALSE;
620   PetscErrorCode ierr;
621 
622   PetscFunctionBegin;
623   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
624   if (pcbddc->DirichletBoundaries) {
625     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundaries,&isequal);CHKERRQ(ierr);
626   }
627   /* last user setting takes precendence -> destroy any other customization */
628   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
629   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
630   pcbddc->DirichletBoundaries = DirichletBoundaries;
631   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
632   PetscFunctionReturn(0);
633 }
634 
635 /*@
636  PCBDDCSetDirichletBoundaries - Set IS defining Dirichlet boundaries for the global problem.
637 
638    Collective
639 
640    Input Parameters:
641 +  pc - the preconditioning context
642 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries
643 
644    Level: intermediate
645 
646    Notes:
647      Provide the information if you used MatZeroRows/Columns routines. Any process can list any global node
648 
649 .seealso: PCBDDC, PCBDDCSetDirichletBoundariesLocal(), MatZeroRows(), MatZeroRowsColumns()
650 @*/
651 PetscErrorCode PCBDDCSetDirichletBoundaries(PC pc,IS DirichletBoundaries)
652 {
653   PetscErrorCode ierr;
654 
655   PetscFunctionBegin;
656   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
657   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
658   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
659   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundaries_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
660   PetscFunctionReturn(0);
661 }
662 
663 static PetscErrorCode PCBDDCSetDirichletBoundariesLocal_BDDC(PC pc,IS DirichletBoundaries)
664 {
665   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
666   PetscBool      isequal = PETSC_FALSE;
667   PetscErrorCode ierr;
668 
669   PetscFunctionBegin;
670   ierr = PetscObjectReference((PetscObject)DirichletBoundaries);CHKERRQ(ierr);
671   if (pcbddc->DirichletBoundariesLocal) {
672     ierr = ISEqual(DirichletBoundaries,pcbddc->DirichletBoundariesLocal,&isequal);CHKERRQ(ierr);
673   }
674   /* last user setting takes precendence -> destroy any other customization */
675   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
676   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
677   pcbddc->DirichletBoundariesLocal = DirichletBoundaries;
678   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
679   PetscFunctionReturn(0);
680 }
681 
682 /*@
683  PCBDDCSetDirichletBoundariesLocal - Set IS defining Dirichlet boundaries for the global problem in local ordering.
684 
685    Collective
686 
687    Input Parameters:
688 +  pc - the preconditioning context
689 -  DirichletBoundaries - parallel IS defining the Dirichlet boundaries (in local ordering)
690 
691    Level: intermediate
692 
693    Notes:
694 
695 .seealso: PCBDDC, PCBDDCSetDirichletBoundaries(), MatZeroRows(), MatZeroRowsColumns()
696 @*/
697 PetscErrorCode PCBDDCSetDirichletBoundariesLocal(PC pc,IS DirichletBoundaries)
698 {
699   PetscErrorCode ierr;
700 
701   PetscFunctionBegin;
702   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
703   PetscValidHeaderSpecific(DirichletBoundaries,IS_CLASSID,2);
704   PetscCheckSameComm(pc,1,DirichletBoundaries,2);
705   ierr = PetscTryMethod(pc,"PCBDDCSetDirichletBoundariesLocal_C",(PC,IS),(pc,DirichletBoundaries));CHKERRQ(ierr);
706   PetscFunctionReturn(0);
707 }
708 
709 static PetscErrorCode PCBDDCSetNeumannBoundaries_BDDC(PC pc,IS NeumannBoundaries)
710 {
711   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
712   PetscBool      isequal = PETSC_FALSE;
713   PetscErrorCode ierr;
714 
715   PetscFunctionBegin;
716   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
717   if (pcbddc->NeumannBoundaries) {
718     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundaries,&isequal);CHKERRQ(ierr);
719   }
720   /* last user setting takes precendence -> destroy any other customization */
721   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
722   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
723   pcbddc->NeumannBoundaries = NeumannBoundaries;
724   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
725   PetscFunctionReturn(0);
726 }
727 
728 /*@
729  PCBDDCSetNeumannBoundaries - Set IS defining Neumann boundaries for the global problem.
730 
731    Collective
732 
733    Input Parameters:
734 +  pc - the preconditioning context
735 -  NeumannBoundaries - parallel IS defining the Neumann boundaries
736 
737    Level: intermediate
738 
739    Notes:
740      Any process can list any global node
741 
742 .seealso: PCBDDC, PCBDDCSetNeumannBoundariesLocal()
743 @*/
744 PetscErrorCode PCBDDCSetNeumannBoundaries(PC pc,IS NeumannBoundaries)
745 {
746   PetscErrorCode ierr;
747 
748   PetscFunctionBegin;
749   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
750   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
751   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
752   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundaries_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
753   PetscFunctionReturn(0);
754 }
755 
756 static PetscErrorCode PCBDDCSetNeumannBoundariesLocal_BDDC(PC pc,IS NeumannBoundaries)
757 {
758   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
759   PetscBool      isequal = PETSC_FALSE;
760   PetscErrorCode ierr;
761 
762   PetscFunctionBegin;
763   ierr = PetscObjectReference((PetscObject)NeumannBoundaries);CHKERRQ(ierr);
764   if (pcbddc->NeumannBoundariesLocal) {
765     ierr = ISEqual(NeumannBoundaries,pcbddc->NeumannBoundariesLocal,&isequal);CHKERRQ(ierr);
766   }
767   /* last user setting takes precendence -> destroy any other customization */
768   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
769   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
770   pcbddc->NeumannBoundariesLocal = NeumannBoundaries;
771   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
772   PetscFunctionReturn(0);
773 }
774 
775 /*@
776  PCBDDCSetNeumannBoundariesLocal - Set IS defining Neumann boundaries for the global problem in local ordering.
777 
778    Collective
779 
780    Input Parameters:
781 +  pc - the preconditioning context
782 -  NeumannBoundaries - parallel IS defining the subdomain part of Neumann boundaries (in local ordering)
783 
784    Level: intermediate
785 
786    Notes:
787 
788 .seealso: PCBDDC, PCBDDCSetNeumannBoundaries()
789 @*/
790 PetscErrorCode PCBDDCSetNeumannBoundariesLocal(PC pc,IS NeumannBoundaries)
791 {
792   PetscErrorCode ierr;
793 
794   PetscFunctionBegin;
795   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
796   PetscValidHeaderSpecific(NeumannBoundaries,IS_CLASSID,2);
797   PetscCheckSameComm(pc,1,NeumannBoundaries,2);
798   ierr = PetscTryMethod(pc,"PCBDDCSetNeumannBoundariesLocal_C",(PC,IS),(pc,NeumannBoundaries));CHKERRQ(ierr);
799   PetscFunctionReturn(0);
800 }
801 
802 static PetscErrorCode PCBDDCGetDirichletBoundaries_BDDC(PC pc,IS *DirichletBoundaries)
803 {
804   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
805 
806   PetscFunctionBegin;
807   *DirichletBoundaries = pcbddc->DirichletBoundaries;
808   PetscFunctionReturn(0);
809 }
810 
811 /*@
812  PCBDDCGetDirichletBoundaries - Get parallel IS for Dirichlet boundaries
813 
814    Collective
815 
816    Input Parameters:
817 .  pc - the preconditioning context
818 
819    Output Parameters:
820 .  DirichletBoundaries - index set defining the Dirichlet boundaries
821 
822    Level: intermediate
823 
824    Notes:
825      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetDirichletBoundaries
826 
827 .seealso: PCBDDC
828 @*/
829 PetscErrorCode PCBDDCGetDirichletBoundaries(PC pc,IS *DirichletBoundaries)
830 {
831   PetscErrorCode ierr;
832 
833   PetscFunctionBegin;
834   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
835   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundaries_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
836   PetscFunctionReturn(0);
837 }
838 
839 static PetscErrorCode PCBDDCGetDirichletBoundariesLocal_BDDC(PC pc,IS *DirichletBoundaries)
840 {
841   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
842 
843   PetscFunctionBegin;
844   *DirichletBoundaries = pcbddc->DirichletBoundariesLocal;
845   PetscFunctionReturn(0);
846 }
847 
848 /*@
849  PCBDDCGetDirichletBoundariesLocal - Get parallel IS for Dirichlet boundaries (in local ordering)
850 
851    Collective
852 
853    Input Parameters:
854 .  pc - the preconditioning context
855 
856    Output Parameters:
857 .  DirichletBoundaries - index set defining the subdomain part of Dirichlet boundaries
858 
859    Level: intermediate
860 
861    Notes:
862      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetDirichletBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetDirichletBoundaries).
863           In the latter case, the IS will be available after PCSetUp.
864 
865 .seealso: PCBDDC
866 @*/
867 PetscErrorCode PCBDDCGetDirichletBoundariesLocal(PC pc,IS *DirichletBoundaries)
868 {
869   PetscErrorCode ierr;
870 
871   PetscFunctionBegin;
872   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
873   ierr = PetscUseMethod(pc,"PCBDDCGetDirichletBoundariesLocal_C",(PC,IS*),(pc,DirichletBoundaries));CHKERRQ(ierr);
874   PetscFunctionReturn(0);
875 }
876 
877 static PetscErrorCode PCBDDCGetNeumannBoundaries_BDDC(PC pc,IS *NeumannBoundaries)
878 {
879   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
880 
881   PetscFunctionBegin;
882   *NeumannBoundaries = pcbddc->NeumannBoundaries;
883   PetscFunctionReturn(0);
884 }
885 
886 /*@
887  PCBDDCGetNeumannBoundaries - Get parallel IS for Neumann boundaries
888 
889    Collective
890 
891    Input Parameters:
892 .  pc - the preconditioning context
893 
894    Output Parameters:
895 .  NeumannBoundaries - index set defining the Neumann boundaries
896 
897    Level: intermediate
898 
899    Notes:
900      The IS returned (if any) is the same passed in earlier by the user with PCBDDCSetNeumannBoundaries
901 
902 .seealso: PCBDDC
903 @*/
904 PetscErrorCode PCBDDCGetNeumannBoundaries(PC pc,IS *NeumannBoundaries)
905 {
906   PetscErrorCode ierr;
907 
908   PetscFunctionBegin;
909   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
910   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundaries_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
911   PetscFunctionReturn(0);
912 }
913 
914 static PetscErrorCode PCBDDCGetNeumannBoundariesLocal_BDDC(PC pc,IS *NeumannBoundaries)
915 {
916   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
917 
918   PetscFunctionBegin;
919   *NeumannBoundaries = pcbddc->NeumannBoundariesLocal;
920   PetscFunctionReturn(0);
921 }
922 
923 /*@
924  PCBDDCGetNeumannBoundariesLocal - Get parallel IS for Neumann boundaries (in local ordering)
925 
926    Collective
927 
928    Input Parameters:
929 .  pc - the preconditioning context
930 
931    Output Parameters:
932 .  NeumannBoundaries - index set defining the subdomain part of Neumann boundaries
933 
934    Level: intermediate
935 
936    Notes:
937      The IS returned could be the same passed in earlier by the user (if provided with PCBDDCSetNeumannBoundariesLocal) or a global-to-local map of the global IS (if provided with PCBDDCSetNeumannBoundaries).
938           In the latter case, the IS will be available after PCSetUp.
939 
940 .seealso: PCBDDC
941 @*/
942 PetscErrorCode PCBDDCGetNeumannBoundariesLocal(PC pc,IS *NeumannBoundaries)
943 {
944   PetscErrorCode ierr;
945 
946   PetscFunctionBegin;
947   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
948   ierr = PetscUseMethod(pc,"PCBDDCGetNeumannBoundariesLocal_C",(PC,IS*),(pc,NeumannBoundaries));CHKERRQ(ierr);
949   PetscFunctionReturn(0);
950 }
951 
952 static PetscErrorCode PCBDDCSetLocalAdjacencyGraph_BDDC(PC pc, PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
953 {
954   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
955   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
956   PetscBool      same_data = PETSC_FALSE;
957   PetscErrorCode ierr;
958 
959   PetscFunctionBegin;
960   if (!nvtxs) {
961     if (copymode == PETSC_OWN_POINTER) {
962       ierr = PetscFree(xadj);CHKERRQ(ierr);
963       ierr = PetscFree(adjncy);CHKERRQ(ierr);
964     }
965     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
966     PetscFunctionReturn(0);
967   }
968   if (mat_graph->nvtxs == nvtxs && mat_graph->freecsr) { /* we own the data */
969     if (mat_graph->xadj == xadj && mat_graph->adjncy == adjncy) same_data = PETSC_TRUE;
970     if (!same_data && mat_graph->xadj[nvtxs] == xadj[nvtxs]) {
971       ierr = PetscMemcmp(xadj,mat_graph->xadj,(nvtxs+1)*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
972       if (same_data) {
973         ierr = PetscMemcmp(adjncy,mat_graph->adjncy,xadj[nvtxs]*sizeof(PetscInt),&same_data);CHKERRQ(ierr);
974       }
975     }
976   }
977   if (!same_data) {
978     /* free old CSR */
979     ierr = PCBDDCGraphResetCSR(mat_graph);CHKERRQ(ierr);
980     /* get CSR into graph structure */
981     if (copymode == PETSC_COPY_VALUES) {
982       ierr = PetscMalloc1(nvtxs+1,&mat_graph->xadj);CHKERRQ(ierr);
983       ierr = PetscMalloc1(xadj[nvtxs],&mat_graph->adjncy);CHKERRQ(ierr);
984       ierr = PetscMemcpy(mat_graph->xadj,xadj,(nvtxs+1)*sizeof(PetscInt));CHKERRQ(ierr);
985       ierr = PetscMemcpy(mat_graph->adjncy,adjncy,xadj[nvtxs]*sizeof(PetscInt));CHKERRQ(ierr);
986       mat_graph->freecsr = PETSC_TRUE;
987     } else if (copymode == PETSC_OWN_POINTER) {
988       mat_graph->xadj    = (PetscInt*)xadj;
989       mat_graph->adjncy  = (PetscInt*)adjncy;
990       mat_graph->freecsr = PETSC_TRUE;
991     } else if (copymode == PETSC_USE_POINTER) {
992       mat_graph->xadj    = (PetscInt*)xadj;
993       mat_graph->adjncy  = (PetscInt*)adjncy;
994       mat_graph->freecsr = PETSC_FALSE;
995     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported copy mode %D",copymode);
996     mat_graph->nvtxs_csr = nvtxs;
997     pcbddc->recompute_topography = PETSC_TRUE;
998   }
999   PetscFunctionReturn(0);
1000 }
1001 
1002 /*@
1003  PCBDDCSetLocalAdjacencyGraph - Set adjacency structure (CSR graph) of the local degrees of freedom.
1004 
1005    Not collective
1006 
1007    Input Parameters:
1008 +  pc - the preconditioning context.
1009 .  nvtxs - number of local vertices of the graph (i.e., the number of local dofs).
1010 .  xadj, adjncy - the connectivity of the dofs in CSR format.
1011 -  copymode - supported modes are PETSC_COPY_VALUES, PETSC_USE_POINTER or PETSC_OWN_POINTER.
1012 
1013    Level: intermediate
1014 
1015    Notes:
1016     A dof is considered connected with all local dofs if xadj[dof+1]-xadj[dof] == 1 and adjncy[xadj[dof]] is negative.
1017 
1018 .seealso: PCBDDC,PetscCopyMode
1019 @*/
1020 PetscErrorCode PCBDDCSetLocalAdjacencyGraph(PC pc,PetscInt nvtxs,const PetscInt xadj[],const PetscInt adjncy[], PetscCopyMode copymode)
1021 {
1022   void (*f)(void) = 0;
1023   PetscErrorCode ierr;
1024 
1025   PetscFunctionBegin;
1026   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1027   if (nvtxs) {
1028     PetscValidIntPointer(xadj,3);
1029     if (xadj[nvtxs]) PetscValidIntPointer(adjncy,4);
1030   }
1031   ierr = PetscTryMethod(pc,"PCBDDCSetLocalAdjacencyGraph_C",(PC,PetscInt,const PetscInt[],const PetscInt[],PetscCopyMode),(pc,nvtxs,xadj,adjncy,copymode));CHKERRQ(ierr);
1032   /* free arrays if PCBDDC is not the PC type */
1033   ierr = PetscObjectQueryFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",&f);CHKERRQ(ierr);
1034   if (!f && copymode == PETSC_OWN_POINTER) {
1035     ierr = PetscFree(xadj);CHKERRQ(ierr);
1036     ierr = PetscFree(adjncy);CHKERRQ(ierr);
1037   }
1038   PetscFunctionReturn(0);
1039 }
1040 
1041 static PetscErrorCode PCBDDCSetDofsSplittingLocal_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1042 {
1043   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1044   PetscInt       i;
1045   PetscBool      isequal = PETSC_FALSE;
1046   PetscErrorCode ierr;
1047 
1048   PetscFunctionBegin;
1049   if (pcbddc->n_ISForDofsLocal == n_is) {
1050     for (i=0;i<n_is;i++) {
1051       PetscBool isequalt;
1052       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofsLocal[i],&isequalt);CHKERRQ(ierr);
1053       if (!isequalt) break;
1054     }
1055     if (i == n_is) isequal = PETSC_TRUE;
1056   }
1057   for (i=0;i<n_is;i++) {
1058     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1059   }
1060   /* Destroy ISes if they were already set */
1061   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1062     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1063   }
1064   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1065   /* last user setting takes precendence -> destroy any other customization */
1066   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1067     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1068   }
1069   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1070   pcbddc->n_ISForDofs = 0;
1071   /* allocate space then set */
1072   if (n_is) {
1073     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1074   }
1075   for (i=0;i<n_is;i++) {
1076     pcbddc->ISForDofsLocal[i] = ISForDofs[i];
1077   }
1078   pcbddc->n_ISForDofsLocal = n_is;
1079   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1080   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1081   PetscFunctionReturn(0);
1082 }
1083 
1084 /*@
1085  PCBDDCSetDofsSplittingLocal - Set index sets defining fields of the local subdomain matrix
1086 
1087    Collective
1088 
1089    Input Parameters:
1090 +  pc - the preconditioning context
1091 .  n_is - number of index sets defining the fields
1092 -  ISForDofs - array of IS describing the fields in local ordering
1093 
1094    Level: intermediate
1095 
1096    Notes:
1097      n_is should be the same among processes. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1098 
1099 .seealso: PCBDDC
1100 @*/
1101 PetscErrorCode PCBDDCSetDofsSplittingLocal(PC pc,PetscInt n_is, IS ISForDofs[])
1102 {
1103   PetscInt       i;
1104   PetscErrorCode ierr;
1105 
1106   PetscFunctionBegin;
1107   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1108   PetscValidLogicalCollectiveInt(pc,n_is,2);
1109   for (i=0;i<n_is;i++) {
1110     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1111     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1112   }
1113   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplittingLocal_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1114   PetscFunctionReturn(0);
1115 }
1116 
1117 static PetscErrorCode PCBDDCSetDofsSplitting_BDDC(PC pc,PetscInt n_is, IS ISForDofs[])
1118 {
1119   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1120   PetscInt       i;
1121   PetscBool      isequal = PETSC_FALSE;
1122   PetscErrorCode ierr;
1123 
1124   PetscFunctionBegin;
1125   if (pcbddc->n_ISForDofs == n_is) {
1126     for (i=0;i<n_is;i++) {
1127       PetscBool isequalt;
1128       ierr = ISEqual(ISForDofs[i],pcbddc->ISForDofs[i],&isequalt);CHKERRQ(ierr);
1129       if (!isequalt) break;
1130     }
1131     if (i == n_is) isequal = PETSC_TRUE;
1132   }
1133   for (i=0;i<n_is;i++) {
1134     ierr = PetscObjectReference((PetscObject)ISForDofs[i]);CHKERRQ(ierr);
1135   }
1136   /* Destroy ISes if they were already set */
1137   for (i=0;i<pcbddc->n_ISForDofs;i++) {
1138     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
1139   }
1140   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
1141   /* last user setting takes precendence -> destroy any other customization */
1142   for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1143     ierr = ISDestroy(&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
1144   }
1145   ierr = PetscFree(pcbddc->ISForDofsLocal);CHKERRQ(ierr);
1146   pcbddc->n_ISForDofsLocal = 0;
1147   /* allocate space then set */
1148   if (n_is) {
1149     ierr = PetscMalloc1(n_is,&pcbddc->ISForDofs);CHKERRQ(ierr);
1150   }
1151   for (i=0;i<n_is;i++) {
1152     pcbddc->ISForDofs[i] = ISForDofs[i];
1153   }
1154   pcbddc->n_ISForDofs = n_is;
1155   if (n_is) pcbddc->user_provided_isfordofs = PETSC_TRUE;
1156   if (!isequal) pcbddc->recompute_topography = PETSC_TRUE;
1157   PetscFunctionReturn(0);
1158 }
1159 
1160 /*@
1161  PCBDDCSetDofsSplitting - Set index sets defining fields of the global matrix
1162 
1163    Collective
1164 
1165    Input Parameters:
1166 +  pc - the preconditioning context
1167 .  n_is - number of index sets defining the fields
1168 -  ISForDofs - array of IS describing the fields in global ordering
1169 
1170    Level: intermediate
1171 
1172    Notes:
1173      Any process can list any global node. Not all nodes need to be listed: unlisted nodes will belong to the complement field.
1174 
1175 .seealso: PCBDDC
1176 @*/
1177 PetscErrorCode PCBDDCSetDofsSplitting(PC pc,PetscInt n_is, IS ISForDofs[])
1178 {
1179   PetscInt       i;
1180   PetscErrorCode ierr;
1181 
1182   PetscFunctionBegin;
1183   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1184   PetscValidLogicalCollectiveInt(pc,n_is,2);
1185   for (i=0;i<n_is;i++) {
1186     PetscValidHeaderSpecific(ISForDofs[i],IS_CLASSID,3);
1187     PetscCheckSameComm(pc,1,ISForDofs[i],3);
1188   }
1189   ierr = PetscTryMethod(pc,"PCBDDCSetDofsSplitting_C",(PC,PetscInt,IS[]),(pc,n_is,ISForDofs));CHKERRQ(ierr);
1190   PetscFunctionReturn(0);
1191 }
1192 
1193 /*
1194    PCPreSolve_BDDC - Changes the right hand side and (if necessary) the initial
1195                      guess if a transformation of basis approach has been selected.
1196 
1197    Input Parameter:
1198 +  pc - the preconditioner contex
1199 
1200    Application Interface Routine: PCPreSolve()
1201 
1202    Notes:
1203      The interface routine PCPreSolve() is not usually called directly by
1204    the user, but instead is called by KSPSolve().
1205 */
1206 static PetscErrorCode PCPreSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1207 {
1208   PetscErrorCode ierr;
1209   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1210   PC_IS          *pcis = (PC_IS*)(pc->data);
1211   Vec            used_vec;
1212   PetscBool      save_rhs = PETSC_TRUE, benign_correction_computed;
1213 
1214   PetscFunctionBegin;
1215   /* if we are working with CG, one dirichlet solve can be avoided during Krylov iterations */
1216   if (ksp) {
1217     PetscBool iscg, isgroppcg, ispipecg, ispipecgrr;
1218     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPCG,&iscg);CHKERRQ(ierr);
1219     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPGROPPCG,&isgroppcg);CHKERRQ(ierr);
1220     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECG,&ispipecg);CHKERRQ(ierr);
1221     ierr = PetscObjectTypeCompare((PetscObject)ksp,KSPPIPECGRR,&ispipecgrr);CHKERRQ(ierr);
1222     if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static || (!iscg && !isgroppcg && !ispipecg && !ispipecgrr)) {
1223       ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1224     }
1225   }
1226   if (pcbddc->benign_apply_coarse_only || pcbddc->switch_static) {
1227     ierr = PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);CHKERRQ(ierr);
1228   }
1229 
1230   /* Creates parallel work vectors used in presolve */
1231   if (!pcbddc->original_rhs) {
1232     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
1233   }
1234   if (!pcbddc->temp_solution) {
1235     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
1236   }
1237 
1238   pcbddc->temp_solution_used = PETSC_FALSE;
1239   if (x) {
1240     ierr = PetscObjectReference((PetscObject)x);CHKERRQ(ierr);
1241     used_vec = x;
1242   } else { /* it can only happen when calling PCBDDCMatFETIDPGetRHS */
1243     ierr = PetscObjectReference((PetscObject)pcbddc->temp_solution);CHKERRQ(ierr);
1244     used_vec = pcbddc->temp_solution;
1245     ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1246     pcbddc->temp_solution_used = PETSC_TRUE;
1247     ierr = VecCopy(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1248     save_rhs = PETSC_FALSE;
1249     pcbddc->eliminate_dirdofs = PETSC_TRUE;
1250   }
1251 
1252   /* hack into ksp data structure since PCPreSolve comes earlier than setting to zero the guess in src/ksp/ksp/interface/itfunc.c */
1253   if (ksp) {
1254     /* store the flag for the initial guess since it will be restored back during PCPostSolve_BDDC */
1255     ierr = KSPGetInitialGuessNonzero(ksp,&pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1256     if (!pcbddc->ksp_guess_nonzero) {
1257       ierr = VecSet(used_vec,0.0);CHKERRQ(ierr);
1258     }
1259   }
1260 
1261   pcbddc->rhs_change = PETSC_FALSE;
1262   /* Take into account zeroed rows -> change rhs and store solution removed */
1263   if (rhs && pcbddc->eliminate_dirdofs) {
1264     IS dirIS = NULL;
1265 
1266     /* DirichletBoundariesLocal may not be consistent among neighbours; gets a dirichlet dofs IS from graph (may be cached) */
1267     ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
1268     if (dirIS) {
1269       Mat_IS            *matis = (Mat_IS*)pc->pmat->data;
1270       PetscInt          dirsize,i,*is_indices;
1271       PetscScalar       *array_x;
1272       const PetscScalar *array_diagonal;
1273 
1274       ierr = MatGetDiagonal(pc->pmat,pcis->vec1_global);CHKERRQ(ierr);
1275       ierr = VecPointwiseDivide(pcis->vec1_global,rhs,pcis->vec1_global);CHKERRQ(ierr);
1276       ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1277       ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1278       ierr = VecScatterBegin(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1279       ierr = VecScatterEnd(matis->rctx,used_vec,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1280       ierr = ISGetLocalSize(dirIS,&dirsize);CHKERRQ(ierr);
1281       ierr = VecGetArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1282       ierr = VecGetArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1283       ierr = ISGetIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1284       for (i=0; i<dirsize; i++) array_x[is_indices[i]] = array_diagonal[is_indices[i]];
1285       ierr = ISRestoreIndices(dirIS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1286       ierr = VecRestoreArrayRead(pcis->vec2_N,&array_diagonal);CHKERRQ(ierr);
1287       ierr = VecRestoreArray(pcis->vec1_N,&array_x);CHKERRQ(ierr);
1288       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1289       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,used_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1290       pcbddc->rhs_change = PETSC_TRUE;
1291       ierr = ISDestroy(&dirIS);CHKERRQ(ierr);
1292     }
1293   }
1294 
1295   /* remove the computed solution or the initial guess from the rhs */
1296   if (pcbddc->rhs_change || (ksp && pcbddc->ksp_guess_nonzero) ) {
1297     /* save the original rhs */
1298     if (save_rhs) {
1299       ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1300       save_rhs = PETSC_FALSE;
1301     }
1302     pcbddc->rhs_change = PETSC_TRUE;
1303     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1304     ierr = MatMultAdd(pc->mat,used_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1305     ierr = VecScale(used_vec,-1.0);CHKERRQ(ierr);
1306     ierr = VecCopy(used_vec,pcbddc->temp_solution);CHKERRQ(ierr);
1307     pcbddc->temp_solution_used = PETSC_TRUE;
1308     if (ksp) {
1309       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_FALSE);CHKERRQ(ierr);
1310     }
1311   }
1312   ierr = VecDestroy(&used_vec);CHKERRQ(ierr);
1313 
1314   /* compute initial vector in benign space if needed
1315      and remove non-benign solution from the rhs */
1316   benign_correction_computed = PETSC_FALSE;
1317   if (rhs && pcbddc->benign_compute_correction && (pcbddc->benign_have_null || pcbddc->benign_apply_coarse_only)) {
1318     /* compute u^*_h using ideas similar to those in Xuemin Tu's PhD thesis (see Section 4.8.1)
1319        Recursively apply BDDC in the multilevel case */
1320     if (!pcbddc->benign_vec) {
1321       ierr = VecDuplicate(rhs,&pcbddc->benign_vec);CHKERRQ(ierr);
1322     }
1323     /* keep applying coarse solver unless we no longer have benign subdomains */
1324     pcbddc->benign_apply_coarse_only = pcbddc->benign_have_null ? PETSC_TRUE : PETSC_FALSE;
1325     if (!pcbddc->benign_skip_correction) {
1326       ierr = PCApply_BDDC(pc,rhs,pcbddc->benign_vec);CHKERRQ(ierr);
1327       benign_correction_computed = PETSC_TRUE;
1328       if (pcbddc->temp_solution_used) {
1329         ierr = VecAXPY(pcbddc->temp_solution,1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1330       }
1331       ierr = VecScale(pcbddc->benign_vec,-1.0);CHKERRQ(ierr);
1332       /* store the original rhs if not done earlier */
1333       if (save_rhs) {
1334         ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1335       }
1336       if (pcbddc->rhs_change) {
1337         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,rhs,rhs);CHKERRQ(ierr);
1338       } else {
1339         ierr = MatMultAdd(pc->mat,pcbddc->benign_vec,pcbddc->original_rhs,rhs);CHKERRQ(ierr);
1340       }
1341       pcbddc->rhs_change = PETSC_TRUE;
1342     }
1343     pcbddc->benign_apply_coarse_only = PETSC_FALSE;
1344   }
1345 
1346   /* dbg output */
1347   if (pcbddc->dbg_flag && benign_correction_computed) {
1348     Vec v;
1349 
1350     ierr = VecDuplicate(pcis->vec1_global,&v);CHKERRQ(ierr);
1351     if (pcbddc->ChangeOfBasisMatrix) {
1352       ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,v);CHKERRQ(ierr);
1353     } else {
1354       ierr = VecCopy(rhs,v);CHKERRQ(ierr);
1355     }
1356     ierr = PCBDDCBenignGetOrSetP0(pc,v,PETSC_TRUE);CHKERRQ(ierr);
1357     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"LEVEL %D: is the correction benign?\n",pcbddc->current_level);CHKERRQ(ierr);
1358     ierr = PetscScalarView(pcbddc->benign_n,pcbddc->benign_p0,pcbddc->dbg_viewer);CHKERRQ(ierr);
1359     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1360     ierr = VecDestroy(&v);CHKERRQ(ierr);
1361   }
1362 
1363   /* set initial guess if using PCG */
1364   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1365   if (x && pcbddc->use_exact_dirichlet_trick) {
1366     ierr = VecSet(x,0.0);CHKERRQ(ierr);
1367     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1368       if (benign_correction_computed) { /* we have already saved the changed rhs */
1369         ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1370       } else {
1371         ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,rhs,pcis->vec1_global);CHKERRQ(ierr);
1372       }
1373       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1374       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_global,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1375     } else {
1376       ierr = VecScatterBegin(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1377       ierr = VecScatterEnd(pcis->global_to_D,rhs,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1378     }
1379     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1380     if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior) {
1381       ierr = VecSet(pcis->vec1_global,0.);CHKERRQ(ierr);
1382       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1383       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,pcis->vec1_global,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1384       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x);CHKERRQ(ierr);
1385     } else {
1386       ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1387       ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1388     }
1389     if (ksp) {
1390       ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
1391     }
1392     pcbddc->exact_dirichlet_trick_app = PETSC_TRUE;
1393   } else if (pcbddc->ChangeOfBasisMatrix && pcbddc->change_interior && benign_correction_computed && pcbddc->use_exact_dirichlet_trick) {
1394     ierr = VecLockPop(pcis->vec1_global);CHKERRQ(ierr);
1395   }
1396   PetscFunctionReturn(0);
1397 }
1398 
1399 /*
1400    PCPostSolve_BDDC - Changes the computed solution if a transformation of basis
1401                      approach has been selected. Also, restores rhs to its original state.
1402 
1403    Input Parameter:
1404 +  pc - the preconditioner contex
1405 
1406    Application Interface Routine: PCPostSolve()
1407 
1408    Notes:
1409      The interface routine PCPostSolve() is not usually called directly by
1410      the user, but instead is called by KSPSolve().
1411 */
1412 static PetscErrorCode PCPostSolve_BDDC(PC pc, KSP ksp, Vec rhs, Vec x)
1413 {
1414   PetscErrorCode ierr;
1415   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1416 
1417   PetscFunctionBegin;
1418   /* add solution removed in presolve */
1419   if (x && pcbddc->rhs_change) {
1420     if (pcbddc->temp_solution_used) {
1421       ierr = VecAXPY(x,1.0,pcbddc->temp_solution);CHKERRQ(ierr);
1422     } else if (pcbddc->benign_compute_correction && pcbddc->benign_vec) {
1423       ierr = VecAXPY(x,-1.0,pcbddc->benign_vec);CHKERRQ(ierr);
1424     }
1425     /* restore to original state (not for FETI-DP) */
1426     if (ksp) pcbddc->temp_solution_used = PETSC_FALSE;
1427   }
1428 
1429   /* restore rhs to its original state (not needed for FETI-DP) */
1430   if (rhs && pcbddc->rhs_change) {
1431     ierr = VecSwap(rhs,pcbddc->original_rhs);CHKERRQ(ierr);
1432     pcbddc->rhs_change = PETSC_FALSE;
1433   }
1434   /* restore ksp guess state */
1435   if (ksp) {
1436     ierr = KSPSetInitialGuessNonzero(ksp,pcbddc->ksp_guess_nonzero);CHKERRQ(ierr);
1437     /* reset flag for exact dirichlet trick */
1438     pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1439   }
1440   PetscFunctionReturn(0);
1441 }
1442 
1443 /*
1444    PCSetUp_BDDC - Prepares for the use of the BDDC preconditioner
1445                   by setting data structures and options.
1446 
1447    Input Parameter:
1448 +  pc - the preconditioner context
1449 
1450    Application Interface Routine: PCSetUp()
1451 
1452    Notes:
1453      The interface routine PCSetUp() is not usually called directly by
1454      the user, but instead is called by PCApply() if necessary.
1455 */
1456 PetscErrorCode PCSetUp_BDDC(PC pc)
1457 {
1458   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
1459   PCBDDCSubSchurs sub_schurs;
1460   Mat_IS*         matis;
1461   MatNullSpace    nearnullspace;
1462   Mat             lA;
1463   IS              lP,zerodiag = NULL;
1464   PetscInt        nrows,ncols;
1465   PetscBool       computesubschurs;
1466   PetscBool       computeconstraintsmatrix;
1467   PetscBool       new_nearnullspace_provided,ismatis;
1468   PetscErrorCode  ierr;
1469 
1470   PetscFunctionBegin;
1471   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&ismatis);CHKERRQ(ierr);
1472   if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PCBDDC preconditioner requires matrix of type MATIS");
1473   ierr = MatGetSize(pc->pmat,&nrows,&ncols);CHKERRQ(ierr);
1474   if (nrows != ncols) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"PCBDDC preconditioner requires a square preconditioning matrix");
1475   matis = (Mat_IS*)pc->pmat->data;
1476   /* the following lines of code should be replaced by a better logic between PCIS, PCNN, PCBDDC and other future nonoverlapping preconditioners */
1477   /* For BDDC we need to define a local "Neumann" problem different to that defined in PCISSetup
1478      Also, BDDC builds its own KSP for the Dirichlet problem */
1479   if (!pc->setupcalled || pc->flag == DIFFERENT_NONZERO_PATTERN) pcbddc->recompute_topography = PETSC_TRUE;
1480   if (pcbddc->recompute_topography) {
1481     pcbddc->graphanalyzed    = PETSC_FALSE;
1482     computeconstraintsmatrix = PETSC_TRUE;
1483   } else {
1484     computeconstraintsmatrix = PETSC_FALSE;
1485   }
1486 
1487   /* check parameters' compatibility */
1488   if (!pcbddc->use_deluxe_scaling) pcbddc->deluxe_zerorows = PETSC_FALSE;
1489   pcbddc->adaptive_selection   = (PetscBool)(pcbddc->adaptive_threshold[0] != 0.0 || pcbddc->adaptive_threshold[1] != 0.0);
1490   pcbddc->adaptive_userdefined = (PetscBool)(pcbddc->adaptive_selection && pcbddc->adaptive_userdefined);
1491   if (pcbddc->adaptive_selection) pcbddc->use_faces = PETSC_TRUE;
1492 
1493   computesubschurs = (PetscBool)(pcbddc->adaptive_selection || pcbddc->use_deluxe_scaling);
1494   if (pcbddc->switch_static) {
1495     PetscBool ismatis;
1496 
1497     ierr = PetscObjectTypeCompare((PetscObject)pc->mat,MATIS,&ismatis);CHKERRQ(ierr);
1498     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"When the static switch is one, the iteration matrix should be of type MATIS");
1499   }
1500 
1501   /* activate all connected components if the netflux has been requested */
1502   if (pcbddc->compute_nonetflux) {
1503     pcbddc->use_vertices = PETSC_TRUE;
1504     pcbddc->use_edges    = PETSC_TRUE;
1505     pcbddc->use_faces    = PETSC_TRUE;
1506   }
1507 
1508   /* Get stdout for dbg */
1509   if (pcbddc->dbg_flag) {
1510     if (!pcbddc->dbg_viewer) {
1511       pcbddc->dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pc));
1512     }
1513     ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1514     ierr = PetscViewerASCIIAddTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1515   }
1516 
1517   /* process topology information */
1518   if (pcbddc->recompute_topography) {
1519     ierr = PCBDDCComputeLocalTopologyInfo(pc);CHKERRQ(ierr);
1520     if (pcbddc->discretegradient) {
1521       ierr = PCBDDCNedelecSupport(pc);CHKERRQ(ierr);
1522     }
1523   }
1524 
1525   /* change basis if requested by the user */
1526   if (pcbddc->user_ChangeOfBasisMatrix) {
1527     /* use_change_of_basis flag is used to automatically compute a change of basis from constraints */
1528     pcbddc->use_change_of_basis = PETSC_FALSE;
1529     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
1530   } else {
1531     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1532     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1533     pcbddc->local_mat = matis->A;
1534   }
1535 
1536   /*
1537      Compute change of basis on local pressures (aka zerodiag dofs) with the benign trick
1538      This should come earlier then PCISSetUp for extracting the correct subdomain matrices
1539   */
1540   ierr = PCBDDCBenignShellMat(pc,PETSC_TRUE);CHKERRQ(ierr);
1541   if (pcbddc->benign_saddle_point) {
1542     PC_IS* pcis = (PC_IS*)pc->data;
1543 
1544     if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->use_change_of_basis || !computesubschurs) pcbddc->benign_change_explicit = PETSC_TRUE;
1545     /* detect local saddle point and change the basis in pcbddc->local_mat (TODO: reuse case) */
1546     ierr = PCBDDCBenignDetectSaddlePoint(pc,&zerodiag);CHKERRQ(ierr);
1547     /* pop B0 mat from local mat */
1548     ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1549     /* give pcis a hint to not reuse submatrices during PCISCreate */
1550     if (pc->flag == SAME_NONZERO_PATTERN && pcis->reusesubmatrices == PETSC_TRUE) {
1551       if (pcbddc->benign_n && (pcbddc->benign_change_explicit || pcbddc->dbg_flag)) {
1552         pcis->reusesubmatrices = PETSC_FALSE;
1553       } else {
1554         pcis->reusesubmatrices = PETSC_TRUE;
1555       }
1556     } else {
1557       pcis->reusesubmatrices = PETSC_FALSE;
1558     }
1559   }
1560 
1561   /* propagate relevant information */
1562   if (matis->A->symmetric_set) {
1563     ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
1564   }
1565   if (matis->A->spd_set) {
1566     ierr = MatSetOption(pcbddc->local_mat,MAT_SPD,matis->A->spd);CHKERRQ(ierr);
1567   }
1568 
1569   /* Set up all the "iterative substructuring" common block without computing solvers */
1570   {
1571     Mat temp_mat;
1572 
1573     temp_mat = matis->A;
1574     matis->A = pcbddc->local_mat;
1575     ierr = PCISSetUp(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1576     pcbddc->local_mat = matis->A;
1577     matis->A = temp_mat;
1578   }
1579 
1580   /* Analyze interface */
1581   if (!pcbddc->graphanalyzed) {
1582     ierr = PCBDDCAnalyzeInterface(pc);CHKERRQ(ierr);
1583     computeconstraintsmatrix = PETSC_TRUE;
1584     if (pcbddc->adaptive_selection && !pcbddc->use_deluxe_scaling && !pcbddc->mat_graph->twodim) {
1585       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot compute the adaptive primal space for a problem with 3D edges without deluxe scaling");
1586     }
1587     if (pcbddc->compute_nonetflux) {
1588       MatNullSpace nnfnnsp;
1589 
1590       if (!pcbddc->divudotp) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Missing divudotp operator");
1591       ierr = PCBDDCComputeNoNetFlux(pc->pmat,pcbddc->divudotp,pcbddc->divudotp_trans,pcbddc->divudotp_vl2l,pcbddc->mat_graph,&nnfnnsp);CHKERRQ(ierr);
1592       /* TODO what if a nearnullspace is already attached? */
1593       if (nnfnnsp) {
1594         ierr = MatSetNearNullSpace(pc->pmat,nnfnnsp);CHKERRQ(ierr);
1595         ierr = MatNullSpaceDestroy(&nnfnnsp);CHKERRQ(ierr);
1596       }
1597     }
1598   }
1599 
1600   /* check existence of a divergence free extension, i.e.
1601      b(v_I,p_0) = 0 for all v_I (raise error if not).
1602      Also, check that PCBDDCBenignGetOrSetP0 works */
1603   if (pcbddc->benign_saddle_point && pcbddc->dbg_flag > 1) {
1604     ierr = PCBDDCBenignCheck(pc,zerodiag);CHKERRQ(ierr);
1605   }
1606   ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
1607 
1608   /* Setup local dirichlet solver ksp_D and sub_schurs solvers */
1609   if (computesubschurs && pcbddc->recompute_topography) {
1610     ierr = PCBDDCInitSubSchurs(pc);CHKERRQ(ierr);
1611   }
1612   /* SetUp Scaling operator (scaling matrices could be needed in SubSchursSetUp)*/
1613   if (!pcbddc->use_deluxe_scaling) {
1614     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1615   }
1616 
1617   /* finish setup solvers and do adaptive selection of constraints */
1618   sub_schurs = pcbddc->sub_schurs;
1619   if (sub_schurs && sub_schurs->schur_explicit) {
1620     if (computesubschurs) {
1621       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1622     }
1623     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1624   } else {
1625     ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
1626     if (computesubschurs) {
1627       ierr = PCBDDCSetUpSubSchurs(pc);CHKERRQ(ierr);
1628     }
1629   }
1630   if (pcbddc->adaptive_selection) {
1631     ierr = PCBDDCAdaptiveSelection(pc);CHKERRQ(ierr);
1632     computeconstraintsmatrix = PETSC_TRUE;
1633   }
1634 
1635   /* infer if NullSpace object attached to Mat via MatSetNearNullSpace has changed */
1636   new_nearnullspace_provided = PETSC_FALSE;
1637   ierr = MatGetNearNullSpace(pc->pmat,&nearnullspace);CHKERRQ(ierr);
1638   if (pcbddc->onearnullspace) { /* already used nearnullspace */
1639     if (!nearnullspace) { /* near null space attached to mat has been destroyed */
1640       new_nearnullspace_provided = PETSC_TRUE;
1641     } else {
1642       /* determine if the two nullspaces are different (should be lightweight) */
1643       if (nearnullspace != pcbddc->onearnullspace) {
1644         new_nearnullspace_provided = PETSC_TRUE;
1645       } else { /* maybe the user has changed the content of the nearnullspace so check vectors ObjectStateId */
1646         PetscInt         i;
1647         const Vec        *nearnullvecs;
1648         PetscObjectState state;
1649         PetscInt         nnsp_size;
1650         ierr = MatNullSpaceGetVecs(nearnullspace,NULL,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1651         for (i=0;i<nnsp_size;i++) {
1652           ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&state);CHKERRQ(ierr);
1653           if (pcbddc->onearnullvecs_state[i] != state) {
1654             new_nearnullspace_provided = PETSC_TRUE;
1655             break;
1656           }
1657         }
1658       }
1659     }
1660   } else {
1661     if (!nearnullspace) { /* both nearnullspaces are null */
1662       new_nearnullspace_provided = PETSC_FALSE;
1663     } else { /* nearnullspace attached later */
1664       new_nearnullspace_provided = PETSC_TRUE;
1665     }
1666   }
1667 
1668   /* Setup constraints and related work vectors */
1669   /* reset primal space flags */
1670   pcbddc->new_primal_space = PETSC_FALSE;
1671   pcbddc->new_primal_space_local = PETSC_FALSE;
1672   if (computeconstraintsmatrix || new_nearnullspace_provided) {
1673     /* It also sets the primal space flags */
1674     ierr = PCBDDCConstraintsSetUp(pc);CHKERRQ(ierr);
1675   }
1676   /* Allocate needed local vectors (which depends on quantities defined during ConstraintsSetUp) */
1677   ierr = PCBDDCSetUpLocalWorkVectors(pc);CHKERRQ(ierr);
1678 
1679   if (pcbddc->use_change_of_basis) {
1680     PC_IS *pcis = (PC_IS*)(pc->data);
1681 
1682     ierr = PCBDDCComputeLocalMatrix(pc,pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1683     if (pcbddc->benign_change) {
1684       ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
1685       /* pop B0 from pcbddc->local_mat */
1686       ierr = PCBDDCBenignPopOrPushB0(pc,PETSC_TRUE);CHKERRQ(ierr);
1687     }
1688     /* get submatrices */
1689     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
1690     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
1691     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
1692     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_BB);CHKERRQ(ierr);
1693     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcis->A_IB);CHKERRQ(ierr);
1694     ierr = MatCreateSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&pcis->A_BI);CHKERRQ(ierr);
1695     /* set flag in pcis to not reuse submatrices during PCISCreate */
1696     pcis->reusesubmatrices = PETSC_FALSE;
1697   } else if (!pcbddc->user_ChangeOfBasisMatrix && !pcbddc->benign_change) {
1698     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1699     ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
1700     pcbddc->local_mat = matis->A;
1701   }
1702 
1703   /* interface pressure block row for B_C */
1704   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP" ,(PetscObject*)&lP);CHKERRQ(ierr);
1705   ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);CHKERRQ(ierr);
1706   if (lA && lP) {
1707     PC_IS*    pcis = (PC_IS*)pc->data;
1708     Mat       B_BI,B_BB,Bt_BI,Bt_BB;
1709     PetscBool issym;
1710     ierr = MatIsSymmetric(lA,PETSC_SMALL,&issym);CHKERRQ(ierr);
1711     if (issym) {
1712       ierr = MatCreateSubMatrix(lA,lP,pcis->is_I_local,MAT_INITIAL_MATRIX,&B_BI);CHKERRQ(ierr);
1713       ierr = MatCreateSubMatrix(lA,lP,pcis->is_B_local,MAT_INITIAL_MATRIX,&B_BB);CHKERRQ(ierr);
1714       ierr = MatCreateTranspose(B_BI,&Bt_BI);CHKERRQ(ierr);
1715       ierr = MatCreateTranspose(B_BB,&Bt_BB);CHKERRQ(ierr);
1716     } else {
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 = MatCreateSubMatrix(lA,pcis->is_I_local,lP,MAT_INITIAL_MATRIX,&Bt_BI);CHKERRQ(ierr);
1720       ierr = MatCreateSubMatrix(lA,pcis->is_B_local,lP,MAT_INITIAL_MATRIX,&Bt_BB);CHKERRQ(ierr);
1721     }
1722     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BI",(PetscObject)B_BI);CHKERRQ(ierr);
1723     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_B_BB",(PetscObject)B_BB);CHKERRQ(ierr);
1724     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BI",(PetscObject)Bt_BI);CHKERRQ(ierr);
1725     ierr = PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_Bt_BB",(PetscObject)Bt_BB);CHKERRQ(ierr);
1726     ierr = MatDestroy(&B_BI);CHKERRQ(ierr);
1727     ierr = MatDestroy(&B_BB);CHKERRQ(ierr);
1728     ierr = MatDestroy(&Bt_BI);CHKERRQ(ierr);
1729     ierr = MatDestroy(&Bt_BB);CHKERRQ(ierr);
1730   }
1731 
1732   /* SetUp coarse and local Neumann solvers */
1733   ierr = PCBDDCSetUpSolvers(pc);CHKERRQ(ierr);
1734   /* SetUp Scaling operator */
1735   if (pcbddc->use_deluxe_scaling) {
1736     ierr = PCBDDCScalingSetUp(pc);CHKERRQ(ierr);
1737   }
1738 
1739   /* mark topography as done */
1740   pcbddc->recompute_topography = PETSC_FALSE;
1741 
1742   /* wrap pcis->A_IB and pcis->A_BI if we did not change explicitly the variables on the pressures */
1743   ierr = PCBDDCBenignShellMat(pc,PETSC_FALSE);CHKERRQ(ierr);
1744 
1745   if (pcbddc->dbg_flag) {
1746     ierr = PetscViewerASCIISubtractTab(pcbddc->dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
1747     ierr = PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
1748   }
1749   PetscFunctionReturn(0);
1750 }
1751 
1752 /*
1753    PCApply_BDDC - Applies the BDDC operator to a vector.
1754 
1755    Input Parameters:
1756 +  pc - the preconditioner context
1757 -  r - input vector (global)
1758 
1759    Output Parameter:
1760 .  z - output vector (global)
1761 
1762    Application Interface Routine: PCApply()
1763  */
1764 PetscErrorCode PCApply_BDDC(PC pc,Vec r,Vec z)
1765 {
1766   PC_IS             *pcis = (PC_IS*)(pc->data);
1767   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1768   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1769   PetscErrorCode    ierr;
1770   const PetscScalar one = 1.0;
1771   const PetscScalar m_one = -1.0;
1772   const PetscScalar zero = 0.0;
1773 
1774 /* This code is similar to that provided in nn.c for PCNN
1775    NN interface preconditioner changed to BDDC
1776    Added support for M_3 preconditioner in the reference article (code is active if pcbddc->switch_static == PETSC_TRUE) */
1777 
1778   PetscFunctionBegin;
1779   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1780   if (pcbddc->ChangeOfBasisMatrix) {
1781     Vec swap;
1782 
1783     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1784     swap = pcbddc->work_change;
1785     pcbddc->work_change = r;
1786     r = swap;
1787     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1788     if (pcbddc->benign_apply_coarse_only && pcbddc->use_exact_dirichlet_trick && pcbddc->change_interior) {
1789       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1790       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1791     }
1792   }
1793   if (pcbddc->benign_have_null) { /* get p0 from r */
1794     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1795   }
1796   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1797     ierr = VecCopy(r,z);CHKERRQ(ierr);
1798     /* First Dirichlet solve */
1799     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1800     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1801     /*
1802       Assembling right hand side for BDDC operator
1803       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1804       - pcis->vec1_B the interface part of the global vector z
1805     */
1806     if (n_D) {
1807       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1808       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1809       if (pcbddc->switch_static) {
1810         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1811 
1812         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1813         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1814         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1815         if (!pcbddc->switch_static_change) {
1816           ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1817         } else {
1818           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1819           ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1820           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1821         }
1822         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1823         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1824         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1825         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1826       } else {
1827         ierr = MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1828       }
1829     } else {
1830       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1831     }
1832     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1833     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1834     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1835   } else {
1836     if (!pcbddc->benign_apply_coarse_only) {
1837       ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1838     }
1839   }
1840 
1841   /* Apply interface preconditioner
1842      input/output vecs: pcis->vec1_B and pcis->vec1_D */
1843   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);
1844 
1845   /* Apply transpose of partition of unity operator */
1846   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
1847 
1848   /* Second Dirichlet solve and assembling of output */
1849   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1850   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1851   if (n_B) {
1852     if (pcbddc->switch_static) {
1853       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1854 
1855       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1856       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1857       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1858       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1859       if (!pcbddc->switch_static_change) {
1860         ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1861       } else {
1862         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1863         ierr = MatMult(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1864         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1865       }
1866       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1867       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1868     } else {
1869       ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
1870     }
1871   } else if (pcbddc->switch_static) { /* n_B is zero */
1872     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1873 
1874     if (!pcbddc->switch_static_change) {
1875       ierr = MatMult(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
1876     } else {
1877       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
1878       ierr = MatMult(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1879       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
1880     }
1881   }
1882   ierr = KSPSolve(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
1883 
1884   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1885     if (pcbddc->switch_static) {
1886       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
1887     } else {
1888       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
1889     }
1890     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1891     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1892   } else {
1893     if (pcbddc->switch_static) {
1894       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
1895     } else {
1896       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
1897     }
1898     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1899     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1900   }
1901   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
1902     if (pcbddc->benign_apply_coarse_only) {
1903       ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
1904     }
1905     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
1906   }
1907 
1908   if (pcbddc->ChangeOfBasisMatrix) {
1909     pcbddc->work_change = r;
1910     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
1911     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
1912   }
1913   PetscFunctionReturn(0);
1914 }
1915 
1916 /*
1917    PCApplyTranspose_BDDC - Applies the transpose of the BDDC operator to a vector.
1918 
1919    Input Parameters:
1920 +  pc - the preconditioner context
1921 -  r - input vector (global)
1922 
1923    Output Parameter:
1924 .  z - output vector (global)
1925 
1926    Application Interface Routine: PCApplyTranspose()
1927  */
1928 PetscErrorCode PCApplyTranspose_BDDC(PC pc,Vec r,Vec z)
1929 {
1930   PC_IS             *pcis = (PC_IS*)(pc->data);
1931   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1932   PetscInt          n_B = pcis->n_B, n_D = pcis->n - n_B;
1933   PetscErrorCode    ierr;
1934   const PetscScalar one = 1.0;
1935   const PetscScalar m_one = -1.0;
1936   const PetscScalar zero = 0.0;
1937 
1938   PetscFunctionBegin;
1939   ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
1940   if (pcbddc->ChangeOfBasisMatrix) {
1941     Vec swap;
1942 
1943     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);CHKERRQ(ierr);
1944     swap = pcbddc->work_change;
1945     pcbddc->work_change = r;
1946     r = swap;
1947     /* save rhs so that we don't need to apply the change of basis for the exact dirichlet trick in PreSolve */
1948     if (pcbddc->benign_apply_coarse_only && pcbddc->exact_dirichlet_trick_app && pcbddc->change_interior) {
1949       ierr = VecCopy(r,pcis->vec1_global);CHKERRQ(ierr);
1950       ierr = VecLockPush(pcis->vec1_global);CHKERRQ(ierr);
1951     }
1952   }
1953   if (pcbddc->benign_have_null) { /* get p0 from r */
1954     ierr = PCBDDCBenignGetOrSetP0(pc,r,PETSC_TRUE);CHKERRQ(ierr);
1955   }
1956   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
1957     ierr = VecCopy(r,z);CHKERRQ(ierr);
1958     /* First Dirichlet solve */
1959     ierr = VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1960     ierr = VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1961     /*
1962       Assembling right hand side for BDDC operator
1963       - pcis->vec1_D for the Dirichlet part (if needed, i.e. pcbddc->switch_static == PETSC_TRUE)
1964       - pcis->vec1_B the interface part of the global vector z
1965     */
1966     if (n_D) {
1967       ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1968       ierr = VecScale(pcis->vec2_D,m_one);CHKERRQ(ierr);
1969       if (pcbddc->switch_static) {
1970         Mat_IS *matis = (Mat_IS*)(pc->mat->data);
1971 
1972         ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
1973         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1974         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1975         if (!pcbddc->switch_static_change) {
1976           ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1977         } else {
1978           ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1979           ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
1980           ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
1981         }
1982         ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1983         ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec1_D,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1984         ierr = VecScatterBegin(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1985         ierr = VecScatterEnd(pcis->N_to_B,pcis->vec2_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1986       } else {
1987         ierr = MatMultTranspose(pcis->A_IB,pcis->vec2_D,pcis->vec1_B);CHKERRQ(ierr);
1988       }
1989     } else {
1990       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1991     }
1992     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1993     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,z,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1994     ierr = PCBDDCScalingRestriction(pc,z,pcis->vec1_B);CHKERRQ(ierr);
1995   } else {
1996     ierr = PCBDDCScalingRestriction(pc,r,pcis->vec1_B);CHKERRQ(ierr);
1997   }
1998 
1999   /* Apply interface preconditioner
2000      input/output vecs: pcis->vec1_B and pcis->vec1_D */
2001   ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_TRUE);CHKERRQ(ierr);
2002 
2003   /* Apply transpose of partition of unity operator */
2004   ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,z);CHKERRQ(ierr);
2005 
2006   /* Second Dirichlet solve and assembling of output */
2007   ierr = VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2008   ierr = VecScatterEnd(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2009   if (n_B) {
2010     if (pcbddc->switch_static) {
2011       Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2012 
2013       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2014       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2015       ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2016       ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2017       if (!pcbddc->switch_static_change) {
2018         ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2019       } else {
2020         ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2021         ierr = MatMultTranspose(matis->A,pcis->vec2_N,pcis->vec1_N);CHKERRQ(ierr);
2022         ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2023       }
2024       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2025       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec2_N,pcis->vec3_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2026     } else {
2027       ierr = MatMultTranspose(pcis->A_BI,pcis->vec1_B,pcis->vec3_D);CHKERRQ(ierr);
2028     }
2029   } else if (pcbddc->switch_static) { /* n_B is zero */
2030     Mat_IS *matis = (Mat_IS*)(pc->mat->data);
2031 
2032     if (!pcbddc->switch_static_change) {
2033       ierr = MatMultTranspose(matis->A,pcis->vec1_D,pcis->vec3_D);CHKERRQ(ierr);
2034     } else {
2035       ierr = MatMult(pcbddc->switch_static_change,pcis->vec1_D,pcis->vec1_N);CHKERRQ(ierr);
2036       ierr = MatMultTranspose(matis->A,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2037       ierr = MatMultTranspose(pcbddc->switch_static_change,pcis->vec2_N,pcis->vec3_D);CHKERRQ(ierr);
2038     }
2039   }
2040   ierr = KSPSolveTranspose(pcbddc->ksp_D,pcis->vec3_D,pcis->vec4_D);CHKERRQ(ierr);
2041   if (!pcbddc->exact_dirichlet_trick_app && !pcbddc->benign_apply_coarse_only) {
2042     if (pcbddc->switch_static) {
2043       ierr = VecAXPBYPCZ(pcis->vec2_D,m_one,one,m_one,pcis->vec4_D,pcis->vec1_D);CHKERRQ(ierr);
2044     } else {
2045       ierr = VecAXPBY(pcis->vec2_D,m_one,m_one,pcis->vec4_D);CHKERRQ(ierr);
2046     }
2047     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2048     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2049   } else {
2050     if (pcbddc->switch_static) {
2051       ierr = VecAXPBY(pcis->vec4_D,one,m_one,pcis->vec1_D);CHKERRQ(ierr);
2052     } else {
2053       ierr = VecScale(pcis->vec4_D,m_one);CHKERRQ(ierr);
2054     }
2055     ierr = VecScatterBegin(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2056     ierr = VecScatterEnd(pcis->global_to_D,pcis->vec4_D,z,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2057   }
2058   if (pcbddc->benign_have_null) { /* set p0 (computed in PCBDDCApplyInterface) */
2059     ierr = PCBDDCBenignGetOrSetP0(pc,z,PETSC_FALSE);CHKERRQ(ierr);
2060   }
2061   if (pcbddc->ChangeOfBasisMatrix) {
2062     pcbddc->work_change = r;
2063     ierr = VecCopy(z,pcbddc->work_change);CHKERRQ(ierr);
2064     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);CHKERRQ(ierr);
2065   }
2066   PetscFunctionReturn(0);
2067 }
2068 
2069 PetscErrorCode PCReset_BDDC(PC pc)
2070 {
2071   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2072   PC_IS          *pcis = (PC_IS*)pc->data;
2073   KSP            kspD,kspR,kspC;
2074   PetscErrorCode ierr;
2075 
2076   PetscFunctionBegin;
2077   /* free BDDC custom data  */
2078   ierr = PCBDDCResetCustomization(pc);CHKERRQ(ierr);
2079   /* destroy objects related to topography */
2080   ierr = PCBDDCResetTopography(pc);CHKERRQ(ierr);
2081   /* destroy objects for scaling operator */
2082   ierr = PCBDDCScalingDestroy(pc);CHKERRQ(ierr);
2083   /* free solvers stuff */
2084   ierr = PCBDDCResetSolvers(pc);CHKERRQ(ierr);
2085   /* free global vectors needed in presolve */
2086   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
2087   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
2088   /* free data created by PCIS */
2089   ierr = PCISDestroy(pc);CHKERRQ(ierr);
2090 
2091   /* restore defaults */
2092   kspD = pcbddc->ksp_D;
2093   kspR = pcbddc->ksp_R;
2094   kspC = pcbddc->coarse_ksp;
2095   ierr = PetscMemzero(pc->data,sizeof(*pcbddc));CHKERRQ(ierr);
2096   pcis->n_neigh                     = -1;
2097   pcis->scaling_factor              = 1.0;
2098   pcis->reusesubmatrices            = PETSC_TRUE;
2099   pcbddc->use_local_adj             = PETSC_TRUE;
2100   pcbddc->use_vertices              = PETSC_TRUE;
2101   pcbddc->use_edges                 = PETSC_TRUE;
2102   pcbddc->symmetric_primal          = PETSC_TRUE;
2103   pcbddc->vertex_size               = 1;
2104   pcbddc->recompute_topography      = PETSC_TRUE;
2105   pcbddc->coarse_size               = -1;
2106   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2107   pcbddc->coarsening_ratio          = 8;
2108   pcbddc->coarse_eqs_per_proc       = 1;
2109   pcbddc->benign_compute_correction = PETSC_TRUE;
2110   pcbddc->nedfield                  = -1;
2111   pcbddc->nedglobal                 = PETSC_TRUE;
2112   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2113   pcbddc->sub_schurs_layers         = -1;
2114   pcbddc->ksp_D                     = kspD;
2115   pcbddc->ksp_R                     = kspR;
2116   pcbddc->coarse_ksp                = kspC;
2117   PetscFunctionReturn(0);
2118 }
2119 
2120 PetscErrorCode PCDestroy_BDDC(PC pc)
2121 {
2122   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2123   PetscErrorCode ierr;
2124 
2125   PetscFunctionBegin;
2126   ierr = PCReset_BDDC(pc);CHKERRQ(ierr);
2127   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
2128   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
2129   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
2130   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",NULL);CHKERRQ(ierr);
2131   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",NULL);CHKERRQ(ierr);
2132   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",NULL);CHKERRQ(ierr);
2133   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",NULL);CHKERRQ(ierr);
2134   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",NULL);CHKERRQ(ierr);
2135   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",NULL);CHKERRQ(ierr);
2136   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",NULL);CHKERRQ(ierr);
2137   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",NULL);CHKERRQ(ierr);
2138   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",NULL);CHKERRQ(ierr);
2139   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2140   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2141   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2142   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2143   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",NULL);CHKERRQ(ierr);
2144   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",NULL);CHKERRQ(ierr);
2145   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",NULL);CHKERRQ(ierr);
2146   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",NULL);CHKERRQ(ierr);
2147   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",NULL);CHKERRQ(ierr);
2148   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",NULL);CHKERRQ(ierr);
2149   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",NULL);CHKERRQ(ierr);
2150   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",NULL);CHKERRQ(ierr);
2151   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",NULL);CHKERRQ(ierr);
2152   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",NULL);CHKERRQ(ierr);
2153   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",NULL);CHKERRQ(ierr);
2154   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",NULL);CHKERRQ(ierr);
2155   ierr = PetscFree(pc->data);CHKERRQ(ierr);
2156   PetscFunctionReturn(0);
2157 }
2158 
2159 static PetscErrorCode PCSetCoordinates_BDDC(PC pc, PetscInt dim, PetscInt nloc, PetscReal *coords)
2160 {
2161   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2162   PCBDDCGraph    mat_graph = pcbddc->mat_graph;
2163   PetscErrorCode ierr;
2164 
2165   PetscFunctionBegin;
2166   ierr = PetscFree(mat_graph->coords);CHKERRQ(ierr);
2167   ierr = PetscMalloc1(nloc*dim,&mat_graph->coords);CHKERRQ(ierr);
2168   ierr = PetscMemcpy(mat_graph->coords,coords,nloc*dim*sizeof(PetscReal));CHKERRQ(ierr);
2169   mat_graph->cnloc = nloc;
2170   mat_graph->cdim  = dim;
2171   mat_graph->cloc  = PETSC_FALSE;
2172   PetscFunctionReturn(0);
2173 }
2174 
2175 static PetscErrorCode PCPreSolveChangeRHS_BDDC(PC pc, PetscBool* change)
2176 {
2177   PetscFunctionBegin;
2178   *change = PETSC_TRUE;
2179   PetscFunctionReturn(0);
2180 }
2181 
2182 static PetscErrorCode PCBDDCMatFETIDPGetRHS_BDDC(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2183 {
2184   FETIDPMat_ctx  mat_ctx;
2185   Vec            work;
2186   PC_IS*         pcis;
2187   PC_BDDC*       pcbddc;
2188   PetscErrorCode ierr;
2189 
2190   PetscFunctionBegin;
2191   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2192   pcis = (PC_IS*)mat_ctx->pc->data;
2193   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2194 
2195   ierr = VecSet(fetidp_flux_rhs,0.0);CHKERRQ(ierr);
2196   /* copy rhs since we may change it during PCPreSolve_BDDC */
2197   if (!pcbddc->original_rhs) {
2198     ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
2199   }
2200   if (mat_ctx->rhs_flip) {
2201     ierr = VecPointwiseMult(pcbddc->original_rhs,standard_rhs,mat_ctx->rhs_flip);CHKERRQ(ierr);
2202   } else {
2203     ierr = VecCopy(standard_rhs,pcbddc->original_rhs);CHKERRQ(ierr);
2204   }
2205   if (mat_ctx->g2g_p) {
2206     /* interface pressure rhs */
2207     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2208     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_rhs,pcbddc->original_rhs,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2209     ierr = VecScatterBegin(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2210     ierr = VecScatterEnd(mat_ctx->g2g_p,standard_rhs,fetidp_flux_rhs,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2211     if (!mat_ctx->rhs_flip) {
2212       ierr = VecScale(fetidp_flux_rhs,-1.);CHKERRQ(ierr);
2213     }
2214   }
2215   /*
2216      change of basis for physical rhs if needed
2217      It also changes the rhs in case of dirichlet boundaries
2218   */
2219   ierr = PCPreSolve_BDDC(mat_ctx->pc,NULL,pcbddc->original_rhs,NULL);CHKERRQ(ierr);
2220   if (pcbddc->ChangeOfBasisMatrix) {
2221     ierr = MatMultTranspose(pcbddc->ChangeOfBasisMatrix,pcbddc->original_rhs,pcbddc->work_change);CHKERRQ(ierr);
2222     work = pcbddc->work_change;
2223    } else {
2224     work = pcbddc->original_rhs;
2225   }
2226   /* store vectors for computation of fetidp final solution */
2227   ierr = VecScatterBegin(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2228   ierr = VecScatterEnd(pcis->global_to_D,work,mat_ctx->temp_solution_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2229   /* scale rhs since it should be unassembled */
2230   /* TODO use counter scaling? (also below) */
2231   ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2232   ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2233   /* Apply partition of unity */
2234   ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2235   /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2236   if (!pcbddc->switch_static) {
2237     /* compute partially subassembled Schur complement right-hand side */
2238     ierr = KSPSolve(pcbddc->ksp_D,mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2239     ierr = MatMult(pcis->A_BI,pcis->vec1_D,pcis->vec1_B);CHKERRQ(ierr);
2240     ierr = VecAXPY(mat_ctx->temp_solution_B,-1.0,pcis->vec1_B);CHKERRQ(ierr);
2241     ierr = VecSet(work,0.0);CHKERRQ(ierr);
2242     ierr = VecScatterBegin(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2243     ierr = VecScatterEnd(pcis->global_to_B,mat_ctx->temp_solution_B,work,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2244     /* ierr = PCBDDCScalingRestriction(mat_ctx->pc,work,mat_ctx->temp_solution_B);CHKERRQ(ierr); */
2245     ierr = VecScatterBegin(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2246     ierr = VecScatterEnd(pcis->global_to_B,work,mat_ctx->temp_solution_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2247     ierr = VecPointwiseMult(mat_ctx->temp_solution_B,pcis->D,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2248   }
2249   /* BDDC rhs */
2250   ierr = VecCopy(mat_ctx->temp_solution_B,pcis->vec1_B);CHKERRQ(ierr);
2251   if (pcbddc->switch_static) {
2252     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2253   }
2254   /* apply BDDC */
2255   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2256   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2257   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2258 
2259   /* Application of B_delta and assembling of rhs for fetidp fluxes */
2260   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
2261   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2262   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2263   /* Add contribution to interface pressures */
2264   if (mat_ctx->l2g_p) {
2265     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
2266     if (pcbddc->switch_static) {
2267       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
2268     }
2269     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2270     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,fetidp_flux_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2271   }
2272   PetscFunctionReturn(0);
2273 }
2274 
2275 /*@
2276  PCBDDCMatFETIDPGetRHS - Compute the right-hand side for FETI-DP linear system using the physical right-hand side
2277 
2278    Collective
2279 
2280    Input Parameters:
2281 +  fetidp_mat      - the FETI-DP matrix object obtained by a call to PCBDDCCreateFETIDPOperators
2282 -  standard_rhs    - the right-hand side of the original linear system
2283 
2284    Output Parameters:
2285 .  fetidp_flux_rhs - the right-hand side for the FETI-DP linear system
2286 
2287    Level: developer
2288 
2289    Notes:
2290 
2291 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetSolution
2292 @*/
2293 PetscErrorCode PCBDDCMatFETIDPGetRHS(Mat fetidp_mat, Vec standard_rhs, Vec fetidp_flux_rhs)
2294 {
2295   FETIDPMat_ctx  mat_ctx;
2296   PetscErrorCode ierr;
2297 
2298   PetscFunctionBegin;
2299   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2300   PetscValidHeaderSpecific(standard_rhs,VEC_CLASSID,2);
2301   PetscValidHeaderSpecific(fetidp_flux_rhs,VEC_CLASSID,3);
2302   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2303   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetRHS_C",(Mat,Vec,Vec),(fetidp_mat,standard_rhs,fetidp_flux_rhs));CHKERRQ(ierr);
2304   PetscFunctionReturn(0);
2305 }
2306 
2307 static PetscErrorCode PCBDDCMatFETIDPGetSolution_BDDC(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2308 {
2309   FETIDPMat_ctx  mat_ctx;
2310   PC_IS*         pcis;
2311   PC_BDDC*       pcbddc;
2312   PetscErrorCode ierr;
2313   Vec            work;
2314 
2315   PetscFunctionBegin;
2316   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2317   pcis = (PC_IS*)mat_ctx->pc->data;
2318   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
2319 
2320   /* apply B_delta^T */
2321   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
2322   ierr = VecScatterBegin(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2323   ierr = VecScatterEnd(mat_ctx->l2g_lambda,fetidp_flux_sol,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2324   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
2325   if (mat_ctx->l2g_p) {
2326     ierr = VecScatterBegin(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2327     ierr = VecScatterEnd(mat_ctx->l2g_p,fetidp_flux_sol,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2328     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
2329   }
2330 
2331   /* compute rhs for BDDC application */
2332   ierr = VecAYPX(pcis->vec1_B,-1.0,mat_ctx->temp_solution_B);CHKERRQ(ierr);
2333   if (pcbddc->switch_static) {
2334     ierr = VecCopy(mat_ctx->temp_solution_D,pcis->vec1_D);CHKERRQ(ierr);
2335     if (mat_ctx->l2g_p) {
2336       ierr = VecScale(mat_ctx->vP,-1.);CHKERRQ(ierr);
2337       ierr = MatMultAdd(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2338     }
2339   }
2340 
2341   /* apply BDDC */
2342   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
2343   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
2344 
2345   /* put values into global vector */
2346   if (pcbddc->ChangeOfBasisMatrix) work = pcbddc->work_change;
2347   else work = standard_sol;
2348   ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2349   ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2350   if (!pcbddc->switch_static) {
2351     /* compute values into the interior if solved for the partially subassembled Schur complement */
2352     ierr = MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);CHKERRQ(ierr);
2353     ierr = VecAYPX(pcis->vec1_D,-1.0,mat_ctx->temp_solution_D);CHKERRQ(ierr);
2354     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr);
2355   }
2356 
2357   ierr = VecScatterBegin(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2358   ierr = VecScatterEnd(pcis->global_to_D,pcis->vec1_D,work,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2359   /* add p0 solution to final solution */
2360   ierr = PCBDDCBenignGetOrSetP0(mat_ctx->pc,work,PETSC_FALSE);CHKERRQ(ierr);
2361   if (pcbddc->ChangeOfBasisMatrix) {
2362     ierr = MatMult(pcbddc->ChangeOfBasisMatrix,work,standard_sol);CHKERRQ(ierr);
2363   }
2364   ierr = PCPostSolve_BDDC(mat_ctx->pc,NULL,NULL,standard_sol);CHKERRQ(ierr);
2365   if (mat_ctx->g2g_p) {
2366     ierr = VecScatterBegin(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2367     ierr = VecScatterEnd(mat_ctx->g2g_p,fetidp_flux_sol,standard_sol,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2368   }
2369   PetscFunctionReturn(0);
2370 }
2371 
2372 /*@
2373  PCBDDCMatFETIDPGetSolution - Compute the physical solution using the solution of the FETI-DP linear system
2374 
2375    Collective
2376 
2377    Input Parameters:
2378 +  fetidp_mat      - the FETI-DP matrix obtained by a call to PCBDDCCreateFETIDPOperators
2379 -  fetidp_flux_sol - the solution of the FETI-DP linear system
2380 
2381    Output Parameters:
2382 .  standard_sol    - the solution defined on the physical domain
2383 
2384    Level: developer
2385 
2386    Notes:
2387 
2388 .seealso: PCBDDC, PCBDDCCreateFETIDPOperators, PCBDDCMatFETIDPGetRHS
2389 @*/
2390 PetscErrorCode PCBDDCMatFETIDPGetSolution(Mat fetidp_mat, Vec fetidp_flux_sol, Vec standard_sol)
2391 {
2392   FETIDPMat_ctx  mat_ctx;
2393   PetscErrorCode ierr;
2394 
2395   PetscFunctionBegin;
2396   PetscValidHeaderSpecific(fetidp_mat,MAT_CLASSID,1);
2397   PetscValidHeaderSpecific(fetidp_flux_sol,VEC_CLASSID,2);
2398   PetscValidHeaderSpecific(standard_sol,VEC_CLASSID,3);
2399   ierr = MatShellGetContext(fetidp_mat,&mat_ctx);CHKERRQ(ierr);
2400   ierr = PetscUseMethod(mat_ctx->pc,"PCBDDCMatFETIDPGetSolution_C",(Mat,Vec,Vec),(fetidp_mat,fetidp_flux_sol,standard_sol));CHKERRQ(ierr);
2401   PetscFunctionReturn(0);
2402 }
2403 
2404 static PetscErrorCode PCBDDCCreateFETIDPOperators_BDDC(PC pc, PetscBool fully_redundant, const char* prefix, Mat *fetidp_mat, PC *fetidp_pc)
2405 {
2406 
2407   FETIDPMat_ctx  fetidpmat_ctx;
2408   Mat            newmat;
2409   FETIDPPC_ctx   fetidppc_ctx;
2410   PC             newpc;
2411   MPI_Comm       comm;
2412   PetscErrorCode ierr;
2413 
2414   PetscFunctionBegin;
2415   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
2416   /* FETIDP linear matrix */
2417   ierr = PCBDDCCreateFETIDPMatContext(pc,&fetidpmat_ctx);CHKERRQ(ierr);
2418   fetidpmat_ctx->fully_redundant = fully_redundant;
2419   ierr = PCBDDCSetupFETIDPMatContext(fetidpmat_ctx);CHKERRQ(ierr);
2420   ierr = MatCreateShell(comm,fetidpmat_ctx->n,fetidpmat_ctx->n,fetidpmat_ctx->N,fetidpmat_ctx->N,fetidpmat_ctx,&newmat);CHKERRQ(ierr);
2421   ierr = MatShellSetOperation(newmat,MATOP_MULT,(void (*)(void))FETIDPMatMult);CHKERRQ(ierr);
2422   ierr = MatShellSetOperation(newmat,MATOP_MULT_TRANSPOSE,(void (*)(void))FETIDPMatMultTranspose);CHKERRQ(ierr);
2423   ierr = MatShellSetOperation(newmat,MATOP_DESTROY,(void (*)(void))PCBDDCDestroyFETIDPMat);CHKERRQ(ierr);
2424   ierr = MatSetOptionsPrefix(newmat,prefix);CHKERRQ(ierr);
2425   ierr = MatAppendOptionsPrefix(newmat,"fetidp_");CHKERRQ(ierr);
2426   ierr = MatSetUp(newmat);CHKERRQ(ierr);
2427   /* FETIDP preconditioner */
2428   ierr = PCBDDCCreateFETIDPPCContext(pc,&fetidppc_ctx);CHKERRQ(ierr);
2429   ierr = PCBDDCSetupFETIDPPCContext(newmat,fetidppc_ctx);CHKERRQ(ierr);
2430   ierr = PCCreate(comm,&newpc);CHKERRQ(ierr);
2431   ierr = PCSetOperators(newpc,newmat,newmat);CHKERRQ(ierr);
2432   ierr = PCSetOptionsPrefix(newpc,prefix);CHKERRQ(ierr);
2433   ierr = PCAppendOptionsPrefix(newpc,"fetidp_");CHKERRQ(ierr);
2434   if (!fetidpmat_ctx->l2g_lambda_only) {
2435     ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
2436     ierr = PCShellSetContext(newpc,fetidppc_ctx);CHKERRQ(ierr);
2437     ierr = PCShellSetApply(newpc,FETIDPPCApply);CHKERRQ(ierr);
2438     ierr = PCShellSetApplyTranspose(newpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2439     ierr = PCShellSetView(newpc,FETIDPPCView);CHKERRQ(ierr);
2440     ierr = PCShellSetDestroy(newpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2441   } else {
2442     KSP      *ksps;
2443     PC       lagpc;
2444     Mat      M,AM,PM;
2445     PetscInt nn;
2446 
2447     ierr = PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_PPmat",(PetscObject*)&M);CHKERRQ(ierr);
2448     ierr = PCSetType(newpc,PCFIELDSPLIT);CHKERRQ(ierr);
2449     ierr = PCFieldSplitSetIS(newpc,"lag",fetidpmat_ctx->lagrange);CHKERRQ(ierr);
2450     ierr = PCFieldSplitSetIS(newpc,"p",fetidpmat_ctx->pressure);CHKERRQ(ierr);
2451     ierr = PCFieldSplitSetType(newpc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
2452     ierr = PCFieldSplitSetSchurFactType(newpc,PC_FIELDSPLIT_SCHUR_FACT_DIAG);CHKERRQ(ierr);
2453     ierr = PCFieldSplitSetSchurPre(newpc,PC_FIELDSPLIT_SCHUR_PRE_USER,M);CHKERRQ(ierr);
2454     ierr = PCFieldSplitSetSchurScale(newpc,1.0);CHKERRQ(ierr);
2455     ierr = PCSetFromOptions(newpc);CHKERRQ(ierr);
2456     ierr = PCSetUp(newpc);CHKERRQ(ierr);
2457 
2458     /* set the solver for the (0,0) block */
2459     ierr = PCFieldSplitGetSubKSP(newpc,&nn,&ksps);CHKERRQ(ierr);
2460     ierr = PCCreate(comm,&lagpc);CHKERRQ(ierr);
2461     ierr = PCSetType(lagpc,PCSHELL);CHKERRQ(ierr);
2462     ierr = KSPGetOperators(ksps[0],&AM,&PM);CHKERRQ(ierr);
2463     ierr = PCSetOperators(lagpc,AM,PM);CHKERRQ(ierr);
2464     ierr = PCShellSetContext(lagpc,fetidppc_ctx);CHKERRQ(ierr);
2465     ierr = PCShellSetApply(lagpc,FETIDPPCApply);CHKERRQ(ierr);
2466     ierr = PCShellSetApplyTranspose(lagpc,FETIDPPCApplyTranspose);CHKERRQ(ierr);
2467     ierr = PCShellSetView(lagpc,FETIDPPCView);CHKERRQ(ierr);
2468     ierr = PCShellSetDestroy(lagpc,PCBDDCDestroyFETIDPPC);CHKERRQ(ierr);
2469     ierr = KSPSetPC(ksps[0],lagpc);CHKERRQ(ierr);
2470     ierr = PCDestroy(&lagpc);CHKERRQ(ierr);
2471     ierr = PetscFree(ksps);CHKERRQ(ierr);
2472   }
2473   /* return pointers for objects created */
2474   *fetidp_mat = newmat;
2475   *fetidp_pc = newpc;
2476   PetscFunctionReturn(0);
2477 }
2478 
2479 /*@C
2480  PCBDDCCreateFETIDPOperators - Create FETI-DP operators
2481 
2482    Collective
2483 
2484    Input Parameters:
2485 +  pc - the BDDC preconditioning context (setup should have been called before)
2486 .  fully_redundant - true for a fully redundant set of Lagrange multipliers
2487 -  prefix - optional options database prefix for the objects to be created (can be NULL)
2488 
2489    Output Parameters:
2490 +  fetidp_mat - shell FETI-DP matrix object
2491 -  fetidp_pc  - shell Dirichlet preconditioner for FETI-DP matrix
2492 
2493    Level: developer
2494 
2495    Notes:
2496      Currently the only operations provided for FETI-DP matrix are MatMult and MatMultTranspose
2497 
2498 .seealso: PCBDDC, PCBDDCMatFETIDPGetRHS, PCBDDCMatFETIDPGetSolution
2499 @*/
2500 PetscErrorCode PCBDDCCreateFETIDPOperators(PC pc, PetscBool fully_redundant, const char *prefix, Mat *fetidp_mat, PC *fetidp_pc)
2501 {
2502   PetscErrorCode ierr;
2503 
2504   PetscFunctionBegin;
2505   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
2506   if (pc->setupcalled) {
2507     ierr = PetscUseMethod(pc,"PCBDDCCreateFETIDPOperators_C",(PC,PetscBool,const char*,Mat*,PC*),(pc,fully_redundant,prefix,fetidp_mat,fetidp_pc));CHKERRQ(ierr);
2508   } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"You must call PCSetup_BDDC() first \n");
2509   PetscFunctionReturn(0);
2510 }
2511 /* -------------------------------------------------------------------------- */
2512 /*MC
2513    PCBDDC - Balancing Domain Decomposition by Constraints.
2514 
2515    An implementation of the BDDC preconditioner based on
2516 
2517 .vb
2518    [1] C. R. Dohrmann. "An approximate BDDC preconditioner", Numerical Linear Algebra with Applications Volume 14, Issue 2, pages 149-168, March 2007
2519    [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
2520    [3] J. Mandel, B. Sousedik, C. R. Dohrmann. "Multispace and Multilevel BDDC", http://arxiv.org/abs/0712.3977
2521    [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
2522 .ve
2523 
2524    The matrix to be preconditioned (Pmat) must be of type MATIS.
2525 
2526    Currently works with MATIS matrices with local matrices of type MATSEQAIJ, MATSEQBAIJ or MATSEQSBAIJ, either with real or complex numbers.
2527 
2528    It also works with unsymmetric and indefinite problems.
2529 
2530    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.
2531 
2532    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).
2533 
2534    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()
2535    Additional information on dofs can be provided by using PCBDDCSetDofsSplitting(), PCBDDCSetDirichletBoundaries(), PCBDDCSetNeumannBoundaries(), and PCBDDCSetPrimalVerticesIS() and their local counterparts.
2536 
2537    Constraints can be customized by attaching a MatNullSpace object to the MATIS matrix via MatSetNearNullSpace(). Non-singular modes are retained via SVD.
2538 
2539    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.
2540    User defined change of basis can be passed to PCBDDC by using PCBDDCSetChangeOfBasisMat()
2541 
2542    The PETSc implementation also supports multilevel BDDC [3]. Coarse grids are partitioned using a MatPartitioning object.
2543 
2544    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.
2545 
2546    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.
2547    Deluxe scaling is not supported yet for FETI-DP.
2548 
2549    Options Database Keys (some of them, run with -h for a complete list):
2550 
2551 .    -pc_bddc_use_vertices <true> - use or not vertices in primal space
2552 .    -pc_bddc_use_edges <true> - use or not edges in primal space
2553 .    -pc_bddc_use_faces <false> - use or not faces in primal space
2554 .    -pc_bddc_symmetric <true> - symmetric computation of primal basis functions. Specify false for unsymmetric problems
2555 .    -pc_bddc_use_change_of_basis <false> - use change of basis approach (on edges only)
2556 .    -pc_bddc_use_change_on_faces <false> - use change of basis approach on faces if change of basis has been requested
2557 .    -pc_bddc_switch_static <false> - switches from M_2 (default) to M_3 operator (see reference article [1])
2558 .    -pc_bddc_levels <0> - maximum number of levels for multilevel
2559 .    -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)
2560 .    -pc_bddc_coarse_redistribute <0> - size of a subset of processors where the coarse problem will be remapped (the value is ignored if not at the coarsest level)
2561 .    -pc_bddc_use_deluxe_scaling <false> - use deluxe scaling
2562 .    -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)
2563 .    -pc_bddc_adaptive_threshold <0.0> - when a value different than zero is specified, adaptive selection of constraints is performed on edges and faces (requires deluxe scaling and MUMPS or MKL_PARDISO installed)
2564 -    -pc_bddc_check_level <0> - set verbosity level of debugging output
2565 
2566    Options for Dirichlet, Neumann or coarse solver can be set with
2567 .vb
2568       -pc_bddc_dirichlet_
2569       -pc_bddc_neumann_
2570       -pc_bddc_coarse_
2571 .ve
2572    e.g -pc_bddc_dirichlet_ksp_type richardson -pc_bddc_dirichlet_pc_type gamg. PCBDDC uses by default KPSPREONLY and PCLU.
2573 
2574    When using a multilevel approach, solvers' options at the N-th level (N > 1) can be specified as
2575 .vb
2576       -pc_bddc_dirichlet_lN_
2577       -pc_bddc_neumann_lN_
2578       -pc_bddc_coarse_lN_
2579 .ve
2580    Note that level number ranges from the finest (0) to the coarsest (N).
2581    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.
2582 .vb
2583      -pc_bddc_coarse_pc_bddc_adaptive_threshold 5 -pc_bddc_coarse_l1_pc_bddc_redistribute 3
2584 .ve
2585    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
2586 
2587    Level: intermediate
2588 
2589    Developer Notes:
2590 
2591    Contributed by Stefano Zampini
2592 
2593 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
2594 M*/
2595 
2596 PETSC_EXTERN PetscErrorCode PCCreate_BDDC(PC pc)
2597 {
2598   PetscErrorCode      ierr;
2599   PC_BDDC             *pcbddc;
2600 
2601   PetscFunctionBegin;
2602   ierr     = PetscNewLog(pc,&pcbddc);CHKERRQ(ierr);
2603   pc->data = (void*)pcbddc;
2604 
2605   /* create PCIS data structure */
2606   ierr = PCISCreate(pc);CHKERRQ(ierr);
2607 
2608   /* create local graph structure */
2609   ierr = PCBDDCGraphCreate(&pcbddc->mat_graph);CHKERRQ(ierr);
2610 
2611   /* BDDC nonzero defaults */
2612   pcbddc->use_local_adj             = PETSC_TRUE;
2613   pcbddc->use_vertices              = PETSC_TRUE;
2614   pcbddc->use_edges                 = PETSC_TRUE;
2615   pcbddc->symmetric_primal          = PETSC_TRUE;
2616   pcbddc->vertex_size               = 1;
2617   pcbddc->recompute_topography      = PETSC_TRUE;
2618   pcbddc->coarse_size               = -1;
2619   pcbddc->use_exact_dirichlet_trick = PETSC_TRUE;
2620   pcbddc->coarsening_ratio          = 8;
2621   pcbddc->coarse_eqs_per_proc       = 1;
2622   pcbddc->benign_compute_correction = PETSC_TRUE;
2623   pcbddc->nedfield                  = -1;
2624   pcbddc->nedglobal                 = PETSC_TRUE;
2625   pcbddc->graphmaxcount             = PETSC_MAX_INT;
2626   pcbddc->sub_schurs_layers         = -1;
2627   pcbddc->adaptive_threshold[0]     = 0.0;
2628   pcbddc->adaptive_threshold[1]     = 0.0;
2629 
2630   /* function pointers */
2631   pc->ops->apply               = PCApply_BDDC;
2632   pc->ops->applytranspose      = PCApplyTranspose_BDDC;
2633   pc->ops->setup               = PCSetUp_BDDC;
2634   pc->ops->destroy             = PCDestroy_BDDC;
2635   pc->ops->setfromoptions      = PCSetFromOptions_BDDC;
2636   pc->ops->view                = PCView_BDDC;
2637   pc->ops->applyrichardson     = 0;
2638   pc->ops->applysymmetricleft  = 0;
2639   pc->ops->applysymmetricright = 0;
2640   pc->ops->presolve            = PCPreSolve_BDDC;
2641   pc->ops->postsolve           = PCPostSolve_BDDC;
2642   pc->ops->reset               = PCReset_BDDC;
2643 
2644   /* composing function */
2645   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDiscreteGradient_C",PCBDDCSetDiscreteGradient_BDDC);CHKERRQ(ierr);
2646   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDivergenceMat_C",PCBDDCSetDivergenceMat_BDDC);CHKERRQ(ierr);
2647   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetChangeOfBasisMat_C",PCBDDCSetChangeOfBasisMat_BDDC);CHKERRQ(ierr);
2648   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesLocalIS_C",PCBDDCSetPrimalVerticesLocalIS_BDDC);CHKERRQ(ierr);
2649   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetPrimalVerticesIS_C",PCBDDCSetPrimalVerticesIS_BDDC);CHKERRQ(ierr);
2650   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetCoarseningRatio_C",PCBDDCSetCoarseningRatio_BDDC);CHKERRQ(ierr);
2651   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevel_C",PCBDDCSetLevel_BDDC);CHKERRQ(ierr);
2652   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetUseExactDirichlet_C",PCBDDCSetUseExactDirichlet_BDDC);CHKERRQ(ierr);
2653   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLevels_C",PCBDDCSetLevels_BDDC);CHKERRQ(ierr);
2654   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundaries_C",PCBDDCSetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2655   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDirichletBoundariesLocal_C",PCBDDCSetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2656   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundaries_C",PCBDDCSetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2657   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetNeumannBoundariesLocal_C",PCBDDCSetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2658   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundaries_C",PCBDDCGetDirichletBoundaries_BDDC);CHKERRQ(ierr);
2659   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetDirichletBoundariesLocal_C",PCBDDCGetDirichletBoundariesLocal_BDDC);CHKERRQ(ierr);
2660   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundaries_C",PCBDDCGetNeumannBoundaries_BDDC);CHKERRQ(ierr);
2661   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCGetNeumannBoundariesLocal_C",PCBDDCGetNeumannBoundariesLocal_BDDC);CHKERRQ(ierr);
2662   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplitting_C",PCBDDCSetDofsSplitting_BDDC);CHKERRQ(ierr);
2663   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetDofsSplittingLocal_C",PCBDDCSetDofsSplittingLocal_BDDC);CHKERRQ(ierr);
2664   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCSetLocalAdjacencyGraph_C",PCBDDCSetLocalAdjacencyGraph_BDDC);CHKERRQ(ierr);
2665   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCCreateFETIDPOperators_C",PCBDDCCreateFETIDPOperators_BDDC);CHKERRQ(ierr);
2666   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetRHS_C",PCBDDCMatFETIDPGetRHS_BDDC);CHKERRQ(ierr);
2667   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCMatFETIDPGetSolution_C",PCBDDCMatFETIDPGetSolution_BDDC);CHKERRQ(ierr);
2668   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_BDDC);CHKERRQ(ierr);
2669   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCSetCoordinates_C",PCSetCoordinates_BDDC);CHKERRQ(ierr);
2670   PetscFunctionReturn(0);
2671 }
2672