PetscSolverFeti.cc 40.8 KB
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//
// Software License for AMDiS
//
// Copyright (c) 2010 Dresden University of Technology 
// All rights reserved.
// Authors: Simon Vey, Thomas Witkowski et al.
//
// This file is part of AMDiS
//
// See also license.opensource.txt in the distribution.


#include "parallel/PetscSolverFeti.h"
#include "parallel/StdMpi.h"
#include "parallel/MpiHelper.h"

namespace AMDiS {

  using namespace std;


#ifdef HAVE_PETSC_DEV 
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  // y = mat * x
  int petscMultMatSchurPrimal(Mat mat, Vec x, Vec y)
  {
    // S_PiPi = K_PiPi - K_PiB inv(K_BB) K_BPi

    void *ctx;
    MatShellGetContext(mat, &ctx);
    PetscSchurPrimalData* data = static_cast<PetscSchurPrimalData*>(ctx);

    MatMult(*(data->mat_b_primal), x, data->tmp_vec_b);
    KSPSolve(*(data->ksp_b), data->tmp_vec_b, data->tmp_vec_b);

    MatMult(*(data->mat_primal_b), data->tmp_vec_b, data->tmp_vec_primal);
    MatMult(*(data->mat_primal_primal), x, y);
    VecAXPBY(y, -1.0, 1.0, data->tmp_vec_primal);

    return 0;
  }


  // y = mat * x
  int petscMultMatFeti(Mat mat, Vec x, Vec y)
  {
    // F = L inv(K_BB) trans(L) + L inv(K_BB) K_BPi inv(S_PiPi) K_PiB inv(K_BB) trans(L)

    void *ctx;
    MatShellGetContext(mat, &ctx);
    PetscFetiData* data = static_cast<PetscFetiData*>(ctx);

    // y = L inv(K_BB) trans(L) x
    MatMultTranspose(*(data->mat_lagrange), x, data->tmp_vec_b);
    KSPSolve(*(data->ksp_b), data->tmp_vec_b, data->tmp_vec_b);
    MatMult(*(data->mat_lagrange), data->tmp_vec_b, y);

    // tmp_vec_primal = inv(S_PiPi) K_PiB inv(K_BB) trans(L)
    MatMult(*(data->mat_primal_b), data->tmp_vec_b, data->tmp_vec_primal);
    KSPSolve(*(data->ksp_schur_primal), data->tmp_vec_primal, data->tmp_vec_primal);

    // tmp_vec_lagrange = L inv(K_BB) K_BPi tmp_vec_primal
    //                  = L inv(K_BB) K_BPi inv(S_PiPi) K_PiB inv(K_BB) trans(L)
    MatMult(*(data->mat_b_primal), data->tmp_vec_primal, data->tmp_vec_b);
    KSPSolve(*(data->ksp_b), data->tmp_vec_b, data->tmp_vec_b);
    MatMult(*(data->mat_lagrange), data->tmp_vec_b, data->tmp_vec_lagrange);

    VecAXPBY(y, 1.0, 1.0, data->tmp_vec_lagrange);

    return 0;
  }


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  // y = PC * x
  PetscErrorCode petscApplyFetiPrecon(PC pc, Vec x, Vec y)
  {
    void *ctx;
    PCShellGetContext(pc, &ctx);
    PetscFetiPreconData* data = static_cast<PetscFetiPreconData*>(ctx);

    MatMultTranspose(*(data->mat_lagrange_scaled), x, data->tmp_vec_b);

    int sizeB;
    int sizeBound;
    VecGetLocalSize(data->tmp_vec_b, &sizeB);
    VecGetLocalSize(data->tmp_vec_bound0, &sizeBound);

    PetscScalar *local_b;
    VecGetArray(data->tmp_vec_b, &local_b);

    PetscScalar *local_bound;
    VecGetArray(data->tmp_vec_bound0, &local_bound);

    for (int i = sizeB - sizeBound, j = 0; i < sizeB; i++, j++)
      local_bound[j] = local_b[i];

    VecRestoreArray(data->tmp_vec_b, &local_b);
    VecRestoreArray(data->tmp_vec_bound0, &local_bound);



    MatMult(*(data->mat_bound_bound), data->tmp_vec_bound0, data->tmp_vec_bound1);

    MatMult(*(data->mat_interior_bound), data->tmp_vec_bound0, data->tmp_vec_interior);
    KSPSolve(*(data->ksp_interior), data->tmp_vec_interior, data->tmp_vec_interior);
    MatMult(*(data->mat_bound_interior), data->tmp_vec_interior, data->tmp_vec_bound0);

    VecAXPBY(data->tmp_vec_bound0, 1.0, -1.0, data->tmp_vec_bound1);



    VecGetArray(data->tmp_vec_b, &local_b);
    VecGetArray(data->tmp_vec_bound0, &local_bound);

    for (int i = sizeB - sizeBound, j = 0; i < sizeB; i++, j++)
      local_b[i] = local_bound[j];

    VecRestoreArray(data->tmp_vec_b, &local_b);
    VecRestoreArray(data->tmp_vec_bound0, &local_bound);




    MatMult(*(data->mat_lagrange_scaled), data->tmp_vec_b, y);

    return 0;
  }


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  void PetscSolverFeti::updateDofData()
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  {
    FUNCNAME("PetscSolverFeti::updateDofData()");
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    TEST_EXIT(meshDistributor->getMesh()->getDim() == 2)
      ("Works for 2D problems only!");

    TEST_EXIT(meshDistributor->getFeSpace()->getBasisFcts()->getDegree() == 1)
      ("Works for linear basis functions only!\n");
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    createPrimals();

    createDuals();

    createLagrange();

    createIndexB();
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  }


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  void PetscSolverFeti::createPrimals()
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  {
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    FUNCNAME("PetscSolverFeti::createPrimals()");  
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    // === Define all vertices on the interior boundaries of the macro mesh ===
    // === to be primal variables.                                          ===

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    primals.clear();
    DofContainerSet& vertices = 
      meshDistributor->getBoundaryDofInfo().geoDofs[VERTEX];
    TEST_EXIT_DBG(vertices.size())("No primal vertices on this rank!\n");
    for (DofContainerSet::iterator it = vertices.begin(); 
	 it != vertices.end(); ++it)
      primals.insert(**it);
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    // === Calculate the number of primals that are owned by the rank and ===
    // === create local indices of the primals starting at zero.          ===

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    globalPrimalIndex.clear();
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    nRankPrimals = 0;
    for (DofIndexSet::iterator it = primals.begin(); it != primals.end(); ++it)
      if (meshDistributor->getIsRankDof(*it)) {
	globalPrimalIndex[*it] = nRankPrimals;
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	nRankPrimals++;
      }

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    // === Get overall number of primals and rank's displacement in the ===
    // === numbering of the primals.                                    ===

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    nOverallPrimals = 0;
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    rStartPrimals = 0;
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    mpi::getDofNumbering(meshDistributor->getMpiComm(),
			 nRankPrimals, rStartPrimals, nOverallPrimals);

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    // === Create global primal index for all primals. ===

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    for (DofMapping::iterator it = globalPrimalIndex.begin();
	 it != globalPrimalIndex.end(); ++it)
      it->second += rStartPrimals;

    MSG_DBG("nRankPrimals = %d   nOverallPrimals = %d\n",
	    nRankPrimals, nOverallPrimals);
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    // === Communicate primal's global index from ranks that own the     ===
    // === primals to ranks that contain this primals but are not owning ===
    // === them.                                                         ===

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    StdMpi<vector<int> > stdMpi(meshDistributor->getMpiComm());
    RankToDofContainer& sendDofs = meshDistributor->getSendDofs();
    for (RankToDofContainer::iterator it = sendDofs.begin();
	 it != sendDofs.end(); ++it)
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt)
	if (globalPrimalIndex.count(**dofIt))
	  stdMpi.getSendData(it->first).push_back(globalPrimalIndex[**dofIt]);
    stdMpi.updateSendDataSize();

    RankToDofContainer& recvDofs = meshDistributor->getRecvDofs();
    for (RankToDofContainer::iterator it = recvDofs.begin();
	 it != recvDofs.end(); ++it) {
      bool recvFromRank = false;
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt)
	if (primals.count(**dofIt) && 
	    meshDistributor->getIsRankDof(**dofIt) == false) {
	  recvFromRank = true;
	  break;
	}

      if (recvFromRank) 
	stdMpi.recv(it->first);
    }
    stdMpi.startCommunication();

    for (RankToDofContainer::iterator it = recvDofs.begin();
	 it != recvDofs.end(); ++it) {
      int i = 0;
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt) {
	if (primals.count(**dofIt) && 
	    meshDistributor->getIsRankDof(**dofIt) == false)
	  globalPrimalIndex[**dofIt] = stdMpi.getRecvData(it->first)[i++];
      }
    }

    TEST_EXIT_DBG(primals.size() == globalPrimalIndex.size())
      ("Number of primals %d, but number of global primals on this rank is %d!\n",
       primals.size(), globalPrimalIndex.size());


    TEST_EXIT_DBG(nOverallPrimals > 0)
      ("There are zero primal nodes in domain!\n");
  }


  void PetscSolverFeti::createDuals()
  {
    FUNCNAME("PetscSolverFeti::createDuals()");
    
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    // === Create for each dual node that is owned by the rank, the set ===
    // === of ranks that contain this node (denoted by W(x_j)).         ===
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    boundaryDofRanks.clear();

    RankToDofContainer& sendDofs = meshDistributor->getSendDofs();
    for (RankToDofContainer::iterator it = sendDofs.begin();
	 it != sendDofs.end(); ++it) {
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt) {
	// If DOF is not primal, i.e., its a dual node
	if (primals.count(**dofIt) == 0) {
	  boundaryDofRanks[**dofIt].insert(mpiRank);
	  boundaryDofRanks[**dofIt].insert(it->first);
	}
      }
    }

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    // === Communicate these sets for all rank owned dual nodes to other ===
    // === ranks that also have this node.                               ===

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    StdMpi<vector<std::set<int> > > stdMpi(meshDistributor->getMpiComm());
    for (RankToDofContainer::iterator it = sendDofs.begin();
	 it != sendDofs.end(); ++it)
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt)
	if (primals.count(**dofIt) == 0)
	  stdMpi.getSendData(it->first).push_back(boundaryDofRanks[**dofIt]);

    stdMpi.updateSendDataSize();

    RankToDofContainer& recvDofs = meshDistributor->getRecvDofs();
    for (RankToDofContainer::iterator it = recvDofs.begin();
	 it != recvDofs.end(); ++it) {
      bool recvFromRank = false;
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt)
	if (primals.count(**dofIt) == 0) {
	  recvFromRank = true;
	  break;
	}

      if (recvFromRank)
	stdMpi.recv(it->first);
    }
    stdMpi.startCommunication();

    for (RankToDofContainer::iterator it = recvDofs.begin();
	 it != recvDofs.end(); ++it) {
      int i = 0;
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt)	
	if (primals.count(**dofIt) == 0)
	  boundaryDofRanks[**dofIt] = stdMpi.getRecvData(it->first)[i++];	      
    }


    // === Create global index of the dual nodes on each rank. ===

    duals.clear();
    globalDualIndex.clear();

    int nRankAllDofs = meshDistributor->getFeSpace()->getAdmin()->getUsedDofs();
    nRankB = nRankAllDofs - primals.size();
    nOverallB = 0;
    rStartB = 0;
    mpi::getDofNumbering(meshDistributor->getMpiComm(),
			 nRankB, rStartB, nOverallB);
    DofContainer allBoundaryDofs;
    meshDistributor->getAllBoundaryDofs(allBoundaryDofs);
    int nRankInteriorDofs = nRankAllDofs - allBoundaryDofs.size();

    int nRankDuals = 0;
    for (DofContainer::iterator it = allBoundaryDofs.begin();
	 it != allBoundaryDofs.end(); ++it) {
      if (primals.count(**it) == 0) {
	duals.insert(**it);
	globalDualIndex[**it] = rStartB + nRankInteriorDofs + nRankDuals;
	nRankDuals++;
      }
    }

    int nOverallDuals = nRankDuals;
    mpi::globalAdd(nOverallDuals);

    MSG_DBG("nRankDuals = %d   nOverallDuals = %d\n",
	    nRankDuals, nOverallDuals);
  }

  
  void PetscSolverFeti::createLagrange()
  {
    FUNCNAME("PetscSolverFeti::createLagrange()");

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    // === Reserve for each dual node, on the rank that owns this node, the ===
    // === appropriate number of Lagrange constraints.                      ===

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    nRankLagrange = 0;
    for (DofIndexSet::iterator it = duals.begin(); it != duals.end(); ++it) {
      if (meshDistributor->getIsRankDof(*it)) {
	dofFirstLagrange[*it] = nRankLagrange;
	int degree = boundaryDofRanks[*it].size();
	nRankLagrange += (degree * (degree - 1)) / 2;
      }
    }

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    // === Get the overall number of Lagrange constraints and create the ===
    // === mapping dofFirstLagrange, that defines for each dual boundary ===
    // === node the first Lagrange constraint global index.              ===

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    nOverallLagrange = 0;
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    rStartLagrange = 0;
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    mpi::getDofNumbering(meshDistributor->getMpiComm(),
			 nRankLagrange, rStartLagrange, nOverallLagrange);

    for (DofIndexSet::iterator it = duals.begin(); it != duals.end(); ++it)
      if (meshDistributor->getIsRankDof(*it))
	dofFirstLagrange[*it] += rStartLagrange;

    MSG_DBG("nRankLagrange = %d  nOverallLagrange = %d\n",
	    nRankLagrange, nOverallLagrange);


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    // === Communicate dofFirstLagrange to all other ranks. ===
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    StdMpi<vector<int> > stdMpi(meshDistributor->getMpiComm());
    RankToDofContainer& sendDofs = meshDistributor->getSendDofs();
    for (RankToDofContainer::iterator it = sendDofs.begin();
	 it != sendDofs.end(); ++it)
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt) {
	if (primals.count(**dofIt) == 0) {
	  TEST_EXIT_DBG(dofFirstLagrange.count(**dofIt))("Should not happen!\n");
	  stdMpi.getSendData(it->first).push_back(dofFirstLagrange[**dofIt]);
	}
      }
    stdMpi.updateSendDataSize();

    RankToDofContainer& recvDofs = meshDistributor->getRecvDofs();
    for (RankToDofContainer::iterator it = recvDofs.begin();
	 it != recvDofs.end(); ++it) {
      bool recvData = false;
      for (DofContainer::iterator dofIt = it->second.begin();
	   dofIt != it->second.end(); ++dofIt)
	if (primals.count(**dofIt) == 0) {
	  recvData = true;
	  break;
	}
	  
      if (recvData)
	stdMpi.recv(it->first);
    }

    stdMpi.startCommunication();

    for (RankToDofContainer::iterator it = recvDofs.begin();
	 it != recvDofs.end(); ++it) {
      int counter = 0;
      for (unsigned int i = 0; i < it->second.size(); i++)
	if (primals.count(*(it->second[i])) == 0)
	  dofFirstLagrange[*(it->second[i])] = stdMpi.getRecvData(it->first)[counter++];
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    }     
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  }


  void PetscSolverFeti::createIndexB()
  {
    FUNCNAME("PetscSolverFeti::createIndeB()");

    globalIndexB.clear();
    DOFAdmin* admin = meshDistributor->getFeSpace()->getAdmin();
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    // === To ensure that all interior node on each rank are listen first in ===
    // === the global index of all B nodes, insert all interior nodes first, ===
    // === without defining a correct index.                                 ===
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    for (int i = 0; i < admin->getUsedSize(); i++)
      if (admin->isDofFree(i) == false && primals.count(i) == 0)
	if (duals.count(i) == 0 && primals.count(i) == 0)
	  globalIndexB[i] = -1;

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    // === Get correct index for all interior nodes. ===

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    nLocalInterior = 0;
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    for (DofMapping::iterator it = globalIndexB.begin(); 
	 it != globalIndexB.end(); ++it) {
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      it->second = nLocalInterior + rStartB;
      nLocalInterior++;
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    }
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    nLocalBound = duals.size();
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    TEST_EXIT_DBG(nLocalInterior + primals.size() + duals.size() == 
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		  static_cast<unsigned int>(admin->getUsedDofs()))
      ("Should not happen!\n");

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    // === And finally, add the global indicies of all dual nodes. ===

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    for (DofIndexSet::iterator it = duals.begin();
	 it != duals.end(); ++it)
      globalIndexB[*it] = globalDualIndex[*it];
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  }


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  void PetscSolverFeti::createMatLagrange()
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  {
    FUNCNAME("PetscSolverFeti::createMatLagrange()");

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    // === Create distributed matrix for Lagrange constraints. ===

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    MatCreateMPIAIJ(PETSC_COMM_WORLD,
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		    nRankLagrange * nComponents, 
		    nRankB * nComponents,
		    nOverallLagrange * nComponents, 
		    nOverallB * nComponents,
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		    2, PETSC_NULL, 2, PETSC_NULL,
		    &mat_lagrange);

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    // === Create for all duals the corresponding Lagrange constraints. On ===
    // === each rank we traverse all pairs (n, m) of ranks, with n < m,    ===
    // === that contain this node. If the current rank number is r, and    ===
    // === n == r, the rank sets 1.0 for the corresponding constraint, if  ===
    // === m == r, than the rank sets -1.0 for the corresponding           ===
    // === constraint.                                                     ===

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    for (DofIndexSet::iterator it = duals.begin(); it != duals.end(); ++it) {
      TEST_EXIT_DBG(dofFirstLagrange.count(*it))("Should not happen!\n");
      TEST_EXIT_DBG(boundaryDofRanks.count(*it))("Should not happen!\n");

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      // Global index of the first Lagrange constriant for this node.
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      int index = dofFirstLagrange[*it];
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      // Copy set of all ranks that contain this dual node.
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      vector<int> W(boundaryDofRanks[*it].begin(), boundaryDofRanks[*it].end());
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      // Number of ranks that contain this dual node.
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      int degree = W.size();

      TEST_EXIT_DBG(globalDualIndex.count(*it))("Should not happen!\n");
      int dualCol = globalDualIndex[*it];

      for (int i = 0; i < degree; i++) {
	for (int j = i + 1; j < degree; j++) {
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	  if (W[i] == mpiRank || W[j] == mpiRank) {
	    // Set the constraint for all components of the system.
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	    for (int k = 0; k < nComponents; k++) {
	      int rowIndex = index * nComponents + k;
	      int colIndex = dualCol * nComponents + k;
	      double value = (W[i] == mpiRank ? 1.0 : -1.0);
	      MatSetValue(mat_lagrange, rowIndex, colIndex, value, 
			  INSERT_VALUES);
	    }
	  }

	  index++;
	}
      }
    }

    MatAssemblyBegin(mat_lagrange, MAT_FINAL_ASSEMBLY);
    MatAssemblyEnd(mat_lagrange, MAT_FINAL_ASSEMBLY);
  }


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  void PetscSolverFeti::createSchurPrimalKsp()
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  {
    FUNCNAME("PetscSolverFeti::createSchurPrimal()");

    petscSchurPrimalData.mat_primal_primal = &mat_primal_primal;
    petscSchurPrimalData.mat_primal_b = &mat_primal_b;
    petscSchurPrimalData.mat_b_primal = &mat_b_primal;
    petscSchurPrimalData.ksp_b = &ksp_b;

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    VecDuplicate(f_b, &(petscSchurPrimalData.tmp_vec_b));
    VecDuplicate(f_primal, &(petscSchurPrimalData.tmp_vec_primal));
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    MatCreateShell(PETSC_COMM_WORLD,
		   nRankPrimals * nComponents, nRankPrimals * nComponents,
		   nOverallPrimals * nComponents, nOverallPrimals * nComponents,
		   &petscSchurPrimalData, 
		   &mat_schur_primal);
    MatShellSetOperation(mat_schur_primal, MATOP_MULT, 
			 (void(*)(void))petscMultMatSchurPrimal);

    KSPCreate(PETSC_COMM_WORLD, &ksp_schur_primal);
    KSPSetOperators(ksp_schur_primal, mat_schur_primal, mat_schur_primal, SAME_NONZERO_PATTERN);
    KSPSetOptionsPrefix(ksp_schur_primal, "solver_sp_");
    KSPSetFromOptions(ksp_schur_primal);
  }


  void PetscSolverFeti::destroySchurPrimalKsp()
  {
    FUNCNAME("PetscSolverFeti::destroySchurPrimal()");

    petscSchurPrimalData.mat_primal_primal = PETSC_NULL;
    petscSchurPrimalData.mat_primal_b = PETSC_NULL;
    petscSchurPrimalData.mat_b_primal = PETSC_NULL;
    petscSchurPrimalData.ksp_b = PETSC_NULL;

    VecDestroy(petscSchurPrimalData.tmp_vec_b);
    VecDestroy(petscSchurPrimalData.tmp_vec_primal);

    MatDestroy(mat_schur_primal);
    KSPDestroy(ksp_schur_primal);
  }


  void PetscSolverFeti::createFetiKsp()
  {
    FUNCNAME("PetscSolverFeti::createFetiKsp()");

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    // === Create FETI-DP solver object. ===

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    petscFetiData.mat_primal_primal = &mat_primal_primal;
    petscFetiData.mat_primal_b = &mat_primal_b;
    petscFetiData.mat_b_primal = &mat_b_primal;
    petscFetiData.mat_lagrange = &mat_lagrange;
    petscFetiData.ksp_b = &ksp_b;
    petscFetiData.ksp_schur_primal = &ksp_schur_primal;


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    VecDuplicate(f_b, &(petscFetiData.tmp_vec_b));
    VecDuplicate(f_primal, &(petscFetiData.tmp_vec_primal));
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    MatGetVecs(mat_lagrange, PETSC_NULL, &(petscFetiData.tmp_vec_lagrange));


    MatCreateShell(PETSC_COMM_WORLD,
		   nRankLagrange, nRankLagrange,
		   nOverallLagrange, nOverallLagrange,
		   &petscFetiData, &mat_feti);
    MatShellSetOperation(mat_feti, MATOP_MULT, (void(*)(void))petscMultMatFeti);


    KSPCreate(PETSC_COMM_WORLD, &ksp_feti);
    KSPSetOperators(ksp_feti, mat_feti, mat_feti, SAME_NONZERO_PATTERN);
    KSPSetOptionsPrefix(ksp_feti, "solver_feti_");
    KSPSetFromOptions(ksp_feti);
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    // === Create FETI-DP Dirichlet preconditioner object. ===

    KSPCreate(PETSC_COMM_SELF, &ksp_interior);
    KSPSetOperators(ksp_interior, mat_interior_interior, mat_interior_interior, SAME_NONZERO_PATTERN);
    KSPSetOptionsPrefix(ksp_interior, "solver_interior_");
    KSPSetFromOptions(ksp_interior);

    
    MatDuplicate(mat_lagrange, MAT_COPY_VALUES, &mat_lagrange_scaled);
    MatScale(mat_lagrange_scaled, 0.5);

    petscFetiPreconData.mat_lagrange_scaled = &mat_lagrange_scaled;
    petscFetiPreconData.mat_interior_interior = &mat_interior_interior;
    petscFetiPreconData.mat_bound_bound = &mat_bound_bound;
    petscFetiPreconData.mat_interior_bound = &mat_interior_bound;
    petscFetiPreconData.mat_bound_interior = &mat_bound_interior;
    petscFetiPreconData.ksp_interior = &ksp_interior;
    petscFetiPreconData.nInterior = nRankB - duals.size();

    VecDuplicate(f_b, &(petscFetiPreconData.tmp_vec_b));

    MatGetVecs(mat_bound_bound, PETSC_NULL, &(petscFetiPreconData.tmp_vec_bound0));
    MatGetVecs(mat_bound_bound, PETSC_NULL, &(petscFetiPreconData.tmp_vec_bound1));
    MatGetVecs(mat_interior_interior, PETSC_NULL, &(petscFetiPreconData.tmp_vec_interior));


    KSPGetPC(ksp_feti, &precon_feti);
    PCSetType(precon_feti, PCSHELL);
    PCShellSetContext(precon_feti, static_cast<void*>(&petscFetiPreconData));
    PCShellSetApply(precon_feti, petscApplyFetiPrecon);
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  }
  

  void PetscSolverFeti::destroyFetiKsp()
  {
    FUNCNAME("PetscSolverFeti::destroyFetiKsp()");

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    // === Destroy FETI-DP solver object. ===

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    petscFetiData.mat_primal_primal = PETSC_NULL;
    petscFetiData.mat_primal_b = PETSC_NULL;
    petscFetiData.mat_b_primal = PETSC_NULL;
    petscFetiData.mat_lagrange = PETSC_NULL;
    petscFetiData.ksp_b = PETSC_NULL;
    petscFetiData.ksp_schur_primal = PETSC_NULL;

    VecDestroy(petscFetiData.tmp_vec_b);
    VecDestroy(petscFetiData.tmp_vec_primal);
    VecDestroy(petscFetiData.tmp_vec_lagrange);

    MatDestroy(mat_feti);
    KSPDestroy(ksp_feti);
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    // === Destroy FETI-DP Dirichlet preconditioner object. ===

    KSPDestroy(ksp_interior);

    petscFetiPreconData.mat_lagrange_scaled = NULL;
    petscFetiPreconData.mat_interior_interior = NULL;
    petscFetiPreconData.mat_bound_bound = NULL;
    petscFetiPreconData.mat_interior_bound = NULL;
    petscFetiPreconData.mat_bound_interior = NULL;
    petscFetiPreconData.ksp_interior = NULL;

    VecDestroy(petscFetiPreconData.tmp_vec_b);
    VecDestroy(petscFetiPreconData.tmp_vec_bound0);
    VecDestroy(petscFetiPreconData.tmp_vec_bound1);
    VecDestroy(petscFetiPreconData.tmp_vec_interior);
    MatDestroy(mat_lagrange_scaled);
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  }


  void PetscSolverFeti::recoverSolution(Vec &vec_sol_b,
					Vec &vec_sol_primal,
					SystemVector &vec)
  {
    FUNCNAME("PetscSolverFeti::recoverSolution()");

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    // === Get local part of the solution for B variables. ===
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    PetscScalar *localSolB;
    VecGetArray(vec_sol_b, &localSolB);


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    // === Create scatter to get solutions of all primal nodes that are ===
    // === contained in rank's domain.                                  ===
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    vector<PetscInt> globalIsIndex, localIsIndex;
    globalIsIndex.reserve(globalPrimalIndex.size() * nComponents);
    localIsIndex.reserve(globalPrimalIndex.size() * nComponents);

    {
      int counter = 0;
      for (DofMapping::iterator it = globalPrimalIndex.begin();
	   it != globalPrimalIndex.end(); ++it) {
	for (int i = 0; i < nComponents; i++) {
	  globalIsIndex.push_back(it->second * nComponents + i);
	  localIsIndex.push_back(counter++);
	}
      }
    }
    
    IS globalIs, localIs;
    ISCreateGeneral(PETSC_COMM_SELF, 
		    globalIsIndex.size(), 
		    &(globalIsIndex[0]),
		    PETSC_USE_POINTER,
		    &globalIs);

    ISCreateGeneral(PETSC_COMM_SELF, 
		    localIsIndex.size(), 
		    &(localIsIndex[0]),
		    PETSC_USE_POINTER,
		    &localIs);

    Vec local_sol_primal;
    VecCreateSeq(PETSC_COMM_SELF, localIsIndex.size(), &local_sol_primal);

    VecScatter primalScatter;
    VecScatterCreate(vec_sol_primal, globalIs, local_sol_primal, localIs, &primalScatter);
    VecScatterBegin(primalScatter, vec_sol_primal, local_sol_primal, 
		    INSERT_VALUES, SCATTER_FORWARD);
    VecScatterEnd(primalScatter, vec_sol_primal, local_sol_primal, 
		  INSERT_VALUES, SCATTER_FORWARD);

    ISDestroy(globalIs);
    ISDestroy(localIs);    
    VecScatterDestroy(primalScatter);    

    PetscScalar *localSolPrimal;
    VecGetArray(local_sol_primal, &localSolPrimal);


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    // === And copy from PETSc local vectors to the DOF vectors. ===
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    for (int i = 0; i < nComponents; i++) {
      DOFVector<double>& dofVec = *(vec.getDOFVector(i));

      for (DofMapping::iterator it = globalIndexB.begin();
	   it != globalIndexB.end(); ++it) {
	int petscIndex = (it->second - rStartB) * nComponents + i;
	dofVec[it->first] = localSolB[petscIndex];
      }

      int counter = 0;
      for (DofMapping::iterator it = globalPrimalIndex.begin();
	   it != globalPrimalIndex.end(); ++it) {
	dofVec[it->first] = localSolPrimal[counter * nComponents + i];
	counter++;
      }
    }



    VecRestoreArray(vec_sol_b, &localSolB);
    VecRestoreArray(local_sol_primal, &localSolPrimal);
    VecDestroy(local_sol_primal);
  }


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  void PetscSolverFeti::fillPetscMatrix(Matrix<DOFMatrix*> *mat, 
					SystemVector *vec)
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  {
    FUNCNAME("PetscSolverFeti::fillPetscMatrix()");   
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    nComponents = vec->getSize();

    // === Create all sets and indices. ===

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    updateDofData();

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    // === Create matrices for the FETI-DP method. ===

    int nRowsRankB = nRankB * nComponents;
    int nRowsOverallB = nOverallB * nComponents;
    int nRowsRankPrimal = nRankPrimals * nComponents;
    int nRowsOverallPrimal = nOverallPrimals * nComponents;
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    int nRowsInterior = nLocalInterior * nComponents;
    int nRowsBound = nLocalBound * nComponents;
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    MatCreateMPIAIJ(PETSC_COMM_WORLD,
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		    nRowsRankB, nRowsRankB, nRowsOverallB, nRowsOverallB,
		    100, PETSC_NULL, 100, PETSC_NULL, &mat_b_b);
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    MatCreateMPIAIJ(PETSC_COMM_WORLD,
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		    nRowsRankPrimal, nRowsRankPrimal, 
		    nRowsOverallPrimal, nRowsOverallPrimal,
		    10, PETSC_NULL, 10, PETSC_NULL, &mat_primal_primal);
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    MatCreateMPIAIJ(PETSC_COMM_WORLD,
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		    nRowsRankB, nRowsRankPrimal, 
		    nRowsOverallB, nRowsOverallPrimal,
		    100, PETSC_NULL, 100, PETSC_NULL, &mat_b_primal);
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    MatCreateMPIAIJ(PETSC_COMM_WORLD,
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		    nRowsRankPrimal, nRowsRankB,
		    nRowsOverallPrimal, nRowsOverallB,
		    100, PETSC_NULL, 100, PETSC_NULL, &mat_primal_b);

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    // === Create matrices for Dirichlet FETI-DP preconditioner. ===

    MatCreateSeqAIJ(PETSC_COMM_SELF,
		    nRowsInterior, nRowsInterior, 100, PETSC_NULL,
		    &mat_interior_interior);

    MatCreateSeqAIJ(PETSC_COMM_SELF,
		    nRowsBound, nRowsBound, 100, PETSC_NULL,
		    &mat_bound_bound);

    MatCreateSeqAIJ(PETSC_COMM_SELF,
		    nRowsInterior, nRowsBound, 100, PETSC_NULL,
		    &mat_interior_bound);

    MatCreateSeqAIJ(PETSC_COMM_SELF,
		    nRowsBound, nRowsInterior, 100, PETSC_NULL,
		    &mat_bound_interior);

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    // === Prepare traverse of sequentially created matrices. ===
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    using mtl::tag::row; using mtl::tag::nz; using mtl::begin; using mtl::end;
    namespace traits = mtl::traits;
    typedef DOFMatrix::base_matrix_type Matrix;

    typedef traits::range_generator<row, Matrix>::type cursor_type;
    typedef traits::range_generator<nz, cursor_type>::type icursor_type;

    vector<int> cols, colsOther;
    vector<double> values, valuesOther;
    cols.reserve(300);
    colsOther.reserve(300);
    values.reserve(300);
    valuesOther.reserve(300);

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    vector<int> colsLocal, colsLocalOther;
    vector<double> valuesLocal, valuesLocalOther;
    colsLocal.reserve(300);
    colsLocalOther.reserve(300);
    valuesLocal.reserve(300);
    valuesLocalOther.reserve(300);

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    // === Traverse all sequentially created matrices and add the values to ===
    // === the global PETSc matrices.                                       ===

    for (int i = 0; i < nComponents; i++) {
      for (int j = 0; j < nComponents; j++) {
	if (!(*mat)[i][j])
	  continue;

	traits::col<Matrix>::type col((*mat)[i][j]->getBaseMatrix());
	traits::const_value<Matrix>::type value((*mat)[i][j]->getBaseMatrix());
	
	// Traverse all rows.
	for (cursor_type cursor = begin<row>((*mat)[i][j]->getBaseMatrix()), 
	       cend = end<row>((*mat)[i][j]->getBaseMatrix()); cursor != cend; ++cursor) {
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	  bool rowPrimal = primals.count(*cursor) != 0;
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	  cols.clear();
	  colsOther.clear();
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	  values.clear();	  
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	  valuesOther.clear();
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	  colsLocal.clear();
	  colsLocalOther.clear();
	  valuesLocal.clear();
	  valuesLocalOther.clear();

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	  // Traverse all columns.
	  for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	       icursor != icend; ++icursor) {

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	    bool colPrimal = primals.count(col(*icursor)) != 0;

	    if (colPrimal) {
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	      // Column is a primal variable.

	      TEST_EXIT_DBG(globalPrimalIndex.count(col(*icursor)))
		("No global primal index for DOF %d!\n", col(*icursor));
	      
	      int colIndex = globalPrimalIndex[col(*icursor)] * nComponents + j;
	      
	      if (rowPrimal) {
		cols.push_back(colIndex);
		values.push_back(value(*icursor));
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	      } else {
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		colsOther.push_back(colIndex);
		valuesOther.push_back(value(*icursor));
	      }
	    } else {
	      // Column is not a primal variable.

	      TEST_EXIT_DBG(globalIndexB.count(col(*icursor)))
		("No global B index for DOF %d!\n", col(*icursor));
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	      int colIndex = globalIndexB[col(*icursor)] * nComponents + j;

	      if (rowPrimal) {
		colsOther.push_back(colIndex);
		valuesOther.push_back(value(*icursor));
	      } else {
		cols.push_back(colIndex);
		values.push_back(value(*icursor));
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	      }
	    }
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	    // === For preconditioner ===

	    if (!rowPrimal && !colPrimal) {
	      int rowIndex = globalIndexB[*cursor] - rStartB;
	      int colIndex = globalIndexB[col(*icursor)] - rStartB;
		
	      if (rowIndex < nLocalInterior) {
		if (colIndex < nLocalInterior) {
		  int colIndex2 = 
		    (globalIndexB[col(*icursor)] - rStartB) * nComponents + j;

		  colsLocal.push_back(colIndex2);
		  valuesLocal.push_back(value(*icursor));
		} else {
		  int colIndex2 = 
		    (globalIndexB[col(*icursor)] - rStartB - nLocalInterior) * nComponents + j;

		  colsLocalOther.push_back(colIndex2);
		  valuesLocalOther.push_back(value(*icursor));
		}
	      } else {
		if (colIndex < nLocalInterior) {
		  int colIndex2 = 
		    (globalIndexB[col(*icursor)] - rStartB) * nComponents + j;

		  colsLocalOther.push_back(colIndex2);
		  valuesLocalOther.push_back(value(*icursor));
		} else {
		  int colIndex2 = 
		    (globalIndexB[col(*icursor)] - rStartB - nLocalInterior) * nComponents + j;

		  colsLocal.push_back(colIndex2);
		  valuesLocal.push_back(value(*icursor));
		}
	      }		
	    }


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	  }
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	  if (rowPrimal) {
	    TEST_EXIT_DBG(globalPrimalIndex.count(*cursor))
	      ("Should not happen!\n");
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	    int rowIndex = globalPrimalIndex[*cursor] * nComponents + i;
	    MatSetValues(mat_primal_primal, 1, &rowIndex, cols.size(),
			 &(cols[0]), &(values[0]), ADD_VALUES);
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	    if (colsOther.size())
	      MatSetValues(mat_primal_b, 1, &rowIndex, colsOther.size(),
			   &(colsOther[0]), &(valuesOther[0]), ADD_VALUES);
	  } else {
	    TEST_EXIT_DBG(globalIndexB.count(*cursor))
	      ("Should not happen!\n");
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	    int rowIndex = globalIndexB[*cursor] * nComponents + i;
	    MatSetValues(mat_b_b, 1, &rowIndex, cols.size(),
			 &(cols[0]), &(values[0]), ADD_VALUES);
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	    if (colsOther.size())
	      MatSetValues(mat_b_primal, 1, &rowIndex, colsOther.size(),
			   &(colsOther[0]), &(valuesOther[0]), ADD_VALUES);
	  }
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	  // === For preconditioner ===

	  if (!rowPrimal) {
	    int rowIndex = globalIndexB[*cursor] - rStartB;

	    if (rowIndex < nLocalInterior) {
	      int rowIndex2 = 
		(globalIndexB[*cursor] - rStartB) * nComponents + i;

	      MatSetValues(mat_interior_interior, 1, &rowIndex2, colsLocal.size(),
			   &(colsLocal[0]), &(valuesLocal[0]), INSERT_VALUES);

	      if (colsLocalOther.size()) 
		MatSetValues(mat_interior_bound, 1, &rowIndex2, colsLocalOther.size(),
			     &(colsLocalOther[0]), &(valuesLocalOther[0]), INSERT_VALUES);
	    } else {
	      int rowIndex2 = 
		(globalIndexB[*cursor] - rStartB - nLocalInterior) * nComponents + i;

	      MatSetValues(mat_bound_bound, 1, &rowIndex2, colsLocal.size(),
			   &(colsLocal[0]), &(valuesLocal[0]), INSERT_VALUES);

	      if (colsLocalOther.size()) 
		MatSetValues(mat_bound_interior, 1, &rowIndex2, colsLocalOther.size(),
			     &(colsLocalOther[0]), &(valuesLocalOther[0]), INSERT_VALUES);

	    }
	  }


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	} 
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