PetscSolverFeti.cc 41 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.


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#include "AMDiS.h"
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#include "parallel/PetscSolverFeti.h"
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#include "parallel/PetscSolverFetiStructs.h"
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#include "parallel/StdMpi.h"
#include "parallel/MpiHelper.h"
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#include "parallel/SubDomainSolver.h"
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#include "io/VtkWriter.h"
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namespace AMDiS {

  using namespace std;

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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);
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    SchurPrimalData* data = static_cast<SchurPrimalData*>(ctx);
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    MatMult(data->subSolver->getMatIntCoarse(), x, data->tmp_vec_b);
    data->subSolver->solveGlobal(data->tmp_vec_b, data->tmp_vec_b);
    MatMult(data->subSolver->getMatCoarseInt(), data->tmp_vec_b, data->tmp_vec_primal);
    MatMult(data->subSolver->getMatCoarseCoarse(), x, y);
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    VecAXPBY(y, -1.0, 1.0, data->tmp_vec_primal);

    return 0;
  }


  // y = mat * x
  int petscMultMatFeti(Mat mat, Vec x, Vec y)
  {
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    //    F = L inv(K_BB) trans(L) + L inv(K_BB) K_BPi inv(S_PiPi) K_PiB inv(K_BB) trans(L)
    // => F = L [I + inv(K_BB) K_BPi inv(S_PiPi) K_PiB] inv(K_BB) trans(L)
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    void *ctx;
    MatShellGetContext(mat, &ctx);
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    FetiData* data = static_cast<FetiData*>(ctx);
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    MatMultTranspose(*(data->mat_lagrange), x, data->tmp_vec_b);
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    data->subSolver->solveGlobal(data->tmp_vec_b, data->tmp_vec_b);
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    MatMult(*(data->mat_lagrange), data->tmp_vec_b, data->tmp_vec_lagrange);
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    MatMult(data->subSolver->getMatCoarseInt(), data->tmp_vec_b, data->tmp_vec_primal);
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    KSPSolve(*(data->ksp_schur_primal), data->tmp_vec_primal, data->tmp_vec_primal);
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   MatMult(data->subSolver->getMatIntCoarse(), data->tmp_vec_primal, data->tmp_vec_b);
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    data->subSolver->solveGlobal(data->tmp_vec_b, data->tmp_vec_b);
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    MatMult(*(data->mat_lagrange), data->tmp_vec_b, y);
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    VecAXPBY(y, 1.0, 1.0, data->tmp_vec_lagrange);
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    return 0;
  }


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  // y = PC * x
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  PetscErrorCode petscApplyFetiDirichletPrecon(PC pc, Vec x, Vec y)
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  {
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    // Get data for the preconditioner
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    void *ctx;
    PCShellGetContext(pc, &ctx);
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    FetiDirichletPreconData* data = static_cast<FetiDirichletPreconData*>(ctx);
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    // Multiply with scaled Lagrange constraint matrix.
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    MatMultTranspose(*(data->mat_lagrange_scaled), x, data->tmp_vec_b);


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    // === Restriction of the B nodes to the boundary nodes. ===
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    int nLocalB;
    int nLocalDuals;
    VecGetLocalSize(data->tmp_vec_b, &nLocalB);
    VecGetLocalSize(data->tmp_vec_duals0, &nLocalDuals);
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    PetscScalar *local_b, *local_duals;
    VecGetArray(data->tmp_vec_b, &local_b);
    VecGetArray(data->tmp_vec_duals0, &local_duals);

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    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_duals[it->second] = local_b[it->first];
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    VecRestoreArray(data->tmp_vec_b, &local_b);
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    VecRestoreArray(data->tmp_vec_duals0, &local_duals);
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    // === K_DD - K_DI inv(K_II) K_ID ===
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    MatMult(*(data->mat_duals_duals), data->tmp_vec_duals0, data->tmp_vec_duals1);
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    MatMult(*(data->mat_interior_duals), data->tmp_vec_duals0, data->tmp_vec_interior);
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    KSPSolve(*(data->ksp_interior), data->tmp_vec_interior, data->tmp_vec_interior);
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    MatMult(*(data->mat_duals_interior), data->tmp_vec_interior, data->tmp_vec_duals0);

    VecAXPBY(data->tmp_vec_duals0, 1.0, -1.0, data->tmp_vec_duals1);


    // === Prolongation from local dual nodes to B nodes.

    VecGetArray(data->tmp_vec_b, &local_b);
    VecGetArray(data->tmp_vec_duals0, &local_duals);

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    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_b[it->first] = local_duals[it->second];
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    VecRestoreArray(data->tmp_vec_b, &local_b);
    VecRestoreArray(data->tmp_vec_duals0, &local_duals);


    // Multiply with scaled Lagrange constraint matrix.
    MatMult(*(data->mat_lagrange_scaled), data->tmp_vec_b, y);

    return 0;
  }


  // y = PC * x
  PetscErrorCode petscApplyFetiLumpedPrecon(PC pc, Vec x, Vec y)
  {
    // Get data for the preconditioner
    void *ctx;
    PCShellGetContext(pc, &ctx);
    FetiLumpedPreconData* data = static_cast<FetiLumpedPreconData*>(ctx);

    // Multiply with scaled Lagrange constraint matrix.
    MatMultTranspose(*(data->mat_lagrange_scaled), x, data->tmp_vec_b);
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    // === Restriction of the B nodes to the boundary nodes. ===
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    int nLocalB;
    int nLocalDuals;
    VecGetLocalSize(data->tmp_vec_b, &nLocalB);
    VecGetLocalSize(data->tmp_vec_duals0, &nLocalDuals);
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    PetscScalar *local_b, *local_duals;
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    VecGetArray(data->tmp_vec_b, &local_b);
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    VecGetArray(data->tmp_vec_duals0, &local_duals);
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    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_duals[it->second] = local_b[it->first];
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    VecRestoreArray(data->tmp_vec_b, &local_b);
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    VecRestoreArray(data->tmp_vec_duals0, &local_duals);


    // === K_DD ===

    MatMult(*(data->mat_duals_duals), data->tmp_vec_duals0, data->tmp_vec_duals1);

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    // === Prolongation from local dual nodes to B nodes.
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    VecGetArray(data->tmp_vec_b, &local_b);
    VecGetArray(data->tmp_vec_duals1, &local_duals);

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    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_b[it->first] = local_duals[it->second];
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    VecRestoreArray(data->tmp_vec_b, &local_b);
    VecRestoreArray(data->tmp_vec_duals0, &local_duals);
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    // Multiply with scaled Lagrange constraint matrix.
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    MatMult(*(data->mat_lagrange_scaled), data->tmp_vec_b, y);

    return 0;
  }


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  PetscSolverFeti::PetscSolverFeti()
    : PetscSolver(),
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      schurPrimalSolver(0),
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      multiLevelTest(false),
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      subDomainSolver(NULL),
      meshLevel(0)
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  {
    FUNCNAME("PetscSolverFeti::PetscSolverFeti()");

    string preconditionerName = "";
    Parameters::get("parallel->solver->precon", preconditionerName);
    if (preconditionerName == "" || preconditionerName == "none") {
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      MSG("Create FETI-DP solver with no preconditioner!\n");
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      fetiPreconditioner = FETI_NONE;
    } else if (preconditionerName == "dirichlet") {
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      MSG("Create FETI-DP solver with Dirichlet preconditioner!\n");
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      fetiPreconditioner = FETI_DIRICHLET;
    } else if (preconditionerName == "lumped") {
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      MSG("Create FETI-DP solver with lumped preconditioner!\n");
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      fetiPreconditioner = FETI_LUMPED;
    } else {
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      ERROR_EXIT("Preconditioner \"%s\" not available!\n", 
		 preconditionerName.c_str());
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    }
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    Parameters::get("parallel->feti->schur primal solver", schurPrimalSolver);
    TEST_EXIT(schurPrimalSolver == 0 || schurPrimalSolver == 1)
      ("Wrong solver \"%d\"for the Schur primal complement!\n", 
       schurPrimalSolver);
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    Parameters::get("parallel->multi level test", multiLevelTest);
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    if (multiLevelTest)
      meshLevel = 1;
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  }


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  void PetscSolverFeti::initialize(vector<const FiniteElemSpace*> feSpaces)
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  {
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    FUNCNAME("PetscSolverFeti::initialize()");

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    TEST_EXIT_DBG(meshLevel + 1 == meshDistributor->getMeshLevelData().getLevelNumber())
      ("Mesh hierarchy does not contain %d levels!\n", meshLevel + 1);

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    if (subDomainSolver == NULL) {
      if (meshLevel == 0) {
	subDomainSolver = 
	  new SubDomainSolver(meshDistributor, mpiComm, mpiSelfComm);
      } else {
	MeshLevelData& levelData = meshDistributor->getMeshLevelData();

	subDomainSolver = 
	  new SubDomainSolver(meshDistributor, 
			      levelData.getMpiComm(meshLevel - 1),
			      levelData.getMpiComm(meshLevel));
      }
    }
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    primalDofMap.init(mpiComm, feSpaces, meshDistributor->getFeSpaces(), 
		      true, true);
    dualDofMap.init(mpiComm, feSpaces, meshDistributor->getFeSpaces(),
		    false, false);
    lagrangeMap.init(mpiComm, feSpaces, meshDistributor->getFeSpaces(),
		     true, true);
    localDofMap.init(mpiComm, feSpaces, meshDistributor->getFeSpaces(),
		     false, false);
    if (fetiPreconditioner == FETI_DIRICHLET)
      interiorDofMap.init(mpiComm, feSpaces,  meshDistributor->getFeSpaces(),
			  false, false);
  }


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

    TEST_EXIT(meshDistributor)("No mesh distributor object defined!\n");
    TEST_EXIT(meshDistributor->getFeSpaces().size() > 0)
      ("No FE space defined in mesh distributor!\n");
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    primalDofMap.clear();
    dualDofMap.clear();
    lagrangeMap.clear();
    localDofMap.clear();
    interiorDofMap.clear();

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    for (unsigned int i = 0; i < meshDistributor->getFeSpaces().size(); i++) {
      const FiniteElemSpace *feSpace = meshDistributor->getFeSpace(i);
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      createPrimals(feSpace);      
      createDuals(feSpace);
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      createLagrange(feSpace);      
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      createIndexB(feSpace);
    }
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    primalDofMap.setDofComm(meshDistributor->getSendDofs(),
			    meshDistributor->getRecvDofs());
    lagrangeMap.setDofComm(meshDistributor->getSendDofs(), 
			   meshDistributor->getRecvDofs());

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    primalDofMap.update();
    dualDofMap.update();
    lagrangeMap.update();
    localDofMap.update();
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    if (fetiPreconditioner != FETI_NONE)
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      interiorDofMap.update();
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    for (unsigned int i = 0; i < meshDistributor->getFeSpaces().size(); i++) {
      const FiniteElemSpace *feSpace = meshDistributor->getFeSpace(i);
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      MSG("FETI-DP data for %d-ith FE space:\n", i);
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      MSG("  nRankPrimals = %d   nOverallPrimals = %d\n", 
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	  primalDofMap[feSpace].nRankDofs, primalDofMap[feSpace].nOverallDofs);
      
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      MSG("  nRankDuals = %d  nOverallDuals = %d\n",
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	  dualDofMap[feSpace].nRankDofs, dualDofMap[feSpace].nOverallDofs);
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      MSG("  nRankLagrange = %d  nOverallLagrange = %d\n",
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	  lagrangeMap[feSpace].nRankDofs, lagrangeMap[feSpace].nOverallDofs);
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      TEST_EXIT_DBG(localDofMap[feSpace].size() + primalDofMap[feSpace].size() == 
		    static_cast<unsigned int>(feSpace->getAdmin()->getUsedDofs()))
	("Should not happen!\n");
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    }
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    // If multi level test, inform sub domain solver about coarse space.
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    subDomainSolver->setDofMapping(&primalDofMap, &localDofMap);
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  }


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  void PetscSolverFeti::createPrimals(const FiniteElemSpace *feSpace)
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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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    /// Set of DOF indices that are considered to be primal variables.
    
    DofIndexSet primals;
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    DofContainerSet& vertices = 
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      meshDistributor->getBoundaryDofInfo(feSpace, meshLevel).geoDofs[VERTEX];
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    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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    for (DofIndexSet::iterator it = primals.begin(); it != primals.end(); ++it)
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      if (meshDistributor->getIsRankDof(feSpace, *it))
	primalDofMap[feSpace].insertRankDof(*it);
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      else
  	primalDofMap[feSpace].insert(*it);
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  }


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  void PetscSolverFeti::createDuals(const FiniteElemSpace *feSpace)
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  {
    FUNCNAME("PetscSolverFeti::createDuals()");
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    // === Create global index of the dual nodes on each rank. ===

    DofContainer allBoundaryDofs;
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    meshDistributor->getAllBoundaryDofs(feSpace, meshLevel, allBoundaryDofs);
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    for (DofContainer::iterator it = allBoundaryDofs.begin();
	 it != allBoundaryDofs.end(); ++it)
      if (!isPrimal(feSpace, **it))
	dualDofMap[feSpace].insertRankDof(**it);
  }

  
  void PetscSolverFeti::createLagrange(const FiniteElemSpace *feSpace)
  {
    FUNCNAME("PetscSolverFeti::createLagrange()");

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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[feSpace].clear();
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    for (DofComm::Iterator it(meshDistributor->getSendDofs(), meshLevel, feSpace); 
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	 !it.end(); it.nextRank())
      for (; !it.endDofIter(); it.nextDof()) {
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	if (!isPrimal(feSpace, it.getDofIndex())) {
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	  boundaryDofRanks[feSpace][it.getDofIndex()].insert(mpiRank);
	  boundaryDofRanks[feSpace][it.getDofIndex()].insert(it.getRank());
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	}
      }
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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());
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    for (DofComm::Iterator it(meshDistributor->getSendDofs(), meshLevel, feSpace);
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	 !it.end(); it.nextRank())
      for (; !it.endDofIter(); it.nextDof())
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	if (!isPrimal(feSpace, it.getDofIndex()))
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	  stdMpi.getSendData(it.getRank()).push_back(boundaryDofRanks[feSpace][it.getDofIndex()]);
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    stdMpi.updateSendDataSize();

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    for (DofComm::Iterator it(meshDistributor->getRecvDofs(), meshLevel, feSpace); 
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	 !it.end(); it.nextRank()) {
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      bool recvFromRank = false;
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      for (; !it.endDofIter(); it.nextDof()) {
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	if (!isPrimal(feSpace, it.getDofIndex())) {
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	  recvFromRank = true;
	  break;
	}
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      }
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      if (recvFromRank)
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	stdMpi.recv(it.getRank());
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    }
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    stdMpi.startCommunication();

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    for (DofComm::Iterator it(meshDistributor->getRecvDofs(), meshLevel, feSpace); 
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	 !it.end(); it.nextRank()) {
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      int i = 0;
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      for (; !it.endDofIter(); it.nextDof())
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	if (!isPrimal(feSpace, it.getDofIndex()))
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	  boundaryDofRanks[feSpace][it.getDofIndex()] = 
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	    stdMpi.getRecvData(it.getRank())[i++];
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    }

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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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    int nRankLagrange = 0;
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    DofMap& dualMap = dualDofMap[feSpace].getMap();
    for (DofMap::iterator it = dualMap.begin(); it != dualMap.end(); ++it) {
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      if (meshDistributor->getIsRankDof(feSpace, it->first)) {
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	lagrangeMap[feSpace].insertRankDof(it->first, nRankLagrange);
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	int degree = boundaryDofRanks[feSpace][it->first].size();
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	nRankLagrange += (degree * (degree - 1)) / 2;
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      } else {
	lagrangeMap[feSpace].insert(it->first);
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      }
    }
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    lagrangeMap[feSpace].nRankDofs = nRankLagrange;
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  }


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  void PetscSolverFeti::createIndexB(const FiniteElemSpace *feSpace)
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  {
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    FUNCNAME("PetscSolverFeti::createIndexB()");
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    DOFAdmin* admin = feSpace->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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    int nLocalInterior = 0;    
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    for (int i = 0; i < admin->getUsedSize(); i++) {
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      if (admin->isDofFree(i) == false && 
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	  isPrimal(feSpace, i) == false &&
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	  dualDofMap[feSpace].isSet(i) == false) {
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	localDofMap[feSpace].insertRankDof(i, nLocalInterior);

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	if (fetiPreconditioner != FETI_NONE)
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	  interiorDofMap[feSpace].insertRankDof(i, nLocalInterior);

	nLocalInterior++;
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      }
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    }
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    // === And finally, add the global indicies of all dual nodes. ===

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    for (DofMap::iterator it = dualDofMap[feSpace].getMap().begin();
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	 it != dualDofMap[feSpace].getMap().end(); ++it)
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      localDofMap[feSpace].insertRankDof(it->first);
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  }


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  void PetscSolverFeti::createMatLagrange(vector<const FiniteElemSpace*> &feSpaces)
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  {
    FUNCNAME("PetscSolverFeti::createMatLagrange()");

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

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    MatCreateMPIAIJ(mpiComm,
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		    lagrangeMap.getRankDofs(), localDofMap.getRankDofs(),
		    lagrangeMap.getOverallDofs(), localDofMap.getOverallDofs(),	
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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 (unsigned int k = 0; k < feSpaces.size(); k++) {
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      DofMap &dualMap = dualDofMap[feSpaces[k]].getMap();
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      for (DofMap::iterator it = dualMap.begin(); it != dualMap.end(); ++it) {
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	TEST_EXIT_DBG(boundaryDofRanks[feSpaces[k]].count(it->first))
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	  ("Should not happen!\n");
	
	// Global index of the first Lagrange constriant for this node.
	int index = lagrangeMap.getMatIndex(k, it->first);
	
	// Copy set of all ranks that contain this dual node.
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	vector<int> W(boundaryDofRanks[feSpaces[k]][it->first].begin(), 
		      boundaryDofRanks[feSpaces[k]][it->first].end());
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	// Number of ranks that contain this dual node.
	int degree = W.size();
	
	for (int i = 0; i < degree; i++) {
	  for (int j = i + 1; j < degree; j++) {
	    if (W[i] == mpiRank || W[j] == mpiRank) {
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	      int colIndex = localDofMap.getMatIndex(k, it->first);
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	      double value = (W[i] == mpiRank ? 1.0 : -1.0);
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	      MatSetValue(mat_lagrange, index, colIndex, value, INSERT_VALUES);
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	    }
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	    index++;	      
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	  }
	}
      }
    }

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


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  void PetscSolverFeti::createSchurPrimalKsp(vector<const FiniteElemSpace*> &feSpaces)
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  {
    FUNCNAME("PetscSolverFeti::createSchurPrimal()");

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    if (schurPrimalSolver == 0) {
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      MSG("Create iterative schur primal solver!\n");

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      schurPrimalData.subSolver = subDomainSolver;
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      VecCreateMPI(mpiComm, 
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		   localDofMap.getRankDofs(), localDofMap.getOverallDofs(),
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		   &(schurPrimalData.tmp_vec_b));
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      VecCreateMPI(mpiComm, 
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		   primalDofMap.getRankDofs(), primalDofMap.getOverallDofs(),
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		   &(schurPrimalData.tmp_vec_primal));

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      MatCreateShell(mpiComm,
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		     primalDofMap.getRankDofs(), primalDofMap.getRankDofs(), 
		     primalDofMap.getOverallDofs(), primalDofMap.getOverallDofs(),
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		     &schurPrimalData, 
		     &mat_schur_primal);
      MatShellSetOperation(mat_schur_primal, MATOP_MULT, 
			   (void(*)(void))petscMultMatSchurPrimal);
      
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      KSPCreate(mpiComm, &ksp_schur_primal);
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      KSPSetOperators(ksp_schur_primal, mat_schur_primal, mat_schur_primal, SAME_NONZERO_PATTERN);
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      KSPSetOptionsPrefix(ksp_schur_primal, "schur_primal_");
      KSPSetType(ksp_schur_primal, KSPGMRES);
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      KSPSetFromOptions(ksp_schur_primal);
    } else {
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      MSG("Create direct schur primal solver!\n");

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      double wtime = MPI::Wtime();

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      int nRowsRankPrimal = primalDofMap.getRankDofs();
      int nRowsOverallPrimal = primalDofMap.getOverallDofs();
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      int nRowsRankB = localDofMap.getRankDofs();
      int nRowsOverallB = localDofMap.getOverallDofs();
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      Mat matBPi;
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      MatCreateMPIAIJ(mpiComm,
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		      nRowsRankB, nRowsRankPrimal, 
		      nRowsOverallB, nRowsOverallPrimal,
		      30, PETSC_NULL, 30, PETSC_NULL, &matBPi);
      Mat matPrimal;
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      PetscInt nCols;
      const PetscInt *cols;
      const PetscScalar *values;
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      map<int, vector<pair<int, double> > > mat_b_primal_cols;

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      for (int i = 0; i < nRowsRankB; i++) {
	PetscInt row = localDofMap.getStartDofs() + i;
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	MatGetRow(subDomainSolver->getMatIntCoarse(), row, &nCols, &cols, &values);
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	for (int j = 0; j < nCols; j++)
	  if (values[j] != 0.0)
	    mat_b_primal_cols[cols[j]].push_back(make_pair(i, values[j]));

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	MatRestoreRow(subDomainSolver->getMatIntCoarse(), row, &nCols, &cols, &values);
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      }

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      TEST_EXIT(static_cast<int>(mat_b_primal_cols.size()) == 
		primalDofMap.getLocalDofs())
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	("Should not happen!\n");
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      for (map<int, vector<pair<int, double> > >::iterator it = mat_b_primal_cols.begin();
	   it != mat_b_primal_cols.end(); ++it) {
	Vec tmpVec;
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	VecCreateSeq(PETSC_COMM_SELF, nRowsRankB, &tmpVec);
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 	for (unsigned int i = 0; i < it->second.size(); i++) 
 	  VecSetValue(tmpVec, 
 		      it->second[i].first, it->second[i].second, INSERT_VALUES);

	VecAssemblyBegin(tmpVec);
	VecAssemblyEnd(tmpVec);

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	subDomainSolver->solve(tmpVec, tmpVec);
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	PetscScalar *tmpValues;
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	VecGetArray(tmpVec, &tmpValues);
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	for (int i  = 0; i < nRowsRankB; i++)
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	  MatSetValue(matBPi, 
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		      localDofMap.getStartDofs() + i,
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		      it->first,
		      tmpValues[i],
		      ADD_VALUES);
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	VecRestoreArray(tmpVec, &tmpValues);

	VecDestroy(&tmpVec);
      }

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      MatAssemblyBegin(matBPi, MAT_FINAL_ASSEMBLY);
      MatAssemblyEnd(matBPi, MAT_FINAL_ASSEMBLY);
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      MatDuplicate(subDomainSolver->getMatCoarseCoarse(), MAT_COPY_VALUES, &mat_schur_primal);
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      MatMatMult(subDomainSolver->getMatCoarseInt(), matBPi, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &matPrimal);
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      MatAXPY(mat_schur_primal, -1.0, matPrimal, DIFFERENT_NONZERO_PATTERN);
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      MatDestroy(&matPrimal);
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      MatDestroy(&matBPi);
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      MatInfo minfo;
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      MatGetInfo(mat_schur_primal, MAT_GLOBAL_SUM, &minfo);
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      MSG("Schur primal matrix nnz = %f\n", minfo.nz_used);

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      KSPCreate(mpiComm, &ksp_schur_primal);
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      KSPSetOperators(ksp_schur_primal, mat_schur_primal, mat_schur_primal,
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		      SAME_NONZERO_PATTERN);
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      KSPSetOptionsPrefix(ksp_schur_primal, "schur_primal_");
      KSPSetType(ksp_schur_primal, KSPPREONLY);
      PC pc_schur_primal;      
      KSPGetPC(ksp_schur_primal, &pc_schur_primal);
      PCSetType(pc_schur_primal, PCLU);
      PCFactorSetMatSolverPackage(pc_schur_primal, MATSOLVERMUMPS);
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      KSPSetFromOptions(ksp_schur_primal);
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      MSG("Creating Schur primal matrix needed %.5f seconds.\n",
	  MPI::Wtime() - wtime);
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    }
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  }


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

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    if (schurPrimalSolver == 0) {
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      schurPrimalData.subSolver = NULL;
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      VecDestroy(&schurPrimalData.tmp_vec_b);
      VecDestroy(&schurPrimalData.tmp_vec_primal);
    }
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    MatDestroy(&mat_schur_primal);
    KSPDestroy(&ksp_schur_primal);
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  }


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  void PetscSolverFeti::createFetiKsp(vector<const FiniteElemSpace*> &feSpaces)
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  {
    FUNCNAME("PetscSolverFeti::createFetiKsp()");

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

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    fetiData.mat_lagrange = &mat_lagrange;
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    fetiData.subSolver = subDomainSolver;
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    fetiData.ksp_schur_primal = &ksp_schur_primal;
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    VecCreateMPI(mpiComm, 
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		 localDofMap.getRankDofs(), localDofMap.getOverallDofs(),
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		 &(fetiData.tmp_vec_b));
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    VecCreateMPI(mpiComm,
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		 lagrangeMap.getRankDofs(), lagrangeMap.getOverallDofs(),
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		 &(fetiData.tmp_vec_lagrange));
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    VecCreateMPI(mpiComm, 
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		 primalDofMap.getRankDofs(), primalDofMap.getOverallDofs(),
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		 &(fetiData.tmp_vec_primal));
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    MatCreateShell(mpiComm,
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		   lagrangeMap.getRankDofs(), lagrangeMap.getRankDofs(),
		   lagrangeMap.getOverallDofs(), lagrangeMap.getOverallDofs(),
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		   &fetiData, &mat_feti);
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    MatShellSetOperation(mat_feti, MATOP_MULT, (void(*)(void))petscMultMatFeti);


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    KSPCreate(mpiComm, &ksp_feti);
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    KSPSetOperators(ksp_feti, mat_feti, mat_feti, SAME_NONZERO_PATTERN);
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    KSPSetOptionsPrefix(ksp_feti, "feti_");
    KSPSetType(ksp_feti, KSPGMRES);
    KSPSetTolerances(ksp_feti, 0, 1e-8, 1e+3, 1000);
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    KSPSetFromOptions(ksp_feti);
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    // === Create FETI-DP preconditioner object. ===
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    if (fetiPreconditioner != FETI_NONE) {
      MatDuplicate(mat_lagrange, MAT_COPY_VALUES, &mat_lagrange_scaled);
      MatScale(mat_lagrange_scaled, 0.5);
    }
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    switch (fetiPreconditioner) {
    case FETI_DIRICHLET:           
      KSPCreate(PETSC_COMM_SELF, &ksp_interior);
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      KSPSetOperators(ksp_interior, mat_interior_interior, mat_interior_interior, 
		      SAME_NONZERO_PATTERN);
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      KSPSetOptionsPrefix(ksp_interior, "precon_interior_");
      KSPSetType(ksp_interior, KSPPREONLY);
      PC pc_interior;
      KSPGetPC(ksp_interior, &pc_interior);
      PCSetType(pc_interior, PCLU);
      PCFactorSetMatSolverPackage(pc_interior, MATSOLVERUMFPACK);
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      KSPSetFromOptions(ksp_interior);
            
      fetiDirichletPreconData.mat_lagrange_scaled = &mat_lagrange_scaled;
      fetiDirichletPreconData.mat_interior_interior = &mat_interior_interior;
      fetiDirichletPreconData.mat_duals_duals = &mat_duals_duals;
      fetiDirichletPreconData.mat_interior_duals = &mat_interior_duals;
      fetiDirichletPreconData.mat_duals_interior = &mat_duals_interior;
      fetiDirichletPreconData.ksp_interior = &ksp_interior;
      
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      VecCreateMPI(mpiComm, 
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		   &(fetiDirichletPreconData.tmp_vec_b));      
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      MatGetVecs(mat_duals_duals, PETSC_NULL, 
		 &(fetiDirichletPreconData.tmp_vec_duals0));
      MatGetVecs(mat_duals_duals, PETSC_NULL, 
		 &(fetiDirichletPreconData.tmp_vec_duals1));
      MatGetVecs(mat_interior_interior, PETSC_NULL, 
		 &(fetiDirichletPreconData.tmp_vec_interior));
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      for (unsigned int i = 0; i < feSpaces.size(); i++) {
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	DofMap &dualMap = dualDofMap[feSpaces[i]].getMap();
	for (DofMap::iterator it = dualMap.begin(); it != dualMap.end(); ++it) {
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	  DegreeOfFreedom d = it->first;
	  int matIndexLocal = localDofMap.getLocalMatIndex(i, d);
	  int matIndexDual = dualDofMap.getLocalMatIndex(i, d);
	  fetiDirichletPreconData.localToDualMap[matIndexLocal] = matIndexDual;
	}
      }

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      KSPGetPC(ksp_feti, &precon_feti);
      PCSetType(precon_feti, PCSHELL);
      PCShellSetContext(precon_feti, static_cast<void*>(&fetiDirichletPreconData));
      PCShellSetApply(precon_feti, petscApplyFetiDirichletPrecon);
      
      break;

    case FETI_LUMPED:
      fetiLumpedPreconData.mat_lagrange_scaled = &mat_lagrange_scaled;
      fetiLumpedPreconData.mat_duals_duals = &mat_duals_duals;

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      for (unsigned int i = 0; i < feSpaces.size(); i++) {
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	DofMap &dualMap = dualDofMap[feSpaces[i]].getMap();
	for (DofMap::iterator it = dualMap.begin(); it != dualMap.end(); ++it) {
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	  DegreeOfFreedom d = it->first;
	  int matIndexLocal = localDofMap.getLocalMatIndex(i, d);
	  int matIndexDual = dualDofMap.getLocalMatIndex(i, d);
	  fetiLumpedPreconData.localToDualMap[matIndexLocal] = matIndexDual;
	}
      }

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      VecCreateMPI(mpiComm, 
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		   localDofMap.getRankDofs(),
		   localDofMap.getOverallDofs(),
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		   &(fetiLumpedPreconData.tmp_vec_b));
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      MatGetVecs(mat_duals_duals, PETSC_NULL, 
		 &(fetiLumpedPreconData.tmp_vec_duals0));
      MatGetVecs(mat_duals_duals, PETSC_NULL, 
		 &(fetiLumpedPreconData.tmp_vec_duals1));
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      KSPGetPC(ksp_feti, &precon_feti);
      PCSetType(precon_feti, PCSHELL);
      PCShellSetContext(precon_feti, static_cast<void*>(&fetiLumpedPreconData));
      PCShellSetApply(precon_feti, petscApplyFetiLumpedPrecon);
      
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      break;
    default:
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      break;
    }
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  }
  

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

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

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    fetiData.mat_lagrange = PETSC_NULL;
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    fetiData.subSolver = NULL;
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    fetiData.ksp_schur_primal = PETSC_NULL;
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    VecDestroy(&fetiData.tmp_vec_b);
    VecDestroy(&fetiData.tmp_vec_lagrange);
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    VecDestroy(&fetiData.tmp_vec_primal);
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    MatDestroy(&mat_feti);
    KSPDestroy(&ksp_feti);
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    // === Destroy FETI-DP preconditioner object. ===

    switch (fetiPreconditioner) {
    case FETI_DIRICHLET:           
      KSPDestroy(&ksp_interior);

      fetiDirichletPreconData.mat_lagrange_scaled = NULL;
      fetiDirichletPreconData.mat_interior_interior = NULL;
      fetiDirichletPreconData.mat_duals_duals = NULL;
      fetiDirichletPreconData.mat_interior_duals = NULL;
      fetiDirichletPreconData.mat_duals_interior = NULL;
      fetiDirichletPreconData.ksp_interior = NULL;
      
      VecDestroy(&fetiDirichletPreconData.tmp_vec_b);
      VecDestroy(&fetiDirichletPreconData.tmp_vec_duals0);
      VecDestroy(&fetiDirichletPreconData.tmp_vec_duals1);
      VecDestroy(&fetiDirichletPreconData.tmp_vec_interior);
      MatDestroy(&mat_lagrange_scaled);
      break;

    case FETI_LUMPED:
      fetiLumpedPreconData.mat_lagrange_scaled = NULL;
      fetiLumpedPreconData.mat_duals_duals = NULL;

      VecDestroy(&fetiLumpedPreconData.tmp_vec_b);
      VecDestroy(&fetiLumpedPreconData.tmp_vec_duals0);
      VecDestroy(&fetiLumpedPreconData.tmp_vec_duals1);
      break;
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    default:
      break;
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    }
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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<const FiniteElemSpace*> feSpaces = getFeSpaces(&vec);

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    vector<PetscInt> globalIsIndex, localIsIndex;
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    globalIsIndex.reserve(primalDofMap.getLocalDofs());
    localIsIndex.reserve(primalDofMap.getLocalDofs());
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    {
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      int cnt = 0;
      for (unsigned int i = 0; i < feSpaces.size(); i++) {
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	DofMap& dofMap = primalDofMap[feSpaces[i]].getMap();
	for (DofMap::iterator it = dofMap.begin();it != dofMap.end(); ++it) {
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	  globalIsIndex.push_back(primalDofMap.getMatIndex(i, it->first));
	  localIsIndex.push_back(cnt++);
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	}
      }
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      TEST_EXIT_DBG(cnt == primalDofMap.getLocalDofs())("Should not happen!\n");
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    }
    
    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);

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    ISDestroy(&globalIs);
    ISDestroy(&localIs);    
    VecScatterDestroy(&primalScatter);    
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    PetscScalar *localSolPrimal;
    VecGetArray(local_sol_primal, &localSolPrimal);

</