solver_petsc.cc
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solver_petsc.cc
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	/**
	* @file solver_petsc.cc
	*
	* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
	* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue May 13 2014
	* @date last modification: Fri Oct 16 2015
	*
	* @brief Solver class implementation for the petsc solver
	*
	* @section LICENSE
	*
	* Copyright (©) 2014, 2015 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include <petscksp.h>
	#include "solver_petsc.hh"
	#include "petsc_wrapper.hh"
	#include "petsc_matrix.hh"
	#include "static_communicator.hh"
	#include "static_communicator_mpi.hh"
	#include "mpi_type_wrapper.hh"
	#include "dof_synchronizer.hh"

	__BEGIN_AKANTU__

	/* -------------------------------------------------------------------------- */
	SolverPETSc::SolverPETSc(SparseMatrix & matrix, const ID & id,
	const MemoryID & memory_id)
	: Solver(matrix, id, memory_id), is_petsc_data_initialized(false),
	petsc_solver_wrapper(new PETScSolverWrapper) {}

	/* -------------------------------------------------------------------------- */
	SolverPETSc::~SolverPETSc() {
	AKANTU_DEBUG_IN();

	this->destroyInternalData();

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	void SolverPETSc::destroyInternalData() {
	AKANTU_DEBUG_IN();

	if (this->is_petsc_data_initialized) {
	PetscErrorCode ierr;
	ierr = KSPDestroy(&(this->petsc_solver_wrapper->ksp));
	CHKERRXX(ierr);
	ierr = VecDestroy(&(this->petsc_solver_wrapper->rhs));
	CHKERRXX(ierr);
	ierr = VecDestroy(&(this->petsc_solver_wrapper->solution));
	CHKERRXX(ierr);
	delete petsc_solver_wrapper;

	this->is_petsc_data_initialized = false;
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolverPETSc::initialize(__attribute__((unused)) SolverOptions & options) {
	AKANTU_DEBUG_IN();

	#if defined(AKANTU_USE_MPI)
	StaticCommunicator & comm = StaticCommunicator::getStaticCommunicator();
	const StaticCommunicatorMPI & mpi_st_comm =
	dynamic_cast<const StaticCommunicatorMPI &>(
	comm.getRealStaticCommunicator());
	this->petsc_solver_wrapper->communicator =
	mpi_st_comm.getMPITypeWrapper().getMPICommunicator();
	#else
	this->petsc_solver_wrapper->communicator = PETSC_COMM_SELF;
	#endif

	PetscErrorCode ierr;
	PETScMatrix * petsc_matrix = static_cast<PETScMatrix *>(this->matrix);
	/// create a solver context
	ierr = KSPCreate(this->petsc_solver_wrapper->communicator,
	&(this->petsc_solver_wrapper->ksp));
	CHKERRXX(ierr);

	/// create the PETSc vector for the right-hand side
	ierr = VecCreate(this->petsc_solver_wrapper->communicator,
	&(this->petsc_solver_wrapper->rhs));
	CHKERRXX(ierr);

	ierr = VecSetSizes((this->petsc_solver_wrapper->rhs),
	petsc_matrix->getLocalSize(), petsc_matrix->getSize());
	CHKERRXX(ierr);
	ierr = VecSetFromOptions((this->petsc_solver_wrapper->rhs));
	CHKERRXX(ierr);

	/// create the PETSc vector for the solution
	ierr = VecDuplicate((this->petsc_solver_wrapper->rhs),
	&(this->petsc_solver_wrapper->solution));
	CHKERRXX(ierr);
	/// set the solution to zero
	ierr = VecZeroEntries(this->petsc_solver_wrapper->solution);
	this->is_petsc_data_initialized = true;
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolverPETSc::setRHS(Array<Real> & rhs) {
	PetscErrorCode ierr;
	PETScMatrix * petsc_matrix = static_cast<PETScMatrix *>(this->matrix);

	UInt nb_component = rhs.getNbComponent();
	UInt size = rhs.getSize();
	for (UInt i = 0; i < size; ++i) {
	for (UInt j = 0; j < nb_component; ++j) {
	UInt i_local = i * nb_component + j;
	if (this->matrix->getDOFSynchronizer().isLocalOrMasterDOF(i_local)) {
	Int i_global =
	this->matrix->getDOFSynchronizer().getDOFGlobalID(i_local);
	AOApplicationToPetsc(petsc_matrix->getPETScMatrixWrapper()->ao, 1,
	&(i_global));
	ierr = VecSetValue((this->petsc_solver_wrapper->rhs), i_global,
	rhs(i, j), INSERT_VALUES);
	CHKERRXX(ierr);
	}
	}
	}

	ierr = VecAssemblyBegin(this->petsc_solver_wrapper->rhs);
	CHKERRXX(ierr);
	ierr = VecAssemblyEnd(this->petsc_solver_wrapper->rhs);
	CHKERRXX(ierr);
	/// ierr = VecCopy((this->petsc_solver_wrapper->rhs),
	/// (this->petsc_solver_wrapper->solution)); CHKERRXX(ierr);
	}

	/* -------------------------------------------------------------------------- */
	void SolverPETSc::solve() {
	AKANTU_DEBUG_IN();

	PetscErrorCode ierr;
	ierr =
	KSPSolve(this->petsc_solver_wrapper->ksp, this->petsc_solver_wrapper->rhs,
	this->petsc_solver_wrapper->solution);
	CHKERRXX(ierr);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolverPETSc::solve(Array<Real> & solution) {
	AKANTU_DEBUG_IN();

	this->solution = &solution;
	this->solve();

	PetscErrorCode ierr;
	PETScMatrix * petsc_matrix = static_cast<PETScMatrix *>(this->matrix);

	// ierr = VecGetOwnershipRange(this->petsc_solver_wrapper->solution,
	// solution_begin, solution_end); CHKERRXX(ierr);
	// ierr = VecGetArray(this->petsc_solver_wrapper->solution, PetscScalar
	// **array); CHKERRXX(ierr);
	UInt nb_component = solution.getNbComponent();
	UInt size = solution.getSize();

	for (UInt i = 0; i < size; ++i) {
	for (UInt j = 0; j < nb_component; ++j) {
	UInt i_local = i * nb_component + j;
	if (this->matrix->getDOFSynchronizer().isLocalOrMasterDOF(i_local)) {
	Int i_global =
	this->matrix->getDOFSynchronizer().getDOFGlobalID(i_local);
	ierr = AOApplicationToPetsc(petsc_matrix->getPETScMatrixWrapper()->ao,
	1, &(i_global));
	CHKERRXX(ierr);
	ierr = VecGetValues(this->petsc_solver_wrapper->solution, 1, &i_global,
	&solution(i, j));
	CHKERRXX(ierr);
	}
	}
	}
	synch_registry->synchronize(_gst_solver_solution);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void SolverPETSc::setOperators() {
	AKANTU_DEBUG_IN();
	PetscErrorCode ierr;
	/// set the matrix that defines the linear system and the matrix for
	/// preconditioning (here they are the same)
	PETScMatrix * petsc_matrix = static_cast<PETScMatrix *>(this->matrix);

	#if PETSC_VERSION_MAJOR >= 3 && PETSC_VERSION_MINOR >= 5
	ierr = KSPSetOperators(this->petsc_solver_wrapper->ksp,
	petsc_matrix->getPETScMatrixWrapper()->mat,
	petsc_matrix->getPETScMatrixWrapper()->mat);
	CHKERRXX(ierr);
	#else
	ierr = KSPSetOperators(this->petsc_solver_wrapper->ksp,
	petsc_matrix->getPETScMatrixWrapper()->mat,
	petsc_matrix->getPETScMatrixWrapper()->mat,
	SAME_NONZERO_PATTERN);
	CHKERRXX(ierr);
	#endif
	/// If this is not called the solution vector is zeroed in the call to
	/// KSPSolve().
	ierr = KSPSetInitialGuessNonzero(this->petsc_solver_wrapper->ksp, PETSC_TRUE);
	CHKERRXX(ierr);
	ierr = KSPSetFromOptions(this->petsc_solver_wrapper->ksp);
	CHKERRXX(ierr);

	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	// void finalize_petsc() {

	// static bool finalized = false;
	// if (!finalized) {

	// cout<<"* INFO * PETSc is finalizing..."<<endl;
	// // finalize PETSc
	// PetscErrorCode ierr = PetscFinalize();CHKERRCONTINUE(ierr);
	// finalized = true;
	// }
	// }

	// SolverPETSc::sparse_vector_type
	// SolverPETSc::operator()(const SolverPETSc::sparse_matrix_type& AA,
	// const SolverPETSc::sparse_vector_type& bb) {

	// #ifdef CPPUTILS_VERBOSE
	// // parallel output stream
	// Output_stream out;
	// // timer
	// cpputils::ctimer timer;
	// out<<"Inside PETSc solver: "<<timer<<endl;
	// #endif

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Inside operator()(const sparse_matrix_type&, const
	// sparse_vector_type&)... "<<timer<<endl;
	// #endif

	// assert(AA.rows() == bb.size());

	// // KSP ksp; //!< linear solver context

	// Vec b; /* RHS */
	// PC pc; /* preconditioner context */
	// PetscErrorCode ierr;
	// PetscInt nlocal;
	// PetscInt n = bb.size();
	// VecScatter ctx;

	// /*
	// Create vectors. Note that we form 1 vector from scratch and
	// then duplicate as needed. For this simple case let PETSc decide how
	// many elements of the vector are stored on each processor. The second
	// argument to VecSetSizes() below causes PETSc to decide.
	// */
	// ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRCONTINUE(ierr);
	// ierr = VecSetSizes(b,PETSC_DECIDE,n);CHKERRCONTINUE(ierr);
	// ierr = VecSetFromOptions(b);CHKERRCONTINUE(ierr);
	// if (!allocated_) {
	// ierr = VecDuplicate(b,&x_);CHKERRCONTINUE(ierr);
	// } else
	// VecZeroEntries(x_);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vectors created... "<<timer<<endl;
	// #endif

	// /* Set hight-hand-side vector */
	// for (sparse_vector_type::const_hash_iterator it = bb.map_.begin(); it !=
	// bb.map_.end(); ++it) {
	// int row = it->first;
	// ierr = VecSetValues(b, 1, &row, &it->second, ADD_VALUES);
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Right hand side set... "<<timer<<endl;
	// #endif

	// /*
	// Assemble vector, using the 2-step process:
	// VecAssemblyBegin(), VecAssemblyEnd()
	// Computations can be done while messages are in transition
	// by placing code between these two statements.
	// */
	// ierr = VecAssemblyBegin(b);CHKERRCONTINUE(ierr);
	// ierr = VecAssemblyEnd(b);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Right-hand-side vector assembled... "<<timer<<endl;

	// ierr = VecView(b,PETSC_VIEWER_STDOUT_WORLD);CHKERRCONTINUE(ierr);

	// Vec b_all;
	// ierr = VecScatterCreateToAll(b, &ctx, &b_all);CHKERRCONTINUE(ierr);
	// ierr =
	// VecScatterBegin(ctx,b,b_all,INSERT_VALUES,SCATTER_FORWARD);CHKERRCONTINUE(ierr);
	// ierr =
	// VecScatterEnd(ctx,b,b_all,INSERT_VALUES,SCATTER_FORWARD);CHKERRCONTINUE(ierr);

	// value_type nrm;
	// VecNorm(b_all,NORM_2,&nrm);
	// out<<" Norm of right hand side... "<<nrm<<endl;
	// #endif

	// /* Identify the starting and ending mesh points on each
	// processor for the interior part of the mesh. We let PETSc decide
	// above. */

	// // PetscInt rstart,rend;
	// // ierr = VecGetOwnershipRange(x_,&rstart,&rend);CHKERRCONTINUE(ierr);
	// ierr = VecGetLocalSize(x_,&nlocal);CHKERRCONTINUE(ierr);

	// /*
	// Create matrix. When using MatCreate(), the matrix format can
	// be specified at runtime.

	// Performance tuning note: For problems of substantial size,
	// preallocation of matrix memory is crucial for attaining good
	// performance. See the matrix chapter of the users manual for details.

	// We pass in nlocal as the "local" size of the matrix to force it
	// to have the same parallel layout as the vector created above.
	// */
	// if (!allocated_) {

	// ierr = MatCreate(PETSC_COMM_WORLD,&A_);CHKERRCONTINUE(ierr);
	// ierr = MatSetSizes(A_,nlocal,nlocal,n,n);CHKERRCONTINUE(ierr);
	// ierr = MatSetFromOptions(A_);CHKERRCONTINUE(ierr);
	// ierr = MatSetUp(A_);CHKERRCONTINUE(ierr);
	// } else {
	// // zero-out matrix
	// MatZeroEntries(A_);
	// }

	// /*
	// Assemble matrix.

	// The linear system is distributed across the processors by
	// chunks of contiguous rows, which correspond to contiguous
	// sections of the mesh on which the problem is discretized.
	// For matrix assembly, each processor contributes entries for
	// the part that it owns locally.
	// */

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Zeroed-out sparse matrix entries... "<<timer<<endl;
	// #endif

	// for (sparse_matrix_type::const_hash_iterator it = AA.map_.begin(); it !=
	// AA.map_.end(); ++it) {

	// // get subscripts
	// std::pair<size_t,size_t> subs = AA.unhash(it->first);
	// PetscInt row = subs.first;
	// PetscInt col = subs.second;
	// ierr = MatSetValues(A_, 1, &row, 1, &col, &it->second,
	// ADD_VALUES);CHKERRCONTINUE(ierr);
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Filled sparse matrix... "<<timer<<endl;
	// #endif

	// /* Assemble the matrix */
	// ierr = MatAssemblyBegin(A_,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);
	// ierr = MatAssemblyEnd(A_,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);

	// if (!allocated_) {
	// // set after the first MatAssemblyEnd
	// // ierr = MatSetOption(A_, MAT_NEW_NONZERO_LOCATIONS,
	// PETSC_FALSE);CHKERRCONTINUE(ierr);
	// ierr = MatSetOption(A_, MAT_NEW_NONZERO_ALLOCATION_ERR,
	// PETSC_FALSE);CHKERRCONTINUE(ierr);
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Sparse matrix assembled... "<<timer<<endl;
	// // view matrix
	// MatView(A_, PETSC_VIEWER_STDOUT_WORLD);

	// MatNorm(A_,NORM_FROBENIUS,&nrm);
	// out<<" Norm of stiffness matrix... "<<nrm<<endl;
	// #endif

	// /*
	// Set operators. Here the matrix that defines the linear system
	// also serves as the preconditioning matrix.
	// */
	// // ierr =
	// KSPSetOperators(ksp,A_,A_,DIFFERENT_NONZERO_PATTERN);CHKERRCONTINUE(ierr);
	// ierr =
	// KSPSetOperators(ksp_,A_,A_,SAME_NONZERO_PATTERN);CHKERRCONTINUE(ierr);

	// //
	// // /*
	// // Set runtime options, e.g.,
	// // -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
	// // These options will override those specified above as long as
	// // KSPSetFromOptions() is called _after_ any other customization
	// // routines.
	// // */
	// // ierr = KSPSetFromOptions(ksp);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Solving system... "<<timer<<endl;
	// #endif

	// /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
	// Solve the linear system
	// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
	// /*
	// Solve linear system
	// */
	// ierr = KSPSolve(ksp_,b,x_);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE

	// /*
	// View solver info; we could instead use the option -ksp_view to
	// print this info to the screen at the conclusion of KSPSolve().
	// */
	// ierr = KSPView(ksp_,PETSC_VIEWER_STDOUT_WORLD);CHKERRCONTINUE(ierr);

	// int iter;
	// KSPGetIterationNumber(ksp_, &iter);
	// out<<" System solved in "<<iter<<" iterations... "<<timer<<endl;
	// KSPConvergedReason reason;
	// ierr = KSPGetConvergedReason(ksp_,&reason);CHKERRCONTINUE(ierr);
	// if (reason < 0)
	// out<<"* WARNING * PETSc solver diverged with flag ";
	// else
	// out<<"* INFO * PETSc solver converged with flag ";

	// if (reason == KSP_CONVERGED_RTOL)
	// out<<"KSP_CONVERGED_RTOL"<<endl;
	// else if (reason == KSP_CONVERGED_ATOL)
	// out<<"KSP_CONVERGED_ATOL"<<endl;
	// else if (reason == KSP_CONVERGED_ITS)
	// out<<"KSP_CONVERGED_ITS"<<endl;
	// else if (reason == KSP_CONVERGED_CG_NEG_CURVE)
	// out<<"KSP_CONVERGED_CG_NEG_CURVE"<<endl;
	// else if (reason == KSP_CONVERGED_CG_CONSTRAINED)
	// out<<"KSP_CONVERGED_CG_CONSTRAINED"<<endl;
	// else if (reason == KSP_CONVERGED_STEP_LENGTH)
	// out<<"KSP_CONVERGED_STEP_LENGTH"<<endl;
	// else if (reason == KSP_CONVERGED_HAPPY_BREAKDOWN)
	// out<<"KSP_CONVERGED_HAPPY_BREAKDOWN"<<endl;
	// else if (reason == KSP_DIVERGED_NULL)
	// out<<"KSP_DIVERGED_NULL"<<endl;
	// else if (reason == KSP_DIVERGED_ITS)
	// out<<"KSP_DIVERGED_ITS"<<endl;
	// else if (reason == KSP_DIVERGED_DTOL)
	// out<<"KSP_DIVERGED_DTOL"<<endl;
	// else if (reason == KSP_DIVERGED_BREAKDOWN)
	// out<<"KSP_DIVERGED_BREAKDOWN"<<endl;
	// else if (reason == KSP_DIVERGED_BREAKDOWN_BICG)
	// out<<"KSP_DIVERGED_BREAKDOWN_BICG"<<endl;
	// else if (reason == KSP_DIVERGED_NONSYMMETRIC)
	// out<<"KSP_DIVERGED_NONSYMMETRIC"<<endl;
	// else if (reason == KSP_DIVERGED_INDEFINITE_PC)
	// out<<"KSP_DIVERGED_INDEFINITE_PC"<<endl;
	// else if (reason == KSP_DIVERGED_NAN)
	// out<<"KSP_DIVERGED_NAN"<<endl;
	// else if (reason == KSP_DIVERGED_INDEFINITE_MAT)
	// out<<"KSP_DIVERGED_INDEFINITE_MAT"<<endl;
	// else if (reason == KSP_CONVERGED_ITERATING)
	// out<<"KSP_CONVERGED_ITERATING"<<endl;

	// PetscReal rnorm;
	// ierr = KSPGetResidualNorm(ksp_,&rnorm);CHKERRCONTINUE(ierr);

	// out<<"PETSc last residual norm computed: "<<rnorm<<endl;

	// ierr = VecView(x_,PETSC_VIEWER_STDOUT_WORLD);CHKERRCONTINUE(ierr);

	// VecNorm(x_,NORM_2,&nrm);
	// out<<" Norm of solution vector... "<<nrm<<endl;

	// #endif

	// /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
	// Check solution and clean up
	// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

	// Vec x_all;

	// ierr = VecScatterCreateToAll(x_, &ctx, &x_all);CHKERRCONTINUE(ierr);
	// ierr =
	// VecScatterBegin(ctx,x_,x_all,INSERT_VALUES,SCATTER_FORWARD);CHKERRCONTINUE(ierr);
	// ierr =
	// VecScatterEnd(ctx,x_,x_all,INSERT_VALUES,SCATTER_FORWARD);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Solution vector scattered... "<<timer<<endl;
	// VecNorm(x_all,NORM_2,&nrm);
	// out<<" Norm of scattered vector... "<<nrm<<endl;
	// // ierr = VecView(x_all,PETSC_VIEWER_STDOUT_WORLD);CHKERRCONTINUE(ierr);
	// #endif

	// /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
	// Get values from solution and store them in the object that will be
	// returned
	// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

	// sparse_vector_type xx(bb.size());

	// /* Set solution vector */
	// double zero = 0.;
	// double val;
	// for (sparse_vector_type::const_hash_iterator it = bb.map_.begin(); it !=
	// bb.map_.end(); ++it) {
	// int row = it->first;
	// ierr = VecGetValues(x_all, 1, &row, &val);
	// if (val != zero)
	// xx[row] = val;
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Solution vector copied... "<<timer<<endl;
	// // out<<" Norm of copied solution vector... "<<norm(xx,
	// Insert_t)<<endl;
	// #endif

	// /*
	// Free work space. All PETSc objects should be destroyed when they
	// are no longer needed.
	// */
	// ierr = VecDestroy(&b);CHKERRCONTINUE(ierr);
	// // ierr = KSPDestroy(&ksp);CHKERRCONTINUE(ierr);

	// // set allocated flag
	// if (!allocated_) {
	// allocated_ = true;
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Temporary data structures destroyed... "<<timer<<endl;
	// #endif

	// return xx;
	// }

	// SolverPETSc::sparse_vector_type SolverPETSc::operator()(const
	// SolverPETSc::sparse_matrix_type& KKpf, const SolverPETSc::sparse_matrix_type&
	// KKpp, const SolverPETSc::sparse_vector_type& UUp) {

	// #ifdef CPPUTILS_VERBOSE
	// // parallel output stream
	// Output_stream out;
	// // timer
	// cpputils::ctimer timer;
	// out<<"Inside SolverPETSc::operator()(const sparse_matrix&, const
	// sparse_matrix&, const sparse_vector&). "<<timer<<endl;
	// #endif

	// Mat Kpf, Kpp;
	// Vec Up, Pf, Pp;

	// PetscErrorCode ierr =
	// MatCreate(PETSC_COMM_WORLD,&Kpf);CHKERRCONTINUE(ierr);
	// ierr = MatCreate(PETSC_COMM_WORLD,&Kpp);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Allocating memory... "<<timer<<endl;
	// #endif

	// ierr = MatSetFromOptions(Kpf);CHKERRCONTINUE(ierr);
	// ierr = MatSetFromOptions(Kpp);CHKERRCONTINUE(ierr);

	// ierr = MatSetSizes(Kpf,PETSC_DECIDE,PETSC_DECIDE, KKpf.rows(),
	// KKpf.columns());CHKERRCONTINUE(ierr);
	// ierr = MatSetSizes(Kpp,PETSC_DECIDE,PETSC_DECIDE, KKpp.rows(),
	// KKpp.columns());CHKERRCONTINUE(ierr);

	// // get number of non-zeros in both diagonal and non-diagonal portions of
	// the matrix

	// std::pair<size_t,size_t> Kpf_nz = KKpf.non_zero_off_diagonal();
	// std::pair<size_t,size_t> Kpp_nz = KKpp.non_zero_off_diagonal();

	// ierr = MatMPIAIJSetPreallocation(Kpf, Kpf_nz.first, PETSC_NULL,
	// Kpf_nz.second, PETSC_NULL); CHKERRCONTINUE(ierr);
	// ierr = MatMPIAIJSetPreallocation(Kpp, Kpp_nz.first, PETSC_NULL,
	// Kpp_nz.second, PETSC_NULL); CHKERRCONTINUE(ierr);
	// ierr = MatSeqAIJSetPreallocation(Kpf, Kpf_nz.first, PETSC_NULL);
	// CHKERRCONTINUE(ierr);
	// ierr = MatSeqAIJSetPreallocation(Kpp, Kpp_nz.first, PETSC_NULL);
	// CHKERRCONTINUE(ierr);

	// for (sparse_matrix_type::const_hash_iterator it = KKpf.map_.begin(); it !=
	// KKpf.map_.end(); ++it) {

	// // get subscripts
	// std::pair<size_t,size_t> subs = KKpf.unhash(it->first);
	// int row = subs.first;
	// int col = subs.second;
	// ierr = MatSetValues(Kpf, 1, &row, 1, &col, &it->second,
	// ADD_VALUES);CHKERRCONTINUE(ierr);
	// }

	// for (sparse_matrix_type::const_hash_iterator it = KKpp.map_.begin(); it !=
	// KKpp.map_.end(); ++it) {

	// // get subscripts
	// std::pair<size_t,size_t> subs = KKpp.unhash(it->first);
	// int row = subs.first;
	// int col = subs.second;
	// ierr = MatSetValues(Kpf, 1, &row, 1, &col, &it->second,
	// ADD_VALUES);CHKERRCONTINUE(ierr);
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Filled sparse matrices... "<<timer<<endl;
	// #endif

	// /*
	// Assemble matrix, using the 2-step process:
	// MatAssemblyBegin(), MatAssemblyEnd()
	// Computations can be done while messages are in transition
	// by placing code between these two statements.
	// */
	// ierr = MatAssemblyBegin(Kpf,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);
	// ierr = MatAssemblyBegin(Kpp,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);
	// ierr = MatAssemblyEnd(Kpf,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);
	// ierr = MatAssemblyEnd(Kpp,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Sparse matrices assembled... "<<timer<<endl;
	// #endif

	// ierr = VecCreate(PETSC_COMM_WORLD,&Up);CHKERRCONTINUE(ierr);
	// ierr = VecSetSizes(Up,PETSC_DECIDE, UUp.size());CHKERRCONTINUE(ierr);
	// ierr = VecSetFromOptions(Up);CHKERRCONTINUE(ierr);

	// ierr = VecCreate(PETSC_COMM_WORLD,&Pf);CHKERRCONTINUE(ierr);
	// ierr = VecSetSizes(Pf,PETSC_DECIDE, KKpf.rows());CHKERRCONTINUE(ierr);
	// ierr = VecSetFromOptions(Pf);CHKERRCONTINUE(ierr);
	// ierr = VecDuplicate(Pf,&Pp);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vectors created... "<<timer<<endl;
	// #endif

	// /* Set hight-hand-side vector */
	// for (sparse_vector_type::const_hash_iterator it = UUp.map_.begin(); it !=
	// UUp.map_.end(); ++it) {
	// int row = it->first;
	// ierr = VecSetValues(Up, 1, &row, &it->second, ADD_VALUES);
	// }

	// /*
	// Assemble vector, using the 2-step process:
	// VecAssemblyBegin(), VecAssemblyEnd()
	// Computations can be done while messages are in transition
	// by placing code between these two statements.
	// */
	// ierr = VecAssemblyBegin(Up);CHKERRCONTINUE(ierr);
	// ierr = VecAssemblyEnd(Up);CHKERRCONTINUE(ierr);

	// // add Kpf*Uf
	// ierr = MatMult(Kpf, x_, Pf);

	// // add Kpp*Up
	// ierr = MatMultAdd(Kpp, Up, Pf, Pp);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Matrices multiplied... "<<timer<<endl;
	// #endif

	// VecScatter ctx;
	// Vec Pp_all;

	// ierr = VecScatterCreateToAll(Pp, &ctx, &Pp_all);CHKERRCONTINUE(ierr);
	// ierr =
	// VecScatterBegin(ctx,Pp,Pp_all,INSERT_VALUES,SCATTER_FORWARD);CHKERRCONTINUE(ierr);
	// ierr =
	// VecScatterEnd(ctx,Pp,Pp_all,INSERT_VALUES,SCATTER_FORWARD);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vector scattered... "<<timer<<endl;
	// #endif

	// /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
	// Get values from solution and store them in the object that will be
	// returned
	// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

	// sparse_vector_type pp(KKpf.rows());

	// // get reaction vector
	// for (int i=0; i<KKpf.rows(); ++i) {

	// PetscScalar v;
	// ierr = VecGetValues(Pp_all, 1, &i, &v);
	// if (v != PetscScalar())
	// pp[i] = v;
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vector copied... "<<timer<<endl;
	// #endif

	// ierr = MatDestroy(&Kpf);CHKERRCONTINUE(ierr);
	// ierr = MatDestroy(&Kpp);CHKERRCONTINUE(ierr);
	// ierr = VecDestroy(&Up);CHKERRCONTINUE(ierr);
	// ierr = VecDestroy(&Pf);CHKERRCONTINUE(ierr);
	// ierr = VecDestroy(&Pp);CHKERRCONTINUE(ierr);
	// ierr = VecDestroy(&Pp_all);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Temporary data structures destroyed... "<<timer<<endl;
	// #endif

	// return pp;
	// }

	// SolverPETSc::sparse_vector_type SolverPETSc::operator()(const
	// SolverPETSc::sparse_vector_type& aa, const SolverPETSc::sparse_vector_type&
	// bb) {

	// assert(aa.size() == bb.size());

	// #ifdef CPPUTILS_VERBOSE
	// // parallel output stream
	// Output_stream out;
	// // timer
	// cpputils::ctimer timer;
	// out<<"Inside SolverPETSc::operator()(const sparse_vector&, const
	// sparse_vector&). "<<timer<<endl;
	// #endif

	// Vec r;

	// PetscErrorCode ierr = VecCreate(PETSC_COMM_WORLD,&r);CHKERRCONTINUE(ierr);
	// ierr = VecSetSizes(r,PETSC_DECIDE, aa.size());CHKERRCONTINUE(ierr);
	// ierr = VecSetFromOptions(r);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vectors created... "<<timer<<endl;
	// #endif

	// // set values
	// for (sparse_vector_type::const_hash_iterator it = aa.map_.begin(); it !=
	// aa.map_.end(); ++it) {
	// int row = it->first;
	// ierr = VecSetValues(r, 1, &row, &it->second, ADD_VALUES);
	// }
	// for (sparse_vector_type::const_hash_iterator it = bb.map_.begin(); it !=
	// bb.map_.end(); ++it) {
	// int row = it->first;
	// ierr = VecSetValues(r, 1, &row, &it->second, ADD_VALUES);
	// }

	// /*
	// Assemble vector, using the 2-step process:
	// VecAssemblyBegin(), VecAssemblyEnd()
	// Computations can be done while messages are in transition
	// by placing code between these two statements.
	// */
	// ierr = VecAssemblyBegin(r);CHKERRCONTINUE(ierr);
	// ierr = VecAssemblyEnd(r);CHKERRCONTINUE(ierr);

	// sparse_vector_type rr(aa.size());

	// for (sparse_vector_type::const_hash_iterator it = aa.map_.begin(); it !=
	// aa.map_.end(); ++it) {
	// int row = it->first;
	// ierr = VecGetValues(r, 1, &row, &rr[row]);
	// }
	// for (sparse_vector_type::const_hash_iterator it = bb.map_.begin(); it !=
	// bb.map_.end(); ++it) {
	// int row = it->first;
	// ierr = VecGetValues(r, 1, &row, &rr[row]);
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vector copied... "<<timer<<endl;
	// #endif

	// ierr = VecDestroy(&r);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Temporary data structures destroyed... "<<timer<<endl;
	// #endif

	// return rr;
	// }

	// SolverPETSc::value_type SolverPETSc::norm(const
	// SolverPETSc::sparse_matrix_type& aa, Element_insertion_type flag) {

	// #ifdef CPPUTILS_VERBOSE
	// // parallel output stream
	// Output_stream out;
	// // timer
	// cpputils::ctimer timer;
	// out<<"Inside SolverPETSc::norm(const sparse_matrix&). "<<timer<<endl;
	// #endif

	// Mat r;

	// PetscErrorCode ierr = MatCreate(PETSC_COMM_WORLD,&r);CHKERRCONTINUE(ierr);
	// ierr = MatSetSizes(r,PETSC_DECIDE,PETSC_DECIDE, aa.rows(),
	// aa.columns());CHKERRCONTINUE(ierr);
	// ierr = MatSetFromOptions(r);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Matrix created... "<<timer<<endl;
	// #endif

	// // set values
	// for (sparse_vector_type::const_hash_iterator it = aa.map_.begin(); it !=
	// aa.map_.end(); ++it) {
	// // get subscripts
	// std::pair<size_t,size_t> subs = aa.unhash(it->first);
	// int row = subs.first;
	// int col = subs.second;

	// if (flag == Add_t)
	// ierr = MatSetValues(r, 1, &row, 1, &col, &it->second, ADD_VALUES);
	// else if (flag == Insert_t)
	// ierr = MatSetValues(r, 1, &row, 1, &col, &it->second, INSERT_VALUES);
	// CHKERRCONTINUE(ierr);
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Matrix filled..."<<timer<<endl;
	// #endif

	// /*
	// Assemble vector, using the 2-step process:
	// VecAssemblyBegin(), VecAssemblyEnd()
	// Computations can be done while messages are in transition
	// by placing code between these two statements.
	// */
	// ierr = MatAssemblyBegin(r,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);
	// ierr = MatAssemblyEnd(r,MAT_FINAL_ASSEMBLY);CHKERRCONTINUE(ierr);

	// value_type nrm;

	// MatNorm(r,NORM_FROBENIUS,&nrm);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Norm computed... "<<timer<<endl;
	// #endif

	// ierr = MatDestroy(&r);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Temporary data structures destroyed... "<<timer<<endl;
	// #endif

	// return nrm;
	// }

	// SolverPETSc::value_type SolverPETSc::norm(const
	// SolverPETSc::sparse_vector_type& aa, Element_insertion_type flag) {

	// #ifdef CPPUTILS_VERBOSE
	// // parallel output stream
	// Output_stream out;
	// // timer
	// cpputils::ctimer timer;
	// out<<"Inside SolverPETSc::norm(const sparse_vector&). "<<timer<<endl;
	// #endif

	// Vec r;

	// PetscErrorCode ierr = VecCreate(PETSC_COMM_WORLD,&r);CHKERRCONTINUE(ierr);
	// ierr = VecSetSizes(r,PETSC_DECIDE, aa.size());CHKERRCONTINUE(ierr);
	// ierr = VecSetFromOptions(r);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vector created... "<<timer<<endl;
	// #endif

	// // set values
	// for (sparse_vector_type::const_hash_iterator it = aa.map_.begin(); it !=
	// aa.map_.end(); ++it) {
	// int row = it->first;
	// if (flag == Add_t)
	// ierr = VecSetValues(r, 1, &row, &it->second, ADD_VALUES);
	// else if (flag == Insert_t)
	// ierr = VecSetValues(r, 1, &row, &it->second, INSERT_VALUES);
	// CHKERRCONTINUE(ierr);
	// }

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Vector filled..."<<timer<<endl;
	// #endif

	// /*
	// Assemble vector, using the 2-step process:
	// VecAssemblyBegin(), VecAssemblyEnd()
	// Computations can be done while messages are in transition
	// by placing code between these two statements.
	// */
	// ierr = VecAssemblyBegin(r);CHKERRCONTINUE(ierr);
	// ierr = VecAssemblyEnd(r);CHKERRCONTINUE(ierr);

	// value_type nrm;

	// VecNorm(r,NORM_2,&nrm);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Norm computed... "<<timer<<endl;
	// #endif

	// ierr = VecDestroy(&r);CHKERRCONTINUE(ierr);

	// #ifdef CPPUTILS_VERBOSE
	// out<<" Temporary data structures destroyed... "<<timer<<endl;
	// #endif

	// return nrm;

	// }

	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //SolverMumps::SolverMumps(SparseMatrix & matrix,
	// // const ID & id,
	// // const MemoryID & memory_id) :
	// //Solver(matrix, id, memory_id), is_mumps_data_initialized(false),
	// rhs_is_local(true) {
	// // AKANTU_DEBUG_IN();
	// //
	// //#ifdef AKANTU_USE_MPI
	// // parallel_method = SolverMumpsOptions::_fully_distributed;
	// //#else //AKANTU_USE_MPI
	// // parallel_method = SolverMumpsOptions::_master_slave_distributed;
	// //#endif //AKANTU_USE_MPI
	// //
	// // CommunicatorEventHandler & comm_event_handler = *this;
	// //
	// // communicator.registerEventHandler(comm_event_handler);
	// //
	// // AKANTU_DEBUG_OUT();
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //SolverMumps::~SolverMumps() {
	// // AKANTU_DEBUG_IN();
	// //
	// // AKANTU_DEBUG_OUT();
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //void SolverMumps::destroyMumpsData() {
	// // AKANTU_DEBUG_IN();
	// //
	// // if(is_mumps_data_initialized) {
	// // mumps_data.job = _smj_destroy; // destroy
	// // dmumps_c(&mumps_data);
	// // is_mumps_data_initialized = false;
	// // }
	// //
	// // AKANTU_DEBUG_OUT();
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //void SolverMumps::onCommunicatorFinalize(const StaticCommunicator & comm) {
	// // AKANTU_DEBUG_IN();
	// //
	// // try{
	// // const StaticCommunicatorMPI & comm_mpi =
	// // dynamic_cast<const StaticCommunicatorMPI
	// &>(comm.getRealStaticCommunicator());
	// // if(mumps_data.comm_fortran ==
	// MPI_Comm_c2f(comm_mpi.getMPICommunicator()))
	// // destroyMumpsData();
	// // } catch(...) {}
	// //
	// // AKANTU_DEBUG_OUT();
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //void SolverMumps::initMumpsData(SolverMumpsOptions::ParallelMethod
	// parallel_method) {
	// // switch(parallel_method) {
	// // case SolverMumpsOptions::_fully_distributed:
	// // icntl(18) = 3; //fully distributed
	// // icntl(28) = 0; //automatic choice
	// //
	// // mumps_data.nz_loc = matrix->getNbNonZero();
	// // mumps_data.irn_loc = matrix->getIRN().values;
	// // mumps_data.jcn_loc = matrix->getJCN().values;
	// // break;
	// // case SolverMumpsOptions::_master_slave_distributed:
	// // if(prank == 0) {
	// // mumps_data.nz = matrix->getNbNonZero();
	// // mumps_data.irn = matrix->getIRN().values;
	// // mumps_data.jcn = matrix->getJCN().values;
	// // } else {
	// // mumps_data.nz = 0;
	// // mumps_data.irn = NULL;
	// // mumps_data.jcn = NULL;
	// //
	// // icntl(18) = 0; //centralized
	// // icntl(28) = 0; //sequential analysis
	// // }
	// // break;
	// // }
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //void SolverMumps::initialize(SolverOptions & options) {
	// // AKANTU_DEBUG_IN();
	// //
	// // mumps_data.par = 1;
	// //
	// // if(SolverMumpsOptions * opt = dynamic_cast<SolverMumpsOptions
	// *>(&options)) {
	// // if(opt->parallel_method ==
	// SolverMumpsOptions::_master_slave_distributed) {
	// // mumps_data.par = 0;
	// // }
	// // }
	// //
	// // mumps_data.sym = 2 * (matrix->getSparseMatrixType() == _symmetric);
	// // prank = communicator.whoAmI();
	// //#ifdef AKANTU_USE_MPI
	// // mumps_data.comm_fortran = MPI_Comm_c2f(dynamic_cast<const
	// StaticCommunicatorMPI
	// &>(communicator.getRealStaticCommunicator()).getMPICommunicator());
	// //#endif
	// //
	// // if(AKANTU_DEBUG_TEST(dblTrace)) {
	// // icntl(1) = 2;
	// // icntl(2) = 2;
	// // icntl(3) = 2;
	// // icntl(4) = 4;
	// // }
	// //
	// // mumps_data.job = _smj_initialize; //initialize
	// // dmumps_c(&mumps_data);
	// // is_mumps_data_initialized = true;
	// //
	// // /*
	// ------------------------------------------------------------------------ */
	// // UInt size = matrix->getSize();
	// //
	// // if(prank == 0) {
	// // std::stringstream sstr_rhs; sstr_rhs << id << ":rhs";
	// // rhs = &(alloc<Real>(sstr_rhs.str(), size, 1, REAL_INIT_VALUE));
	// // } else {
	// // rhs = NULL;
	// // }
	// //
	// // /// No outputs
	// // icntl(1) = 0;
	// // icntl(2) = 0;
	// // icntl(3) = 0;
	// // icntl(4) = 0;
	// // mumps_data.nz_alloc = 0;
	// //
	// // if (AKANTU_DEBUG_TEST(dblDump)) icntl(4) = 4;
	// //
	// // mumps_data.n = size;
	// //
	// // if(AKANTU_DEBUG_TEST(dblDump)) {
	// // strcpy(mumps_data.write_problem, "mumps_matrix.mtx");
	// // }
	// //
	// // /*
	// ------------------------------------------------------------------------ */
	// // // Default Scaling
	// // icntl(8) = 77;
	// //
	// // icntl(5) = 0; // Assembled matrix
	// //
	// // SolverMumpsOptions * opt = dynamic_cast<SolverMumpsOptions *>(&options);
	// // if(opt)
	// // parallel_method = opt->parallel_method;
	// //
	// // initMumpsData(parallel_method);
	// //
	// // mumps_data.job = _smj_analyze; //analyze
	// // dmumps_c(&mumps_data);
	// //
	// // AKANTU_DEBUG_OUT();
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //void SolverMumps::setRHS(Array<Real> & rhs) {
	// // if(prank == 0) {
	// // matrix->getDOFSynchronizer().gather(rhs, 0, this->rhs);
	// // } else {
	// // matrix->getDOFSynchronizer().gather(rhs, 0);
	// // }
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //void SolverMumps::solve() {
	// // AKANTU_DEBUG_IN();
	// //
	// // if(parallel_method == SolverMumpsOptions::_fully_distributed)
	// // mumps_data.a_loc = matrix->getA().values;
	// // else
	// // if(prank == 0) {
	// // mumps_data.a = matrix->getA().values;
	// // }
	// //
	// // if(prank == 0) {
	// // mumps_data.rhs = rhs->values;
	// // }
	// //
	// // /// Default centralized dense second member
	// // icntl(20) = 0;
	// // icntl(21) = 0;
	// //
	// // mumps_data.job = _smj_factorize_solve; //solve
	// // dmumps_c(&mumps_data);
	// //
	// // AKANTU_DEBUG_ASSERT(info(1) != -10, "Singular matrix");
	// // AKANTU_DEBUG_ASSERT(info(1) == 0,
	// // "Error in mumps during solve process, check mumps
	// user guide INFO(1) ="
	// // << info(1));
	// //
	// // AKANTU_DEBUG_OUT();
	// //}
	// //
	// ///*
	// -------------------------------------------------------------------------- */
	// //void SolverMumps::solve(Array<Real> & solution) {
	// // AKANTU_DEBUG_IN();
	// //
	// // solve();
	// //
	// // if(prank == 0) {
	// // matrix->getDOFSynchronizer().scatter(solution, 0, this->rhs);
	// // } else {
	// // matrix->getDOFSynchronizer().scatter(solution, 0);
	// // }
	// //
	// // AKANTU_DEBUG_OUT();
	// //}

	__END_AKANTU__

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