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test_model_solver_dynamic_petsc.cc
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			/**
			* @file test_model_solver_dynamic.cc
			*
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Wed Apr 13 2016
			* @date last modification: Tue Feb 20 2018
			*
			* @brief Test default dof manager
			*
			*
			* Copyright (©) 2016-2018 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 "communicator.hh"
			#include "element_group.hh"
			#include "mesh.hh"
			#include "mesh_accessor.hh"
			#include "non_linear_solver.hh"
			/* -------------------------------------------------------------------------- */
			#include "boundary_condition_functor.hh"
			#include "mpi_communicator_data.hh"
			/* -------------------------------------------------------------------------- */
			#include "dumpable_inline_impl.hh"
			#include "dumper_element_partition.hh"
			#include "dumper_iohelper_paraview.hh"
			/* -------------------------------------------------------------------------- */
			#include <fstream>
			/* -------------------------------------------------------------------------- */
			#include <petscmat.h>
			#include <petscsnes.h>
			#include <petscvec.h>
			/* -------------------------------------------------------------------------- */

			#ifndef EXPLICIT
			#define EXPLICIT true
			#endif

			template <typename func>
			void CHECK_ERR_CXX(func && func_, PetscErrorCode ierr) {
			if (PetscUnlikely(ierr != 0)) {
			const char * desc;
			PetscErrorMessage(ierr, &desc, nullptr);
			AKANTU_EXCEPTION("Error in PETSc call to \'" << func_ << "\': " << desc);
			}
			}

			using namespace akantu;

			static void genMesh(Mesh & mesh, UInt nb_nodes);

			class MyModel {
			public:
			MyModel(Real F, Mesh & mesh, bool lumped)
			: nb_dofs(mesh.getNbNodes()), nb_elements(mesh.getNbElement(_segment_2)),
			lumped(lumped), E(1.), A(1.), rho(1.), mesh(mesh),
			displacement(nb_dofs, 1, "disp"), velocity(nb_dofs, 1, "velo"),
			acceleration(nb_dofs, 1, "accel"), blocked(nb_dofs, 1, "blocked"),
			forces(nb_dofs, 1, "force_ext"),
			internal_forces(nb_dofs, 1, "force_int"),
			stresses(nb_elements, 1, "stress"), strains(nb_elements, 1, "strain"),
			initial_lengths(nb_elements, 1, "L0") {

			auto n_global = mesh.getNbGlobalNodes();
			int n_local = 0;

			std::vector<PetscInt> nodes_global_ids(nb_dofs);
			for (auto && data : enumerate(nodes_global_ids)) {
			auto n = std::get<0>(data);
			n_local += mesh.isLocalOrMasterNode(n);
			std::get<1>(data) = mesh.getNodeGlobalId(n);
			}

			mpi_comm = dynamic_cast<MPICommunicatorData &>(
			mesh.getCommunicator().getCommunicatorData())
			.getMPICommunicator();

			MeshAccessor mesh_accessor(mesh);

			ierr = ISLocalToGlobalMappingCreate(
			mpi_comm, 1, mesh.getNbNodes(), nodes_global_ids.data(),
			PETSC_COPY_VALUES, &petsc_local_to_global);
			CHECK_ERR_CXX("ISLocalToGlobalMappingCreate", ierr);

			auto setName = [](auto && Obj, auto && name) {
			PetscObjectSetName(reinterpret_cast<PetscObject>(Obj), name);
			};

			ierr = VecCreate(mpi_comm, &rhs);
			ierr = VecSetSizes(rhs, n_local, n_global);
			ierr = VecSetFromOptions(rhs);
			ierr = VecSetLocalToGlobalMapping(rhs, petsc_local_to_global);
			setName(rhs, "rhs");

			ierr = VecDuplicate(rhs, &x);
			ierr = VecDuplicate(rhs, &x_save);
			ierr = VecDuplicate(rhs, &dx);
			ierr = VecDuplicate(rhs, &f_int);
			ierr = VecDuplicate(rhs, &f_dirichlet);
			setName(x, "x");
			setName(x_save, "x save");
			setName(dx, "dx");
			setName(f_int, "f_int");
			setName(f_dirichlet, "f_dirichlet");

			ierr = MatCreate(mpi_comm, &M);
			ierr = MatSetSizes(M, n_local, n_local, n_global, n_global);
			ierr = MatSetFromOptions(M);
			ierr = MatSetOption(M, MAT_SYMMETRIC, PETSC_TRUE);
			ierr = MatSetOption(M, MAT_ROW_ORIENTED, PETSC_TRUE);
			ierr = MatSetUp(M);
			ierr = MatSetLocalToGlobalMapping(M, petsc_local_to_global,
			petsc_local_to_global);
			setName(M, "M");

			assembleMass();

			ierr = MatDuplicate(M, MAT_DO_NOT_COPY_VALUES, &K);
			setName(K, "K");
			ierr = MatDuplicate(M, MAT_DO_NOT_COPY_VALUES, &J);
			setName(J, "J");

			ierr = SNESCreate(mpi_comm, &snes);
			ierr = SNESSetFromOptions(snes);
			ierr = SNESSetFunction(snes, rhs, MyModel::FormFunction, this);
			ierr = SNESSetJacobian(snes, J, J, MyModel::FormJacobian, this);

			PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_ASCII_INDEX);

			displacement.set(0.);
			velocity.set(0.);
			acceleration.set(0.);

			forces.set(0.);
			blocked.set(false);
			blocked(0, 0) = true;
			blocked(nb_dofs - 1, 0) = true;
			displacement(0, 0) = 0;
			displacement(nb_dofs - 1, 0) = 1;

			for (auto && data :
			zip(make_view(this->mesh.getConnectivity(_segment_2), 2),
			make_view(this->initial_lengths))) {
			const auto & conn = std::get<0>(data);
			auto & L = std::get<1>(data);

			auto p1 = this->mesh.getNodes()(conn(0), _x);
			auto p2 = this->mesh.getNodes()(conn(1), _x);

			L = std::abs(p2 - p1);
			}
			}

			// static PetscErrorCode SNESMonitor(SNES snes,PetscInt its,PetscReal
			// fnorm,void *ctx) {
			// auto & _this = reinterpret_cast<MyModel >(ctx);
			// //SNESMonitorDefault(snes, its, fnorm, PETSC_VIEWER_STDOUT_WORLD);
			// }

			static PetscErrorCode FormFunction(SNES /snes/, Vec /dx/, Vec /f/,
			void * ctx) {
			auto & _this = reinterpret_cast<MyModel >(ctx);
			_this.assembleResidual();
			return 0;
			}

			static PetscErrorCode FormJacobian(SNES /snes/, Vec /dx/, Mat /J/,
			Mat /P/, void * ctx) {
			auto & _this = reinterpret_cast<MyModel >(ctx);
			_this.assembleJacobian();
			return 0;
			}

			~MyModel() {
			ierr = MatDestroy(&M);
			ierr = MatDestroy(&K);
			ierr = MatDestroy(&J);

			ierr = VecDestroy(&rhs);
			ierr = VecDestroy(&x);
			ierr = VecDestroy(&dx);
			ierr = VecDestroy(&x_save);
			ierr = VecDestroy(&f_int);

			PetscFinalize();
			}

			void solveStep() {
			std::cout << "solveStep" << std::endl;
			copy(x_save, displacement);

			ierr = SNESSolve(snes, NULL, dx);
			CHECK_ERR_CXX("SNESSolve", ierr);

			setSolutionToDisplacement();
			assembleResidual();
			}

			void applyBC() {
			std::vector<PetscInt> rows;
			for (auto && data : enumerate(blocked)) {
			if (std::get<1>(data)) {
			rows.push_back(std::get<0>(data));
			}
			}

			copy(x, displacement);
			ierr = MatZeroRowsColumnsLocal(J, rows.size(), rows.data(), 1., x,
			f_dirichlet);
			VecView(f_dirichlet, PETSC_VIEWER_STDOUT_WORLD);
			CHECK_ERR_CXX("MatZeroRowsColumnsLocal", ierr);
			}

			void setSolutionToDisplacement() {
			std::cout << "setSolutionToDisplacement" << std::endl;
			ierr = VecWAXPY(x, 1, x_save, dx);
			copy(displacement, x);
			}

			void assembleJacobian() {
			std::cout << "assembleJacobian" << std::endl;
			setSolutionToDisplacement();

			assembleStiffness();

			ierr = MatZeroEntries(J);
			CHECK_ERR_CXX("MatZeroEntries", ierr);

			ierr = MatAXPY(J, 1., K, SAME_NONZERO_PATTERN);
			CHECK_ERR_CXX("MatAXPY", ierr);

			MatView(J, PETSC_VIEWER_STDOUT_WORLD);
			applyBC();
			MatView(J, PETSC_VIEWER_STDOUT_WORLD);
			}

			void assembleMass() {
			std::cout << "assembleMass" << std::endl;
			ierr = MatZeroEntries(M);
			CHECK_ERR_CXX("MatZeroEntries", ierr);

			Array<Real> m_all_el(this->nb_elements, 4);

			Matrix<Real> m(2, 2);
			m(0, 0) = m(1, 1) = 2;
			m(0, 1) = m(1, 0) = 1;

			// under integrated
			// m(0, 0) = m(1, 1) = 3./2.;
			// m(0, 1) = m(1, 0) = 3./2.;

			// lumping the mass matrix
			// m(0, 0) += m(0, 1);
			// m(1, 1) += m(1, 0);
			// m(0, 1) = m(1, 0) = 0;

			for (auto && data :
			zip(make_view(this->mesh.getConnectivity(_segment_2), 2),
			make_view(m_all_el, 2, 2))) {
			const auto & conn = std::get<0>(data);
			auto & m_el = std::get<1>(data);
			UInt n1 = conn(0);
			UInt n2 = conn(1);

			Real p1 = this->mesh.getNodes()(n1, _x);
			Real p2 = this->mesh.getNodes()(n2, _x);

			Real L = std::abs(p2 - p1);

			m_el = m;
			m_el = rho A * L / 6.;

			Vector<Int> conn_int(conn.size());
			for (auto && data : zip(conn_int, conn)) {
			std::get<0>(data) = std::get<1>(data);
			}

			ierr = MatSetValuesLocal(M, conn_int.size(), conn_int.storage(),
			conn_int.size(), conn_int.storage(), m.storage(),
			ADD_VALUES);
			}

			ierr = MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY);
			ierr = MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY);
			ierr = MatSetOption(M, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE);

			PetscViewer viewer;
			ierr = PetscViewerASCIIOpen(mpi_comm, "M.mtx", &viewer);
			PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATRIXMARKET);
			ierr = MatView(M, viewer);
			PetscViewerPopFormat(viewer);
			ierr = PetscViewerDestroy(&viewer);
			// this->getDOFManager().assembleElementalMatricesToMatrix(
			// "M", "disp", m_all_el, _segment_2);

			is_mass_assembled = true;
			}

			// MatrixType getMatrixType(const ID &) { return _symmetric; }

			// void assembleMatrix(const ID & matrix_id) {
			// if (matrix_id == "K") {
			// if (not is_stiffness_assembled)
			// this->assembleStiffness();
			// } else if (matrix_id == "M") {
			// if (not is_mass_assembled)
			// this->assembleMass();
			// } else if (matrix_id == "C") {
			// // pass, no damping matrix
			// } else {
			// AKANTU_EXCEPTION("This solver does not know what to do with a matrix "
			// << matrix_id);
			// }
			// }

			void assembleLumpedMatrix(const ID & matrix_id) {
			std::cout << "assembleLumpedMatrix" << std::endl;
			AKANTU_EXCEPTION("This solver does not know what to do with a matrix "
			<< matrix_id);
			}

			void assembleStiffness() {
			std::cout << "assembleStiffness" << std::endl;
			// SparseMatrix & K = this->getDOFManager().getMatrix("K");
			// K.zero();
			ierr = MatZeroEntries(K);
			CHECK_ERR_CXX("MatZeroEntries", ierr);

			Matrix<Real> k(2, 2);
			k(0, 0) = k(1, 1) = 1;
			k(0, 1) = k(1, 0) = -1;

			Array<Real> k_all_el(this->nb_elements, 4);

			auto k_it = k_all_el.begin(2, 2);
			auto cit = this->mesh.getConnectivity(_segment_2).begin(2);
			auto cend = this->mesh.getConnectivity(_segment_2).end(2);

			for (; cit != cend; ++cit, ++k_it) {
			const auto & conn = *cit;
			UInt n1 = conn(0);
			UInt n2 = conn(1);

			Real p1 = this->mesh.getNodes()(n1, _x);
			Real p2 = this->mesh.getNodes()(n2, _x);

			Real L = std::abs(p2 - p1);

			auto & k_el = *k_it;
			k_el = k;
			k_el = E A / L;

			Vector<Int> conn_int(conn.size());
			for (auto && data : zip(conn_int, conn)) {
			std::get<0>(data) = std::get<1>(data);
			}

			ierr = MatSetValuesLocal(K, conn_int.size(), conn_int.storage(),
			conn_int.size(), conn_int.storage(),
			k_el.storage(), ADD_VALUES);
			}

			ierr = MatAssemblyBegin(K, MAT_FINAL_ASSEMBLY);
			CHECK_ERR_CXX("MatAssemblyBegin", ierr);

			ierr = MatAssemblyEnd(K, MAT_FINAL_ASSEMBLY);
			CHECK_ERR_CXX("MatAssemblyEnd", ierr);

			ierr = MatSetOption(K, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE);
			CHECK_ERR_CXX("MatSetOption", ierr);

			PetscViewer viewer;
			ierr = PetscViewerASCIIOpen(mpi_comm, "K.mtx", &viewer);
			CHECK_ERR_CXX("PetscViewerASCIIOpen", ierr);

			PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATRIXMARKET);
			ierr = MatView(K, viewer);
			CHECK_ERR_CXX("MatView", ierr);

			PetscViewerPopFormat(viewer);
			ierr = PetscViewerDestroy(&viewer);
			CHECK_ERR_CXX("PetscViewerDestroy", ierr);

			// this->getDOFManager().assembleElementalMatricesToMatrix(
			// "K", "disp", k_all_el, _segment_2);

			is_stiffness_assembled = true;
			}

			void copy(Array<Real> & y, Vec x) {
			std::cout << "copy <-" << std::endl;
			const PetscScalar * x_local;
			ierr = VecGetArrayRead(x, &x_local);

			for (auto && data : zip(y, range(x_local + 0, x_local + y.size()))) {
			std::get<0>(data) = std::get<1>(data);
			}
			ierr = VecRestoreArrayRead(x, &x_local);

			// VecView(x, PETSC_VIEWER_STDOUT_WORLD);
			// std::cout << y.getID() << " " << Vector<Real>(y.storage(), y.size())
			// << std::endl;
			}

			void print(const Array<Real> & x) const {
			std::cout << x.getID() << " " << Vector<Real>(x.storage(), x.size())
			<< std::endl;
			}

			void copy(Vec x, const Array<Real> & y) {
			std::cout << "copy ->" << std::endl;
			PetscScalar * x_local;
			ierr = VecGetArray(x, &x_local);

			for (auto && data : zip(y, range(x_local + 0, x_local + y.size()))) {
			std::get<1>(data) = std::get<0>(data);
			}
			ierr = VecRestoreArray(x, &x_local);

			// std::cout << y.getID() << " " << Vector<Real>(y.storage(), y.size())
			// << std::endl;
			// VecView(x, PETSC_VIEWER_STDOUT_WORLD);
			}

			void assembleResidual() {
			std::cout << "assembleResidual" << std::endl;
			// this->getDOFManager().assembleToResidual("disp", forces);
			setSolutionToDisplacement();
			copy(rhs, forces);
			// VecAXPY(rhs, -1., f_dirichlet);

			print(displacement);
			this->assembleResidual(_not_ghost);
			// this->synchronize(SynchronizationTag::_user_1);

			// this->getDOFManager().assembleToResidual("disp", internal_forces, -1.);
			VecAXPY(rhs, 1., f_int);

			for (auto && data : enumerate(blocked)) {
			if (std::get<1>(data)) {
			VecSetValueLocal(rhs, std::get<0>(data), 0., INSERT_VALUES);
			}
			}
			VecAssemblyBegin(rhs);
			VecAssemblyEnd(rhs);

			VecView(rhs, PETSC_VIEWER_STDOUT_WORLD);
			}

			void assembleResidual(GhostType ghost_type) {
			std::cout << "assembleResidual" << std::endl;
			VecZeroEntries(f_int);

			auto cit = this->mesh.getConnectivity(_segment_2, ghost_type).begin(2);
			auto cend = this->mesh.getConnectivity(_segment_2, ghost_type).end(2);

			auto strain_it = this->strains.begin();
			auto stress_it = this->stresses.begin();
			auto L_it = this->initial_lengths.begin();

			for (; cit != cend; ++cit, ++strain_it, ++stress_it, ++L_it) {
			const auto & conn = *cit;
			UInt n1 = conn(0);
			UInt n2 = conn(1);

			Real u1 = this->displacement(n1, _x);
			Real u2 = this->displacement(n2, _x);

			strain_it = (u2 - u1) / L_it;
			stress_it = E *strain_it;
			Real f_n = A * *stress_it;

			std::cout << n1 << "[" << u1 << "]"
			<< " <-> " << n2 << "[" << u2 << "]"
			<< " : " << f_n << std::endl;

			ierr = VecSetValueLocal(f_int, n1, -f_n, ADD_VALUES);
			ierr = VecSetValueLocal(f_int, n2, f_n, ADD_VALUES);
			}

			ierr = VecAssemblyBegin(f_int);
			ierr = VecAssemblyEnd(f_int);
			// this->getDOFManager().assembleElementalArrayLocalArray(
			// forces_internal_el, internal_forces, _segment_2, ghost_type);
			}

			Real getPotentialEnergy() {
			std::cout << "getPotentialEnergy" << std::endl;
			copy(x, displacement);
			Vec Ax;

			ierr = VecDuplicate(x, &Ax);
			ierr = MatMult(K, x, Ax);
			PetscScalar res;
			ierr = VecDot(x, Ax, &res);

			return res / 2.;
			}

			Real getKineticEnergy() {
			std::cout << "getKineticEnergy" << std::endl;
			return 0;
			}

			// Real getExternalWorkIncrement() {
			// Real res = 0;

			// auto it = velocity.begin();
			// auto end = velocity.end();
			// auto if_it = internal_forces.begin();
			// auto ef_it = forces.begin();
			// auto b_it = blocked.begin();

			// for (UInt node = 0; it != end; ++it, ++if_it, ++ef_it, ++b_it, ++node) {
			// if (mesh.isLocalOrMasterNode(node))
			// res += (b_it ? -if_it : ef_it) *it;
			// }

			// mesh.getCommunicator().allReduce(res, SynchronizerOperation::_sum);

			// return res * this->getTimeStep();
			// }

			// void predictor() {}
			// void corrector() {}

			// /* ------------------------------------------------------------------------
			// */ UInt getNbData(const Array<Element> & elements,
			// const SynchronizationTag &) const {
			// return elements.size() * sizeof(Real);
			// }

			// void packData(CommunicationBuffer & buffer, const Array<Element> &
			// elements,
			// const SynchronizationTag & tag) const {
			// if (tag == SynchronizationTag::_user_1) {
			// for (const auto & el : elements) {
			// buffer << this->stresses(el.element);
			// }
			// }
			// }

			// void unpackData(CommunicationBuffer & buffer, const Array<Element> &
			// elements,
			// const SynchronizationTag & tag) {
			// if (tag == SynchronizationTag::_user_1) {
			// auto cit = this->mesh.getConnectivity(_segment_2, _ghost).begin(2);

			// for (const auto & el : elements) {
			// Real stress;
			// buffer >> stress;

			// Real f = A * stress;

			// Vector<UInt> conn = cit[el.element];
			// this->internal_forces(conn(0), _x) += -f;
			// this->internal_forces(conn(1), _x) += f;
			// }
			// }
			// }

			Real getExternalWorkIncrement() {
			std::cout << "getExternalWorkIncrement" << std::endl;
			return 0.;
			}

			template <class Functor> void applyBC(Functor && func, const ID & group_id) {
			auto & group = mesh.getElementGroup(group_id).getNodeGroup().getNodes();

			auto blocked_dofs = make_view(blocked, 1).begin();
			auto disps = make_view(displacement, 1).begin();
			auto poss = make_view(mesh.getNodes(), 1).begin();
			for (auto && node : group) {
			auto disp = Vector<Real>(disps[node]);
			auto pos = Vector<Real>(poss[node]);
			auto flags = Vector<bool>(blocked_dofs[node]);
			func(node, flags, disp, pos);
			}
			}

			const Mesh & getMesh() const { return mesh; }

			UInt getSpatialDimension() const { return 1; }

			auto & getBlockedDOFs() { return blocked; }

			void setTimeStep(Real dt) {
			std::cout << "setTimeStep" << std::endl;
			this->dt = dt;
			}

			private:
			PetscErrorCode ierr{0};
			MPI_Comm mpi_comm;
			ISLocalToGlobalMapping petsc_local_to_global;

			UInt nb_dofs;
			UInt nb_elements;

			bool lumped;

			bool is_stiffness_assembled{false};
			bool is_mass_assembled{false};
			bool is_lumped_mass_assembled{false};

			Mat K{nullptr}, J{nullptr}, M{nullptr};
			Vec rhs{nullptr}, x{nullptr}, x_save{nullptr}, dx{nullptr}, f_int{nullptr},
			f_dirichlet{nullptr};

			SNES snes;

			Real dt{0};
			Array<Real> save_displacement;

			public:
			Real E, A, rho;

			Mesh & mesh;
			Array<Real> displacement;
			Array<Real> velocity;
			Array<Real> acceleration;
			Array<bool> blocked;
			Array<Real> forces;
			Array<Real> internal_forces;

			Array<Real> stresses;
			Array<Real> strains;

			Array<Real> initial_lengths;
			};

			/* -------------------------------------------------------------------------- */
			class Sinusoidal : public BC::Dirichlet::DirichletFunctor {
			public:
			Sinusoidal(MyModel & model, Real amplitude, Real pulse_width, Real t)
			: model(model), A(amplitude), k(2 * M_PI / pulse_width),
			t(t), v{std::sqrt(model.E / model.rho)} {}

			void operator()(UInt n, Vector<bool> & /flags/, Vector<Real> & disp,
			const Vector<Real> & coord) const {
			auto x = coord(_x);
			model.velocity(n, _x) = k * v * A * sin(k * (x - v * t));
			disp(_x) = A * cos(k * (x - v * t));
			}

			private:
			MyModel & model;
			Real A{1.};
			Real k{2 * M_PI};
			Real t{1.};
			Real v{1.};
			};

			/* -------------------------------------------------------------------------- */
			int main(int argc, char * argv[]) {
			initialize(argc, argv);

			PetscInitialize(&argc, &argv, nullptr, nullptr);

			UInt prank = Communicator::getStaticCommunicator().whoAmI();
			UInt global_nb_nodes = 3;
			UInt max_steps = 400;
			Real time_step = 0.001;
			Mesh mesh(1);
			Real F = -9.81;
			bool _explicit = EXPLICIT;
			// const Real pulse_width = 0.2;
			const Real A = 0.01;

			if (prank == 0)
			genMesh(mesh, global_nb_nodes);

			mesh.distribute();

			// mesh.makePeriodic(_x);

			MyModel model(F, mesh, _explicit);

			// model.forces.zero();
			// model.blocked.zero();

			// model.applyBC(Sinusoidal(model, A, pulse_width, 0.), "all");
			// model.applyBC(BC::Dirichlet::FlagOnly(_x), "border");

			// if (!_explicit) {
			// model.getNewSolver("dynamic", TimeStepSolverType::_dynamic,
			// NonLinearSolverType::_newton_raphson);
			// model.setIntegrationScheme("dynamic", "disp",
			// IntegrationSchemeType::_trapezoidal_rule_2,
			// IntegrationScheme::_displacement);
			// } else {
			// model.getNewSolver("dynamic", TimeStepSolverType::_dynamic_lumped,
			// NonLinearSolverType::_lumped);
			// model.setIntegrationScheme("dynamic", "disp",
			// IntegrationSchemeType::_central_difference,
			// IntegrationScheme::_acceleration);
			// }

			model.setTimeStep(time_step);

			if (prank == 0) {
			std::cout << std::scientific;
			std::cout << std::setw(14) << "time"
			<< "," << std::setw(14) << "wext"
			<< "," << std::setw(14) << "epot"
			<< "," << std::setw(14) << "ekin"
			<< "," << std::setw(14) << "total"
			<< "," << std::setw(14) << "max_disp"
			<< "," << std::setw(14) << "min_disp" << std::endl;
			}
			Real wext = 0.;

			// model.getDOFManager().clearResidual();
			// model.assembleResidual();

			Real epot = 0; // model.getPotentialEnergy();
			Real ekin = 0; // model.getKineticEnergy();
			Real einit = ekin + epot;
			Real etot = ekin + epot - wext - einit;

			Real max_disp = 0., min_disp = 0.;
			for (auto && disp : model.displacement) {
			max_disp = std::max(max_disp, disp);
			min_disp = std::min(min_disp, disp);
			}

			if (prank == 0) {
			std::cout << std::setw(14) << 0. << "," << std::setw(14) << wext << ","
			<< std::setw(14) << epot << "," << std::setw(14) << ekin << ","
			<< std::setw(14) << etot << "," << std::setw(14) << max_disp
			<< "," << std::setw(14) << min_disp << std::endl;
			}

			// #if EXPLICIT == false
			// NonLinearSolver & solver =
			// model.getDOFManager().getNonLinearSolver("dynamic");

			// solver.set("max_iterations", 20);
			// #endif

			auto * dumper = new DumperParaview("dynamic", "./paraview");
			mesh.registerExternalDumper(*dumper, "dynamic", true);
			mesh.addDumpMesh(mesh);

			mesh.addDumpFieldExternalToDumper("dynamic", "displacement",
			model.displacement);
			mesh.addDumpFieldExternalToDumper("dynamic", "velocity", model.velocity);
			mesh.addDumpFieldExternalToDumper("dynamic", "forces", model.forces);
			mesh.addDumpFieldExternalToDumper("dynamic", "acceleration",
			model.acceleration);

			mesh.dump();
			max_steps = 1;
			for (UInt i = 1; i < max_steps + 1; ++i) {
			// model.applyBC(Sinusoidal(model, A, pulse_width, time_step * (i - 1)),
			// "border");

			model.solveStep();
			mesh.dump();

			epot = model.getPotentialEnergy();
			ekin = model.getKineticEnergy();
			wext += model.getExternalWorkIncrement();
			etot = ekin + epot - wext - einit;

			Real max_disp = 0., min_disp = 0.;
			for (auto && disp : model.displacement) {
			max_disp = std::max(max_disp, disp);
			min_disp = std::min(min_disp, disp);
			}

			if (prank == 0) {
			std::cout << std::setw(14) << time_step * i << "," << std::setw(14)
			<< wext << "," << std::setw(14) << epot << "," << std::setw(14)
			<< ekin << "," << std::setw(14) << etot << "," << std::setw(14)
			<< max_disp << "," << std::setw(14) << min_disp << std::endl;
			}
			}

			// output.close();
			// finalize();
			// PetscFinalize();

			return EXIT_SUCCESS;
			}

			/* -------------------------------------------------------------------------- */
			void genMesh(Mesh & mesh, UInt nb_nodes) {
			MeshAccessor mesh_accessor(mesh);
			Array<Real> & nodes = mesh_accessor.getNodes();
			Array<UInt> & conn = mesh_accessor.getConnectivity(_segment_2);

			nodes.resize(nb_nodes);

			// auto & all = mesh.createNodeGroup("all_nodes");

			for (UInt n = 0; n < nb_nodes; ++n) {
			nodes(n, _x) = n * (1. / (nb_nodes - 1));
			// all.add(n);
			}

			// mesh.createElementGroupFromNodeGroup("all", "all_nodes");

			conn.resize(nb_nodes - 1);
			for (UInt n = 0; n < nb_nodes - 1; ++n) {
			conn(n, 0) = n;
			conn(n, 1) = n + 1;
			}

			// Array<UInt> & conn_points = mesh_accessor.getConnectivity(_point_1);
			// conn_points.resize(2);

			// conn_points(0, 0) = 0;
			// conn_points(1, 0) = nb_nodes - 1;

			// auto & border = mesh.createElementGroup("border", 0);
			// border.add({_point_1, 0, _not_ghost}, true);
			// border.add({_point_1, 1, _not_ghost}, true);

			mesh_accessor.makeReady();
			}

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