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test_model_solver_dynamic.cc
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/**
* @file test_dof_manager_default.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date Wed Feb 24 12:28:44 2016
*
* @brief Test default dof manager
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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 "dof_manager.hh"
#include "mesh.hh"
#include "mesh_accessor.hh"
#include "model_solver.hh"
#include "sparse_matrix.hh"
/* -------------------------------------------------------------------------- */
#include <fstream>
/* -------------------------------------------------------------------------- */
#ifndef EXPLICIT
#define EXPLICIT true
#endif
using namespace akantu;
class MyModel;
static void genMesh(Mesh & mesh, UInt nb_nodes);
/**
* =\o-----o-----o-> F
* | |
* |---- L ----|
*/
class MyModel : public ModelSolver {
public:
MyModel(Real F, Mesh & mesh, bool lumped)
: ModelSolver(mesh, "model_solver", 0),
displacement(mesh.getNbNodes(), 1, "disp"),
velocity(mesh.getNbNodes(), 1, "velo"),
acceleration(mesh.getNbNodes(), 1, "accel"),
blocked(mesh.getNbNodes(), 1, "blocked"),
forces(mesh.getNbNodes(), 1, "force_ext"),
internal_forces(mesh.getNbNodes(), 1, "force_int"), mesh(mesh),
nb_dofs(mesh.getNbNodes()), E(1.), A(1.), rho(1.), lumped(lumped) {
this->initDOFManager();
this->getDOFManager().registerDOFs("disp", displacement, _dst_nodal);
this->getDOFManager().registerDOFsDerivative("disp", 1, velocity);
this->getDOFManager().registerDOFsDerivative("disp", 2, acceleration);
this->getDOFManager().registerBlockedDOFs("disp", blocked);
this->getDOFManager().getNewMatrix("K", _symmetric);
this->getDOFManager().getNewMatrix("M", "K");
this->getDOFManager().getNewMatrix("J", "K");
this->getDOFManager().getNewLumpedMatrix("M");
if (lumped) {
this->assembleLumpedMass();
} else {
this->assembleMass();
this->assembleStiffness();
}
this->assembleJacobian();
displacement.set(0.);
velocity.set(0.);
acceleration.set(0.);
forces.set(0.);
blocked.set(false);
forces(nb_dofs - 1, _x) = F;
// displacement(nb_dofs - 1, _x) = .1;
blocked(0, _x) = true;
}
void assembleLumpedMass() {
Array<Real> & M = this->getDOFManager().getLumpedMatrix("M");
M.clear();
Array<Real> m_all_el(this->nb_dofs - 1, 2);
Array<Real>::vector_iterator m_it = m_all_el.begin(2);
Array<UInt>::const_vector_iterator cit =
this->mesh.getConnectivity(_segment_2).begin(2);
Array<UInt>::const_vector_iterator cend =
this->mesh.getConnectivity(_segment_2).end(2);
for (; cit != cend; ++cit, ++m_it) {
const Vector<UInt> & 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);
Real M_n = rho * A * L / 2;
(*m_it)(0) = (*m_it)(1) = M_n;
}
this->getDOFManager().assembleElementalArrayLocalArray(
m_all_el, M, _segment_2, _not_ghost);
}
void assembleMass() {
SparseMatrix & M = this->getDOFManager().getMatrix("M");
M.clear();
Array<Real> m_all_el(this->nb_dofs - 1, 4);
Array<Real>::matrix_iterator m_it = m_all_el.begin(2, 2);
Array<UInt>::const_vector_iterator cit =
this->mesh.getConnectivity(_segment_2).begin(2);
Array<UInt>::const_vector_iterator cend =
this->mesh.getConnectivity(_segment_2).end(2);
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 (; cit != cend; ++cit, ++m_it) {
const Vector<UInt> & 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);
Matrix<Real> & m_el = *m_it;
m_el = m;
m_el *= rho * A * L / 6.;
}
this->getDOFManager().assembleElementalMatricesToMatrix(
"M", "disp", m_all_el, _segment_2);
}
void assembleJacobian() {}
void assembleStiffness() {
SparseMatrix & K = this->getDOFManager().getMatrix("K");
K.clear();
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_dofs - 1, 4);
Array<Real>::matrix_iterator k_it = k_all_el.begin(2, 2);
Array<UInt>::const_vector_iterator cit =
this->mesh.getConnectivity(_segment_2).begin(2);
Array<UInt>::const_vector_iterator cend =
this->mesh.getConnectivity(_segment_2).end(2);
for (; cit != cend; ++cit, ++k_it) {
const Vector<UInt> & 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);
Matrix<Real> & k_el = *k_it;
k_el = k;
k_el *= E * A / L;
}
this->getDOFManager().assembleElementalMatricesToMatrix(
"K", "disp", k_all_el, _segment_2);
}
void assembleResidual() {
this->getDOFManager().assembleToResidual("disp", forces);
Array<Real> forces_internal_el(this->nb_dofs - 1, 2);
Array<Real>::vector_iterator f_it = forces_internal_el.begin(2);
Array<UInt>::const_vector_iterator cit =
this->mesh.getConnectivity(_segment_2).begin(2);
Array<UInt>::const_vector_iterator cend =
this->mesh.getConnectivity(_segment_2).end(2);
for (; cit != cend; ++cit, ++f_it) {
const Vector<UInt> & 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);
Real u1 = this->displacement(n1, _x);
Real u2 = this->displacement(n2, _x);
Real f_n = E * A / L * (u2 - u1);
Vector<Real> & f = *f_it;
f(0) = -f_n;
f(1) = f_n;
}
internal_forces.clear();
this->getDOFManager().assembleElementalArrayLocalArray(
forces_internal_el, internal_forces, _segment_2, _not_ghost);
this->getDOFManager().assembleToResidual("disp", internal_forces, -1.);
}
Real getPotentialEnergy() {
Real res = 0;
if (!lumped) {
res = this->mulVectMatVect(this->displacement,
this->getDOFManager().getMatrix("K"),
this->displacement);
} else {
Array<UInt>::const_vector_iterator cit =
this->mesh.getConnectivity(_segment_2).begin(2);
Array<UInt>::const_vector_iterator cend =
this->mesh.getConnectivity(_segment_2).end(2);
for (; cit != cend; ++cit) {
const Vector<UInt> & 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);
Real u1 = this->displacement(n1, _x);
Real u2 = this->displacement(n2, _x);
Real strain = (u2 - u1) / L;
res += strain * E * strain * A * L;
}
}
return res / 2.;
}
Real getKineticEnergy() {
Real res = 0;
if (!lumped) {
res = this->mulVectMatVect(
this->velocity, this->getDOFManager().getMatrix("M"), this->velocity);
} else {
Array<Real> & m = this->getDOFManager().getLumpedMatrix("M");
Array<Real>::const_scalar_iterator it = velocity.begin();
Array<Real>::const_scalar_iterator end = velocity.end();
Array<Real>::const_scalar_iterator m_it = m.begin();
for (; it != end; ++it, ++m_it) {
res += *m_it * *it * *it;
}
}
return res / 2.;
}
Real mulVectMatVect(const Array<Real> & x, const SparseMatrix & A,
const Array<Real> & y) {
Array<Real> Ay(this->nb_dofs);
A.matVecMul(y, Ay);
Real res = 0.;
Array<Real>::const_scalar_iterator it = Ay.begin();
Array<Real>::const_scalar_iterator end = Ay.end();
Array<Real>::const_scalar_iterator x_it = x.begin();
for (; it != end; ++it, ++x_it) {
res += *x_it * *it;
}
return res;
}
void predictor() {}
void corrector() {}
Array<Real> displacement;
Array<Real> velocity;
Array<Real> acceleration;
Array<bool> blocked;
Array<Real> forces;
Array<Real> internal_forces;
private:
Mesh & mesh;
UInt nb_dofs;
Real E, A, rho;
bool lumped;
};
/* -------------------------------------------------------------------------- */
int main(int argc, char * argv[]) {
initialize(argc, argv);
UInt nb_nodes = 201;
UInt max_steps = 2000;
Real time_step = 0.001;
Mesh mesh(1);
Real F = -9.81;
bool _explicit = EXPLICIT;
genMesh(mesh, nb_nodes);
MyModel model(F, mesh, _explicit);
if (!_explicit) {
model.getNewSolver("dynamic", _tsst_dynamic, _nls_newton_raphson);
model.setIntegrationScheme("dynamic", "disp", _ist_trapezoidal_rule_2,
IntegrationScheme::_displacement);
} else {
model.getNewSolver("dynamic", _tsst_dynamic_lumped, _nls_lumped);
model.setIntegrationScheme("dynamic", "disp", _ist_central_difference,
IntegrationScheme::_acceleration);
}
model.setTimeStep(time_step);
const Array<Real> & disp = model.displacement;
const Array<Real> & velo = model.velocity;
const Array<Real> & reac = model.internal_forces;
// #if EXPLICIT == true
// std::ofstream output("output_dynamic_explicit.csv");
// #else
// std::ofstream output("output_dynamic_implicit.csv");
// #endif
std::cout << std::setw(8) << "time"
<< "," << std::setw(8) << "disp"
<< "," << std::setw(8) << "velo"
<< "," << std::setw(8) << "reac"
<< "," << std::setw(8) << "wext"
<< "," << std::setw(8) << "epot"
<< "," << std::setw(8) << "ekin"
<< "," << std::setw(8) << "total"
<< std::endl;
Real wext = 0;
Real epot = model.getPotentialEnergy();
Real ekin = model.getKineticEnergy();
Real einit = ekin + epot;
std::cout << std::setw(8) << 0.
<< "," << std::setw(8) << disp(nb_nodes - 1, _x)
<< "," << std::setw(8) << velo(nb_nodes - 1, _x)
<< "," << std::setw(8) << (-reac(0, _x))
<< "," << std::setw(8) << wext
<< "," << std::setw(8) << epot
<< "," << std::setw(8) << ekin
<< "," << std::setw(8) << (ekin + epot - wext - einit)
<< std::endl;
#if EXPLICIT == false
// NonLinearSolver & solver =
// model.getDOFManager().getNonLinearSolver("dynamic");
#endif
for (UInt i = 1; i < max_steps + 1; ++i) {
model.solveStep();
// #if EXPLICIT == false
// UInt nb_iter = solver.get("nb_iterations");
// Real error = solver.get("error");
// bool converged = solver.get("converged");
// std::cout << error << " " << nb_iter << " -> " << converged << std::endl;
// #endif
wext += F * velo(nb_nodes - 1, 0) * time_step;
epot = model.getPotentialEnergy();
ekin = model.getKineticEnergy();
Real etot = ekin + epot - wext - einit;
std::cout << std::setw(8) << time_step * i
<< "," << std::setw(8) << disp(nb_nodes - 1, _x)
<< "," << std::setw(8) << velo(nb_nodes - 1, _x)
<< "," << std::setw(8) << (-reac(0, _x))
<< "," << std::setw(8) << wext
<< "," << std::setw(8) << epot
<< "," << std::setw(8) << ekin
<< "," << std::setw(8) << (etot)
<< std::endl;
if (std::abs(etot) > 1e-7) {
AKANTU_DEBUG_ERROR("The total energy of the system is not conserved!");
}
}
// output.close();
finalize();
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);
for (UInt n = 0; n < nb_nodes; ++n) {
nodes(n, _x) = n * (1. / (nb_nodes - 1));
}
conn.resize(nb_nodes - 1);
for (UInt n = 0; n < nb_nodes - 1; ++n) {
conn(n, 0) = n;
conn(n, 1) = n + 1;
}
}
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