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generalized_trapezoidal.hh
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/**
* @file generalized_trapezoidal.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Jul 04 2011
* @date last modification: Wed Jan 31 2018
*
* @brief Generalized Trapezoidal Method. This implementation is taken from
* Méthodes numériques en mécanique des solides by Alain Curnier \note{ISBN:
* 2-88074-247-1}
*
*
* Copyright (©) 2010-2018 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_GENERALIZED_TRAPEZOIDAL_HH_
#define AKANTU_GENERALIZED_TRAPEZOIDAL_HH_
#include "integration_scheme_1st_order.hh"
namespace akantu {
/**
* The two differentiate equation (thermal and kinematic) are :
* \f{eqnarray*}{
* C\dot{u}_{n+1} + Ku_{n+1} = q_{n+1}\\
* u_{n+1} = u_{n} + (1-\alpha) \Delta t \dot{u}_{n} + \alpha \Delta t
*\dot{u}_{n+1}
* \f}
*
* To solve it :
* Predictor :
* \f{eqnarray*}{
* u^0_{n+1} &=& u_{n} + (1-\alpha) \Delta t v_{n} \\
* \dot{u}^0_{n+1} &=& \dot{u}_{n}
* \f}
*
* Solve :
* \f[ (a C + b K^i_{n+1}) w = q_{n+1} - f^i_{n+1} - C \dot{u}^i_{n+1} \f]
*
* Corrector :
* \f{eqnarray*}{
* \dot{u}^{i+1}_{n+1} &=& \dot{u}^{i}_{n+1} + a w \\
* u^{i+1}_{n+1} &=& u^{i}_{n+1} + b w
* \f}
*
* a and b depends on the resolution method : temperature (u) or temperature
*rate (\f$\dot{u}\f$)
*
* For temperature : \f$ w = \delta u, a = 1 / (\alpha \Delta t) , b = 1 \f$ @n
* For temperature rate : \f$ w = \delta \dot{u}, a = 1, b = \alpha \Delta t \f$
*/
class GeneralizedTrapezoidal : public IntegrationScheme1stOrder {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
GeneralizedTrapezoidal(DOFManager & dof_manager, const ID & dof_id,
Real alpha = 0);
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
void predictor(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
const Array<bool> & blocked_dofs) const override;
void corrector(const SolutionType & type, Real delta_t, Array<Real> & u,
Array<Real> & u_dot, const Array<bool> & blocked_dofs,
const Array<Real> & delta) const override;
void assembleJacobian(const SolutionType & type, Real delta_t) override;
public:
/// the coeffichent \f$ b \f$ in the description
Real getTemperatureCoefficient(const SolutionType & type,
Real delta_t) const override;
/// the coeffichent \f$ a \f$ in the description
Real getTemperatureRateCoefficient(const SolutionType & type,
Real delta_t) const override;
private:
template <SolutionType type>
void allCorrector(Real delta_t, Array<Real> & u, Array<Real> & u_dot,
const Array<bool> & blocked_dofs,
const Array<Real> & delta) const;
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public:
AKANTU_GET_MACRO(Alpha, alpha, Real);
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
private:
/// the \f$\alpha\f$ parameter
Real alpha;
/// last release of K matrix
UInt k_release;
};
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
/**
* Forward Euler (explicit) -> condition on delta_t
*/
class ForwardEuler : public GeneralizedTrapezoidal {
public:
ForwardEuler(DOFManager & dof_manager, const ID & dof_id)
: GeneralizedTrapezoidal(dof_manager, dof_id, 0.){};
std::vector<std::string> getNeededMatrixList() override { return {"M"}; }
};
/**
* Trapezoidal rule (implicit), midpoint rule or Crank-Nicolson
*/
class TrapezoidalRule1 : public GeneralizedTrapezoidal {
public:
TrapezoidalRule1(DOFManager & dof_manager, const ID & dof_id)
: GeneralizedTrapezoidal(dof_manager, dof_id, .5){};
};
/**
* Backward Euler (implicit)
*/
class BackwardEuler : public GeneralizedTrapezoidal {
public:
BackwardEuler(DOFManager & dof_manager, const ID & dof_id)
: GeneralizedTrapezoidal(dof_manager, dof_id, 1.){};
};
/* -------------------------------------------------------------------------- */
} // namespace akantu
#endif /* AKANTU_GENERALIZED_TRAPEZOIDAL_HH_ */

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