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generalized_trapezoidal.hh
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/**
* @file generalized_trapezoidal.hh
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Thu Jun 30 16:40:59 2011
*
* @brief Generalized Trapezoidal Method. This implementation is taken from
* Méthodes numériques en mécanique des solides by Alain Curnier \note{ISBN:
* 2-88074-247-1}
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_GENERALIZED_TRAPEZOIDAL_HH__
#define __AKANTU_GENERALIZED_TRAPEZOIDAL_HH__
#include "integration_scheme_1st_order.hh"
__BEGIN_AKANTU__
/**
* The two differentiate equation (thermal and cinematic) 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} + \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 (\dot{u})
* 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(Real alpha) : alpha(alpha) {};
virtual ~GeneralizedTrapezoidal() {};
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
virtual void integrationSchemePred(Real delta_t,
Vector<Real> & u,
Vector<Real> & u_dot,
Vector<bool> & boundary);
virtual void integrationSchemeCorrTemp(Real delta_t,
Vector<Real> & u,
Vector<Real> & u_dot,
Vector<bool> & boundary,
Vector<Real> & delta);
virtual void integrationSchemeCorrTempRate(Real delta_t,
Vector<Real> & u,
Vector<Real> & u_dot,
Vector<bool> & boundary,
Vector<Real> & delta);
public:
/// the coeffichent @f{b@f} in the description
template<IntegrationSchemeCorrectorType type>
Real getTemperatureCoefficient(Real delta_t);
/// the coeffichent @f{a@f} in the description
template<IntegrationSchemeCorrectorType type>
Real getTemperatureRateCoefficient(Real delta_t);
private:
template<IntegrationSchemeCorrectorType type>
void integrationSchemeCorr(Real delta_t,
Vector<Real> & u,
Vector<Real> & u_dot,
Vector<bool> & boundary,
Vector<Real> & delta);
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public:
AKANTU_GET_MACRO(Alpha, alpha, Real);
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
private:
/// the @f$\alpha@f$ parameter
const Real alpha;
};
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#if defined (AKANTU_INCLUDE_INLINE_IMPL)
# include "generalized_trapezoidal_inline_impl.cc"
#endif
/**
* Forward Euler (explicit) -> condition on delta_t
*/
class ForwardEuler : public GeneralizedTrapezoidal {
public:
ForwardEuler() : GeneralizedTrapezoidal(0.) {};
};
/**
* Trapezoidal rule (implicit), midpoint rule or Crank-Nicolson
*/
class TrapezoidalRule1 : public GeneralizedTrapezoidal {
public:
TrapezoidalRule1() : GeneralizedTrapezoidal(.5) {};
};
/**
* Backward Euler (implicit)
*/
class BackwardEuler : public GeneralizedTrapezoidal {
public:
BackwardEuler() : GeneralizedTrapezoidal(1.) {};
};
__END_AKANTU__
#endif /* __AKANTU_GENERALIZED_TRAPEZOIDAL_HH__ */

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