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rAKA akantu
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}
*
* @section LICENSE
*
* 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
time_step
)
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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