/usr/include/sofa/component/odesolver/NewmarkImplicitSolver.h is in libsofa1-dev 1.0~beta4-10ubuntu2.
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* SOFA, Simulation Open-Framework Architecture, version 1.0 beta 4 *
* (c) 2006-2009 MGH, INRIA, USTL, UJF, CNRS *
* *
* This library 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 2.1 of the License, or (at *
* your option) any later version. *
* *
* This library 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 this library; if not, write to the Free Software Foundation, *
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. *
*******************************************************************************
* SOFA :: Modules *
* *
* Authors: The SOFA Team and external contributors (see Authors.txt) *
* *
* Contact information: contact@sofa-framework.org *
******************************************************************************/
#ifndef SOFA_COMPONENT_ODESOLVER_NEWMARKIMPLICITSOLVER_H
#define SOFA_COMPONENT_ODESOLVER_NEWMARKIMPLICITSOLVER_H
#include <sofa/core/componentmodel/behavior/OdeSolver.h>
#include <sofa/component/odesolver/OdeSolverImpl.h>
namespace sofa
{
namespace component
{
namespace odesolver
{
using namespace sofa::defaulttype;
/** Implicit time integrator using Newmark scheme.
*
* This integration scheme is based on the following equations:
*
* $x_{t+h} = x_t + h v_t + h^2/2 ( (1-2\beta) a_t + 2\beta a_{t+h} )$
* $v_{t+h} = v_t + h ( (1-\gamma) a_t + \gamma a_{t+h} )$
*
* Applied to a mechanical system where $ M a_t + (r_M M + r_K K) v_t + K x_t = f_ext$, we need to solve the following system:
*
* $ M a_{t+h} + (r_M M + r_K K) v_{t+h} + K x_{t+h} = f_ext $
* $ M a_{t+h} + (r_M M + r_K K) ( v_t + h ( (1-\gamma) a_t + \gamma a_{t+h} ) ) + K ( x_t + h v_t + h^2/2 ( (1-2\beta) a_t + 2\beta a_{t+h} ) ) = f_ext $
* $ ( M + h \gamma (r_M M + r_K K) + h^2 \beta K ) a_{t+h} = f_ext - (r_M M + r_K K) ( v_t + h (1-\gamma) a_t ) - K ( x_t + h v_t + h^2/2 (1-2\beta) a_t ) $
* $ ( (1 + h \gamma r_M) M + (h^2 \beta + h \gamma r_K) K ) a_{t+h} = f_ext - (r_M M + r_K K) v_t - K x_t - (r_M M + r_K K) ( h (1-\gamma) a_t ) - K ( h v_t + h^2/2 (1-2\beta) a_t ) $
* $ ( (1 + h \gamma r_M) M + (h^2 \beta + h \gamma r_K) K ) a_{t+h} = a_t - (r_M M + r_K K) ( h (1-\gamma) a_t ) - K ( h v_t + h^2/2 (1-2\beta) a_t ) $
*
* The current implementation first computes $a_t$ directly (as in the explicit solvers), then solves the previous system to compute $a_{t+dt}$, and finally computes the new position and velocity.
*
*/
class SOFA_COMPONENT_ODESOLVER_API NewmarkImplicitSolver : public sofa::component::odesolver::OdeSolverImpl
{
public:
Data<double> f_rayleighStiffness;
Data<double> f_rayleighMass;
Data<double> f_velocityDamping;
Data<bool> f_verbose;
Data<double> f_gamma;
Data<double> f_beta;
NewmarkImplicitSolver();
void solve (double dt, sofa::core::componentmodel::behavior::BaseMechanicalState::VecId xResult, sofa::core::componentmodel::behavior::BaseMechanicalState::VecId vResult);
/// Given a displacement as computed by the linear system inversion, how much will it affect the velocity
virtual double getVelocityIntegrationFactor() const
{
return 1.0; // getContext()->getDt();
}
/// Given a displacement as computed by the linear system inversion, how much will it affect the position
virtual double getPositionIntegrationFactor() const
{
return getContext()->getDt(); //*getContext()->getDt());
}
/// Given an input derivative order (0 for position, 1 for velocity, 2 for acceleration),
/// how much will it affect the output derivative of the given order.
///
/// This method is used to compute the compliance for contact corrections.
/// For example, a backward-Euler dynamic implicit integrator would use:
/// Input: x_t v_t a_{t+dt}
/// x_{t+dt} 1 dt dt^2
/// v_{t+dt} 0 1 dt
///
/// If the linear system is expressed on s = a_{t+dt} dt, then the final factors are:
/// Input: x_t v_t a_t s
/// x_{t+dt} 1 dt 0 dt
/// v_{t+dt} 0 1 0 1
/// a_{t+dt} 0 0 0 1/dt
/// The last column is returned by the getSolutionIntegrationFactor method.
double getIntegrationFactor(int inputDerivative, int outputDerivative) const
{
const double dt = getContext()->getDt();
double matrix[3][3] = {
{ 1, dt, 0},
{ 0, 1, 0},
{ 0, 0, 0}};
if (inputDerivative >= 3 || outputDerivative >= 3)
return 0;
else
return matrix[outputDerivative][inputDerivative];
}
/// Given a solution of the linear system,
/// how much will it affect the output derivative of the given order.
double getSolutionIntegrationFactor(int outputDerivative) const
{
const double dt = getContext()->getDt();
double vect[3] = { dt, 1, 1/dt};
if (outputDerivative >= 3)
return 0;
else
return vect[outputDerivative];
}
};
} // namespace odesolver
} // namespace component
} // namespace sofa
#endif
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