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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 *
******************************************************************************/
#include <sofa/component/odesolver/CentralDifferenceSolver.h>
#include <sofa/simulation/common/MechanicalVisitor.h>
#include <sofa/core/ObjectFactory.h>
#include <math.h>
#include <iostream>
#include "sofa/helper/system/thread/CTime.h"
namespace sofa
{
namespace component
{
namespace odesolver
{
using namespace sofa::defaulttype;
using namespace core::componentmodel::behavior;
CentralDifferenceSolver::CentralDifferenceSolver()
: f_rayleighMass( initData(&f_rayleighMass,0.1,"rayleighMass","Rayleigh damping coefficient related to mass"))
{
}
/**
*
* Given current and last position $u_n$ and $u_{n-1}$, the next position $u_{n+1}$ is computed as follow:
*
* Velocity: $\dot{u}_{n-1/2} = \frac{u_n - u_{n-1}}{dt}$ $\dot{u}_{n+1/2} = \frac{u_{n+1} - u_n}{dt}$ $\dot{u}_n = \frac{u_{n+1} - u_{n-1}}{2dt}$
*
* Acceleration: $\ddot{u}_n = \frac{\dot{u}_{n+1/2} - \dot{u}_{n-1/2}}{dt}$
*
* Equilibrium: $M \ddot{u}_n + C \dot{u}_n + K u_n = P_n$
*
* Solving for $u_{n+1}$, given $u_n$ and $u_{n-1}$:
*
* $\ddot{u}_n = \frac{u_{n+1} - 2u_n + u_{n-1}}{dt^2}$
*
* $( M + \frac{dt}{2} C ) u_{n+1} = dt^2 P_n - (dt^2 K - 2M) u_n - ( M - \frac{dt}{2} C ) u_{n-1}$
* $ M u_{n+1} = dt^2 P_n - dt^2 K u_n + 2 M u_n - M u_{n-1}$
*
* Solving for $\dot{u}_{n+1/2}$, given $u_n$ and $u_{n-1/2}$:
*
* $\dot{u}_n = \frac{\dot{u}_{n+1/2} + \dot{u}_{n-1/2}}{2}$
*
* $M \frac{\dot{u}_{n+1/2} - \dot{u}_{n-1/2}}{dt} + C \frac{\dot{u}_{n+1/2} + \dot{u}_{n-1/2}}{2} + K u_n = P_n$
*
* $(\frac{M}{dt} + \frac{C}{2}) \dot{u}_{n+1/2} = P_n - K u_n - ( \frac{M}{dt} - \frac{C}{2} ) \dot{u}_{n-1/2} $
*
* If using rayleigh damping: $C = rM$
*
* $(\frac{1}{dt} + \frac{r}{2})M \dot{u}_{n+1/2} = P_n - K u_n - ( \frac{1}{dt} - \frac{r}{2} ) M \dot{u}_{n-1/2} $
*
* $ \dot{u}_{n+1/2} = \frac{\frac{1}{dt} - \frac{r}{2}}{\frac{1}{dt} + \frac{r}{2}} \dot{u}_{n-1/2} + \frac{1}{\frac{1}{dt} + \frac{r}{2}} M^{-1} ( P_n - K u_n ) $
*
* $u_{n+1} = u_n + dt \dot{u}_{n+1/2}$
*
*/
void CentralDifferenceSolver::solve(double dt)
{
MultiVector pos(this, VecId::position());
MultiVector vel(this, VecId::velocity());
MultiVector f(this, VecId::force());
MultiVector dx(this, VecId::dx());
const double r = f_rayleighMass.getValue();
addSeparateGravity(dt); // v += dt*g . Used if mass wants to added G separately from the other forces to v.
//projectVelocity(vel); // initial velocities are projected to the constrained space
// compute the current force
computeForce(f); // f = P_n - K u_n
accFromF(dx, f); // dx = M^{-1} ( P_n - K u_n )
projectResponse(dx); // dx is projected to the constrained space
// apply the solution
if (r==0)
{
#ifdef SOFA_NO_VMULTIOP // unoptimized version
vel.peq( dx, dt ); // vel = vel + dt M^{-1} ( P_n - K u_n )
pos.peq( vel, dt ); // pos = pos + h vel
#else // single-operation optimization
typedef core::componentmodel::behavior::BaseMechanicalState::VMultiOp VMultiOp;
VMultiOp ops;
ops.resize(2);
// vel += dx * dt
ops[0].first = (VecId)vel;
ops[0].second.push_back(std::make_pair((VecId)vel,1.0));
ops[0].second.push_back(std::make_pair((VecId)dx,dt));
// pos += vel * dt
ops[1].first = (VecId)pos;
ops[1].second.push_back(std::make_pair((VecId)pos,1.0));
ops[1].second.push_back(std::make_pair((VecId)vel,dt));
simulation::MechanicalVMultiOpVisitor vmop(ops);
vmop.execute(getContext());
#endif
}
else
{
#ifdef SOFA_NO_VMULTIOP // unoptimized version
vel.teq( (1/dt - r/2)/(1/dt + r/2) );
vel.peq( dx, 1/(1/dt + r/2) ); // vel = \frac{\frac{1}{dt} - \frac{r}{2}}{\frac{1}{dt} + \frac{r}{2}} vel + \frac{1}{\frac{1}{dt} + \frac{r}{2}} M^{-1} ( P_n - K u_n )
pos.peq( vel, dt ); // pos = pos + h vel
#else // single-operation optimization
typedef core::componentmodel::behavior::BaseMechanicalState::VMultiOp VMultiOp;
VMultiOp ops;
ops.resize(2);
// vel += dx * dt
ops[0].first = (VecId)vel;
ops[0].second.push_back(std::make_pair((VecId)vel,(1/dt - r/2)/(1/dt + r/2)));
ops[0].second.push_back(std::make_pair((VecId)dx,1/(1/dt + r/2)));
// pos += vel * dt
ops[1].first = (VecId)pos;
ops[1].second.push_back(std::make_pair((VecId)pos,1.0));
ops[1].second.push_back(std::make_pair((VecId)vel,dt));
simulation::MechanicalVMultiOpVisitor vmop(ops);
vmop.execute(getContext());
#endif
}
#ifdef SOFA_HAVE_LAPACK
applyConstraints();
#endif
}
SOFA_DECL_CLASS(CentralDifferenceSolver)
int CentralDifferenceSolverClass = core::RegisterObject("Explicit time integrator using central difference (also known as Verlet of Leap-frop)")
.add< CentralDifferenceSolver >()
.addAlias("CentralDifference");
;
} // namespace odesolver
} // namespace component
} // namespace sofa
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