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CentralDifferenceSolver.cpp
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CentralDifferenceSolver.cpp
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/******************************************************************************
* SOFA, Simulation Open-Framework Architecture *
* (c) 2006 INRIA, USTL, UJF, CNRS, MGH *
* *
* This program 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 program 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 program. If not, see <http://www.gnu.org/licenses/>. *
*******************************************************************************
* Authors: The SOFA Team and external contributors (see Authors.txt) *
* *
* Contact information: contact@sofa-framework.org *
******************************************************************************/
#include <sofa/component/odesolver/forward/CentralDifferenceSolver.h>
#include <sofa/core/visual/VisualParams.h>
#include <sofa/simulation/MechanicalOperations.h>
#include <sofa/simulation/VectorOperations.h>
#include <sofa/core/ObjectFactory.h>
namespace sofa::component::odesolver::forward
{
using core::VecId;
using namespace sofa::defaulttype;
using namespace core::behavior;
CentralDifferenceSolver::CentralDifferenceSolver()
: f_rayleighMass( initData(&f_rayleighMass,(SReal)0.0,"rayleighMass","Rayleigh damping coefficient related to mass"))
, d_threadSafeVisitor(initData(&d_threadSafeVisitor, false, "threadSafeVisitor", "If true, do not use realloc and free visitors in fwdInteractionForceField."))
{
}
/**
*
* 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(const core::ExecParams* params, SReal dt, sofa::core::MultiVecCoordId xResult, sofa::core::MultiVecDerivId vResult)
{
sofa::simulation::common::VectorOperations vop( params, this->getContext() );
sofa::simulation::common::MechanicalOperations mop( params, this->getContext() );
mop->setImplicit(false); // this solver is explicit only
MultiVecCoord pos(&vop, core::VecCoordId::position() );
MultiVecDeriv vel(&vop, core::VecDerivId::velocity() );
MultiVecCoord pos2(&vop, xResult /*core::VecCoordId::position()*/ );
MultiVecDeriv vel2(&vop, vResult /*core::VecDerivId::velocity()*/ );
MultiVecDeriv dx(&vop, core::VecDerivId::dx()); dx.realloc(&vop, !d_threadSafeVisitor.getValue(), true);
MultiVecDeriv f (&vop, core::VecDerivId::force() );
const SReal r = f_rayleighMass.getValue();
mop.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
mop.computeForce(f); // f = P_n - K u_n
mop.accFromF(dx, f); // dx = M^{-1} ( P_n - K u_n )
mop.projectResponse(dx); // dx is projected to the constrained space
mop.solveConstraint(dx, core::ConstraintOrder::ACC);
// apply the solution
if (r==0)
{
#ifdef SOFA_NO_VMULTIOP // unoptimized version
vel2.eq( vel, dx, dt ); // vel = vel + dt M^{-1} ( P_n - K u_n )
mop.solveConstraint(vel2,core::ConstraintOrder::VEL);
pos2.eq( pos, vel2, dt ); // pos = pos + h vel
mop.solveConstraint(pos2,core::ConstraintOrder::POS);
#else // single-operation optimization
typedef core::behavior::BaseMechanicalState::VMultiOp VMultiOp;
VMultiOp ops;
ops.resize(2);
// vel += dx * dt
ops[0].first = vel2;
ops[0].second.push_back(std::make_pair(vel.id(),1.0));
ops[0].second.push_back(std::make_pair(dx.id(),dt));
// pos += vel * dt
ops[1].first = pos2;
ops[1].second.push_back(std::make_pair(pos.id(),1.0));
ops[1].second.push_back(std::make_pair(vel2.id(),dt));
vop.v_multiop(ops);
mop.solveConstraint(vel2,core::ConstraintOrder::VEL);
mop.solveConstraint(pos2,core::ConstraintOrder::POS);
#endif
}
else
{
#ifdef SOFA_NO_VMULTIOP // unoptimized version
vel2.eq( vel, (1/dt - r/2)/(1/dt + r/2) );
vel2.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 )
pos2.eq( pos, vel2, dt ); // pos = pos + h vel
#else // single-operation optimization
typedef core::behavior::BaseMechanicalState::VMultiOp VMultiOp;
VMultiOp ops;
ops.resize(2);
// vel += dx * dt
ops[0].first = vel2;
ops[0].second.push_back(std::make_pair(vel.id(),1.0));
ops[0].second.push_back(std::make_pair(vel.id(),-1.0 + (1/dt - r/2)/(1/dt + r/2)));
ops[0].second.push_back(std::make_pair(dx.id(),1/(1/dt + r/2)));
// pos += vel * dt
ops[1].first = pos2;
ops[1].second.push_back(std::make_pair(pos.id(),1.0));
ops[1].second.push_back(std::make_pair(vel2.id(),dt));
vop.v_multiop(ops);
mop.solveConstraint(vel2,core::ConstraintOrder::VEL);
mop.solveConstraint(pos2,core::ConstraintOrder::POS);
#endif
}
}
int CentralDifferenceSolverClass = core::RegisterObject("Explicit time integrator using central difference (also known as Verlet of Leap-frog)")
.add< CentralDifferenceSolver >()
.addAlias("CentralDifference");
} // namespace sofa::component::odesolver::forward