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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/NewmarkImplicitSolver.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;
NewmarkImplicitSolver::NewmarkImplicitSolver()
: f_rayleighStiffness( initData(&f_rayleighStiffness,0.1,"rayleighStiffness","Rayleigh damping coefficient related to stiffness") )
, f_rayleighMass( initData(&f_rayleighMass,0.1,"rayleighMass","Rayleigh damping coefficient related to mass"))
, f_velocityDamping( initData(&f_velocityDamping,0.,"vdamping","Velocity decay coefficient (no decay if null)") )
, f_verbose( initData(&f_verbose,false,"verbose","Dump system state at each iteration") )
, f_gamma( initData(&f_gamma, 0.5, "gamma", "Newmark scheme gamma coefficient") )
, f_beta( initData(&f_beta, 0.25, "beta", "Newmark scheme beta coefficient") )
{
}
void NewmarkImplicitSolver::solve(double dt, sofa::core::componentmodel::behavior::BaseMechanicalState::VecId xResult, sofa::core::componentmodel::behavior::BaseMechanicalState::VecId vResult)
{
MultiVector pos(this, VecId::position());
MultiVector vel(this, VecId::velocity());
MultiVector f(this, VecId::force());
MultiVector b(this, VecId::V_DERIV);
MultiVector a(this, VecId::V_DERIV);
MultiVector aResult(this, VecId::V_DERIV);
const double h = dt;
const double gamma = f_gamma.getValue();
const double beta = f_beta.getValue();
const double rM = f_rayleighMass.getValue();
const double rK = f_rayleighStiffness.getValue();
const bool verbose = f_verbose.getValue();
/* 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.
*/
// 1. Compute a_t (stored in a)
if (rM == 0.0 && rK == 0.0)
{
computeForce(f); // f = f_ext - K x
}
else
{
// accumulation through mappings is disabled as it will be done by
// addMBKv after all factors are computed
computeForce(f, true, false); // f = f_ext - K x
// values are not cleared so that contributions from computeForce
// are kept and accumulated through mappings once at the end
addMBKv(f, -rM, 0, rK, false, true); // f -= (r_M M + r_K K) v
}
accFromF(a, f);
projectResponse(a); // b is projected to the constrained space
if( verbose )
serr<<"NewmarkImplicitSolver, a0 = "<< a <<sendl;
// 2. Compute right hand term of equation on a_{t+h}
b = a; // b = a
if (rM != 0.0 || rK != 0.0 || beta != 0.5)
{
propagateDx(a);
addMBKdx(b, -h*(1-gamma)*rM, 0, h*(1-gamma)*rK + h*h*(1-2*beta)/2); // b += ( -h (1-\gamma)(r_M M + r_K K) - h^2/2 (1-2\beta) K ) a
}
addMBKv(b, 0, 0, h); // b += -h K v
if( verbose )
serr<<"NewmarkImplicitSolver, b = "<< b <<sendl;
projectResponse(b); // b is projected to the constrained space
if( verbose )
serr<<"NewmarkImplicitSolver, projected b = "<< b <<sendl;
// 3. Solve system of equations on a_{t+h}
MultiMatrix matrix(this);
matrix = MechanicalMatrix::K * (-h*h*beta - h*rK) + MechanicalMatrix::M * (1 + h*gamma*rM);
//if( verbose )
// serr<<"NewmarkImplicitSolver, matrix = "<< MechanicalMatrix::K * (h*h*beta + h*rK) + MechanicalMatrix::M * (1 + h*gamma*rM) << " = " << matrix <<sendl;
matrix.solve(aResult, b);
projectResponse(aResult);
if( verbose )
serr<<"NewmarkImplicitSolver, a1 = "<< aResult <<sendl;
// 4. Compute the new position and velocity
MultiVector newPos(this, xResult);
MultiVector newVel(this, vResult);
#ifdef SOFA_NO_VMULTIOP // unoptimized version
// x_{t+h} = x_t + h v_t + h^2/2 ( (1-2\beta) a_t + 2\beta a_{t+h} )
b.eq(vel, a, h*(0.5-beta));
b.peq(aResult, h*beta);
newPos.eq(pos, b, h);
// v_{t+h} = v_t + h ( (1-\gamma) a_t + \gamma a_{t+h} )
newVel.eq(vel, a, h*(1-gamma));
newVel.peq(aResult, h*gamma);
#else // single-operation optimization
typedef core::componentmodel::behavior::BaseMechanicalState::VMultiOp VMultiOp;
VMultiOp ops;
ops.resize(3);
ops[0].first = (VecId)b;
ops[0].second.push_back(std::make_pair((VecId)vel,1.0));
ops[0].second.push_back(std::make_pair((VecId)a, h*(0.5-beta)));
ops[0].second.push_back(std::make_pair((VecId)aResult, h*beta));
ops[1].first = (VecId)newPos;
ops[1].second.push_back(std::make_pair((VecId)pos,1.0));
ops[1].second.push_back(std::make_pair((VecId)b,h));
ops[2].first = (VecId)newVel;
ops[2].second.push_back(std::make_pair((VecId)vel,1.0));
ops[2].second.push_back(std::make_pair((VecId)a, h*(1-gamma)));
ops[2].second.push_back(std::make_pair((VecId)aResult, h*gamma));
simulation::MechanicalVMultiOpVisitor vmop(ops);
vmop.execute(this->getContext());
#endif
addSeparateGravity(dt, newVel); // v += dt*g . Used if mass wants to added G separately from the other forces to v.
if (f_velocityDamping.getValue()!=0.0)
newVel *= exp(-h*f_velocityDamping.getValue());
if( verbose )
{
serr<<"NewmarkImplicitSolver, final x = "<< newPos <<sendl;
serr<<"NewmarkImplicitSolver, final v = "<< newVel <<sendl;
}
#ifdef SOFA_HAVE_LAPACK
applyConstraints();
#endif
}
SOFA_DECL_CLASS(NewmarkImplicitSolver)
int NewmarkImplicitSolverClass = core::RegisterObject("Implicit time integrator using Newmark scheme")
.add< NewmarkImplicitSolver >()
.addAlias("Newmark");
;
} // namespace odesolver
} // namespace component
} // namespace sofa
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