/*
* OpenPixi - Open Particle-In-Cell (PIC) Simulator
* Copyright (C) 2012 OpenPixi.org
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
package org.openpixi.pixi.physics.solver;
import org.openpixi.pixi.physics.*;
import org.openpixi.pixi.physics.force.Force;
import org.openpixi.pixi.physics.particles.Particle;
/**
* This class is based on the simple Euler-Richardson algorithm (it
* represents a neat way of finding the numerical solutions of a differential
* equation, based on the Euler algorithm).
*
* <p>See also:
* <a href="http://www.physics.udel.edu/~bnikolic/teaching/phys660/numerical_ode/node4.html">
* http://www.physics.udel.edu/~bnikolic/teaching/phys660/numerical_ode/node4.html</a>
* </p>
*/
public class EulerRichardson implements Solver{
public EulerRichardson()
{
super();
}
/**
* Euler - Richardson algorithm.
* @param p before the update: x(t), v(t), a(t);
* after the update: x(t+dt), v(t+dt), a(t+dt/2)
*/
public void step(Particle p, Force f, double step)
{
//saving the starting value of the position & velocity
double xstart = p.getX();
double ystart = p.getY();
double vxstart = p.getVx();
double vystart = p.getVy();
//a(t) = F(v(t), x(t)) / m
p.setAx(f.getForceX(p) / p.getMass());
p.setAy(f.getForceY(p) / p.getMass());
//starting the Euler-Richardson algorithm (the equations correspond with the ones on the above mentioned website)
//v(t + dt / 2) = v(t) + a(t) * dt / 2
p.setVx(p.getVx() + p.getAx() * step / 2);
p.setVy(p.getVy() + p.getAy() * step / 2);
//x(t + dt / 2) = x(t) + v(t) * dt / 2
p.setX(p.getX() + p.getVx() * step / 2);
p.setY(p.getY() + p.getVy() * step / 2);
//a(t + dt / 2) = F(v(t + dt / 2), x(t + dt / 2)) / m
p.setAx(f.getForceX(p) / p.getMass());
p.setAy(f.getForceY(p) / p.getMass());
//x(t + dt) = x(t) + v(t + dt / 2) * dt
p.setX(xstart + p.getVx() * step);
p.setY(ystart + p.getVy() * step);
//v(t + dt) = v(t) + a(t + dt / 2) * dt
p.setVx(vxstart + p.getAx() * step);
p.setVy(vystart + p.getAy() * step);
}
public void prepare(Particle p, Force f, double step) {
}
public void complete(Particle p, Force f, double step){
}
}