/// <summary>
/// Copy a Particle
/// </summary>
/// <param name="mass"></param>
public Particle(Particle particle)
{
mass = particle.mass;
position = particle.position;
momentum = particle.momentum;
interactions = particle.interactions;
}
/// <summary>
/// Allow timeInterval to pass for the Particle with given netForce applied.
/// Recommend putting Particle into a PhysicalSystem and using a PhysicalSystem.Iterate() instead.
/// </summary>
/// <param name="timeInterval"></param>
/// <param name="netForce"></param>
public void Iterate(Time timeInterval, Force netForce)
{
Momentum changeInMomentum = timeInterval * netForce;
Displacement changeInPosition = timeInterval * Velocity(momentum + changeInMomentum / 2.0);
momentum += changeInMomentum;
position += changeInPosition;
}
/// <summary>
/// Update the positions and momenta of all particles in the system using Runge-Kutta method...
/// Does not seem to be working correctly. Leave private until debugged.
/// </summary>
/// <param name="timeInterval">The amount of time passing during this iteration</param>
private void RK4Iterate(Time timeInterval)
{
List <Task> tasks = new List <Task>();
// store temporary particle data for Runge-Kutta method
Particle[] virtualParticles = new Particle[particles.Count];
Momentum[,] momenta = new Momentum[particles.Count, 4];
Displacement[,] displacements = new Displacement[particles.Count, 4];
// initialize virtualParticles
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(InitializeParticle(particleIndex));
}
Task.WaitAll(tasks.ToArray());
// first iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(CalculateRungeKuttaCoefficients(particleIndex, 0));
}
Task.WaitAll(tasks.ToArray());
// update before 2nd iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(UpdateParticleBefore2ndOr3rdIteration(particleIndex, 0));
}
Task.WaitAll(tasks.ToArray());
// 2nd iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(CalculateRungeKuttaCoefficients(particleIndex, 1));
}
Task.WaitAll(tasks.ToArray());
// update before 3rd iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(UpdateParticleBefore2ndOr3rdIteration(particleIndex, 1));
}
Task.WaitAll(tasks.ToArray());
// 3rd iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(CalculateRungeKuttaCoefficients(particleIndex, 2));
}
Task.WaitAll(tasks.ToArray());
// update before 4th iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(UpdateParticleBefore4thIteration(particleIndex));
}
Task.WaitAll(tasks.ToArray());
// 4th iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(CalculateRungeKuttaCoefficients(particleIndex, 3));
}
Task.WaitAll(tasks.ToArray());
// update actual particles using the Runge-Kutta coefficients
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(UpdateParticleUsingRungeKuttaCoefficients(particleIndex));
}
Task.WaitAll(tasks.ToArray());
async Task InitializeParticle(int particleIndex)
{
virtualParticles[particleIndex] = new Particle(particles[particleIndex]);
for (int iterationNumber = 0; iterationNumber < 4; iterationNumber++)
{
momenta[particleIndex, iterationNumber] = new Momentum();
}
}
async Task CalculateRungeKuttaCoefficients(int particleIndex, int iterationNumber)
{
displacements[particleIndex, iterationNumber] =
timeInterval * particles[particleIndex].Velocity();
foreach (Interaction interaction in virtualParticles[particleIndex].interactions)
{
momenta[particleIndex, iterationNumber] +=
timeInterval * interaction.InteractionForce(virtualParticles[particleIndex], interaction.B);
}
}
async Task UpdateParticleBefore2ndOr3rdIteration(int particleIndex, int iterationJustFinished)
{
virtualParticles[particleIndex] = new Particle(particles[particleIndex]);
virtualParticles[particleIndex].momentum +=
momenta[particleIndex, iterationJustFinished]; // / 2.0;
virtualParticles[particleIndex].position +=
displacements[particleIndex, iterationJustFinished]; // / 2.0;
}
async Task UpdateParticleBefore4thIteration(int particleIndex)
{
virtualParticles[particleIndex] = new Particle(particles[particleIndex]);
virtualParticles[particleIndex].momentum +=
momenta[particleIndex, 2];
virtualParticles[particleIndex].position +=
displacements[particleIndex, 2];
}
async Task UpdateParticleUsingRungeKuttaCoefficients(int particleIndex)
{
//particles[particleIndex].position += (displacements[particleIndex, 0] +
// 2.0 * displacements[particleIndex, 1] + 2.0 * displacements[particleIndex, 2] +
// displacements[particleIndex, 3]) / 6.0;
//particles[particleIndex].momentum += (momenta[particleIndex, 0] +
// 2.0 * momenta[particleIndex, 1] + 2.0 * momenta[particleIndex, 2] +
// momenta[particleIndex, 3]) / 6.0;
particles[particleIndex].position += (displacements[particleIndex, 0] +
displacements[particleIndex, 1]) / 2.0;
particles[particleIndex].momentum += (momenta[particleIndex, 0] +
momenta[particleIndex, 1]) / 2.0;
}
}
/// <summary>
/// Heun's method for numerical integration
/// </summary>
/// <param name="timeStep"></param>
private void HeunIntegration(Time timeStep)
{
List <Task> tasks = new List <Task>();
// store temporary particle data for Runge-Kutta method
Displacement[] initialPositions = new Displacement[particles.Count];
Momentum[] initialMomenta = new Momentum[particles.Count];
Momentum[,] momenta = new Momentum[particles.Count, 2];
Displacement[,] displacements = new Displacement[particles.Count, 2];
// store initial condition
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(StoreInitialConditions(particleIndex));
}
Task.WaitAll(tasks.ToArray());
// first iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(CalculateRungeKuttaCoefficients(particleIndex, 0));
}
Task.WaitAll(tasks.ToArray());
// update particles based on linear estimate
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(LinearUpdate(particleIndex));
}
Task.WaitAll(tasks.ToArray());
// 2nd iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(CalculateRungeKuttaCoefficients(particleIndex, 1));
}
Task.WaitAll(tasks.ToArray());
// update actual particles using the Runge-Kutta coefficients
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(UpdateParticles(particleIndex));
}
Task.WaitAll(tasks.ToArray());
async Task StoreInitialConditions(int particleIndex)
{
initialPositions[particleIndex] = particles[particleIndex].position;
initialMomenta[particleIndex] = particles[particleIndex].momentum;
}
async Task CalculateRungeKuttaCoefficients(int particleIndex, int iterationNumber)
{
displacements[particleIndex, iterationNumber] =
timeStep * particles[particleIndex].Velocity();
Force netForce = new Force();
foreach (Interaction interaction in particles[particleIndex].interactions)
{
netForce += interaction.InteractionForce();
}
momenta[particleIndex, iterationNumber] = timeStep * netForce;
}
async Task LinearUpdate(int particleIndex)
{
particles[particleIndex].position += timeStep * particles[particleIndex].Velocity(
particles[particleIndex].momentum + momenta[particleIndex, 0] / 2.0);
particles[particleIndex].momentum += momenta[particleIndex, 0];
}
async Task UpdateParticles(int particleIndex)
{
particles[particleIndex].position = initialPositions[particleIndex] +
(displacements[particleIndex, 0] + displacements[particleIndex, 1]) / 2.0;
particles[particleIndex].momentum = initialMomenta[particleIndex] +
(momenta[particleIndex, 0] + momenta[particleIndex, 1]) / 2.0;
}
}
/// <summary>
/// Update the positions and momenta of all particles in the system
/// using the 2nd-order Runge-Kutta method.
/// Doesn't perform as well as NotQuiteRK2(). Am I interpretting the Runge-Kutta method incorrectly?
/// </summary>
/// <param name="timeInterval">The amount of time passing during this iteration</param>
private void RK2Iterate(Time timeInterval)
{
List <Task> tasks = new List <Task>();
// store temporary particle data for Runge-Kutta method
Displacement[] initialPositions = new Displacement[particles.Count];
Momentum[] initialMomenta = new Momentum[particles.Count];
Momentum[,] momenta = new Momentum[particles.Count, 2];
Displacement[,] displacements = new Displacement[particles.Count, 2];
// store initial condition
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(StoreInitialConditions(particleIndex));
}
Task.WaitAll(tasks.ToArray());
// first iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(FirstIteration(particleIndex));
}
Task.WaitAll(tasks.ToArray());
// 2nd iteration
for (int particleIndex = 0; particleIndex < particles.Count; particleIndex++)
{
tasks.Add(SecondIteration(particleIndex));
}
Task.WaitAll(tasks.ToArray());
async Task StoreInitialConditions(int particleIndex)
{
initialPositions[particleIndex] = particles[particleIndex].position;
initialMomenta[particleIndex] = particles[particleIndex].momentum;
}
async Task FirstIteration(int particleIndex)
{
Force netForce = new Force();
foreach (Interaction interaction in particles[particleIndex].interactions)
{
netForce += interaction.InteractionForce();
}
// The first iteration in RK2 only moves a half step.
Momentum changeInMomentum = timeInterval * netForce / 2.0;
particles[particleIndex].position += timeInterval *
particles[particleIndex].Velocity(
particles[particleIndex].momentum + changeInMomentum / 2.0) / 2.0;
particles[particleIndex].momentum += changeInMomentum;
}
async Task SecondIteration(int particleIndex)
{
Force netForce = new Force();
foreach (Interaction interaction in particles[particleIndex].interactions)
{
netForce += interaction.InteractionForce();
}
Momentum changeInMomentum = timeInterval * netForce;
particles[particleIndex].position = initialPositions[particleIndex] + timeInterval *
particles[particleIndex].Velocity(
particles[particleIndex].momentum + changeInMomentum / 2.0);
particles[particleIndex].momentum = initialMomenta[particleIndex] + changeInMomentum;
}
}
/// <summary>
/// The Velocity of this Particle given a momentum
/// </summary>
/// <returns>The Velocity of this Particle given a momentum</returns>
public Velocity Velocity(Momentum p)
{
return(p / mass);
}