/// <summary>
/// Constructor.
/// </summary>
public Evolver(RunParams parms, VDelegate V, string outputDir)
{
m_gridSizeX = parms.GridSize.Width;
m_gridSizeY = parms.GridSize.Height;
m_latticeSpacing = parms.LatticeSpacing;
m_totalTime = parms.TotalTime;
m_deltaT = parms.TimeStep;
m_totalNumTimeSteps = (int)Math.Round(parms.TotalTime / parms.TimeStep) + 1;
m_currentTimeStepIndex = 0;
m_mass1 = parms.Mass1;
m_mass2 = parms.Mass2;
m_totalMass = (parms.Mass1 + parms.Mass2);
m_reducedMass = (parms.Mass1 * parms.Mass2) / m_totalMass;
m_potential = V;
m_initialMomentum1 = new Vec2(parms.InitialWavePacketMomentum1);
m_initialMomentum2 = new Vec2(parms.InitialWavePacketMomentum2);
m_initialPosition1 = new Vec2(parms.InitialWavePacketCenter1);
m_initialPosition2 = new Vec2(parms.InitialWavePacketCenter2);
m_sigmaRel = parms.InitialWavePacketSize * Math.Sqrt(m_totalMass / m_mass2);
m_sigmaCm = parms.InitialWavePacketSize * Math.Sqrt(m_mass1 / m_totalMass);
m_dampingBorderWidth = parms.DampingBorderWidth;
m_dampingFactor = parms.DampingFactor;
m_numFramesToSave = parms.NumFramesToSave;
m_lastSavedFrame = -1;
m_outputDir = outputDir;
m_multiThread = parms.MultiThread;
m_visscherWf = null;
}
/// <summary>
/// Worker method.
/// </summary>
protected override void WorkerMethod()
{
// Reset counters
m_currentTimeStepIndex = 0;
m_lastSavedFrame = -1;
// Precompute the potential everywhere on the grid
float[][] V = PrecomputeV();
// Create the initial relative wavefunction
Vec2 r0 = m_initialPosition1 - m_initialPosition2;
Vec2 p0 = (m_mass2 / m_totalMass) * m_initialMomentum1 - (m_mass1 / m_totalMass) * m_initialMomentum2;
int sx = 2 * m_gridSizeX - 1; // The range of r = r1-r2 is twice the range of r1, r2
int sy = 2 * m_gridSizeY - 1;
WaveFunction initialWf = WaveFunctionUtils.CreateGaussianWavePacket(
sx, sy, m_latticeSpacing, true, m_reducedMass, r0, m_sigmaRel, p0, m_multiThread
);
m_visscherWf = new VisscherWf(initialWf, V, m_reducedMass, m_deltaT, m_multiThread);
initialWf = null; // Allow initialWf to be garbage collected
TimeStepCompleted();
if (IsCancelled)
{
return;
}
// Main loop: Evolve the relative wavefunction
while (m_currentTimeStepIndex < m_totalNumTimeSteps)
{
// Evolve the wavefunction by one timestep
EvolveByOneTimeStep(m_visscherWf, V);
m_currentTimeStepIndex++;
// Report progress to the client
TimeStepCompleted();
if (IsCancelled)
{
return;
}
}
}
/// <summary>
/// Damps the wavefunction amplitude near the region boundary.
/// </summary>
private void ApplyDamping(VisscherWf wf)
{
int sx = wf.GridSizeX;
int sy = wf.GridSizeY;
int d = m_dampingBorderWidth;
float[] factors = new float[d];
for (int i = 0; i < d; i++)
{
factors[i] = (float)(1.0 - m_dampingFactor * m_deltaT * (1.0 - Math.Sin(((Math.PI / 2) * i) / d)));
}
// Top border
for (int y = 0; y < d; y++)
{
float[] wfDataIPy = wf.ImagPartP[y];
float[] wfDataIMy = wf.ImagPartM[y];
float[] wfDataRy = wf.RealPart[y];
float f = factors[y];
for (int x = 0; x < sx; x++)
{
wfDataRy[x] *= f;
wfDataIPy[x] *= f;
wfDataIMy[x] *= f;
}
}
// Bottom border
for (int y = sy - d; y < sy; y++)
{
float[] wfDataIPy = wf.ImagPartP[y];
float[] wfDataIMy = wf.ImagPartM[y];
float[] wfDataRy = wf.RealPart[y];
float f = factors[sy - 1 - y];
for (int x = 0; x < sx; x++)
{
wfDataRy[x] *= f;
wfDataIPy[x] *= f;
wfDataIMy[x] *= f;
}
}
// Left and right borders
for (int y = 0; y < sy; y++)
{
float[] wfDataIPy = wf.ImagPartP[y];
float[] wfDataIMy = wf.ImagPartM[y];
float[] wfDataRy = wf.RealPart[y];
for (int x = 0; x < d; x++)
{
float f = factors[x];
wfDataRy[x] *= f;
wfDataIPy[x] *= f;
wfDataIMy[x] *= f;
}
for (int x = sx - d; x < sx; x++)
{
float f = factors[sx - 1 - x];
wfDataRy[x] *= f;
wfDataIPy[x] *= f;
wfDataIMy[x] *= f;
}
}
}
/// <summary>
/// Evolves the wavefunction by a single time step
/// </summary>
private void EvolveByOneTimeStep(VisscherWf wf, float[][] V)
{
int sx = wf.GridSizeX;
int sy = wf.GridSizeY;
int sxm1 = sx - 1;
int sym1 = sy - 1;
float keFactor = 1.0f / (2 * m_reducedMass * wf.LatticeSpacing * wf.LatticeSpacing);
float alpha = 5.0f;
float beta = -4.0f / 3.0f;
float delta = 1.0f / 12.0f;
// Compute the next real part in terms of the current imaginary part
TdseUtils.Misc.ForLoop(0, sy, y =>
{
int yp = (y < sym1) ? y + 1 : 0;
int ypp = (yp < sym1) ? yp + 1 : 0;
int ym = (y > 0) ? y - 1 : sym1;
int ymm = (ym > 0) ? ym - 1 : sym1;
float[] V_y = V[y];
float[] wfR_y = wf.RealPart[y];
float[] wfI_y = wf.ImagPartP[y];
float[] wfI_ym = wf.ImagPartP[ym];
float[] wfI_yp = wf.ImagPartP[yp];
float[] wfI_ymm = wf.ImagPartP[ymm];
float[] wfI_ypp = wf.ImagPartP[ypp];
for (int x = 0; x < sx; x++)
{
int xp = (x < sxm1) ? x + 1 : 0;
int xpp = (xp < sxm1) ? xp + 1 : 0;
int xm = (x > 0) ? x - 1 : sxm1;
int xmm = (xm > 0) ? xm - 1 : sxm1;
// A discretization of the 2nd derivative, whose error term is O(a^6)
float ke = keFactor * (
alpha * wfI_y[x] +
beta * (wfI_y[xm] + wfI_y[xp] + wfI_ym[x] + wfI_yp[x]) +
delta * (wfI_y[xmm] + wfI_y[xpp] + wfI_ymm[x] + wfI_ypp[x])
);
float pe = V_y[x] * wfI_y[x];
wfR_y[x] += m_deltaT * (ke + pe);
}
}, m_multiThread);
// Swap prev and post imaginary parts
float[][] temp = wf.ImagPartM;
wf.ImagPartM = wf.ImagPartP;
wf.ImagPartP = temp;
// Compute the next imaginary part in terms of the current real part
TdseUtils.Misc.ForLoop(0, sy, y =>
{
int yp = (y < sym1) ? y + 1 : 0;
int ypp = (yp < sym1) ? yp + 1 : 0;
int ym = (y > 0) ? y - 1 : sym1;
int ymm = (ym > 0) ? ym - 1 : sym1;
float[] V_y = V[y];
float[] wfIM_y = wf.ImagPartM[y];
float[] wfIP_y = wf.ImagPartP[y];
float[] wfR_y = wf.RealPart[y];
float[] wfR_ym = wf.RealPart[ym];
float[] wfR_yp = wf.RealPart[yp];
float[] wfR_ymm = wf.RealPart[ymm];
float[] wfR_ypp = wf.RealPart[ypp];
for (int x = 0; x < sx; x++)
{
int xp = (x < sxm1) ? x + 1 : 0;
int xpp = (xp < sxm1) ? xp + 1 : 0;
int xm = (x > 0) ? x - 1 : sxm1;
int xmm = (xm > 0) ? xm - 1 : sxm1;
// A discretization of the 2nd derivative, whose error term is O(a^6)
float ke = keFactor * (
alpha * wfR_y[x] +
beta * (wfR_y[xm] + wfR_y[xp] + wfR_ym[x] + wfR_yp[x]) +
delta * (wfR_y[xmm] + wfR_y[xpp] + wfR_ymm[x] + wfR_ypp[x])
);
float pe = V_y[x] * wfR_y[x];
wfIP_y[x] = wfIM_y[x] - m_deltaT * (ke + pe);
}
}, m_multiThread);
// Optionally perform damping to suppress reflection and transmission at the borders.
if ((m_dampingBorderWidth > 0) && (m_dampingFactor > 0.0f))
{
ApplyDamping(wf);
}
}