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gevolution.hpp
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//////////////////////////
// gevolution.hpp
//////////////////////////
//
// Geneva algorithms for evolution of metric perturbations
// and relativistic free-streaming particles (gevolution)
//
// 1. Suite of Fourier-based methods for the computation of the
// relativistic scalar (Phi, Phi-Psi) and vector modes [see J. Adamek,
// R. Durrer, and M. Kunz, Class. Quant. Grav. 31, 234006 (2014)]
//
// 2. Collection of "update position" and "update velocity/momentum" methods
// [see J. Adamek, D. Daverio, R. Durrer, and M. Kunz, JCAP 1607, 053 (2016)]
//
// 3. Collection of projection methods for the construction of the
// stress-energy-tensor
//
// 4. Fourier-space projection methods for the computation of the
// curl and divergence of the velocity field
//
// Author: Julian Adamek (Université de Genève & Observatoire de Paris & Queen Mary University of London)
//
// Last modified: April 2019
//
//////////////////////////
#ifndef GEVOLUTION_HEADER
#define GEVOLUTION_HEADER
#ifndef Cplx
#define Cplx Imag
#endif
using namespace std;
using namespace LATfield2;
//////////////////////////
// prepareFTsource (1)
//////////////////////////
// Description:
// construction of real-space source tensor for Fourier-based solvers
//
// Arguments:
// phi reference to field configuration
// Tij reference to symmetric tensor field containing the space-space
// components of the stress-energy tensor (rescaled by a^3)
// Sij reference to allocated symmetric tensor field which will contain
// the source tensor (may be identical to Tji)
// coeff scaling coefficient for Tij ("8 pi G dx^2 / a")
//
// Returns:
//
//////////////////////////
template <class FieldType>
void prepareFTsource(Field<FieldType> &phi, Field<FieldType> &Tij, Field<FieldType> &Sij, const double coeff)
{
Site x(phi.lattice());
for (x.first(); x.test(); x.next())
{
// 0-0-component:
Sij(x, 0, 0) = coeff * Tij(x, 0, 0);
#ifdef PHINONLINEAR
#ifdef ORIGINALMETRIC
Sij(x, 0, 0) -= 4. * phi(x) * (phi(x - 0) + phi(x + 0) - 2. * phi(x));
Sij(x, 0, 0) -= 0.5 * (phi(x + 0) - phi(x - 0)) * (phi(x + 0) - phi(x - 0));
#else
Sij(x, 0, 0) += 0.5 * (phi(x + 0) - phi(x - 0)) * (phi(x + 0) - phi(x - 0));
#endif
#endif
// 1-1-component:
Sij(x, 1, 1) = coeff * Tij(x, 1, 1);
#ifdef PHINONLINEAR
#ifdef ORIGINALMETRIC
Sij(x, 1, 1) -= 4. * phi(x) * (phi(x - 1) + phi(x + 1) - 2. * phi(x));
Sij(x, 1, 1) -= 0.5 * (phi(x + 1) - phi(x - 1)) * (phi(x + 1) - phi(x - 1));
#else
Sij(x, 1, 1) += 0.5 * (phi(x + 1) - phi(x - 1)) * (phi(x + 1) - phi(x - 1));
#endif
#endif
// 2-2-component:
Sij(x, 2, 2) = coeff * Tij(x, 2, 2);
#ifdef PHINONLINEAR
#ifdef ORIGINALMETRIC
Sij(x, 2, 2) -= 4. * phi(x) * (phi(x - 2) + phi(x + 2) - 2. * phi(x));
Sij(x, 2, 2) -= 0.5 * (phi(x + 2) - phi(x - 2)) * (phi(x + 2) - phi(x - 2));
#else
Sij(x, 2, 2) += 0.5 * (phi(x + 2) - phi(x - 2)) * (phi(x + 2) - phi(x - 2));
#endif
#endif
// 0-1-component:
Sij(x, 0, 1) = coeff * Tij(x, 0, 1);
#ifdef PHINONLINEAR
Sij(x, 0, 1) += phi(x + 0) * phi(x + 1) - phi(x) * phi(x + 0 + 1);
#ifdef ORIGINALMETRIC
Sij(x, 0, 1) -= 1.5 * phi(x) * phi(x);
Sij(x, 0, 1) += 1.5 * phi(x + 0) * phi(x + 0);
Sij(x, 0, 1) += 1.5 * phi(x + 1) * phi(x + 1);
Sij(x, 0, 1) -= 1.5 * phi(x + 0 + 1) * phi(x + 0 + 1);
#else
Sij(x, 0, 1) += 0.5 * phi(x) * phi(x);
Sij(x, 0, 1) -= 0.5 * phi(x + 0) * phi(x + 0);
Sij(x, 0, 1) -= 0.5 * phi(x + 1) * phi(x + 1);
Sij(x, 0, 1) += 0.5 * phi(x + 0 + 1) * phi(x + 0 + 1);
#endif
#endif
// 0-2-component:
Sij(x, 0, 2) = coeff * Tij(x, 0, 2);
#ifdef PHINONLINEAR
Sij(x, 0, 2) += phi(x + 0) * phi(x + 2) - phi(x) * phi(x + 0 + 2);
#ifdef ORIGINALMETRIC
Sij(x, 0, 2) -= 1.5 * phi(x) * phi(x);
Sij(x, 0, 2) += 1.5 * phi(x + 0) * phi(x + 0);
Sij(x, 0, 2) += 1.5 * phi(x + 2) * phi(x + 2);
Sij(x, 0, 2) -= 1.5 * phi(x + 0 + 2) * phi(x + 0 + 2);
#else
Sij(x, 0, 2) += 0.5 * phi(x) * phi(x);
Sij(x, 0, 2) -= 0.5 * phi(x + 0) * phi(x + 0);
Sij(x, 0, 2) -= 0.5 * phi(x + 2) * phi(x + 2);
Sij(x, 0, 2) += 0.5 * phi(x + 0 + 2) * phi(x + 0 + 2);
#endif
#endif
// 1-2-component:
Sij(x, 1, 2) = coeff * Tij(x, 1, 2);
#ifdef PHINONLINEAR
Sij(x, 1, 2) += phi(x + 1) * phi(x + 2) - phi(x) * phi(x + 1 + 2);
#ifdef ORIGINALMETRIC
Sij(x, 1, 2) -= 1.5 * phi(x) * phi(x);
Sij(x, 1, 2) += 1.5 * phi(x + 1) * phi(x + 1);
Sij(x, 1, 2) += 1.5 * phi(x + 2) * phi(x + 2);
Sij(x, 1, 2) -= 1.5 * phi(x + 1 + 2) * phi(x + 1 + 2);
#else
Sij(x, 1, 2) += 0.5 * phi(x) * phi(x);
Sij(x, 1, 2) -= 0.5 * phi(x + 1) * phi(x + 1);
Sij(x, 1, 2) -= 0.5 * phi(x + 2) * phi(x + 2);
Sij(x, 1, 2) += 0.5 * phi(x + 1 + 2) * phi(x + 1 + 2);
#endif
#endif
}
}
//////////////////////////
// prepareFTsource (2)
//////////////////////////
// Description:
// construction of real-space source field for Fourier-based solvers
//
// Arguments:
// phi reference to field configuration (first Bardeen potential)
// chi reference to field configuration (difference between Bardeen potentials, phi-psi)
// source reference to fully dressed source field (rescaled by a^3)
// bgmodel background model of the source (rescaled by a^3) to be subtracted
// result reference to allocated field which will contain the result (may be identical to source)
// coeff diffusion coefficient ("3 H_conformal dx^2 / dtau")
// coeff2 scaling coefficient for the source ("4 pi G dx^2 / a")
// coeff3 scaling coefficient for the psi-term ("3 H_conformal^2 dx^2")
//
// Returns:
//
//////////////////////////
template <class FieldType>
void prepareFTsource(Field<FieldType> &phi, Field<FieldType> &chi, Field<FieldType> &source,
const FieldType bgmodel, Field<FieldType> &result, const double coeff, const double coeff2, const double coeff3)
{
Site x(phi.lattice());
for (x.first(); x.test(); x.next())
{
result(x) = coeff2 * (source(x) - bgmodel);
#ifdef PHINONLINEAR
#ifdef ORIGINALMETRIC
result(x) *= 1. - 4. * phi(x);
result(x) -= 0.375 * (phi(x - 0) - phi(x + 0)) * (phi(x - 0) - phi(x + 0));
result(x) -= 0.375 * (phi(x - 1) - phi(x + 1)) * (phi(x - 1) - phi(x + 1));
result(x) -= 0.375 * (phi(x - 2) - phi(x + 2)) * (phi(x - 2) - phi(x + 2));
#else
result(x) *= 1. - 2. * phi(x);
result(x) += 0.125 * (phi(x - 0) - phi(x + 0)) * (phi(x - 0) - phi(x + 0));
result(x) += 0.125 * (phi(x - 1) - phi(x + 1)) * (phi(x - 1) - phi(x + 1));
result(x) += 0.125 * (phi(x - 2) - phi(x + 2)) * (phi(x - 2) - phi(x + 2));
#endif
#endif
result(x) += (coeff3 - coeff) * phi(x) - coeff3 * chi(x);
}
}
#ifdef FFT3D
//////////////////////////
// projectFTscalar
//////////////////////////
// Description:
// projection of the Fourier image of a tensor field on the trace-free
// longitudinal (scalar) component
//
// Arguments:
// SijFT reference to the Fourier image of the input tensor field
// chiFT reference to allocated field which will contain the Fourier
// image of the trace-free longitudinal (scalar) component
//
// Returns:
//
//////////////////////////
void projectFTscalar(Field<Cplx> &SijFT, Field<Cplx> &chiFT, const int add = 0)
{
const int linesize = chiFT.lattice().size(1);
int i;
Real *gridk2;
Cplx *kshift;
rKSite k(chiFT.lattice());
gridk2 = (Real *)malloc(linesize * sizeof(Real));
kshift = (Cplx *)malloc(linesize * sizeof(Cplx));
for (i = 0; i < linesize; i++)
{
gridk2[i] = 2. * (Real)linesize * sin(M_PI * (Real)i / (Real)linesize);
kshift[i] = gridk2[i] * Cplx(cos(M_PI * (Real)i / (Real)linesize), -sin(M_PI * (Real)i / (Real)linesize));
gridk2[i] *= gridk2[i];
}
k.first();
if (k.coord(0) == 0 && k.coord(1) == 0 && k.coord(2) == 0)
{
chiFT(k) = Cplx(0., 0.);
k.next();
}
if (add)
{
for (; k.test(); k.next())
{
chiFT(k) += ((gridk2[k.coord(1)] + gridk2[k.coord(2)] - 2. * gridk2[k.coord(0)]) * SijFT(k, 0, 0) +
(gridk2[k.coord(0)] + gridk2[k.coord(2)] - 2. * gridk2[k.coord(1)]) * SijFT(k, 1, 1) +
(gridk2[k.coord(0)] + gridk2[k.coord(1)] - 2. * gridk2[k.coord(2)]) * SijFT(k, 2, 2) -
6. * kshift[k.coord(0)] * kshift[k.coord(1)] * SijFT(k, 0, 1) -
6. * kshift[k.coord(0)] * kshift[k.coord(2)] * SijFT(k, 0, 2) -
6. * kshift[k.coord(1)] * kshift[k.coord(2)] * SijFT(k, 1, 2)) /
(2. * (gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)]) * (gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)]) * linesize);
}
}
else
{
for (; k.test(); k.next())
{
chiFT(k) = ((gridk2[k.coord(1)] + gridk2[k.coord(2)] - 2. * gridk2[k.coord(0)]) * SijFT(k, 0, 0) +
(gridk2[k.coord(0)] + gridk2[k.coord(2)] - 2. * gridk2[k.coord(1)]) * SijFT(k, 1, 1) +
(gridk2[k.coord(0)] + gridk2[k.coord(1)] - 2. * gridk2[k.coord(2)]) * SijFT(k, 2, 2) -
6. * kshift[k.coord(0)] * kshift[k.coord(1)] * SijFT(k, 0, 1) -
6. * kshift[k.coord(0)] * kshift[k.coord(2)] * SijFT(k, 0, 2) -
6. * kshift[k.coord(1)] * kshift[k.coord(2)] * SijFT(k, 1, 2)) /
(2. * (gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)]) * (gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)]) * linesize);
}
}
free(gridk2);
free(kshift);
}
//////////////////////////
// evolveFTvector
//////////////////////////
// Description:
// projects the Fourier image of a tensor field on the spin-1 component
// used as a source for the evolution of the vector perturbation
//
// Arguments:
// SijFT reference to the Fourier image of the input tensor field
// BiFT reference to the Fourier image of the vector perturbation
// a2dtau conformal time step times scale factor squared (a^2 * dtau)
//
// Returns:
//
//////////////////////////
void evolveFTvector(Field<Cplx> &SijFT, Field<Cplx> &BiFT, const Real a2dtau)
{
const int linesize = BiFT.lattice().size(1);
int i;
Real *gridk2;
Cplx *kshift;
rKSite k(BiFT.lattice());
Real k4;
gridk2 = (Real *)malloc(linesize * sizeof(Real));
kshift = (Cplx *)malloc(linesize * sizeof(Cplx));
for (i = 0; i < linesize; i++)
{
gridk2[i] = 2. * (Real)linesize * sin(M_PI * (Real)i / (Real)linesize);
kshift[i] = gridk2[i] * Cplx(cos(M_PI * (Real)i / (Real)linesize), -sin(M_PI * (Real)i / (Real)linesize));
gridk2[i] *= gridk2[i];
}
k.first();
if (k.coord(0) == 0 && k.coord(1) == 0 && k.coord(2) == 0)
{
BiFT(k, 0) = Cplx(0., 0.);
BiFT(k, 1) = Cplx(0., 0.);
BiFT(k, 2) = Cplx(0., 0.);
k.next();
}
for (; k.test(); k.next())
{
k4 = gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)];
k4 *= k4;
BiFT(k, 0) += Cplx(0., -2. * a2dtau / k4) * (kshift[k.coord(0)].conj() * ((gridk2[k.coord(1)] + gridk2[k.coord(2)]) * SijFT(k, 0, 0) - gridk2[k.coord(1)] * SijFT(k, 1, 1) - gridk2[k.coord(2)] * SijFT(k, 2, 2) - 2. * kshift[k.coord(1)] * kshift[k.coord(2)] * SijFT(k, 1, 2)) + (gridk2[k.coord(1)] + gridk2[k.coord(2)] - gridk2[k.coord(0)]) * (kshift[k.coord(1)] * SijFT(k, 0, 1) + kshift[k.coord(2)] * SijFT(k, 0, 2)));
BiFT(k, 1) += Cplx(0., -2. * a2dtau / k4) * (kshift[k.coord(1)].conj() * ((gridk2[k.coord(0)] + gridk2[k.coord(2)]) * SijFT(k, 1, 1) - gridk2[k.coord(0)] * SijFT(k, 0, 0) - gridk2[k.coord(2)] * SijFT(k, 2, 2) - 2. * kshift[k.coord(0)] * kshift[k.coord(2)] * SijFT(k, 0, 2)) + (gridk2[k.coord(0)] + gridk2[k.coord(2)] - gridk2[k.coord(1)]) * (kshift[k.coord(0)] * SijFT(k, 0, 1) + kshift[k.coord(2)] * SijFT(k, 1, 2)));
BiFT(k, 2) += Cplx(0., -2. * a2dtau / k4) * (kshift[k.coord(2)].conj() * ((gridk2[k.coord(0)] + gridk2[k.coord(1)]) * SijFT(k, 2, 2) - gridk2[k.coord(0)] * SijFT(k, 0, 0) - gridk2[k.coord(1)] * SijFT(k, 1, 1) - 2. * kshift[k.coord(0)] * kshift[k.coord(1)] * SijFT(k, 0, 1)) + (gridk2[k.coord(0)] + gridk2[k.coord(1)] - gridk2[k.coord(2)]) * (kshift[k.coord(0)] * SijFT(k, 0, 2) + kshift[k.coord(1)] * SijFT(k, 1, 2)));
}
free(gridk2);
free(kshift);
}
//////////////////////////
// projectFTvector
//////////////////////////
// Description:
// projects the Fourier image of a vector field on the transverse component
// and solves the constraint equation for the vector perturbation
//
// Arguments:
// SiFT reference to the Fourier image of the input vector field
// BiFT reference to the Fourier image of the vector perturbation (can be identical to input)
// coeff rescaling coefficient (default 1)
// modif modification k^2 -> k^2 + modif (default 0)
//
// Returns:
//
//////////////////////////
void projectFTvector(Field<Cplx> &SiFT, Field<Cplx> &BiFT, const Real coeff = 1., const Real modif = 0.)
{
const int linesize = BiFT.lattice().size(1);
int i;
Real *gridk2;
Cplx *kshift;
rKSite k(BiFT.lattice());
Real k2;
Cplx tmp(0., 0.);
gridk2 = (Real *)malloc(linesize * sizeof(Real));
kshift = (Cplx *)malloc(linesize * sizeof(Cplx));
for (i = 0; i < linesize; i++)
{
gridk2[i] = 2. * (Real)linesize * sin(M_PI * (Real)i / (Real)linesize);
kshift[i] = gridk2[i] * Cplx(cos(M_PI * (Real)i / (Real)linesize), -sin(M_PI * (Real)i / (Real)linesize));
gridk2[i] *= gridk2[i];
}
k.first();
if (k.coord(0) == 0 && k.coord(1) == 0 && k.coord(2) == 0)
{
BiFT(k, 0) = Cplx(0., 0.);
BiFT(k, 1) = Cplx(0., 0.);
BiFT(k, 2) = Cplx(0., 0.);
k.next();
}
for (; k.test(); k.next())
{
k2 = gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)];
tmp = (kshift[k.coord(0)] * SiFT(k, 0) + kshift[k.coord(1)] * SiFT(k, 1) + kshift[k.coord(2)] * SiFT(k, 2)) / k2;
BiFT(k, 0) = (SiFT(k, 0) - kshift[k.coord(0)].conj() * tmp) * 4. * coeff / (k2 + modif);
BiFT(k, 1) = (SiFT(k, 1) - kshift[k.coord(1)].conj() * tmp) * 4. * coeff / (k2 + modif);
BiFT(k, 2) = (SiFT(k, 2) - kshift[k.coord(2)].conj() * tmp) * 4. * coeff / (k2 + modif);
}
free(gridk2);
free(kshift);
}
//////////////////////////
// projectFTtensor
//////////////////////////
// Description:
// projection of the Fourier image of a tensor field on the transverse
// trace-free tensor component
//
// Arguments:
// SijFT reference to the Fourier image of the input tensor field
// hijFT reference to allocated field which will contain the Fourier
// image of the transverse trace-free tensor component
//
// Returns:
//
//////////////////////////
void projectFTtensor(Field<Cplx> &SijFT, Field<Cplx> &hijFT)
{
const int linesize = hijFT.lattice().size(1);
int i;
Real *gridk2;
Cplx *kshift;
rKSite k(hijFT.lattice());
Cplx SxxFT, SxyFT, SxzFT, SyyFT, SyzFT, SzzFT;
Real k2, k6;
gridk2 = (Real *)malloc(linesize * sizeof(Real));
kshift = (Cplx *)malloc(linesize * sizeof(Cplx));
for (i = 0; i < linesize; i++)
{
gridk2[i] = 2. * (Real)linesize * sin(M_PI * (Real)i / (Real)linesize);
kshift[i] = gridk2[i] * Cplx(cos(M_PI * (Real)i / (Real)linesize), -sin(M_PI * (Real)i / (Real)linesize));
gridk2[i] *= gridk2[i];
}
k.first();
if (k.coord(0) == 0 && k.coord(1) == 0 && k.coord(2) == 0)
{
for (i = 0; i < hijFT.components(); i++)
hijFT(k, i) = Cplx(0., 0.);
k.next();
}
for (; k.test(); k.next())
{
SxxFT = SijFT(k, 0, 0);
SxyFT = SijFT(k, 0, 1);
SxzFT = SijFT(k, 0, 2);
SyyFT = SijFT(k, 1, 1);
SyzFT = SijFT(k, 1, 2);
SzzFT = SijFT(k, 2, 2);
k2 = gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)];
k6 = k2 * k2 * k2 * linesize;
hijFT(k, 0, 0) = ((gridk2[k.coord(0)] - k2) * ((gridk2[k.coord(0)] - k2) * SxxFT + 2. * kshift[k.coord(0)] * (kshift[k.coord(1)] * SxyFT + kshift[k.coord(2)] * SxzFT)) + ((gridk2[k.coord(0)] + k2) * (gridk2[k.coord(1)] + k2) - 2. * k2 * k2) * SyyFT + ((gridk2[k.coord(0)] + k2) * (gridk2[k.coord(2)] + k2) - 2. * k2 * k2) * SzzFT + 2. * (gridk2[k.coord(0)] + k2) * kshift[k.coord(1)] * kshift[k.coord(2)] * SyzFT) / k6;
hijFT(k, 0, 1) = (2. * (gridk2[k.coord(0)] - k2) * (gridk2[k.coord(1)] - k2) * SxyFT + (gridk2[k.coord(2)] + k2) * kshift[k.coord(0)].conj() * kshift[k.coord(1)].conj() * SzzFT + (gridk2[k.coord(0)] - k2) * kshift[k.coord(1)].conj() * (kshift[k.coord(0)].conj() * SxxFT + 2. * kshift[k.coord(2)] * SxzFT) + (gridk2[k.coord(1)] - k2) * kshift[k.coord(0)].conj() * (kshift[k.coord(1)].conj() * SyyFT + 2. * kshift[k.coord(2)] * SyzFT)) / k6;
hijFT(k, 0, 2) = (2. * (gridk2[k.coord(0)] - k2) * (gridk2[k.coord(2)] - k2) * SxzFT + (gridk2[k.coord(1)] + k2) * kshift[k.coord(0)].conj() * kshift[k.coord(2)].conj() * SyyFT + (gridk2[k.coord(0)] - k2) * kshift[k.coord(2)].conj() * (kshift[k.coord(0)].conj() * SxxFT + 2. * kshift[k.coord(1)] * SxyFT) + (gridk2[k.coord(2)] - k2) * kshift[k.coord(0)].conj() * (kshift[k.coord(2)].conj() * SzzFT + 2. * kshift[k.coord(1)] * SyzFT)) / k6;
hijFT(k, 1, 1) = ((gridk2[k.coord(1)] - k2) * ((gridk2[k.coord(1)] - k2) * SyyFT + 2. * kshift[k.coord(1)] * (kshift[k.coord(0)] * SxyFT + kshift[k.coord(2)] * SyzFT)) + ((gridk2[k.coord(1)] + k2) * (gridk2[k.coord(0)] + k2) - 2. * k2 * k2) * SxxFT + ((gridk2[k.coord(1)] + k2) * (gridk2[k.coord(2)] + k2) - 2. * k2 * k2) * SzzFT + 2. * (gridk2[k.coord(1)] + k2) * kshift[k.coord(0)] * kshift[k.coord(2)] * SxzFT) / k6;
hijFT(k, 1, 2) = (2. * (gridk2[k.coord(1)] - k2) * (gridk2[k.coord(2)] - k2) * SyzFT + (gridk2[k.coord(0)] + k2) * kshift[k.coord(1)].conj() * kshift[k.coord(2)].conj() * SxxFT + (gridk2[k.coord(1)] - k2) * kshift[k.coord(2)].conj() * (kshift[k.coord(1)].conj() * SyyFT + 2. * kshift[k.coord(0)] * SxyFT) + (gridk2[k.coord(2)] - k2) * kshift[k.coord(1)].conj() * (kshift[k.coord(2)].conj() * SzzFT + 2. * kshift[k.coord(0)] * SxzFT)) / k6;
hijFT(k, 2, 2) = ((gridk2[k.coord(2)] - k2) * ((gridk2[k.coord(2)] - k2) * SzzFT + 2. * kshift[k.coord(2)] * (kshift[k.coord(0)] * SxzFT + kshift[k.coord(1)] * SyzFT)) + ((gridk2[k.coord(2)] + k2) * (gridk2[k.coord(0)] + k2) - 2. * k2 * k2) * SxxFT + ((gridk2[k.coord(2)] + k2) * (gridk2[k.coord(1)] + k2) - 2. * k2 * k2) * SyyFT + 2. * (gridk2[k.coord(2)] + k2) * kshift[k.coord(0)] * kshift[k.coord(1)] * SxyFT) / k6;
}
free(gridk2);
free(kshift);
}
//////////////////////////
// solveModifiedPoissonFT
//////////////////////////
// Description:
// Modified Poisson solver using the standard Fourier method
//
// Arguments:
// sourceFT reference to the Fourier image of the source field
// potFT reference to the Fourier image of the potential
// coeff coefficient applied to the source ("4 pi G / a")
// modif modification k^2 -> k^2 + modif (default 0 gives standard Poisson equation)
//
// Returns:
//
//////////////////////////
void solveModifiedPoissonFT(Field<Cplx> &sourceFT, Field<Cplx> &potFT, Real coeff, const Real modif = 0.)
{
const int linesize = potFT.lattice().size(1);
int i;
Real *gridk2;
Real *sinc;
rKSite k(potFT.lattice());
gridk2 = (Real *)malloc(linesize * sizeof(Real));
coeff /= -((long)linesize * (long)linesize * (long)linesize);
for (i = 0; i < linesize; i++)
{
gridk2[i] = 2. * (Real)linesize * sin(M_PI * (Real)i / (Real)linesize);
gridk2[i] *= gridk2[i];
}
k.first();
if (k.coord(0) == 0 && k.coord(1) == 0 && k.coord(2) == 0)
{
if (modif == 0.)
potFT(k) = Cplx(0., 0.);
else
potFT(k) = sourceFT(k) * coeff / modif;
k.next();
}
for (; k.test(); k.next())
{
potFT(k) = sourceFT(k) * coeff / (gridk2[k.coord(0)] + gridk2[k.coord(1)] + gridk2[k.coord(2)] + modif);
}
free(gridk2);
}
#endif
Real update_q_5th(double dtau, double dx, part_simple *part, double *ref_dist, part_simple_info partInfo, Field<Real> **fields, Site *sites, int nfield, double *params, double *outputs, int noutputs)
{
#define phi (*fields[0])
#define chi (*fields[1])
#define Bi (*fields[2])
#define achi (*fields[3])
#define xphi (sites[0])
#define xchi (sites[1])
#define xB (sites[2])
#define xachi (sites[3])
// modified so that params = [a,BiScale,phi0,M,boxsize]
Real gradphi[3] = {0, 0, 0};
Real aphi = 0.;
Real pgradB[3] = {0, 0, 0};
Real fac = 0.;
// Real Acnf = 1.;
// Real dAcnf = 0.;
Real daphix = 0.;
Real daphiy = 0.;
Real daphiz = 0.;
//-------modification----------
// gradient of aphi
if (nfield >= 4 && fields[3] != NULL)
{
fac = params[2];
aphi = ((1 - ref_dist[0]) * (1. - ref_dist[1]) * (1. - ref_dist[2]) * achi(xachi) + ref_dist[0] * (1. - ref_dist[1]) * (1. - ref_dist[2]) * achi(xachi + 0) + (1 - ref_dist[0]) * ref_dist[1] * (1. - ref_dist[2]) * achi(xachi + 1) + ref_dist[0] * ref_dist[1] * (1. - ref_dist[2]) * achi(xachi + 0 + 1) + (1 - ref_dist[0]) * (1. - ref_dist[1]) * ref_dist[2] * achi(xachi + 2) + ref_dist[0] * (1. - ref_dist[1]) * ref_dist[2] * achi(xachi + 2 + 0) + (1 - ref_dist[0]) * ref_dist[1] * ref_dist[2] * achi(xachi + 2 + 1) + ref_dist[0] * ref_dist[1] * ref_dist[2] * achi(xachi + 2 + 0 + 1)) * fac;
daphix = fac * ((1. - ref_dist[1]) *
(1. - ref_dist[2]) * (achi(xachi + 0) - achi(xachi)) +
ref_dist[1] * (1. - ref_dist[2]) * (achi(xachi + 1 + 0) - achi(xachi + 1)) + (1. - ref_dist[1]) * ref_dist[2] * (achi(xachi + 2 + 0) - achi(xachi + 2)) + ref_dist[1] * ref_dist[2] * (achi(xachi + 2 + 1 + 0) - achi(xachi + 2 + 1)));
daphiy = fac * ((1. - ref_dist[0]) * (1. - ref_dist[2]) * (achi(xachi + 1) - achi(xachi)) + ref_dist[0] * (1. - ref_dist[2]) * (achi(xachi + 1 + 0) - achi(xachi + 0)) + (1. - ref_dist[0]) * ref_dist[2] * (achi(xachi + 2 + 1) - achi(xachi + 2)) + ref_dist[0] * ref_dist[2] * (achi(xachi + 2 + 1 + 0) - achi(xachi + 2 + 0)));
daphiz = fac * ((1. - ref_dist[0]) * (1. - ref_dist[1]) * (achi(xachi + 2) - achi(xachi)) + ref_dist[0] * (1. - ref_dist[1]) * (achi(xachi + 2 + 0) - achi(xachi + 0)) + (1. - ref_dist[0]) * ref_dist[1] * (achi(xachi + 2 + 1) - achi(xachi + 1)) + ref_dist[0] * ref_dist[1] * (achi(xachi + 2 + 1 + 0) - achi(xachi + 1 + 0)));
gradphi[0] = -aphi * daphix;
gradphi[1] = -aphi * daphiy;
gradphi[2] = -aphi * daphiz;
// dAcnf = aphi*aphi/2.;
// Acnf = 1. + aphi*aphi/2.;
}
Real v2 = (*part).vel[0] * (*part).vel[0] + (*part).vel[1] * (*part).vel[1] + (*part).vel[2] * (*part).vel[2];
Real e2 = v2 + params[0] * params[0];
// gradient of phi
gradphi[0] += (1. - ref_dist[1]) * (1. - ref_dist[2]) * (phi(xphi + 0) - phi(xphi));
gradphi[1] += (1. - ref_dist[0]) * (1. - ref_dist[2]) * (phi(xphi + 1) - phi(xphi));
gradphi[2] += (1. - ref_dist[0]) * (1. - ref_dist[1]) * (phi(xphi + 2) - phi(xphi));
gradphi[0] += ref_dist[1] * (1. - ref_dist[2]) * (phi(xphi + 1 + 0) - phi(xphi + 1));
gradphi[1] += ref_dist[0] * (1. - ref_dist[2]) * (phi(xphi + 1 + 0) - phi(xphi + 0));
gradphi[2] += ref_dist[0] * (1. - ref_dist[1]) * (phi(xphi + 2 + 0) - phi(xphi + 0));
gradphi[0] += (1. - ref_dist[1]) * ref_dist[2] * (phi(xphi + 2 + 0) - phi(xphi + 2));
gradphi[1] += (1. - ref_dist[0]) * ref_dist[2] * (phi(xphi + 2 + 1) - phi(xphi + 2));
gradphi[2] += (1. - ref_dist[0]) * ref_dist[1] * (phi(xphi + 2 + 1) - phi(xphi + 1));
gradphi[0] += ref_dist[1] * ref_dist[2] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 2 + 1));
gradphi[1] += ref_dist[0] * ref_dist[2] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 2 + 0));
gradphi[2] += ref_dist[0] * ref_dist[1] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 1 + 0));
gradphi[0] *= (v2 + e2) / e2;
gradphi[1] *= (v2 + e2) / e2;
gradphi[2] *= (v2 + e2) / e2;
if (nfield >= 2 && fields[1] != NULL) // chi-field
{
gradphi[0] -= (1. - ref_dist[1]) * (1. - ref_dist[2]) * (chi(xchi + 0) - chi(xchi));
gradphi[1] -= (1. - ref_dist[0]) * (1. - ref_dist[2]) * (chi(xchi + 1) - chi(xchi));
gradphi[2] -= (1. - ref_dist[0]) * (1. - ref_dist[1]) * (chi(xchi + 2) - chi(xchi));
gradphi[0] -= ref_dist[1] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 1));
gradphi[1] -= ref_dist[0] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 0));
gradphi[2] -= ref_dist[0] * (1. - ref_dist[1]) * (chi(xchi + 2 + 0) - chi(xchi + 0));
gradphi[0] -= (1. - ref_dist[1]) * ref_dist[2] * (chi(xchi + 2 + 0) - chi(xchi + 2));
gradphi[1] -= (1. - ref_dist[0]) * ref_dist[2] * (chi(xchi + 2 + 1) - chi(xchi + 2));
gradphi[2] -= (1. - ref_dist[0]) * ref_dist[1] * (chi(xchi + 2 + 1) - chi(xchi + 1));
gradphi[0] -= ref_dist[1] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 1));
gradphi[1] -= ref_dist[0] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 0));
gradphi[2] -= ref_dist[0] * ref_dist[1] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 1 + 0));
gradphi[0] += 2.0 * aphi * daphix;
gradphi[1] += 2.0 * aphi * daphiy;
gradphi[2] += 2.0 * aphi * daphiz;
}
e2 = sqrt(e2);
if (nfield >= 3 && fields[2] != NULL) // B-field
{
pgradB[0] = ((1. - ref_dist[2]) * (Bi(xB + 0, 1) - Bi(xB, 1)) + ref_dist[2] * (Bi(xB + 2 + 0, 1) - Bi(xB + 2, 1))) * (*part).vel[1];
pgradB[0] += ((1. - ref_dist[1]) * (Bi(xB + 0, 2) - Bi(xB, 2)) + ref_dist[1] * (Bi(xB + 1 + 0, 2) - Bi(xB + 1, 2))) * (*part).vel[2];
pgradB[0] += (1. - ref_dist[1]) * (1. - ref_dist[2]) * ((ref_dist[0] - 1.) * Bi(xB - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB, 0) + ref_dist[0] * Bi(xB + 0, 0)) * (*part).vel[0];
pgradB[0] += ref_dist[1] * (1. - ref_dist[2]) * ((ref_dist[0] - 1.) * Bi(xB + 1 - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB + 1, 0) + ref_dist[0] * Bi(xB + 1 + 0, 0)) * (*part).vel[0];
pgradB[0] += (1. - ref_dist[1]) * ref_dist[2] * ((ref_dist[0] - 1.) * Bi(xB + 2 - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB + 2, 0) + ref_dist[0] * Bi(xB + 2 + 0, 0)) * (*part).vel[0];
pgradB[0] += ref_dist[1] * ref_dist[2] * ((ref_dist[0] - 1.) * Bi(xB + 2 + 1 - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB + 2 + 1, 0) + ref_dist[0] * Bi(xB + 2 + 1 + 0, 0)) * (*part).vel[0];
pgradB[1] = ((1. - ref_dist[0]) * (Bi(xB + 1, 2) - Bi(xB, 2)) + ref_dist[0] * (Bi(xB + 1 + 0, 2) - Bi(xB + 0, 2))) * (*part).vel[2];
pgradB[1] += ((1. - ref_dist[2]) * (Bi(xB + 1, 0) - Bi(xB, 0)) + ref_dist[2] * (Bi(xB + 1 + 2, 0) - Bi(xB + 2, 0))) * (*part).vel[0];
pgradB[1] += (1. - ref_dist[0]) * (1. - ref_dist[2]) * ((ref_dist[1] - 1.) * Bi(xB - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB, 1) + ref_dist[1] * Bi(xB + 1, 1)) * (*part).vel[1];
pgradB[1] += ref_dist[0] * (1. - ref_dist[2]) * ((ref_dist[1] - 1.) * Bi(xB + 0 - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB + 0, 1) + ref_dist[1] * Bi(xB + 0 + 1, 1)) * (*part).vel[1];
pgradB[1] += (1. - ref_dist[0]) * ref_dist[2] * ((ref_dist[1] - 1.) * Bi(xB + 2 - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB + 2, 1) + ref_dist[1] * Bi(xB + 2 + 1, 1)) * (*part).vel[1];
pgradB[1] += ref_dist[0] * ref_dist[2] * ((ref_dist[1] - 1.) * Bi(xB + 2 + 0 - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB + 2 + 0, 1) + ref_dist[1] * Bi(xB + 2 + 0 + 1, 1)) * (*part).vel[1];
pgradB[2] = ((1. - ref_dist[1]) * (Bi(xB + 2, 0) - Bi(xB, 0)) + ref_dist[1] * (Bi(xB + 2 + 1, 0) - Bi(xB + 1, 0))) * (*part).vel[0];
pgradB[2] += ((1. - ref_dist[0]) * (Bi(xB + 2, 1) - Bi(xB, 1)) + ref_dist[0] * (Bi(xB + 2 + 0, 1) - Bi(xB + 0, 1))) * (*part).vel[1];
pgradB[2] += (1. - ref_dist[0]) * (1. - ref_dist[1]) * ((ref_dist[2] - 1.) * Bi(xB - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB, 2) + ref_dist[2] * Bi(xB + 2, 2)) * (*part).vel[2];
pgradB[2] += ref_dist[0] * (1. - ref_dist[1]) * ((ref_dist[2] - 1.) * Bi(xB + 0 - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB + 0, 2) + ref_dist[2] * Bi(xB + 0 + 2, 2)) * (*part).vel[2];
pgradB[2] += (1. - ref_dist[0]) * ref_dist[1] * ((ref_dist[2] - 1.) * Bi(xB + 1 - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB + 1, 2) + ref_dist[2] * Bi(xB + 2 + 1, 2)) * (*part).vel[2];
pgradB[2] += ref_dist[0] * ref_dist[1] * ((ref_dist[2] - 1.) * Bi(xB + 1 + 0 - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB + 1 + 0, 2) + ref_dist[2] * Bi(xB + 1 + 0 + 2, 2)) * (*part).vel[2];
gradphi[0] += pgradB[0] / e2 / params[1];
gradphi[1] += pgradB[1] / e2 / params[1];
gradphi[2] += pgradB[2] / e2 / params[1];
}
v2 = 0.;
for (int i = 0; i < 3; i++)
{
(*part).vel[i] -= dtau * e2 * gradphi[i] / dx;
v2 += (*part).vel[i] * (*part).vel[i];
}
return v2 / params[0] / params[0];
#undef phi
#undef chi
#undef Bi
#undef achi
#undef xphi
#undef xchi
#undef xB
#undef xachi
}
//////////////////////////
// update_q
//////////////////////////
// Description:
// Update momentum method (arbitrary momentum)
// Note that vel[3] in the particle structure is used to store q[3] in units
// of the particle mass, such that as q^2 << m^2 a^2 the meaning of vel[3]
// is ~ v*a.
//
// Arguments:
// dtau time step
// dx lattice unit
// part pointer to particle structure
// ref_dist distance vector to reference point
// partInfo global particle properties (unused)
// fields array of pointers to fields appearing in geodesic equation
// fields[0] = phi
// fields[1] = chi
// fields[2] = Bi
// sites array of sites on the respective lattices
// nfield number of fields
// params array of additional parameters
// params[0] = a
// params[1] = scaling coefficient for Bi
// outputs array of reduction variables
// noutputs number of reduction variables
//
// Returns: squared velocity of particle after update
//
//////////////////////////
Real update_q(double dtau, double dx, part_simple *part, double *ref_dist,
part_simple_info partInfo, Field<Real> **fields,
Site *sites, int nfield, double *params, double *outputs, int noutputs)
{
#define phi (*fields[0])
#define chi (*fields[1])
#define Bi (*fields[2])
#define xphi (sites[0])
#define xchi (sites[1])
#define xB (sites[2])
Real gradphi[3] = {0, 0, 0};
Real pgradB[3] = {0, 0, 0};
Real v2 = (*part).vel[0] * (*part).vel[0] + (*part).vel[1] * (*part).vel[1] + (*part).vel[2] * (*part).vel[2];
Real e2 = v2 + params[0] * params[0];
gradphi[0] = (1. - ref_dist[1]) * (1. - ref_dist[2]) * (phi(xphi + 0) - phi(xphi));
gradphi[1] = (1. - ref_dist[0]) * (1. - ref_dist[2]) * (phi(xphi + 1) - phi(xphi));
gradphi[2] = (1. - ref_dist[0]) * (1. - ref_dist[1]) * (phi(xphi + 2) - phi(xphi));
gradphi[0] += ref_dist[1] * (1. - ref_dist[2]) * (phi(xphi + 1 + 0) - phi(xphi + 1));
gradphi[1] += ref_dist[0] * (1. - ref_dist[2]) * (phi(xphi + 1 + 0) - phi(xphi + 0));
gradphi[2] += ref_dist[0] * (1. - ref_dist[1]) * (phi(xphi + 2 + 0) - phi(xphi + 0));
gradphi[0] += (1. - ref_dist[1]) * ref_dist[2] * (phi(xphi + 2 + 0) - phi(xphi + 2));
gradphi[1] += (1. - ref_dist[0]) * ref_dist[2] * (phi(xphi + 2 + 1) - phi(xphi + 2));
gradphi[2] += (1. - ref_dist[0]) * ref_dist[1] * (phi(xphi + 2 + 1) - phi(xphi + 1));
gradphi[0] += ref_dist[1] * ref_dist[2] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 2 + 1));
gradphi[1] += ref_dist[0] * ref_dist[2] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 2 + 0));
gradphi[2] += ref_dist[0] * ref_dist[1] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 1 + 0));
gradphi[0] *= (v2 + e2) / e2;
gradphi[1] *= (v2 + e2) / e2;
gradphi[2] *= (v2 + e2) / e2;
if (nfield >= 2 && fields[1] != NULL)
{
gradphi[0] -= (1. - ref_dist[1]) * (1. - ref_dist[2]) * (chi(xchi + 0) - chi(xchi));
gradphi[1] -= (1. - ref_dist[0]) * (1. - ref_dist[2]) * (chi(xchi + 1) - chi(xchi));
gradphi[2] -= (1. - ref_dist[0]) * (1. - ref_dist[1]) * (chi(xchi + 2) - chi(xchi));
gradphi[0] -= ref_dist[1] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 1));
gradphi[1] -= ref_dist[0] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 0));
gradphi[2] -= ref_dist[0] * (1. - ref_dist[1]) * (chi(xchi + 2 + 0) - chi(xchi + 0));
gradphi[0] -= (1. - ref_dist[1]) * ref_dist[2] * (chi(xchi + 2 + 0) - chi(xchi + 2));
gradphi[1] -= (1. - ref_dist[0]) * ref_dist[2] * (chi(xchi + 2 + 1) - chi(xchi + 2));
gradphi[2] -= (1. - ref_dist[0]) * ref_dist[1] * (chi(xchi + 2 + 1) - chi(xchi + 1));
gradphi[0] -= ref_dist[1] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 1));
gradphi[1] -= ref_dist[0] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 0));
gradphi[2] -= ref_dist[0] * ref_dist[1] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 1 + 0));
}
e2 = sqrt(e2);
if (nfield >= 3 && fields[2] != NULL)
{
pgradB[0] = ((1. - ref_dist[2]) * (Bi(xB + 0, 1) - Bi(xB, 1)) + ref_dist[2] * (Bi(xB + 2 + 0, 1) - Bi(xB + 2, 1))) * (*part).vel[1];
pgradB[0] += ((1. - ref_dist[1]) * (Bi(xB + 0, 2) - Bi(xB, 2)) + ref_dist[1] * (Bi(xB + 1 + 0, 2) - Bi(xB + 1, 2))) * (*part).vel[2];
pgradB[0] += (1. - ref_dist[1]) * (1. - ref_dist[2]) * ((ref_dist[0] - 1.) * Bi(xB - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB, 0) + ref_dist[0] * Bi(xB + 0, 0)) * (*part).vel[0];
pgradB[0] += ref_dist[1] * (1. - ref_dist[2]) * ((ref_dist[0] - 1.) * Bi(xB + 1 - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB + 1, 0) + ref_dist[0] * Bi(xB + 1 + 0, 0)) * (*part).vel[0];
pgradB[0] += (1. - ref_dist[1]) * ref_dist[2] * ((ref_dist[0] - 1.) * Bi(xB + 2 - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB + 2, 0) + ref_dist[0] * Bi(xB + 2 + 0, 0)) * (*part).vel[0];
pgradB[0] += ref_dist[1] * ref_dist[2] * ((ref_dist[0] - 1.) * Bi(xB + 2 + 1 - 0, 0) + (1. - 2. * ref_dist[0]) * Bi(xB + 2 + 1, 0) + ref_dist[0] * Bi(xB + 2 + 1 + 0, 0)) * (*part).vel[0];
pgradB[1] = ((1. - ref_dist[0]) * (Bi(xB + 1, 2) - Bi(xB, 2)) + ref_dist[0] * (Bi(xB + 1 + 0, 2) - Bi(xB + 0, 2))) * (*part).vel[2];
pgradB[1] += ((1. - ref_dist[2]) * (Bi(xB + 1, 0) - Bi(xB, 0)) + ref_dist[2] * (Bi(xB + 1 + 2, 0) - Bi(xB + 2, 0))) * (*part).vel[0];
pgradB[1] += (1. - ref_dist[0]) * (1. - ref_dist[2]) * ((ref_dist[1] - 1.) * Bi(xB - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB, 1) + ref_dist[1] * Bi(xB + 1, 1)) * (*part).vel[1];
pgradB[1] += ref_dist[0] * (1. - ref_dist[2]) * ((ref_dist[1] - 1.) * Bi(xB + 0 - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB + 0, 1) + ref_dist[1] * Bi(xB + 0 + 1, 1)) * (*part).vel[1];
pgradB[1] += (1. - ref_dist[0]) * ref_dist[2] * ((ref_dist[1] - 1.) * Bi(xB + 2 - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB + 2, 1) + ref_dist[1] * Bi(xB + 2 + 1, 1)) * (*part).vel[1];
pgradB[1] += ref_dist[0] * ref_dist[2] * ((ref_dist[1] - 1.) * Bi(xB + 2 + 0 - 1, 1) + (1. - 2. * ref_dist[1]) * Bi(xB + 2 + 0, 1) + ref_dist[1] * Bi(xB + 2 + 0 + 1, 1)) * (*part).vel[1];
pgradB[2] = ((1. - ref_dist[1]) * (Bi(xB + 2, 0) - Bi(xB, 0)) + ref_dist[1] * (Bi(xB + 2 + 1, 0) - Bi(xB + 1, 0))) * (*part).vel[0];
pgradB[2] += ((1. - ref_dist[0]) * (Bi(xB + 2, 1) - Bi(xB, 1)) + ref_dist[0] * (Bi(xB + 2 + 0, 1) - Bi(xB + 0, 1))) * (*part).vel[1];
pgradB[2] += (1. - ref_dist[0]) * (1. - ref_dist[1]) * ((ref_dist[2] - 1.) * Bi(xB - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB, 2) + ref_dist[2] * Bi(xB + 2, 2)) * (*part).vel[2];
pgradB[2] += ref_dist[0] * (1. - ref_dist[1]) * ((ref_dist[2] - 1.) * Bi(xB + 0 - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB + 0, 2) + ref_dist[2] * Bi(xB + 0 + 2, 2)) * (*part).vel[2];
pgradB[2] += (1. - ref_dist[0]) * ref_dist[1] * ((ref_dist[2] - 1.) * Bi(xB + 1 - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB + 1, 2) + ref_dist[2] * Bi(xB + 2 + 1, 2)) * (*part).vel[2];
pgradB[2] += ref_dist[0] * ref_dist[1] * ((ref_dist[2] - 1.) * Bi(xB + 1 + 0 - 2, 2) + (1. - 2. * ref_dist[2]) * Bi(xB + 1 + 0, 2) + ref_dist[2] * Bi(xB + 1 + 0 + 2, 2)) * (*part).vel[2];
gradphi[0] += pgradB[0] / e2 / params[1];
gradphi[1] += pgradB[1] / e2 / params[1];
gradphi[2] += pgradB[2] / e2 / params[1];
}
v2 = 0.;
for (int i = 0; i < 3; i++)
{
(*part).vel[i] -= dtau * e2 * gradphi[i] / dx;
v2 += (*part).vel[i] * (*part).vel[i];
}
return v2 / params[0] / params[0];
#undef phi
#undef chi
#undef Bi
#undef xphi
#undef xchi
#undef xB
}
//////////////////////////
// update_q_Newton
//////////////////////////
// Description:
// Update momentum method (Newtonian version)
// Note that vel[3] in the particle structure is used to store q[3] in units
// of the particle mass, such that the meaning of vel[3] is v*a.
//
// Arguments:
// dtau time step
// dx lattice unit
// part pointer to particle structure
// ref_dist distance vector to reference point
// partInfo global particle properties (unused)
// fields array of pointers to fields appearing in geodesic equation
// fields[0] = psi
// fields[1] = chi
// sites array of sites on the respective lattices
// nfield number of fields (should be 1)
// params array of additional parameters
// params[0] = a
// outputs array of reduction variables
// noutputs number of reduction variables
//
// Returns: squared velocity of particle after update
//
//////////////////////////
Real update_q_Newton(double dtau, double dx, part_simple *part, double *ref_dist, part_simple_info partInfo, Field<Real> **fields, Site *sites, int nfield, double *params, double *outputs, int noutputs)
{
#define psi (*fields[0])
#define xpsi (sites[0])
#define chi (*fields[1])
#define xchi (sites[1])
Real gradpsi[3] = {0, 0, 0};
gradpsi[0] = (1. - ref_dist[1]) * (1. - ref_dist[2]) * (psi(xpsi + 0) - psi(xpsi));
gradpsi[1] = (1. - ref_dist[0]) * (1. - ref_dist[2]) * (psi(xpsi + 1) - psi(xpsi));
gradpsi[2] = (1. - ref_dist[0]) * (1. - ref_dist[1]) * (psi(xpsi + 2) - psi(xpsi));
gradpsi[0] += ref_dist[1] * (1. - ref_dist[2]) * (psi(xpsi + 1 + 0) - psi(xpsi + 1));
gradpsi[1] += ref_dist[0] * (1. - ref_dist[2]) * (psi(xpsi + 1 + 0) - psi(xpsi + 0));
gradpsi[2] += ref_dist[0] * (1. - ref_dist[1]) * (psi(xpsi + 2 + 0) - psi(xpsi + 0));
gradpsi[0] += (1. - ref_dist[1]) * ref_dist[2] * (psi(xpsi + 2 + 0) - psi(xpsi + 2));
gradpsi[1] += (1. - ref_dist[0]) * ref_dist[2] * (psi(xpsi + 2 + 1) - psi(xpsi + 2));
gradpsi[2] += (1. - ref_dist[0]) * ref_dist[1] * (psi(xpsi + 2 + 1) - psi(xpsi + 1));
gradpsi[0] += ref_dist[1] * ref_dist[2] * (psi(xpsi + 2 + 1 + 0) - psi(xpsi + 2 + 1));
gradpsi[1] += ref_dist[0] * ref_dist[2] * (psi(xpsi + 2 + 1 + 0) - psi(xpsi + 2 + 0));
gradpsi[2] += ref_dist[0] * ref_dist[1] * (psi(xpsi + 2 + 1 + 0) - psi(xpsi + 1 + 0));
if (nfield >= 2 && fields[1] != NULL)
{
gradpsi[0] -= (1. - ref_dist[1]) * (1. - ref_dist[2]) * (chi(xchi + 0) - chi(xchi));
gradpsi[1] -= (1. - ref_dist[0]) * (1. - ref_dist[2]) * (chi(xchi + 1) - chi(xchi));
gradpsi[2] -= (1. - ref_dist[0]) * (1. - ref_dist[1]) * (chi(xchi + 2) - chi(xchi));
gradpsi[0] -= ref_dist[1] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 1));
gradpsi[1] -= ref_dist[0] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 0));
gradpsi[2] -= ref_dist[0] * (1. - ref_dist[1]) * (chi(xchi + 2 + 0) - chi(xchi + 0));
gradpsi[0] -= (1. - ref_dist[1]) * ref_dist[2] * (chi(xchi + 2 + 0) - chi(xchi + 2));
gradpsi[1] -= (1. - ref_dist[0]) * ref_dist[2] * (chi(xchi + 2 + 1) - chi(xchi + 2));
gradpsi[2] -= (1. - ref_dist[0]) * ref_dist[1] * (chi(xchi + 2 + 1) - chi(xchi + 1));
gradpsi[0] -= ref_dist[1] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 1));
gradpsi[1] -= ref_dist[0] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 0));
gradpsi[2] -= ref_dist[0] * ref_dist[1] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 1 + 0));
}
Real v2 = 0.;
for (int i = 0; i < 3; i++)
{
(*part).vel[i] -= dtau * params[0] * gradpsi[i] / dx;
v2 += (*part).vel[i] * (*part).vel[i];
}
return v2 / params[0] / params[0];
#undef psi
#undef xpsi
#undef chi
#undef xchi
}
Real update_q_Newton_5th(double dtau, double dx, part_simple *part, double *ref_dist, part_simple_info partInfo, Field<Real> **fields, Site *sites, int nfield, double *params, double *outputs, int noutputs)
{
#define phi (*fields[0])
#define xphi (sites[0])
#define chi (*fields[1])
#define xchi (sites[1])
#define achi (*fields[2])
#define xachi (sites[2])
Real gradpsi[3] = {0, 0, 0};
Real daphix, daphiy, daphiz, fac, aphif, Acnf, dAcnf;
gradpsi[0] = (1. - ref_dist[1]) * (1. - ref_dist[2]) * (phi(xphi + 0) - phi(xphi));
gradpsi[1] = (1. - ref_dist[0]) * (1. - ref_dist[2]) * (phi(xphi + 1) - phi(xphi));
gradpsi[2] = (1. - ref_dist[0]) * (1. - ref_dist[1]) * (phi(xphi + 2) - phi(xphi));
gradpsi[0] += ref_dist[1] * (1. - ref_dist[2]) * (phi(xphi + 1 + 0) - phi(xphi + 1));
gradpsi[1] += ref_dist[0] * (1. - ref_dist[2]) * (phi(xphi + 1 + 0) - phi(xphi + 0));
gradpsi[2] += ref_dist[0] * (1. - ref_dist[1]) * (phi(xphi + 2 + 0) - phi(xphi + 0));
gradpsi[0] += (1. - ref_dist[1]) * ref_dist[2] * (phi(xphi + 2 + 0) - phi(xphi + 2));
gradpsi[1] += (1. - ref_dist[0]) * ref_dist[2] * (phi(xphi + 2 + 1) - phi(xphi + 2));
gradpsi[2] += (1. - ref_dist[0]) * ref_dist[1] * (phi(xphi + 2 + 1) - phi(xphi + 1));
gradpsi[0] += ref_dist[1] * ref_dist[2] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 2 + 1));
gradpsi[1] += ref_dist[0] * ref_dist[2] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 2 + 0));
gradpsi[2] += ref_dist[0] * ref_dist[1] * (phi(xphi + 2 + 1 + 0) - phi(xphi + 1 + 0));
gradpsi[0] -= (1. - ref_dist[1]) * (1. - ref_dist[2]) * (chi(xchi + 0) - chi(xchi));
gradpsi[1] -= (1. - ref_dist[0]) * (1. - ref_dist[2]) * (chi(xchi + 1) - chi(xchi));
gradpsi[2] -= (1. - ref_dist[0]) * (1. - ref_dist[1]) * (chi(xchi + 2) - chi(xchi));
gradpsi[0] -= ref_dist[1] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 1));
gradpsi[1] -= ref_dist[0] * (1. - ref_dist[2]) * (chi(xchi + 1 + 0) - chi(xchi + 0));
gradpsi[2] -= ref_dist[0] * (1. - ref_dist[1]) * (chi(xchi + 2 + 0) - chi(xchi + 0));
gradpsi[0] -= (1. - ref_dist[1]) * ref_dist[2] * (chi(xchi + 2 + 0) - chi(xchi + 2));
gradpsi[1] -= (1. - ref_dist[0]) * ref_dist[2] * (chi(xchi + 2 + 1) - chi(xchi + 2));
gradpsi[2] -= (1. - ref_dist[0]) * ref_dist[1] * (chi(xchi + 2 + 1) - chi(xchi + 1));
gradpsi[0] -= ref_dist[1] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 1));
gradpsi[1] -= ref_dist[0] * ref_dist[2] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 2 + 0));
gradpsi[2] -= ref_dist[0] * ref_dist[1] * (chi(xchi + 2 + 1 + 0) - chi(xchi + 1 + 0));
fac = params[2];
aphif = ((1 - ref_dist[0]) * (1. - ref_dist[1]) * (1. - ref_dist[2]) * achi(xachi) + ref_dist[0] * (1. - ref_dist[1]) * (1. - ref_dist[2]) * achi(xachi + 0) + (1 - ref_dist[0]) * ref_dist[1] * (1. - ref_dist[2]) * achi(xachi + 1) + ref_dist[0] * ref_dist[1] * (1. - ref_dist[2]) * achi(xachi + 0 + 1) + (1 - ref_dist[0]) * (1. - ref_dist[1]) * ref_dist[2] * achi(xachi + 2) + ref_dist[0] * (1. - ref_dist[1]) * ref_dist[2] * achi(xachi + 2 + 0) + (1 - ref_dist[0]) * ref_dist[1] * ref_dist[2] * achi(xachi + 2 + 1) + ref_dist[0] * ref_dist[1] * ref_dist[2] * achi(xachi + 2 + 0 + 1)) * fac;
daphix = fac * ((1. - ref_dist[1]) *
(1. - ref_dist[2]) * (achi(xachi + 0) - achi(xachi)) +
ref_dist[1] * (1. - ref_dist[2]) * (achi(xachi + 1 + 0) - achi(xachi + 1)) + (1. - ref_dist[1]) * ref_dist[2] * (achi(xachi + 2 + 0) - achi(xachi + 2)) + ref_dist[1] * ref_dist[2] * (achi(xachi + 2 + 1 + 0) - achi(xachi + 2 + 1)));
daphiy = fac * ((1. - ref_dist[0]) * (1. - ref_dist[2]) * (achi(xachi + 1) - achi(xachi)) + ref_dist[0] * (1. - ref_dist[2]) * (achi(xachi + 1 + 0) - achi(xachi + 0)) + (1. - ref_dist[0]) * ref_dist[2] * (achi(xachi + 2 + 1) - achi(xachi + 2)) + ref_dist[0] * ref_dist[2] * (achi(xachi + 2 + 1 + 0) - achi(xachi + 2 + 0)));
daphiz = fac * ((1. - ref_dist[0]) * (1. - ref_dist[1]) * (achi(xachi + 2) - achi(xachi)) + ref_dist[0] * (1. - ref_dist[1]) * (achi(xachi + 2 + 0) - achi(xachi + 0)) + (1. - ref_dist[0]) * ref_dist[1] * (achi(xachi + 2 + 1) - achi(xachi + 1)) + ref_dist[0] * ref_dist[1] * (achi(xachi + 2 + 1 + 0) - achi(xachi + 1 + 0)));
gradpsi[0] += aphif * daphix;
gradpsi[1] += aphif * daphiy;
gradpsi[2] += aphif * daphiz;
Real v2 = 0.;
for (int i = 0; i < 3; i++)
{
(*part).vel[i] -= dtau * params[0] * gradpsi[i] / dx;
v2 += (*part).vel[i] * (*part).vel[i];
}
return v2 / params[0] / params[0];
#undef phi
#undef xphi
#undef achi
#undef xachi
#undef chi
#undef xchi
}
void update_pos_5th(double dtau, double dx, part_simple *part, double *ref_dist, part_simple_info partInfo, Field<Real> **fields, Site *sites, int nfield, double *params, double *outputs, int noutputs)
{
Real v[3];
Real phi = 0.;
Real chi = 0.;
Real aphi = 0.;
Real fac = 0.;
Real dAcnf = 0.;
Real Acnf = 1.;
if (nfield >= 4)
{
// Modification to add effect of conformal coupling on canonical momentum
fac = params[2]; // phi0/M
aphi = (*fields[3])(sites[3]) * (1. - ref_dist[0]) * (1. - ref_dist[1]) * (1. - ref_dist[2]);
aphi += (*fields[3])(sites[3] + 0) * ref_dist[0] * (1. - ref_dist[1]) * (1. - ref_dist[2]);
aphi += (*fields[3])(sites[3] + 1) * (1. - ref_dist[0]) * ref_dist[1] * (1. - ref_dist[2]);
aphi += (*fields[3])(sites[3] + 0 + 1) * ref_dist[0] * ref_dist[1] * (1. - ref_dist[2]);
aphi += (*fields[3])(sites[3] + 2) * (1. - ref_dist[0]) * (1. - ref_dist[1]) * ref_dist[2];
aphi += (*fields[3])(sites[3] + 0 + 2) * ref_dist[0] * (1. - ref_dist[1]) * ref_dist[2];
aphi += (*fields[3])(sites[3] + 1 + 2) * (1. - ref_dist[0]) * ref_dist[1] * ref_dist[2];
aphi += (*fields[3])(sites[3] + 0 + 1 + 2) * ref_dist[0] * ref_dist[1] * ref_dist[2];
aphi *= fac;
dAcnf = aphi * aphi / 2.;
Acnf = 1. + dAcnf;
}
Real v2 = (*part).vel[0] * (*part).vel[0] + (*part).vel[1] * (*part).vel[1] + (*part).vel[2] * (*part).vel[2];
Real e2 = v2 + params[0] * params[0];
if (nfield >= 1)
{
phi = (*fields[0])(sites[0]) * (1. - ref_dist[0]) * (1. - ref_dist[1]) * (1. - ref_dist[2]);
phi += (*fields[0])(sites[0] + 0) * ref_dist[0] * (1. - ref_dist[1]) * (1. - ref_dist[2]);
phi += (*fields[0])(sites[0] + 1) * (1. - ref_dist[0]) * ref_dist[1] * (1. - ref_dist[2]);
phi += (*fields[0])(sites[0] + 0 + 1) * ref_dist[0] * ref_dist[1] * (1. - ref_dist[2]);
phi += (*fields[0])(sites[0] + 2) * (1. - ref_dist[0]) * (1. - ref_dist[1]) * ref_dist[2];
phi += (*fields[0])(sites[0] + 0 + 2) * ref_dist[0] * (1. - ref_dist[1]) * ref_dist[2];
phi += (*fields[0])(sites[0] + 1 + 2) * (1. - ref_dist[0]) * ref_dist[1] * ref_dist[2];
phi += (*fields[0])(sites[0] + 0 + 1 + 2) * ref_dist[0] * ref_dist[1] * ref_dist[2];
phi -= dAcnf;
}
if (nfield >= 2)
{
chi = (*fields[1])(sites[1]) * (1. - ref_dist[0]) * (1. - ref_dist[1]) * (1. - ref_dist[2]);
chi += (*fields[1])(sites[1] + 0) * ref_dist[0] * (1. - ref_dist[1]) * (1. - ref_dist[2]);
chi += (*fields[1])(sites[1] + 1) * (1. - ref_dist[0]) * ref_dist[1] * (1. - ref_dist[2]);
chi += (*fields[1])(sites[1] + 0 + 1) * ref_dist[0] * ref_dist[1] * (1. - ref_dist[2]);
chi += (*fields[1])(sites[1] + 2) * (1. - ref_dist[0]) * (1. - ref_dist[1]) * ref_dist[2];
chi += (*fields[1])(sites[1] + 0 + 2) * ref_dist[0] * (1. - ref_dist[1]) * ref_dist[2];
chi += (*fields[1])(sites[1] + 1 + 2) * (1. - ref_dist[0]) * ref_dist[1] * ref_dist[2];
chi += (*fields[1])(sites[1] + 0 + 1 + 2) * ref_dist[0] * ref_dist[1] * ref_dist[2];
chi -= 2.0 * dAcnf;
}
v2 = (1. + (3. - v2 / e2) * phi - chi) / sqrt(e2);
v[0] = (*part).vel[0] * v2;
v[1] = (*part).vel[1] * v2;
v[2] = (*part).vel[2] * v2;
if (nfield >= 3)
{
Real b[3];
b[0] = (*fields[2])(sites[2], 0) * (1. - ref_dist[1]) * (1. - ref_dist[2]);
b[1] = (*fields[2])(sites[2], 1) * (1. - ref_dist[0]) * (1. - ref_dist[2]);
b[2] = (*fields[2])(sites[2], 2) * (1. - ref_dist[0]) * (1. - ref_dist[1]);
b[1] += (*fields[2])(sites[2] + 0, 1) * ref_dist[0] * (1. - ref_dist[2]);
b[2] += (*fields[2])(sites[2] + 0, 2) * ref_dist[0] * (1. - ref_dist[1]);
b[0] += (*fields[2])(sites[2] + 1, 0) * ref_dist[1] * (1. - ref_dist[2]);
b[2] += (*fields[2])(sites[2] + 1, 2) * (1. - ref_dist[0]) * ref_dist[1];
b[0] += (*fields[2])(sites[2] + 2, 0) * (1. - ref_dist[1]) * ref_dist[2];
b[1] += (*fields[2])(sites[2] + 2, 1) * (1. - ref_dist[0]) * ref_dist[2];
b[1] += (*fields[2])(sites[2] + 2 + 0, 1) * ref_dist[0] * ref_dist[2];
b[0] += (*fields[2])(sites[2] + 2 + 1, 0) * ref_dist[1] * ref_dist[2];
b[2] += (*fields[2])(sites[2] + 1 + 0, 2) * ref_dist[0] * ref_dist[1];
for (int l = 0; l < 3; l++)
(*part).pos[l] += dtau * (v[l] + b[l] / params[1]) * Acnf;
}
else
{
for (int l = 0; l < 3; l++)
(*part).pos[l] += dtau * v[l] * Acnf;
}