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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
//////////////////////////
// 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] / params[1] / e2;
gradphi[1] += pgradB[1] / params[1] / e2;
gradphi[2] += pgradB[2] / params[1] / e2;
}
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
}
//////////////////////////
// update_pos
//////////////////////////
// Description:
// Update position 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:
//
//////////////////////////
void update_pos(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 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];
Real phi = 0;
Real chi = 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];
}
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];
}
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]);
}
else
{
for (int l=0;l<3;l++) (*part).pos[l] += dtau*v[l];
}
}
//////////////////////////
// update_pos_Newton
//////////////////////////
// Description:
// Update position 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 (unused)
// part pointer to particle structure
// ref_dist distance vector to reference point (unused)
// partInfo global particle properties (unused)
// fields array of pointers to fields appearing in geodesic equation (unused)
// sites array of sites on the respective lattices (unused)
// nfield number of fields (unused)
// params array of additional parameters
// params[0] = a
// outputs array of reduction variables (unused)
// noutputs number of reduction variables (unused)
//
// Returns:
//
//////////////////////////
void update_pos_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)
{
for (int l=0;l<3;l++) (*part).pos[l] += dtau * (*part).vel[l] / params[0];
}
//////////////////////////
// projection_T00_project
//////////////////////////
// Description:
// Particle-mesh projection for T00, including geometric corrections
//
// Arguments:
// pcls pointer to particle handler
// T00 pointer to target field
// a scale factor at projection (needed in order to convert
// canonical momenta to energies)
// phi pointer to Bardeen potential which characterizes the
// geometric corrections (volume distortion); can be set to
// NULL which will result in no corrections applied
// coeff coefficient applied to the projection operation (default 1)
//
// Returns:
//
//////////////////////////
template<typename part, typename part_info, typename part_dataType>
void projection_T00_project(Particles<part, part_info, part_dataType> * pcls, Field<Real> * T00, double a = 1., Field<Real> * phi = NULL, double coeff = 1.)
{
if (T00->lattice().halo() == 0)
{
cout<< "projection_T00_project: target field needs halo > 0" << endl;
exit(-1);
}
Site xPart(pcls->lattice());
Site xField(T00->lattice());
typename std::list<part>::iterator it;
Real referPos[3];
Real weightScalarGridUp[3];
Real weightScalarGridDown[3];
Real dx = pcls->res();
double mass = coeff / (dx*dx*dx);
mass *= *(double*)((char*)pcls->parts_info() + pcls->mass_offset());
mass /= a;
Real e = a, f = 0.;
Real * q;
size_t offset_q = offsetof(part,vel);
Real localCube[8]; // XYZ = 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111
Real localCubePhi[8];
for (int i=0; i<8; i++) localCubePhi[i] = 0.0;
for (xPart.first(),xField.first(); xPart.test(); xPart.next(),xField.next())
{
if (pcls->field()(xPart).size != 0)
{
for(int i=0; i<3; i++) referPos[i] = xPart.coord(i)*dx;
for(int i=0; i<8; i++) localCube[i] = 0.0;
if (phi != NULL)
{
localCubePhi[0] = (*phi)(xField);
localCubePhi[1] = (*phi)(xField+2);
localCubePhi[2] = (*phi)(xField+1);
localCubePhi[3] = (*phi)(xField+1+2);
localCubePhi[4] = (*phi)(xField+0);
localCubePhi[5] = (*phi)(xField+0+2);
localCubePhi[6] = (*phi)(xField+0+1);
localCubePhi[7] = (*phi)(xField+0+1+2);
}
for (it=(pcls->field())(xPart).parts.begin(); it != (pcls->field())(xPart).parts.end(); ++it)
{
for (int i=0; i<3; i++)
{
weightScalarGridUp[i] = ((*it).pos[i] - referPos[i]) / dx;
weightScalarGridDown[i] = 1.0l - weightScalarGridUp[i];
}
if (phi != NULL)
{
q = (Real*)((char*)&(*it)+offset_q);
f = q[0] * q[0] + q[1] * q[1] + q[2] * q[2];
e = sqrt(f + a * a);
f = 3. * e + f / e;
}
//000
localCube[0] += weightScalarGridDown[0]*weightScalarGridDown[1]*weightScalarGridDown[2]*(e+f*localCubePhi[0]);
//001
localCube[1] += weightScalarGridDown[0]*weightScalarGridDown[1]*weightScalarGridUp[2]*(e+f*localCubePhi[1]);
//010
localCube[2] += weightScalarGridDown[0]*weightScalarGridUp[1]*weightScalarGridDown[2]*(e+f*localCubePhi[2]);
//011
localCube[3] += weightScalarGridDown[0]*weightScalarGridUp[1]*weightScalarGridUp[2]*(e+f*localCubePhi[3]);
//100
localCube[4] += weightScalarGridUp[0]*weightScalarGridDown[1]*weightScalarGridDown[2]*(e+f*localCubePhi[4]);
//101
localCube[5] += weightScalarGridUp[0]*weightScalarGridDown[1]*weightScalarGridUp[2]*(e+f*localCubePhi[5]);
//110
localCube[6] += weightScalarGridUp[0]*weightScalarGridUp[1]*weightScalarGridDown[2]*(e+f*localCubePhi[6]);
//111
localCube[7] += weightScalarGridUp[0]*weightScalarGridUp[1]*weightScalarGridUp[2]*(e+f*localCubePhi[7]);
}
(*T00)(xField) += localCube[0] * mass;
(*T00)(xField+2) += localCube[1] * mass;
(*T00)(xField+1) += localCube[2] * mass;
(*T00)(xField+1+2) += localCube[3] * mass;
(*T00)(xField+0) += localCube[4] * mass;
(*T00)(xField+0+2) += localCube[5] * mass;
(*T00)(xField+0+1) += localCube[6] * mass;
(*T00)(xField+0+1+2) += localCube[7] * mass;
}
}
}
#define projection_T00_comm scalarProjectionCIC_comm
//////////////////////////
// projection_T0i_project
//////////////////////////
// Description:
// Particle-mesh projection for T0i, including geometric corrections
//