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#include <PsatdAlgorithm.H>
#include <WarpXConst.H>
#include <cmath>
using namespace amrex;
/* \brief Initialize coefficients for the update equation */
PsatdAlgorithm::PsatdAlgorithm(const SpectralKSpace& spectral_kspace,
const DistributionMapping& dm,
const int norder_x, const int norder_y,
const int norder_z, const bool nodal, const Real dt)
// Compute and assign the modified k vectors
: modified_kx_vec(spectral_kspace.getModifiedKComponent(dm,0,norder_x,nodal)),
#if (AMREX_SPACEDIM==3)
modified_ky_vec(spectral_kspace.getModifiedKComponent(dm,1,norder_y,nodal)),
modified_kz_vec(spectral_kspace.getModifiedKComponent(dm,2,norder_z,nodal))
#else
modified_kz_vec(spectral_kspace.getModifiedKComponent(dm,1,norder_z,nodal))
#endif
{
const BoxArray& ba = spectral_kspace.spectralspace_ba;
// Allocate the arrays of coefficients
C_coef = SpectralCoefficients(ba, dm, 1, 0);
S_ck_coef = SpectralCoefficients(ba, dm, 1, 0);
X1_coef = SpectralCoefficients(ba, dm, 1, 0);
X2_coef = SpectralCoefficients(ba, dm, 1, 0);
X3_coef = SpectralCoefficients(ba, dm, 1, 0);
// Fill them with the right values:
// Loop over boxes and allocate the corresponding coefficients
// for each box owned by the local MPI proc
for (MFIter mfi(ba, dm); mfi.isValid(); ++mfi){
const Box& bx = ba[mfi];
// Extract pointers for the k vectors
const Real* modified_kx = modified_kx_vec[mfi].dataPtr();
#if (AMREX_SPACEDIM==3)
const Real* modified_ky = modified_ky_vec[mfi].dataPtr();
#endif
const Real* modified_kz = modified_kz_vec[mfi].dataPtr();
// Extract arrays for the coefficients
Array4<Real> C = C_coef[mfi].array();
Array4<Real> S_ck = S_ck_coef[mfi].array();
Array4<Real> X1 = X1_coef[mfi].array();
Array4<Real> X2 = X2_coef[mfi].array();
Array4<Real> X3 = X3_coef[mfi].array();
// Loop over indices within one box
ParallelFor(bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
{
// Calculate norm of vector
const Real k_norm = std::sqrt(
std::pow(modified_kx[i], 2) +
#if (AMREX_SPACEDIM==3)
std::pow(modified_ky[j], 2) +
std::pow(modified_kz[k], 2));
#else
std::pow(modified_kz[j], 2));
#endif
// Calculate coefficients
constexpr Real c = PhysConst::c;
constexpr Real ep0 = PhysConst::ep0;
if (k_norm != 0){
C(i,j,k) = std::cos(c*k_norm*dt);
S_ck(i,j,k) = std::sin(c*k_norm*dt)/(c*k_norm);
X1(i,j,k) = (1. - C(i,j,k))/(ep0 * c*c * k_norm*k_norm);
X2(i,j,k) = (1. - S_ck(i,j,k)/dt)/(ep0 * k_norm*k_norm);
X3(i,j,k) = (C(i,j,k) - S_ck(i,j,k)/dt)/(ep0 * k_norm*k_norm);
} else { // Handle k_norm = 0, by using the analytical limit
C(i,j,k) = 1.;
S_ck(i,j,k) = dt;
X1(i,j,k) = 0.5 * dt*dt / ep0;
X2(i,j,k) = c*c * dt*dt / (6.*ep0);
X3(i,j,k) = - c*c * dt*dt / (3.*ep0);
}
});
}
};
/* Advance the E and B field in spectral space (stored in `f`)
* over one time step */
void
PsatdAlgorithm::pushSpectralFields(SpectralFieldData& f) const{
// Loop over boxes
for (MFIter mfi(f.fields); mfi.isValid(); ++mfi){
const Box& bx = f.fields[mfi].box();
// Extract arrays for the fields to be updated
Array4<Complex> fields = f.fields[mfi].array();
// Extract arrays for the coefficients
Array4<const Real> C_arr = C_coef[mfi].array();
Array4<const Real> S_ck_arr = S_ck_coef[mfi].array();
Array4<const Real> X1_arr = X1_coef[mfi].array();
Array4<const Real> X2_arr = X2_coef[mfi].array();
Array4<const Real> X3_arr = X3_coef[mfi].array();
// Extract pointers for the k vectors
const Real* modified_kx_arr = modified_kx_vec[mfi].dataPtr();
#if (AMREX_SPACEDIM==3)
const Real* modified_ky_arr = modified_ky_vec[mfi].dataPtr();
#endif
const Real* modified_kz_arr = modified_kz_vec[mfi].dataPtr();
// Loop over indices within one box
ParallelFor(bx,
[=] AMREX_GPU_DEVICE(int i, int j, int k) noexcept
{
// Record old values of the fields to be updated
using Idx = SpectralFieldIndex;
const Complex Ex_old = fields(i,j,k,Idx::Ex);
const Complex Ey_old = fields(i,j,k,Idx::Ey);
const Complex Ez_old = fields(i,j,k,Idx::Ez);
const Complex Bx_old = fields(i,j,k,Idx::Bx);
const Complex By_old = fields(i,j,k,Idx::By);
const Complex Bz_old = fields(i,j,k,Idx::Bz);
// Shortcut for the values of J and rho
const Complex Jx = fields(i,j,k,Idx::Jx);
const Complex Jy = fields(i,j,k,Idx::Jy);
const Complex Jz = fields(i,j,k,Idx::Jz);
const Complex rho_old = fields(i,j,k,Idx::rho_old);
const Complex rho_new = fields(i,j,k,Idx::rho_new);
// k vector values, and coefficients
const Real kx = modified_kx_arr[i];
#if (AMREX_SPACEDIM==3)
const Real ky = modified_ky_arr[j];
const Real kz = modified_kz_arr[k];
#else
constexpr Real ky = 0;
const Real kz = modified_kz_arr[j];
#endif
constexpr Real c2 = PhysConst::c*PhysConst::c;
constexpr Real inv_ep0 = 1./PhysConst::ep0;
constexpr Complex I = Complex{0,1};
const Real C = C_arr(i,j,k);
const Real S_ck = S_ck_arr(i,j,k);
const Real X1 = X1_arr(i,j,k);
const Real X2 = X2_arr(i,j,k);
const Real X3 = X3_arr(i,j,k);
// Update E (see WarpX online documentation: theory section)
fields(i,j,k,Idx::Ex) = C*Ex_old
+ S_ck*(c2*I*(ky*Bz_old - kz*By_old) - inv_ep0*Jx)
- I*(X2*rho_new - X3*rho_old)*kx;
fields(i,j,k,Idx::Ey) = C*Ey_old
+ S_ck*(c2*I*(kz*Bx_old - kx*Bz_old) - inv_ep0*Jy)
- I*(X2*rho_new - X3*rho_old)*ky;
fields(i,j,k,Idx::Ez) = C*Ez_old
+ S_ck*(c2*I*(kx*By_old - ky*Bx_old) - inv_ep0*Jz)
- I*(X2*rho_new - X3*rho_old)*kz;
// Update B (see WarpX online documentation: theory section)
fields(i,j,k,Idx::Bx) = C*Bx_old
- S_ck*I*(ky*Ez_old - kz*Ey_old)
+ X1*I*(ky*Jz - kz*Jy);
fields(i,j,k,Idx::By) = C*By_old
- S_ck*I*(kz*Ex_old - kx*Ez_old)
+ X1*I*(kz*Jx - kx*Jz);
fields(i,j,k,Idx::Bz) = C*Bz_old
- S_ck*I*(kx*Ey_old - ky*Ex_old)
+ X1*I*(kx*Jy - ky*Jx);
});
}
};
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