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#include <PsatdAlgorithm.H>
#include <WarpXConst.H>
#include <cmath>
using namespace amrex;
PsatdAlgorithm::PsatdAlgorithm(const SpectralKSpace& spectral_kspace,
const DistributionMapping& dm,
const int norder_x, const int norder_y,
const int norder_z, const Real dt)
{
const BoxArray& ba = spectral_kspace.spectralspace_ba;
// Allocate the 1D vectors
modified_kx_vec = spectral_kspace.AllocateAndFillModifiedKComponent( dm, 0, norder_x );
#if (AMREX_SPACEDIM==3)
modified_ky_vec = spectral_kspace.AllocateAndFillModifiedKComponent( dm, 1, norder_y );
modified_kz_vec = spectral_kspace.AllocateAndFillModifiedKComponent( dm, 2, norder_z );
#else
modified_kz_vec = spectral_kspace.AllocateAndFillModifiedKComponent( dm, 1, norder_z );
#endif
// 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
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 ) +
#endif
std::pow( modified_kz[k], 2 ) );
// 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);
}
});
}
};
void
PsatdAlgorithm::pushSpectralFields( SpectralFieldData& f ) const{
// Loop over boxes
for ( MFIter mfi(f.Ex); mfi.isValid(); ++mfi ){
const Box& bx = f.Ex[mfi].box();
// Extract arrays for the fields to be updated
Array4<Complex> Ex_arr = f.Ex[mfi].array();
Array4<Complex> Ey_arr = f.Ey[mfi].array();
Array4<Complex> Ez_arr = f.Ez[mfi].array();
Array4<Complex> Bx_arr = f.Bx[mfi].array();
Array4<Complex> By_arr = f.By[mfi].array();
Array4<Complex> Bz_arr = f.Bz[mfi].array();
// Extract arrays for J and rho
Array4<const Complex> Jx_arr = f.Jx[mfi].array();
Array4<const Complex> Jy_arr = f.Jy[mfi].array();
Array4<const Complex> Jz_arr = f.Jz[mfi].array();
Array4<const Complex> rho_old_arr = f.rho_old[mfi].array();
Array4<const Complex> rho_new_arr = f.rho_new[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
const Complex Ex_old = Ex_arr(i,j,k);
const Complex Ey_old = Ey_arr(i,j,k);
const Complex Ez_old = Ez_arr(i,j,k);
const Complex Bx_old = Bx_arr(i,j,k);
const Complex By_old = By_arr(i,j,k);
const Complex Bz_old = Bz_arr(i,j,k);
// Shortcut for the values of J and rho
const Complex Jx = Jx_arr(i,j,k);
const Complex Jy = Jy_arr(i,j,k);
const Complex Jz = Jz_arr(i,j,k);
const Complex rho_old = rho_old_arr(i,j,k);
const Complex rho_new = rho_new_arr(i,j,k);
// k vector values, and coefficients
const Real kx = modified_kx_arr[i];
#if (AMREX_SPACEDIM==3)
const Real ky = modified_ky_arr[j];
#else
constexpr Real ky = 0;
#endif
const Real kz = modified_kz_arr[k];
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)
Ex_arr(i,j,k) = C*Ex_old
+ S_ck*( c2*I*(ky*Bz_old - kz*By_old) - inv_ep0*Jx )
- I*( X2*rho_new - X3*rho_old )*kx;
Ey_arr(i,j,k) = C*Ey_old
+ S_ck*( c2*I*(kz*Bx_old - kx*Bz_old) - inv_ep0*Jy )
- I*( X2*rho_new - X3*rho_old )*ky;
Ez_arr(i,j,k) = 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)
Bx_arr(i,j,k) = C*Bx_old
- S_ck*I*(ky*Ez_old - kz*Ey_old)
+ X1*I*(ky*Jz - kz*Jy );
By_arr(i,j,k) = C*By_old
- S_ck*I*(kz*Ex_old - kx*Ez_old)
+ X1*I*(kz*Jx - kx*Jz );
Bz_arr(i,j,k) = C*Bz_old
- S_ck*I*(kx*Ey_old - ky*Ex_old)
+ X1*I*(kx*Jy - ky*Jx );
});
}
};
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