diff options
Diffstat (limited to 'Source/FieldSolver/SpectralSolver/PsatdAlgorithm.cpp')
| -rw-r--r-- | Source/FieldSolver/SpectralSolver/PsatdAlgorithm.cpp | 174 |
1 files changed, 174 insertions, 0 deletions
diff --git a/Source/FieldSolver/SpectralSolver/PsatdAlgorithm.cpp b/Source/FieldSolver/SpectralSolver/PsatdAlgorithm.cpp new file mode 100644 index 000000000..56e58bcc4 --- /dev/null +++ b/Source/FieldSolver/SpectralSolver/PsatdAlgorithm.cpp @@ -0,0 +1,174 @@ +#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) + +#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); + } + }); + } +}; + +/* 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.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); + }); + } +}; |