Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity
It addresses the need for efficient and accurate kinetic models of plasmas in the moderately coupled regime, which is a bottleneck for classical Landau formulations.
The paper introduces a data-driven collisional operator for one-component plasmas that extends beyond the weakly coupled regime by incorporating an anisotropic, non-stationary collision kernel. A fast spectral separation method achieves O(N log N) complexity via FFT, preserving conservation laws and the H-theorem, and accurately captures moderately coupled plasma dynamics.
We present a generalized, data-driven collisional operator for one-component plasmas, learned from molecular dynamics simulations, to extend the collisional kinetic model beyond the weakly coupled regime. The proposed operator features an anisotropic, non-stationary collision kernel that accounts for particle correlations typically neglected in classical Landau formulations. To enable efficient numerical evaluation, we develop a fast spectral separation method that represents the kernel as a low-rank tensor product of univariate basis functions. This formulation admits an $O(N \log N)$ algorithm via fast Fourier transforms and preserves key physical properties, including discrete conservation laws and the H-theorem, through a structure-preserving central difference discretization. Numerical experiments demonstrate that the proposed model accurately captures plasma dynamics in the moderately coupled regime beyond the standard Landau model while maintaining high computational efficiency and structure-preserving properties.