A spectral collocation method for the Landau equation in plasma physics

TL;DR

This paper introduces a spectral collocation method tailored for the Landau collision operator in plasma physics, achieving high accuracy and efficiency in numerical solutions by leveraging the operator's structure.

Contribution

The paper develops a spectral collocation approach specifically designed for Coulomb interactions in the Landau equation, reducing computational complexity while maintaining spectral accuracy.

Findings

Method preserves total mass exactly.

Momentum and energy are approximated with spectral accuracy.

Numerical results demonstrate efficiency in 3D velocity space.

Abstract

In this paper we present a spectral collocation method for the fast evaluation of the Landau collision operator for plasma physics, which allows us to obtain spectrally accurate numerical solutions. The method is inspired by the seminal work [36], but it is specifically designed for Coulombian interactions, taking into account the particular structure of the operator. It allows us to reduce the number of discrete convolutions to provide an approximation of the Landau operator. Then, we show that the method preserves the total mass whereas momentum and energy are approximated with spectral accuracy. Numerical results for the Landau equation in three dimensions in velocity space are presented to illustrate the efficiency of the present approach.