# A spectral collocation method for the Landau equation in plasma physics

arXiv: https://arxiv.org/abs/2006.15885 · HTML: https://mlsanity.com/paper/2006.15885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [opPINN: Physics-Informed Neural Network with operator learning to approximate solutions to the Fokker-Planck-Landau equation](https://mlsanity.com/paper/2207.01765/) (2022)

## Abstract (arXiv)

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.