Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma

TL;DR

This paper presents a tensor train-based low-rank approximation method to efficiently model the Farley-Buneman instability in ionospheric plasma, significantly reducing computational complexity and memory usage.

Contribution

It introduces an adaptive low-rank tensor approach for kinetic equations in plasma modeling, improving computational efficiency over traditional methods.

Findings

Solution storage reduced by a factor of tens.

Efficient separation of space and velocity variables achieved.

Method verified through MATLAB implementation.

Abstract

We consider the numerical modeling of the Farley-Buneman instability development in the earth's ionosphere plasma. The ion behavior is governed by the kinetic Landau equation in the four-dimensional phase space, and since the finite difference discretization on a tensor product grid is used, this equation becomes the most computationally challenging part of the scheme. To relax the complexity and memory consumption, an adaptive model reduction using the low-rank separation of variables, namely the Tensor Train format, is employed. The approach was verified via the prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.