A Parallel Low-Rank Solver for the Six-Dimensional Vlasov-Maxwell Equations

TL;DR

This paper introduces a parallel low-rank solver for the six-dimensional Vlasov-Maxwell equations, enabling efficient and accurate plasma simulations by reducing computational costs through velocity space compression.

Contribution

The paper presents a novel parallel low-rank solver for the full six-dimensional Vlasov-Maxwell equations, extending low-rank methods to electromagnetic plasma simulations.

Findings

Accurately models plasma turbulence and magnetic reconnection.

Reduces computational cost significantly compared to full grid methods.

Maintains mass conservation and Gauss's law in simulations.

Abstract

Continuum Vlasov simulations can be utilized for highly accurate modelling of fully kinetic plasmas. Great progress has been made recently regarding the applicability of the method in realistic plasma configurations. However, a reduction of the high computational cost that is inherent to fully kinetic simulations would be desirable, especially at high velocity space resolutions. For this purpose, low-rank approximations can be employed. The so far available low-rank solvers are restricted to either electrostatic systems or low dimensionality and can therefore not be applied to most space, astrophysical and fusion plasmas. In this paper we present a new parallel low-rank solver for the full six-dimensional electromagnetic Vlasov-Maxwell equations with a compression of the particle distribution function in velocity space. Special attention is paid to mass conservation and Gauss's law. The low-rank Vlasov solver is applied to standard benchmark problems of plasma turbulence and magnetic reconnection and compared to the full grid method. It yields accurate results at significantly reduced computational cost.