# Discontinuous Galerkin algorithms for fully kinetic plasmas

## TL;DR

This paper introduces a high-order discontinuous Galerkin algorithm for solving the Vlasov-Maxwell system in plasma physics, emphasizing efficiency and accuracy in high-dimensional simulations.

## Contribution

It develops a novel high-order discontinuous Galerkin method with cost-reduction features for kinetic plasma simulations, validated through various benchmarks.

## Key findings

- Accurate high-order solutions for plasma distribution functions.
- Effective reduction of computational cost in high-dimensional simulations.
- Successful benchmarks demonstrating method efficacy.

## Abstract

We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge-Kutta method. Since the Vlasov equation in the Vlasov-Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.