An exponential integrator for a highly oscillatory Vlasov equation

TL;DR

This paper introduces an exponential integrator within a Particle-In-Cell framework that achieves uniform accuracy for highly oscillatory 1D Vlasov-Poisson equations, enabling larger time steps regardless of oscillation frequency.

Contribution

It presents a novel exponential time differencing scheme that maintains accuracy as the small parameter approaches zero, improving simulation efficiency for oscillatory plasma models.

Findings

Achieves uniform accuracy across parameter regimes

Allows larger time steps compared to traditional methods

Demonstrates effectiveness on 1D Vlasov-Poisson system

Abstract

In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an exponential time differencing approach, the scheme is able to use large time steps with respect to the typical size of the fast oscillations of the solution.