An interpolating particle method for the Vlasov-Poisson equation

TL;DR

This paper introduces a new particle method for the Vlasov-Poisson equation that reconstructs the distribution function between particles using mesh-free interpolation, leading to improved accuracy and noise reduction.

Contribution

It proposes a novel particle method where particles represent distribution function values, enhancing accuracy over traditional point charge methods.

Findings

Significantly increased accuracy in simulations.

Reduced noise compared to conventional particle methods.

Preserves many benefits of traditional schemes.

Abstract

In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the particles, the distribution function is reconstructed using mesh-free interpolation. Our numerical experiments confirm that this approach results in significantly increased accuracy and noise reduction. At the same time, many benefits of the conventional schemes are preserved.