Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations

TL;DR

This paper introduces Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations that preserve geometric structures, ensuring accurate long-term simulations through finite element spatial discretization and splitting time integration.

Contribution

It develops a novel Poisson-preserving particle-in-cell method combining finite element spatial discretization with Hamiltonian splitting in time for Vlasov-Maxwell equations.

Findings

The method preserves the discrete non-canonical Poisson structure.

The algorithm is explicit and Poisson preserving.

It enables efficient long-time simulations of plasma dynamics.

Abstract

In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.