Abstract Particle-in-cell (PIC) methods have a long history in the study of laser-plasma
interactions. Early electromagnetic codes used the Yee staggered grid for field variables …

We present a novel framework for finite element particle-in-cell methods based on the
discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We …

Many problems encountered in plasma physics require a description by kinetic equations,
which are posed in an up to six-dimensional phase space. A direct discretization of this …

A spectral method for the numerical solution of the multi-dimensional Vlasov–Maxwell
equations is presented. The plasma distribution function is expanded in Fourier (for the …

A new splitting is proposed for solving the Vlasov–Maxwell system. This splitting is based on
a decomposition of the Hamiltonian of the Vlasov–Maxwell system and allows for the …

Abstract The Vlasov–Maxwell equations are used for the kinetic description of magnetized
plasmas. As they are posed in an up to 3+ 3 dimensional phase space, solving this problem …

Discontinuous Galerkin methods are developed for solving the Vlasov--Maxwell system,
methods that are designed to be systematically as accurate as one wants with provable …

Methods for the numerical discretization of the Vlasov equation should efficiently use the
phase-space discretization and should introduce only enough numerical dissipation to …

Numerical methods that approximate the solution of the Vlasov--Poisson equation by a low-
rank representation have been considered recently. These methods can be extremely …

The purpose of the present paper is to compare two semi-Lagrangian methods in the context
of the four-dimensional Vlasov–Poisson equation. More specifically, our goal is to compare …