This paper reviews Vlasov-based numerical methods used to model plasma in space
physics and astrophysics. Plasma consists of collectively behaving charged particles that …

This overview is devoted to splitting methods, a class of numerical integrators intended for
differential equations that can be subdivided into different problems easier to solve than the …

Dynamical low-rank approximation, as has been demonstrated recently, can be extremely
efficient in solving kinetic equations. However, a major deficiency is that it does not preserve …

Plasma supports collective modes and particle–wave interactions that lead to complex
behaviour in, for example, inertial fusion energy applications. While plasma can sometimes …

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 …

The efficient numerical solution of many kinetic models in plasma physics is impeded by the
stiffness of these systems. Exponential integrators are attractive in this context as they …

In this paper, Particle-in-Cell algorithms for the Vlasov–Poisson system are presented based
on its Poisson bracket structure. The Poisson equation is solved by finite element methods …

In this paper, we present a new class of conservative semi-Lagrangian schemes for kinetic
equations. They are based on the conservative reconstruction technique introduced in [1] …

High-resolution simulations of particle-based kinetic plasma models typically require a high
number of particles and thus often become computationally intractable. This is exacerbated …

Maintaining the stability and shape of a plasma is a crucial task in many technological
applications ranging from beam shaping to fusion energy. This is often challenging as …