A common problem with direct Vlasov solvers is ensuring that the distribution function
remains positive. A related problem is to guarantee that the numerical scheme does not …

Vlasov methods, which instead of following the particle trajectories, solve directly the Vlasov
equation on a grid of phase space have proven to be an efficient alternative to the Particle-In …

A new scheme for solving the Vlasov equation using a phase space grid is proposed. The
algorithm is based on the conservation of the flux of particles, and the distribution function is …

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 …

In this paper, we give a fairly exhaustive review of the literature on numerical simulations of
the Vlasov equation. We first recall the range of applications of the Vlasov equation and …

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

A method for computing the numerical solution of Vlasov type equations on massively
parallel computers is presented. In contrast with Particle In Cell methods which are known to …

A new scheme for solving the Vlasov equation using an unstructured mesh for the phase
space is proposed. The algorithm is based on the semi-Lagrangian method which exploits …

Conservative methods for the numerical solution of the Vlasov equation are developed in
the context of the one-dimensional splitting. In the case of constant advection, these …

A fast, accurate and robust method to obtain a numerical solution to the Vlasov equation is
presented. The method is based on time splitting to separate the initial equation into a set of …