WENO schemes applied to the quasi-relativistic Vlasov--Maxwell model for laser-plasma interaction

In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov--Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge--Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments

Convergence analysis of Strang splitting for Vlasov-type equations

A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that under suitable assumptions the convergence is of second order in the time step \tau. As an example, it is verified that the Vlasov-Poisson equation in 1+1 dimensions fits into the framework of this analysis. Also, numerical experiments for the latter case are presented.Comment: submitted to the SIAM Journal on Numerical Analysi

Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations

International audienceThe Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson's equation, which rules the evolution of the self-consistent electric field. In this paper, we introduce a new class of forward Semi-Lagrangian schemes for the Vlasov-Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. The convergence in L1 norm of the schemes is proved and error estimates are obtained

Convergence of a semi-Lagrangian scheme for the reduced Vlasov-Maxwell system for laser-plasma interaction

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