Semi-Lagrangian particle methods for high-dimensional Vlasov-Poisson systems

Georges-Henri Cottet (1)

1 EDP - Equations aux Dérivées Partielles

This paper deals with the implementation of high order semi-Lagrangian particle methods to handle high dimensional Vlasov-Poisson systems. It is based on recent developments in the numerical analysis of particle methods and the paper focuses on specific algorithmic features to handle large dimensions. The methods are tested with uniform particle distributions in particular against a recent multi-resolution wavelet based method on a 4D plasma instability case and a 6D gravitational case. Conservation properties, accuracy and computational costs are monitored. The excellent accuracy/cost trade-off shown by the method opens new perspective for accurate simulations of high dimensional kinetic equations by particle methods.

Domaines: Analyse numérique [math.NA]

Georges-Henri Cottet. Semi-Lagrangian particle methods for high-dimensional Vlasov-Poisson systems. Journal of Computational Physics, 2018, 365, pp.362 - 375. ⟨10.1016/j.jcp.2018.03.042⟩. ⟨hal-01584107v3⟩