Uniformly accurate forward semi-Lagrangian methods for highly oscillatory Vlasov-Poisson equations.

Nicolas Crouseilles 1, 2 Mohammed Lemou 1, 2 Florian Méhats 1, 2 Xiaofei Zhao 1
2 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : This work is devoted to the numerical simulation of a Vlasov-Poisson equation modeling charged particles in a beam submitted to a highly oscillatory external electric field. A numerical scheme is constructed for this model. This scheme is uniformly accurate with respect to the size of the fast time oscillations of the solution, which means that no time step refinement is required to simulate the problem. The scheme combines the forward semi-Lagrangian method with a class of Uniformly Accurate (UA) time integrators to solve the characteristics. These UA time integrators are derived by means of a two-scale formulation of the characteristics, with the introduction of an additional periodic variable. Numerical experiments are done to show the efficiency of the proposed methods compared to conventional approaches.
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Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2017, 15 (2), pp.723-744. 〈10.1137/16M1059497〉
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Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao. Uniformly accurate forward semi-Lagrangian methods for highly oscillatory Vlasov-Poisson equations.. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2017, 15 (2), pp.723-744. 〈10.1137/16M1059497〉. 〈hal-01286947〉

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