Uniformly Accurate Forward Semi-Lagrangian Methods for Highly Oscillatory Vlasov--Poisson Equations | Zendy

Nicolas Crouseilles | Zendy; Mohammed Lemou | Zendy; Florian Méhats | Zendy; Xiaofei Zhao | Zendy

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Uniformly Accurate Forward Semi-Lagrangian Methods for Highly Oscillatory Vlasov--Poisson Equations

Author(s) -

Nicolas Crouseilles,

Mohammed Lemou,

Florian Méhats,

Xiaofei Zhao

Publication year - 2017

Publication title -

multiscale modeling and simulation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.037

H-Index - 70

eISSN - 1540-3467

pISSN - 1540-3459

DOI - 10.1137/16m1059497

Subject(s) - integrator , lagrangian , poisson's equation , poisson distribution , mathematics , scheme (mathematics) , variable (mathematics) , work (physics) , mathematical analysis , classical mechanics , physics , voltage , statistics , quantum mechanics , thermodynamics

International audienceThis 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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