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Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Hyperbolic equations and systems Kinematics Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  30 July 2015

Emmanuel Frénod ,
Sever A. Hirstoaga ,
Mathieu Lutz  and
Eric Sonnendrücker
Emmanuel Frénod
Affiliation:
Université Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France Inria Nancy-Grand Est, TONUS Project & IRMA (UMR CNRS 7501), Université de Strasbourg, France
Sever A. Hirstoaga*
Affiliation:
Inria Nancy-Grand Est, TONUS Project & IRMA (UMR CNRS 7501), Université de Strasbourg, France
Mathieu Lutz
Affiliation:
IRMA (UMR CNRS 7501) Université de Strasbourg, 7 rue René Descartes, F-67084 Strasbourg & Inria Nancy-Grand Est, TONUS Project, France
Eric Sonnendrücker
Affiliation:
Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany & TU Munich, Zentrum Mathematik - M16, Boltzmannstr. 3, 85747 Garching, Germany
*
*Corresponding author. Email addresses: [email protected] (E. Frénod), [email protected] (S. A. Hirstoaga), [email protected] (M. Lutz), [email protected] (E. Sonnendrücker)
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Abstract

With the aim of solving in a four dimensional phase space a multi-scale Vlasov-Poisson system, we propose in a Particle-In-Cell framework a robust time-stepping method that works uniformly when the small parameter vanishes. As an exponential integrator, the scheme is able to use large time steps with respect to the typical size of the solution’s fast oscillations. In addition, we show numerically that the method has accurate long time behaviour and that it is asymptotic preserving with respect to the limiting Guiding Center system.

Keywords

Vlasov-Poisson systemGuiding-CenterParticle-In-Cell methodhighly oscillatory ODEslong-time simulation

MSC classification

Secondary: 65L04: Stiff equations 65M99: None of the above, but in this section 35L03: Initial value problems for first-order hyperbolic equations 70B05: Kinematics of a particle
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 2 , August 2015 , pp. 263 - 296
Copyright
Copyright © Global-Science Press 2015 

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