Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator

Emmanuel Frénod; Sever A. Hirstoaga; Mathieu Lutz

doi:10.1016/j.crme.2014.06.006

Theoretical and numerical approaches for Vlasov–Maxwell equations

Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator

Emmanuel Frénod ^1,² ; Sever A. Hirstoaga ^2,³; Mathieu Lutz ^2,³

¹ Université Bretagne-Sud, UMR 6205, LMBA, 56000 Vannes, France
² TONUS Project, Inria Nancy Grand-Est, France
³ IRMA (UMR CNRS 7501), Université de Strasbourg, France

Comptes Rendus. Mécanique, Theoretical and numerical approaches for Vlasov-maxwell equations, Volume 342 (2014) no. 10-11, pp. 595-609.

Abstract

We change a previous time-stepping algorithm for solving a multi-scale Vlasov–Poisson system within a Particle-In-Cell method, in order to perform accurate long-time simulations. As an exponential integrator, the new scheme allows us to use large time steps compared to the size of the oscillations in the solution.

Received: 2014-03-11
Accepted: 2014-06-08
Published online: 2014-08-05

DOI: 10.1016/j.crme.2014.06.006

Mots-clés : Vlasov–Poisson system, Paraxial approximation, Particle-In-Cell method, Highly oscillatory ODEs, Exponential time differencing, Long-time simulation

Author's affiliations:

Emmanuel Frénod ^{1, 2}; Sever A. Hirstoaga ^{2, 3}; Mathieu Lutz ^{2, 3}

¹ Université Bretagne-Sud, UMR 6205, LMBA, 56000 Vannes, France
² TONUS Project, Inria Nancy Grand-Est, France
³ IRMA (UMR CNRS 7501), Université de Strasbourg, France

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     author = {Emmanuel Fr\'enod and Sever A. Hirstoaga and Mathieu Lutz},
     title = {Long-time simulation of a highly oscillatory {Vlasov} equation with an exponential integrator},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {595--609},
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     doi = {10.1016/j.crme.2014.06.006},
     language = {en},
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Emmanuel Frénod; Sever A. Hirstoaga; Mathieu Lutz. Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator. Comptes Rendus. Mécanique, Theoretical and numerical approaches for Vlasov-maxwell equations, Volume 342 (2014) no. 10-11, pp. 595-609. doi : 10.1016/j.crme.2014.06.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.06.006/

References
Cited by

[1] E. Frénod; S.A. Hirstoaga; E. Sonnendrücker An exponential integrator for a highly oscillatory Vlasov equation, Discrete Contin. Dyn. Syst. Ser. S, Volume 8 (2015) no. 1, pp. 169-183

[2] E. Frénod; F. Salvarani; E. Sonnendrücker Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method, Math. Models Methods Appl. Sci., Volume 19 (2009) no. 2, pp. 175-197

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[4] M. Lutz Application of Lie Transform Techniques for simulation of a charged particle beam, Discrete Contin. Dyn. Syst. Ser. S, Volume 8 (2015) no. 1, pp. 185-221

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