Comptes Rendus
no. 10-11
Theoretical and numerical approaches for Vlasov–Maxwell equations
Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator
Emmanuel Frénod1, 2  ; Sever A. Hirstoaga2, 3 ; Mathieu Lutz2, 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, Volume 342 (2014) no. 10-11, pp. 595-609.

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.

Reçu le :
Accepté le :
Publié le :
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
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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     title = {Long-time simulation of a highly oscillatory {Vlasov} equation with an exponential integrator},
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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, 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/

[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

[3] C.K. Birdsall; A.B. Langdon Plasma Physics via Computer Simulation, Institute of Physics, Bristol and Philadelphia, 1991

[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

[5] S.M. Cox; P.C. Matthews Exponential time differencing for stiff systems, J. Comput. Phys., Volume 176 (2002), pp. 430-455

[6] M. Hochbrück; A. Ostermann Exponential integrators, Acta Numer., Volume 19 (2010), pp. 209-286

[7] J.K. Hale Ordinary Differential Equations, John Wiley, New York, 1969

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