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

Part of the special issue:

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

Keywords: 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

@article{CRMECA_2014__342_10-11_595_0,
     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},
     year = {2014},
     publisher = {Elsevier},
     volume = {342},
     number = {10-11},
     doi = {10.1016/j.crme.2014.06.006},
     language = {en},
}

TY  - JOUR
AU  - Emmanuel Frénod
AU  - Sever A. Hirstoaga
AU  - Mathieu Lutz
TI  - Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator
JO  - Comptes Rendus. Mécanique
PY  - 2014
SP  - 595
EP  - 609
VL  - 342
IS  - 10-11
PB  - Elsevier
DO  - 10.1016/j.crme.2014.06.006
LA  - en
ID  - CRMECA_2014__342_10-11_595_0
ER  -

%0 Journal Article
%A Emmanuel Frénod
%A Sever A. Hirstoaga
%A Mathieu Lutz
%T Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator
%J Comptes Rendus. Mécanique
%D 2014
%P 595-609
%V 342
%N 10-11
%I Elsevier
%R 10.1016/j.crme.2014.06.006
%G en
%F CRMECA_2014__342_10-11_595_0

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

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

[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

Cited by Sources:

Comments - Policy