Volume 18, Issue 2
Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field

Emmanuel Frénod, Sever A. Hirstoaga, Mathieu Lutz & Eric Sonnendrücker

Commun. Comput. Phys., 18 (2015), pp. 263-296.

Published online: 2018-04

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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.

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@Article{CiCP-18-263, author = {Emmanuel Frénod , and Sever A. Hirstoaga , and Mathieu Lutz , and Eric Sonnendrücker , }, title = {Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {2}, pages = {263--296}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.070214.160115a}, url = {http://global-sci.org/intro/article_detail/cicp/11028.html} }
TY - JOUR T1 - Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field AU - Emmanuel Frénod , AU - Sever A. Hirstoaga , AU - Mathieu Lutz , AU - Eric Sonnendrücker , JO - Communications in Computational Physics VL - 2 SP - 263 EP - 296 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.070214.160115a UR - https://global-sci.org/intro/article_detail/cicp/11028.html KW - AB -

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.

Emmanuel Frénod, Sever A. Hirstoaga, Mathieu Lutz & Eric Sonnendrücker. (2020). Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field. Communications in Computational Physics. 18 (2). 263-296. doi:10.4208/cicp.070214.160115a
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