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Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field

Philippe Chartier 1, 2, * Nicolas Crouseilles 2, 1 Mohammed Lemou 1, 3, 2 Florian Méhats 2, 1 Xiaofei Zhao 2
* Corresponding author
2 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent uniformly accurate methods, our schemes remain insensitive to the stiffness of the problem, in terms of both accuracy and computational cost. The specific difficulty (and the resulting novelty of our approach) stems from the presence of a non-periodic oscillation, which necessitates a careful ad-hoc reformulation of the equations. Our results are illustrated numerically on several examples.
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Submitted on : Wednesday, February 7, 2018 - 10:18:33 PM
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Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao. Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field. Mathematics of Computation, American Mathematical Society, 2019, 88 (320), pp.2697-2736. ⟨10.1090/mcom/3436⟩. ⟨hal-01703477⟩

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