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Splitting methods for rotations: application to vlasov equations

Joackim Bernier 1, * Fernando Casas 2 Nicolas Crouseilles 1
* Corresponding author
1 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 work, a splitting strategy is introduced to approximate two-dimensional rotation motions. Unlike standard approaches based on directional splitting which usually lead to a wrong angular velocity and then to large error, the splitting studied here turns out to be exact in time. Combined with spectral methods, the so-obtained numerical method is able to capture the solution to the associated partial differential equation with a very high accuracy. A complete numerical analysis of this method is given in this work. Then, the method is used to design highly accurate time integrators for Vlasov type equations: the Vlasov-Maxwell system and the Vlasov-HMF model. Finally , several numerical illustrations and comparisons with methods from the literature are discussed.
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Submitted on : Wednesday, July 10, 2019 - 11:59:56 AM
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Joackim Bernier, Fernando Casas, Nicolas Crouseilles. Splitting methods for rotations: application to vlasov equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2020, 42 (2), pp.A666-A697. ⟨10.1137/19M1273918⟩. ⟨hal-02178952⟩

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