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Journal Articles Computers & Mathematics with Applications Year : 2023

A Parareal algorithm for a highly oscillating Vlasov-Poisson system with reduced models for the coarse solving

Abstract

In this paper, we introduce a new strategy for solving highly oscillatory two-dimensional Vlasov-Poisson systems by means of a specific version of the parareal algorithm. The novelty consists in using reduced models, obtained from the two-scale convergence theory, for the coarse solving. The reduced models are useful to approximate the original Vlasov-Poisson model at a low computational cost since they are free of high oscillations. Both models are numerically solved in a particle-in-cell framework. We illustrate this strategy with numerical experiments based on long time simulations of a charged beam in a focusing channel and under the influence of a rapidly oscillating external electric field. On the basis of computing times, we provide an analysis of the efficiency of the parareal algorithm in terms of speedup.
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hal-03903280 , version 1 (16-12-2022)

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Laura Grigori, Sever A Hirstoaga, Julien Salomon. A Parareal algorithm for a highly oscillating Vlasov-Poisson system with reduced models for the coarse solving. Computers & Mathematics with Applications, 2023, 130, pp.137-148. ⟨10.1016/j.camwa.2022.12.004⟩. ⟨hal-03903280⟩
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