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Journal Articles Journal of Computational Physics Year : 2021

Reduced model-based parareal simulations of oscillatory singularly perturbed ordinary differential equations

Abstract

We propose a new strategy for solving by the parareal algorithm highly oscillatory ordinary differential equations which are characteristics of a six-dimensional Vlasov equation. For the coarse solvers we use reduced models, obtained from two-scale asymptotic expansions. Such reduced models have a low computational cost since they are free of high oscillations. The parareal method allows to improve their accuracy in a few iterations through corrections by fine solvers of the full model. We demonstrate the accuracy and the efficiency of the strategy in numerical experiments of short time and long time simulations of charged particles submitted to a large magnetic field. In addition, the convergence of the parareal method is obtained uniformly with respect to the vanishing stiff parameter.
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Dates and versions

hal-03104042 , version 1 (08-01-2021)

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Laura Grigori, Sever Hirstoaga, Van-Thanh Nguyen, Julien Salomon. Reduced model-based parareal simulations of oscillatory singularly perturbed ordinary differential equations. Journal of Computational Physics, 2021, 436, pp.110282. ⟨10.1016/j.jcp.2021.110282⟩. ⟨hal-03104042⟩
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