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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:436

Article

Grigori, Laura^1,2  Hirstoaga, Sever A.^1,2  Nguyen, Van-Thanh^1,2  Salomon, Julien^2,3 

[1] Sorbonne Univ, Project Team ALPINES, INRIA, F-75589 Paris 12, France

[2] Univ Paris, CNRS, Lab Jacques Louis Lions LJLL, F-75589 Paris 12, France

[3] Sorbonne Univ, Project Team ANGE, INRIA, F-75589 Paris 12, France

关键词: Parareal algorithm;    Two-scale expansion;    Multi-scale models;    Vlasov characteristics;    Electric and magnetic fields;   

DOI  :  10.1016/j.jcp.2021.110282

来源: Elsevier

【 摘 要 】

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 the two-scale asymptotic expansions in [4]. 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. (c) 2021 Elsevier Inc. All rights reserved. Superscript/Subscript Available

【 授权许可】

Free