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arXiv · 2502.13700

A dynamic domain semi-Lagrangian method for stochastic Vlasov equations

Jianbo Cui·Derui Sheng·Chenhui Zhang·Tau Zhou
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Abstract

We propose a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noises, which arise in plasma physics and astrophysics. This method combines the volume-preserving property of stochastic characteristics with a dynamic domain adaptation strategy and a reconstruction procedure. It offers a substantial reduction in computational costs compared to the traditional semi-Lagrangian techniques for stochastic problems. Furthermore, we present the first-order convergence analysis of the proposed method, partially addressing the conjecture in the work [C.-E. Br\'{e}hier and D. Cohen, J. Comput. Dyn., 2024] on the convergence order of numerical methods for stochastic Vlasov equations. Several numerical tests are provided to show good performance of the proposed method.

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Jianbo Cui, Derui Sheng, Chenhui Zhang, Tau Zhou. 2025-02-19. A dynamic domain semi-Lagrangian method for stochastic Vlasov equations. https://doi.org/10.1016/j.jcp.2025.114335

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