A dynamic domain semi-Lagrangian method for stochastic Vlasov equations
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.
Keywords
Cite
@article{arxiv.2502.13700,
title = {A dynamic domain semi-Lagrangian method for stochastic Vlasov equations},
author = {Jianbo Cui and Derui Sheng and Chenhui Zhang and Tau Zhou},
journal= {arXiv preprint arXiv:2502.13700},
year = {2026}
}