A dynamic domain semi-Lagrangian method for stochastic Vlasov equations

TL;DR

This paper introduces a dynamic domain semi-Lagrangian method tailored for stochastic Vlasov equations, effectively reducing computational costs while ensuring convergence, with validation through numerical experiments.

Contribution

It presents a novel dynamic domain semi-Lagrangian approach for stochastic Vlasov equations, including the first-order convergence analysis and practical efficiency improvements.

Findings

Significant reduction in computational costs.

First-order convergence proven for the method.

Numerical tests demonstrate good performance.

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.