A Review on Stochastic Multi-symplectic Methods for Stochastic Maxwell Equations  

作　　者：Liying Zhang Chuchu Chen Jialin Hong Lihai Ji 

机构地区：[1]School of Mathematical Science,China University of Mining and Technology,Beijing 100083,China [2]LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [4]Institute of Applied Physics and Computational Mathematics,Beijing 100094,China

出　　处：《Communications on Applied Mathematics and Computation》2019年第3期467-501,共35页应用数学与计算数学学报（英文）

摘　　要：Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical methods when applied to stochastic Hamiltonian partial differential equations (PDEs), such as long-time behavior, geometric structure preserving, and physical properties preserving. Stochastic Maxwell equations driven by either additive noise or multiplicative noise are a system of stochastic Hamiltonian PDEs intrinsically, which play an important role in fields such as stochastic electromagnetism and statistical radiophysics. Thereby, the construction and the analysis of various numerical methods for stochastic Maxwell equations which inherit the stochastic multi-symplecticity, the evolution laws of energy and divergence of the original system are an important and promising subject. The first stochastic multi-symplectic method is designed and analyzed to stochastic Maxwell equations by Hong et al.(A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise. J. Comput. Phys. 268:255-268, 2014). Subsequently, there have been developed various stochastic multi-symplectic methods to solve stochastic Maxwell equations. In this paper, we make a review on these stochastic multi-symplectic methods for solving stochastic Maxwell equations driven by a stochastic process. Meanwhile, the theoretical results of well-posedness and conservation laws of the stochastic Maxwell equations are included.

关 键 词：STOCHASTIC MULTI-SYMPLECTIC METHODS STOCHASTIC HAMILTONIAN partial differential EQUATIONS STOCHASTIC Maxwell EQUATIONS Structure-preserving METHODS 

分 类 号：O1[理学—数学]