An energy-conserving method for stochastic Maxwell equations with multiplicative noise

JOURNAL OF COMPUTATIONAL PHYSICS

卷:351

Article

Hong, Jialin¹  Ji, Lihai²  Zhang, Liying³  Cai, Jiaxiang⁴ 

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China

[3] China Univ Min & Technol, Sch Math Sci, Beijing 100083, Peoples R China

[4] Huaiyin Normal Univ, Sch Math Sci, Huaian 210046, Jiangsu, Peoples R China

关键词: Energy-conserving method;    Three-dimensional stochastic Maxwell equations;    Multiplicative noise;    Geometric structure;   

DOI  :  10.1016/j.jcp.2017.09.030

来源: Elsevier

【 摘 要 】

In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic multi-symplectic conservation law), and the energy of system is a conservative quantity almost surely. We propose a stochastic multi-symplectic energy-conserving method for the equations by using the wavelet collocation method in space and stochastic symplectic method in time. Numerical experiments are performed to verify the excellent abilities of the proposed method in providing accurate solution and preserving energy. The mean square convergence result of the method in temporal direction is tested numerically, and numerical comparisons with finite difference method are also investigated. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free