An energy-conserving method for stochastic Maxwell equations with multiplicative noise
An energy-conserving method for stochastic Maxwell equations with multiplicative noise
复制标题
具有乘性噪声的随机麦克斯韦方程组的能量守恒方法
DOI：
10.1016/j.jcp.2017.09.030
复制
发表时间：
2017-12-15
影响因子：
4.1
通讯作者：
Cai, Jiaxiang
中科院分区：
文献类型：
--
作者：
Hong, Jialin;Ji, Lihai;Cai, Jiaxiang
本文证明了带乘性噪声的三维随机麦克斯韦方程是具有几何结构（即随机多辛守恒律）的随机Hamilton偏微分方程，系统的能量几乎必然是守恒量.在空间上利用小波配点方法，在时间上利用随机辛方法，提出了一种求解该方程的随机多辛能量守恒方法。数值实验验证了该方法在提供精确解和保持能量方面的优异性能。通过数值计算，检验了该方法在时间方向上的均方收敛性，并与有限差分法进行了数值比较。(C)2017爱思唯尔公司All rights reserved.
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.