Exponential integrators for stochastic Maxwell's equations driven by Itô noise

被引：16

作者：

Cohen D. ^{[1
]}

Cui J. ^{[2
]}

Hong J. ^{[3
,4
]}

Sun L. ^{[3
,4
]}

机构：

[1] Department of Mathematics and Mathematical Statistics, Umeå University, Umeå

[2] School of Mathematics, Georgia Institute of Technology, Atlanta, 30332, GA

[3] LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing

[4] School of Mathematical Science, University of Chinese Academy of Sciences, Beijing

来源：

Journal of Computational Physics | 2020年 / 410卷

基金：

中国国家自然科学基金;

关键词：

Average divergence; Average energy; Exponential integrator; Stochastic Maxwell's equation; Strong convergence; Trace formula;

D O I：

10.1016/j.jcp.2020.109382

中图分类号：

学科分类号：

摘要：

This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of the mild solution, we first prove that the strong order of the numerical approximation is [Formula presented] for general multiplicative noise. Combining a proper decomposition with the stochastic Fubini's theorem, the strong order of the proposed scheme is shown to be 1 for additive noise. Moreover, for linear stochastic Maxwell's equation with additive noise, the proposed time integrator is shown to preserve exactly the symplectic structure, the evolution of the energy as well as the evolution of the divergence in the sense of expectation. Several numerical experiments are presented in order to verify our theoretical findings. © 2020 Elsevier Inc.

引用

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