Exponential integrators for stochastic Maxwell's equations driven by Itô noise
Artikel i vetenskaplig tidskrift, 2020

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.

Strong convergence

Stochastic Maxwell's equation

Average energy

Trace formula

Exponential integrator

Average divergence


David Cohen

Umeå universitet

Jianbo Cui

Georgia Institute of Technology

Jialin Hong

Chinese Academy of Sciences

Liying Sun

Chinese Academy of Sciences

Journal of Computational Physics

0021-9991 (ISSN) 1090-2716 (eISSN)

Vol. 410 109382






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