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

David Cohen, Jianbo Cui, Jialin Hong, Liying Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number109382
Pages (from-to)1-21
Number of pages21
JournalJournal of Computational Physics
Volume410
DOIs
Publication statusPublished - 1 Jun 2020
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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