Exponential Integrators for Stochastic Maxwell's Equations Driven by Itô Noise
This work provides efficient numerical methods for simulating stochastic Maxwell's equations, which are important for applications in electromagnetics and plasma physics.
The authors develop explicit exponential integrators for stochastic Maxwell's equations, achieving strong order 1/2 for multiplicative noise and strong order 1 for additive noise, with exact preservation of symplectic structure, energy, and divergence for the linear additive case.
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 $\frac 12$ for general multiplicative noise. Combing 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.