Two operator splitting methods for three-dimensional stochastic Maxwell equations with multiplicative noise

TL;DR

This paper introduces two energy-preserving operator splitting methods for three-dimensional stochastic Maxwell equations with multiplicative noise, ensuring energy conservation and first-order temporal convergence.

Contribution

The paper presents two novel stochastic splitting methods that preserve energy and efficiently solve 3D stochastic Maxwell equations with multiplicative noise.

Findings

Methods strictly preserve discrete energy conservation law.

Numerical experiments confirm energy conservation and first-order convergence.

Both methods effectively decouple the equations into simpler subsystems.

Abstract

In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into simple one-dimensional subsystems and construct two stochastic splitting methods, Splitting Method I and Splitting Method II, through a combination of spatial compact difference methods and the midpoint rule in time discretization for the deterministic parts, and exact unitary analytical solutions for the stochastic parts. Theoretical proofs show that both methods strictly preserve the discrete energy conservation law. Finally, numerical experiments fully verify the energy conservation of the methods and demonstrate that the temporal convergence order of the two splitting methods is first-order.