Wiener chaos expansion for stochastic Maxwell equations driven by Wiener process

TL;DR

This paper introduces a Wiener chaos expansion-based algorithm for stochastic Maxwell equations driven by Wiener process, significantly improving computational efficiency and accuracy over traditional Monte Carlo methods by directly solving solution statistics.

Contribution

It presents a novel Wiener chaos expansion algorithm that reduces stochastic Maxwell equations to deterministic form, enhancing efficiency and inheriting multi-symplecticity.

Findings

Algorithm outperforms Monte Carlo in efficiency and accuracy

Numerical experiments confirm the effectiveness of the Wiener chaos expansion

Method preserves multi-symplectic structure of the equations

Abstract

A novel and efficient algorithm based on the Wiener chaos expansion is proposed for the stochastic Maxwell equations driven by Wiener process. The proposed algorithm can reduce the original stochastic system to the deterministic case and separate the randomness in the computation. Therefore, it can yield a significant improvement of efficiency and lead to less computational errors compared to the Monte Carlo method, since the statistics of the solution can be solved directly without repeating over many realizations. In particular, the proposed algorithm could inherit the multi-symplecticity. Numerical experiments are dedicated to performing the efficiency and accuracy of the Wiener chaos expansion algorithm.