Wiener chaos expansion for stochastic Maxwell equations driven by Wiener process

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.