TY - JOUR T1 - Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell's Equations with Random Inputs AU - Wang , Xiang AU - Li , Jichun AU - Fang , Zhiwei JO - Communications in Computational Physics VL - 1 SP - 211 EP - 236 PY - 2020 DA - 2020/11 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0011 UR - https://global-sci.org/intro/article_detail/cicp/18428.html KW - Maxwell's equations, uncertainty quantification, edge element. AB -

This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell's equations with uncertain permittivity, permeability and initial conditions. We develop the mathematical analysis of the error estimate for single level Monte Carlo method, multi-level Monte Carlo method, and the quasi-Monte Carlo method. The theoretical results are supplemented by numerical experiments.