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 - <p style="text-align: justify;">This article is devoted to three quadrature methods for the rapid solution
of stochastic time-dependent Maxwell&#39;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.</p>