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

This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell’s equations with uncertain permittivity,perme-ability 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.