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

Abstract

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.