Analysis and Application of Stochastic Collocation Methods for Maxwell's Equations with Random Inputs (Advances in Applied Mathematics and Mechanics, 2021)
In this paper we develop and analyze the stochastic collocation method forsolving the time-dependent Maxwell's equations with random coefficients and subjectto random initial conditions. We provide a rigorous regularity analysis of the solutionwith respect to the random variables. To our best knowledge, this is the first theoreticalresults derived for the standard Maxwell's equations with random inputs. The rate ofconvergence is proved depending on the regularity of the solution. Numerical resultsare presented to confirm the theoretical analysis.