Stochastic Galerkin methods for transient Maxwell's equations with random geometries

Abstract

The generalized polynomial chaos expansion was broadly introduced to model systems with uncertain inputs, including random material properties and random computational geometries. This paper focuses solving electromagnetic field when the geometry contains multi-randomness. A linear transformation always maps spatial random variables into grids with fixed length. Hence a great advantage of the method is that the numerical mesh is not changed despite geometrical variations. We applied efficient stochastic Galerkin methods to time-domain Maxwell's equations when thicknesses of two-layer media are uncertain. High-order Runge-Kutta discontinuous Galerkin methods were performed on the resulting system of the expansion coefficients.