Stochastic-Galerkin Finite-Difference Time-Domain for Waves in Random Layered Media

The authors introduce a Stochastic Finite-Difference Time Domain solver formulation based on Stochastic Galerkin Method. The solver can calculate the statistics of the wave in time domain, including mean, standard deviation at each time step. The method uses a single simulation of an expanded system, without the need for repeated simulations like Monte Carlo analysis. We demonstrate the method is accurate for computing random total waves in layered media with Gaussian random permittivity and conductivity. We also demonstrate the method for simulating materials with Bernoulli distributed random profiles, which is used to model material that may or may not exist. Results accuracy and computation time compare favorably to Monte Carlo simulations.