An Efficient 3-D Stochastic HIE-FDTD Algorithm for Investigation of Statistical Variation in Electromagnetic Field

We propose a stochastic hybrid implicit–explicit finite-difference time-domain method (S-HIE-FDTD) to compute the mean and variance of the electromagnetic (EM) fields using a single simulation, given those of the conductivity and permittivity in the computation domain. The mean and variance field update equations underlying the proposed method are derived from the field update equations of the “traditional” deterministic HIE-FDTD. The Courant–Friedrichs–Lewy condition of the S-HIE-FDTD depends on the spatial discretization sizes only in two dimensions; therefore, for computation domains with fine geometric features only in the remaining dimension, it uses a time step size that is larger than that of fully explicit schemes. Indeed, numerical results demonstrate that the proposed method is faster than the previously developed stochastic FDTD in computing the mean and variance of the EM fields in two different problems: wave propagation through a multilayer human tissue and transmission through a frequency selective surface.