Enhanced Multilevel Monte Carlo Method Applied to FDTD for Probability Distribution Estimation

Multilevel Monte Carlo (MLMC) method, enhanced by a smoothing technique based on kernel density estimation (KDE), is coupled with the finite-difference time-domain (FDTD) algorithm in order to estimate the probability distribution of any quantity of interest (QoI) for uncertainty quantification (UQ) in electromagnetic problems. It is shown that such enhanced MLMC-FDTD is faster than conventional Monte Carlo FDTD (MC-FDTD) while inheriting its advantages of robustness, simplicity, and generality, unlike other uncertainty analysis methods, such as the perturbation and the moment methods that cannot be used to straightforwardly estimate probability distribution or the polynomial chaos method that suffers from the curse of dimensionality problem or even fails.