Multilevel Monte Carlo FDTD estimation of the cumulative distribution function with kernel smoothing technique

This paper addresses the multilevel Monte Carlo finite-difference time-domain (MLMC-FDTD) method for the estimation of the cumulative distribution function (CDF) of an electromagnetic quantity when material parameters in the problem are modeled as random variables. In order to alleviate the effects of the discontinuity of the indicator function, the kernel density estimation (KDE) technique is used. The technique can consider correlations between random parameters. It is shown that MLMC-FDTD has a faster convergence rate compared with Monte Carlo FDTD (MC-FDTD) and that the estimations of the CDF become smoother with the help of KDE. In addition, MLMC-FDTD preserves the advantages of MC-FDTD, such as robustness and simplicity, and proves to be a powerful approach, superior to other methods.