Probability Density Function Estimation in Multilevel Monte Carlo FDTD Method

We apply the multilevel Monte Carlo (MLMC) method with the finite-difference time-domain method (FDTD) to estimate the probability density function (PDF) and the cumulative distribution function (CDF) of any quantity of interest for uncertainty quantification in electromagnetic problems. It is shown that, compared with the standard Monte Carlo FDTD (MC-FDTD), the MLMC-FDTD method can provide accurate estimations with high computational efficiency. In addition, as opposed to the polynomial chaos FDTD (PC-FDTD) method that suffers the curse of dimensionality or failure, the MLMC-FDTD method is more reliable.