Multilevel Monte Carlo FDTD Method for Uncertainty Quantification

The recent multilevel Monte Carlo method is here proposed for uncertainty quantification in electromagnetic problems solved by the finite-difference time-domain (FDTD) method, when material parameters are modeled as random variables. It improves the estimations of the mean and variance of the quantities of interest computed on a FDTD spatial grid by sampling at coarser levels of discretization. The proposed approach can amply reduce the computational cost of the standard Monte Carlo FDTD, at the price of a small reduction of its accuracy. It is advantageous with respect to polynomial chaos FDTD, when the latter fails or becomes prohibitive for computational requirements. It also appears to widely outperform stochastic FDTD in terms of accuracy.