Multilevel Monte Carlo FDTD method for uncertainty quantification

The recent multilevel Monte Carlo (MLMC) 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 (MC-FDTD), at the price of a small reduction of its accuracy. It is advantageous with respect to Polynomial Chaos FDTD (PC-FDTD), when the latter fails or becomes prohibitive for computational requirements. It also appears to widely outperform Stochastic FDTD (S-FDTD) in terms of accuracy.