A 3-D Stochastic FVTD Method Based on Reduced-Order Modeling for Statistically Random Media in Nano-Electromagnetic Applications

A spectrally optimized stochastic finite-volume time-domain technique is developed in this paper for the consistent analysis of 3-D nanoscale devices with statistically varying media heterogeneities. The novel algorithm is found on a compact block state-space framework and offers single-run evaluations of the mean value and standard deviation, thus evading the excessive system requirements of typical multiple-realization Monte Carlo FDTD approaches. Moreover, an energy-conserving flux concept guarantees the precise discretization of electromagnetic fields in regions of abrupt geometric details. In this manner, the complicated structure of nanocomposite applications is very reliably modeled, even for sub-wavelength field uncertainties, as deduced by several numerical configurations.