An Unconditionally Stable Stochastic CDI-FDTD Method for Electromagnetic Wave Propagation in Media With Uncertain Material Properties

The electromagnetic parameters of practical materials are inherently susceptible to stochastic fluctuations arising from individual variability and environmental perturbations, thereby introducing uncertainty into the electromagnetic response of complex systems. To comprehensively capture such randomness, a stochastic complying-divergence implicit finite-difference time-domain (S-CDI-FDTD) scheme is developed, in which the statistical Delta method is systematically incorporated to quantify and propagate parameter-induced uncertainties. This approach enables the simultaneous acquisition of both the mean and variance of EM fields through a single simulation, thus providing an efficient framework for modeling EM systems involving random media. Numerical analyses confirm that the proposed method strictly adheres to Gauss’s divergence law while maintaining unconditional stability. Several numerical examples further verify the accuracy and effectiveness of the S-CDI-FDTD scheme for EM simulations in random media.