A Stochastic Finite-Difference Time-Domain (FDTD) Method for Assessing Material and Geometric Uncertainties in Rectangular Objects

The uncertainties present in a variety of electromagnetic (EM) problems may have important effects on the output parameters of interest. Unfortunately, deterministic schemes are not applicable in such cases, as they only utilize the nominal value of each random variable. In this work, a two-dimensional (2D) finite-difference time-domain (FDTD) algorithm is presented, which is suitable for assessing randomness in the electrical properties, as well as in the dimensions of orthogonal objects. The proposed technique is based on the stochastic FDTD method and manages to extract the mean and the standard deviation of the involved field quantities in one realization. This approach is applied to three test cases, where uncertainty exists in the electrical and geometrical parameters of various materials. The numerical results demonstrate the validity of our scheme, as similar outcomes are extracted compared to the Monte Carlo (MC) algorithm.