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

Abstract

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.

A stochastic contour path finite‐difference time‐domain method for uncertainty analysis of metal slot size

“…K. Masumnia-Bisheh presented geometrically S-FDTD as a way to quantify geometric uncertainties but only for 1-D and 2-D problems [19]. C. Salis developed the two-dimensional stochastic FDTD method for the analyses of geometry and media uncertainties together while the results only agreed with the results of the MC method at the peak of the waveform and diverged from the results of the MC method at the tail of the waveform [20,21]. The value of correlation coefficient will affect the accuracy of variance [22].…”

Stochastic FDTD for stochastic problems with axial symmetry

“…So the efficiency of S‐FDTD is promisingly high than that of MC or gPC. The S‐FDTD is used in many EM fields, including wave propagation in unmagnetised plasma [17], superconducting transmission lines [18], simple object with geometric uncertainties [19], Holland's thin wire [20] and so on. On the other hand, the limitation of S‐FDTD is that the variance estimation of the field needs careful choice of the correlation coefficient [21, 22].…”