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Random media uncertainties exhibit a significant impact on the properties of electromagnetic fields that usually deterministic models tend to neglect. As a result, these models fail to quantify the variation in the calculated electromagnetic fields, leading to inaccurate outcomes. This paper aims to introduce an unconditionally stable finite-difference time-domain (FDTD) method for assessing two-dimensional random media uncertainties in one simulation.

The proposed technique is an extension of the stochastic FDTD (S-FDTD) scheme, which approximates the variance of a given field component using the Delta method. Specifically in this paper, the Delta method is applied to the locally one-dimensional (LOD) FDTD scheme (hence named S-LOD-FDTD), to achieve unconditional stability. The validity of this algorithm is tested by solving two-dimensional random media problems and comparing the results with other methods, such as the Monte-Carlo (MC) and the S-FDTD techniques.

This paper provides numerical results that prove the unconditional stability of the S-LOD-FDTD technique. Also, the comparison with the MC and the S-FDTD methods shows that reliable outcomes can be extracted even with larger time steps, thus making this technique more efficient than the other two aforementioned schemes.

The S-LOD-FDTD method requires the proper quantification of various correlation coefficients between the calculated fields and the electrical parameters, to achieve reliable results. This cannot be known beforehand and the only known way to calculate them is to run a fraction of MC simulations.

This paper introduces a new unconditional stable technique for measuring material uncertainties in one realization.

The fabrication of electromagnetic (EM) components may induce randomness in several design parameters. In such cases, an uncertainty assessment is of high importance, as simulating the performance of those devices via deterministic approaches may lead to a misinterpretation of the extracted outcomes. This paper aims to present a novel heuristic for the sparse representation of the polynomial chaos (PC) expansion of the output of interest, aiming at calculating the involved coefficients with a small computational cost.

This paper presents a novel heuristic that aims to develop a sparse PC technique based on anisotropic index sets. Specifically, this study’s approach generates those indices by using the mean elementary effect of each input. Accurate outcomes are extracted in low computational times, by constructing design of experiments (DoE) which satisfy the D-optimality criterion.

The method proposed in this study is tested on three test problems; the first one involves a transmission line that exhibits several random dielectrics, while the second and the third cases examine the effects of various random design parameters to the transmission coefficient of microwave filters. Comparisons with the Monte Carlo technique and other PC approaches prove that accurate outcomes are obtained in a smaller computational cost, thus the efficiency of the PC scheme is enhanced.

This paper introduces a new sparse PC technique based on anisotropic indices. The proposed method manages to accurately extract the expansion coefficients by locating D-optimal DoE.