Dimensionality Reduction of the Polynomial Chaos Technique Based on the Method of Moments

Abstract

A variety of electromagnetic problems present a high level of uncertainty in several aspects, which is interpreted as a variability in specific input variables. In many examples, certain stochastic parameters may exhibit a low or even a negligible contribution to the outputs of interest. However, neglecting a high number of random variables may result in computational errors of the examined quantities in a given problem. For this reason, we propose a hybrid algorithm, which is based on the combination of the polynomial chaos (PC) approach and the method of moments (MoM). A dimensionality reduction of the PC technique is performed by considering the trivial random inputs as deterministic. The computational errors in the output values are mitigated through the utilization of the MoM. The numerical results, which present comparisons with the traditional PC approach, the MoM, and the Monte Carlo technique, prove the validity of the proposed scheme.

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