On the Accuracy of Polynomial Models in Stochastic Computational Electromagnetics Simulations Involving Dielectric Uncertainties

Uncertainties inherent in the measured electromagnetic properties of most materials give rise to statistical uncertainty in field values obtained in computational electromagnetics (CEM) simulations. A number of recently proposed techniques for quantifying uncertainty in CEM simulations use polynomial expansions to approximate these stochastic field variations. We investigate the accuracy of polynomial approximations using three canonical scattering scenarios with dielectric uncertainties. Analytical expressions for field values are used to assess the accuracy of the standard deviation of the field quantities derived from the polynomial approximations. The accuracy of the polynomial approximations is shown to be strongly dependent on the mean dielectric properties of the scatterers. Extremely high-order expansions are necessary to achieve accurate approximations in some instances. The computational cost of high-order polynomial approximations limits the utility of polynomial basis function expansions in uncertainty quantification techniques for CEM.