An Efficient SSFEM-POD Scheme for Wideband Stochastic Analysis of Permittivity Variations

Abstract

Stochastic analysis using polynomial chaos expansion (PCE)-based spectral stochastic finite-element method (SSFEM) is computationally expensive and is impacted by the curse of dimensionality. In this article, a low-dimensional basis is developed to approximate the problem using proper orthogonal decomposition (POD) to employ the PCE-based SSFEM, thereby resulting in an efficient intrusive formulation for uncertainty quantification (UQ) over a wide frequency band. Galerkin’s projection of vector finite elements for an electromagnetic (EM) problem with relative permittivity variations in multiple dielectric regions is formulated. The proposed method is shown to be computationally efficient and gives accurate results for a range of frequencies with single computation. It is also shown that this approach does not scale adversely with the number of stochastic parameters and has significantly lower memory requirement.