Spectral Stochastic FEM for Uncertainty Quantification Due to Multiple Dielectric Variabilities

Abstract

The impact of fabrication uncertainties such as random variations in material properties of the media on the electromagnetic system response is usually ignored due to computational cost. This is evaluated in this study using a spectral representation of these random parameters. The finite-element formulation for electromagnetics with edge elements is extended to include these stochastic variations. The numerical results are found to match the Monte Carlo simulation with a very large number of samples. The system matrix is found to be sparse, and hence, the method discussed is shown to be computationally efficient. Since this approach can handle uncertainty in multiple subregions, such as dielectric inserts in a waveguide, it can be used to analyze the sensitivity of practical electromagnetic systems over a range of frequencies.