Uncertainty Quantification and Parameter Estimation in the Finite-Difference Frequency-Domain Method Using Polynomial Chaos

Abstract

A new numerical method is proposed for uncertainty quantification in the two-dimensional finite-difference frequency-domain (FDFD) method. The method is based on an intrusive polynomial chaos expansion (PCE) of the Helmholtz equation in terms of the material properties. The resulting PCE-FDFD method is validated against Monte-Carlo simulations for an electromagnetic scattering problem at 1.0 GHz. Good agreement is found between the statistics of the electric fields computed using the proposed method and the Monte-Carlo results, with a factor 15-120 reduction in the computational costs. The PCE-FDFD method is also applied to estimate the material properties from exterior measurements by formulating an objective function and applying constrained optimisation techniques. A maximum 1.7% error in the material properties was observed for a test geometry with six unknowns and 20 sample points.

TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media

“…Remark 2.1. For some applications using electromagnetic waves, the Helmholtz equation is used as a good approximation [56][57][58]. In this case, the parameters involved are the electric permittivity ε, the magnetic permeability µ and the electric conductivity σ, the latter inducing damping.…”