volume | PIER Journals

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.

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Dr. Andrew C. M. Austin