Vol. 101

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2021-02-25

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

By Andrew C. M. Austin
Progress In Electromagnetics Research M, Vol. 101, 117-126, 2021
doi:10.2528/PIERM20123101

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.

Citation


Andrew C. M. Austin, "Uncertainty Quantification and Parameter Estimation in the Finite-Difference Frequency-Domain Method Using Polynomial Chaos," Progress In Electromagnetics Research M, Vol. 101, 117-126, 2021.
doi:10.2528/PIERM20123101
http://www.jpier.org/PIERM/pier.php?paper=20123101

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