1. An efficient iterative method for reconstructing the refractive index in complex domains from far field data.
- Author
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Hawkins, Stuart C., Stals, Linda, and Bagheri, Sherwin
- Subjects
- *
ELECTROMAGNETIC wave scattering , *SCATTERING (Physics) , *METAL inclusions , *INTEGRAL equations , *REFRACTIVE index , *IRON & steel plates - Abstract
We present a computational method for reconstructing the refractive index of an unknown complex-shaped two-dimensional medium with embedded metal inclusions from its transverse magnetic electromagnetic scattering properties. We present a novel hybrid surface-volume integral equation that generalises the Lippmann–Schwinger equation to media containing embedded scatterers. Using this hybrid equation, we show that the Frechet derivative of the forward-mapping satisfies a particular inhomogeneous wave scattering problem. We solve the inhomogeneous wave scattering problem using a novel coupled FEM-BEM formulation. Our numerical scheme is based on a thin plate spline ansatz for the refractive index, which can be constructed using a relatively small number of control points, and can be efficiently constructed and evaluated even for the complex-shaped multiply-connected domains of interest. Numerical experiments demonstrate the effectiveness of our method by reconstructing several challenging media. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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