An efficient iterative method for reconstructing the refractive index in complex domains from far field data

Stuart Hawkins, Linda Stals, Sherwin Bagheri

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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.
Original languageEnglish
Article number115573
Pages (from-to)1-17
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume438
DOIs
Publication statusPublished - 1 Mar 2024

Bibliographical note

© 2023 The Author(s). Published by Elsevier B.V. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

  • Helmholtz equation
  • Frechet derivative
  • Integral equation
  • Finite element method
  • Coupled FEM-BEM
  • Inverse problem

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