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Electromagnetic inverse shape problem for coated obstacles

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An Erratum to this article was published on 12 July 2016

Abstract

We address the inverse problem of retrieving the shape of an obstacle with impedance in the form of a surface wave operator using the knowledge of electromagnetic scattering amplitude at a fixed frequency. We prove unique reconstructions from infinitely many measures. We then provide a characterization of the scattering amplitude derivative with respect to the obstacle shape. This derivative includes the case of shape dependent impedance parameters. We then employ a gradient-descent algorithm with H 1 boundary regularisation of the descent direction to numerically solve the inverse problem. The procedure is validated for three dimensional geometries using synthetic data.

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Authors and Affiliations

  1. Department of Mathematics, University College London, Gower street, London, WC1E 6BT, United Kingdom

    N. Chaulet

  2. INRIA Saclay Ile de France et Ecole Polytechnique, Route de Saclay, 91128, Palaiseau Cedex, France

    H. Haddar

Authors
  1. N. Chaulet
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  2. H. Haddar
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Corresponding author

Correspondence to N. Chaulet.

Additional information

Communicated by: Jan Hesthaven

The research of N. C. is supported by the Medical Research Council Grant MR/K00767X/1.

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Chaulet, N., Haddar, H. Electromagnetic inverse shape problem for coated obstacles. Adv Comput Math 41, 1179–1205 (2015). https://doi.org/10.1007/s10444-015-9406-3

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  • DOI: https://doi.org/10.1007/s10444-015-9406-3

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