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The inverse scattering problem for cavities with impedance boundary condition

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Abstract

We consider the inverse scattering problem of determining the shape of a cavity with impedance boundary condition from sources and measurements placed on a curve inside the cavity. It is shown that both the shape \(\partial D\) of the cavity and the surface impedance λ are uniquely determined by the measured data and numerical methods are given for determining both \(\partial D\) and λ where neither one is known a priori. Numerical examples are given showing the viability of our method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China

    Hai-Hua Qin

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    David Colton

Authors
  1. Hai-Hua Qin
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  2. David Colton
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Correspondence to David Colton.

Additional information

Communicated by Yuesheng Xu and Honqqi Yang.

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Qin, HH., Colton, D. The inverse scattering problem for cavities with impedance boundary condition. Adv Comput Math 36, 157–174 (2012). https://doi.org/10.1007/s10444-011-9179-2

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  • DOI: https://doi.org/10.1007/s10444-011-9179-2

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