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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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
Keywords
- Inverse scattering problem
- Maxwell’s equations
- Generalized Impedance Boundary Conditions
- Shape derivative
- Steepest descent method