Open Access
2018 Inverse scattering for shape and impedance revisited
Rainer Kress, William Rundell
J. Integral Equations Applications 30(2): 293-311 (2018). DOI: 10.1216/JIE-2018-30-2-293


The inverse scattering problem under consideration is to reconstruct both the shape and the impedance function of an impenetrable two-dimensional obstacle from the far field pattern for scattering of time-harmonic acoustic or E-polarized electromagnetic plane waves. We propose an inverse algorithm that is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. This extends the approach we suggested for an inverse boundary value problem for harmonic functions in Kress and Rundell(2005) and is a counterpart of our earlier work on inverse scattering for shape and impedance in Kress and Rundell(2001). We present the mathematical foundation of the method and exhibit its feasibility by numerical examples.


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Rainer Kress. William Rundell. "Inverse scattering for shape and impedance revisited." J. Integral Equations Applications 30 (2) 293 - 311, 2018.


Published: 2018
First available in Project Euclid: 13 September 2018

zbMATH: 06979942
MathSciNet: MR3853574
Digital Object Identifier: 10.1216/JIE-2018-30-2-293

Primary: 35J05 , 35J25 , 45Q05

Keywords: boundary integral equations , Helmholtz equation , inverse scattering , regularized Newton iterations

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.30 • No. 2 • 2018
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