Reconstruction of Neumann eigenvalues and support of sound hard obstacles

Document Type

Article

Publication Date

1-1-2014

Abstract

Recent study in inverse scattering theory shows that Dirichlet and transmission eigenvalues for sound soft obstacles and inhomogeneous non-absorbing media, respectively, can be reconstructed from scattering data. The purpose of the current paper is to show that Neumann eigenvalues can be estimated from scattering data and to provide a thorough numerical study. To reconstruct an eigenvalue, one usually chooses a point inside the obstacle and solves some linear ill-posed integral equations for wavenumbers in an interval containing the eigenvalue. For a specific eigenvalue, it is noted that there are points inside the obstacle which cannot be used. In addition, we present some numerical examples relating to the behavior of the solutions of the integral equations for points outside the obstacle. Finally, an eigenvalue method is employed to reconstruct the support of the obstacle. © 2014 IOP Publishing Ltd.

Publication Title

Inverse Problems

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