A boundary integral equation method for the transmission eigenvalue problem

We propose a new integral equation formulation to characterize and compute transmission eigenvalues for constant refractive index that play an important role in inverse scattering problems for penetrable media. As opposed to the recently developed approach by Cossonnière and Haddar [1,2] which relie...

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Bibliographic Details
Published in:Applicable analysis 2017-01, Vol.96 (1), p.23-38
Main Authors: Cakoni, Fioralba, Kress, Rainer
Format: Article
Language:English
Subjects:
Boundary integral equations
Computational efficiency
Constants
Eigenvalues
inhomogeneous media
Integral equations
Inverse problems
inverse scattering
Mathematical analysis
Numerical analysis
Operators
Reduction
Scattering
transmission eigenvalues
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Summary:We propose a new integral equation formulation to characterize and compute transmission eigenvalues for constant refractive index that play an important role in inverse scattering problems for penetrable media. As opposed to the recently developed approach by Cossonnière and Haddar [1,2] which relies on a two by two system of boundary integral equations our analysis is based on only one integral equation in terms of Dirichlet-to-Neumann or Robin-to-Dirichlet operators which results in a noticeable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further we employ the numerical algorithm for analytic non-linear eigenvalue problems that was recently proposed by Beyn [3] for the numerical computation of transmission eigenvalues via this new integral equation.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2016.1189537