270
Views
23
CrossRef citations to date
0
Altmetric
Articles

A boundary integral equation method for the transmission eigenvalue problem

&
Pages 23-38 | Received 03 Feb 2016, Accepted 10 May 2016, Published online: 16 Jun 2016
 

Abstract

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.

AMS Subject Classifications:

Acknowledgements

This research was initiated while R.K. was visiting F.C. at the University of Delaware. The hospitality and the support are gratefully acknowledged.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of F.C. was supported in parts by the AFOSR [grant number FA9550-13-1-0199]; NSF [grant number DMS1602802].

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,361.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.