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Interior Transmission Eigenvalues for Anisotropic Media

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Integral Methods in Science and Engineering, Volume 1

Abstract

In this paper, the numerical calculation of interior transmission eigenvalues for anisotropic media in two dimensions is considered. This is achieved by reformulating the original problem into a system of boundary integral equations. The resulting nonlinear eigenvalue problem is solved with a recent method using complex-valued contour integrals. Numerical results show that one is also able to calculate complex-valued interior transmission eigenvalues, although the existence of those is still open.

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Acknowledgements

The research of the second author was supported in part by a grant from the United States Air Force Office of Scientific Research.

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Authors and Affiliations

  1. Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany

    A. Kleefeld

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    D. Colton

Authors
  1. A. Kleefeld
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  2. D. Colton
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Corresponding author

Correspondence to A. Kleefeld .

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Editors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Christian Constanda

  2. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Matteo Dalla Riva

  3. Department of Mathematics, University of Padova, Padova, Italy

    Pier Domenico Lamberti

  4. Systems Analysis, Prognosis and Control, Fraunhofer Institute for Industrial Math, Kaiserslautern, Germany

    Paolo Musolino

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Kleefeld, A., Colton, D. (2017). Interior Transmission Eigenvalues for Anisotropic Media. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_12

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