IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-72456-0_32.html
   My bibliography  Save this book chapter

Integral Equation Methods in Inverse Obstacle Scattering with a Generalized Impedance Boundary Condition

In: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Author

Listed:
  • Rainer Kress

    (Universität Göttingen, Institut für Numerische und Angewandte Mathematik)

Abstract

The inverse problem under consideration is to reconstruct the shape of an impenetrable two-dimensional obstacle with a generalized impedance boundary condition from the far field pattern for scattering of time-harmonic acoustic or E-polarized electromagnetic plane waves. We propose an inverse algorithm that extends the approach suggested by Johansson and Sleeman (IMA J. Appl. Math. 72(1):96–112, 2007) for the case of the inverse problem for a sound-soft or perfectly conducting scatterer. It is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem which extends the integral equation method proposed by Cakoni and Kress (Inverse Prob. 29(1):015005, 2013) for a related boundary value problem for the Laplace equation. In addition, we also present an algorithm for reconstructing the impedance function when the shape of the scatterer is known. We present the mathematical foundations of the methods and exhibit their feasibility by numerical examples.

Suggested Citation

  • Rainer Kress, 2018. "Integral Equation Methods in Inverse Obstacle Scattering with a Generalized Impedance Boundary Condition," Springer Books, in: Josef Dick & Frances Y. Kuo & Henryk Woźniakowski (ed.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pages 721-740, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-72456-0_32
    DOI: 10.1007/978-3-319-72456-0_32
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-319-72456-0_32. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.