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A finite difference method for the inverse scattering problem at fixed frequency

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Inverse Problems in Mathematical Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 422))

Abstract

We consider the problem of computing numerically the potential f in the Helmholtz equation Δu + k2(1 − f)u = 0 from plane wave irradiation at a fixed frequency κ. We discretize the differential equation in the plane by a five point difference star on a grid with siepsize h. It turns out that the resulting bilinear system can be solved recursively for f and u. We study the stability of this recursion. We find that the method enjoyes some stability properties provided hκ is chosen properly. The complexity of the method is O(h−4).

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Authors and Affiliations

  1. Fachbereich Mathematik, Germany

    F. Natterer & F. Wübbeling

Authors
  1. F. Natterer
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  2. F. Wübbeling
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Editor information

Lassi Päivärinta Erkki Somersalo

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© 1993 Springer-Verlag

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Natterer, F., Wübbeling, F. (1993). A finite difference method for the inverse scattering problem at fixed frequency. In: Päivärinta, L., Somersalo, E. (eds) Inverse Problems in Mathematical Physics. Lecture Notes in Physics, vol 422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57195-7_18

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  • DOI: https://doi.org/10.1007/3-540-57195-7_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57195-7

  • Online ISBN: 978-3-540-47947-5

  • eBook Packages: Springer Book Archive

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