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Mathematical and Computational Aspects pp 59–77Cite as

Boundary Integral Equation Methods for Canonical Problems in Diffraction Theory (Invited contribution)

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Part of the book series: Boundary Elements IX ((BOUNDARY,volume 9/1))

Abstract

For many years, diffraction theory was governed by one method of complex function theory: the classical Wiener-Hopf technique, see Noble1. New insights for Sommerfeld diffraction problems were recently obtained (Speck2,3; Meister and Speck4,5,6; Speck, Hurd and Meister7) with tools from operator theory (Devinatz and Shinbrot8; Talenti9; Eskin10; Meister and Speck11; Mikhlin and Prössdorf12; Speck13) and from some progress in the factoring of non-rational function matrices, see Khrapkov14, Daniele15, Hurd16 and, in another direction, see Rawlins and Williams17, Williams18 and Jones19,20. In the present paper we are going to study rigorously boundary and transmission problems for the two-dimensional Helmholtz equation outside of two parallel lines or half-lines, which form the canonical geometry here.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule, 6100, Darmstadt, West Germany

    E. Meister & F.-O. Speck

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  1. E. Meister
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  2. F.-O. Speck
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C. A. Brebbia W. L. Wendland G. Kuhn

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© 1987 Springer-Verlag Berlin Heidelberg

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Meister, E., Speck, FO. (1987). Boundary Integral Equation Methods for Canonical Problems in Diffraction Theory (Invited contribution) . In: Brebbia, C.A., Wendland, W.L., Kuhn, G. (eds) Mathematical and Computational Aspects. Boundary Elements IX, vol 9/1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21908-9_5

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  • DOI: https://doi.org/10.1007/978-3-662-21908-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-21910-2

  • Online ISBN: 978-3-662-21908-9

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