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Multiscale Methods for Boundary Integral Equations and Their Application to Boundary Value Problems in Scattering Theory and Geodesy

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Boundary Elements: Implementation and Analysis of Advanced Algorithms

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM,volume 50))

Summary

In the present paper we give an overview on multiscale algorithms for the solution of boundary integral equations which are based on the use of wavelets. These methods have been introduced first by Beylkin, Coifman, and Rokhlin [5]. They have been developed and thoroughly investigated in the work of Alpert [1], Dahmen, Proessdorf, Schneider [16–19], Harten, Yad-Shalom [25], v.Petersdorff, Schwab [33–35], and Rathsfeld [39–40]. We describe the wavelet algorithm and the theoretical results on its stability, convergence, and complexity. Moreover, we discuss the application of the method to the solution of a two-dimensional scattering problem of acoustic or electromagnetic waves and to the solution of a fixed geodetic boundary value problem for the gravity field of the earth. The computational tests confirm the high compression rates and the saving of computation time predicted by the theory.

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Author information

Authors and Affiliations

  1. Berliner Institut für Optik, GmbH, Rudower Chaussee 6, D-12484, Berlin, Germany

    Bernd H. Kleemann

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117, Berlin, Germany

    Andreas Rathsfeld

  3. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstr. 7, D-64289, Darmstadt, Germany

    Reinhold Schneider

Authors
  1. Bernd H. Kleemann
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  2. Andreas Rathsfeld
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  3. Reinhold Schneider
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Editors and Affiliations

  1. Lehrstuhl Praktische Mathematik, Mathematisches Seminar II, Christian-Albrechts-Universität Kiel, Hermann-Rodewald-Str. 3, 24098, Kiel, Germany

    Wolfgang Hackbusch

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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

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Kleemann, B.H., Rathsfeld, A., Schneider, R. (1996). Multiscale Methods for Boundary Integral Equations and Their Application to Boundary Value Problems in Scattering Theory and Geodesy. In: Hackbusch, W., Wittum, G. (eds) Boundary Elements: Implementation and Analysis of Advanced Algorithms. Notes on Numerical Fluid Mechanics (NNFM), vol 50. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89941-5_1

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  • DOI: https://doi.org/10.1007/978-3-322-89941-5_1

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-89943-9

  • Online ISBN: 978-3-322-89941-5

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