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A survey of Fourier smoothing analysis results

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Multigrid Methods III

Abstract

Collecting and completing results scattered in the literature, an extensive survey of Fourier smoothing analysis results is presented. Recent developments concerning the influence of damping and modifying incomplete factorizations, and concerning a heuristic method by which the influence of boundary conditions can be successfully accounted for, will be discussed. A new Gauss-Seidel variant, called Gauss-Seidel-Jacobi, is presented. The set of test problems consists of the rotated anisotropic diffusion equation and the convection diffusion equation. Only a few smoothing methods work for all test problems. Unfortunately, these methods have certain drawbacks. Either they do not lend themselves well for vector and parallel computing, or their generalization to general systems of equations is problematic.

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Author information

Authors and Affiliations

  1. Department of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600, AJ Delft, The Netherlands

    P. Wesseling

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  1. P. Wesseling
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Editors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Universität Kiel, Olshausenstrasse 40, D-2300, Kiel 1, Germany

    W. Hackbusch

  2. Gesellschaft für Mathematik und Datenverarbeitung mbH, Postfach 1240, Schloss Birlinghoven, D-5205, Sankt Augustin 1, Germany

    U. Trottenberg

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© 1991 Springer Basel AG

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Wesseling, P. (1991). A survey of Fourier smoothing analysis results. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5712-3_7

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  • DOI: https://doi.org/10.1007/978-3-0348-5712-3_7

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5714-7

  • Online ISBN: 978-3-0348-5712-3

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