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Schwarz iterations for the efficient solution of screen problems with boundary elements

Schwarz-Iterationen für die effiziente Lösung von Schirmproblemem mit Randelementmethoden

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Abstract

This paper investigates two domain decomposition algorithms for the numerical solution of boundary integral equations of the first kind. The schemes are based on theh-type boundary element Galerkin method to which the multiplicative and the additive Schwarz methods are applied. As for twodimensional problems, the rates of convergence of both methods are shown to be independent of the number of unknowns. Numerical results for standard model problems arising from Laplaces' equation with Dirichlet or Neumann boundary conditions in both two and three dimensions are discussed. A multidomain decomposition strategy is indicated by means of a screen problem in three dimensions, so as to obtain satisfactory experimental convergence rates.

Zusammenfassung

Es werden zwei Gebietszerlegungsalgorithmen für die numerische Behandlung von Randintegralgleichungen der ersten Art untersucht. Die Verfahren beruhen auf derh-Version der Galerkinmethode für Randelemente, auf die die multiplikative und die additive Schwarz-Methode angewandt werden. Für zweidimensionale Probleme wird gezeigt, daß die Konvergenzraten beider Methoden unabhängig von der Anzahl der Unbekannten sind. Numerische Resultate für einfache zweidimensionale und dreidimensionale Modellprobleme, die von der Laplace-Gleichung mit Dirichlet oder Neumann-Randbedingungen stammen, werden diskutiert. Eine Gebietszerlegungsstrategie für den Fall vieler Teilgebiete wird anhand eines dreidimensionalen Schirmproblems demonstriert.

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Authors and Affiliations

  1. Wingerstraße 45, D-69207, Sandhausen, Federal Republic of Germany

    M. Hahne

  2. Institut für Angewandte Mathematik, University of Hannover, Welfengarten 1, D-30167, Hannover, Federal Republic of Germany

    E. P. Stephan

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  1. M. Hahne
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  2. E. P. Stephan
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Hahne, M., Stephan, E.P. Schwarz iterations for the efficient solution of screen problems with boundary elements. Computing 56, 61–85 (1996). https://doi.org/10.1007/BF02238292

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  • DOI: https://doi.org/10.1007/BF02238292

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