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On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation

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Summary

Brakhage and Werner, Leis and Panich suggested to reduce the exterior Dirichlet boundary value problem for the Helmholtz equation to an integral equation of the second kind which is uniquely solvable for all frequencies by seeking the solution in the form of a combined double- and single-layer potential. We present an analysis of the appropriate choice of the parameter coupling the double- and single-layer potential in order to minimize the condition number of the integral operator.

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Authors and Affiliations

  1. Institut für Numerische und Angewandte Mathematik, Lotzestraße 16-18, D-3400, Göttingen (Fed. Rep.)

    R. Kreß

  2. Lehrstuhl für Mathematik, Forsttechnische Hochschule Sofia, Sofia, Bulgaria

    W. T. Spassov

Authors
  1. R. Kreß
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  2. W. T. Spassov
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Additional information

This research was carried out while the second author was visiting the University of Göttingen on a DAAD-stipendium

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Kreß, R., Spassov, W.T. On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation. Numer. Math. 42, 77–95 (1983). https://doi.org/10.1007/BF01400919

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  • DOI: https://doi.org/10.1007/BF01400919

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