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Stable boundary element domain decomposition methods for the Helmholtz equation

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Abstract

In this paper, we present a stable boundary element domain decomposition method to solve boundary value problems of the Helmholtz equation via a tearing and interconnecting approach. A possible non-uniqueness of the solution of local boundary value problems due to the appearance of local eigensolutions is resolved by using modified interface conditions of Robin type, which results in a Galerkin boundary element discretization which is robust for all local wave numbers. Numerical examples confirm the stability of the proposed approach.

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  1. Institut für Numerische Mathematik, TU Graz, Steyrergasse 30, 8010, Graz, Austria

    O. Steinbach & M. Windisch

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  1. O. Steinbach
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  2. M. Windisch
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Correspondence to O. Steinbach.

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Steinbach, O., Windisch, M. Stable boundary element domain decomposition methods for the Helmholtz equation. Numer. Math. 118, 171–195 (2011). https://doi.org/10.1007/s00211-010-0315-6

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  • DOI: https://doi.org/10.1007/s00211-010-0315-6

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