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Numerical instabilities of the integral approach to the interior boundary-value problem for the two-dimensional Helmholtz equation

✍ Scribed by F. Mattioli

Publisher: John Wiley and Sons
Year: 1980
Tongue: English
Weight: 571 KB
Volume: 15
Category: Article
ISSN: 0029-5981
DOI: 10.1002/nme.1620150903

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✦ Synopsis

Abstract

The integral equations arising from the Green's formula, applied to the two‐dimensional Helmholtz equation defined in a limited domain, are considered and the presence of instabilities in their numerical solution, when a real Green's function is adopted, is pointed out.

A complete study has been carried out for a circular domain and the conditions under which such instabilities can occur in a domain of arbitrary geometry have been investigated. In particular, it has been shown that in every case the use of a complex Green's function is able to avoid their presence.

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