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Collocation approach to the Helmholtz eigenvalue problem on multiply connected domains

✍ Scribed by Paolo Amore; Diego Chowell

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 776 KB
Volume: 329
Category: Article
ISSN: 0022-460X
DOI: 10.1016/j.jsv.2009.11.013

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✦ Synopsis

We present a collocation approach to the numerical solution of the Helmholtz eigenvalue problem on multiply connected domains of arbitrary shape in two dimensions. A suitable representation of the Helmholtz equation on an uniform grid is obtained and the problem is converted to the calculation of the first few eigenvalues and eigenvectors of a large sparse matrix. The accuracy of this approach is tested by performing a comparison with results available in the literature. The flexibility and simplicity of the method make easy the application to arbitrary geometries.

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