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Solution of the Helmholtz eigenvalue problem via the boundary element method

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Kirkup, Stephen Martin ORCID: 0000-0002-9680-7778 and Amini, S. (1993) Solution of the Helmholtz eigenvalue problem via the boundary element method. International Journal for Numerical Methods in Engineering, 36 (2). pp. 321-330. ISSN 0029-5981

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Official URL: http://dx.doi.org/10.1002/nme.1620360210

Abstract

The numerical solution of the Helmholtz eigenvalue problem is considered. The application of the boundary element method reduces it to that of a non-linear eigenvalue problem. Through a polynomial approximation with respect to the wavenumber, the non-linear eigenvalue problem is reduced to a standard generalised eigenvalue problem. The method is applied to the test problems of a three-dimensional sphere with an axisymmetric boundary condition and a two-dimensional square.

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