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Solution of the Helmholtz eigenvalue problem via the boundary element method
Author(s) -
Kirkup S. M.,
Amini S.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620360210
Subject(s) - mathematics , eigenvalues and eigenvectors , mathematical analysis , boundary element method , helmholtz equation , boundary value problem , helmholtz free energy , method of fundamental solutions , divide and conquer eigenvalue algorithm , finite element method , boundary (topology) , boundary knot method , physics , quantum mechanics , thermodynamics
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 generalized 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.