WIT Press


New Boundary Element Analysis Of Acoustic Problems With The Fictitious Eigenvalue Issue

Price

Free (open access)

Paper DOI

10.2495/BE070061

Volume

44

Pages

9

Published

2007

Size

347 kb

Author(s)

M. Tanaka, Y. Arai & T.Matsumoto

Abstract

This paper is concerned with a new approach for avoiding the fictitious eigenfrequency problem to boundary element analysis of three-dimensional acoustic problems governed by Helmholtz equation. It is well known that in solving without any care the external acoustic problem which includes internal sub-domains by means of the boundary integral equation, the solution is disturbed at fictitious eigenfrequencies corresponding to the internal sub-domains. The present paper proposes a new boundary element analysis to circumvent such the fictitious eigenfrequency problem, which is an alternative boundary integral equation approach to the Burton-Miller one. The present approach is implemented, and its validity and effectiveness are demonstrated through numerical computation of typical examples. 1 Introduction Whenever the acoustic problems which include the sub-domains without vibration are solved by means of the usual boundary integral equation without any care, the so-called fictitious eigenvalue issue is encountered. It is well known that the solution of the external acoustic problem is violated near the eigenfrequencies of the inside sub-domains. In practice, if we locate a few source points in the subdomains without vibration and solve the system of equations by the method of least squares, we can circumvent the above eigenvalue issue [1–3]. Nevertheless, in finding the optimal shapes of acoustic fields, for example, it is almost impossible to apply the above practical mehtod, as the current shape is changing and the final,

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