New Boundary Element Analysis Of Acoustic
Problems With The Fictitious Eigenvalue Issue
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,
Keywords
Related Book
Other papers in this volume
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