Abstract
This paper is concerned with an approach for avoiding the fictitious eigenfrequency problem in boundary element analysis of two-dimensional acoustic problems governed by Helmholtz equation. It is well known that in solving without any care the external acoustic problem by means of the boundary integral equation, the solution is violated at the eigenfrequencies of the internal problem. The present paper shows the effectiveness to circumvent the fictitious eigenfrequency problem by using the combined integral equation, which is originally proposed by Burton-Miller for constant elements, when employing the quadratic boundary element. On the other hand, we also propose a new approach to avoid that problem, which is for the quadratic boundary element. In this new approach, the Burton-Miller integral equation is used at the end points of element, while the normal derivative boundary integral equation multiplied by some parameter is applied to the other node of element. The proposed approach is implemented, and its effectiveness is demonstrated through comparison of the numerical results obtained by the developed computer code with other solutions.
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