A New Boundary Element Analysis of 3-D Acoustic Fields Avoiding the Fictitious Eigenfrequency Problem

This paper is concerned with a new approach for avoiding the fictitious eigenfrequency problem in boundary element analysis of three-dimensional acoustic problems governed by Helmholtz equation. It is well known that, in solving without any care an external acoustic problem with internal sub-domains by means of the boundary integral equation, its numerical solution is violated at so-called fictitious eigenfrequencies corresponding to the internal sub-domains. The present paper proposes a new boundary element analysis to circumvent such a fictitious eigenfrequency problem by using dual boundary integral equation for nodal points on the boundary. One equation is the combined integral equation proposed by Burton-Miller. The other equation is the normal derivative boundary integral equation multiplied by the same coupling parameter as in the Burton-Miller expression. The quadrilateral element is employed in this study, and the Burton-Miller combined boundary integral equation is used at the middle nodes of element, while only the normal derivative boundary integral equation multiplied by the same coupling parameter is applied to the vertex nodes of element, and vice versa. The proposed approach is implemented, and its validity and effectiveness are demonstrated through numerical computation of the typical problems.