Fictitious eigenfrequencies in the BEM for interior acoustic problems

Abstract

It is widely known that the boundary element method (BEM) without any special treatment suffers from the fictitious eigenfrequency problem for the numerical solutions of exterior acoustic problems. This problem has drawn much attention and been extensively studied over the last several decades. However, this paper is concerned with the existence and influence of the fictitious eigenfrequencies when using the BEM for the numerical solutions of interior acoustic problems. To this end, an eigenvalue analysis technique is developed for the acoustic BEM. The nonlinear eigenvalue problem caused by the acoustic BEM is converted into an ordinary linear one by using a contour integral method. Therefore, the conversion is fulfilled by solving a series of BEM systems of equations without any special or complicated treatment of the governing equations or the linear systems. Three interior acoustic examples including two with simply connected domains and one with a multiply connected domain are used to reveal the existence and influence of the fictitious eigenfrequencies. Furthermore, the Burton–Miller formulation with a variable coupling parameter is found to be able to remove such fictitious eigenfrequencies, and the optimal choice of the coupling parameter is investigated.