A review of the coupling parameter of the Burton and Miller boundary element method

The phenomenon of irregular frequencies or spurious modes in boundary element techniques for acoustic problems has been well investigated and a number of methods have been presented to overcome this problem. The most popular methods seem to be the Combined Helmholtz Integral Equation Formulation (CHIEF) and the Burton and Miller formulation. This contribution deals with the latter and its only parameter, i.e. the so-called coupling parameter. It is known for more than four decades that this parameter must be complex for radiation from rigid bodies with particle velocity prescribed. During the 1980ies, a number of authors proposed the value of i/k. This value is proving to be an excellent choice for the high frequency limit. However, it turned out that the optimal choice of the coupling parameter depends on a few more parameters including the harmonic time dependence and the formulation of the integral equation itself. This paper discusses these influences for a specific EAA benchmark case which has only recently been proposed, i.e. the radiatterer.