On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem

Abstract

Most commonly used boundary integral formulations of the exterior problem in time-harmonic acoustics, which are valid for all wave-numbers, involve a non-zero coupling parameter. In this paper we analyse the qualitative behaviour of the direct boundary integral formulation due to Burton and Miller. In particular we include a regularised formulation for the Neumann problem. By deriving the eigensystems of the operators we are able to obtain ′almost optimal′ values for the coupling parameter, as a function of the wave-number, so as to minimize the condition number of various formulations