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 #x2032;almost optimal#x2032; values for the coupling parameter, as a function of the wave-number, so as to minimize the condition number of various formulations
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