A comparison between various boundary integral formulations of the exterior acoustic problem

Abstract Classical boundary integral formulations of the Helmholtz equation in the exterior domain either via the Helmholtz formulae (leading to direct formulations) or via layer potential representation of the solution (leading to indirect formulations) fail to have a unique solution for certain real values of the wavenumber. In this paper we consider three of the most commonly used formulations which are valid for all wavenumbers. We carry out a systematic comparison between these formulations, investigating their suitability for use in a general boundary element code. We study the effect of parameters in these formulations on the stability and the attainable accuracy of the discretised equations. The computational aspects of our boundary element methods, such as the numerical evaluation of singular integrals and the efficient solution of the resulting linear systems are also discussed.

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