The direct boundary integral equation due to Burton and Miller (1971) is used for the solution of the Helmholtz equation in the exterior domain. The formulation is complex, involving four integral (pseudo-differential) operators. Here we show that it is possible and advantageous to choose the coupling parameter, η, inherent in the formulation, to depend on the boundary points. By setting the coupling parameter, η(p), to zero, over a large part of the surface, we are able to reduce the set up time without greatly affecting the conditioning of the equation.

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