Considering an exterior domain with smooth closed boundary curve we introduce a fully discrete scheme for the solution of the acoustic boundary value problem of the Neumann type. We use a boundary integral formulation of the problem which leads to a hypersingular boundary integral equation. Our discretization scheme for the latter equation can be con-sidered as a discrete version of the trigonometric collocation method and has arbitrarily high convergence rate, even exponential if the solution and the curve are analytic.
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Siegfried Prössdorf, J.-J. Saranen, A Fully Discrete Approximation Method for the Exterior Neumann Problem of the Helmholtz Equation. Z. Anal. Anwend. 13 (1994), no. 4, pp. 683–695DOI 10.4171/ZAA/483