Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1994-12-31
A Fully Discrete Approximation Method for the Exterior Neumann Problem of the Helmholtz EquationSiegfried Prössdorf and J.-J. Saranen (1) University of Oulu, Finland
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.
Keywords: Helmholtz equation, exterior problems, hypersingular operators, discrete approximation methods
Prössdorf Siegfried, Saranen J.-J.: A Fully Discrete Approximation Method for the Exterior Neumann Problem of the Helmholtz Equation. Z. Anal. Anwend. 13 (1994), 683-695. doi: 10.4171/ZAA/483