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A fully discrete approximation method for the exterior Neumann problem of the Helmholtz equation. (English) Zbl 0822.65095
Authors’ abstract: 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 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 considered 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.
Reviewer: C.L.Koul (Jaipur)

65N38 Boundary element methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
76Q05 Hydro- and aero-acoustics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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