A Fully Discrete Approximation Method for the Exterior Neumann Problem of the Helmholtz Equation

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 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.