Discrete non-local absorbing boundary condition for exterior problems governed by Helmholtz equation

The finite element method is employed to approximate the solutions of the H elmholtz equation for water wave radiation and scattering in an unbounded d omain. A discrete, non-local and non-reflecting boundary condition is speci fied at an artificial external boundary by the DNL method, yielding an equi valent problem that is solved in a bounded domain. This procedure formulate s a boundary value problem in a bounded region by imposing a relation in th e discrete medium between the nodal values at the two last layers. For plan e geometry, this relation can be found by straightforward eigenvalue decomp osition. For circular geometry, the plane condition is applied at the exter nal layer and this condition is condensed through a structured annular regi on, resulting in a condition at an inner radius. Exterior problems with a b ounded internal physical obstacle are considered. It is well-known that the se kind of problems are well-posed, and have a unique solution. Numerical s tudies based on standard Galerkin methodology examine the dependence of the DNL condition with respect to the circular annular region width. The DNL c ondition is compared with local boundary conditions of several orders. Nume rical examples confirm the important improvement in accuracy obtained by th e DNL method over standard conditions. Copyright (C) 1999 John Wiley & Sons , Ltd.