Finite element formulation of exact non-reflecting boundary conditions forthe time-dependent wave equation

A modified version of an exact Non-reflecting Boundary Condition (NRBC) fir st derived by Grote and Keller is implemented in a finite element formulati on for the scalar wave equation. The NRBC annihilate the first N wave harmo nics on a spherical truncation boundary, and may be viewed as an extension of the second-order local boundary condition derived by Bayliss and Turkel. Two alternative finite element formulations are given. In the first, the b oundary operator is implemented directly as a 'natural' boundary condition in the weak form of the initial-boundary value problem. In the second, the operator is implemented indirectly by introducing auxiliary variables on th e truncation boundary. Several versions of implicit and explicit time-integ ration schemes are presented for solution of the finite element semidiscret e equations concurrently with the first-order differential equations associ ated with the NRBC and an auxiliary variable. Numerical studies are perform ed to assess the accuracy and convergence properties of the NRBC when imple mented in the finite element method. The results demonstrate that the finit e element formulation of the (modified) NRBC is remarkably robust, and high ly accurate. Copyright (C) 1999 John Wiley & Sons, Ltd.