High‐order absorbing boundary conditions incorporated in a spectral element formulation

Abstract

AbstractThe solution of the time‐dependent wave equation in a semi‐infinite wave guide is considered. An artificial boundary ℬ︁ is introduced, which encloses a finite computational domain. On ℬ︁ the Hagstrom–Warburton (H–W) local high‐order absorbing boundary condition (ABC) is imposed. In contrast to previous studies, which involved either finite difference schemes or low‐order finite element schemes, here the way to incorporate the H–W ABC into a spectral element formulation is shown. To this end, the Seriani–Priolo spectral element is used in space and a 4th‐order Runge–Kutta scheme is employed in time. This leads to exponential convergence in both the polynomial order of the spectral element, and in the order of the ABC, and thus avoids the convergence rate inconsistency which is otherwise present. The combined ABC‐spectral formulation enables one to obtain extremely accurate solutions of wave problems in unbounded domains. This is demonstrated via a number of numerical examples. Copyright © 2008 John Wiley & Sons, Ltd.