zbMATH — the first resource for mathematics

Absorbing boundary conditions for dispersive waves. (English) Zbl 0955.65061
Geers, Thomas L. (ed.), IUTAM symposium on computational methods for unbounded domains. Proceedings of the IUTAM symposium held in Boulder, CO, USA, July 27-31, 1997. Dordrecht: Kluwer Academic Publishers. Fluid Mech. Appl. 49, 217-220 (1998).
Summary: The goal of an absorbing boundary condition is to simulate the outward radiation of energy at an artificial computational boundary. To that end, the boundary condition should make a valid statement about outgoing waves, at least in an approximation sense, but this statement should not require a priori knowledge of the pointwise values of the wave field. Typically, such a boundary condition involves a wave velocity. However, in the case of dispersive waves there are two kinds of velocity, phase velocity and group velocity, and each of the velocities varies with wavenumber and frequency. This variation of velocity is a central issue in the construction of absorbing boundary conditions for dispersive waves. The present abstract summarizes a technique developed by R. L. Higdon [SIAM J. Numer. Anal. 31, No. 1, 64-100 (1994; Zbl 0798.65113)].
For the entire collection see [Zbl 0930.00077].

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation