A radiation box domain truncation scheme for the wave equation

Abstract

Abstract We consider the wave equation in an unbounded domain and are interested in domain truncation methods. Our aim is to develop a numerical scheme that allows calculations for truncated waveguide geometries with periodic coefficient functions. The scheme is constructed with radiation boxes that are attached to the artificially introduced boundaries. A Dirichlet-to-Neumann operator $N$ is calculated in these radiation boxes. Efficiency of the scheme is obtained by calculating $N$ not with an iteration, but with a single run through the time interval. We observe speed-up factors of up to $20$ in comparison to calculations without domain truncation.