A Higdon-like non-reflecting boundary condition for the Klein–Gordon equation with evanescent waves

• Augmented Higdon NRBC to absorb evanescent waves.
• Stability and absorption properties analyzed.
• Applied to 2-D Klein–Gordon equation in a finite difference scheme.
• Accuracy and long-time stability demonstrated by examples.

The non-reflecting boundary condition developed by Higdon and automated by Givoli and Neta is highly effective at absorbing propagating waves in a finite difference setting, but it does not absorb evanescent waves. In this paper, we augment the Higdon scheme with additional terms to absorb these evanescent waves in the context of the two-dimensional Klein–Gordon equation. Numerical examples illustrate the performance of this technique.