Exact transparent boundary conditions for the 2D Helmholtz equation

In this paper, exact transparent boundary conditions (TBC) for the 2D Helmholtz equation are reported. Their properties, as well as the transition to the limiting case of the narrow-angle TBC for the 2D parabolic equation are discussed. A finite-difference implementation of thus derived one-directional evolutionary type TBC is developed and a fully discrete exact transparent boundary condition is obtained. A number of numerical experiments is conducted in the free space demonstrating how the derived TBC can be used to correctly describe wide-angle wave scattering problems. In the last section, the analysis is extended to the problems involving the back-scattering encountered in the reflection optics and ground penetrating radar.