On the application of some radiation boundary conditions

Some of the more common radiation boundary conditions are examined to identify their underlying physical principles and inherent accuracy (or errors). It is found that the Sommerfeld and Mur conditions are closely related to the first- and second-order Bayliss-Turkel conditions, the major difference being that the latter are for a line source a distance r away from the boundary, while the former are for a plane wave. This distance r is not simply related to the curvature of the surface of a nearby scatterer. The error in the Bayliss-Turkel second-order condition is known to be proportional to r^-4. A calculation of the actual magnitude of this term shows the r^-4 behavior to be correct but irrelevant for practical computations