A note on the radiation boundary conditions for the Helmholtz equation

The radiation boundary conditions in two dimensions are derived in the body-fitted coordinate system using the method of successive approximations for the wave envelope function. Results are valid for a convex scatterer with continuous radius of curvature on the surface of the scatterer. In the special case when the computational boundary is circular, the boundary operators derived are identical to the Bayliss operators. The on-surface radiation condition is examined. It is shown that, for a large conducting circular cylinder, a boundary operator of infinite order should be used due to the breakdown of the asymptotic expansions of the boundary operators on the surface of the scatterer. The leading order result based on the boundary operator of infinite order applied on the surface of the cylinder is the same as the result obtained by the method of physical optics