Unified formulation of radiation conditions for the wave equation

A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of %ctitious surface densities, governed by second-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to di>erent choice of the coe?cients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms of selected directions with ideal transmission is presented. A mechanical interpretation of the %ctitious surface densities enables identi%cation of suitable conditions at corners and boundaries of the radiating surface. Numerical examples illustrate excellent results with one or two %ctitious layers with suitable corner and boundary conditions.