Perfect boundary conditions for parabolic water-wave models

Abstract
Generalized impedance boundary conditions are presented for parabolic wave models, which provide either perfect diffractive boundary conditions or perfect transmitting boundary conditions. The diffractive conditions permit the modelling of waves in illuminated regions without computations in the shadow regions, while the transmitting conditions allow incident and scattered waves to propagate out of the model. The theory is developed for the simplest parabolic model and for a class of wide-angle parabolic models. Numerical results are presented.