Finite element methods applied to nearly one-way wave propagation

A numerical method is developed for approximately solving stationary wave propagation problems for which most of the energy propagates in an angle and of less than 90% about a fixed direction. This property often occurs in realistic physical models. The numerical method is based on factoring out the principal propagation direction in the solution and then applying the finite element method. The method is applied to wave propagation in a duct or waveguide and to the exterior scattering problem. It is shown both theoretically and by means of numerical examples that this method requires considerably less grid points and computational cost than standard discretization methods