A new spectral method for numerical solution of the unbounded rough surface scattering problem

A new spectral method is developed to solve the unbounded rough surface scattering problem. An unbounded rough surface is referred to as a non-local perturbation of an infinite plane surface such that the whole rough surface lies within a finite distance of the original plane. The method uses a transformed field expansion to reduce the boundary value problem with a complex scattering surface into a successive sequence of transmission problems of a planar surface. Hermite orthonormal basis functions are adopted to further simplify these problems to fully decoupled one-dimensional two-point boundary value problems, which are solved efficiently by the Legendre-Galerkin method. Numerical results indicate that the method is efficient, accurate, and well-suited for solving the scattering problem by unbounded rough surfaces.