High-order numerical solutions in frequency-independent computational times for scattering applications associated with surfaces with composite roughness

Abstract

We introduce a new numerical scheme capable of producing, in frequency independent computational times, high-order solutions to scattering problems associated with surfaces with composite roughness. The procedure can be interpreted as providing a high-order version of the classical (low-order) two-scale method and, as such, it can produce solutions of significantly higher quality with comparable computational effort. The basic strategy consists of a suitable combination of (1) a high-order boundary perturbation treatment that views the highly oscillatory components of the surface as a (possibly large) deformation of the slowly varying portion; and (2) an accurate solution method applicable to single-scattering configurations for the sequence of high-frequency scattering problems that results from (1), which entails a fixed, frequency-independent computational cost. More precisely, the boundary variation procedure in (1) allows for the representation of the fields as a convergent sum of terms which are recursively defined as solutions to scattering problems on the slowly varying portion of the surface, with high-frequency incidences that are derived from its highly oscillatory components.