Broadband numerical simulations of scattering from rough surfaces

Abstract

Numerical simulation of rough surface scattering via discretization of the Helmholtz-Kirchhoff integral equation (HKIE) is a powerful, yet computationally expensive method to study rough surface scattering. In this work, simulations are performed using Fourier synthesis of the numerical solution of the HKIE using the boundary element method (BEM). Each frequency component is solved using BEM employing a good approximation of a plane wave as an incident field. The surface length requirements on this incident field depend on angle, and all simulations are performed using plane waves whose angular width is less than one degree, and whose mean grazing angle is greater than 20 degrees. This requirement resulted in problems with over 22,000 degrees of freedom and approximately 3000 individual frequencies. This broadband technique is employed to study the dependence of the scattered intensity on surface parameters as well as the bandwidth of the transmitted pulse. Simulations are performed both on surfaces with truncated power law spectra, as well as rippled surfaces with power-law roughness superimposed.