Application of the CBFM-ACA approach to the scattering from natural media consisting of randomly distributed discrete scatterers

In this paper, we present an efficient numerical method for the simulation of ElectroMagnetic (EM) scattering from discrete random media consisting of a large number of dielectric electrically small spheres. The scattering problem is formulated in terms of the Volume Integral Equation (VIE) for the electric field that is thereafter converted into a matrix system by using the Galerkin´s Method of Moments (MoM) with electrostatic dipole functions. The MoM matrix system is solved by employing the Characteristic Basis Function Method (CBFM) that is based on plane-wave-spectrum (PWS) generated Characteristic Basis Functions (CBFs). In order to rapidly construct the CBFs, Born and isolated scatterer approximations are tested. The computed CBFs together with the Adaptive Cross Approximation (ACA) algorithm are afterwards used to build the reduced matrix system in a time-efficient manner.