Improved hybrid discretisation of volume integral equation with the characteristic basis function method for analysing scattering from complex dielectric objects

Abstract

The improved hybrid discretisation of volume integral equation (VIE) combined with the characteristic basis function method is proposed to analyse the scattering from complex dielectric objects in this study. To mitigate the excessive number of discrete elements which arise from the conformal discretisation on the complex dielectric objects, the hybrid discretisation is developed. For the conventional hybrid discretisation, the conformal Schaubert–Wilton–Glisson (SWG) basis functions are used to discretise the homogeneous regions, meanwhile, the non-conformal half-SWG basis functions are employed to discretise the boundary regions which separate different materials or multiscale structures. The hybrid discretisation takes advantage of the merits of both conformal and non-conformal basis functions and improves the computational efficiency for solving the VIE. In our study, a kind of edge basis function defined within boundary tetrahedral elements substitutes for the SWG basis functions to model the boundary regions, leading to the further reduction on the number of basis functions. Moreover, the characteristic basis functions extracted from the low-level basis functions are employed to construct the reduced matrix of which the size is considerably smaller than that of the system matrix derived from the VIE. Several numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.