Computation of scattered fields from inhomogeneous objects by volume integral equation methods

Abstract

The volume integral equation (VIE) formulations have been very accurate and efficient methods in modeling of inhomogeneous objects in electromagnetic areas. Over the years, various volume integral equation formations have been developed. In these formulations, the dielectric object is discretized into small sub-domains, such as tetrahedrons. Then basis functions are defined in each sub-domain and the electric field or current is represented by unknown coefficient multiplied by the basis function. Among the basis sets used in 3D VIE formulations, the divergence-conforming tetrahedral basis defined by Schaubert, Wilton and Glisson is one of the most widely used. This basis is used for modeling the electric current or electric flux in a dielectric object. Another basis function that has been applied to the VIE method is curl-conforming edge basis, which is used to model the electric field in the VIE formulations and it keeps the tangential continuity of electric field. Other basis functions such as pulse bases, hexahedral bases and high-order basis functions have also been used in the literature. In this paper, we apply the curl-conforming VIE formulations to compute the scattered fields from inhomogeneous objects. Given the application of inhomogeneous objects in different application areas, such as biomedical imaging and geophysical exploration, it is of great importance to develop accurate and efficient modeling methods. This VIE method allows us to compute the scattered fields of these objects accurately and efficiently. Our simulation results show this method provides very accurate solutions.