Contraction Integral Equation for Modeling of EM Scattering by 3-D Bodies Buried in Multilayered Anisotropic Medium

Integral equation (IE) is regarded as an efficient method for 3-D modeling of electromagnetic (EM) responses. The main contribution of this article is to develop a contraction integral equation (CIE) algorithm with a high performance for modeling of EM scattering by 3-D bodies buried in multilayered anisotropic medium. The introducing of contraction operator can ensure that the discretized IE will be iteratively convergent in large conductivity contrast between abnormal bodies and background medium. Moreover, the contraction operator can also accelerate the iteration convergence of the IE. During the discretization process of CIE, direct waves are extracted from dyadic Green's functions (DGFs) of multilayered medium, and the singular integrals of direct waves are eliminated using equivalent sphere and ellipsoid methods. By splitting DGF into convolution terms and correlation terms, 3-D FFT can be used to accelerate the product evaluation of DGFs integral and scattering current encountered in each iteration. Validity of the proposed CIE is verified by comparing with the existing finite volume method. Modeling results show that the conventional IE will be iteratively divergent when the conductivity contrast between bodies and background is large, but the CIE is always iteratively convergent even under very large conductivity contrast.