An alternative polynomial expansion for electromagnetic field estimation inside three-dimensional dielectric scatterers is presented in this article. In a continuation with the previous work of authors, the Tensor-Volume Integral Equation (TVIE) is solved by using the Galerkin-based moment method (MoM) consisting of a combination of entire-domain and sub-domain basis functions including three-dimensional polynomials. Instead of using trivial power polynomials, Legendre polynomials are adopted for electromagnetic fields expansion in this study. They have the advantage of being a set of orthogonal functions, which allows the use of high-order basis functions without introducing an ill-condition MoM matrix. The accuracy of such approach in MoM is verified by comparing its numerical results with that of exact analytical method such as Mie theory and conventional procedures in MoM. Besides, it is also confirmed that the condition number of the MoM matrix obtained with the proposed approach is lower than that of the previous approaches.

This paper includes different approaches for analysis of a thin-wire antenna in the presence of de-ionized water box at different temperatures as a high-permittivity three-dimensional dielectric body. In continuation with the previous work of authors, first, the coupled tensor-volume/line integral equations is solved by using Galerkin-based moment method (MoM) consisting of a combination of entire-domain and sub-domain basis functions including three-dimensional polynomials with different degrees. Then, the accuracy of such MoM, specifically for a high-permittivity dielectric scatterer, is substantiated by comparing its numerical results with that of FDTD method and some experimental data.

A new approach for solution of the Tensor-Volume Integral Equation (TVIE) using Galerkin-based moment method (MoM) for three-dimensional dielectric bodies is proposed. Two problems of plane wave scattering by a dielectric sphere and a thin-wire antenna in close proximity to a dielectric body are investigated. In both cases, cubic modeling is applied and a combination of entire-domain and sub-domain basis functions, including three-dimensional polynomial functions with different degrees is utilized for field expansion inside dielectric bodies. Power polynomial is adopted for this purpose and its property is discussed over the proposed mixed-domain MoM formulation. Numerical examples show that based on the proposed method, a relative fast algorithm and suitable accuracy are achieved compared with conventional MoM. The accuracy of the proposed method is verified by comparing it with the Mie theory, conventional MoM and the FDTD method.