The use of the edge basis function for non-conformal solution of electric current volume integral equation

A novel kind of basis function which is defined only in a single tetrahedron element and is along the edge of a tetrahedron element is derived in this paper. Then, it is used for the discretization of the electric current volume integral equation. Compared with the traditional used Schaubert-Wilton-Glisson (SWG) basis function, the proposed one permits the use of non-conformal meshes. Details for the calculation of impedance matrix elements are developed. The high order singularity of the Green's function caused by the gradient-divergence operator has been decreased to the order of 1/R. Therefore, it is much easier to be implemented than other non-conformal solution schemes presented in literatures. To validate the proposed scheme, numerical results for electromagnetic scattering from several inhomogeneous dielectric objects are presented. It is shown that the proposed scheme gives accurate results for electromagnetic scattering analysis from dielectric bodies. Particularly, the use of the non-conformal meshes greatly improves the solution efficiency of volume integral equation for high-contrast permittivity or multiscale cases.