Ali Deng

Numerical study of a novel MFIE formulation using monopolar RWG basis functions

Abstract Numerical character of a new magnetic field integral equation (MFIE) formulation solved by the method of moments (MoM) is studied. In this new formulation, monopolar Rao–Wilton–Glisson (RWG) functions are used as both the basis and the testing functions. Calculation details for the impedance matrix elements of this new formulation are presented with a form suitable for programming. Numerical results for electromagnetic scattering analysis of several small sharp-edged conducting objects show that the new formulation using the monopolar RWG basis functions is much more accurate than the traditional one using the RWG and the monopolar RWG basis functions.

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

Abstract 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.

Electromagnetic scattering analysis using a combined magnetic field integral equation for small objects with flat surfaces

The contribution of the Greens function to the scattered magnetic field is not well expressed in the traditionally used magnetic field integral equation (MFIE) when the source and field points lie on the same plane. This decreases the accuracy of MFIE for objects with flat surfaces. To solve this problem, the normal magnetic field integral equation resulting from the use of the normal boundary condition is considered. It is then combined with the traditionally used MFIE into a new MFIE formulation, named the combined magnetic field integral equation (CMFIE). Through the use of an appropriate combination parameter, the omitted contribution of the Greens function to the scattered magnetic fields in the traditionally used MFIE can be recovered in this new CMFIE. Numerical results validate the analysis and show that the proposed MFIE formulation is much more accurate than the traditional one for small objects with flat surfaces.