The Combined Enforcement of Normal and Tangential Boundary Conditions on the PEC-Material Interfaces in the Volume-Surface Integral Equation

Abstract

In the moment method solution of the volume-surface integral equation (VSIE) modeling composite objects, the normal and tangential boundary conditions (TBCs) of electric and magnetic fields are combined and collectively enforced on the perfect electric conductor (PEC)–material interfaces (PMIs). The numbers of both electric and magnetic volumetric unknowns are therefore significantly reduced. Based on the enforcement of the normal boundary condition (BC), the Schaubert-Wilton-Glisson (SWG) coefficients of the volume currents that are defined on the PEC-terminated tetrahedral faces can be straightforwardly calculated, which are no longer volumetric unknowns. Similarly, due to the enforcement of the TBC, two coefficients of the four SWG bases defined on a tetrahedron, at least one of whose faces is PEC-terminated, can be determined by the other two using the weighted least-square (LS) method. Furthermore, due to the explicit satisfaction of BCs, the proposed BCs-based VSIE improves the solution accuracy. The efficiency and validity of the proposed approach are verified by reliable numerical experiments, in which both the isotropic and anisotropic materials are involved.