Trilinear hexahedral finite elements with higher-order polynomial field expansions for hybrid SIE/FE large-domain electromagnetic modeling

The surface integral equation (SIE) formulation in conjunction with the method of moments (MoM) is the "best" choice for modeling of 3D open-region antenna and scattering problems. Partial differential-equation numerical methods, such as the class of finite-element (FE) techniques, are extremely efficient at modeling of 3D structures that predominantly consist of arbitrary shaped heterogeneous (isotropic or anisotropic) nonmetallic material sections. The best way to fully benefit from both approaches in most general practical cases is to hybridize them in an appropriate fashion. Finite elements in the form of electrically large trilinear hexahedrons with higher-order polynomial field expansions are proposed. Numerical benefits from using higher-order expansions for FE modeling are demonstrated on a simple one-dimensional example.