Numerical solution of electrodynamics boundary problem for conducting surface-dielectric body system

Abstract

A development of method [1] for numerical solution of electrodynamics boundary problem with arbitrary conducting surfaces in case of presence of arbitrary dielectric bodies is presented. Consideration of dielectric bodies is accomplished by means of introducing additional terms with unknown polarization current into the system of integral equations, as well as using parametric mapping technique for representing a curvilinear dielectric body and the Galerkin method with boundary and finite elements. Volume polarization current inside the dielectric body is represented in the form of curvilinear finite elements with piecewise constant base functions. Parametric description of curvilinear generalized hexahedron’s geometry for representing a wide class of dielectric bodies is developed. The method and the software that implements it are tested by calculating input impedance of surface radiators with flat and curvilinear structures equipped with finite sized dielectric substrate in the frequency band with 10:1 ratio between upper and lower frequencies. It is demonstrated that calculated using this method dependencies of input impedance on frequency and values of substrate’s dielectric permeability correlate well with referred results obtained using the well-known HFSS and CST Microwave Studio software.