Entire-domain Galerkin method for analysis of metallic antennas and scatterers

The paper presents the general theory of an entire-domain Galerkin method for the analysis of metallic (i.e. perfectly conducting) antennas and scatterers. The antenna and scatterer surfaces are approximated by generalised quadrangles (i.e. curved curvilinear quadrangles defined by means of parametric equations, whose edges coincide with local coordinate lines). Surface currents are expanded in such local coordinate systems and the general form of the corresponding electric field integral equation is derived. A procedure is decribed for obtaining entire-domain basis functions which satisfy automatically the continuity equation along the surface element interconnections and free edges, and the expressions are derived for the impedance matrix elements in this case. Starting from the general theory, two new particular methods are presented. The first is intended for the analysis of general structures, and is based on application of truncated cones and bilinear surfaces for the approximation of geometry. The second is aimed for the analysis of spherical scatterer, and is based on the application of generalised rectangular elements which follow the sphere shape. Both methods use polynomials for approximation of currents. Very good agreement of the results obtained by the proposed method with available experimental and numerical results is achieved by using small number of unknowns per wavelength squared (about ten for large surfaces of simple form).