Combining the Characteristic Basis Function Method with rooftops and razor-blade testing functions over NURBS patches

The Characteristic Basis Function Method (CBFM) is an efficient technique for overcoming the great burden placed on the computational resources in the conventional Method of Moments (MoM) when used to solve electrically large problems. It is an iteration-free approach that does not suffer from convergence problems as many of the iterative techniques are known to do when dealing with ill-conditioned matrices. The underlying concept of the CBFM is the generation of macro-basis functions that are associated with the subdomains (blocks), in which the large geometry is divided. The CBFM has been continuously evolving, and new approaches to the generation of the CBFs have appeared in recent years, including one that combines high-frequency Physical Optics currents in smooth parts of the object, with MoM type of subdomain functions in regions with fine details. A novel implementation of the CBFM is presented in this communication, in which the Characteristic Basis Functions (CBFs) are represented by means of rooftops that are generated from Non-Uniform Rational B-Splines (NURBS) in the parametric (u,v) domain. The testing procedure makes use of razor-blade functions corresponding to each rooftop.