Method of applying single higher order polynomial basis function over multiple domains

Abstract

A novel method has been devised where one set of higher order polynomial-based basis functions can be applied over several wire segments, thus permitting to decouple the number of unknowns from the number of segments, and so from the geometrical approximation accuracy. The method extends the current state of art from using the composite piecewise uniform, linear and sinusoidal basis and testing functions onto polynomials. The method has been derived within the framework of a method of moments (MoM) with higher-order polynomial basis functions, and applied to a surface form of the electrical field integral equation, under thin wire approximation. The main advantage of the proposed method is in permitting to reduce the required number of unknowns when modelling curved structures and structures including electrically small features. Derivation of the computational complexity in terms of floating point operations (FLOP) showed a possible speed gain nearly an order of the number of unknowns of direct MoM.