Higher order interpolatory vector bases for computational electromagnetics

Abstract

Low-order vector basis functions compatible with the Nedelec (1980) representations are widely used for electromagnetic field problems. Higher-order functions are receiving wider application, but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases. In this paper, fully interpolatory higher order vector basis functions of the Nedelec type are defined in a unified and consistent manner for the most common element shapes. It is shown that these functions can be obtained as the product of zeroth-order Nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties of the vector functions are discussed, and expressions for the vector functions of arbitrary polynomial order are presented. Sample numerical results confirm the faster convergence of the higher order functions.