HIGHER-ORDER INTERPOLATORY VECTOR BASES FOR COMPUTATIONAL ELECTROMAGNETICS

Low-order vector basis functions compatible with the Nedelec represent ations are widely used for electromagnetic field problems, Higher-orde r 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 el ement shapes, It is shown that these functions can be obtained as the product of zeroth-order Nedelec representations and interpolatory poly nomials with specialty arranged arrays of interpolation points, The co mpleteness properties of the vector functions are discussed, and expre ssions for the vector functions of arbitrary polynomial order are pres ented, Sample numerical results confirm the faster convergence of the higher order functions.