Higher order interpolatory vector bases for computational electromagnetics

Author

Graglia, Roberto D. ; Wilton, Donald R. ; Peterson, Andrew F.

Author_Institution

Dipt. di Elettronica, Politecnico di Torino, Italy

Volume

45

Issue

3

fYear

1997

fDate

3/1/1997 12:00:00 AM

Firstpage

329

Lastpage

342

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

Keywords

convergence of numerical methods; electromagnetism; finite element analysis; interpolation; polynomials; vectors; completeness properties; computational electromagnetics; convergence; electromagnetic field problems; element shapes; finite element method; higher order interpolatory vector bases; higher-order functions; interpolatory higher order vector basis functions; interpolatory polynomials; polynomial order; zeroth-order Nedelec representations; Computational electromagnetics; Convergence of numerical methods; Electromagnetic fields; Electromagnetic radiation; Electromagnetic scattering; Finite element methods; Interpolation; Numerical analysis; Polynomials; Shape;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/8.558649

Filename

558649