Second-order Nédélec tetrahedral element for computational electromagnetics

✍ Scribed by L. E. García-Castillo; M. Salazar-Palma

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 278 KB
• Volume: 13
• Category: Article
• ISSN: 0894-3370
• DOI: 10.1002/(sici)1099-1204(200003/06)13:2/3<261::aid-jnm360>3.0.co;2-l

✦ Synopsis

The practical implementation of the second-order tetrahedral version of NeH deH lec's "rst family of curlconforming elements [1] (NeH deH lec. Numerische Mathematik 1980; 35:315}341) is presented. Following the de"nition of the element given by NeH deH lec, the second-order vectorial basis functions of the element are deduced. The element thus obtained exhibits some important di!erences with respect to other second-order curl-conforming elements which have appeared in the literature. For example, the degrees of freedom associated to the faces of the tetrahedra are de"ned in terms of the surface integral of the tangential component of the "eld over the faces of the tetrahedra. The di!erences in the de"nition of the degrees of freedom lead to a di!erent location of the nodes on the tetrahedron boundary, and also to a di!erent set of basis functions. The basis functions thus obtained have all the same polynomial order than the order of the element, i.e., quadratic for the particular element presented here, and they lead to better conditioned FEM matrices than other second-order curl-conforming elements appeared in the literature. In order to analyse the features of the second-order tetrahedral element presented in this paper, it is used for the discretization of the double-curl vector formulation in terms of the electric or magnetic "eld, for the computation of the resonance modes of inhomogeneous and arbitrarily shaped three-dimensional cavities. Numerical results are given. A comparison of the rate of convergence achieved with the second-order element with respect to the "rst-order element is presented.