Premium
Computation of resonant modes for axisymmetric Maxwell cavities using hp ‐version edge finite elements
Author(s) -
Hiptmair R.,
Ledger P. D.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1241
Subject(s) - finite element method , rotational symmetry , computation , curl (programming language) , eigenfunction , convergence (economics) , exponential function , mathematics , mathematical analysis , maxwell's equations , computer science , geometry , physics , algorithm , eigenvalues and eigenvectors , engineering , structural engineering , quantum mechanics , economics , programming language , economic growth
The computation of the resonant frequencies for closed cavities is not a trivial task: Multi‐materials and sharp corners all give rise to highly singular eigenfunctions. However, an approach using hp ‐finite elements is well suited to such problems and, with the correct combination of h ‐ and p ‐refinements, it yields the theoretically predicated exponential rates of convergence. In this paper, we present a novel approach to the solution of axisymmetric cavity problems which uses a hierarchic H 1 and H (curl) conforming finite element basis. A selection of numerical examples is included and these demonstrate that the exponential rates of convergence are achieved in practice. Copyright © 2005 John Wiley & Sons, Ltd.