NDLI: On the Convergence of Galerkin Finite Element Approximations of Electromagnetic Eigenproblems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fernandes, Paolo Raffetto, Mirco Caorsi, Salvatore
Copyright Year	2000
Abstract	The convergence of Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators is studied. Since the operator involved is noncompact, the first part of the analysis is carried out in terms of the specific definition of convergence that is known to be appropriate for this case. Then, a slightly stronger definition of convergence is proposed, which is tuned to the features a practitioner of the numerical simulation of electromagnetic devices requires for a good computational model of a resonant cavity. For both definitions, necessary and sufficient conditions are introduced and discussed. Moreover, it is proved that the convergence of an approximation in the stronger sense is unaffected by the presence of different materials filling the cavity resonator. Exploiting this basic feature of the newly defined convergence, the previously developed theory is applied to generalize the convergence proof for the lowest order edge element approximations to the case of anisotropic, inhomogeneous and discontinuous material properties. Results clarifying the relationships among the various conditions occurring in our analysis and examples showing what may happen when not all the conditions for convergence hold true are also reported and contribute to a clear picture about the origin and the behavior of spurious modes.
Starting Page	580
Ending Page	607
Page Count	28
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142999357506
e-ISSN	10957170
Issue Number	2
Volume Number	38
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods spurious modes convergence noncompact operators Eigenvalue problems electromagnetic eigenproblems edge elements discontinuous material properties Galerkin finite element approximations Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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