Towards a good characterization of spectrally correct finite element methods in electromagnetics

S. Caorsi (Department of Electronics, University of Pavia, Pavia, Italy)
P. Fernandes (CNR‐IMA, Genoa, Italy)
M. Raffetto (DIBE‐University of Genoa, Genoa, Italy)

Abstract

Spurious modes often appear in the computed spectrum when an electromagnetic eigenproblem is solved by the finite element method. Demonstrates that the inclusion condition, often claimed as the theoretical reason for the absence of (non‐zero frequency) spurious modes, is a sufficient but not necessary condition for that. Does this by proving that edge elements, which are spectrally correct, do not satisfy the inclusion condition. As intermediate steps towards this result, proves the equivalence of the inclusion condition to a less cryptic one and gives two more easily‐checked necessary conditions for the latter. Concludes that from this investigation, the inclusion condition seems too strong to be useful as a sufficient condition. Works out the present analysis in the framework of spectral approximation theory for non‐compact operators, which emerges as a basic tool for a deeper understanding of the whole question of spurious modes.

Keywords

Citation

S. Caorsi, P. Fernandes and M. Raffetto (1996) "Towards a good characterization of spectrally correct finite element methods in electromagnetics", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 15 No. 4, pp. 21-35

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DOI

: https://doi.org/10.1108/03321649610154195

Publisher

:

MCB UP Ltd

Copyright © 1996, MCB UP Limited

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