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Full-wave analysis of dielectric waveguides at a given frequency


Authors: L. Vardapetyan and L. Demkowicz
Journal: Math. Comp. 72 (2003), 105-129
MSC (2000): Primary 65N30, 35L15
Published electronically: May 1, 2002
MathSciNet review: 1933815
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Abstract: New variational formulation to compute propagation constants is proposed. Based on it, vector finite element method is proved to exclude spurious modes provided finite elements possess discrete compactness property. Convergence analysis is conducted in the framework of collectively compact operators. Reported theoretical results apply to a wide class of vector finite elements including two families of Nedelec and their generalization, the $hp$-edge elements. Numerical experiments fully support theoretical estimates for convergence rates.


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Additional Information

L. Vardapetyan
Affiliation: The Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Taylor Hall 2.400, Austin, Texas 78712
Email: leonv@research.bell-labs.com

L. Demkowicz
Affiliation: The Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Taylor Hall 2.400, Austin, Texas 78712
Email: leszek@ticam.utexas.edu

DOI: https://doi.org/10.1090/S0025-5718-02-01411-4
Keywords: Maxwell's equations, waveguide eigenmodes, full-wave analysis, $hp$ finite elements
Received by editor(s): January 11, 2000
Received by editor(s) in revised form: February 20, 2001
Published electronically: May 1, 2002
Article copyright: © Copyright 2002 American Mathematical Society