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Giani, Stefano (2010) Convergent adaptive finite element methods for photonic crystal applications. Mathematical Models and Methods in Applied Sciences (M3AS) . ISSN 0218-2025 (Submitted)

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Abstract

We prove the convergence of an adaptive finite element method for computing the band structure of 2D

periodic photonic crystals with or without compact defects in both the TM and TE polarization cases. These

eigenvalue problems involve non-coercive elliptic operators with discontinuous coefficients. The error analysis

extends the theory of convergence of adaptive methods for elliptic eigenvalue problems to photonic crystal

problems, and in particular deals with various complications which arise essentially from the lack of coercivity

of the elliptic operator with discontinuous coefficients. We prove the convergence of the adaptive method in

an oscillation-free way and with no extra assumptions on the initial mesh, beside the conformity and shape

regularity. Also we present and prove the convergence of an adaptive method to compute efficiently an entire

band in the spectrum. This method is guaranteed to converge to the correct global maximum and minimum

of the band, which is a very useful piece of information in practice. Our numerical results cover both the cases

of periodic structures with and without compact defects.

Item Type:	Article
RIS ID:	https://nottingham-repository.worktribe.com/output/1012632
Additional Information:	Preprint of an article submitted for consideration in Mathematical Models and Methods in Applied Sciences (M3AS) © 2010 copyright World Scientific Publishing Company. http://www.worldscinet.com/m3as/mkt/editorial.shtml
Schools/Departments:	University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User:	Giani, Dr Stefano
Date Deposited:	11 Jan 2011 19:00
Last Modified:	04 May 2020 20:25
URI:	https://eprints.nottingham.ac.uk/id/eprint/1418

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