Convergent adaptive finite element methods for photonic crystal applications

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
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:Faculty of Science > School of Mathematical Sciences
ID Code:1418
Deposited By:Giani, Dr Stefano
Deposited On:11 Jan 2011 19:00
Last Modified:23 Jun 2011 07:52

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