Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor
An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals
Giani, S.
Authors
Abstract
In this paper we propose and analyze an hp-adaptive discontinuous finite element method for computing the band structure of 2D periodic photonic crystals. The spectrum of a 2D photonic crystal is approximated by computing the discrete spectrum of members of a family of periodic Hermitian eigenvalue problems on the primitive cell, parametrized by a two-dimensional parameter — the quasimomentum. We propose a residual-based error estimator and show that it is reliable and efficient for all eigenvalue problems in the family. In particular we prove that if the error estimator converges to zero, then the distance of the computed eigenfunction from the true eigenspace also converges to zero, and so the computed eigenvalue converges to a true eigenvalue. The results hold for eigenvalues of any multiplicity. We illustrate the benefits of the resulting hp-adaptive method numerically, both for fully periodic crystals and also for crystals with defects.
Citation
Giani, S. (2012). An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals. Journal of Computational and Applied Mathematics, 236(18), 4810-4826. https://doi.org/10.1016/j.cam.2012.02.007
Journal Article Type | Article |
---|---|
Publication Date | 2012-12 |
Deposit Date | Feb 12, 2013 |
Journal | Journal of Computational and Applied Mathematics |
Print ISSN | 0377-0427 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 236 |
Issue | 18 |
Pages | 4810-4826 |
DOI | https://doi.org/10.1016/j.cam.2012.02.007 |
Keywords | Eigenvalue problem, Finite element method, A posteriori error estimates. |
You might also like
An hp-adaptive discontinuous Galerkin method for phase field fracture
(2023)
Journal Article
Convolutional neural network framework for wind turbine electromechanical fault detection
(2023)
Journal Article
On Effects of Concentrated Loads on Perforated Sensitive Shells of Revolution
(2023)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search