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Complex dispersion relation calculations with the symmetric interior penalty method
Author(s) -
Engström C.,
Wang M.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2926
Subject(s) - eigenvalues and eigenvectors , mathematics , rate of convergence , mathematical analysis , hermitian matrix , dispersion relation , convergence (economics) , dispersion (optics) , krylov subspace , space (punctuation) , galerkin method , linear system , physics , finite element method , computer science , pure mathematics , quantum mechanics , channel (broadcasting) , economics , thermodynamics , economic growth , operating system , computer network
A high‐order discontinuous Galerkin method for calculations of complex dispersion relations of two‐dimensional photonic crystals is presented. The medium is characterized by a complex‐valued permittivity and we relate for this absorptive system the spectral parameter to the time frequency. We transform the non‐linear eigenvalue problem for a Lorentz material in air into a non‐Hermitian linear eigenvalue problem and uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact of the penalty term numerically and illustrate the high convergence rate of the method. Copyright © 2010 John Wiley & Sons, Ltd.