Complex dispersion relation calculations with the symmetric interior penalty method
(2010) In International Journal for Numerical Methods in Engineering 84(7). p.849-863- Abstract
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.
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https://lup.lub.lu.se/record/df9d305e-5801-46d1-8f81-b407821c7114
- author
- Engström, C. LU and Wang, M. LU
- publishing date
- 2010-11
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Absorptive, Bandstructure, Discontinuous Galerkin method, Non-linear eigenvalue problem, Photonic crystal
- in
- International Journal for Numerical Methods in Engineering
- volume
- 84
- issue
- 7
- pages
- 15 pages
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- scopus:78049303077
- ISSN
- 0029-5981
- DOI
- 10.1002/nme.2926
- language
- English
- LU publication?
- no
- id
- df9d305e-5801-46d1-8f81-b407821c7114
- date added to LUP
- 2023-03-24 11:15:50
- date last changed
- 2023-03-24 15:07:03
@article{df9d305e-5801-46d1-8f81-b407821c7114, abstract = {{<p>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.</p>}}, author = {{Engström, C. and Wang, M.}}, issn = {{0029-5981}}, keywords = {{Absorptive; Bandstructure; Discontinuous Galerkin method; Non-linear eigenvalue problem; Photonic crystal}}, language = {{eng}}, number = {{7}}, pages = {{849--863}}, publisher = {{John Wiley & Sons Inc.}}, series = {{International Journal for Numerical Methods in Engineering}}, title = {{Complex dispersion relation calculations with the symmetric interior penalty method}}, url = {{http://dx.doi.org/10.1002/nme.2926}}, doi = {{10.1002/nme.2926}}, volume = {{84}}, year = {{2010}}, }