Linearization techniques for band structure calculations in absorbing photonic crystals
(2012) In International Journal for Numerical Methods in Engineering 89(2). p.180-191- Abstract
Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail.... (More)
Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques.
(Less)
- author
- Effenberger, C. ; Kressner, D. and Engström, C. LU
- publishing date
- 2012-01-13
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Band structure calculation, Krylov subspace method, Linearization, Lorentz model, Photonic crystal, Rational eigenvalue problem
- in
- International Journal for Numerical Methods in Engineering
- volume
- 89
- issue
- 2
- pages
- 12 pages
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- scopus:84655167725
- ISSN
- 0029-5981
- DOI
- 10.1002/nme.3235
- language
- English
- LU publication?
- no
- id
- 644f69cb-a82c-47aa-bf4b-3c84bfc48f89
- date added to LUP
- 2023-03-24 11:12:06
- date last changed
- 2023-03-24 14:29:19
@article{644f69cb-a82c-47aa-bf4b-3c84bfc48f89, abstract = {{<p>Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques.</p>}}, author = {{Effenberger, C. and Kressner, D. and Engström, C.}}, issn = {{0029-5981}}, keywords = {{Band structure calculation; Krylov subspace method; Linearization; Lorentz model; Photonic crystal; Rational eigenvalue problem}}, language = {{eng}}, month = {{01}}, number = {{2}}, pages = {{180--191}}, publisher = {{John Wiley & Sons Inc.}}, series = {{International Journal for Numerical Methods in Engineering}}, title = {{Linearization techniques for band structure calculations in absorbing photonic crystals}}, url = {{http://dx.doi.org/10.1002/nme.3235}}, doi = {{10.1002/nme.3235}}, volume = {{89}}, year = {{2012}}, }