<div class="csl-bib-body">
<div class="csl-entry">Leumüller, M. (2018). <i>Computing resonances in metallic photonic crystals</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.58260</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2018.58260
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/5392
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dc.description.abstract
Resonance problems arise in many fields of research. An example are photonic crystals, in which the propagation of waves is defined by resonances. Photonic crystals with band gaps are of special interest. Band gaps are regions of frequencies which cannot propagate through the crystal. To calculate the band structure of photonic crystals many linear resonance problems need to be solved. Fast and reliable linear eigenvalue solvers are needed. Lately, metallic photonic crystals have become more interesting. Differently from photonic crystals the electric permittivity of metallic photonic crystals depends on the frequency leading to rational resonance problems. These problems come with a high computational cost. In this thesis, we introduce an efficient eigenvalue solver for large rational eigenvalue problems. At first, the resonance problems for two and three dimensional metallic photonic crystal are derived from Maxwells equations. Then, they are discretised with Bloch periodic high order finite elements in Netgen/NGSolve. The arising large rational matrix eigenvalue problems are linearised with a rational linearisation schema and solved by the shift-and-invert Arnoldi method. By combining linearisation with the shiftand-invert Arnoldi, systems of linear equations with dimensions larger than the original matrix size have to be solve in each iteration. With the introduced rational linearisation these large systems of linear equations can be reduced to the original problem size. The proposed combination of these two algorithms is applied to two and three dimensional metallic photonic crystals and compared to the shift-andinvert Arnoldi with a standard polynomial linearisation. The appearance of plasmon frequencies is witnessed and the influence on the solver is studied. We show that the proposed method is a reliable and fast solver for large rational eigenvalue problems.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
metallic photonic crystals
en
dc.subject
eigenvalue problems
en
dc.title
Computing resonances in metallic photonic crystals
en
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2018.58260
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Michael Leumüller
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC15152292
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dc.description.numberOfPages
35
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-115596
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
tuw.author.orcid
0000-0001-7431-3390
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dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.languageiso639-1
en
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item.fulltext
with Fulltext
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item.openaccessfulltext
Open Access
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item.mimetype
application/pdf
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item.openairetype
master thesis
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item.grantfulltext
open
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.cerifentitytype
Publications
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crisitem.author.dept
E101-03-1 - Forschungsgruppe Computational Mathematics in Engineering
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crisitem.author.orcid
0000-0001-7431-3390
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crisitem.author.parentorg
E101-03 - Forschungsbereich Scientific Computing and Modelling