<div class="csl-bib-body">
<div class="csl-entry">Danczul, T. (2021). <i>Model order reduction for fractional diffusion problems</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2021.92900</div>
</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2021.92900
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/19205
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dc.description.abstract
In this thesis we present a unified framework to efficiently approximate solutions to fractional diffusion problems of elliptic and parabolic type. After finite element discretization, we take the point of view that the solution is obtained by a matrix-vector product of the form f(L)b, where L is the discretization matrix of the spatial operator, b a prescribed vector, and f a parametric function. To alleviate the computational expenses, a model order reduction strategy in the form of a rational Krylov method is applied which projects the matrix to a low-dimensional space where a direct evaluation of the eigensystem is feasible. The particular choice of the subspace depends on a collection of parameters, the so-called poles. On the basis of the third Zolotar\"ev problem, we propose a variety of attractive pole selection strategies which allow us to efficiently query the solution map for multiple instances of the parameter. We either prove exponential convergence rates or provide the description of a computable error certificate to assess the quality of several poles where no analytical results are available.The analytical findings are confirmed by numerical experiments, including a systematic comparison of the presented schemes and a parameter study which provides deep insights in the effect of the fractional parameters.
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
fractional diffusion
en
dc.subject
rational Krylov space
en
dc.subject
model order reduction
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dc.title
Model order reduction for fractional diffusion problems
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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.2021.92900
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Tobias Danczul
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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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dc.contributor.referee
Bonito, Andrea
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dc.contributor.referee
Rozza, Gianluigi
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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dc.type.qualificationlevel
Doctoral
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dc.identifier.libraryid
AC16410454
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dc.description.numberOfPages
218
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
tuw.author.orcid
0000-0003-1279-2087
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dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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tuw.referee.staffStatus
external
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tuw.referee.staffStatus
external
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item.cerifentitytype
Publications
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item.openaccessfulltext
Open Access
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item.fulltext
with Fulltext
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item.languageiso639-1
en
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item.grantfulltext
open
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item.openairetype
doctoral thesis
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item.openairecristype
http://purl.org/coar/resource_type/c_db06
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item.mimetype
application/pdf
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crisitem.author.dept
E101-03-1 - Forschungsgruppe Computational Mathematics in Engineering
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crisitem.author.parentorg
E101-03 - Forschungsbereich Scientific Computing and Modelling