<div class="csl-bib-body">
<div class="csl-entry">Gangl, P., & Sturm, K. (2020). Asymptotic analysis and topological derivative for 3D quasi-linear magnetostatics. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, <i>55</i>, 853–875. https://doi.org/10.1051/m2an/2020060</div>
</div>
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dc.identifier.issn
1292-8119
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/141423
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dc.description.abstract
In this paper we study the asymptotic behaviour of the quasilinear curl-curl equation of 3D magnetostatics with respect to a singular perturbation of the differential operator and prove the existence of the topological derivative using a Lagrangian approach. We follow the strategy proposed in our recent previous work (arXiv:1907.13420) where a systematic and concise way for the derivation of topological derivatives for quasi-linear elliptic problems in H1 is introduced. In order to prove the asymptotics for the state equation we make use of an appropriate Helmholtz decomposition. The evaluation of the topological derivative at any spatial point requires the solution of a nonlinear transmission problem. We discuss an efficient way for the numerical evaluation of the topological derivative in the whole design domain using precomputation in an offline stage. This allows us to use the topological derivative for the design optimization of an electrical machine.
de
dc.description.abstract
In this paper we study the asymptotic behaviour of the quasilinear curl-curl equation of 3D magnetostatics with respect to a singular perturbation of the differential operator and prove the existence of the topological derivative using a Lagrangian approach. We follow the strategy proposed in our recent previous work (arXiv:1907.13420) where a systematic and concise way for the derivation of topological derivatives for quasi-linear elliptic problems in H1 is introduced. In order to prove the asymptotics for the state equation we make use of an appropriate Helmholtz decomposition. The evaluation of the topological derivative at any spatial point requires the solution of a nonlinear transmission problem. We discuss an efficient way for the numerical evaluation of the topological derivative in the whole design domain using precomputation in an offline stage. This allows us to use the topological derivative for the design optimization of an electrical machine.
en
dc.language.iso
en
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dc.relation.ispartof
ESAIM: Control, Optimisation and Calculus of Variations
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dc.subject
Shape Optimization
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dc.title
Asymptotic analysis and topological derivative for 3D quasi-linear magnetostatics
en
dc.type
Artikel
de
dc.type
Article
en
dc.description.startpage
853
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dc.description.endpage
875
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dc.type.category
Original Research Article
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tuw.container.volume
55
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tuw.journal.peerreviewed
true
-
tuw.peerreviewed
true
-
wb.publication.intCoWork
International Co-publication
-
tuw.researchTopic.id
C4
-
tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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dcterms.isPartOf.title
ESAIM: Control, Optimisation and Calculus of Variations
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tuw.publication.orgunit
E101-02 - Forschungsbereich Numerik
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tuw.publisher.doi
10.1051/m2an/2020060
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dc.identifier.eissn
1262-3377
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dc.description.numberOfPages
23
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wb.sci
true
-
wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.facultyfocus
Analysis und Scientific Computing
de
wb.facultyfocus
Analysis and Scientific Computing
en
wb.facultyfocus.faculty
E100
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item.cerifentitytype
Publications
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item.cerifentitytype
Publications
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no Fulltext
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restricted
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.openairetype
Artikel
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item.openairetype
Article
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item.languageiso639-1
en
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crisitem.author.dept
E101-02 - Forschungsbereich Numerik
-
crisitem.author.parentorg
E101 - Institut für Analysis und Scientific Computing