<div class="csl-bib-body">
<div class="csl-entry">Scaglioni, A., An, X., Dick, J., Feischl, M., & Tran, T. H. (2024, February 27). <i>Sparse grid approximation of stochastic dynamic micromagnetics</i> [Conference Presentation]. SIAM Conference on Uncertainty Quantification (UQ24), Trieste, Italy. http://hdl.handle.net/20.500.12708/195507</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/195507
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dc.description.abstract
We consider the Stochastic Landau-Lifshitz-Gilbert (SLLG) problem as an example of parabolic stochastic PDE (SPDE) driven by Gaussian noise. Beyond being a popular model for magnetic materials immersed in heat baths, the forward uncertainty quantification (UQ) task poses several interesting challenges that did not appear simultaneously in previous works: The equation is strongly nonlinear, time-dependent, and has a non-convex side constraint. We first use the Doss-Sussman transform to convert the SPDE into a random coefficient PDE. We then employ the Lévy-Ciesielski parametrization of the Wiener process to obtain a parametric coefficient PDE. We study the regularity and sparsity properties of the parameter-to-solution map, which features countably many unbounded parameters and low regularity compared to other elliptic and parabolic model problems in UQ. We use a novel technique to establish uniform holomorphic regularity of the parameter-to-solution map based on a Gronwall-type estimate combined with previously known methods that employ the implicit function theorem. This regularity result is used to design a piecewise-polynomial sparse grid approximation through a profit maximization approach. We prove algebraic dimension-independent convergence and validate the result with numerical experiments. If time allows, we discuss the finite element discretization and multi-level approximation.
en
dc.language.iso
en
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dc.subject
Computational Mathematics
en
dc.subject
Numerical Analysis
en
dc.subject
Uncertainty quantification
en
dc.subject
Micromagnetics
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dc.title
Sparse grid approximation of stochastic dynamic micromagnetics
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
Cancer Council New South Wales, Australia
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dc.contributor.affiliation
UNSW Sydney, Australia
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dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
C4
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tuw.researchTopic.id
C6
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tuw.researchTopic.id
C1
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.name
Modeling and Simulation
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tuw.researchTopic.name
Computational Materials Science
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tuw.researchTopic.value
40
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tuw.researchTopic.value
40
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tuw.researchTopic.value
20
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tuw.publication.orgunit
E101-02-3 - Forschungsgruppe Computational PDEs
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tuw.author.orcid
0000-0003-0142-6022
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tuw.event.name
SIAM Conference on Uncertainty Quantification (UQ24)
en
tuw.event.startdate
27-02-2024
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tuw.event.enddate
01-03-2024
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Trieste
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tuw.event.country
IT
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tuw.event.presenter
Scaglioni, Andrea
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.grantfulltext
restricted
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item.languageiso639-1
en
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairetype
conference paper not in proceedings
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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crisitem.author.dept
E101-02-3 - Forschungsgruppe Computational PDEs
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crisitem.author.dept
Cancer Council New South Wales, Australia
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crisitem.author.dept
UNSW Sydney
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crisitem.author.dept
E101-02-3 - Forschungsgruppe Computational PDEs
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crisitem.author.dept
E192-04 - Forschungsbereich Formal Methods in Systems Engineering