Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2907 | |
dc.contributor.author | Eigel, Martin | |
dc.contributor.author | Gruhlke, Robert | |
dc.contributor.author | Moser, Dieter | |
dc.date.accessioned | 2022-07-05T14:37:19Z | |
dc.date.available | 2022-07-05T14:37:19Z | |
dc.date.issued | 2021 | |
dc.description.abstract | We develop a new fuzzy arithmetic framework for efficient possibilistic uncertainty quantification. The considered application is an edge detection task with the goal to identify interfaces of blurred images. In our case, these represent realisations of composite materials with possibly very many inclusions. The proposed algorithm can be seen as computational homogenisation and results in a parameter dependent representation of composite structures. For this, many samples for a linear elasticity problem have to be computed, which is significantly sped up by a highly accurate low-rank tensor surrogate. To ensure the continuity of the underlying effective material tensor map, an appropriate diffeomorphism is constructed to generate a family of meshes reflecting the possible material realisations. In the application, the uncertainty model is propagated through distance maps with respect to consecutive symmetry class tensors. Additionally, the efficacy of the best/worst estimate analysis of the homogenisation map as a bound to the average displacement for chessboard like matrix composites with arbitrary star-shaped inclusions is demonstrated. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9625 | |
dc.identifier.uri | https://doi.org/10.34657/8663 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2907 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Fuzzy-stochastic partial differential equations | eng |
dc.subject.other | possibility | eng |
dc.subject.other | polymorphic uncertainty modeling | eng |
dc.subject.other | uncertainty quantification | eng |
dc.subject.other | low-rank hierarchical tensor formats | eng |
dc.subject.other | parametric partial differential equations | eng |
dc.subject.other | linear elasticity | eng |
dc.subject.other | homogenisation | eng |
dc.subject.other | tensor trains | eng |
dc.title | Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 34 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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