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Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction

  • In this paper, a methodology for fine scale modeling of large scale linear elastic structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modelled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed bysolving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential toIn this paper, a methodology for fine scale modeling of large scale linear elastic structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modelled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed bysolving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential to reduce the size of the local spaces and the number of training samples compared to the uncorrelated samplingzeige mehrzeige weniger

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Metadaten
Autor*innen:Philipp Diercks, K. Veroy, Annika Robens-Radermacher, Jörg F. Unger
Dokumenttyp:Forschungsdatensatz
Veröffentlichungsform:Graue Literatur
Sprache:Englisch
Jahr der Erstveröffentlichung:2024
Organisationseinheit der BAM:7 Bauwerkssicherheit
7 Bauwerkssicherheit / 7.7 Modellierung und Simulation
Herausgeber (Institution):Bundesanstalt für Materialforschung und -prüfung (BAM)
Verlag:Arxiv; Cornell Tech
Verlagsort:New York, NY
DDC-Klassifikation:Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurwissenschaften und zugeordnete Tätigkeiten
Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurbau
Freie Schlagwörter:Localized model order reduction; Multiscale methods; Proper orthogonal; Variational multiscale method
Themenfelder/Aktivitätsfelder der BAM:Infrastruktur
Infrastruktur / Verkehrsinfrastrukturen
Material
Material / Materialdesign
Art der Ressource:Software
Ort der Datenerhebung:Berlin, Germany
Beginndatum der Datenerstellung:25.01.2022
DOI:10.48550/arXiv.2201.10374
URL:https://arxiv.org/abs/2201.10374
Beschreibung der Datei(en) :Multiscale paper mit Code (Ancillary Files)
Verfügbarkeit des Dokuments:Datei für die Öffentlichkeit verfügbar ("Open Access")
Lizenz (Deutsch):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
Datum der Freischaltung:11.04.2024
Referierte Publikation:Nein
Schriftenreihen ohne Nummerierung:Forschungsdatensätze der BAM
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