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 sampling…
Autor*innen: | Philipp Diercks, K. Veroy, Annika Robens-Radermacher, Jörg F. Unger |
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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): | Creative Commons - CC BY - Namensnennung 4.0 International |
Datum der Freischaltung: | 11.04.2024 |
Referierte Publikation: | Nein |
Schriftenreihen ohne Nummerierung: | Forschungsdatensätze der BAM |