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  <doc>
    <id>59803</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>researchdata</type>
    <publisherName>Arxiv; Cornell Tech</publisherName>
    <publisherPlace>New York, NY</publisherPlace>
    <creatingCorporation>Bundesanstalt für Materialforschung und -prüfung (BAM)</creatingCorporation>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
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    <title language="eng">Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction</title>
    <abstract language="eng">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 to reduce the size of the local spaces and the number of training samples compared to the uncorrelated sampling</abstract>
    <identifier type="doi">10.48550/arXiv.2201.10374</identifier>
    <identifier type="url">https://arxiv.org/abs/2201.10374</identifier>
    <enrichment key="ScientificResourceTypeGeneral">Software</enrichment>
    <enrichment key="ScientificGeolocation">Berlin, Germany</enrichment>
    <enrichment key="ScientificNote">Multiscale paper mit Code (Ancillary Files)</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="ScientificDateCreatedStart">25.01.2022</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Philipp Diercks</author>
    <author>K. Veroy</author>
    <author>Annika Robens-Radermacher</author>
    <author>Jörg F. Unger</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Multiscale methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Variational multiscale method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Localized model order reduction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Proper orthogonal</value>
    </subject>
    <collection role="ddc" number="620">Ingenieurwissenschaften und zugeordnete Tätigkeiten</collection>
    <collection role="ddc" number="624">Ingenieurbau</collection>
    <collection role="institutes" number="">7 Bauwerkssicherheit</collection>
    <collection role="themenfelder" number="">Infrastruktur</collection>
    <collection role="themenfelder" number="">Material</collection>
    <collection role="fulltextaccess" number="">Datei für die Öffentlichkeit verfügbar ("Open Access")</collection>
    <collection role="literaturgattung" number="">Graue Literatur</collection>
    <collection role="institutes" number="">7.7 Modellierung und Simulation</collection>
    <collection role="unnumberedseries" number="">Forschungsdatensätze der BAM</collection>
    <collection role="themenfelder" number="">Materialdesign</collection>
    <collection role="themenfelder" number="">Verkehrsinfrastrukturen</collection>
  </doc>
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