Affiliation:
1. Department 7.7 Modeling and Simulation Bundesanstalt für Materialforschung und ‐prüfung (BAM) Berlin Germany
2. Centre for Analysis, Scientific Computing and Applications (CASA) Department of Mathematics and Computer Science University of Eindhoven Eindhoven The Netherlands
Abstract
AbstractIn this article, 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 modeled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed by solving 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.
Funder
Deutsche Forschungsgemeinschaft
H2020 European Research Council
Subject
Applied Mathematics,General Engineering,Numerical Analysis
Cited by
4 articles.
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