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

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Philipp Diercks , Karen Veroy , Annika Robens‐Radermacher , Jörg F. Unger ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2201.10374

In this paper, a methodology for fine scale modeling of large scale 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 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.

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Finite Element Method

Algorithm

Mathematics

Computer Science

Mathematical Analysis

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Oversampling Reduction (mathematics) Uncorrelated Scale (ratio) Finite element method Boundary (topology) Algorithm Mathematics Mathematical optimization Computer science Sampling (signal processing) Boundary value problem Domain decomposition methods Domain (mathematical analysis) Applied mathematics Mathematical analysis Geometry Statistics Physics Quantum mechanics Computer vision Bandwidth (computing) Computer network Thermodynamics Filter (signal processing)

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2201.10374
PDF: https://arxiv.org/pdf/2201.10374
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Cited By: 1
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DOI: https://doi.org/10.48550/arxiv.2201.10374

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

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Language: en

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Publication year: 2022

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Publication date: 2022-01-25

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Authors: Philipp Diercks, Karen Veroy, Annika Robens‐Radermacher, Jörg F. Unger

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Landing page: https://arxiv.org/abs/2201.10374

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Concepts: Oversampling, Reduction (mathematics), Uncorrelated, Scale (ratio), Finite element method, Boundary (topology), Algorithm, Mathematics, Mathematical optimization, Computer science, Sampling (signal processing), Boundary value problem, Domain decomposition methods, Domain (mathematical analysis), Applied mathematics, Mathematical analysis, Geometry, Statistics, Physics, Quantum mechanics, Computer vision, Bandwidth (computing), Computer network, Thermodynamics, Filter (signal processing)

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Cited by: 1

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abstract_inverted_index.modelled	38
abstract_inverted_index.samples.	96
abstract_inverted_index.sparsity	121
abstract_inverted_index.standard	124
abstract_inverted_index.training	157
abstract_inverted_index.influence	28
abstract_inverted_index.numerical	130
abstract_inverted_index.potential	144
abstract_inverted_index.preserves	119
abstract_inverted_index.proposed,	14
abstract_inverted_index.sampling.	163
abstract_inverted_index.subdomain	109
abstract_inverted_index.addressing	50
abstract_inverted_index.approaches	93
abstract_inverted_index.conditions	76
abstract_inverted_index.conforming	115
abstract_inverted_index.correlated	89
abstract_inverted_index.efficiency	136
abstract_inverted_index.meaningful	88
abstract_inverted_index.multiscale	19
abstract_inverted_index.physically	87
abstract_inverted_index.reduction.	26
abstract_inverted_index.structures	12
abstract_inverted_index.conditions.	70
abstract_inverted_index.constructed	61
abstract_inverted_index.experiments	131
abstract_inverted_index.methodology	4
abstract_inverted_index.procedures.	128
abstract_inverted_index.separation.	56
abstract_inverted_index.variational	18
abstract_inverted_index.applications	51
abstract_inverted_index.contribution	106
abstract_inverted_index.displacement	48
abstract_inverted_index.oversampling	65
abstract_inverted_index.uncorrelated	95, 162
abstract_inverted_index.decomposition	22
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	4
sustainable_development_goals[0].id	https://metadata.un.org/sdg/11
sustainable_development_goals[0].score	0.6200000047683716
sustainable_development_goals[0].display_name	Sustainable cities and communities
citation_normalized_percentile