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

TL;DR

This paper introduces a multiscale modeling approach combining variational multiscale methods, domain decomposition, and model order reduction to efficiently simulate large, heterogeneous structures without clear scale separation.

Contribution

It develops a localized model order reduction technique with correlated sampling, improving accuracy and reducing computational costs compared to uncorrelated methods.

Findings

Accurate modeling of large heterogeneous structures demonstrated.

Reduced local space sizes and training samples improve efficiency.

Method preserves finite element sparsity and conforming coupling.

Abstract

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.