Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

Language
en
Document Type
Article
Issue Date
2020-01-14
First published
2019-02-01
Issue Year
2019
Authors
Brands, Benjamin
Davydov, Denis
Mergheim, Julia
Steinmann, Paul
Editor
Publisher
MDPI
Abstract

The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE 2 method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss–Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE 2 framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies.

Journal Title
Mathematical and Computational Applications
Volume
24
Issue
1
Citation
Mathematical and Computational Applications 24.1 (2019). <https://www.mdpi.com/2297-8747/24/1/20>
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