Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods
Chair of Applied Mechanics, Friedrich-Alexander Universität Erlangen-Nürnberg, Egerlandstraße 5, 91058 Erlangen, Germany
Author to whom correspondence should be addressed.
Received: 10 December 2018 / Revised: 29 January 2019 / Accepted: 29 January 2019 / Published: 1 February 2019
PDF [2862 KB, uploaded 26 February 2019]
The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE
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
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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Brands, B.; Davydov, D.; Mergheim, J.; Steinmann, P. Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods. Math. Comput. Appl. 2019, 24, 20.
Brands B, Davydov D, Mergheim J, Steinmann P. Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods. Mathematical and Computational Applications. 2019; 24(1):20.
Brands, Benjamin; Davydov, Denis; Mergheim, Julia; Steinmann, Paul. 2019. "Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods." Math. Comput. Appl. 24, no. 1: 20.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
Multiple requests from the same IP address are counted as one view.