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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
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Math. Comput. Appl. 2019, 24(1), 20; https://doi.org/10.3390/mca24010020
Received: 10 December 2018 / Revised: 29 January 2019 / Accepted: 29 January 2019 / Published: 1 February 2019
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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. View Full-Text
Keywords: model order reduction; POD; DEIM; gappy POD; GNAT; ECSW; empirical cubature; hyper-reduction; reduced integration domain; computational homogenisation model order reduction; POD; DEIM; gappy POD; GNAT; ECSW; empirical cubature; hyper-reduction; reduced integration domain; computational homogenisation
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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.

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