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  A simple and flexible model order reduction method for FFT-based homogenization problems using a sparse sampling technique

Kochmann, J., Manjunatha, K., Gierden, C., Wulfinghoff, S., Svendsen, B., & Reese, S. (2019). A simple and flexible model order reduction method for FFT-based homogenization problems using a sparse sampling technique. Computer Methods in Applied Mechanics and Engineering, 347, 622-638. doi:10.1016/j.cma.2018.11.032.

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 Creators:
Kochmann, Julian1, Author              
Manjunatha, Kiran2, Author              
Gierden, Christian2, Author              
Wulfinghoff, Stephan3, Author              
Svendsen, Bob4, 5, Author              
Reese, Stefanie1, Author              
Affiliations:
1Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany, ou_persistent22              
2Institute of Applied Mechanics, RWTH Aachen University, D-52074, Aachen, Germany, ou_persistent22              
3Institute for Materials Science, Kiel University, 24105 Kiel, Germany, ou_persistent22              
4Material Mechanics, Faculty of Georesources and Materials Engineering, RWTH Aachen University, Schinkelstraße 2, D-52062 Aachen, Germany, ou_persistent22              
5Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Max Planck Society, ou_1863381              

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Free keywords: Composite materials; Convex optimization; Fast Fourier transforms; Frequency domain analysis; Homogenization method, Constitutive assumption; Elastoplastic matrix; Fixed point iteration; Homogenization problems; Model order reduction; Off-line computation; Reconstruction algorithms; Sparse representation, Compressed sensing
 Abstract: This work is concerned with the development of a novel model order reduction technique for FFT solvers. The underlying concept is a compressed sensing technique which allows the reconstruction of highly incomplete data using non-linear recovery algorithms based on convex optimization, provided the data is sparse or has a sparse representation in a transformed basis. In the context of FFT solvers, this concept is utilized to identify a reduced set of frequencies on a sampling pattern in the frequency domain based on which the Lippmann–Schwinger equation is discretized. Classical fixed-point iterations are performed to solve the local problem. Compared to the unreduced solution, a significant speed-up in CPU times at a negligibly small loss of accuracy in the overall constitutive response is observed. The generation of highly resolved local fields is easily possible in a post-processing step using reconstruction algorithms which are available as open source routines. The developed reduction technique does not require any time-consuming offline computations, e.g. for the generation of snapshots, is not restricted to any kinematic or constitutive assumptions and its implementation is straightforward. Composites consisting of elastic inclusions embedded in an i) elastic and ii) elastoplastic matrix are investigated as representative simulation examples. © 2018 Elsevier B.V.

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Language(s): eng - English
 Dates: 2019-04-15
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1016/j.cma.2018.11.032
 Degree: -

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Title: Computer Methods in Applied Mechanics and Engineering
  Abbreviation : Comput. Methods in Appl. Mech. Eng.
Source Genre: Journal
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Publ. Info: Amsterdam : Elsevier B.V.
Pages: - Volume / Issue: 347 Sequence Number: - Start / End Page: 622 - 638 Identifier: ISSN: 0045-7825
CoNE: https://pure.mpg.de/cone/journals/resource/954925455953