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An Adaptive Way of Choosing Significant Snapshots for Proper Orthogonal Decomposition

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IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 36))

Abstract

In structural engineering problems, the resulting partial differential equations (PDEs) are often solved using the finite element method (FEM). The number of degrees of freedom (DOF) and hence the computational time increases depending upon the complexity of the problem (linear/nonlinear) and discretization of space and time. The proper orthogonal decomposition (POD)  yields a valuable set of vector bases which can be used in model order reduction (MOR) techniques to reduce the computational time. However, for nonlinear problems the trade-off with respect to accuracy to gain speedup is still high. In this context, we present an adaptive method to choose snapshots, which leads to a POD technique with either increased accuracy or increased speed-up for a fixed accuracy compared to the classical POD.

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Acknowledgements

We would like to thank the German Research Foundation (Deutsche Forschungsgemeinschaft(DFG)) for the financial support of the SPP 1886 with the title “Polymorphic uncertainty modelling for the numerical design of structures”.

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Authors and Affiliations

  1. Institute of Applied Mechanics, RWTH Aachen, Mies-van-der-Rohe-Str. 1, 52074, Aachen, Germany

    Steffen Kastian & Stefanie Reese

Authors
  1. Steffen Kastian
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  2. Stefanie Reese
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Correspondence to Steffen Kastian .

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Editors and Affiliations

  1. Institute of Engineering and Computational Mechanics, University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Jörg Fehr

  2. Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Bernard Haasdonk

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Kastian, S., Reese, S. (2020). An Adaptive Way of Choosing Significant Snapshots for Proper Orthogonal Decomposition. In: Fehr, J., Haasdonk, B. (eds) IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018. IUTAM Bookseries, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-21013-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-21013-7_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21012-0

  • Online ISBN: 978-3-030-21013-7

  • eBook Packages: EngineeringEngineering (R0)

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