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Model Order Reduction of Differential Algebraic Equations Arising from the Simulation of Gas Transport Networks

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Book cover Progress in Differential-Algebraic Equations

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

We explore the Tractability Index of Differential Algebraic Equations (DAEs) that emerge in the simulation of gas transport networks. Depending on the complexity of the network, systems of index 1 or index 2 can arise. It is then shown that these systems can be rewritten as Ordinary Differential Equations (ODEs). We furthermore apply Model Order Reduction (MOR) techniques such as Proper Orthogonal Decomposition (POD) to a network of moderate size and complexity and show that one can reduce the system size significantly.

Mathematics Subject Classification (2010) 65280

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Author information

Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Sara Grundel & Peter Benner

  2. Institute of Mathematics, Humboldt Universität zu Berlin, Berlin, Germany

    Lennart Jansen & Caren Tischendorf

  3. Fraunhofer SCAI, Sankt Augustin, Germany

    Nils Hornung & Tanja Clees

Authors
  1. Sara Grundel
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  2. Lennart Jansen
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  3. Nils Hornung
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  4. Tanja Clees
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  5. Caren Tischendorf
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  6. Peter Benner
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Corresponding author

Correspondence to Sara Grundel .

Editor information

Editors and Affiliations

  1. Technische Universität Darmstadt, Graduate School CE, Darmstadt, Germany

    Sebastian Schöps

  2. Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Andreas Bartel

  3. Bergische Univeirsität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Michael Günther

  4. Eindhoven University of Technology, Dept. Mathematics & Comp. Sci., Eindhoven, The Netherlands

    E. Jan W. ter Maten

  5. Bergische Universität Wuppertal, Dept. Safety Control Engineering, Wuppertal, Germany

    Peter C Müller

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Grundel, S., Jansen, L., Hornung, N., Clees, T., Tischendorf, C., Benner, P. (2014). Model Order Reduction of Differential Algebraic Equations Arising from the Simulation of Gas Transport Networks. In: Schöps, S., Bartel, A., Günther, M., ter Maten, E., Müller, P. (eds) Progress in Differential-Algebraic Equations. Differential-Algebraic Equations Forum. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44926-4_9

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