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Scaling Invariant Interpolation for Singularly Perturbed Vector Fields (SPVF)

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Coping with Complexity: Model Reduction and Data Analysis

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 75))

Abstract

The problem of modelling, numerical simulations and interpretation of the simulations results of complex systems arising in reacting flows requires more and more sophisticated methods of qualitative system analysis. Recently, the concept of invariant, slow/fast, attractive manifolds has proven to be an efficient tool for such an analysis. In particular, it allows us to study main properties of detailed models describing the reacting flow by considering appropriate low dimensional manifolds, which appear naturally in the system state/composition space as a manifestation of a restricted number of real degrees of freedom exhibited by the system.In order to answer the question of what are the minimal number of the real degrees of freedom (real system dimension) and to approximate low dimensional manifolds (i.e., reduced system’s phase spaces) the concept of Singularly Perturbed Vector Fields (SPVF) has been suggested lately [1]. In the current work a scales invariant version of the SPVF will be presented and discussed.

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Acknowledgements

This research was supported by the Deutsche Forschungsgemeinschaft (DFG). Bykov thanks the Centre for Advanced Studies in Mathematics at the Ben-Gurion University of the Negev (BGU) for financial support of his stay at the BGU during spring 2009.

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Authors and Affiliations

  1. Karlsruher Institut fuer Technologie, Institut fuer Technische Thermodynamik, Engelbert-Arndold-Strasse 4, Geb. 10.91, 76131, Karlsruhe, Germany

    Viatcheslav Bykov & Ulrich Maas

  2. Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva, 84105, Israel

    Vladimir Gol’dshtein

Authors
  1. Viatcheslav Bykov
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  2. Vladimir Gol’dshtein
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  3. Ulrich Maas
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Correspondence to Viatcheslav Bykov .

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Editors and Affiliations

  1. Dept. Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Alexander N. Gorban

  2. Dept. Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200a, Leuven, 3001, Belgium

    Dirk Roose

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Bykov, V., Gol’dshtein, V., Maas, U. (2011). Scaling Invariant Interpolation for Singularly Perturbed Vector Fields (SPVF). In: Gorban, A., Roose, D. (eds) Coping with Complexity: Model Reduction and Data Analysis. Lecture Notes in Computational Science and Engineering, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14941-2_5

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