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Projection Generated Homogenization

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Multiscale Problems in Science and Technology

Abstract

Homogenization is a class of analytical techniques for approximating multiscale differential equations. The number of scales are reduced and the resulting equations are easier to analyze or numerically approximate. The classical homogenization technique is based on asymptotic expansions. We shall introduce a homogenization procedure based on projections of differential or discrete approximation operators onto coarser subspaces. The projection procedure is quite general and we give a presentation of a framework in Hilbert spaces. We apply the framework to a simple differential equation with oscillatory coefficients and to two discrete problems. One is wavelet based numerical homogenization and the other a multiscale finite element method.3

The first author was partially supported by the NSF grant 0012151000. The second author was partially supported by the NSF KDI grant DMS-9872890.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, 90095-1555

    Björn Engquist

  2. Department of Numerical Analysis and Computer Science, Royal Institute of Technology, 100 44, Stockholm

    Björn Engquist

  3. PACM, Department of Mathematics, Princeton University, Princeton, NJ, 08544-1000

    Olof Runborg

Authors
  1. Björn Engquist
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  2. Olof Runborg
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Nenad Antonić

  2. Dept. of Applied Analysis and Scientific Computing, CWI Amsterdam, P.O.Box 94079, Kruislaan 413, 1090 GB, Amsterdam, The Netherlands

    C. J. van Duijn

  3. IWR, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Willi Jäger

  4. Analyse Numérique, Bât 101 U.F.R. Mathématiques, Université Lyon 1, 43, Bd. du 11 Novembre 1918, 69622, Villeurbanne Cedex, France

    Andro Mikelić

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© 2002 Springer-Verlag Berlin Heidelberg

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Engquist, B., Runborg, O. (2002). Projection Generated Homogenization. In: Antonić, N., van Duijn, C.J., Jäger, W., Mikelić, A. (eds) Multiscale Problems in Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56200-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-56200-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43584-6

  • Online ISBN: 978-3-642-56200-6

  • eBook Packages: Springer Book Archive

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