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Multiscale Model Reduction with Generalized Multiscale Finite Element Methods in Geomathematics

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Handbook of Geomathematics

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Abstract

In this chapter, we discuss multiscale model reduction using Generalized Multiscale Finite Element Methods (GMsFEM) in a number of geomathematical applications. GMsFEM has been recently introduced (Efendiev et al. 2012) and applied to various problems. In the current chapter, we consider some of these applications and outline the basic methodological concepts.

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Acknowledgements

We would like to thank Ms. Guanglian Li and Mr. Shubin Fu for their assistance in compiling some results. YE’s work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE- FG02-13ER26165. MP’s work is partially supported by he U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC0009286 as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Scientific Computation (ISC), Texas A&M University, ∎, 77843, College Station, USA

    Yalchin Efendiev

Authors
  1. Yalchin Efendiev
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  2. Michael Presho
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Corresponding author

Correspondence to Yalchin Efendiev .

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Editors and Affiliations

  1. Geomathematische Gruppe, TU Kaiserslautern FB Mathematik, Kaiserslautern, Germany

    Willi Freeden

  2. University of Central Florida Dept. Mathematics, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Inst. Analysis, TU Braunschweig FB 1 Mathematik und Informatik, Braunschweig, Germany

    Thomas Sonar

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Efendiev, Y., Presho, M. (2014). Multiscale Model Reduction with Generalized Multiscale Finite Element Methods in Geomathematics. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27793-1_68-2

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  • DOI: https://doi.org/10.1007/978-3-642-27793-1_68-2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Online ISBN: 978-3-642-27793-1

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