Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Eric Chung, Yalchin Efendiev*, Thomas Y. Hou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

96 Scopus citations

Abstract

In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.

Original languageEnglish (US)
Pages (from-to)69-95
Number of pages27
JournalJournal of Computational Physics
Volume320
DOIs
StatePublished - Sep 1 2016

Keywords

  • Heterogeneous media
  • Multiscale
  • Multiscale finite element method
  • Numerical homogenization
  • Porous media

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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