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Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Adaptive multiscale model reduction with generalized multiscale finite element methods
Authors: Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.;

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

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.

Country
United States
Keywords

Multiscale, Physics and Astronomy (miscellaneous), Flows in porous media; filtration; seepage, Porous media, numerical homogenization, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, heterogeneous media, 510, Computer Science Applications, porous media, Multiscale finite element method, multiscale, FOS: Mathematics, Mathematics - Numerical Analysis, multiscale finite element method, Numerical homogenization, Heterogeneous media, Finite element methods applied to problems in fluid mechanics

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    164
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 1%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
164
Top 1%
Top 1%
Top 1%
Green
hybrid