Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Eric Chung; Yalchin Efendiev; Thomas Y. Hou

doi:10.1016/j.jcp.2016.04.054

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 journal › Article › peer-review

170 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 language	English (US)
Pages (from-to)	69-95
Number of pages	27
Journal	Journal of Computational Physics
Volume	320
DOIs	https://doi.org/10.1016/j.jcp.2016.04.054
State	Published - Sep 1 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

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)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2016.04.054

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title = "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.",

keywords = "Heterogeneous media, Multiscale, Multiscale finite element method, Numerical homogenization, Porous media",

author = "Eric Chung and Yalchin Efendiev and Hou, {Thomas Y.}",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

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doi = "10.1016/j.jcp.2016.04.054",

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AU - Chung, Eric

AU - Efendiev, Yalchin

AU - Hou, Thomas Y.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Heterogeneous media

KW - Multiscale

KW - Multiscale finite element method

KW - Numerical homogenization

KW - Porous media

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DO - 10.1016/j.jcp.2016.04.054

M3 - Article

AN - SCOPUS:84971463425

SN - 0021-9991

VL - 320

SP - 69

EP - 95

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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