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Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Chung, Eric and Efendiev, Yalchin and Hou, Thomas Y. (2016) Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods. Journal of Computational Physics, 320 . pp. 69-95. ISSN 0021-9991. http://resolver.caltech.edu/CaltechAUTHORS:20160624-151830832

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2016.04.054DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021999116301097PublisherArticle
https://arxiv.org/abs/1604.08312arXivDiscussion Paper
Additional Information:© 2016 Elsevier Inc. Received 15 February 2016. Accepted 27 April 2016. Available online 13 May 2016. YE would like to thank the partial support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165 and National Priorities Research Program (NPRP) grant 7-1482-1278 from the Qatar National Research Fund. TYH’s research was in part supported by DOE Grant DE-FG02-06ER257, and NSF Grant Nos.DMS-1318377, DMS-1159138. EC’s research was in part supported by Hong Kong RGC General Research Fund Project No. 400813.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-13ER26165
Qatar National Research Fund7-1482-1278
Department of Energy (DOE)DE-FG02-06ER25727
NSFDMS-1318377
NSFDMS-1159138
Hong Kong Research Grant Council400813
Subject Keywords:Multiscale; Multiscale finite element method; Heterogeneous media; Porous media; Numerical homogenization
Record Number:CaltechAUTHORS:20160624-151830832
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160624-151830832
Official Citation:Eric Chung, Yalchin Efendiev, Thomas Y. Hou, Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods, Journal of Computational Physics, Volume 320, 1 September 2016, Pages 69-95, ISSN 0021-9991, http://dx.doi.org/10.1016/j.jcp.2016.04.054. (http://www.sciencedirect.com/science/article/pii/S0021999116301097)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68668
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Jun 2016 12:03
Last Modified:13 Apr 2017 19:42

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