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. doi:10.1016/j.jcp.2016.04.054. https://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.
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| 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. | ||||||||||||||
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| Subject Keywords: | Multiscale; Multiscale finite element method; Heterogeneous media; Porous media; Numerical homogenization | ||||||||||||||
| DOI: | 10.1016/j.jcp.2016.04.054 | ||||||||||||||
| Record Number: | CaltechAUTHORS:20160624-151830832 | ||||||||||||||
| Persistent URL: | https://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: | 11 Nov 2021 04:03 |
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