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Title: An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media

Abstract

Abstract Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact that offline computations are typically performed locally and global information is missing in these offline information. To tackle this difficulty, we develop an online local adaptivity technique for local multiscale model reduction problems. We design new online basis functions within Discontinuous Galerkin method based on local residuals and some optimally estimates. The resulting basis functions are able to capture the solution efficiently and accurately, and are added to the approximation iteratively. Moreover, we show that the iterative procedure is convergent with a rate independent of physical scales if the initial space is chosen carefully. Our analysis also gives a guideline on how to choose the initial space. We present some numerical examples to show the performance of the proposed method.

Authors:
; ;
Publication Date:
Research Org.:
Texas A & M Univ., College Station, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1537203
DOE Contract Number:  
SC0010713
Resource Type:
Journal Article
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 21; Journal Issue: 2; Journal ID: ISSN 1815-2406
Publisher:
Global Science Press
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Chung, Eric T., Efendiev, Yalchin, and Leung, Wing Tat. An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media. United States: N. p., 2017. Web. doi:10.4208/cicp.230815.090516a.
Chung, Eric T., Efendiev, Yalchin, & Leung, Wing Tat. An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media. United States. doi:10.4208/cicp.230815.090516a.
Chung, Eric T., Efendiev, Yalchin, and Leung, Wing Tat. Wed . "An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media". United States. doi:10.4208/cicp.230815.090516a.
@article{osti_1537203,
title = {An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media},
author = {Chung, Eric T. and Efendiev, Yalchin and Leung, Wing Tat},
abstractNote = {Abstract Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact that offline computations are typically performed locally and global information is missing in these offline information. To tackle this difficulty, we develop an online local adaptivity technique for local multiscale model reduction problems. We design new online basis functions within Discontinuous Galerkin method based on local residuals and some optimally estimates. The resulting basis functions are able to capture the solution efficiently and accurately, and are added to the approximation iteratively. Moreover, we show that the iterative procedure is convergent with a rate independent of physical scales if the initial space is chosen carefully. Our analysis also gives a guideline on how to choose the initial space. We present some numerical examples to show the performance of the proposed method.},
doi = {10.4208/cicp.230815.090516a},
journal = {Communications in Computational Physics},
issn = {1815-2406},
number = 2,
volume = 21,
place = {United States},
year = {2017},
month = {2}
}