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

Handle URI:
http://hdl.handle.net/10754/623175
Title:
An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media
Authors:
Chung, Eric T.; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Leung, Wing Tat
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.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
Chung ET, Efendiev Y, Leung WT (2017) An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media. Communications in Computational Physics 21: 401–422. Available: http://dx.doi.org/10.4208/cicp.230815.090516a.
Publisher:
Global Science Press
Journal:
Communications in Computational Physics
Issue Date:
7-Feb-2017
DOI:
10.4208/cicp.230815.090516a
Type:
Article
ISSN:
1815-2406; 1991-7120
Sponsors:
This research is partially supported by the Hong Kong RGC General Research Fund (Project number: 400813). YE would like to thank the partial support from NSF 1620318, the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics programunderAwardNumberDE-FG02-13ER26165 and National Priorities Research Program grant 7-1482-1278 from the Qatar National Research Fund
Additional Links:
https://www.cambridge.org/core/journals/communications-in-computational-physics/article/div-classtitlean-online-generalized-multiscale-discontinuous-galerkin-method-gmsdgm-for-flows-in-heterogeneous-mediadiv/418FDB6625A730285F94991DC65E042F
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorChung, Eric T.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorLeung, Wing Taten
dc.date.accessioned2017-04-13T11:50:59Z-
dc.date.available2017-04-13T11:50:59Z-
dc.date.issued2017-02-07en
dc.identifier.citationChung ET, Efendiev Y, Leung WT (2017) An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media. Communications in Computational Physics 21: 401–422. Available: http://dx.doi.org/10.4208/cicp.230815.090516a.en
dc.identifier.issn1815-2406en
dc.identifier.issn1991-7120en
dc.identifier.doi10.4208/cicp.230815.090516aen
dc.identifier.urihttp://hdl.handle.net/10754/623175-
dc.description.abstractOffline 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.en
dc.description.sponsorshipThis research is partially supported by the Hong Kong RGC General Research Fund (Project number: 400813). YE would like to thank the partial support from NSF 1620318, the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics programunderAwardNumberDE-FG02-13ER26165 and National Priorities Research Program grant 7-1482-1278 from the Qatar National Research Funden
dc.publisherGlobal Science Pressen
dc.relation.urlhttps://www.cambridge.org/core/journals/communications-in-computational-physics/article/div-classtitlean-online-generalized-multiscale-discontinuous-galerkin-method-gmsdgm-for-flows-in-heterogeneous-mediadiv/418FDB6625A730285F94991DC65E042Fen
dc.subjectdiscontinuous Galerkin methoden
dc.subjectheterogeneous mediaen
dc.subjectMultiscale methoden
dc.subjectonline basis functionsen
dc.titleAn Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Mediaen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalCommunications in Computational Physicsen
dc.contributor.institutionDepartment of Mathematics, Chinese University of Hong Kong, Hong Kongen
dc.contributor.institutionDepartment of Mathematics, Texas AandM University, College Station, TX, 77843-3368, United Statesen
kaust.authorEfendiev, Yalchin R.en
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