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

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    Type
    Article
    Authors
    Chung, Eric T.
    Efendiev, Yalchin R. cc
    Leung, Wing Tat
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Porous Media SRI Center (NumPor)
    Date
    2017-02-07
    Online Publication Date
    2017-02-07
    Print Publication Date
    2017-02
    Permanent link to this record
    http://hdl.handle.net/10754/623175
    
    Metadata
    Show full item record
    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.
    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.
    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
    Publisher
    Global Science Press
    Journal
    Communications in Computational Physics
    DOI
    10.4208/cicp.230815.090516a
    arXiv
    1504.04417
    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
    ae974a485f413a2113503eed53cd6c53
    10.4208/cicp.230815.090516a
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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