Fast online generalized multiscale finite element method using constraint energy minimization
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AbstractLocal multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online stage with a specific input parameter to solve the global problem at a reduced computational cost. Recently, online approaches have been introduced, where multiscale basis functions are adaptively constructed in some regions to reduce the error significantly. In multiscale methods, it is desired to have only 1–2 iterations to reduce the error to a desired threshold. Using Generalized Multiscale Finite Element Framework [10], it was shown that by choosing sufficient number of offline basis functions, the error reduction can be made independent of physical parameters, such as scales and contrast. In this paper, our goal is to improve this. Using our recently proposed approach [4] and special online basis construction in oversampled regions, we show that the error reduction can be made sufficiently large by appropriately selecting oversampling regions. Our numerical results show that one can achieve a three order of magnitude error reduction, which is better than our previous methods. We also develop an adaptive algorithm and enrich in selected regions with large residuals. In our adaptive method, we show that the convergence rate can be determined by a user-defined parameter and we confirm this by numerical simulations. The analysis of the method is presented.
Acceptance Date17/11/2017
All Author(s) ListEric T. Chung, Yalchin Efendiev, Wing Tat Leung
Journal nameJournal of Computational Physics
Year2018
Month2
Day15
Volume Number355
Pages450 - 463
ISSN0021-9991
eISSN1090-2716
LanguagesEnglish-United Kingdom
KeywordsOnline basis functions, Multiscale finite element method, High contrast flow

Last updated on 2020-06-08 at 03:13