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- Title
A Reduced Generalized Multiscale Basis Method for Parametrized Groundwater Flow Problems in Heterogeneous Porous Media.
- Authors
He, Xinguang; Li, Qiuqi; Jiang, Lijian
- Abstract
In this paper, we develop a reduced generalized multiscale basis method for efficiently solving the parametrized groundwater flow problems in heterogeneous porous media. Recently proposed generalized multiscale finite element (GMsFE) method is one of the accurate and efficient methods to solve the multiscale problems on a coarse grid. However, the GMsFE basis functions usually depend on the random parameters in the parametrized model, which substantially impacts on the computation efficiency when the parametrized equation needs to be solved many times for many instances of parameters. To enhance computation efficiency, we construct reduced generalized multiscale basis functions independent of parameters from the high‐dimensional GMsFE space and generate a reduced‐order multiscale model by projecting the parameterized flow governing equation onto the low‐dimensional reduced GMsFE space. Then, in order to improve the online computation of reduced‐order model, we apply a matrix discrete empirical interpolation method to affinely decompose the nonaffine parametrized systems arising from the discretization of governing equation. Finally, a few numerical experiments are carried out for the parametrized transient flow problems in heterogeneous porous media to illustrate the efficiency and accuracy of the proposed model reduction method. The results show that the proposed reduced generalized multiscale basis method can significantly improve computation efficiency while maintaining comparative accuracy for the groundwater flow problems by selecting a suitable coarse mesh size and an optimal number of reduced GMsFE basis functions at each of coarse nodes. Key Points: A reduced generalized multiscale basis method is developed for solving parametrized transient flow problems with multiscale inputsMethod is designed by incorporating reduced generalized multiscale bases and matrix discrete empirical interpolation into reduction modelThe proposed reduction method significantly enhance computation efficiency while maintaining accuracy for parametrized flow problems
- Subjects
MULTISCALE modeling; GROUNDWATER; POROUS materials; PARAMETERS (Statistics); STIFF computation (Differential equations)
- Publication
Water Resources Research, 2019, Vol 55, Issue 3, p2390
- ISSN
0043-1397
- Publication type
Article
- DOI
10.1029/2018WR023954