Paper Info
Title
Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients.
Abstract
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the offline stage, we construct a small number of reduced basis functions within each coarse grid block, which can then be used to approximate the multiscale finite element basis functions. In addition, we coarsen the corresponding random space through a clustering algorithm. In the online stage, we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis. The new GMsFEM can be applied to multiscale SPDE starting with a relatively coarse grid, without requiring the coarsest grid to resolve the smallest-scale of the solution. The new method offers considerable savings in solving multiscale SPDEs. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.
Year
DOI
Venue
2018
10.1016/j.jcp.2018.05.041
Journal of Computational Physics
Keywords
Field
DocType
Stochastic partial differential equations (SPDEs),Generalized multiscale finite element method (GMsFEM),Multiscale basis functions,Karhunen–Loève expansion,Uncertainty quantification (UQ),Clustering algorithm
Small number,Elliptic pdes,Mathematical optimization,Finite element method,Basis function,Cluster analysis,Mathematics,Scale separation,Grid
Journal
Volume
ISSN
Citations 
371
0021-9991
0
PageRank 
References 
Authors
0.34
15
4
Name
Order
Citations
PageRank
Eric T. Chung138846.61
Yalchin Efendiev258167.04
Wing Tat Leung3619.28
Zhiwen Zhang4102.75