An enriched multiscale mortar space for high contrast flow problems

Tsz Shun Eric CHUNG Shubin Fu Yanfang Yang

Numerical Analysis and Scientific Computing mathscidoc:1910.43507

arXiv preprint arXiv:1609.02610, 2016.9
Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the standard mortar spaces are not robust, and some enrichments are necessary in order to obtain an efficient and robust mortar space. In this paper, we consider a class of flow problems in high contrast heterogeneous media, and develop a systematic approach to obtain an enriched multiscale mortar space. Our approach is based on the constructions of local multiscale basis functions. The multiscale basis functions are constructed from local problems by following the framework of the Generalized Multiscale Finite Element Method (GMsFEM). In particular, we first create a local snapshot space. Then we select the dominated modes within the snapshot space using an appropriate Proper Orthogonal Decomposition (POD) technique. These multiscale basis functions show better accuracy than polynomial basis for multiscale problems. Using the proposed multiscale mortar space, we will construct a multiscale finite element method to solve the flow problem on a coarse grid and a preconditioning technique for the fine scale discretization of the flow problem. In particular, we develop a multiscale mortar mixed finite element method using the mortar space. In addition, we will design a two-level additive preconditioner and a two-level hybrid preconditioner based on the proposed mortar space for the iterative method applied to the fine scale discretization of the flow problem. We present several numerical examples to demonstrate
No keywords uploaded!
[ Download ] [ 2019-10-20 18:13:24 uploaded by Tsz_Shun_Eric_CHUNG ] [ 521 downloads ] [ 0 comments ]
@inproceedings{tsz2016an,
  title={An enriched multiscale mortar space for high contrast flow problems},
  author={Tsz Shun Eric CHUNG, Shubin Fu, and Yanfang Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181324311377036},
  booktitle={arXiv preprint arXiv:1609.02610},
  year={2016},
}
Tsz Shun Eric CHUNG, Shubin Fu, and Yanfang Yang. An enriched multiscale mortar space for high contrast flow problems. 2016. In arXiv preprint arXiv:1609.02610. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181324311377036.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved