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Generalized multiscale finite element methods for wave propagation in heterogeneous media

Tsz Shun Eric CHUNG Yalchin Efendiev Wing Tat Leung

TBD mathscidoc:1910.43465

Multiscale Modeling & Simulation, 12, (4), 1691-1721, 2014.11
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to their complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids. In this paper, we present a multiscale finite element method for wave propagation on a coarse grid. The proposed method is based on the generalized multiscale finite element method (GMsFEM) (see [Y. Efendiev, J. Galvis, and T. Hou, <i>J. Comput. Phys.</i>, 251 (2012), pp. 116--135]). To construct multiscale basis functions, we start with two snapshot spaces in each coarse-grid block, where one represents the degrees of freedom on the boundary and the other represents the degrees of freedom in the interior. We use local spectral problems to identify important modes in each snapshot space. These local spectral
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@inproceedings{tsz2014generalized,
  title={Generalized multiscale finite element methods for wave propagation in heterogeneous media},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175816211580994},
  booktitle={Multiscale Modeling &amp; Simulation},
  volume={12},
  number={4},
  pages={1691-1721},
  year={2014},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, and Wing Tat Leung. Generalized multiscale finite element methods for wave propagation in heterogeneous media. 2014. Vol. 12. In Multiscale Modeling &amp; Simulation. pp.1691-1721. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020175816211580994.
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