Mixed GMsFEM for the simulation of waves in highly heterogeneous media

Tsz Shun Eric CHUNG Wing Tat Leung

Numerical Analysis and Scientific Computing mathscidoc:1910.43545

Journal of Computational and Applied Mathematics, 306, 69-86, 2016.11
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of simulating waves at a much lower cost. Our method is based on a mixed Galerkin type method with carefully designed basis functions that can capture various scales in the solution. The basis functions are constructed based on some local snapshot spaces and local spectral problems defined on them. The spectral problems give a natural ordering of the basis functions in the snapshot space and allow systematically enrichment of basis functions. In addition, by using a staggered coarse mesh, our method is energy conserving and has block diagonal mass matrix, which are desirable properties for wave propagation. We will prove that our method has spectral convergence, and
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@inproceedings{tsz2016mixed,
  title={Mixed GMsFEM for the simulation of waves in highly heterogeneous media},
  author={Tsz Shun Eric CHUNG, and Wing Tat Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020182512407318074},
  booktitle={Journal of Computational and Applied Mathematics},
  volume={306},
  pages={69-86},
  year={2016},
}
Tsz Shun Eric CHUNG, and Wing Tat Leung. Mixed GMsFEM for the simulation of waves in highly heterogeneous media. 2016. Vol. 306. In Journal of Computational and Applied Mathematics. pp.69-86. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020182512407318074.
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