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Reiterated multiscale model reduction using the generalized multiscale finite element method

Tsz Shun Eric CHUNG Yalchin Efendiev Wing Tat Leung Maria Vasilyeva

Numerical Analysis and Scientific Computing mathscidoc:1910.43563

International Journal for Multiscale Computational Engineering, 14, (6), 2016
Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the solutions of local problems can be expensive to compute due to scale disparity. In this setting, one can basically apply a homogenization or multiscale method reiteratively to solve for the local problems. This process is known as reiterated homogenization and has many variations in the numerical context. Though the process seems to be a straightforward extension of two-level process, it requires some careful implementation and the concept development for problems without scale separation and high contrast. In this paper, we consider the generalized multiscale finite element method (GMsFEM) and apply it iteratively to construct its multiscale basis functions. The main idea of the
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@inproceedings{tsz2016reiterated,
  title={Reiterated multiscale model reduction using the generalized multiscale finite element method},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, Wing Tat Leung, and Maria Vasilyeva},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202427270369092},
  booktitle={International Journal for Multiscale Computational Engineering},
  volume={14},
  number={6},
  year={2016},
}
Tsz Shun Eric CHUNG, Yalchin Efendiev, Wing Tat Leung, and Maria Vasilyeva. Reiterated multiscale model reduction using the generalized multiscale finite element method. 2016. Vol. 14. In International Journal for Multiscale Computational Engineering. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202427270369092.
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