BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients

Hyea Hyun Kim Tsz Shun Eric CHUNG Junxian Wang

Numerical Analysis and Scientific Computing mathscidoc:1910.43478

Journal of Computational Physics, 349, 191-214, 2017.11
Abstract BDDC and FETI-DP algorithms are developed for three-dimensional elliptic problems with adaptively enriched coarse components. It is known that these enriched components are necessary in the development of robust preconditioners. To form the adaptive coarse components, carefully designed generalized eigenvalue problems are introduced for each faces and edges, and the coarse components are formed by using eigenvectors with their corresponding eigenvalues larger than a given tolerance T O L. Upper bounds for condition numbers of the preconditioned systems are shown to be C T O L, with the constant C depending only on the maximum number of edges and faces per subdomain, and the maximum number of subdomains sharing an edge. Numerical results are presented to test the robustness of the proposed approach.
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@inproceedings{hyea2017bddc,
  title={BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients},
  author={Hyea Hyun Kim, Tsz Shun Eric CHUNG, and Junxian Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180157591246007},
  booktitle={Journal of Computational Physics},
  volume={349},
  pages={191-214},
  year={2017},
}
Hyea Hyun Kim, Tsz Shun Eric CHUNG, and Junxian Wang. BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients. 2017. Vol. 349. In Journal of Computational Physics. pp.191-214. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020180157591246007.
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