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Parallel Solver for \(\boldsymbol{H}\)(div) Problems Using Hybridization and AMG

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Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

Abstract

A scalable parallel solver for \(\boldsymbol{H}\)(div) problems discretized by arbitrary order finite elements on general unstructured meshes is proposed. The solver is based on hybridization and algebraic multigrid (AMG). The hybridization part of the solver requires the fine-grid element matrix information. Weak and strong scaling are examined through several numerical tests which demonstrate that the proposed solver provides a competitive alternative to ADS (Kolev and Vassilevski, SIAM J Sci Comput 34(6):A3079–A3098, 2012), a state-of-the-art solver for \(\boldsymbol{H}\)(div) problems. In fact, it outperforms ADS for higher order elements.

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Acknowledgements

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The work was partially supported by ARO under US Army Federal Grant # W911NF-15-1-0590.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX, 77843, USA

    Chak S. Lee

  2. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, 808, L-561, Livermore, CA, 94551, USA

    Panayot S. Vassilevski

  3. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, 97201, USA

    Panayot S. Vassilevski

Authors
  1. Chak S. Lee
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  2. Panayot S. Vassilevski
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Corresponding author

Correspondence to Panayot S. Vassilevski .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Lee, C.S., Vassilevski, P.S. (2017). Parallel Solver for \(\boldsymbol{H}\)(div) Problems Using Hybridization and AMG. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_6

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