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Performance comparisons of geometric multigrid solvers and balancing domain decomposition solvers

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Computing and Visualization in Science

Abstract

Multigrid and domain-decomposition methods are now widely used in large-scale simulation studies. Meanwhile, many types of preconditioners are available for speeding the convergence. Users of analysis models are interested in the method or preconditioner that minimizes the computing time. In this paper, we analyze a thermal problem and a solid problem using two free, open-source software programs—the UG4 framework and the ADVENTURE system—based on geometric multigrid (GM) solvers and balancing domain-decomposition (BDD) solvers. We examine and report the computing times and iteration numbers to convergence of the two programs, and generate a common software interface between the UG4 framework and ADVENTURE system. Through this software interface, we can compare the solvers of the two software systems using the same mesh data. The results were presented on the CX400 system at the Information Technology Center of Nagoya University, Japan. The convergence rate of GM solver improved after suitable smoothing and scaling to finer grids. The BDD solver is suitable for large-scale analyses of structures with detailed and complex geometries.

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Acknowledgements

This research is financially supported by one of Japan Science and Technology (JST), CREST projects and the German Research Foundation (DFG). The CREST projects named “Development of Numerical Library Based on Hierarchical Domain Decomposition for Postpeta Scale Simulation”.

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Authors and Affiliations

  1. Center for Computational Mechanics Research, Toyo University, 2100 Kujirai, Kawagoe, Saitama, 3508585, Japan

    Hongjie Zheng

  2. Faculty of Information Sciences and Arts, Toyo University, 2100 Kujirai, Kawagoe, Saitama, 3508585, Japan

    Ryuji Shioya & Hiroshi Kawai

  3. Goethe Center for Scientific Computing (G-SCS), Goethe University, Frankfurt am Main, Kettenhofweg 139, 60325, Frankfurt, Germany

    Sebastian Reiter & Gabriel Wittum

Authors
  1. Hongjie Zheng
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  2. Ryuji Shioya
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  3. Hiroshi Kawai
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  4. Sebastian Reiter
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  5. Gabriel Wittum
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Correspondence to Ryuji Shioya.

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Communicated by Babett Lemke.

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Zheng, H., Shioya, R., Kawai, H. et al. Performance comparisons of geometric multigrid solvers and balancing domain decomposition solvers. Comput. Visual Sci. 23, 5 (2020). https://doi.org/10.1007/s00791-020-00323-4

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