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Scalable parallel elastic–plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

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Abstract

A domain decomposition method for large-scale elastic–plastic problems is proposed. The proposed method is based on a quasi-Newton method in conjunction with a balancing domain decomposition preconditioner. The use of a quasi-Newton method overcomes two problems associated with the conventional domain decomposition method based on the Newton–Raphson method: (1) avoidance of a double-loop iteration algorithm, which generally has large computational complexity, and (2) consideration of the local concentration of nonlinear deformation, which is observed in elastic–plastic problems with stress concentration. Moreover, the application of a balancing domain decomposition preconditioner ensures scalability. Using the conventional and proposed domain decomposition methods, several numerical tests, including weak scaling tests, were performed. The convergence performance of the proposed method is comparable to that of the conventional method. In particular, in elastic–plastic analysis, the proposed method exhibits better convergence performance than the conventional method.

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Acknowledgements

The present study was supported in part by MEXT Post-K Project Priority Issue 6: Accelerated Development of Innovative Clean Energy Systems and by JSPS KAKENHI Grant Number JP16K05988. The authors would like to thank the members of the ADVENTURE Project for their helpful discussions.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510, Japan

    Yasunori Yusa & Hiroshi Okada

  2. Department of Systems Innovation, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo, 113-8656, Japan

    Tomonori Yamada & Shinobu Yoshimura

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  1. Yasunori Yusa
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  2. Hiroshi Okada
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  3. Tomonori Yamada
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Correspondence to Yasunori Yusa.

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Yusa, Y., Okada, H., Yamada, T. et al. Scalable parallel elastic–plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner. Comput Mech 62, 1563–1581 (2018). https://doi.org/10.1007/s00466-018-1579-4

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