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swPTS: an efficient parallel Thomas split algorithm for tridiagonal systems on Sunway manycore processors

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Abstract

Tridiagonal system solver is a basic kernel and has been well-supported in mainstream numerical libraries. The purpose of this paper is to devise an efficient parallel algorithm to solve a large-scale tridiagonal system. Based on the performance analysis of the classic Thomas algorithm and matrix splitting method, we propose a parallel Thomas split (PTS) algorithm. Compared with the matrix splitting method, the PTS algorithm can achieve an acceleration of 10.34\(\times \). Furthermore, we propose a Sunway parallel Thomas split (swPTS) algorithm based on the sw26010pro manycore processor. In the swPTS algorithm, we propose a specific data partitioning scheme to implement MPI+Athread parallelism. In the reduced set of equations, a new reduction approach for the Sunway architecture is proposed. Experiments show that the parallel elimination stage of our swPTS algorithm achieves up to 38.31\(\times \) speedup over a PTS algorithm, and overall reaches 5.74\(\times \) speedup over a Thomas algorithm.

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The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant (62002186) and the Unveiling Project of Qilu University of Technology (Shandong Academy of Sciences) (2022JBZ01-01).

Funding

This work was supported by the National Natural Science Foundation of China under Grant (62002186) and the Unveiling Project of Qilu University of Technology (Shandong Academy of Sciences) (2022JBZ01-01).

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Authors and Affiliations

  1. Key Laboratory of Computing Power Network and Information Security, Ministry of Education Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan, China

    Min Tian, Qi Liu, Jingshan Pan, Ying Gou & Zanjun Zhang

  2. Shandong Provincial Key Laboratory of Computer Networks, Shandong Fundamental Research Center for Computer Science, Jinan, China

    Min Tian, Qi Liu, Jingshan Pan, Ying Gou & Zanjun Zhang

  3. Shanxi Key Laboratory of Large Scale Electromagnetic Computing, Xidian University, Xi’an, Shaanxi, China

    Zanjun Zhang

Authors
  1. Min Tian
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  2. Qi Liu
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  3. Jingshan Pan
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  4. Ying Gou
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  5. Zanjun Zhang
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Contributions

MT conceived and designed the algorithm, and QL implemented and tested it. MT and QL wrote the main manuscript text and others prepared Figures 1–10. All authors reviewed the manuscript.

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Correspondence to Qi Liu.

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Tian, M., Liu, Q., Pan, J. et al. swPTS: an efficient parallel Thomas split algorithm for tridiagonal systems on Sunway manycore processors. J Supercomput 80, 4682–4706 (2024). https://doi.org/10.1007/s11227-023-05641-1

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