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Multi-core parallel BRSMF method for 2D3T radiation diffusion equations

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Abstract

In this paper, we firstly present a block robust structured multifrontal factorization method (in brief, BRSMF) using block diagonalonal structure of three temperature matrices, and then we propose a multi-core parallelization of BRSMF (in brief, MBRSMF) method based on the current mainstream parallel computer multi-core architecture. MBRSMF method parallelizes the nested dissection ordering, symbolic decomposition and numerical decomposition of BRSMF method, which aims to effectively solve three temperature linear systems on the multi-core computer. The multi-core parallelization of symbolic decomposition and numerical decomposition is based on the binary elimination tree. Theoretical analysis proves MBRSMF method has better load balancing capability. Numerical experiments show that the MBRSMF method is effective.

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Acknowledgements

The authors would like to thank the referees and editors for their helpful and detailed suggestions for revising this manuscript.

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Authors and Affiliations

  1. Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng, 475004, P.R. China

    Xian-yu Zuo, Qiang Ge & Baojun Qiao

  2. School of Computer and Information Engineering, Henan University, Kaifeng, 475004, P.R. China

    Xian-yu Zuo, Qian-qian Wang & Ming-hu Fan

  3. School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, Henan, 450015, P.R. China

    Li-tao Zhang

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  1. Xian-yu Zuo
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  2. Qian-qian Wang
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  3. Qiang Ge
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  4. Baojun Qiao
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  5. Ming-hu Fan
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  6. Li-tao Zhang
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Correspondence to Ming-hu Fan or Li-tao Zhang.

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The project is supported in partly by National Key Research and Development Program of China (2019YFE0126600), Major Project of Science and Technology of Henan Province (201400210300), Science and Technological Research of Key Projects of Henan Province (212102210393, 202102110121, 202102210352, 202102210368), Science and Technological Research of Kaifeng (2002001), Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions (20zx003).

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Zuo, Xy., Wang, Qq., Ge, Q. et al. Multi-core parallel BRSMF method for 2D3T radiation diffusion equations. Wireless Netw 27, 4363–4373 (2021). https://doi.org/10.1007/s11276-021-02646-7

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