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An efficient parallel solution for Caputo fractional reaction–diffusion equation

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Abstract

The computational complexity of Caputo fractional reaction–diffusion equation is \(O(MN^2)\) compared with \(O(MN)\) of traditional reaction–diffusion equation, where \(M\), \(N\) are the number of time steps and grid points. A efficient parallel solution for Caputo fractional reaction–diffusion equation with explicit difference method is proposed. The parallel solution, which is implemented with MPI parallel programming model, consists of three procedures: preprocessing, parallel solver and postprocessing. The parallel solver involves the parallel tridiagonal matrix vector multiplication, vector vector addition and constant vector multiplication. The sum of constant vector multiplication is optimized. As to the authors’ knowledge, this is the first parallel solution for Caputo fractional reaction–diffusion equation. The experimental results show that the parallel solution compares well with the analytic solution. The parallel solution on single Intel Xeon X5540 CPU runs more than three times faster than the serial solution on single X5540 CPU core, and scales quite well on a distributed memory cluster system.

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Acknowledgments

This research work is supported by 973 Program of China under grant No. 61312701001. We would like to thank the anonymous reviewers for their helpful comments also.

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Authors and Affiliations

  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Chunye Gong, Weimin Bao & Guojian Tang

  2. Science and Technology on Space Physics Libratory, Beijing, 100076, China

    Chunye Gong, Weimin Bao & Guojian Tang

  3. Department of Computer Sciences, National University of Defense Technology, Changsha, 410073, China

    Chunye Gong, Bo Yang & Jie Liu

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  1. Chunye Gong
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  2. Weimin Bao
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Correspondence to Chunye Gong.

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Gong, C., Bao, W., Tang, G. et al. An efficient parallel solution for Caputo fractional reaction–diffusion equation. J Supercomput 68, 1521–1537 (2014). https://doi.org/10.1007/s11227-014-1123-z

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  • DOI: https://doi.org/10.1007/s11227-014-1123-z

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