NDLI: An efficient parallel solution for Caputo fractional reaction

Content Provider	Springer Nature Link
Author	Gong, Chunye Bao, Weimin Tang, Guojian Yang, Bo Liu, Jie
Copyright Year	2014
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.
Starting Page	1521
Ending Page	1537
Page Count	17
File Format	PDF
ISSN	09208542
Journal	The Journal of Supercomputing
Volume Number	68
Issue Number	3
e-ISSN	15730484
Language	English
Publisher	Springer US
Publisher Date	2014-02-24
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fractional differential equation Reaction-diffusion equation High performance computing Parallel computing Finite difference method Programming Languages, Compilers, Interpreters Processor Architectures Computer Science
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Information Systems Hardware and Architecture Software

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