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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 820162, 7 pages
http://dx.doi.org/10.1155/2014/820162
Research Article

Solving the Caputo Fractional Reaction-Diffusion Equation on GPU

1School of Computer Science, National University of Defense Technology, Changsha 410073, China
2Science and Technology on Space Physics Laboratory, Beijing 100076, China
3College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
4Department of Engineering Science, University of Oxford, Oxford OX2 0ES, UK

Received 1 April 2014; Accepted 27 May 2014; Published 17 June 2014

Academic Editor: Dorian Popa

Copyright © 2014 Jie Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a parallel GPU solution of the Caputo fractional reaction-diffusion equation in one spatial dimension with explicit finite difference approximation. The parallel solution, which is implemented with CUDA 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 most time consuming loop of vector-vector addition and constant vector multiplication is optimized and impressive performance improvement is got. The experimental results show that the GPU solution compares well with the exact solution. The optimized GPU solution on NVIDIA Quadro FX 5800 is 2.26 times faster than the optimized parallel CPU solution on multicore Intel Xeon E5540 CPU.