Solving the Caputo Fractional Reaction-Diffusion Equation on GPU

Jie Liu, Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang
School of Computer Science, National University of Defense Technology, Changsha 410073, China
Discrete Dynamics in Nature and Society, Volume 2014, Article ID 820162, 7 pages, 2014


   title={Solving the Caputo Fractional Reaction-Diffusion Equation on GPU},

   author={Liu, Jie and Gong, Chunye and Bao, Weimin and Tang, Guojian and Jiang, Yuewen},



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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.
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