Solving the Caputo Fractional Reaction-Diffusion Equation on GPU. (17th June 2014)

• Record Type: Journal Article
• Authors: Liu, Jie; Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen
• Other Names: Popa Dorian Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2014(2014)
• Publication Date: 2014-06-17
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2014/820162
• Languages: English
• ISSNs: 1026-0226

Abstract

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.