GPU-acceleration of parallel unconditionally stable group explicit finite difference method

K. Parand, Saeed Zafarvahedian, Sayyed A. Hossayni
Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19839, Iran
arXiv:1310.3422 [cs.NA], (12 Oct 2013)


   author={Parand}, K. and {Zafarvahedian}, S. and {Hossayni}, S.~A.},

   title={"{GPU-acceleration of parallel unconditionally stable group explicit finite difference method}"},

   journal={ArXiv e-prints},




   keywords={Computer Science – Numerical Analysis, Physics – Computational Physics},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Since researchers and practitioners realized the potential of using GPU for general purpose, their application has been extended to other fields out of computer graphics scope. The main objective of this paper is to evaluate the impact of using GPU in solution of the transient diffusion type equation by parallel and stable group explicit finite difference method. To accomplish that, GPU and CPU-based (multi-core) approaches were developed. Moreover, we proposed an optimal synchronization arrangement for its implementation pseudo-code. Also, the interrelation of GPU parallel programming and initializing the algorithm variables was discussed, using numerical experiences. The GPU-approach results are faster than a much expensive parallel 8-thread CPU-based approach results. The GPU, used in this paper, is an ordinary laptop GPU (GT 335M) and is accessible for everyone; so, the results are expected to encourage whole of the researcher society to use GPUs and improve their research efficiency.
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