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Efficient magnetohydrodynamic simulations on graphics processing units with CUDA

Hon-Cheng Wong, Un-Hong Wong, Xueshang Feng, Zesheng Tang
NAOC-MUST Collaborative Research Laboratory on Lunar and Planetary Exploration, Macau University of Science and Technology, Macao SAR, China
arXiv:0908.4362 [physics.comp-ph] (30 Aug 2009)

@article{wong2009efficient,

   title={Efficient magnetohydrodynamic simulations on graphics processing units with CUDA},

   author={Wong, H.C. and Wong, U.H. and Feng, X. and Tang, Z.},

   journal={Arxiv preprint arXiv:0908.4362},

   year={2009}

}

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Magnetohydrodynamic (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution methods for solving the ideal MHD equations are computationally expensive and Beowulf clusters or even supercomputers are often used to run the codes that implemented these methods. With the advent of the Compute Unified Device Architecture (CUDA), modern graphics processing units (GPUs) provide an alternative approach to parallel computing for scientific simulations. In this paper we present, to the author’s knowledge, the first implementation of MHD simulations entirely on GPUs with CUDA, named GPU-MHD, to accelerate the simulation process. GPU-MHD supports both single and double precision computation. A series of numerical tests have been performed to validate the correctness of our code. Accuracy evaluation by comparing single and double precision computation results is also given. Performance measurements of both single and double precision are conducted. These measurements show that our GPU-based implementation achieves speedups (in single precision) of about 10 (1D problems with 4096 grid points), 200 (2D problems with 1024^2 grid points), and 84 (3D problems with 128^3 grid points), respectively, compared to the corresponding serial CPU MHD implementation. For double precision computation, GPU-MHD still can achieve about 60% speed of the corresponding single precision computation. In addition, we extend GPU-MHD to support the visualization of the simulation results and thus the whole MHD simulation and visualization process can be performed entirely on GPUs.
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