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Numerical Study of Geometric Multigrid Methods on CPU–GPU Heterogeneous Computers

Chunsheng Feng, Shi Shu, Jinchao Xu, Chen-Song Zhang
Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, China
arXiv:1208.4247v1 [math.NA] (21 Aug 2012)

@article{2012arXiv1208.4247F,

   author={Feng, Chunsheng and Shu, Shi and Xu, Jinchao and Zhang, Chen-Song},

   title={Numerical Study of Geometric Multigrid Methods on CPU–GPU Heterogeneous Computers},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1208.4247},

   primaryClass={"math.NA"},

   keywords={Numerical Analysis, Computational Physics},

   year={2012},

   month={aug}

}

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The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from many types of partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously. Graphics processing units (GPUs) have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements. A central challenge in implementing GMG on GPUs, though, is that computational work on coarse levels cannot fully utilize the capacity of a GPU. In this work, we perform numerical studies of GMG on CPU–GPU heterogeneous computers. Furthermore, we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver, Fast Fourier Transform, in the cuFFT library developed by NVIDIA.
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