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A scalable hybrid algorithm based on domain decomposition and algebraic multigrid for solving partial differential equations on a cluster of CPU/GPUs

Li Luo, Chao Yang, Yubo Zhao, Xiao-Chuan Cai
Shenzhen Inst. of Adv. Tech., Chinese Academy of Sciences, Shenzhen 518055, P. R. China
2nd Intl. Workshop on GPUs and Scientific Applications, in conjunction with 2011 Intl. Conference on Parallel Architectures and Compilation Techniques (PACT 2011), 2011

@inproceedings{luo2011scalable,

   title={A scalable hybrid algorithm based on domain decomposition and algebraic multigrid for solving partial differential equations on a cluster of CPU/GPUs},

   author={Luo, L. and Yang, C. and Zhao, Y. and Cai, X.C.},

   booktitle={2nd International Workshop on GPUs and Scientific Applications (GPUScA 2011)},

   pages={45},

   year={2011}

}

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Several of the top ranked supercomputers are based on the hybrid architecture consisting of a large number of CPUs and GPUs. Very high performance has been obtained for problems with special structures, such as FFT-based image processing or N-body based particle calculations. However, for the class of problems described by partial differential equations discretized by finite difference (or other mesh based methods such as finite element) methods, obtaining even reasonably good performance on a CPU/GPU cluster is challenging. In this paper, we propose and test a hybrid algorithm that matches the architecture of the cluster. The scalability of the approach is realized by a domain decomposition method, and the high performance on GPU is realized by using a smoothed aggregation based algebraic multigrid method. Incomplete factorization, which performs beautifully on CPU but poorly on GPU, is completely avoided in the approach. We report some numerical results obtained by using up to 32 CPU/GPU pairs for solving a PDE problem with up to 32 millions unknowns.
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