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A Parallel Preconditioned Conjugate Gradient Solver for the Poisson Problem on a Multi-GPU Platform

Marco Ament, Gunter Knittel, Daniel Weiskopf, W. Strasser
VISUS Visualization Research Center, Universitat Stuttgart, Stuttgart, Germany
18th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP), 2010, p.583-592

@conference{ament2010parallel,

   title={A Parallel Preconditioned Conjugate Gradient Solver for the Poisson Problem on a Multi-GPU Platform},

   author={Ament, M. and Knittel, G. and Weiskopf, D. and Stra{ss}er, W.},

   booktitle={Parallel, Distributed and Network-Based Processing (PDP), 2010 18th Euromicro International Conference on},

   pages={583–592},

   issn={1066-6192},

   year={2010},

   organization={IEEE}

}

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We present a parallel conjugate gradient solver for the Poisson problem optimized for multi-GPU platforms. Our approach includes a novel heuristic Poisson preconditioner well suited for massively-parallel SIMD processing. Furthermore, we address the problem of limited transfer rates over typical data channels such as the PCI-express bus relative to the bandwidth requirements of powerful GPUs. Specifically, naive communication schemes can severely reduce the achievable speedup in such communication-intense algorithms. For this reason, we employ overlapping memory transfers to establish a high level of concurrency and to improve scalability. We have implemented our model on a high-performance workstation with multiple hardware accelerators. We discuss the mathematical principles, give implementation details, and present the performance and the scalability of the system.
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