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Numerical Precision and Benchmarking Very-High-Order Integration of Particle Dynamics on GPU Accelerators

K.A. Hawick, D.P. Playne, M.G.B. Johnson
Computer Science, Institute for Information and Mathematical Sciences, Massey University, North Shore 102-904, Auckland, New Zealand
Computational Science Technical Note CSTN-120, 2011

@inproceedings{hawick2011numerical,

   title={Numerical Precision and Benchmarking Very-High-Order Integration of Particle Dynamics on GPU Accelerators},

   author={Hawick, KA and Playne, DP and Johnson, MGB},

   booktitle={Proc. International Conference on Computer Design (CDES’11), number CDE4469, Las Vegas, USA},

   year={2011}

}

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GPUs offer a powerful acceleration platform for many scientific applications. Numerical integration of classical Newtonian dynamical particles often requires very high-order numerical accuracy. We assess the floating-point precision and performance of various GPUs for applications involving high-order time-step integration methods for particle model simulations using N-squared interactions. We demonstrate how high-order algorithms can be expressed in Compute Unified Device Architecture (CUDA) and present some detailed benchmark data. We show the high numerical power of high-order integration methods such as Hairer’s 10th order method and relate its performance to its precision requirements.
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