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Experimental Evaluation of Multiprecision Strategies for GMRES on GPUs

Jennifer A. Loe, Christian A. Glusa, Ichitaro Yamazaki, Erik G. Boman, Sivasankaran Rajamanickam
Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico, USA 87123
arXiv:2105.07544 [math.NA], (16 May 2021)

@misc{loe2021experimental,

   title={Experimental Evaluation of Multiprecision Strategies for GMRES on GPUs},

   author={Jennifer A. Loe and Christian A. Glusa and Ichitaro Yamazaki and Erik G. Boman and Sivasankaran Rajamanickam},

   year={2021},

   eprint={2105.07544},

   archivePrefix={arXiv},

   primaryClass={math.NA}

}

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Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems require double precision accuracy in several domains. This conflict between hardware trends and application needs has resulted in a need for multiprecision strategies at the linear algebra algorithms level if we want to exploit the hardware to its full potential while meeting the accuracy requirements. In this paper, we focus on preconditioned sparse iterative linear solvers, a key kernel in several CSE applications. We present a study of multiprecision strategies for accelerating this kernel on GPUs. We seek the best methods for incorporating multiple precisions into the GMRES linear solver; these include iterative refinement and parallelizable preconditioners. Our work presents strategies to determine when multiprecision GMRES will be effective and to choose parameters for a multiprecision iterative refinement solver to achieve better performance. We use an implementation that is based on the Trilinos library and employs Kokkos Kernels for performance portability of linear algebra kernels. Performance results demonstrate the promise of multiprecision approaches and demonstrate even further improvements are possible by optimizing low-level kernels.
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