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.

中文翻译：

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GPU上GMRES的多精度策略的实验评估

由于功耗较低，数据移动减少和计算性能提高，因此对低精度计算的支持在加速器硬件中变得越来越普遍。但是，计算科学与工程（CSE）问题需要在多个领域中提高双精度精度。如果我们想在满足精度要求的前提下充分利用硬件的潜力，则硬件趋势与应用程序需求之间的这种冲突导致需要在线性代数算法级别上采用多精度策略。在本文中，我们将重点放在预处理的稀疏迭代线性求解器上，它是几种CSE应用程序中的关键内核。我们提出了一种在GPU上加速该内核的多精度策略的研究。我们正在寻求将多种精度纳入GMRES线性求解器的最佳方法。这些包括迭代优化和可并行化的预处理器。我们的工作提出了确定多精度GMRES何时有效的策略，并为多精度迭代优化求解器选择参数以获得更好的性能。我们使用基于Trilinos库的实现，并采用Kokkos Kernels来实现线性代数内核的性能可移植性。性能结果证明了多精度方法的前景，并表明通过优化低级内核甚至可以进一步改进。我们使用基于Trilinos库的实现，并采用Kokkos Kernels来实现线性代数内核的性能可移植性。性能结果证明了多精度方法的前景，并表明通过优化低级内核甚至可以进一步改进。我们使用基于Trilinos库的实现，并采用Kokkos Kernels来实现线性代数内核的性能可移植性。性能结果证明了多精度方法的前景，并表明通过优化低级内核甚至可以进一步改进。