GMRES多精度策略在GPU上的实验评估
Experimental Evaluation of Multiprecision Strategies for GMRES on GPUs
摘要：
由于更低的功耗、更少的数据移动和更高的计算性能，对较低精度计算的支持在加速器硬件中变得越来越普遍。然而，计算科学和工程（CSE）问题需要在几个领域的双精度精度。这种硬件趋势和应用需求之间的冲突，导致需要在线性代数算法级别的多精度策略，如果我们想充分利用硬件的潜力，同时满足精度要求。在本文中，我们专注于预处理稀疏迭代线性求解器，在几个CSE应用程序的关键内核。我们提出了一个多精度的GPU上加速这个内核的策略的研究。我们寻求最好的方法，将多个精度到GMRES线性求解器，这些包括迭代细化和并行预处理。我们的工作提出了策略，以确定多精度GMRES将是有效的，并选择多精度迭代细化求解器的参数，以实现更好的性能。我们使用的实现是基于Trilinos库，并采用Kokkos内核的性能可移植性的线性代数内核。性能结果证明了多精度方法的承诺，并证明了通过优化低级内核可以实现进一步的改进。
英文摘要：
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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