Ackmann Jan, Dueben Peter D, Palmer Tim, Smolarkiewicz Piotr K
University of Oxford Oxford UK.
European Centre for Medium Range Weather Forecasts Reading UK.
J Adv Model Earth Syst. 2022 Sep;14(9):e2022MS003148. doi: 10.1029/2022MS003148. Epub 2022 Sep 10.
Semi-implicit (SI) time-stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision arithmetic in the elliptic solvers. Precision levels as low as half (16 bits) are used and a detailed evaluation of the impact of reduced precision on the solver convergence and the solution quality is performed. This study is conducted in the context of a novel SI shallow-water model on the sphere, purposely designed to mimic numerical intricacies of modern all-scale weather and climate (W&C) models. The governing algorithm of the shallow-water model is based on the non-oscillatory MPDATA methods for geophysical flows, whereas the resulting elliptic problem employs a strongly preconditioned non-symmetric Krylov-subspace Generalized Conjugated-Residual (GCR) solver, proven in advanced atmospheric applications. The classical longitude/latitude grid is deliberately chosen to retain the stiffness of global W&C models. The analysis of the precision reduction is done on a software level, using an emulator, whereas the performance is measured on actual reduced precision hardware. The reduced-precision experiments are conducted for established dynamical-core test-cases, like the Rossby-Haurwitz wavenumber 4 and a zonal orographic flow. The study shows that selected key components of the elliptic solver, most prominently the preconditioning and the application of the linear operator, can be performed at the level of half precision. For these components, the use of half precision is found to yield a speed-up of a factor 4 compared to double precision for a wide range of problem sizes.
用于大气和海洋模型的半隐式（SI）时间步长方案需要在现代超级计算机上高效运行的椭圆型求解器。本文报告了我们在椭圆型求解器中使用混合精度算法时对潜在计算节省的研究。使用了低至半精度（16位）的精度级别，并对精度降低对求解器收敛和求解质量的影响进行了详细评估。这项研究是在一个新颖的球面上的SI浅水模型的背景下进行的，该模型特意设计用于模拟现代全尺度天气和气候（W&C）模型的数值复杂性。浅水模型的控制算法基于用于地球物理流动的非振荡MPDATA方法，而由此产生的椭圆问题采用了一种强预处理的非对称Krylov子空间广义共轭残差（GCR）求解器，该求解器在先进的大气应用中已得到验证。特意选择经典的经纬度网格以保留全球W&C模型的刚性。在软件层面使用模拟器对精度降低进行分析，而在实际的降低精度硬件上测量性能。针对已建立的动力学核心测试用例进行了降低精度的实验，如罗斯比 - 豪维茨波数4和纬向地形气流。研究表明，椭圆型求解器的选定关键组件，最显著的是预处理和线性算子的应用，可以在半精度级别上执行。对于这些组件，发现使用半精度与双精度相比，在广泛的问题规模范围内可实现4倍的加速。
