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Parallel Scalability of Elliptic Solvers in Weather and Climate Prediction

椭圆求解器在天气和气候预测中的并行可扩展性

基本信息

批准号：
NE/J005576/1
负责人：
Robert Scheichl
金额：
$ 22.94万
依托单位：
University of Bath
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2011
资助国家：
英国
起止时间：
2011 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=NE%2FJ005576%2F1
关键词：
Parallel Scalability Elliptic Solvers Weather

项目摘要

The UK Met Office is one of the world leaders in weather and climate prediction, and the Met Office's global forecast model is used by many other centres worldwide to drive their individual local area models. However, many short scale phenomena as well as important longterm dynamics are still difficult to predict accurately due to the limited spatial resolution of global models and the additional errors introduced by local area models. Novel computing architectures with more than 10^5 cores provide a chance to push these boundaries and to keep the UK Met Office at the forefront of developments. Decades of experience with numerical weather and climate prediction have produced a good understanding of the core dynamics inherent in atmospheric flow and of their stable and accurate numerical approximations. As outlined in the call, the Met Office's Unified Model uses lattitude-longitude grids and achieves high efficiency on parallel computers with up to 1000 cores. However, (artificial) grid clustering at the poles renders these grids impractical for large-scale computations, and so one of the core tasks in this NERC Programme is the search for suitable alternative grids. Several separate proposals address this issue. However, the equations governing atmospheric flow form a time-dependent system of differential equations which strongly couple the solution everywhere on the globe (the famous "butterfly effect"). Most current atmospheric dynamics models use semi-implicit time discretisation schemes which provide some global coupling of the equations at each time step. This prevents the system from becoming unstable and as a consequence it allows for larger time steps than fully explicit schemes, which include no global coupling. Since the cost of the forecast is proportional to the number of time steps, a scheme that allows for larger time steps (with satisfactory accuracy) seems preferable. But these benefits come at a price, especially in the context of large-scale problems and on massively parallel architectures. An elliptic system for the pressure has to be solved in each time step, leading to a very large, ill-conditioned algebraic system, the solution of which is difficult to parallelise efficiently. There are two main factors that make the scaling of this elliptic solve to large problem sizes and to large processor numbers difficult: algorithmic scalability and parallel scalability. Since the solution operator for the elliptic equation couples the pressures globally, only multilevel iterative solvers which use a hierarchy of discretisations on grids of varying resolution allow optimal, linear growth in cost (algorithmic scalability). But in a massively parallel computing environment, where global communication is costly, it is necessary to implement these solvers well, keeping most of the communication local, to ensure that the computational cost continues to scale optimally to 100K or more processors (parallel scalability).This proposal addresses this problem and will thus facilitate the best possible decisions on the design of the Met Office's future dynamical core, thus guaranteeing the UK's competitiveness in this key societal/technological challenge. An optimal scalability of semi-implicit schemes has not been achieved in atmospheric flow up to now, but success of the Project Partners, IWR Heidelberg and Lawrence Livermore National Lab, on simpler model elliptic problems shows that it is possible. The PIs experience over the years in obtaining optimal scalability of elliptic solvers on the most current architectures in various application areas, most notably for elliptic problems from atmospheric flow discretised on latitude-longitude grids up to 256 cores, as well as his status as one of the world's leading theoretical analysts of multilevel iterative elliptic solvers and his links to other world leading groups in this field, mean that that he is ideally equipped to achieve this goal.

英国气象局是世界上天气和气候预测的领先者之一，英国气象局的全球预报模式被世界各地的许多其他中心用来推动各自的局部地区模式。然而，由于全球模式的空间分辨率有限以及局地模式引入的附加误差，许多短尺度现象以及重要的长期动态仍然难以准确预测。拥有超过10^5个核心的新型计算体系结构提供了一个机会来突破这些界限，并使英国气象局保持在发展的前沿。几十年的数值天气和气候预测经验使人们对大气流动固有的核心动力及其稳定和准确的数值近似有了很好的了解。正如电话会议中概述的那样，英国气象局的统一模型使用经纬度网格，并在拥有多达1000个核心的并行计算机上实现了高效率。然而，极点的(人工)网格聚类使得这些网格不适用于大规模计算，因此该NERC计划的核心任务之一是寻找合适的替代网格。有几个单独的提案解决了这个问题。然而，控制大气流动的方程形成了一个依赖于时间的微分方程组，它强烈地耦合了全球各地的解(著名的“蝴蝶效应”)。大多数当前的大气动力学模型使用半隐式时间离散化方案，在每个时间步提供方程的一些全局耦合。这防止了系统变得不稳定，因此它允许比完全显式格式更大的时间步长，而完全显式格式不包括全局耦合。由于预测的成本与时间步数成正比，因此允许更大的时间步长(具有令人满意的精度)的方案似乎更可取。但这些好处是有代价的，特别是在大规模问题和大规模并行体系结构的背景下。压力的椭圆型系统必须在每个时间步中求解，这导致了一个非常大的、病态的代数系统，其解很难有效地并行化。有两个主要因素使得这种椭圆解的可伸缩性难以扩展到大问题规模和大处理器数量：算法可伸缩性和并行可伸缩性。由于椭圆型方程的解运算符在全局范围内耦合压力，因此只有在不同分辨率的网格上使用离散化层次的多层迭代求解器才允许成本的最佳线性增长(算法可伸缩性)。但在全球通信成本高昂的大规模并行计算环境中，有必要很好地实施这些解算器，将大部分通信保持在本地，以确保计算成本继续以最佳方式扩展到100K或更多处理器(并行可伸缩性)。这项建议解决了这个问题，从而将有助于就英国气象局未来动态核心的设计做出可能的最佳决策，从而确保英国在这一关键社会/技术挑战中的竞争力。到目前为止，半隐式格式在大气流动中还没有达到最优的可伸缩性，但IWR Heidelberg和Lawrence Livermore国家实验室在更简单的模式椭圆型问题上的成功表明这是可能的。多年来，PI在各种应用领域的最新架构上获得椭圆解算器的最佳可扩展性方面的经验，最著名的是从纬度-经度网格上离散的大气流到256个核心的椭圆问题，以及他作为世界领先的多级迭代椭圆解算器理论分析师之一的地位以及他与该领域其他世界领先团队的联系，这意味着他是实现这一目标的理想人选。