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.

英国气象局是天气和气候预测领域的世界领先者之一，全球许多其他中心都使用英国气象局的全球预报模型来驱动各自的本地区域模型。然而，由于全局模型的空间分辨率有限以及局部区域模型引入的额外误差，许多短尺度现象以及重要的长期动态仍然难以准确预测。具有超过 10^5 核心的新型计算架构提供了突破这些界限的机会，并使英国气象局保持在发展的最前沿。数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学及其稳定而准确的数值近似有了很好的理解。正如电话中所述，英国气象局的统一模型使用经纬度网格，并在最多 1000 个内核的并行计算机上实现了高效率。然而，极点处的（人工）网格聚类使得这些网格对于大规模计算来说不切实际，因此该 NERC 计划的核心任务之一是寻找合适的替代网格。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与时间相关的微分方程组，该系统与全球各地的解强耦合（著名的“蝴蝶效应”）。当前大多数大气动力学模型都使用半隐式时间离散方案，该方案在每个时间步长处提供一些方程的全局耦合。这可以防止系统变得不稳定，因此它允许比完全显式方案（不包括全局耦合）更大的时间步长。由于预测的成本与时间步数成正比，因此允许更大时间步长（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架构的背景下。压力的椭圆系统必须在每个时间步长中求解，从而导致非常大的病态代数系统，其求解很难有效地并行化。有两个主要因素使得该椭圆求解难以扩展到大问题规模和大处理器数量：算法可扩展性和并行可扩展性。由于椭圆方程的解算子全局耦合压力，因此只有在不同分辨率的网格上使用离散层次的多级迭代求解器才能实现成本的最佳线性增长（算法可扩展性）。但在大规模并行计算环境中，全局通信成本高昂，因此有必要很好地实现这些求解器，将大部分通信保持在本地，以确保计算成本继续最佳地扩展到 100K 或更多处理器（并行可扩展性）。该提案解决了这个问题，从而有助于就英国气象局未来动力核心的设计做出最佳决策，从而保证英国在这一关键社会/技术挑战中的竞争力。迄今为止，半隐式方案的最佳可扩展性尚未在大气流动中实现，但项目合作伙伴 IWR 海德堡和劳伦斯·利弗莫尔国家实验室在更简单的模型椭圆问题上的成功表明这是可能的。 PI 多年来在各种应用领域的最新架构上获得椭圆求解器的最佳可扩展性方面拥有丰富的经验，尤其是在多达 256 个核心的经纬度网格上离散化的大气流的椭圆问题，以及他作为世界领先的多级迭代椭圆求解器理论分析师以及他与该领域其他世界领先团体的联系意味着他完全有能力实现这一目标。