Preconditioning elliptic operators in high-performance all-scale atmospheric models on unstructured meshes

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2024-10-15 DOI:10.1016/j.jcp.2024.113503

Mike Gillard , Joanna Szmelter , Francesco Cocetta

{"title":"Preconditioning elliptic operators in high-performance all-scale atmospheric models on unstructured meshes","authors":"Mike Gillard , Joanna Szmelter , Francesco Cocetta","doi":"10.1016/j.jcp.2024.113503","DOIUrl":null,"url":null,"abstract":"<div><div>Effective simulation of all-scale atmospheric flows – e.g., cloud-resolving global weather – involves semi-implicit integration of the non-hydrostatic compressible Euler equations under gravity on a rotating sphere. Such integrations depend on complex non-symmetric elliptic solvers. The condition number of the underlying sparse linear operator is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>10</mn></mrow></msup><mo>)</mo></math></span>, which necessitates bespoke operator preconditioning. This paper highlights the development and implementation on unstructured meshes of specialised preconditioners for the non-symmetric Krylov-subspace solver. These developments are set in the context of a massively-parallel high-performance computing environment, aimed at architectures evolving towards exascale.</div><div>The baroclinic instability benchmark bearing representative features relevant to numerical weather prediction (NWP) has been selected to study the performance of the preconditioning options. The reported results illustrate the improved performance with the new preconditioning options. In particular, the Jacobi based option, for the computational meshes tested in this study, provides an excellent time to solution improvement.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113503"},"PeriodicalIF":3.8000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021999124007514","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

Effective simulation of all-scale atmospheric flows – e.g., cloud-resolving global weather – involves semi-implicit integration of the non-hydrostatic compressible Euler equations under gravity on a rotating sphere. Such integrations depend on complex non-symmetric elliptic solvers. The condition number of the underlying sparse linear operator is

O (10^{10})

, which necessitates bespoke operator preconditioning. This paper highlights the development and implementation on unstructured meshes of specialised preconditioners for the non-symmetric Krylov-subspace solver. These developments are set in the context of a massively-parallel high-performance computing environment, aimed at architectures evolving towards exascale.

The baroclinic instability benchmark bearing representative features relevant to numerical weather prediction (NWP) has been selected to study the performance of the preconditioning options. The reported results illustrate the improved performance with the new preconditioning options. In particular, the Jacobi based option, for the computational meshes tested in this study, provides an excellent time to solution improvement.

查看原文本刊更多论文

在非结构网格上对高性能全尺度大气模型中的椭圆算子进行预处理

全尺度大气流动的有效模拟--例如云解析全球天气--涉及旋转球体上重力作用下的非静水可压缩欧拉方程的半隐式积分。这种积分依赖于复杂的非对称椭圆求解器。底层稀疏线性算子的条件数为 O(1010)，因此需要定制算子预处理。本文重点介绍了在非结构化网格上开发和实施非对称克雷洛夫子空间求解器专用预处理的情况。这些开发是在大规模并行高性能计算环境下进行的，目标是向超大规模架构发展。为了研究预处理选项的性能，我们选择了与数值天气预报（NWP）相关的具有代表性特征的巴氏不稳定性基准。报告结果表明，采用新的预处理选项后，性能有所提高。特别是，对于本研究中测试的计算网格，基于雅可比的选项提供了极佳的求解时间改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.