数据与计算发展前沿 ›› 2025, Vol. 7 ›› Issue (5): 41-53.

CSTR: 32002.14.jfdc.CN10-1649/TP.2025.05.004

doi: 10.11871/jfdc.issn.2096-742X.2025.05.004

• 专刊：国产算力新力量，助力科学计算应用新发展 • 上一篇    下一篇

基于国产DCU加速器的混合精度多重网格预条件算法及应用

张林杰1(),邢欣1,赵梨2,*(),冯春生1,3,4   

  1. 1.湘潭大学数学与计算科学学院，湖南 湘潭 411105
    2.中国科学院数学与系统科学研究院，北京 100190
    3.湖南国家应用数学中心，湖南 湘潭 411105
    4.湖南韶峰应用数学研究院，湖南 湘潭 411105
  • 收稿日期:2025-02-28 出版日期:2025-10-20 发布日期:2025-10-23
  • 通讯作者: 赵梨
  • 作者简介:张林杰，湘潭大学数学与计算科学学院，博士研究生，主要研究方向为代数多重网格法、并行计算。
    本文承担工作为：算法设计、数值实验和论文撰写。
    ZHANG Linjie is a Ph.D. candidate at the School of Mathematics and Computational Science, Xiangtan University His primarily research interests include algebraic multigrid methods and parallel computing.
    In this paper, he is primarily responsible for algorithm design, numerical experiments, and manuscript writing.
    E-mail: 158876192@qq.com|赵梨，中国科学院数学与系统科学研究院，博士后，主要研究方向为代数多重网格法、并行计算、油藏数值模拟等。
    本文承担工作为：算法设计和论文撰写。
    ZHAO Li is a postdoctoral researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His main research interests include algebraic multigrid methods, parallel computing, and reservoir numerical simulation.
    In this paper, he is primarily responsible for algorithm design and manuscript writing.
    E-mail: lizhao@lsec.cc.ac.cn
  • 基金资助:
    国家重点研发计划“高性能计算”重点专项课题(2023YFB3001604);工信部产业技术基础平台重点项目(2023-276-1-1);光合基金 A 类项目(202302011094);湖南省重大科技创新平台项目(2024JC1003);中国石油勘探开发研究院合作项目(HBYT-ZBZX-FWTP-2025-0721);湖南省研究生科研创新项目(CX20230629);湘潭大学研究生科研创新项目(XDCX2024Y166)

A Mixed Precision Multigrid Preconditioning Algorithm for Domestic DCU Accelerator and Its Application

ZHANG Linjie1(),XING Xin1,ZHAO Li2,*(),FENG Chunsheng1,3,4   

  1. 1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
    2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
    3. National Center for Applied Mathematics in Hunan, Xiangtan, Hunan 411105, China
    4. Hunan Shaofeng Institute for Applied Mathematics, Xiangtan, Hunan 411105, China
  • Received:2025-02-28 Online:2025-10-20 Published:2025-10-23
  • Contact: ZHAO Li

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摘要：

【目的】 多重网格法是求解椭圆型偏微分方程离散系统的一种极为有效的方法，其高效异构并行算法的研究与软件研制一直是科学与工程计算领域的重点和难点。【方法】 本文面向国产加速卡，提出了一种异构并行的多重网格方法，并将其应用于求解非等温油藏问题的限制压力-温度残量（CPTR）预条件方法中。在此基础上，设计了两种异构并行混合精度加速算法。【结论】 数值实验表明，异构并行多重网格法和CPTR预条件方法均具有显著的加速效果，分别实现了36倍和10倍以上的加速；此外，混合精度策略在保证计算精度的同时，进一步提升了CPTR预条件方法的性能，与双精度版本相比可提速15%-32%。

关键词: 多重网格法, 多阶段预条件方法, 混合精度, 异构并行, 国产加速器, 油藏模拟

Abstract:

[Objective] The multigrid method is an extremely effective approach for solving discretized systems of elliptic partial differential equations. The research and software development of its high-efficiency heterogeneous parallel algorithms have been key challenges in the field of scientific and engineering computing. [Methods] This paper proposes a heterogeneous parallel multigrid method tailored for domestic accelerators and applies it to solve the non-isothermal reservoir problem using the Constrained Pressure-Temperature Residual (CPTR) preconditioner. Based on this, two heterogeneous parallel mixed-precision acceleration algorithms are designed. [Conclusions] Numerical experiments show that both the heterogeneous parallel multigrid method and the CPTR preconditioner achieve significant acceleration, with a speedup of 36 and over 10, respectively. Additionally, the mixed-precision strategy improves the performance of the CPTR preconditioner while maintaining computational accuracy, achieving a performance improvement of 15%-32% compared to the double-precision version.

Key words: multigrid methods, multistage preconditioners, mixed precision, heterogeneous parallelism, domestic accelerators, reservoir simulation