面向流体力学仿真的大型稀疏矩阵混合精度 GMRES 加速算法

Senwei Zheng, Jiaqing Kou, Weiwei Zhang

科研成果: 期刊稿件文章同行评审

摘要

Due to low computational power consumption and high efficiency, GPUs/TPUs/NPUs with single/half-precision computing units make the main computing mode for artificial intelligence, but they can’t be directly applied to solve differential equations requiring high floating-point accuracy, nor can they directly replace double-precision units. With the combined advantages of single and double precisions, a mixed-precision solution scheme balancing efficiency and accuracy, was proposed for large sparse linear equations. The sparse GMRES-IR algorithm for large sparse matrices was developed. Firstly, the characteristics of matrix data distributions in fluid dynamics simulation problems were analyzed. With double precision for pre-processing and single precision for detailed iteration, the single precision calculation was applied to the main time-consuming part of the algorithm, to enhance computational efficiency. Solutions of 33 linear equation systems from open-source datasets validate the accuracy and efficiency of the proposed method. The results show that, on a single-core CPU, under the same accuracy requirements, the proposed mixed-precision algorithm can achieve an acceleration effect of up to 2.5 times, and the effect is more prominent for large-scale matrices.

投稿的翻译标题A Mixed-Precision GMRES Acceleration Algorithm for Large Sparse Matrices in Fluid Dynamics Simulation
源语言繁体中文
页(从-至)40-54
页数15
期刊Applied Mathematics and Mechanics
46
1
DOI
出版状态已出版 - 1月 2025

关键词

  • computational fluid dynamics
  • GMRES
  • linear equations
  • mixed-precision

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