面向流体力学仿真的大型稀疏矩阵混合精度GMRES加速算法

郑森炜; 寇家庆; 张伟伟

doi:10.21656/1000-0887.450167

面向流体力学仿真的大型稀疏矩阵混合精度GMRES加速算法

doi: 10.21656/1000-0887.450167

郑森炜¹,
寇家庆^1,2,3,
张伟伟^1,2,3, ,

1. 西北工业大学航空学院，西安 710072;
2. 西北工业大学流体力学智能化国际联合研究所，西安 710072;
3. 飞行器基础布局全国重点实验室，西安 710072

详细信息

作者简介:
郑森炜（2001—），男，硕士生(E-mail: senweiz@mail.nwpu.edu.cn);寇家庆（1993—），男，教授，博士生导师(E-mail: jqkou@nwpu.edu.cn);张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).

通讯作者:
张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).

中图分类号: O35
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出版历程
- 收稿日期: 2024-06-05
- 修回日期: 2024-07-10

A Mixed-Precision GMRES Acceleration Algorithm for Large Sparse Matrices in Fluid Dynamics Simulation

ZHENG Senwei¹,
KOU Jiaqing^1,2,3,
ZHANG Weiwei^{1,2,3
, ,}

1. School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;
2. International Joint Institute of Artificial Intelligence on Fluid Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;
3. National Key Laboratory of Aircraft Configuration Design, Xi’an 710072, P.R.China

摘要

摘要: 由于计算能耗低、效率高，以单精度/半精度计算单元为主的GPU/TPU/NPU等算力已成为人工智能计算的主要模式，但无法直接应用于浮点精度需求高的微分方程求解，不能直接替代双精度算力.通过结合单/双精度各自的优势，提出了兼顾效率和精度的大型稀疏线性方程组的混合精度求解格式.发展了面向稀疏大型矩阵的GMRES细化迭代算法（sparse GMRES-IR）.首先分析了流体力学仿真问题中的矩阵数据分布特点，通过双精度做预处理，单精度细化迭代，使单精度计算应用于算法主要耗时部分，发挥了计算效率优势.通过求解开源数据集提供的33个线性方程组验证了所提出方法的精度和效率.结果表明，在单核CPU上，相同精度要求下，提出的单双混合精度算法可以实现最高2.5倍的加速效果，且在大规模矩阵下效果更突出.
- 混合精度 /
- 计算流体力学 /
- 线性方程组 /
- GMRES
Abstract: 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.
- mixed-precision /
- computational fluid dynamics /
- linear equations /
- GMRES

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参考文献(27)

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面向流体力学仿真的大型稀疏矩阵混合精度GMRES加速算法

doi: 10.21656/1000-0887.450167

作者简介:
郑森炜（2001—），男，硕士生(E-mail: senweiz@mail.nwpu.edu.cn);寇家庆（1993—），男，教授，博士生导师(E-mail: jqkou@nwpu.edu.cn);张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).

通讯作者:
张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).

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A Mixed-Precision GMRES Acceleration Algorithm for Large Sparse Matrices in Fluid Dynamics Simulation

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目录

留言板

面向流体力学仿真的大型稀疏矩阵混合精度GMRES加速算法

doi: 10.21656/1000-0887.450167

作者简介: 郑森炜（2001—），男，硕士生(E-mail: senweiz@mail.nwpu.edu.cn);寇家庆（1993—），男，教授，博士生导师(E-mail: jqkou@nwpu.edu.cn);张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).

通讯作者: 张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).

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出版历程

A Mixed-Precision GMRES Acceleration Algorithm for Large Sparse Matrices in Fluid Dynamics Simulation

计量

出版历程

目录

作者简介:
郑森炜（2001—），男，硕士生(E-mail: senweiz@mail.nwpu.edu.cn);寇家庆（1993—），男，教授，博士生导师(E-mail: jqkou@nwpu.edu.cn);张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).

通讯作者:
张伟伟（1979—），男，教授，博士生导师(通讯作者. E-mail: aeroelastic@nwpu.edu.cn).