TY - JOUR
T1 - 面向流体力学仿真的大型稀疏矩阵混合精度 GMRES 加速算法
AU - Zheng, Senwei
AU - Kou, Jiaqing
AU - Zhang, Weiwei
N1 - Publisher Copyright:
© 2025 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.
PY - 2025/1
Y1 - 2025/1
N2 - 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.
AB - 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.
KW - computational fluid dynamics
KW - GMRES
KW - linear equations
KW - mixed-precision
UR - http://www.scopus.com/inward/record.url?scp=85216970421&partnerID=8YFLogxK
U2 - 10.21656/1000-0887.450167
DO - 10.21656/1000-0887.450167
M3 - 文章
AN - SCOPUS:85216970421
SN - 1000-0887
VL - 46
SP - 40
EP - 54
JO - Applied Mathematics and Mechanics
JF - Applied Mathematics and Mechanics
IS - 1
ER -