面向流体力学仿真的大型稀疏矩阵混合精度 GMRES 加速算法

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.