Parallel optimization and application of unstructured sparse triangular solver on new generation of Sunway architecture

Abstract

Large-scale sparse linear equation solver plays an important role in both numerical simulation and artificial intelligence, and sparse triangular equation solver is a key step in solving sparse linear equation systems. Its parallel optimization can effectively improve the efficiency of solving sparse linear equation systems. In this paper, we design and implement a parallel algorithm for solving sparse triangular equations in combination with the features of the new generation of Sunway architecture, and optimize the access and communication respectively for 949 real equations and 32 complex equations in the SuiteSparse collection. The solution efficiency of the algorithm presented in this paper outperforms the cuSparse algorithm on NVIDIA V100 GPU platforms in more than 71% of the cases, and the speedup is even better in solving larger cases (matrix size greater than 10,000): our method increases the speedup from 1.29 time of the previous version to an average speedup of 5.54 and the best speedup of 32.18 over the sequential method on the next generation of Sunway architecture when using 64 slave cores.