A review for parallel optimization techniques of solving ultra-large-scale sparse linear equations

As a critical computation in numerical simulation applications such as large-scale scientific computing and industrial simulation, the solving rate of sparse linear equations directly determines the execution efficiency of computing tasks. However, sparse matrix computations are characterized by low computational intensity and high memory occupation, which results in performance bottlenecks in solving sparse linear equations. Many studies employ parallel optimization techniques to enhance the efficiency of solving sparse linear equations, but they all encounter many challenges such as low storage efficiency, load imbalance, and discontinuous memory access. Therefore, this paper first analyzes the challenges in improving the efficiency of solving sparse linear equations. Then the parallel optimization methods to improve the efficiency of solving ultra-large-scale sparse linear equations are sorted out from four key aspects, including: optimization for the sparse matrix storage format, optimization for solving ultra-large-scale sparse linear equations, optimization for the basic operator of sparse matrix computation and mainstream sparse linear solver. Finally, this work concludes with a summary and a discussion of the directions that parallel optimization research in the future will go in solving ultra-large-scale sparse linear equations.