Abstract: Algebraic multi-grid (AMG) is one of the most commonly used algorithms for solving large-scale sparse linear algebra equations in the field of scientific engineering computing and industrial simulation. For each grid layer in the Setup phase, AMG needs to calculate the coarse grid matrix Ac=RAP  through the product of three sparse matrix based on the restriction operator R, the current fine grid matrix A, and the interpolation operator P, which has become the main bottleneck in the parallel performance of AMG. This paper first discovers that the performance bottleneck of the RAP parallel algorithm in mainstream AMG solvers is caused by the quadratic complexity of branch judgments. Then,  utilize the row-based order characteristics of the sparse matrix format CSR, and propose a RAP parallel algorithm called MiniBranRAP with linear complexity of branch judgment counts. The algorithm is integrated into the JXPAMG solver, and the effectiveness of the algorithm is verified through practical examples. The numerical test results show that, for 6 typical examples from practical applications, compared with the latest version of Hypre's BoomerAMG solver, the JXPAMG solver based on MiniBranRAP can speed up the computation efficiency of the Setup phase by an average of 3.3 times and a maximum of 9.3 times on 28 processors. 

Key words: algebraic multi-grid (AMG), coarse grid matrix computation, branch, Hypre, JXPAMG