DescriptionThe smoothed aggregation algebraic multigrid (SA-AMG) method is among the fastest solvers for large-scale linear equations, Ax=b. The SA-AMG method achieves good convergence and scalability by damping various wavelength components efficiently. To achieve this damping, this method creates multi-level matrices which are hierarchically smaller in dimension than the original matrix. Moreover, the convergence can be further improved by setting near-kernel vectors p, which satisfy Ap≈0 and p≠0. Generally, the same number of near-kernel vectors are used at each level. In the present work, we propose a method that extracts and adds near-kernel vectors at each level. We evaluate the performance of the solver that extracts the near-kernel vectors and adds them at each level. We use the three-dimensional elastic problem and employ up to 512 processes on the FX10 supercomputer system. By using this method, the performance is improved compared with previous work.