A supplementary strategy for coarsening in algebraic multigrid

Abstract

Algebraic multigrid (AMG) is an efficient iterative method for solving linear equation systems arising from the elliptic partial differential equations. The coarsening algorithm, which determines the coarse-variable set in the classical AMG, is a critical component. This paper targets at reducing the overall solution time of the classical AMG by improving the quality of the coarse-variable set obtained by the coarsening algorithm. We combine the classical coarsening algorithm with the compatible relaxation (CR)-based coarsening algorithm to construct the coarse-variable set. The combined coarsening algorithm constructs the coarse-variable set within two stages. In the first stage, a basic coarse-variable set is built by the classical coarsening algorithm, e.g., PMIS. In the second stage, the quality of the set is measured based on compatible relaxation, and the variables that converge slowly in the CR relaxation are added into the previous set. We test various model problems, as well as some linear equation systems arising from real applications, to verify the effectiveness of our method.