Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods

Abstract

In this paper, we propose a multiplicative Schwartz-type block multi-color Gauss-Seidel (MS-BMC-GS) smoother for algebraic multigrid (AMG) methods. AMG is an excellent solver and one of the most effective preconditioners for Krylov subspace methods such as the conjugate gradient method. The achievable degree of parallelism, convergence ratio, and computational cost of AMG strongly depend on the chosen smoother. As multiple unknowns are relaxed simultaneously, the MS-BMC-GS smoother realizes higher convergence than the existing parallel Gauss-Seidel smoother. Although this increases the amount of computation, the increase in the computational time is mitigated by the high cache hit ratio owing to the novel blocking technique. Numerical experiments demonstrate that MS-BMC-GS outperforms the block multi-color GS smoother by 18%.