A novel ILU preconditioning method with a block structure suitable for SIMD vectorization

Abstract

Incomplete LU (ILU) preconditioning is typically used when an iterative solver is applied on an asymmetric system of linear equations. A fill-in selection policy significantly affects the ILU preconditioned iterative solver. In this study, by introducing a new fill-in control method based on blocks into ILU preconditioning, we propose a new ILU preconditioning method called ILUB preconditioning. In this method, the effect of the permitted fill-ins on the solver convergence is fully exploited because the resulting preconditioner matrix involves dense matrix blocks that can be processed efficiently using SIMD instructions. We implemented sequential and parallel ILUB preconditioned GMRES solvers and evaluated the solver performance in numerical tests. The numerical results demonstrated that ILUB preconditioning outperformed conventional ILU(0) preconditioning.