Hybrid Multi-elimination ILU Preconditioners on GPUs

Abstract

Iterative solvers for sparse linear systems often benefit from using preconditioners. While there exist implementations for many iterative methods that leverage the computing power of accelerators, porting the latest developments in preconditioners to accelerators has been challenging. In this paper we develop a selfadaptive multi-elimination preconditioner for graphics processing units (GPUs). The preconditioner is based on a multi-level incomplete LU factorization and uses a direct dense solver for the bottom-level system. For test matrices from the University of Florida matrix collection, we investigate the influence of handling the triangular solvers in the distinct iteration steps in either single or double precision arithmetic. Integrated into a Conjugate Gradient method, we show that our multi-elimination algorithm is highly competitive against popular preconditioners, including multi-colored symmetric Gauss-Seidel relaxation preconditioners, and (multi-colored symmetric) ILU for numerous problems.