Development of a Restricted Additive Schwarz Preconditioner for Sparse Linear Systems on NVIDIA GPU

Hui Liu, Song Yu, Zhangxin Chen, Ben Hsieh, and Lei Shao

Abstract

In this paper, we develop, study and implement a restricted additive Schwarz (RAS) preconditioner for speedup of the solution of sparse linear systems on NVIDIA Tesla GPU. A novel algorithm for constructing this preconditioner is proposed. This algorithm involves two phases. In the first phase, the construction of the RAS preconditioner is transformed to an incomplete-LU problem. In the second phase, a parallel triangular solver is developed and the incomplete-LU problem is solved by this solver. Numerical experiments show that the speedup of this preconditioner is sufficiently high.