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


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.