Accelerating Preconditioned Iterative Linear Solvers on GPU

Hui Liu, Zhangxin Chen, Bo Yang
Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada
International Journal of Numerical Analysis and Modeling, Series B, Volume 5, Number 1-2, Pages 136-146, 2014


   title={Accelerating Preconditioned Iterative Linear Solvers on GPU},

   author={Liu, Hui and Chen, Zhangxin and Yang, Bo},



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Linear systems are required to solve in many scientific applications and the solution of these systems often dominates the total running time. In this paper, we introduce our work on developing parallel linear solvers and preconditioners for solving large sparse linear systems using NVIDIA GPUs. We develop a new sparse matrix-vector multiplication kernel and a sparse BLAS library for GPUs. Based on the BLAS library, several Krylov subspace linear solvers, and algebraic multi-grid (AMG) solvers and commonly used preconditioners are developed, including GMRES, CG, BICGSTAB, ORTHOMIN, classical AMG solver, polynomial preconditioner, ILU(k) and ILUT preconditioner, and domain decomposition preconditioner. Numerical experiments show that these linear solvers and preconditioners are efficient for solving the large linear systems.
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