Development of Krylov and AMG Linear Solvers for Large-Scale Sparse Matrices on GPUs

摘要

This paper introduces our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for a single GPU and multiple GPUs are implemented. A HEC matrix format and a communication mechanism are established. Also, a set of specific algorithms for solving preconditioned systems in parallel environments are designed, including ILU(k), RAS and parallel triangular solvers. Based on these work, several Krylov solvers and AMG solvers are developed. According to numerical experiments, favorable acceleration performance is obtained from our Krylov solver and AMG solver under various parameter conditions.