A GMRES Solver with ILU(k) Preconditioner for Large-Scale Sparse Linear Systems on Multiple GPUs

Abstract

Most time of reservoir simulation is spent on the solution of large-scale sparse linear systems. The Krylov subspace solvers and the ILU preconditioners are the most commonly used methods for solving such systems. Based on excellent parallel computing performance, GPUs have been a promising hardware architecture. The work of developing preconditioned Krylov solvers on GPUs is necessary and challengeable. We devote our efforts into the development of the GMRES and the ILU(k) preconditioner on a multiple-GPU architecture and achieve favorable speedup effects. Our GPU computation includes the algorithms such as SPMV, nested RAS, decoupled ILU(k) and parallel triangular solver, etc. The numerical experiments prove that our preconditioned GMRES algorithm is feasible and works well on a multiple-GPU workstation.