Abstract: Large sparse linear equations often appear in scientific computation and engineering.There are many iterative methods and preconditioning techniques for solving these linear equations.Diagonal-based incomplete LU (DILU) is a preconditioning technique similar to incomplete LU (ILU) factorization.DILU is applied in OpenFOAM,an open source computational fluid dynamics software,and is a very important preconditioning technique in OpenFOAM.DILU has not received extensive attention outside OpenFOAM,and there is no complete GPU-based implementation so far.This paper compares DILU preconditioned BiCGStab with ILU preconditioned BiCGStab,and the time elapses in preconditioner constructions.The numeric experiments suggest that DILU may be more efficient and stable than ILU.As for GPU-based parallel implementations,this paper discusses two parallel schemes,that are level-set scheme and synchronization-free scheme,and gives related algorithms and some codes under these two parallel schemes.It compares the performances of DILU preconditioning technique under two parallel schemes.The numeric results show that each scheme has its own advantages and disadvantages in different equations,and we can select one according to their performances in practice.This paper compares the performance of DILU preconditioning on GPU and CPU,and the results show that GPU is more competitive.The applications that have performance bottlenecks on linear systems solutions can be improved by moving to GPU platforms.

Key words: CUDA, DILU, GPU, Iterative methods, Open FOAM, Preconditioning, Sparse triangular equations