Performance comparison of parallel ILU preconditioners for the incompressible Navier-Stokes equations

In this paper, the performances of various ILU type parallel preconditioners for the finite element discretization of the incompressible Naiver-Stokes equations have been investigated. The solution algorithm of the incompressible Navier-Stokes equation is based on a fractional 4-step method combined with P1P1 finite element and the parallel preconditioners have been implemented by using the domain decomposition method and MPI library. The performances have been measured for momentum and pressure equation, respectively. The speedup of the pressure equation is found to be less than that of the momentum equation because the pressure equation requires a larger communication overhead by a larger iteration numbers of an iterative solver while element-matrix generation and assemble process is nearly scalable for both equations. The performance of the parallel preconditioners are dependent on time-step size, the Reynolds number and the number of the domains. Although BIWO (block ILU without overlapping) works well both for momentum and pressure equation, MDLU (modified distributed ILU(O)) is recommended for an ill-conditioned matrix or a large number of subdomains. Further, we have conducted the time complexity and spectral analysis of the preconditioned matrices to analyze the performance of the preconditioners.