The performance of ILU (0), SPAI, and AINV as smoothers in an algebraic multigrid solver -

Abstract

Incomplete LU decomposition with no fill-in ILU (0) has been used as a standard smoother with algebraic multigrid solvers in many applications. With recent developments new techniques have emerged following the sparse approximate inverse approach. Methods like Sparse Approximate inverse (SPAI) and AINV have been implemented as preconditioners but rarely as smoothers. In this work, the ILU (0), SPAI and AINV will be implemented as smoothers in both scalar and block versions within an algebraic multigrid solver. A comparative assessment of the performance of these techniques as smoothers in an algebraic multigrid solver will be performed in the context of a finite volume discretization method. The smoothers are implemented in uFVM, an in-house MATLAB® based CFD code, then in an open source CFD toolbox OpenFOAM®. The results of SPAI in uFVM show how it is computationally expensive and not robust, thus it was not considered in OpenFOAM®. Using OpenFOAM®, two turbulent fluid flow test cases with high aspect ratio are used to compare the smoothers. Residual convergence rates, number of iterations as well as CPU time are used to evaluate the performance. For segregated flow solver, AINV and ILU (0) show robustness having same convergence rate, number of iterations and CPU time with slight difference; however, ILU (0) outperforms AINV in every aspect for coupled flow solver.