Scheduled relaxation Jacobi method as preconditioner of Krylov subspace techniques for large-scale Poisson problems

Abstract

This article presents an assessment of the scheduled relaxation Jacobi (SRJ) method for the solution of large-scale Poisson problems arising in the numerical simulation of large eddy turbulent flow in large complex geometry. The SRJ schemes are used both as standalone solvers and as preconditioners to Krylov subspace solvers. The Navier-Stokes equation is solved using structured Cartesian grids (both uniform as well as nonuniform grids). Geometrical complexities are handled using the immersed boundary method (IBM) method. The performance of SRJ schemes as a standalone solver is first validated with the help of a rectangular channel flow problem whose exact solution is known. Numerical experiments are performed to evaluate the performance of SRJ schemes as preconditioners to two robust and efficient Krylov subspace solvers (PCG and BiCGSTAB), and compared with different preconditioners such as Jacobi (diagonal preconditioner), SOR(k) and multigrid preconditioners. SRJ schemes as standalone solver perform quite similarly as predicted before in literature. However, as preconditioner particularly some SRJ schemes work best among the rest for three-dimensional problems.