Relaxed Jacobi method as multigrid smoother and preconditioner.

The solution of the Poisson equation raised from large-scale problems requires iterative techniques. Multilevel and Krylov subspace methods have been proven to be the most efficient among various iterative methods. Recently, the scheduled relaxation Jacobi technique has been developed, which can be used as a stand-alone iterative solver as well as a preconditioner to the Krylov subspace methods. The relaxed Jacobi (RJ) method has also been implemented as a smoother in the multigrid method, with no-post smoothening. Here, the focus is to test the performance of relaxed Jacobi when applied to the large scale Poisson problems. Multigrid methods with both post-smoothening and pre-smoothening operations have been conducted in this paper. The methodology is applied to a rectangular domain using structured Cartesian grids. Also, multigrid methods with relaxed Jacobi smoothers are used as preconditioners to Krylov subspace solvers, and their performances are compared with the red-black Gauss-Seidel smoothers. Similar to the results in the literature, RJ smoothers to multigrid techniques provide better results than Gauss-Seidel smoothers when no-post smoothening operations are carried out. However, the use of post-smoothening operations changed the entire dynamic of the RJ smoothers. [ABSTRACT FROM AUTHOR]