Analysis of hierarchical SSOR for three dimensional isotropic model problem

Abstract

In this paper, we study a hierarchical SSOR (HSSOR) method which could be used as a standalone method or as a smoother for a two-grid method. It is found that the method leads to faster convergence compared to more costly incomplete LU (ILU(0)) with no fill-in, the SSOR, and the Block SSOR method. Moreover, for a two-grid method, numerical experiments suggests that HSSOR can be a better replacement for SSOR smoother both having no storage requirements and have no construction costs. Using Fourier analysis, ex- pressions for the eigenvalues and the condition number of HSSOR preconditioned problem is derived for the three-dimensional isotropic model problem.