ABSTRACT
SOR method reduces to the Gauss-Seidel method. The maximum rate of convergence is achieved for some optimum value of w, denoted by WOPI , which lies between 1.0 and 2.0.
In some special cases, the optimum over-relaxation factor W Opl can be predicted theoretically. For a rectangular region with Dirichlet boundary conditions (i.e., specified values of the dependent variable), wopro can be estimated from [Frankel (1950)]:
where
where 1= (imax - 1) is the number of spatial increments in the x direction, J = (jmax - 1) is the number of spatial increments in the y direction, and f3 = !'U/!1y is the grid aspect ratio. Values of W Opl for the 10 cm by 15 cm physical space considered in the heat diffusion problem are presented in Table 9.5 for several grid sizes.
