Theorem The successive overrelaxation method with optimum relaxation factor converges at least twice as fast as the Chebyshev semi-iterative method with respect to the Jacobi method, and therefore at least twice as fast as any semi-iterative method with respect to the Jacobi method. Furthermore, as the number of iterations tends to infinity, the successive overrelaxation method becomes exactly twice as fast as the Chebyshev semi-iterative method. [Pg.179]

A comparison of the successive overrelaxation method and semi-iterative [Pg.188]

Both point-by-point and line-by-line overrelaxation methods were used to resolve the algebraic equations. ° An overrelaxation parameter of 1.5-1.8 was typically used. The two methods required similar computational times. An upwind scheme was used for all variables for high-Pe problems, while a central-difference scheme was used for low Pe. For some high-Pe cases, a central-difference scheme was used for the potential, but no appreciable differences in the results were observed. [Pg.379]

Figure 6 Error reduction rate of the successive overrelaxation method. The smaller slope of the curve for small values of the relative error indicates the poor performance of solvers based on this method. |

In terms of actual arithmetic operations, the direct inversion of large submatrices combined with an iterative method tends to increase the amount of arithmetic operations per mesh point. This is, of course, to be balanced by an increase in the rate of convergence. In the case of the iterative method SLOR, either in two or three space dimensions, it fortunately can be shown [6] by suitable normalization of equations, that no additional arithmetic operations are required for the successive line overrelaxation method (SLOR) over what is required by the successive point overrelaxation method, while an improvement in rate of convergence is always obtained. [Pg.176]

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