A Parallel Successive Overrelaxation method for solving the Convection Diffusion equation ¹

A. A. Consta, N. M. Missirlis² and F. I. Tzaferis
Department of Informatics and Telecommunications,
University of Athens
Panepistimioupolis, 15784 Athens, GREECE

Abstract:

In this paper we introduce the local Modified Extrapolated Successive Overrelaxation (LMESOR) method. This method is suitable for parallel implementation since each node in the mesh has its own parameter, thus avoiding global communication. The related theory of convergence is developed. Optimum values for the involved parameters of the LMESOR method are obtained in case the eigenvalues of the Jacobi iteration matrix are imaginary. It is proved that the more $\underline{\mu}$ approaches to $\overline{\mu}$, the faster the convergence of LMESOR, where $\underline{\mu}, \overline{\mu}$ are the smallest and largest in absolute value eigenvalues of the iteration operator of the Jacobi method. Numerical results verify our theory.

Subject classification : AMS(MOS), 65F10.
Keywords : Iterative methods , linear systems, semi-iterative methods, Fourier analysis, Successive Overrelaxation method, convection diffusion equation.