An Adaptive Preconditioner Matrix on N-P Group AOR Iterative Poisson Solver

Abstract

Hadjidimos [1], proved that the Accelerated OverRelaxation (AOR) is more powerful compared with the other well-known method called the Successive OverRelaxation (SOR) for solving linear systems of equations. The formulation of group iterative schemes for approximating the solution of the two dimensional elliptic partial differential equations have been the subject of intensive study during the last few years. The recent convergence results of nine-point (N-P) group iterative schemes from the Successive OverRelaxation (SOR) family have been presented by Saeed [2]. In this paper, we extend the work of Saeed [2] with the new application of suitable preconditioning techniques to the N-P Group iterative schemes from the Accelerated OverRelaxation (AOR) for solving Poisson’s Equation. The results reveal the significant improvement in number of iterations and execution timings of the proposed preconditioned Group iterative method compared to Preconditioned N-P SOR.