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

  • Abdulkafi Mohammed Saeed Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Keywords: Preconditioning Techniques, Nine-Point Group Iterative Method, AOR

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.

Author Biography

Abdulkafi Mohammed Saeed, Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Assistant ProfessorDepartment of Mathematics

References

Hadjidimos, A. (1978). Accelerated overrelaxation method. Mathematics of Computation 32, 149-157.

Saeed, A. M. (2016). Solving Poisson’s Equation Using Preconditioned Nine-Point Group SOR Iterative Method. International Journal of Mathematics and Statistics Invention (IJMSI) 4 (8), 20-26.

Ali, N. H. M. & Saeed A. M. (2013). Preconditioned Modified Explicit Decoupled Group for the Solution of Steady State Navier-Stokes Equation. Applied Mathematics & Information Sciences.7 (5), 1837-1844.

Saeed A. M. and Ali, N. H. M. (2014). Accelerated Solution of Two Dimensional Diffusion Equation, World Applied Sciences Journal 32 (9), 1906-1912.

Saeed A. M. (2014). Fast Iterative Solver For The 2-D Convection Diffusion Equations. Journal of Advances In Mathematics 9 (6), 2773-2782.

Martins M. M, Evans D. J, Yousif W. (2001) Further results on the preconditioned SOR method, International Journal of Computer Mathematics, 77(4), 603-610.

Ali, N. H. M. & Saeed A. M.(2012). Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value ‎Problems, Abstract and Applied Analysis, 2012, 1-14.

Published
2016-12-01
How to Cite
Saeed, A. (2016). An Adaptive Preconditioner Matrix on N-P Group AOR Iterative Poisson Solver. Journal of Progressive Research in Mathematics, 10(1), 1448-1453. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/952
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Articles