MEGSOR iterative method for the triangle element solution of 2D Poisson equations

In previous studies of finite difference approaches, the 4 Point-Modified Explicit Group (MEG) iterative method with or without a weighted parameter, ω, has been pointed out to be much faster as compared to the existing four point block iterative methods. The main characteristic of the MEG iterative method is to reduce computational complexity compared to the full-sweep or half-sweep methods. Due to the effectiveness of this method, the primary goal of this paper is to demonstrate the use of the 4 Point- Modified Explicit Group (MEG) iterative method together with a weighted parameter, namely 4 Point-MEGSOR. The effectiveness of this method has been shown via results of numerical experiments, which are recorded and analyzed, show that that the 4 Point-MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

[1]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[2]  Mohamed Othman,et al.  The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) Method for Diffusion Equation , 2004, CIS.

[3]  Abdul Rahman Abdullah,et al.  A Comparative Study of Parallel Strategies for the Solution of Elliptic Pde's , 1996, Parallel Algorithms Appl..

[4]  Mohamed Othman,et al.  Red-Black Half-Sweep Iterative Method Using Triangle Finite Element Approximation for 2D Poisson Equations , 2007, International Conference on Computational Science.

[5]  Norhashidah Hj. Mohd. Ali Yuzaimi Yunus,et al.  Splitting strategies for preconditioned explicit group schemes , 2006 .

[6]  Abdul Rahman Abdullah.  The four point explicit decoupled group (EDG) Method: a fast poisson solver , 1991, Int. J. Comput. Math..

[7]  David J. Evans,et al.  Explicit De-coupled Group Iterative Methods and their Parallel Implementations , 1995, Parallel Algorithms Appl..

[8]  Mohamed Othman,et al.  The halfsweeps multigrid method as a fast multigrid poisson solver , 1998, Int. J. Comput. Math..

[9]  M. Othman,et al.  An efficient multigrid poisson solver , 1999, Int. J. Comput. Math..

[10]  Seymour V. Parter.  Estimates for multigrid methods based on red-black Gauss-Seidel smoothings , 1988 .

[11]  V. Rosenberg,et al.  Methods for the Numerical Solution of Partial Differential Equations , 1969 .

[12]  Genki Yagawa,et al.  Recent developments of free mesh method , 2000 .

[13]  Tulong Zhu,et al.  A new meshless regular local boundary integral equation (MRLBIE) approach , 1999 .

[14]  David J. Evans,et al.  The explicit block relaxation method as a grid smoother in the multigrid v-cycle scheme , 1990, Int. J. Comput. Math..

[15]  D. J. Evans,et al.  Fast group explicit algorithms for diffusion problems , 1989 .

[16]  P. E. Lewis,et al.  The Finite Element Method: Principles and Applications , 1991 .

[17]  J. Chandra,et al.  Adaptive Computational Methods for Partial Differential Equations , 1984 .

[18]  M. Othman,et al.  An efficient four points modified explicit group poisson solver , 2000, Int. J. Comput. Math..

[19]  Mohamed Othman,et al.  Red-Black EDG SOR Iterative Method Using Triangle Element Approximation for 2D Poisson Equations , 2007, ICCSA.

[20]  E. H. Twizell.  Computational methods for partial differential equations , 1984 .

[21]  C. Fletcher.  Computational Galerkin Methods , 1983 .

[22]  Azzam Ibrahim,et al.  Solving the two dimensional diffusion equation by the four point explicit decoupled group (edg) iterative method , 1995, Int. J. Comput. Math..

[23]  Jun Zhang.  Acceleration of five-point red-black Gauss-Seidel in multigrid for Poisson equation , 1996 .

[24]  Mohamed Othman,et al.  Quarter-sweep iterative alternating decomposition explicit algorithm applied to diffusion equations , 2004, Int. J. Comput. Math..