Modified Explicit Group AOR Methods in the Solution of Elliptic Equations
Norhashidah Hj, Norhashidah Hj. Mohd. Ali, Foo Kai Pin · 2012
The recent convergence results of faster group iterative schemes from the Accelerated OverRelaxation (AOR) family has initiated considerable interest in exploring theehavior of these methods in the solution of partial differential equations (pdes). Martins et al. (2002) formulated the Explicit Group (EG) (AOR) which was shown to have greater rate of convergence than the standard five-point AOR method in solving the elliptic equation. In 2007, the Explicit Decoupled Accelerated OverRelaxation (EDG(AOR)) method was developed in solving the same partial differential equations, where lesser execution timings and fewer iteration counts were required when compared with the original EG(AOR) method (4). In a recent work, another explicit group method was proposed, namely the Modified Explicit Decoupled Group (MEDG) method (2, 3) as an addition to this family of four-point explicit group methods in solving the Poisson equation. The method was formulated using a combination of the rotated five-point finite difference approximation on the 2h Ω grid together with the five-point centred difference approximation on the h Ω and 2h Ω grids and was shown to have a better rate of convergence than the original EDG method. In this paper, we formulate the Modified EDG group scheme in juxtaposition with the AOR method to investigate its performance compared with the earlier group iterative