Performance Analysis of the Modified Group AOR Algorithms in Elliptic PDEs

In a recent work, the Modified Explicit Decoupled Group (MEDG) method [3, 4] was formulated as an addition to the 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 (sqrt(2))h grid stencil together with the five-point centred difference approximation on the h and 2h grid stencils. This new group method was shown to have a better convergence rate than the previous group methods from the same family. In this paper, we formulate the MEDG group scheme in combination with the Accelerated Over Relaxation (AOR) method. Numerical experimentations of this new modified AOR group method will show significant improvement in computational complexity and execution timings compared to the group AOR formulation presented in [1].