Preconditioned Modified Explicit Decoupled Group Method in the Solution of Elliptic PDEs
Abdulkafi Mohammed Saeed, Norhashidah Hj, Norhashidah Hj. Mohd. Ali · 2010
Many physical phenomena in static field problems particularly in the electromagnetic field and the incompressible potential flow field are described by elliptic partial differential equations (pdes). Improved techniques using explicit group methods derived from the standard and skewed (rotated) finite difference operators have been developed over the last few years in solving the linear systems that arise from the discretization of these elliptic pdes (Ali et al., 2004; Evans and Yousif, 1990; Othman and Abdullah, 2000; Yousif and Evans, 1995). The convergence rates of these iterative methods depend on the spectral properties of the coefficient matrices resulted from these group discretization formulas. The formulation of suitable preconditioners which can improve the convergence rates of these iterative schemes are crucial to the development of these new group methods. This paper is concerned with the application of suitable preconditioning technique to a recently developed scheme, the Modified Explicit Decoupled Group (MEDG) iterative method due to Ali and Ng (2008), for solving the two dimensional elliptic pdes. Numerical experiments are conducted on each developed non-preconditioned and preconditioned schemes for comparison purposes. The results show the improvements in the convergence rate and the efficiency of the newly formulated preconditioned iterative scheme.