A New Iterative Eliiptic PDE Solver on a Distributed PC Cluster

Abstract

Advancement in parallel computers technology has greatly influenced the numerical methods used for solving partial differential equations (pdes). A lot of attention has been devoted to the development of numerical schemes which are suitable for the parallel environment. In this work, we investigate the parallel implementation of the four-point Modified Explicit Decoupled Group (MEDG) method which was introduced by Ali and Ng (2007) as a fast solver for the two dimensional Poisson pde. The method was shown to be more superior than all the methods belonging to the four-points explicit group family namely the Explicit Group (EG) [8], Explicit Decoupled Group (EDG) [1] and Modified Explicit Group (MEG) [7]. This paper presents the preliminary results of the parallel algorithms implemented on a distributed memory PC cluster. Two parallelizing strategies comprising of the two-color zebra and the four-color chessboard orderings in solving a two dimensional Poisson model problem will be discussed.