A Parallel four points modified explicit group algorithm on shared memory multiprocessors

Abstract

The four points modified explicit group (MEG) method for solving 2D Poisson equation was introduced by Othman and Abdullah [“An efficient Four Points Modified Explicit Group Poisson Solver”, Int. J. Comput. Math., 76 (2000) 203–217], which was shown to be superior to the four points-explicit decoupled group (EDG) and explicit group (EG) methods due to Abdullah [“The Four Explicit Decoupled Group (EDG) Method: A Fast Poisson Solver”, Int. J. Comput. Math., 38 (1991) 60–70] and Evans and Biggins [“The solution of elliptic partial differential equations by A New Block Over-Relaxation Technique”, Int. J. Comput. Math., 10 (1982) 269–282], respectively. These methods were found to be suitable for parallel implementation [see Evans, D.J. and Yousif, W.S. “The implementation of the Explicit Block Iterative Methods on the balance 8000 parallel computer”, Parallel Computing, 16 (1990) 81–97; Yousif, W.S. and Evans, D.J. “Explicit De-coupled Group Iterative Methods and their parallel implementations”, Parallel Algorithms and Applications, 7 (1995) 53–71]. In this paper, the implementation of the parallel four points MEG algorithm with the red black and four colors ordering strategies for solving the same equation on shared memory multiprocessors are presented. The experiment results of the test problem are included and compared with the parallel four points- EG and EDG algorithms.