A COMPARATIVE STUDY OF EXPLICIT GROUP ITERATIVE SOLVERS ON A CLUSTER OF WORKSTATIONS.

In this paper, a group iterative scheme based on rotated (cross) live-point unite difference discretisation, i.e. the four-point explicit decoupled group (EDG) is considered in solving a second order elliptic partial differential equation (PDE). This method was firstly introduced by Abdullah ["The four point EDO method: a fast poisson solver", Int. J. Comput. Math., 38 (1991) 61-70], where the method was found to be more superior than the common existing methods based on the standard live-point unite difference discretisation, The method was further extended to different type of PEW's, where similar improved results were established [Ali N.H.M., Abdullah, A.R. Four Point EDG: A Fast Solver For The Navier-Stokes Equation, M.H.Hamza (ed.) Proceedings of the IASTED International Conference on Modelling Simulation And Optimization, Gold Coast, Australia, May 6-9(1996) (CD Rom-File 242-165.pdf), ISBN: 0-88986-197-8; Ali, N,H.M., Abdullah, A.R. New Parallel Point iterative Solutions For the Diffusion-Convection Equation Proceedings of the International Conference on Parallel and Distributed Computing and Networks Singapore, Aug. 11-13 (1997) 136-139; Ali, N.H.M., Abdullah, AR. "New rotated iterative algorithms for the solution of a coupled system of elliptic equations" Int. J. Comput. Math. 74 (1999) 223-251). These new iterative algorithms had been developed to run on the Sequent Balance, a shared memory parallel computer [A.R. Abdullah, N.M. Ali, The Comparative Study of Parallel Strategies For The Solution of Elliptic PDE's Parallel Algorithms and Applications Vol. 10 (1996) 93-103; Ali, N.H.M., Abdullah, A.R. "Parallel four point explicit decoupled group (EDG) method for elliptic PDE' s" Proceedings of the Seventh IASTED/ISMM international Conference on Parallel and Distributed Computing and Systems (1995) 302-304 (Washington DC); Ali. N.H.M., Abdullah, A.R. New Parallel Point Iterative Solutions For the Diffusion-Convection Equation Proceedings of the International Conference on Parallel and Distributed Computing and Networks, Singapore. Aug. 11-13 (1997) 136-139: Yousif, W.S., Evans, D.J. "Explicit decoupled group iterative methods and their parallel implementations" Parallel Algorithms and Applications 7 (1995) 53-71] where they were shown to be suitable to be implemented in parallel. In this work, the four-point group algorithm was ported to run on a cluster of Sun workstations using a parallel virtual machine (PVM) programming environment together with the four-point explicit group EG method [Evans. D.J., Yousif. W.S. "The implementation of the explicit block iterative methods on the balance 8000 parallel computer" Parallel Computing 16 (1990) 81 -97]. We describe the parallel implementations of these methods in solving the Poisson equation and the results of some computational experiments are compared and reported. [ABSTRACT FROM AUTHOR]