Sains Ma1aysiana 27: 107-117 (1998)                                                                                     Pengajian Kuantitatif/

                                                                                                                                           Quantitative Studies

A New Technique Point Iterative Method for Solving Poisson

Equation on MIMD Computer System

Mohamed Othman

Department of Computer Science

Universiti Putra Malaysia

43400 UPM Serdang Selangor D.E.

e-mail: mothman@fsas.upm.edu.my

Abdul Rahman Abdullah

Department of Industrial Computing

Universiti Kebangsaan Malaysia

43600 UKM Bangi Selangor D.E.

e-mail: ara@mmscsb.po.my

ABSTRACT

This paper describes a new technique known as a quarter-sweep point iterative method applied to linear systems arising from the discretization of the two dimensional Poisson equation with Dirichlet boundary conditions. The method is shown to be very much faster as compared to the half- and full- sweep iterative methods. The numerical results of the test problem are included to confirm our recommendation.

ABSTRAK

Dalam makalah ini diterangkan satu teknik baru yang dikenali sebagai kaedah lelaran titik suku-sapuan yang digunakan pada sistem linear yang diperoleh daripada pendiskretan persamaan Poisson dua matra dengan syarat sempadan Dirichlet. Kaedah ini mempunyai masa pelaksanaan yang lebih pantas jika dibandingkan dengan kaedah lelaran separuh- dan penuh-sapuan. Keputusan berangka daripada masalah kajian disertakan untuk mengesahkan pernyataan yang telah dicadangkan.

RUJUKAN/REFERENCES

Abdullah, A.R. 1991. The Four Points Explicit Decoupled Group (EDG) Method: A Fast Poisson Solver. Intern. Journal of Computers and Mathematics 38: 61-70.

Arsmah Ibrahim, 1993. The Study of the Iterative Solution of the Boundary ValueProblems by the Finite Difference Methods. Ph.D. Thesis. Universiti Kebangsaan Malaysia.

Dahlquist, D. & Bjorck, A. 1974. Numerical Methods. New York: Prentice Hall.

Fedorenko, RP. 1961. A Relaxation Method for Solving Elliptic Difference Equations. USSR Computational Mathematics and Mathematical Physics 1(5): 922-927.

Othman, M. & Abdullah, A.R 1997. The Four Points Modified Explicit Group (MEG) Method for Solving Poisson Equation. Intern. Journal of Computer and Mathematics (submitted).

Smith, G.D. 1978. Numerical Solution of Partial Differential Equations. New York: Oxford Press.

Varga, R.S. 1984. A Survey of Recent Results on Iterative Methods for Solving Large Sparse Linear Systems. In Birkhoff, G. & Schoenstadt, A. (eds.). Elliptic Problem Solver II. London: Academic Press.

Yousif, W.S. 1984. New Block Iterative Methods for the Numerical Solution of Boundary Value Problems. Ph.D. Thesis. Loughborough University of Technology.

Yousif, W.S. & Evans, D.J. 1986. Explicit Group Over-Relaxation Methods for Solving Elliptic Partial Differential Equations. Mathematics and Computer in Simulation 28: 453-466.

Young, D.M. 1971. Iterative Solution of Large Linear System. London: Academic Press.