Sains Ma1aysiana 28: 161-172 (1999)                                                                                          Pengajian Kuantitatif/

                                                                                                                                                                Quantitative Studies

Beberapa Kaedah Lelaran Kumpulan Tak Tersirat

Nyah-Pasangan dengan Separuh Sapuan

Multigrid bagi Persamaan Poisson

(Some explicit decoupled group iterative methods with

half sweeps multigrid for the Poisson equation)

Jumaat Bin Sulaiman

Matematik, Sekolah Sains & Teknologi

Universiti Malaysia Sabah, Beg Berkunci 2073

88999 Kota Kinabalu, Sabah.

Abd. Rahman Bin Abdullah

Jabatan Komputeran Industri, Fakulti Teknologi & Sains Maklumat

Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor D.E. Malaysia

ABSTRACT

This paper presents the implementation of some Explicit Decoupled Group (EDG) iterative method with half sweeps multigrid to solve the two dimensional Poisson equation. The concept of half sweeps multigrid was investigated by Mohamed Othman and Abdul Rahman Abdullah. The results from the EDG iterative methods with half sweeps multigrid will be compared with the results of the Gauss-Siedel and four Point Explicit Group (EG) iterative method with fullsweeps multigrid.

ABSTRAK

Dalam makalah ini dibincangkan pelaksanaan beberapa skema kaedah lelaran Kumpulan Tak Tersirat Nyah-Pasangan (KTTNP) dengan mutigrid separuh sapuan dilaksanakan bagi menyelesaikan persamaan Poisson dua matra. Konsep multigrid separuh sapuan telah dikaji oleh Mohamed Othman dan Abdul Rahman Abdullah. Keputusan-keputusan yang diperoleh daripada kaedah lelaran KTTNP dengan multigrid separuh sapuan dibandingkan dengan kaedah lelaran Gauss-Siedel dan empat Titik Kumpulan Tak Tersirat dengan multigrid sapuan penuh.

RUJUKAN/REFERENCES

Abdul Rahman Abdullah. 1991. The Four Point Explicit Decoupled Group (EDG) Method. A fast Poisson Solver. Int. J. Computer Math. 38: 61-70.

Briggs, W.L. 1987. A Multigrid Tutorial. Pennsylvania: Lancaster Press. Evans, D.J. & Yousif, W.S., 1990. The Explicit Block Relaxation Method As A Grid Smoother In The Multigrid V -Cycle Scheme. Int. J. Computer Math. 34: 71-75.

Hackbusch, W. 1980. Multi-Grid and Applications. Springer Series in Computational Mathematics, 4. Berlin: Springer-Verlag.

Jumat Sulaiman. 1998. Kajian Pelaksanaan Kaedah Multigrid Bagi Persamaan Poisson dan Resapan-Olakan. Tesis Sarjana Teknologj Maklumat. Universiti Kebangsaan Malaysia.

Mohamed Othman & Abdul Rahman Abdullah. 1998. The Halfsweeps Multigrid Method As A Fast Multigrid Poisson Solver. Diterima untuk diterbitkan di Int. J. Computer Math. 69: 12.

Yousif, W.S. & Evans, D.J. 1995. Explicit De-Coupled Group Iterative Methods and Their Parallel Implementations. Parallel Algoritms and Applications 7: 53-71.