Sains Malaysiana 42(6)(2013): 837–844

Investigation of Steady State Problems via Quarter Sweep Schemes

(Kajian Terhadap Masalah Berkeadaan Mantap Menggunakan Skema Sapuan Suku)

Ng Yit Hoe* & Mohammad Khatim Hasan

School of Information Technology, Faculty of Information Science and Technology

Universiti Kebangsaan Malaysia, 43650 Bangi, Selangor D.E. Malaysia

Diserahkan: 19 Julai 2012/Diterima: 14 November 2012

ABSTRACT

Numerical application helps researchers in simulating various problems and used for solving partial differential equation. Half sweep and quarter sweep approach have been applied onto iterative method to gain approximation solution. In this paper, the implementation of full sweep successive over relaxation (FSSOR), half sweep successive over relaxation (HSSOR) and quarter sweep successive over relaxation (QSSOR) methods and full sweep accelerated over relaxation (FSAOR), half sweep accelerated over relaxation (HSAOR) and quarter sweep accelerated over relaxation (QSAOR) for its numerical engines are shown. QSSOR and QSAOR method was the fastest among FSSOR, HSSOR, FSAOR and HSAOR methods. Additionally, QSAOR performance is more accurate than QSSOR.

Keywords: Elliptic problem; iterative scheme; numerical simulation; Poisson; quarter sweep approach

ABSTRAK

Aplikasi berangka membantu penyelidik dalam mensimulasikan pelbagai masalah dan digunakan untuk menyelesaikan persamaan terbitan separa. Pendekatan sapuan separuh dan sapuan suku telah digunakan ke atas kaedah lelaran untuk mendapatkan penyelesaian penghampiran. Dalam kertas ini, implementasi kaedah-kaedah pengenduran berlebihan berturut-turut sapuan penuh (FSSOR), pengenduran berlebihan berturut-turut sapuan separuh (HSSOR) dan pengenduran berlebihan berturut-turut sapuan suku (QSSOR) dan pemecutan berlebihan berturut-turut sapuan penuh (FSAOR), pemecutan berlebihan berturut-turut sapuan separuh (HSAOR) dan pemecutan berlebihan berturut-turut sapuan suku (QSAOR) untuk enjin berangka ditunjukkan. Kaedah QSSOR dan QSAOR adalah terpantas dalam kalangan kaedah-kaedah FSSOR, HSSOR, FSAOR dan HSAOR. Di samping itu, prestasi QSAOR adalah lebih tepat daripada QSSOR.

Kata kunci: Masalah eliptik; pendekatan sapuan suku; poisson; simulasi berangka; skim lelaran

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*Pengarang untuk surat-menyurat; email: fido_ng87@yahoo.com