Author
Abdul Rahman Abdullah
Bio: Abdul Rahman Abdullah is an academic researcher from National University of Malaysia. The author has contributed to research in topics: Iterative method & Poisson's equation. The author has an hindex of 8, co-authored 24 publications receiving 556 citations.
Papers
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TL;DR: This paper introduces a four point explicit decoupled group (EDG) iterative method as a new Poisson solver and is shown to be very much faster compared to existing explicit group (EG) methods.
Abstract: The aim of this paper is to introduce a four point explicit decoupled group (EDG) iterative method as a new Poisson solver. The method is shown to be very much faster compared to existing explicit group (EG) methods due to D. J. Evans and M. J. Biggins (1982) and W. Yousif and D. J. Evans (1985). Some numerical experiments are included to confirm our recommendation.
209 citations
TL;DR: A four points modified explicit group method for solving a two dimensional Poisson equation with Dirichlet boundary condition is introduced and is shown to be superior compared to the existing four points–explicit group and explicit decoupled group methods.
Abstract: In this paper, wc introduce a four points modified explicit group method for solving a two dimensional Poisson equation with Dirichlet boundary condition. The method is shown to be superior compared to the existing four points–explicit group and explicit decoupled group methods due to D. J. Evans and M. J. Biggins (1982) and A. R. Abdullah (1991), respectively, Some experiment results of the test problem are given in order to confirm our claim.
118 citations
TL;DR: The rotated four-point explicit decoupled group (EDG) iterative method for solving two dimensional parabolic PDE is introduced and its performance is compared with some methods of natural ordering.
Abstract: In this paper, the rotated four-point explicit decoupled group (EDG) iterative method for solving two dimensional parabolic PDE is introduced. Its performance is compared with some methods of natural ordering.
77 citations
TL;DR: The computational implementation of the strategies to both EDG and EG methods for solving elliptic p.d.e.'s on a MIMD Sequent Balance 8000 parallel computer are presented and discussed.
Abstract: The four point explicit decoupled group (EDG) iterative method (A. R. Abdullah, 1991) and the explicit group (EG) method (D. J. Evans and M. J. Biggins, 1982; W. Yousif and D. J. Evans, 1986) were introduced as alternative numerical methods for the solution of elliptic p.d.e.'s. These methods were found to be suitable for parallel implementation (N. M. Ali and A. R. Abdullah, 1995; D. J. Evans and W. S. Yousif, 1990). In this paper, several parallel strategies for implementation on both EDG and EG methods for solving elliptic p.d.e.'s were introduced. The computational implementation of the strategies to both EDG and EG methods for solving elliptic p.d.e.'s on a MIMD Sequent Balance 8000 parallel computer are presented and discussed.
40 citations
TL;DR: The idea of halfsweeps iterative method is used to develop the halfsweep multigrid method to solve the 2-D elliptic partial differential equation with the Dirichlet boundary conditions and is shown to be very much faster compared with the fullsweeps multigrids method.
Abstract: The idea of halfsweeps iterative method (introduced by A. R. Abdullah, 1991) is used to develop the halfsweeps multigrid method to solve the 2-D elliptic partial differential equation with the Dirichlet boundary conditions. The method is shown to be very much faster compared with the fullsweeps multigrid method due to M. M. Gupta et al, 1995. Some numerical experiments are included to confirm our recommendation.
34 citations
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TL;DR: A four points modified explicit group method for solving a two dimensional Poisson equation with Dirichlet boundary condition is introduced and is shown to be superior compared to the existing four points–explicit group and explicit decoupled group methods.
Abstract: In this paper, wc introduce a four points modified explicit group method for solving a two dimensional Poisson equation with Dirichlet boundary condition. The method is shown to be superior compared to the existing four points–explicit group and explicit decoupled group methods due to D. J. Evans and M. J. Biggins (1982) and A. R. Abdullah (1991), respectively, Some experiment results of the test problem are given in order to confirm our claim.
118 citations
TL;DR: This paper extends the 4-point explicit de-coupled group (EDG) iterative method to the 6 and 9-poinl EDG methods for the solution of elliptic partial differential equations and shows graphically the technique of implementing the new grouping.
Abstract: In this paper we extend the 4-point explicit de-coupled group (EDG) iterative method, Abdullah (1991), to the 6 and 9-poinl EDG methods for the solution of elliptic partial differential equations. We will show graphically the technique of implementing the new grouping. Performance results for the algorithms are presented and a comparison with the 4-point scheme confirm the new groups to be computationally superior. Further, the implementations of the parallel 4, 6 and 9-point EDG methods on the Sequent Balance 8000 multiprocessor arc discussed and results from experiments performed are presented.
89 citations
TL;DR: The rotated four-point explicit decoupled group (EDG) iterative method for solving two dimensional parabolic PDE is introduced and its performance is compared with some methods of natural ordering.
Abstract: In this paper, the rotated four-point explicit decoupled group (EDG) iterative method for solving two dimensional parabolic PDE is introduced. Its performance is compared with some methods of natural ordering.
77 citations
01 Jan 2004
TL;DR: In this article, the authors apply the Half-sweep Iterative Alternating Decomposition Explicit (HSIADE) method for solving one-dimensional diffusion problems and derive the formulation of the HSIADE method.
Abstract: The primary goal of this paper is to apply the Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for solving one-dimensional diffusion problems. The formulation of the HSIADE method is also derived. Some numerical experiments are conducted that to verify the HSIADE method is more efficient than the Full-Sweep method.
63 citations
16 Dec 2004
TL;DR: The primary goal of this paper is to apply the Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for solving one-dimensional diffusion problems.
Abstract: The primary goal of this paper is to apply the Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for solving one-dimensional diffusion problems. The formulation of the HSIADE method is also derived. Some numerical experiments are conducted that to verify the HSIADE method is more efficient than the Full-Sweep method.
62 citations