New Parallel Group Accelerated Overrelaxation Algorithms For The Solution Of 2-D Poisson And Diffusion Equations
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Date
2011-12
Authors
Foo, Kai Pin
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Finite difference method is commonly used to solve partial differential
equations (PDEs) which arise from fluid mechanics and thermodynamics problem.
However, the discretization of these PDEs oftenly lead to large sparse linear systems
which require large amount of execution times to solve.
The development in accelerated iterative techniques and parallel computing
technologies can be utilized to surmount this problem. Point iterative schemes which
are based on the standard five point discretization and the rotated five point
discretization are commonly used to solve the Poisson equation. In addition, block or
group iterative schemes where the mesh points are grouped into block have been
shown to reduce the number of iterations and execution timings because the solution
at the mesh points can be updated in groups or blocks instead of pointwise. Among
these group iterative schemes, the Explicit Group (EG) method (Yousif and Evans,
1986) and Explicit Decoupled Group (EDG) method (Abdullah, 1990) have been
extensively researched and have been shown to converge faster than their pointwise
counterparts. In order to improve the rate of convergence of these methods, the
common accelerated methods such as Successive OverRelaxation (SOR) method and
Accelerated OverRelaxation (AOR) method may be applied to these methods and
have been shown to reduce the number of iterations.
Description
Keywords
Parallel group accelerated overrelaxation algorithms , solution of 2-D poisson and diffusion equations