Preconditioned Explicit Decoupled Group Methods For Solving Elliptic Partial Differential Equations
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Date
2011-04
Authors
Saeed Ahmed, Abdulkafi Mohammed
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The highly concern development of finite difference methods was
stimulated by the need to cope with today’s complex problems in science and
technology. The current requirement for faster solutions and for solving large
size problems arises in a variety of applications in science, such as modeling,
simulation of large systems and fluid dynamics. Therefore, studies regarding
several accelerated techniques have been carried out to achieve these
requirements. There are several discretisation techniques that can be used to
construct approximation equations for approximating partial differential
equations (PDEs) such as finite difference, finite element and finite volume.
These approximation equations will be used to generate the corresponding
systems of linear equations which are normally large and sparse. The iterative
methods are more efficient compared to the other methods since the storage
space required for iterative solutions on a computer is less when the coefficient
matrix of the system is sparse. Group explicit iterative methods based on the
rotated finite difference approximations have been shown to be much faster
than the methods based on the standard five-point formula in solving PDEs
which are due to the formers’ overall lower computational complexities. There
are some new alternative approaches towards increasing the rate of
convergence in solving large linear system resulting from the discretisation of
these methods.
Description
Keywords
Preconditioned Explicit Decoupled , Elliptic Partial