THE SOLUTION OF 2D ELLIPTIC EQUATION
USING MODIFIED GEOMETRIC MEAN METHOD
ON SKEWED GRID WITH RED-BLACK ORDERING
Shaliza Hayati A. Wahab1, A'qilah Ahmad Dahalan2,
Azali Saudi3
1,3Intelligent Robotics Lab
Faculty of Computing and Informatics
Universiti Malaysia Sabah
Kota Kinabalu, MALAYSIA
2Department of Mathematics
Centre for Defence Foundation Studies
National Defence University of Malaysia
Kuala Lumpur, MALAYSIA

Abstract

This paper presents the development of a new variant of two-stage Geometric Mean (GM) method for solving 2D elliptic equation. The proposed iterative scheme, called the Skewed Modified Geometric Mean (SkMGM), is derived from finite difference approximation discretized on a skewed grid with red-black ordering. The skewed finite difference scheme combined with red-black ordering is shown to be suitable for parallel implementation. The developed SkMGM scheme is compared with the other methods on the standard grid to confirm the effectiveness of the proposed method in terms of computational complexity and execution time. It is shown that the new proposed method gives the least number of iterations and fastest execution time compared to the other tested methods.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 6
Year: 2020

DOI: 10.12732/ijam.v33i6.6

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