The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering
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...
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Centre for Environment Social and Economic Research
2020
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my.ums.eprints.289182021-07-11T14:02:09Z https://eprints.ums.edu.my/id/eprint/28918/ The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering Shaliza Hayati A. Wahab A'Qilah Ahmad Dahalan Azali Saudi 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 redblack 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. Centre for Environment Social and Economic Research 2020 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/28918/1/The%20solution%20of%202D%20elliptic%20equation%20using%20modified%20geometric%20mean%20method%20on%20skewed%20grid%20with%20red-black%20ordering%20abstract.pdf text en https://eprints.ums.edu.my/id/eprint/28918/2/The%20solution%20of%202D%20elliptic%20equation%20using%20modified%20geometric%20mean%20method%20on%20skewed%20grid%20with%20red-black%20ordering%20fulltext.pdf Shaliza Hayati A. Wahab and A'Qilah Ahmad Dahalan and Azali Saudi (2020) The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering. International Journal of Applied Mathematics and Statistics, 33. pp. 1027-1047. ISSN 0973-1377 http://diogenes.bg/ijam/contents/2020-33-6/6/ http://dx.doi.org/10.12732/ijam.v33i6.6 |
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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 redblack 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. |
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Article |
author |
Shaliza Hayati A. Wahab A'Qilah Ahmad Dahalan Azali Saudi |
spellingShingle |
Shaliza Hayati A. Wahab A'Qilah Ahmad Dahalan Azali Saudi The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering |
author_facet |
Shaliza Hayati A. Wahab A'Qilah Ahmad Dahalan Azali Saudi |
author_sort |
Shaliza Hayati A. Wahab |
title |
The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering |
title_short |
The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering |
title_full |
The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering |
title_fullStr |
The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering |
title_full_unstemmed |
The solution of 2D elliptic equation using modified geometric mean method on skewed grid with red-black ordering |
title_sort |
solution of 2d elliptic equation using modified geometric mean method on skewed grid with red-black ordering |
publisher |
Centre for Environment Social and Economic Research |
publishDate |
2020 |
url |
https://eprints.ums.edu.my/id/eprint/28918/1/The%20solution%20of%202D%20elliptic%20equation%20using%20modified%20geometric%20mean%20method%20on%20skewed%20grid%20with%20red-black%20ordering%20abstract.pdf https://eprints.ums.edu.my/id/eprint/28918/2/The%20solution%20of%202D%20elliptic%20equation%20using%20modified%20geometric%20mean%20method%20on%20skewed%20grid%20with%20red-black%20ordering%20fulltext.pdf https://eprints.ums.edu.my/id/eprint/28918/ http://diogenes.bg/ijam/contents/2020-33-6/6/ http://dx.doi.org/10.12732/ijam.v33i6.6 |
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