An adaptive hierarchical matrix on point iterative Poisson solver
In this paper, an adaptive hierarchical matrix (H-matrix) points iterative method based solution was proposed to solve two-dimensional Poisson problem with Dirichlet boundary condition. The finite difference approximation was used to discretize the problem, which led to a system of linear equation....
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/52329/ http://psasir.upm.edu.my/id/eprint/52329/1/10.%20Nik%20n%20MO.pdf |
| _version_ | 1848852075826380800 |
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| author | Nik Mazlan, Nik Amir Syafiq Othman, Mohamed Senu, Norazak |
| author_facet | Nik Mazlan, Nik Amir Syafiq Othman, Mohamed Senu, Norazak |
| author_sort | Nik Mazlan, Nik Amir Syafiq |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, an adaptive hierarchical matrix (H-matrix) points iterative method based solution was proposed to solve two-dimensional Poisson problem with Dirichlet boundary condition. The finite difference approximation was used to discretize the problem, which led to a system of linear equation. Two types of admissibility conditions, standard and weak, produces two different H-matrix structures, HS- and HW- respectively. The adaption of the H-matrices to a linear system leads to the saving of memory utilization. An experiment was conducted which compares the proposed HW-matrix with the benchmarked HS-matrix. The results showed the superiority of the proposed method when comparing both H-matrix structures. |
| first_indexed | 2025-11-15T10:32:19Z |
| format | Article |
| id | upm-52329 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:32:19Z |
| publishDate | 2016 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-523292017-06-05T09:15:37Z http://psasir.upm.edu.my/id/eprint/52329/ An adaptive hierarchical matrix on point iterative Poisson solver Nik Mazlan, Nik Amir Syafiq Othman, Mohamed Senu, Norazak In this paper, an adaptive hierarchical matrix (H-matrix) points iterative method based solution was proposed to solve two-dimensional Poisson problem with Dirichlet boundary condition. The finite difference approximation was used to discretize the problem, which led to a system of linear equation. Two types of admissibility conditions, standard and weak, produces two different H-matrix structures, HS- and HW- respectively. The adaption of the H-matrices to a linear system leads to the saving of memory utilization. An experiment was conducted which compares the proposed HW-matrix with the benchmarked HS-matrix. The results showed the superiority of the proposed method when comparing both H-matrix structures. Institute for Mathematical Research, Universiti Putra Malaysia 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/52329/1/10.%20Nik%20n%20MO.pdf Nik Mazlan, Nik Amir Syafiq and Othman, Mohamed and Senu, Norazak (2016) An adaptive hierarchical matrix on point iterative Poisson solver. Malaysian Journal of Mathematical Sciences, 10 (3). pp. 369-382. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol10no3/10.%20Nik%20n%20MO.pdf |
| spellingShingle | Nik Mazlan, Nik Amir Syafiq Othman, Mohamed Senu, Norazak An adaptive hierarchical matrix on point iterative Poisson solver |
| title | An adaptive hierarchical matrix on point iterative Poisson solver |
| title_full | An adaptive hierarchical matrix on point iterative Poisson solver |
| title_fullStr | An adaptive hierarchical matrix on point iterative Poisson solver |
| title_full_unstemmed | An adaptive hierarchical matrix on point iterative Poisson solver |
| title_short | An adaptive hierarchical matrix on point iterative Poisson solver |
| title_sort | adaptive hierarchical matrix on point iterative poisson solver |
| url | http://psasir.upm.edu.my/id/eprint/52329/ http://psasir.upm.edu.my/id/eprint/52329/ http://psasir.upm.edu.my/id/eprint/52329/1/10.%20Nik%20n%20MO.pdf |