A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems
The problems of radiative transfer give rise to interesting integral equations that must be faced with efficient numerical solver. Very often the integral equations are discretized to large-scale nonlinear equations and solved by Newton's-like methods. Generally, these kind of methods require t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25070/ http://psasir.upm.edu.my/id/eprint/25070/1/20570.pdf |
| _version_ | 1848845209156190208 |
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| author | Yusuf, Muhammad Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor |
| author_facet | Yusuf, Muhammad Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor |
| author_sort | Yusuf, Muhammad Waziri |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The problems of radiative transfer give rise to interesting integral equations that must be faced with efficient numerical solver. Very often the integral equations are discretized to large-scale nonlinear equations and solved by Newton's-like methods. Generally, these kind of methods require the computation and storage of the Jacobian matrix or its approximation. In this paper, we present a new approach that was based on approximating the Jacobian inverse into a diagonal matrix by means of variational technique. Numerical results on well-known benchmarks integral equations involved in the radiative transfer authenticate the reliability and efficiency of the approach. The fact that the proposed method can solve the integral equations without function derivative and matrix storage can be considered as a clear advantage over some other variants of Newton's method. |
| first_indexed | 2025-11-15T08:43:10Z |
| format | Article |
| id | upm-25070 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:43:10Z |
| publishDate | 2011 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-250702019-10-11T00:39:32Z http://psasir.upm.edu.my/id/eprint/25070/ A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems Yusuf, Muhammad Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor The problems of radiative transfer give rise to interesting integral equations that must be faced with efficient numerical solver. Very often the integral equations are discretized to large-scale nonlinear equations and solved by Newton's-like methods. Generally, these kind of methods require the computation and storage of the Jacobian matrix or its approximation. In this paper, we present a new approach that was based on approximating the Jacobian inverse into a diagonal matrix by means of variational technique. Numerical results on well-known benchmarks integral equations involved in the radiative transfer authenticate the reliability and efficiency of the approach. The fact that the proposed method can solve the integral equations without function derivative and matrix storage can be considered as a clear advantage over some other variants of Newton's method. Hindawi Publishing Corporation 2011 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/25070/1/20570.pdf Yusuf, Muhammad Waziri and Leong, Wah June and Abu Hassan, Malik and Monsi, Mansor (2011) A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems. Mathematical Problems in Engineering, 2011 (467017). pp. 1-12. ISSN 1024-123X; ESSN: 1563-5147 https://www.hindawi.com/journals/mpe/2011/467017/ 10.1155/2011/467017 |
| spellingShingle | Yusuf, Muhammad Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems |
| title | A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems |
| title_full | A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems |
| title_fullStr | A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems |
| title_full_unstemmed | A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems |
| title_short | A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems |
| title_sort | low memory solver for integral equations of chandrasekhar type in the radiative transfer problems |
| url | http://psasir.upm.edu.my/id/eprint/25070/ http://psasir.upm.edu.my/id/eprint/25070/ http://psasir.upm.edu.my/id/eprint/25070/ http://psasir.upm.edu.my/id/eprint/25070/1/20570.pdf |