Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm
The main work of this paper focuses on identifying the heat flux in inverse problem of two-dimensional nonhomogeneous parabolic equation, which has wide application in the industrial field such as steel-making and continuous casting. Firstly, the existence of the weak solution of the inverse problem...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6616326 |
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| _version_ | 1841524588629983232 |
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| author | Xinfu Pang Yang Yu Haibo Li Yuan Wang Jinhui Zhao |
| author_facet | Xinfu Pang Yang Yu Haibo Li Yuan Wang Jinhui Zhao |
| author_sort | Xinfu Pang |
| collection | DOAJ |
| description | The main work of this paper focuses on identifying the heat flux in inverse problem of two-dimensional nonhomogeneous parabolic equation, which has wide application in the industrial field such as steel-making and continuous casting. Firstly, the existence of the weak solution of the inverse problem is discussed. With the help of forward solution and dual equation, this paper proves the Lipchitz continuity of the cost function and derives the Lipchitz constant. Furthermore, in order to accelerate the convergence rate and reduce the running time, this paper presents a sufficient descent Levenberg–Marquard algorithm with adaptive parameter (SD-LMAP) to solve this inverse problem. At last, compared with other methods, the results of simulation experiment show that this algorithm can obviously reduce the running time and iterative number. |
| format | Article |
| id | doaj-art-ff487866c47a481dbd1d7a70d5d516f5 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ff487866c47a481dbd1d7a70d5d516f52025-02-03T05:52:58ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66163266616326Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard AlgorithmXinfu Pang0Yang Yu1Haibo Li2Yuan Wang3Jinhui Zhao4School of Automation, Shenyang Institute of Engineering, Shenyang 110136, ChinaSchool of Automation, Shenyang Aerospace University, Shenyang 110136, ChinaSchool of Automation, Shenyang Institute of Engineering, Shenyang 110136, ChinaSchool of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, ChinaCollege of Electrical Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, ChinaThe main work of this paper focuses on identifying the heat flux in inverse problem of two-dimensional nonhomogeneous parabolic equation, which has wide application in the industrial field such as steel-making and continuous casting. Firstly, the existence of the weak solution of the inverse problem is discussed. With the help of forward solution and dual equation, this paper proves the Lipchitz continuity of the cost function and derives the Lipchitz constant. Furthermore, in order to accelerate the convergence rate and reduce the running time, this paper presents a sufficient descent Levenberg–Marquard algorithm with adaptive parameter (SD-LMAP) to solve this inverse problem. At last, compared with other methods, the results of simulation experiment show that this algorithm can obviously reduce the running time and iterative number.http://dx.doi.org/10.1155/2021/6616326 |
| spellingShingle | Xinfu Pang Yang Yu Haibo Li Yuan Wang Jinhui Zhao Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm Journal of Mathematics |
| title | Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm |
| title_full | Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm |
| title_fullStr | Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm |
| title_full_unstemmed | Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm |
| title_short | Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm |
| title_sort | estimation of heat flux in two dimensional nonhomogeneous parabolic equation based on a sufficient descent levenberg marquard algorithm |
| url | http://dx.doi.org/10.1155/2021/6616326 |
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