Application of the meshless generalized finite difference method to inverse heat source problems
•Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data. The generalized finite difference method (GFDM) is a relatively new...
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| Vydáno v: | International journal of heat and mass transfer Ročník 108; s. 721 - 729 |
|---|---|
| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.05.2017
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| Témata: | |
| ISSN: | 0017-9310, 1879-2189 |
| On-line přístup: | Získat plný text |
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| Abstract | •Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data.
The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. This paper documents the first attempt to apply the method for recovering the heat source in steady-state heat conduction problems. In order to guarantee the uniqueness of the solution, the heat source here is assumed to satisfy a second-order partial differential equation, and thereby transforming the problem into a fourth-order partial differential equation, which can be solved conveniently and stably by using the GFDM. Numerical analysis are presented on three benchmark test problems with both smooth and piecewise smooth geometries. The stability and sensitivity of the scheme with respect to the amount of noise added into the input data are analyzed. The numerical results obtained show that the proposed algorithm is accurate, computationally efficient and numerically stable for the numerical solution of inverse heat source problems. |
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| AbstractList | •Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data.
The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. This paper documents the first attempt to apply the method for recovering the heat source in steady-state heat conduction problems. In order to guarantee the uniqueness of the solution, the heat source here is assumed to satisfy a second-order partial differential equation, and thereby transforming the problem into a fourth-order partial differential equation, which can be solved conveniently and stably by using the GFDM. Numerical analysis are presented on three benchmark test problems with both smooth and piecewise smooth geometries. The stability and sensitivity of the scheme with respect to the amount of noise added into the input data are analyzed. The numerical results obtained show that the proposed algorithm is accurate, computationally efficient and numerically stable for the numerical solution of inverse heat source problems. |
| Author | Zhang, Chuanzeng Gu, Yan Wang, Lei He, Xiaoqiao Chen, Wen |
| Author_xml | – sequence: 1 givenname: Yan surname: Gu fullname: Gu, Yan email: guyan1913@163.com organization: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, PR China – sequence: 2 givenname: Lei orcidid: 0000-0002-2104-6169 surname: Wang fullname: Wang, Lei email: shywanglei@126.com organization: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, PR China – sequence: 3 givenname: Wen surname: Chen fullname: Chen, Wen organization: Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 210098, PR China – sequence: 4 givenname: Chuanzeng surname: Zhang fullname: Zhang, Chuanzeng organization: Department of Civil Engineering, University of Siegen, Paul-Bonatz-Str. 9-11, D-57076 Siegen, Germany – sequence: 5 givenname: Xiaoqiao surname: He fullname: He, Xiaoqiao organization: Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong |
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