An improved local radial point interpolation method for transient heat conduction analysis

doi:10.1088/1674-1056/22/6/060206

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60206-060206.doi: 10.1088/1674-1056/22/6/060206

An improved local radial point interpolation method for transient heat conduction analysis

王峰^a, 林皋^a, 郑保敬^b, 胡志强^a

a Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China;
b School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

收稿日期:2012-09-16 修回日期:2013-01-10 出版日期:2013-05-01 发布日期:2013-05-01
基金资助:
Project supported by the Key Program of the National Natural Science Foundation of China (Grand No. 51138001), the China-German Cooperation Project (Grand No. GZ566), the Innovative Research Groups Funded by the National Natural Science Foundation of China (Grand No. 51121005), and the Special Funds for the Basic Scientific Research Expenses for the Central University (Grant No. DUT13LK16).

An improved local radial point interpolation method for transient heat conduction analysis

Wang Feng (王峰)^a, Lin Gao (林皋)^a, Zheng Bao-Jing (郑保敬)^b, Hu Zhi-Qiang (胡志强)^a

a Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China;
b School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

Received:2012-09-16 Revised:2013-01-10 Online:2013-05-01 Published:2013-05-01
Contact: Wang Feng E-mail:wangfengdut@gmail.com
Supported by:
Project supported by the Key Program of the National Natural Science Foundation of China (Grand No. 51138001), the China-German Cooperation Project (Grand No. GZ566), the Innovative Research Groups Funded by the National Natural Science Foundation of China (Grand No. 51121005), and the Special Funds for the Basic Scientific Research Expenses for the Central University (Grant No. DUT13LK16).

摘要/Abstract

摘要： The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with the transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions could hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for domain integral. The essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions.

关键词: thin plate splines, transient heat conduction, penalty function method, local radial point interpolation method

Abstract: The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with the transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions could hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for domain integral. The essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions.

Key words: thin plate splines, transient heat conduction, penalty function method, local radial point interpolation method

中图分类号: (Numerical approximation and analysis)

02.60.-x

02.60.Pn (Numerical optimization) 44.10.+i (Heat conduction)

王峰, 林皋, 郑保敬, 胡志强. An improved local radial point interpolation method for transient heat conduction analysis[J]. 中国物理B, 2013, 22(6): 60206-060206.

Wang Feng (王峰), Lin Gao (林皋), Zheng Bao-Jing (郑保敬), Hu Zhi-Qiang (胡志强). An improved local radial point interpolation method for transient heat conduction analysis[J]. Chin. Phys. B, 2013, 22(6): 60206-060206.

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An improved local radial point interpolation method for transient heat conduction analysis

An improved local radial point interpolation method for transient heat conduction analysis

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