中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60206-060206.doi: 10.1088/1674-1056/22/6/060206
王峰a, 林皋a, 郑保敬b, 胡志强a
Wang Feng (王峰)a, Lin Gao (林皋)a, Zheng Bao-Jing (郑保敬)b, Hu Zhi-Qiang (胡志强)a
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.
中图分类号: (Numerical approximation and analysis)