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论文类型：期刊论文

发表时间：2013-06-01

发表刊物：CHINESE PHYSICS B

收录刊物：SCIE、EI、ISTIC、Scopus

卷号：22

期号：6

ISSN号：1674-1056

关键字：thin plate splines; transient heat conduction; penalty function method; local radial point interpolation method

摘要：The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions 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 a domain integral. 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.