Improved EMD Based on Piecewise Cubic Hermite Interpolation and Mirror Extension

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

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Scattered Hermite interpolation using radial basis functions

Linear Algebra and its Applications ◽

10.1016/0024-3795(94)90007-8 ◽

1994 ◽

Vol 207 ◽

pp. 135-146 ◽

Cited By ~ 12

Author(s):

Xingping Sun

Keyword(s):

Radial Basis Functions ◽

Hermite Interpolation ◽

Basis Functions ◽

Radial Basis

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Hermite interpolation with simple planar PH curves by speed reparametrization

Computer Aided Geometric Design ◽

10.1016/j.cagd.2007.11.006 ◽

2008 ◽

Vol 25 (4-5) ◽

pp. 214-229 ◽

Cited By ~ 14

Author(s):

Jae Hoon Kong ◽

Seung Pil Jeong ◽

Sunhong Lee ◽

Gwang Il Kim

Keyword(s):

Hermite Interpolation

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Hermite interpolation by piecewise polynomial surfaces with polynomial area element

Computer Aided Geometric Design ◽

10.1016/j.cagd.2017.02.003 ◽

2017 ◽

Vol 51 ◽

pp. 30-47 ◽

Cited By ~ 2

Author(s):

Michal Bizzarri ◽

Miroslav Lávička ◽

Zbyněk Šír ◽

Jan Vršek

Keyword(s):

Hermite Interpolation ◽

Piecewise Polynomial ◽

Area Element

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Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

Journal of Applied Mathematics ◽

10.1155/2014/857840 ◽

2014 ◽

Vol 2014 ◽

pp. 1-18 ◽

Cited By ~ 2

Author(s):

Yuanpeng Zhu ◽

Xuli Han ◽

Shengjun Liu

Keyword(s):

Error Estimate ◽

Hermite Interpolation ◽

Sufficient Conditions ◽

Basis Functions ◽

Shape Parameters ◽

Interpolation Spline ◽

Triangular Domain ◽

Type Algorithm ◽

Special Case ◽

Monotonicity Preserving

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, theG1continuous conditions are deduced for the joining of two patches.

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