A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

doi:10.1088/1674-1056/23/4/040203

中国物理B ›› 2014, Vol. 23 ›› Issue (4): 40203-040203.doi: 10.1088/1674-1056/23/4/040203

A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

葛红霞^a, 程荣军^b

a Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

收稿日期:2013-08-10 修回日期:2013-10-08 出版日期:2014-04-15 发布日期:2014-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11072117), the Natural Science Foundation of Ningbo City, China (Grant No. 2013A610103), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6090131), the DisciplinaryProject of Ningbo City, China (Grant No. SZXL1067), and the K. C. Wong Magna Fund in Ningbo University, China.

A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Ge Hong-Xia (葛红霞)^a, Cheng Rong-Jun (程荣军)^b

a Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Received:2013-08-10 Revised:2013-10-08 Online:2014-04-15 Published:2014-04-15
Contact: Ge Hong-Xia E-mail:gehongxia@nbu.edu.cn
About author:02.60.Lj; 03.65.Ge
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11072117), the Natural Science Foundation of Ningbo City, China (Grant No. 2013A610103), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6090131), the DisciplinaryProject of Ningbo City, China (Grant No. SZXL1067), and the K. C. Wong Magna Fund in Ningbo University, China.

摘要/Abstract

摘要： Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging interpolation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.

关键词: meshless method, moving Kriging interpolation, time-fractional diffusion equation

Abstract: Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging interpolation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.

Key words: meshless method, moving Kriging interpolation, time-fractional diffusion equation

中图分类号: (Ordinary and partial differential equations; boundary value problems)

02.60.Lj

03.65.Ge (Solutions of wave equations: bound states)

葛红霞, 程荣军. A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation[J]. 中国物理B, 2014, 23(4): 40203-040203.

Ge Hong-Xia (葛红霞), Cheng Rong-Jun (程荣军). A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation[J]. Chin. Phys. B, 2014, 23(4): 40203-040203.

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A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

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