Radial point interpolation based finite difference method for mechanics problems

A radial point interpolation based finite difference method (RFDM) is proposed in this paper. In this novel method, radial point interpolation using local irregular nodes is used together with the conventional finite difference procedure to achieve both the adaptivity to irregular domain and the sta...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 68; no. 7; pp. 728 - 754
Main Authors: Liu, G. R., Zhang, Jian, Li, Hua, Lam, K. Y., Kee, Bernard B. T.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 12.11.2006
Wiley
Subjects:
Collocation methods
Computational techniques
Exact sciences and technology
Finite difference method
Finite element method
Fundamental areas of phenomenology (including applications)
generalized finite difference method
Interpolation
least-square
Mathematical analysis
Mathematical methods in physics
Mathematical models
meshfree method
numerical analysis
Physics
radial basis function
radial point interpolation
Stability
Symmetry
meshfree method
radial point interpolation
least-square
Radial basis function
Finite element method
generalized finite difference method
Symmetric matrix
Meshless method
numerical analysis
Modelling
Node method
Collocation method
Least square fit
Finite difference method
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:A radial point interpolation based finite difference method (RFDM) is proposed in this paper. In this novel method, radial point interpolation using local irregular nodes is used together with the conventional finite difference procedure to achieve both the adaptivity to irregular domain and the stability in the solution that is often encountered in the collocation methods. A least‐square technique is adopted, which leads to a system matrix with good properties such as symmetry and positive definiteness. Several numerical examples are presented to demonstrate the accuracy and stability of the RFDM for problems with complex shapes and regular and extremely irregular nodes. The results are examined in detail in comparison with other numerical approaches such as the radial point collocation method that uses local nodes, conventional finite difference and finite element methods. Copyright © 2006 John Wiley & Sons, Ltd.
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.1733