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Evaluation of Multi-Order Derivatives by Local Radial Basis Function Differential Quadrature Method

Published online by Cambridge University Press:  16 October 2012

L. H. Shen ,
K. H. Tseng  and
D. L. Young
L. H. Shen
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
K. H. Tseng
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
D. L. Young*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Corresponding author ([email protected])
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Abstract

It is difficult to obtain the derivative values from most mesh dependent numerical procedures in general. This study proposes an efficient computational tool to accurately evaluate the multi-order derivatives by the radial basis functions and local differential quadrature (LRBF-DQ) algorithm. Most of the traditional derivative calculations can be only adopted to evaluate the differential values with the regular meshes. Moreover, the traditional numerical schemes are very restricted by the order of the shape functions. The present technique can be applied to both the structured and unstructured meshes as well as meshless numerical algorithms – such as RBFs and LDQ method. In addition, the proposed model can be also used to estimate multi-order or mixed partial derivative values because its test function using RBFs is a multi-order differentiable function. All of the evaluation of derivative results will be compared with the exact solutions and other numerical techniques. Consequently, this study provides an effective algorithm of post process to accurately calculate the multi-order derivative values for any numerical schemes.

Keywords

Multi-order derivativesRadial basis functionsLocal differential quadrature
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013 , pp. 67 - 78
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

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