A Parametric Study for Higher-order Derivatives Based on Moving Least Square Difference Methods

초록

In this paper, higher-order derivatives (which are often required in asymptotic methods and non-local elasticity) are calculated by employing a moving least square difference method. We carried out a parametric study to understand the characteristics of the difference method, which is based on a Taylor series expansion. It is convenient to use the Taylor series as a basis for the calculation of higher-order derivatives, because they are primary variables in the series. In this way, one can directly obtain their derivatives without carrying out differentiations. Three parameters are selected to systematically investigate the accuracy of higher-order derivatives: the order of polynomial basis, the number of nodes, and the support size. The numerical results clearly indicate that such parameters should be carefully selected to ensure the accuracy of higher-order derivatives. Finally, some optimal values are suggested for the parameters.

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