Evaluation of Multi-order Derivatives and Data Interpolation by Meshless Local Differential Quadrature Method
Date Issued
2010
Date
2010
Author(s)
Tseng, Kang-Hsi
Abstract
This thesis modified a local differential quadrature (LDQ) method with radial basis functions (RBFs) to deal with two kinds of problems: evaluating derivatives and interpolating data. First of all, it is difficult to obtain the differential values from numerical procedures in general. 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 function. The present technique is able to be applied to both of the structured and unstructured meshes due to a meshless numerical algorithm - RBF and LDQ method. In addition, the proposed model can be applied to estimate multi-order or mixed partial differential values because its test function (RBFs) is a multi-order differentiable function. Furthermore, the derivatives can be obtained quite accurately because the present scheme agrees with the governing equation for the first method and characteristic of weighting coefficients for the second method. Secondly, it is tough to interpolate the unknown data from the known scattered data. To be more accurately, most of the interpolation methods can be only applied to structured grid. Besides, most of them do not consider the governing equation and gradients. This investigation proposed a convenient and accurate tool to construct the unknown data from nearby relative knots. Present interpolation methods are operated under two conceptions: one is to consider the governing equations, and the other is to take account of the gradients. All of the results were tested with the structured and unstructured meshes and compared with exact solutions and other numerical techniques. Consequently, this study provides an effective algorithm to calculate the multi-order differential values and interpolate the new data accurately.
Subjects
multi-order derivatives
interpolation
meshless
local differential quadrature (LDQ)
radial basis function (RBF)
least squares method
Type
thesis
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