The Interpolation Techniques for Functions and Derivatives Based on Localized Meshless Numerical Method
Date Issued
2011
Date
2011
Author(s)
Chan, Yi-Ling
Abstract
An interpolation technique based on the local radial basis functions differential quadrature (LRBF-DQ) method is developed to interpolate the unknown data by a set of irregularly scattered data. By employing the multiquadric function (MQ) as the test functions, the LRBF-DQ method is a meshless numerical scheme with high accuracy.
In this study, the unknown data are interpolated by utilizing the field gradients or the governing equations of the problem, thus the interpolated data satisfies the geometric properties or the physical principles. Several 2D and 3D examples are presented to validate the current interpolation method. The results interpolated by the presented method are compared with those interpolated by the linear polynomial fitting (LPF) method and the quadratic polynomial fitting (QPF) method. The interpolation results show that the presented methods are more accurate and robust than the conventional interpolation methods. Moreover, for the sake of tackling the strongly convection-dominated problems, the upwind scheme is applied to the LRBF-DQ method. The convection phenomena can be described more accurately and efficiently by the upwind technique based LRBF-DQ method than the conventional LRBF-DQ method. The proposed upwind technique based LRBF-DQ method is further applied to the data interpolation, and the results also have good performances.
Subjects
meshless
local differential quadrature
radial basis functions
interpolation
upwind
Type
thesis
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