scholarly journals Moving least squares interpolation with thin-plate splines and radial basis functions

1992 ◽  
Vol 24 (12) ◽  
pp. 177-185 ◽  
Author(s):  
K. Šalkauskas
Keyword(s):  
Least Squares ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Basis Functions ◽  
Moving Least Squares ◽  
Thin Plate Splines ◽  
Radial Basis ◽  
Moving Least Squares Interpolation

DIV-CURL WEIGHTED MINIMIZING SPLINES

2007 ◽  
Vol 05 (02) ◽  
pp. 95-122 ◽  
Author(s):  
M. N. BENBOURHIM ◽  
A. BOUHAMIDI
Keyword(s):  
Vector Field ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Approximation Problem ◽  
Scattered Data ◽  
Scalar Function ◽  
Basis Functions ◽  
Thin Plate Splines ◽  
Numerical Examples ◽  
Radial Basis

The paper deals with a div-curl approximation problem by weighted minimizing splines. The weighted minimizing splines are an extension of the well-known thin plate splines and are radial basis functions which allow the approximation or the interpolation of a scalar function from given scattered data. In this paper, we show that the theory of the weighted minimizing splines may also be used for the approximation or for the interpolation of a vector field controlled by the divergence and the curl of the vector field. Numerical examples are given to show the efficiency of this method.

scholarly journals Enhancing SPH using Moving Least-Squares and Radial Basis Functions

2006 ◽  
pp. 103-112
Author(s):  
Robert Brownlee ◽  
Paul Houston ◽  
Jeremy Levesley ◽  
Stephan Rosswog
Keyword(s):  
Least Squares ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Moving Least Squares ◽  
Radial Basis

Multilevel RBF collocation method for the fourth-order thin plate problem

2020 ◽  
pp. 2050079
Author(s):  
Lanling Ding ◽  
Zhiyong Liu ◽  
Qiuyan Xu
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Fourth Order ◽  
Basis Function ◽  
Research Method ◽  
Meshfree Method ◽  
Basis Functions ◽  
Radial Basis

The radial basis functions meshfree method is a research method for thin plate problem which has gradually developed into a more mature meshfree method. It includes finite element, radial basis functions meshfree collocation method, etc. In this paper, we introduce the multilevel radial basis function collocation method for the fourth-order thin plate problem. We use nonsymmetric Kansa multilevel radial basis function collocation method to solve the fourth-order thin plate problem. Two numerical examples based on Wendland’s [Formula: see text] and [Formula: see text] functions are given to examine that the convergence of the multilevel radial basis function collocation method which is good for solving the fourth-order thin plate problem.

COMPARATIVE STUDY OF THE MULTIQUADRIC AND THIN-PLATE SPLINE RADIAL BASIS FUNCTIONS FOR THE TRANSIENT-CONVECTIVE DIFFUSION PROBLEMS

2006 ◽  
Vol 17 (08) ◽  
pp. 1151-1169 ◽  
Author(s):  
A. DURMUS ◽  
I. BOZTOSUN ◽  
F. YASUK
Keyword(s):  
Radial Basis Functions ◽  
Thin Plate ◽  
Numerical Solutions ◽  
Convective Diffusion ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Thin Plate Spline ◽  
Collocation Methods ◽  
Radial Basis ◽  
Diffusion Problems

The numerical solutions of the unsteady transient-convective diffusion problems are investigated by using multiquadric (MQ) and thin-plate spline (TPS) radial basis functions (RBFs) based on mesh-free collocation methods with global basis functions. The results of radial basis functions are compared with the mesh-dependent boundary element and finite difference methods as well as the analytical solution for high Péclet numbers. It is reported that for low Péclet numbers, MQ-RBF provides excellent agreement, while for high Péclet numbers, TPS-RBF is better than MQ-RBF.

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