SemiAnalytical Solution to Heat Transfer Problems Using Fourier Transform Technique, Radial Basis Functions, and the Method of Fundamental Solutions

2007 ◽  
Vol 52 (5) ◽  
pp. 409-427 ◽  
Author(s):  
E. V. Glushkov ◽  
N. V. Glushkova ◽  
C. S. Chen
Keyword(s):  
Heat Transfer ◽  
Fourier Transform ◽  
Radial Basis Functions ◽  
Fundamental Solutions ◽  
Basis Functions ◽  
Method Of Fundamental Solutions ◽  
Radial Basis ◽  
Transfer Problems

Fundamental Solutions of PDEs as Radial Basis Functions in Multivariate Interpolation

2007 ◽  
Vol 7 (4) ◽  
pp. 321-340
Author(s):  
A. Masjukov
Keyword(s):  
Radial Basis Functions ◽  
Interpolation Method ◽  
A Priori ◽  
Fundamental Solutions ◽  
Basis Functions ◽  
Scale Parameters ◽  
Radial Basis ◽  
Undecidable Problem ◽  
The Right ◽  
Smooth Approximations

AbstractFor bivariate and trivariate interpolation we propose in this paper a set of integrable radial basis functions (RBFs). These RBFs are found as fundamental solutions of appropriate PDEs and they are optimal in a special sense. The condition number of the interpolation matrices as well as the order of convergence of the inter- polation are estimated. Moreover, the proposed RBFs provide smooth approximations and approximate fulfillment of the interpolation conditions. This property allows us to avoid the undecidable problem of choosing the right scale parameter for the RBFs. Instead we propose an iterative procedure in which a sequence of improving approx- imations is obtained by means of a decreasing sequence of scale parameters in an a priori given range. The paper provides a few clear examples of the advantage of the proposed interpolation method.

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