Open AccessRadial basis function method modelling borehole heat transfer: the practical application
Author(s) -
Audrius Indriulionis,
Pranas Vaitkus
Publication year - 2016
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.a.2016.04
Subject(s) - tikhonov regularization , radial basis function , work (physics) , regularization (linguistics) , mathematics , partial differential equation , heat exchanger , mathematical analysis , computer science , inverse problem , physics , thermodynamics , artificial intelligence , artificial neural network , machine learning
. In this work, the method of radial basis function (RBF) is used for the borehole heat exchanger transfers (BHET) problems. The RBF method is an efficient mesh free technique for the numerical solution of partial differential equations. The condition number of the system of linear equations (matrix A) is large it means that the ill-conditioning of matrix A makes the numerical solution unstable. Tikhonov regularization (TR) method are presented to solve such ill-conditioned systems. In this work, generalized cross-validation (GCV) method is carried out to determine the regularization parameter ξ for the TR method that minimizes the GCV function. The some practical results of numerical experiments are presented.