Radial basis function method modelling borehole heat transfer: the practical application

Abstract

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 ksi for the TR method that minimizes the GCV function. The some practical results of numerical experiments are presented.

Keywords

• borehole heat exchanger transfer (BHET)
• radial basis function (RBF)
• Tikhonov regularization (TR)
• generalized cross-validation (GCV)