Testing the use of radial basis function augmented with polynomials as basis functions in the boundary element method for heat transfer problems

Abstract

The accuracy of the numerical solution obtained by the Boundary Element Method (BEM) is directly affected by the type of interpolation function used. Meanwhile, interpolation by radial basis function augmented with polynomials has been shown to be more accurate than Lagrange interpolation for a range of different functions. Therefore, this paper is concerned with the application of such functions as the interpolation functions for all boundary values in the boundary element method for the numerical solution of two-dimensional heat transfer problems. Numerical examples with different geometries and temperature distributions are presented and comparisons with both isogeometric and classical formulation are made to demonstrate the accuracy of the proposed method.