Properties of Gaussian radial basis functions in the dual reciprocity boundary element method

Abstract

In this paper, the computational and convergence properties of Gaussian radial basis function approximations employed in the Dual Reciprocity Boundary Element Method are studied. The Gaussian function has some desirable features for practical use; however, its performance is strongly influenced by its decay parameter since too small a value produces isolated peaks and too large values will make the approximation procedure ill-conditioned. It is shown herein that the approximating series of Gaussians is convergent, and that error bounds of the approximation can be estimated.