A new radial basis function for Helmholtz problems

Abstract

In this paper, a new radial basis function (RBF) is proposed to solve Helmholtz problems in the traditional collocation method. Since the matrix equation arising from the RBF interpolation is ill-conditioned, a regularized singular value decomposition method is used to obtain a more accurate solution. Numerical examples of both direct and inverse problems are presented to demonstrate the effectiveness and applicability of the proposed RBF versus the traditional multiquadric RBF.