A new radial basis function for Helmholtz problems

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. (C) 2012 Elsevier Ltd. All rights reserved.