Particular solutions of 3D Helmholtz-type equations using compactly supported radial basis functions

In this paper we show how to obtain analytic particular solutions for inhomogeneous Helmholtz-type equations in 3D when the source terms are compactly supported radial basis functions (CS-RBFs) (J. Approx. Theory, 93 (1998) 258). Using these particular solutions we demonstrate the solvability of boundary value problems for the inhomogeneous Helmholtz-type equation by approximating the source term by CS-RBFs and solving the resulting homogeneous equation by the method of fundamental solutions. The proposed technique is a truly mesh-free method and is especially attractive for large-scale industrial problems. A numerical example is given which illustrates the efficiency of the proposed method. (C) 2000 Elsevier Science Ltd. All rights reserved.