Meshfree boundary particle method applied to Helmholtz problems

This paper is concerned with the boundary particle method (BPM), a new boundary-only radial basis function collocation schemes. The method is developed based on the multiple reciprocity principle and applying either high-order nonsingular general solutions or singular fundamental solutions as the radial basis function. Like the multiple reciprocity BEM (MR-BEM), the BPM does not require any inner nodes for inhomogeneous problems and therefore is a truly boundary-only technique. On the other hand, unlike the MR-BEM, the BPM is meshfree, integration-free, symmetric, and mathematically simple technique. In particular, the method requires much less computational effort for the discretization than the MR-BEM. In this study, the accuracy and efficiency of the BPM are numerically demonstrated in some 2D inhomogeneous Helmholtz problems under complicated geometries. q 2002 Elsevier Science Ltd. All rights reserved.