A comparison of the RBF-based meshfree boundary knot and the boundary particle methods

Abstract

A comparison of the RBF-based meshfree boundary knot and the boundary particle methods W. Chen1 Summary This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BKM employs the multiple reciprocity technique. Unlike the method of fundamental solution, the two methods use the non-singular general solution instead of the singular fundamental solution to circumvent the controversial artificial boundary outside the physical domain. Compared with the boundary element method, both BKM and BPM are meshfree, super-convergent, integration-free, symmetric, and mathematically simple collocation techniques for general PDEs. In particular, the BPM does not require any inner nodes for inhomogeneous problems. In this study, the accuracy, efficiency, and applicability of the two methods are numerically tested to some 2D, 3D Helmholtz, diffusion, and convection-diffusion problems under complicated geometries. Their advantages and disadvantages are compared and discussed based on numerical observations. keywords: boundary knot method; boundary particle method; radial basis function; meshfree.