An Efficient Scheme for Meshless Analysis Based on Radial Basis Functions

Abstract: A meshless method based on radial point interpolation was recently developed as an effective tool for solving partial differential equations, and has been widely applied to a number of different problems. In addition to the primary advantage of the meshless methods that the computation is performed without any connectivity information between field nodes, the radial point interpolation-based meshless method has several advantages such as the stability of the shape functions and simple implementation of boundary condition enforcement. This paper introduces a new scheme for the radial point interpolation-based meshless method. This method enables fast computation by modifying the construction and evaluation of the shape functions. Numerical examples are also presented to show that a reliable solution can be obtained with low computational cost.