Boundary meshfree methods based on the boundary point interpolation methods

Abstract

A group of meshfree method based on Boundary Integral Equation (BIE) have been proposed and developed in order to overcome drawbacks in the conversional Boundary Element Method (BEM) that require boundary elements in constructing shape functions. In this paper, two boundary meshfree methods that use point interpolation methods (PIM), the Boundary Point Interpolation Method (BPIM) using the polynomial PIM and the Boundary Radial Point Interpolation Method (BRPIM) using the radial PIM, are reviewed and assessed. The numerical implementations of these two methods are examined and compared with each other on several technical issues in great details, including the size of the support domain, the convergence, the performance, and so on. These two boundary-type meshfree methods are also compared with the Boundary Node Method (BNM) and the conversional BEM in both efficiency and performance. Several numerical examples of 2-D elastostatics are analyzed using BPIM and BRPIM. It is found that the BPIM and BRPIM are very easy to implement, and very robust for obtaining numerical solutions for problems of computational mechanics. Key issues related the future development of boundary meshfree methods are also discussed.