A stabilized moving Kriging interpolation method and its application in boundary node method

Abstract

Moving Kriging interpolation (MKI) is an important approximation method to construct shape functions in meshless methods. We analyzed the stability of MKI and found that it will become unstable when the nodal spacing decreases. Thus, we developed a stabilized MKI method by using shifted and scaled polynomial basis functions. Then, we applied the stabilized MKI to boundary node method for Laplace's problems and Poisson's problems to study the advantages. For Poisson's problems, the radial integration method is introduced to compute the domain integrals. We also applied the stabilized MKI to element-free Galerkin method to solve elastodynamic problems. Examples are provided to show the accuracy and stability of the stabilized MKI and the boundary node method and element-free Galerkin method based on the stabilized MKI.