Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods

Abstract

The radial point interpolation method (RPIM) based on local supported radial basis function (RBF) and the Galerkin weak form has been developed and successfully applied to many engineering problems. Recently, a new meshfree method was proposed based on the universal moving Kriging interpolation. This paper studies the difference between the meshfree shape functions created based on the point interpolation and the Kriging interpolation. It is found that both the two methods yield the same shape function as long as the same radial basis function or semivariogram is adopted for interpolation. Although the two methods lead to the same shape function, the theorem in Kriging formulation may provide an alternative theoretical support for the RPIM. Some common semivariograms used in Kriging may also be incorporated in the RPIM. In addition, in order to satisfy the conformability requirements, a penalty technique is introduced in this paper to form a conforming Kriging, which can pass the standard patch test exactly.