Boundary Point Method Based On Sliding Kriging Interpolation Study

The meshfree (or meshless) method is a newly developed computational technique for solving partial differential equations. The meshfree method, which was born with the objective of eliminating part of the difficulties associated with reliance on a mesh to construct the approximation, builds the approximate functions by a group of arbitrarily distributed nodes only. The meshfree method also has simpler implementation procedures and possesses the advantage of high precision. Another key feature of the meshfree method is that it has good stability. The meshfree method has become a hot direction in computational mechanics.There are two types of the meshfree method: the boundary-type meshfree method and the domain-type meshfree method. The boundary-type meshfree method is a new computational technique based on the traditional boundary element method, which constructs the shape functions using the approximation in the meshfree method. The boundary-type meshfree method also possesses the advantages of dimensionality reduction and high precision. However, there exists an inconvenience that the boundary conditions cannot be implemented with ease; the moving-least squares method can form ill-conditioned or singular equations sometimes. To overcome these disadvantages, combining the moving Kriging interpolation with the boundary integral equation method, the moving Kriging interpolation-based boundary node method (MKIBNM) is developed in this paper. The present method is used for solution of two-dimensional potential problems and elasticity problems, the main researches of this issue are as follows:The shape function, which constructed based on the moving Kriging interpolation, is discussed at first. The shape function possesses the Kroneckerδproperty and the property of partitions of unity. The moving Kriging interpolation method is used for the curve fitting and surface fitting. Some selected numerical examples are presented to illustrate the efficiency of this method. Combining the moving Kriging interpolation with the boundary integral equation method for potential problem, the moving Kriging interpolation-based boundary node method for potential problem is developed. The formulae of the MKIBNM for two-dimensional potential problems are obtained. The present method has lower computation cost than the traditional boundary node method, and possesses the advantage of good stability. Furthermore, the boundary conditions also can be implemented easily.Combining the moving Kriging interpolation with the boundary integral equation method for elasticity problem, the moving Kriging interpolation-based boundary node method for elasticity problem is presented. The formulae of the MKIBNM for two-dimensional elasticity problems are given.The corresponding MATLAB codes of the MKIBNM above have been written. Some numerical examples are solved to demonstrate the validity of the present methods.