Study of a new meshless method(IMLS Method of Square Sphere) and its application

According to some recent studies of meshless methods,a new technique of meshless methods was presented – the meshless Interpolating Moving Least Square(IMLS) method in square sphere.The method showed new formula in the approximations of the unknown variable,the choice of weighted function and the numerical integration in the square sphere.Concerning the method,the technique of IMLS was adopted for the approximations of the unknown variable,and the square sphere was used for the geometric form of the local influence field.The adoption of these techniques presented the features of mesh free that the nodes were placed and the numerical integration was performed without a mesh.The Dirichlet boundary condition was also satisfied.The method could be easily applied to initial or boundary value problems of PDE.Besides,excellent convergence rate,high accuracy and good efficiency of the method were demonstrated by the examples in the problem of 1D consolidation and the 2D elastic mechanics.It was very promising in engineering applications.