Based On Compactly Supported Radial Basis Functions And Wavelet Basis Function Meshless Method

The finite element method (FEM) is now the main method to resolve the boundary value problems. It is based on the element and the piecewise interpolation shape function and it's convergence has also been proved. At present, there are many general and professional FEM programs which have been developed into a standard method. However, there exist many problems beyond the reach of the FEM, such as the industry model shaping, the discontinuous problems. Due these question, the Meshless method has been developed in recent years. It needs only point information and can be used to resolve the large deformation and nonlinear problems without giving the element information. The compactly supported radial function and the wavelet function have excellent local character and are suited to be applied in the Meshless method. In this paper, the Meshless method based on the compactly supported positive definite radial function and the wavelet function is put forward. The actual work done in this paper is as follows.Firstly, the paper introduces the development and existing question of the Meshless method. Furthermore, the paper also discusses the details of the method such as the selecting of field function, discretizing of the governing equation and dealing of the boundary condition.Secondly, from the view of the mathematics, the paper describes the compactly supported positive definite radial function and the wavelet function theory which are the mathematics basis of the application in the Meshless method. Based on the introduction, the meshless method based on weak variational forms is proposed and the related formulae are also deduced.Thirdly, a node integration method is proposed, hi order to verify the idea above, a Fortran program is also made. Through the numerical analysis, the result suggests that the theory of the Variational Meshless method based on the compactly supported radial function and wavelet function is right and the node integration method is reasonable.Finally, the paper discusses the advantage and disadvantage of the proposed method. The meshless method based on multiply scale analysis is also suggested in the future research.