THE DEVELOPMENT OF NUMERICAL METHODS: FROM CONTINUUM MODEL TO DISCRETE PARTICLE MODEL

Numerical Methods have experienced the development from continuum model to discrete particle model. With the developmentof the latter, the meshless method emerges and it possesses great potential in the nanometer era. In this paper, the background and the principle of meshless method are addressed. Comparison is made between the meshless method and other numerical methods. Meanwhile, some major problems, such as basis function, weight function, influential radius, essential boundary conditions, integral and discrete schemes are discussed. Some applications of the method are summarized. In addition, natural element method, multi-scale analysis, mean value theorem and local boundary integral equation are reviewed and the prospectof the meshless method is explored.