【摘要】 数值方法经历了由连续介质到离散粒子模型的进展过程。无网格粒子方法正是离散粒子模型发展的产物,它在纳米时代显示出具大的发展潜能。介绍了无网格粒子方法的背景、原理及其与其他数值方法的区别,探讨了无网格法的基函数、权函数、影响半径、本质边界条件、积分与离散方案等热点问题,列举了这种数值方法的应用现状。最后,介绍了自然单元法、多尺度计算概念、中值定理与局部边界积分方程等,并对无网格粒子方法在未来的发展进行展望。更多还原

【Abstract】 Numerical Methods have experienced the development from continuum model to discrete particle model. With the development of 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 prospect of the meshless method is explored.更多还原