无网格法的研究进展

ADVANCES IN THE STUDIES ON MESHLESS METHODS

对现有的无网格法（Meshless methods）进行了综述。描述了无网格法的近似方案、权函数的选择、变分形式和离散方程以及数值求解的实现。研究了无网格法对不连续问题和边界条件的处理、无网格法与有限元法的耦合。采用Element-free Galerkin（无网格伽辽金,EFG）方法编制了相应程序,并给出了两个计算例子。在现有研究的基础上提出了无网格法未来发展的几个方向。

Main procedures of meshless methods are reviewed and discussed. The approximation of meshless methods, the selection of weight function, the variational form and the discrete equation, and the numerical implementation are described. The discontinuous approximations and the approach of boundary conditions, and the coupling meshless methods to finite elements are studied. Two examples which use the EFG method are presented. Based on the investigation on the recent advances of the methods, the future development tendency of meshless methods is discussed and outlined.