无网格方法中结点搜索算法的改进

Improvement of Node-searching Method in Meshless Method

在采用无网格方法进行数值计算时,常常涉及到结点搜索问题.在处理复杂区域问题时,求解区域中分布的结点数量非常大.如果用传统的全局结点搜索算法时计算量将十分巨大,因此,提出了求解域分解法以减小结点搜索的计算量.采用该方法时,结点搜索的范围就可以由整个求解域缩减到几个相关的子域中,从而大大地减少了无网格方法计算中的结点搜索时间.用该方法对理想流体的位势流动进行了数值模拟,发现:随结点数的增加,无网格方法所用时间与有限元方法相比越来越大;但与全局结点搜索无网格方法相比,本方法大大节省了计算时间.

In numerical simulation using meshless method, it usually concerns with searching nodes that are needed. In dealing with complex problems, there must be a great number of nodes distributed in computational domain. If traditional Node-Searching method is used here, it will be a burdensome task for the computer. So this paper proposed a new numerical arithmetic, Domain-Dividing method which meant that the domain could be divided into several subdomains. Therefore, one can search some corresponding subdomains but not the entire domain for the necessary nodes. It adopts the Node-Searching arithmetic to simulate the ideal flow over a cylinder, and shows that with the increase of the nodes in domain, the computational time of meshless method gets longer than that of finite element method, however compared with meshless method using conventional Node-Searching method, the arithmetic proposed here can spare much more time for searching nodes.