摘要
为克服目前无网格法布点技术仅适用于特定问题的缺点,在分析节点生成技术数学本质的基础上,提出了一种基于模拟退火算法的无网格节点生成技术。该算法结合k-means方法和模拟退火算法(SA)求解约束条件下的多峰值函数全局最小值,在待求计算域内和边界自动生成无网格计算节点,且节点为计算域对应质心Voronoi结构的质心点。该算法可以普遍用于包括凹域和多连通域等任意形状域的布点计算,尤其适用于给定边界节点位置情况下域内无网格节点的生成问题。将所生成节点用线段连接起来,也可以直接得到有限元网格。
A k-means method was combined with a simulated annealing （SA） algorithm to determine point sets for meshless numerical analysis algorithems. The method can be used in all kinds of domains since it calculates the global minimum of a constrained multi-extrema function to get high-quality centroidal Voronoi tessellations for the region. The method can be used in any irregular domain including concave and multiply connected domains, and is especially useful for problems with prescribed boundary points. In addition, the method can be used to generate finite element meshes by just connecting the points with lines.
出处
《清华大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2008年第6期959-962,共4页
Journal of Tsinghua University(Science and Technology)
基金
国家自然科学基金资助项目(50639060
50579029)
