局部网格生成中初始探索圆半径的搜索算法

无网格不一致性的基于节点的局部网格生成(NLMG)算法是基于节点的局部有限元方法(NLFEM)实现无缝连接的核心算法之一,而快速合理的确定中心节点的初始探索圆半径是降低NLMG算法计算量和确保其可靠性的关键一步。本文提出了基于均匀桶的快速局部搜索算法(UBFLSM),并将其成功应用于NLMG算法,解决了初始探索圆半径和探索圆半径优化后候选卫星点集的确定这两个难点,确保NLMG算法无网格不一致性。并/串行数值试验(实现从网格生成到总刚度矩阵生成之间的无缝连接)均表明,该算法是快速及可靠的。

Searching algorithm for initial exploring circle radius in NLMG

Node-based Local Mesh Generation(NLMG) algorithm that is free of grid inconsistency is one of core algorithms in the Node-based Local Finite Element Method(NLFEM) to achieve the seamless connection between mesh generation and stiffness matrix computing.Besides,evaluating the radius of initial exploring circle of each current central node quickly and reasonably is a decisive step to reduce the computing cost and to ensure the reliability of the NLMG algorithm.This paper develops the Uniform Bucket-based Fast Local Search Method(UBFLSM) used in NLMG algorithm,and then applies it successfully to find the appropriate initial exploring circle radius and to prepare the candidate nodes set as well.Comparing with the other two methods such as the Global search method and the Uniform Bucket-based Local Search Method,the UBFLSM save computing cost remarkably.About the optimal bucket density,the paper advises to make the number of uniform buckets to be about half of the number of the nodes used in the solving domain for the two dimensional problem.Both parallel and sequential numerical experiment results,given in Tab.1 and 2 and Fig.5 through 7 in the full paper,show that UBFLSM can be implemented in NLMG algorithms effectively and reliably.