一种有限元网格节点编号的优化算法

Optimal Algorithm of Node Numbering in Finite Element Mesh

为提高有限元的计算效率,减少计算数据所需在存储量,提出节点编号优化算法。通过对在网格半带宽最小时的节点排列的一些特征进行分析,从其中归纳出3条规律,通过算例验证了该规律的正确性和可靠性。结果表明,对于任意划分的有限元网格,利用该方法对节点重新编号,可得到较小的半带宽值,节省了计算机的内存空间,提高了计算效率。

For the sake of enhancing the efficiency of finite element computation, and reducing the needed amount of storage of computation data. In the paper, an optimal method for node labels in the finite element is presented, which is an inductive and deductive method. By the analysis to the order features of the nodes when the network bandwidth is the minimum value, we can induce three regulars. Testing a large number of examples, which show that the presented scheme can reduce bandwidth for arbitrary mesh by renumbering the nodes, proves the correctness and reliability of the regulars. Thus the memory of computer is saved and the compute efficiency is improved.