Synthetic Bandwidth Optimization Algorithm of Finite Element Node Numbering

摘要

A new synthetic algorithm for node renumbering optimization problem is put forward to enhance computational efficiency in finite element method (FEM). At First, it is more reasonable to sort the nodes in a certain layer by the nodal span or nodal quotient, not by the nodal degree, in the GPS algorithm, so a smaller bandwidth can be obtained. And then, by employing a set of suitable rules for node exchanges, the bandwidth is sequentially optimized by an iterative algorithm called as gradually advanced bandwidth optimization algorithm (GABOA). In the end, the validity and reliability of the method is checked and validated by a few numerical experiments including a real-life node renumbering scheme on micromachined gyroscope structure. It is shown that the GABOA is more suitable to the bandwidth post-optimization problem. In most cases, GABOA can reduce the bandwidth of current node renumbering scheme, even though this bandwidth has been considered as an optimum result of GPS or other bandwidth reduction, algorithms.