AN IMPROVED NODAL ORDERING FOR REDUCING THE BANDWIDTH IN FEM

Abstract

In finite element method, reducing the bandwidth of sparse symmetric matrices plays a key role to have an efficient solution. This problem can be simulated as a vertex numbering problem on a graph, where each edge represents two connected nodes in finite element mesh. In this paper, a new algorithm is proposed for a nodal ordering of the standard and randomly structured graphs to reduce the bandwidth of sparse symmetric matrices. A fast search algorithm for the location of pseudo-peripheral nodes is presented. This algorithm results in a bandwidth smaller than or equal to some existing algorithms such as the Cuthill–Mckee (CM) and the modified Gibbs–Poole– Stockmeyer (MGPS). With this approach, the bandwidth is reduced in more than 50% of instances of benchmark tests compared with the outcomes of the existing algorithms.