An improved algorithm for matrix bandwidth and profile reduction in finite element analysis

Abstract

In finite element analysis, methods for the solution of sparse linear systems of equations usually start out with reordering the coefficient matrix to reduce its bandwidth or profile. The location of pseudo-peripheral nodes is an important factor in the bandwidth and profile reduction algorithm. This paper presents a heuristic parameter, called the width-depth ratio and denoted by κ. With such a parameter, suitable pseudo-peripheral nodes would be found; the distance between which could be much close to or even to be the diameter of a graph compared with Gibbs-Poole-Stockmeyer (GPS) algorithm. As the new parameter was implemented in GPS algorithm, an improved bandwidth and profile reduction algorithm is proposed. Simulation results show that with the proposed algorithm, sometimes bandwidth and profile could be reduced by as great as 33.33% and 11.65%, respectively, compared with the outcomes in GPS algorithm, while the execution time of both algorithms is close. Empirical results show that the proposed algorithm is superior to GPS algorithm in reducing bandwidth or profile.