Multilevel hybrid spectral element ordering algorithms

For frontal solvers to perform well on finite‐element problems it is essential that the elements are ordered for a small wavefront. Multilevel element ordering algorithms have their origins in the profile reduction algorithm of Sloan but for large problems often give significantly smaller wavefronts. We examine a number of multilevel variants with the aim of finding the best methods to include within a new state‐of‐the‐art frontal solver for finite‐element applications that we are currently developing. Numerical experiments are performed using a range of problems arising from real applications and comparisons are made with existing element ordering algorithms. Copyright © 2005 John Wiley & Sons, Ltd.