A multilevel hierarchical preconditioner for thin elastic solids

Abstract

In this study, a multilevel, recursively defined preconditioner, for use with the Preconditioned Conjugate Gradient (PCG) algorithm in connection with the finite element analysis of elastostatics is developed. The preconditioner is constructed from a sequence of hierarchical vector spaces arising from the p‐version of the finite element method. Results from parametric studies evaluating the effects of skewed elements, orthotropic material properties, and extreme span ratios, for p=2 and 3 are given. The results indicate that the preconditioner may be used to produce an efficient solver. The efficiency of the iterative procedure is illustrated using thin elastic solids. Results indicate that the preconditioner developed herein can be used to produce an efficient iterative solver for two‐ and three‐dimensional problems in structural mechanics. © 1998 John Wiley & Sons, Ltd.