A multilevel hierarchical preconditioner for thin elastic solids

In this study, a multilevel, recursively de ned preconditioner, for use with the Preconditioned Conjugate Gradient (PCG) algorithm in connection with the nite element analysis of elastostatics is developed. The preconditioner is constructed from a sequence of hierarchical vector spaces arising from the p-version of the nite element method. Results from parametric studies evaluating the e ects of skewed elements, orthotropic material properties, and extreme span ratios, for p=2 and 3 are given. The results indicate that the precon- ditioner may be used to produce an e cient solver. The e ciency of the iterative procedure is illustrated using thin elastic solids. Results indicate that the preconditioner developed herein can be used to produce an e cient iterative solver for two- and three-dimensional problems in structural mechanics.