Parallel multilevel preconditioners for thin smooth shell finite element analysis

Abstract

In recent years multilevel preconditioners like BPX have become more and more popular for solving second-order elliptic finite element discretizations by iterative methods. P. Oswald has adapted these methods for discretizations of the fourth order biharmonic problem by rectangular conforming Bogner-Fox-Schmit elements and non-conforming Adini elements and has derived optimal estimates for the condition numbers of the preconditioned linear systems. In this paper we generalize the results from Oswald to the construction of parallel BPX and multilevel diagonal scaling (MDS-BPX) preconditioners for the elasticity problem of thin smooth shells in connection with Koiter's shell theory. We use the two discretizations mentioned above and the preconditioned conjugate gradient method as iterative method. The parallelization concept is based on a non-overlapping domain decomposition data structure. We describe the implementations of the parallel multilevel preconditioners. Finally, we show numerical results for some shells representing elliptic, parabolic, hyperbolic and more complicated classes. In addition, the influence of the thickness parameter and the loading on the preconditioner are investigated experimentally. Copyright © 1999 John Wiley & Sons, Ltd.