Parallel multilevel preconditioners for thin smooth shell finite element analysis. (Q2713564)

An algorithm is proposed for the finite element analysis of smooth shell problems. The author uses Koiter's shell theory and two types of finite elements: Bogner-Fox-Schmit or non-conforming Adini elements over uniform rectangular partitions of the subdomains, for all three components of the displacement vector field. He generalizes some results of \textit{P. Oswald} and \textit{H. Matthes} [Nonoverlapping domain decomposition method for parallelizing and preconditioning iterative procedures for the solution of plate and shell problems Technische Universität Chemnitz-Zwickau Fakultät Matematik (1997; Zbl 0931.74072)], concerning (i) additive multilevel preconditioners of Bramble, Pasciak and Xu and (ii) multilevel diagonal scaling of \textit{X. Zhang}, to general smooth elastic shells.NEWLINENEWLINEAn efficient implementation of the multilevel preconditioners in conjugate gradient method is based on a non-overlapping Dirichlet domain decomposition method of Haase, Langer and Meyer. The detailed description of the algorithm and a proof of an auxiliary lemma is available in some preprints. Numerical examples for plates, arches, spheres, hyperboloids and some more complicated shapes of the shells are presented. The efficiency of the parallelization with regard to the number of subdomains (i.e., to the number of processors) is studied in detail.