Two-Level Domain Decomposition Preconditioning For The p-Version Finite Element Method In Three Dimensions

. This paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiffness matrices only. The method is applied to the p-version finite element method for three-dimensional elasticity. We treat each element as a subdomain and compute explicit convergence bounds. 1. Introduction. This paper is concerned with a class of methods of the domain decomposition type for the solution of linear systems arising by discretization of selfadjoint elliptic systems. The general principle is then applied to the p-version finite element method for the elasticity problem, which yields a natural, discretization-driven decomposition and parallelization of the problem. We show that one can obt...