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.