On the spectrum of Schur complements of 2D elastic clusters joined by rigid edge modes and hybrid domain decomposition

The hybrid FETI-DP method proposed by Klawonn and Rheinbach uses a two-level decomposition of the domain into subdomains and clusters. Here we give bounds on the regular condition number of the clusters obtained by interconnecting the Schur complements of square elastic subdomains by the average rigid body modes of adjacent edges. Using the angles of subspaces and bounds on the spectrum of the subdomains' Schur complements, we show that the conditioning of clusters comprising in x m square subdomains increases proportionally to m. The estimate supports the scalability of the unpreconditioned hybrid FETI-DP method for both linear and contact problems. The numerical experiments confirm the efficiency of a coarse grid split between the primal and dual variables and indicate that hybrid FETI-DP with large clusters is a competitive tool for solving huge elasticity problems.