Keywords: FETI method, domain decomposition, convergence, dual operator conditioning, gluing conditions, corner nodes quartets, aggregation into clusters.

FETI-type domain decomposition methods are one of the most effective solvers for systems of linear equations, e.g. those arising during FEM-discretization of problems from mechanics. The main idea is to decompose the domain of interest into non-overlapping subdomains, including doubling nodes at subdomain interfaces, "gluing" these doubled nodes using Lagrange multipliers, and then eliminating the primary unknowns. For simplicity, we will stick to the problem of 2D linear elasticity. Gluing conformally discretized subdomains is straightforward for doubled nodes and leads to rows in the gluing matrix containing two non-zero values: 1 and -1. These rows of the gluing matrix are usually normalized. However, a problem arises for the nodes lying in the place where 4 neigbouring subdomains meet in one point. There exist a number of ways of gluing degrees of freedom belonging to these nodes. This paper investigates variants of interconnecting corresponding quartets of coincident subdomain corners for the 2D decomposed, FEM-discretized, problem of linear elasticity. Both the convergence and spectral properties (conditioning) of the corresponding dual operators for each variant of interconnection for TFETI and for HTFETI, for 2 ways of aggregation of subdomains in larger complexes called clusters, are compared.

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