Since the introduction of Finite Element Tearing and Interconnecting (FETI) by 10 Farhat and Roux in 1991, the method has been recognized to be an efficient parallel technique 11 for the solution of partial differential equations. In 2003 Langer and Steinbach formulated its 12 boundary element counterpart (BETI), which reduces the problem dimension to subdomain 13 boundaries. Recently, we have ...

We propose a class of method for the adaptive selection of the coarse space of the BDDC and FETI-DP iterative substructuring methods. The methods work by adding coarse degrees of freedom constructed from eigenvectors associated with intersections of selected pairs of adjacent substructures. It is assumed that the starting coarse degrees of freedom are already sufficient to prevent relative rigi...

Our goal is to solve nonlinear contact problems. We consider bodies in contact with each other divided into subdomains, which in turn are unions of elements. The contact surface between the bodies is unknown a priori, and we have a nonpenetration condition between the bodies, which is essentially an inequality constraint. We choose to use an active set method to solve such problems, which has b...

In this paper, we present some numerical results for a Balancing and a FETI method for the solution of a linear system arising from the edge element approximation of a vector field problem in two dimensions. The two methods are presented as projected preconditioned conjugate algorithms and give comparable performances in our tests. Our numerical results show that their condition number is indep...

The Boundary Element Tearing and Interconnecting (BETI) methods have recently been introduced as boundary element counterparts of the well–established Finite Element Tearing and Interconnecting (FETI) methods. In this paper we present inexact data–sparse versions of the BETI methods which avoid the elimination of the primal unknowns and dense matrices. However, instead of symmetric and positive...

Interface boundary conditions are the key ingredient to design efficient domain decomposition methods. However, convergence cannot be obtained for any method in a number of iterations less than the number of subdomains minus one in the case of a one-way splitting. This optimal convergence can be obtained with generalized Robin type boundary conditions associated with an operator equal to the Sc...