VŠB – Technical University of Ostrava

The thesis focuses on the solution of both coercive and semi–coercive contact problems by using the Boundary Element Tearing and Interconnecting (BETI) method, which represents a boundary element counterpart of the Finite Element Tearing and Interconnecting (FETI) method. The BETI approach, which uses “tearing” the domain into non–overlapping subdomains and subsequent “gluing” along the artificial interfaces by Lagrange multipliers, is based on the symmetric discretization of the local Steklov–Poincaré operator and its suitable boundary element approximation. We combine BETI with the preconditioning by the projectors to the so–called natural coarse grid and apply recently proposed optimal algorithms for the solution of bound and equality constrained quadratic programming problems in order to develop a theoretically supported scalable solver for elliptic boundary variational inequalities. In the following text, we cover particularly the application of BETI to two chosen model contact problems. The first one is a 2D semi–coercive multibody contact problem described by the Laplace operator and the second one is a 3D coercive contact problem of linear homogeneous isotropic elastostatics. The theoretical results are validated by the numerical experiments which demonstrate the scalability of the presented method. Finally, we discuss our first results obtained for 3D Hertz problem.