Scalable TFETI based algorithm with adaptive augmentation for contact problems with variationally consistent discretization of contact conditions.

Abstract A variationally consistent approximation of contact conditions by means of biorthogonal mortars was introduced by Wohlmuth as a powerful theoretically supported tool for the discretization of contact problems. This approach is especially useful when a potential contact interface is large and curved or when nonmatching grids are applied, but its effective implementation into FETI based algorithms is not straightforward due to the ill conditioning of related inequality constraints. In this paper we review the mortar discretization and theoretical results on scalability of the FETI based algorithm and show that the recently proposed adaptive augmentation can overcome the difficulties caused by the ill-conditioning of constraints. We demonstrate the (weak) numerical scalability by numerical experiments and present the results for a difficult real world problem discretized by mortars that show the power of the new algorithm – the number of iterations required to the solution of this problem discretized by mortars is just one third of that required by the original algorithm for the same problem discretized by node-to-node constraints. Highlights • The paper reviews the bounds on the conditioning of matrices arising from mortar discretization of non-penetration conditions. • The theoretical results support the scalability of FETI methods for the solution of multibody frictionless contact problems are given. • The (weak) scalability is demonstrated by the solution of a variant of the Hertz problem. • Moreover, the solution of a difficult real world problem shows that the new algorithm autperforms its predecessors. [ABSTRACT FROM AUTHOR]