On conditioning of constraints arising from variationally consistent discretization of contact problems and duality based solvers

Abstract

Variationally consistent approximation of the non-penetration conditions and friction laws was introduced by Wohlmuth [Acta Numer. 20 (2011) 569–734] as a powerful tool for the effective discretization of contact problems. This approach is especially useful when the potential contact interface is large and curved or when non-matching grids are applied. The point of this note is to give bounds on the singular values of the constraint matrices arising from the variationally consistent approximation and to indicate their application in the analysis of the scalable duality based domain decomposition algorithms for the solution of multi-body contact problems [Comput. Methods Appl. Mech. Eng. 247–248 (2012), 37–50.]. The theoretical results are illustrated by numerical experiments.