  In this paper, a fully aggregation-based algebraic multigrid strategy is
developed for nonlinear contact problems of saddle point type using a mortar
finite element approach. While the idea of extending multigrid methods to
saddle point systems can already be found, e.g., in the context of Stokes and
Oseen equations in literature, the main contributions of this work are (i) the
development and open-source implementation of an interface aggregation strategy
specifically suited for generating Lagrange multiplier aggregates that are
required for coupling structural equilibrium equations with contact constraints
and (ii) a review of saddle point smoothers in the context of constrained
interface problems. The new interface aggregation strategy perfectly fits into
an aggregation-based multigrid framework and can easily be combined with
segregated transfer operators, which allow to preserve the saddle point
structure on the coarse levels. Further analysis provides insight into saddle
point smoothers applied to contact problems, while numerical experiments
illustrate the robustness of the new method. We have implemented the proposed
algorithm within the MueLu package of the open-source Trilinos project.
Numerical examples demonstrate the robustness of the proposed method in complex
dynamic contact problems as well as its scalability up to 23.9 million unknowns
on 480 MPI ranks.
