Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

Abstract

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 is not new and can be found, e.g., in the context of Stokes and Oseen equations in literature, the main contributions of this work are (i) the development 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) an analysis of saddle point smoothers in the context of constrained interface problems. The proposed method is simpler to implement, computationally less expensive than the ideas from [1], and -in the authors' opinion -the presented approach is more intuitive for contact 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.

Distributed prediction of unsafe reconfiguration scenarios of modular robotic Programmable Matter

“…A special version must be devised, however, to take into account the specific computing architecture of the modular robot and the contact conditions. One of such methods has been recently proposed [31], [32]. • It is possible to reduce the number of degrees of freedom of the system by applying multi-scale methods or model order reduction techniques [33], [34].…”