Multilevel augmented Lagrangian solvers for overconstrained contact formulations*

• Main Authors: Krause Rolf, Weiser Martin
• Format: Article
• Language: English
• Published: EDP Sciences 2021-08-01
• Series: ESAIM: Proceedings and Surveys
• Online Access: https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107116.pdf

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.