Multilevel augmented Lagrangian solvers for overconstrained contact formulations

Rolf Krause, Martin Weiser, Didier Auroux, Jean-Baptiste Caillau, Régis Duvigneau, Abderrahmane Habbal, Christine Malot, Olivier Pantz, Luc Pronzato, Ludovic Rifford, Roland Ruelle, Chiara Soresi
2021 ESAIM Proceedings and Surveys  
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
more » ... tigrid 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.
doi:10.1051/proc/202171175 fatcat:s65g5ahg4vefpho6lz7s47gmem