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Multilevel augmented Lagrangian solvers for overconstrained contact formulations

  • 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.
Author:Rolf KrauseORCiD, Martin WeiserORCiD
Document Type:In Proceedings
Parent Title (English):ESAIM: ProcS
First Page:175
Last Page:184
Year of first publication:2021
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