Geodesic
Multilevel augmented Lagrangian solvers for overconstrained contact formulations
Rolf Krause1 ; Martin Weiser2
1 Università della Svizzera italiana, Via G. Buffi 13, 6990 Lugano, Switzerland
2 Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany
ESAIM. Proceedings, Tome 71 (2021), pp. 175-184.

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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.
DOI : 10.1051/proc/202171175

Rolf Krause 1 ; Martin Weiser 2

1 Università della Svizzera italiana, Via G. Buffi 13, 6990 Lugano, Switzerland
2 Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany 
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     title = {Multilevel augmented {Lagrangian} solvers for overconstrained contact formulations},
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Rolf Krause; Martin Weiser. Multilevel augmented Lagrangian solvers for overconstrained contact formulations. ESAIM. Proceedings, Tome 71 (2021), pp. 175-184. doi : 10.1051/proc/202171175. http://geodesic.mathdoc.fr/articles/10.1051/proc/202171175/

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