Volume 71, August 2021FGS’2019 - 19th French-German-Swiss conference on Optimization
|Page(s)||175 - 184|
|Published online||01 September 2021|
Multilevel augmented Lagrangian solvers for overconstrained contact formulations*
Università della Svizzera italiana, Via G. Buffi 13, 6990 Lugano, Switzerland
2 Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany
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.
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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