Alternating direction method of multiplier for the unilateral contact problem with an automatic penalty parameter selection. (English) Zbl 1481.49031
Summary: We propose an alternating direction method of multiplier (ADMM) for the unilateral (frictionless) contact problem with an optimal parameter selection. We first introduce an auxiliary unknown to seprate the linear elasticity subproblem from the unilateral contact condition. Then an alternating direction is applied to the corresponding augmented Lagrangian. By eliminating the primal and auxiliary unknowns, at the discrete level, we derive a pure dual algorithm, starting point for the convergence analysis and the optimal parameter approximation. Numerical experiments are proposed to illustrate the efficiency of the proposed (optimal) penalty parameter selection method.
MSC:
| 49M37 | Numerical methods based on nonlinear programming |
| 49J10 | Existence theories for free problems in two or more independent variables |
| 74M15 | Contact in solid mechanics |
Software:
KOKO Mesh GeneratorReferences:
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