A primal–dual active set strategy for nonlinear multibody contact problems. (English) Zbl 1093.74056

Summary: Non-conforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations. For the discretization of a nonlinear multibody contact problem, we use the mortar approach with a dual Lagrange multiplier space. To handle the nonlinearity of the contact conditions, we apply a primal-dual active set strategy to find the actual contact zone. The algorithm can be easily generalized to multibody contact problems. A suitable basis transformation guarantees the same algebraic structure in the multibody situation as in the one body case. Using an inexact primal-dual active set strategy in combination with a multigrid method yields an efficient iterative solver. Different numerical examples for one and multibody contact problems illustrate the performance of the method.


74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74B05 Classical linear elasticity


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