A primal–dual active set strategy for non-linear multibody contact problems

Non-conforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations. For the discretization of a non-linear multibody contact problem, we use the mortar approach with a dual Lagrange multiplier space. To handle the non-linearity 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.