Efficient simulation of multi-body contact problems on complex geometries: A flexible decomposition approach using constrained minimization

We consider the numerical simulation of non-linear multi-body contact problems in elasticity on complex three-dimensional geometries. In the case of warped contact boundaries and non-matching finite element meshes, particular emphasis has to be put on the discretization of the transmission of forces and the non-penetration conditions at the contact interface. We enforce the discrete contact constraints by means of a non-conforming domain decomposition method, which allows for optimal error estimates. Here, we develop an efficient method to assemble the discrete coupling operator by computing the triangulated intersection of opposite element faces in a locally adjusted projection plane but carrying out the required quadrature on the faces directly. Our new element-based algorithm does not use any boundary parameterizations and is also suitable for isoparametric elements. The emerging non-linear system is solved by a monotone multigrid method of optimal complexity. Several numerical examples in 3D illustrate the effectiveness of our approach.