Two-Level preconditioning method for solving saddle point systems in contact computation

In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. Given that the saddle point matrix is indefinite, solving these systems presents significant challenges. For a two-dimensional tied contact problem, an efficient two-level preconditioning method is developed. This method utilizes physical quantities for coarsening, introducing two types of interpolation operators and corresponding smoothing algorithms. Additionally, the constructed coarse grid operator exhibits symmetry and positive definiteness, adequately reflecting the contact constraints. Numerical results show the effectiveness of the method.