Abstract:
Generally, imposing contact constraints with Lagrange multiplier method on the numerical simulation of contact problems in structural mechanics, it can cause a large-scale discrete saddle point system. Due to the indefiniteness of the saddle point matrix and the resolve difficulty, a two-level preconditioning method with novel interpolation approach was proposed to solve the two-dimensional tied contact problem. It was arranged that single-step convergence could be achieved with any smooth method when the coarse grid system was solved accurately. Furthermore, the constructed coarse grid operator should be symmetric positive definite, reflect the contact constraints effectively. The results of numerical experiments show that this method can achieve convergence with a relatively small number of iterations and high computational efficiency in various contact models, can reduce the computation time up to 80% compared with the SIMPLE method. Furthermore, this method presents strong robustness under different contact constraint conditions, being suitable for large-scale computation.