Parameter unbounded Uzawa and penalty-splitted accelerated algorithms for frictionless contact problems
This work addresses the slow convergence and high sensitivity to penalty or augmentation parameters that plague conventional splitting iterative methods for frictionless contact problems. To overcome these limitations, the authors propose a two-step displacement–contact force splitting strategy that integrates the Uzawa algorithm with penalty-operator splitting and incorporates Crossed-Secant fixed-point acceleration. The method requires only repeated solves with the standard stiffness matrix and, for the first time, achieves efficient convergence without bounds on algorithmic parameters—thereby eliminating the stringent parameter restrictions inherent in traditional approaches. Numerical experiments on both academic and industrial three-dimensional contact examples demonstrate significantly accelerated convergence, confirming the method’s efficiency and robustness.