A Self-Adaptive Alternating Direction Multiplier Method for Frictionless Elastic Contact Problems北大核心CSCD

A self⁃adaptive alternating direction multiplier method was designed for frictionless elastic contact problems. An augmented Lagrange function was introduced for the variational formulation of the problem with an auxiliary variable, to deduce a minimization problem and an equivalent saddle⁃point problem. Then the alter⁃ nating direction multiplier method was used to solve the problem. To enhance the performance of the algo⁃ rithm, a self⁃adaptive rule based on the iterative function on the boundary was proposed to automatically select the proper penalty parameter. The advantage of this algorithm is that, each iteration only needs to solve a linear variational problem and explicitly calculate the auxiliary variable and the Lagrange multiplier. The convergence of the algorithm was analyzed theoretically. The numerical results illustrate the feasibility and effectiveness of the proposed method. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.