A Self-Adaptive Alternating Direction Multiplier Method for Frictionless Elastic Contact Problems

YUAN Xin; ZHANG Shougui

doi:10.21656/1000-0887.440079

Volume 44 Issue 8

Aug. 2023

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YUAN Xin, ZHANG Shougui. A Self-Adaptive Alternating Direction Multiplier Method for Frictionless Elastic Contact Problems[J]. Applied Mathematics and Mechanics, 2023, 44(8): 989-998. doi: 10.21656/1000-0887.440079

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A Self-Adaptive Alternating Direction Multiplier Method for Frictionless Elastic Contact Problems

doi: 10.21656/1000-0887.440079

YUAN Xin,
ZHANG Shougui^,

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China

Received Date: 2023-03-24
Rev Recd Date: 2023-04-24
Publish Date: 2023-08-01

Abstract

Abstract

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 alternating direction multiplier method was used to solve the problem. To enhance the performance of the algorithm, 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.
- elastic contact problem,
- alternating direction multiplier method,
- self-adaptive rule,
- augmented Lagrange function

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References(18)

References

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