求解双层弹性膜单侧接触问题的自适应交替方向乘子法
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作者单位:

1.重庆师范大学 数学科学学院;2.中冶赛迪重庆信息技术有限公司

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基金项目:

国家自然科学基金项目(面上项目,重点项目,重大项目)


An Alternating Direction Multiplier Method for the Unilateral Contact of Two Membranes
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Affiliation:

1.Chongqing Normal University;2.CISDI Information Technology Co. , Ltd.

Fund Project:

The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    【目的】对一类双层弹性膜单侧接触问题,提出了基于自适应罚参数的交替方向乘子法。【方法】利用辅助变量构造增广Lagrange函数,通过引入鞍点问题处理不等式约束。然后用交替方向乘子法对该问题进行数值求解,每次迭代包括两个线性椭圆问题,显式求解辅助变量和Lagrange乘子。【结果】基于迭代函数的自适应法则自动调整罚参数,给出了算法收敛性和自适应罚参数近似方法。【结论】最后用有限元离散化数值结果验证了算法的有效性。

    Abstract:

    [Purposes]We propose an alternating direction method of multiplier for approximation solution of the unilateral contact problem of two membranes, with a self-adaptive penalty parameter. [Methods]By using augmented Lagrange functional with an auxiliary unknown, a saddle-point problem is introduced to deal with the inequality constrained. Then the alternating direction method of multiplier is applied to the corresponding problem, and each iteration consists of two linear elliptic problems while the auxiliary unknown and the Lagrange multiplier are computed explicitly. A self-adaptive rule based iterative functions is used to automatically adjust the penalty parameter. [Findings]We show the convergence of the method and give the self-adaptive penalty parameter approximation. [Conclusions]Finally, the numerical experiments with the finite element discretization are given to illustrate the efficiency of the proposed method.

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  • 收稿日期:2023-11-15
  • 最后修改日期:2024-04-01
  • 录用日期:2024-06-19
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