A Hybrid Iterative Method for Elliptic Variational Inequalities of the Second Kind

doi:10.1007/s42967-024-00423-9

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (3): 910-928.doi: 10.1007/s42967-024-00423-9

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A Hybrid Iterative Method for Elliptic Variational Inequalities of the Second Kind

Yujian Cao^1,2, Jianguo Huang¹, Haoqin Wang³

1 School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China;
2 Alibaba Inc, Hangzhou 310056, Zhejiang, China;
3 Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2024-01-05 修回日期:2024-04-11 接受日期:2024-04-21 出版日期:2025-09-20 发布日期:2025-05-23
通讯作者: Jianguo Huang, jghuang@sjtu.edu.cn;Yujian Cao, 591795085@qq.com;Haoqin Wang, wanghaoqin@amss.ac.cn E-mail:jghuang@sjtu.edu.cn;591795085@qq.com;wanghaoqin@amss.ac.cn
基金资助:
The authors would like to thank two referees for valuable comments leading to an improvement of the earlier version of the paper. J. Huang was partially supported by the China National Key R&D Project (Grant No. 2020YFA0709800) and the National Natural Science Foundation of China (Grant No. 12071289).

A Hybrid Iterative Method for Elliptic Variational Inequalities of the Second Kind

Yujian Cao^1,2, Jianguo Huang¹, Haoqin Wang³

1 School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China;
2 Alibaba Inc, Hangzhou 310056, Zhejiang, China;
3 Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2024-01-05 Revised:2024-04-11 Accepted:2024-04-21 Online:2025-09-20 Published:2025-05-23
Supported by:
The authors would like to thank two referees for valuable comments leading to an improvement of the earlier version of the paper. J. Huang was partially supported by the China National Key R&D Project (Grant No. 2020YFA0709800) and the National Natural Science Foundation of China (Grant No. 12071289).

摘要/Abstract

摘要： A hybrid iterative method is proposed for numerically solving the elliptic variational inequality (EVI) of the second kind, through combining the regularized semi-smooth Newton method and the Int-Deep method. The convergence rate analysis and numerical examples on contact problems show this algorithm converges rapidly and is efficient for solving EVIs.

关键词: Deep learning, Semi-smooth Newton method, Elliptic variational inequality (EVI), Convergence rate analysis

Abstract: A hybrid iterative method is proposed for numerically solving the elliptic variational inequality (EVI) of the second kind, through combining the regularized semi-smooth Newton method and the Int-Deep method. The convergence rate analysis and numerical examples on contact problems show this algorithm converges rapidly and is efficient for solving EVIs.

Key words: Deep learning, Semi-smooth Newton method, Elliptic variational inequality (EVI), Convergence rate analysis

中图分类号:

Yujian Cao, Jianguo Huang, Haoqin Wang. A Hybrid Iterative Method for Elliptic Variational Inequalities of the Second Kind[J]. Communications on Applied Mathematics and Computation, 2025, 7(3): 910-928.

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A Hybrid Iterative Method for Elliptic Variational Inequalities of the Second Kind

A Hybrid Iterative Method for Elliptic Variational Inequalities of the Second Kind

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