Adaptive Learning on the Grids for Elliptic Hemivariational Inequalities

This paper introduces a deep learning method for solving an elliptic hemivariational inequality (HVI). In this method, an expectation minimization problem is first formulated based on the variational principle of underlying HVI, which is solved by stochastic optimization algorithms using three diffe...

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Bibliographic Details
Main Authors Huang, Jianguo, Wang, Chunmei, Wang, Haoqin
Format Journal Article
LanguageEnglish
Published 10.04.2021
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
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Summary:This paper introduces a deep learning method for solving an elliptic hemivariational inequality (HVI). In this method, an expectation minimization problem is first formulated based on the variational principle of underlying HVI, which is solved by stochastic optimization algorithms using three different training strategies for updating network parameters. The method is applied to solve two practical problems in contact mechanics, one of which is a frictional bilateral contact problem and the other of which is a frictionless normal compliance contact problem. Numerical results show that the deep learning method is efficient in solving HVIs and the adaptive mesh-free multigrid algorithm can provide the most accurate solution among the three learning methods.
DOI:10.48550/arxiv.2104.04881