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.
A Discontinuous Galerkin Method for H(curl)-Elliptic Hemivariational Inequalities
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Department of Mathematics, University of Iowa（爱荷华大学数学系）；School of Mathematical Sciences, Inner Mongolia University（内蒙古大学数学科学学院）
