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Volume 6, Issue 5, 1 October 2022, Pages 483-498
Abstract. In this paper, we propose a deep neural network-based numerical method for solving contact problems. Focusing on a static frictionless unilateral contact problem, we derive its weak formulation and prove that the solution of the weak formulation is also the minimizer of the corresponding energy functional. By converting the original contact problem into a minimization problem, a deep neural network is adopted to approximate the solution and solve the minimization problem. Numerical results demonstrate the effectiveness and accuracy of our method.
How to Cite this Article:
Xing Shen, Xiaoliang Cheng, Kewei Liang, Xilu Wang, Zhenghua Wu, A deep neural network-based numerical method for solving contact problems, J. Nonlinear Var. Anal. 6 (2022), 483-498.