A MULTIGRID SEMISMOOTH NEWTON METHOD FOR SEMILINEAR CONTACT PROBLEMS

• 来源期刊: 计算数学（英文版）
• 关键词: Contact problems Semismooth Newton methods Multigrid methods Error estimates
• 年，卷（期）: 2017,（4）
• 页码范围: 486-528
• 页数: 43页
• 语种: 英文
• DOI: 10.4208/jcm.1702-m2016-0679

摘要

This paper develops and analyzes multigrid semismooth Newton methods for a class of inequality-constrained optimization problems in function space which are motivated by and include linear elastic contact problems of Signorini type.We show that after a suitable Moreau-Yosida type regularization of the problem superlinear local convergence is obtained for a class of semismooth Newton methods.In addition,estimates for the order of the error introduced by the regularization are derived.The main part of the paper is devoted to the analysis of a multilevel preconditioner for the semismooth Newton system.We prove a rigorous bound for the contraction rate of the multigrid cycle which is robust with respect to sufficiently small regularization parameters and the number of grid levels.Moreover,it applies to adaptively refined grids.The paper concludes with numerical results.