A MULTIGRID SEMISMOOTH NEWTON METHOD FOR SEMILINEAR CONTACT PROBLEMS

作     者：Michael Ulbrich Stefan Ulbrich Daniela Bratzke 

作者机构：Technische Universitat Miinchen Department of Mathematics Garching b. Munchen Germany Technische Universitiit Darmstadt Department of Mathematics Darmstadt Germany Technische Universitat Darmstadt Department of Mathematics Darmstadt Germany 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2017年第35卷第4期

页      面：486-528页

核心收录：

学科分类：07[理学] 

基　　金：supported by DFG 

主　　题：Contact problems Semismooth Newton methods Multigrid methods Errorestimates. 

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 tile 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.