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A Multigrid Semismooth Newton Method for Semilinear Contact Problems

A Multigrid Semismooth Newton Method for Semilinear Contact Problems
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Year:    2017

Author:    Michael Ulbrich, Stefan Ulbrich, Daniela Bratzke

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 4 : pp. 486–528

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1702-m2016-0679

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 4 : pp. 486–528

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    43

Keywords:    Contact problems Semismooth Newton methods Multigrid methods Error estimates.

Author Details

Michael Ulbrich

Stefan Ulbrich

Daniela Bratzke

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