Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem

Abstract A semismooth Newton method, based on variational inequalities and generalized derivative, is designed and analysed for unilateral contact problem between two membranes. The problem is first formulated as a corresponding regularized problem with a nonlinear function, which can be solved by t...

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Main Authors: Shougui Zhang, Yueyue Yan, Ruisheng Ran
Format: Article
Language:English
Published: SpringerOpen 2019-01-01
Series:Journal of Inequalities and Applications
Subjects:
Online Access:http://link.springer.com/article/10.1186/s13660-019-1955-4
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author Shougui Zhang
Yueyue Yan
Ruisheng Ran
author_facet Shougui Zhang
Yueyue Yan
Ruisheng Ran
author_sort Shougui Zhang
collection DOAJ
description Abstract A semismooth Newton method, based on variational inequalities and generalized derivative, is designed and analysed for unilateral contact problem between two membranes. The problem is first formulated as a corresponding regularized problem with a nonlinear function, which can be solved by the semismooth Newton method. We prove the convergence of the method in the function space. To improve the performance of the semismooth Newton method, we use the path-following method to adjust the parameter automatically. Finally, some numerical results are presented to illustrate the performance of the proposed method.
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spelling doaj.art-29efaad47e0a416d82d1ca3e2b28a2a22022-12-22T01:18:15ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-01-012019111310.1186/s13660-019-1955-4Path-following and semismooth Newton methods for the variational inequality arising from two membranes problemShougui Zhang0Yueyue Yan1Ruisheng Ran2School of Mathematical Sciences, Chongqing Normal UniversitySchool of Mathematical Sciences, Chongqing Normal UniversityCollege of Computer and Information Science, Chongqing Normal UniversityAbstract A semismooth Newton method, based on variational inequalities and generalized derivative, is designed and analysed for unilateral contact problem between two membranes. The problem is first formulated as a corresponding regularized problem with a nonlinear function, which can be solved by the semismooth Newton method. We prove the convergence of the method in the function space. To improve the performance of the semismooth Newton method, we use the path-following method to adjust the parameter automatically. Finally, some numerical results are presented to illustrate the performance of the proposed method.http://link.springer.com/article/10.1186/s13660-019-1955-4Unilateral contactElastic membranesVariational inequalitySemismooth Newton methodPath-following method
spellingShingle Shougui Zhang
Yueyue Yan
Ruisheng Ran
Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
Journal of Inequalities and Applications
Unilateral contact
Elastic membranes
Variational inequality
Semismooth Newton method
Path-following method
title Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
title_full Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
title_fullStr Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
title_full_unstemmed Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
title_short Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
title_sort path following and semismooth newton methods for the variational inequality arising from two membranes problem
topic Unilateral contact
Elastic membranes
Variational inequality
Semismooth Newton method
Path-following method
url http://link.springer.com/article/10.1186/s13660-019-1955-4
work_keys_str_mv AT shouguizhang pathfollowingandsemismoothnewtonmethodsforthevariationalinequalityarisingfromtwomembranesproblem
AT yueyueyan pathfollowingandsemismoothnewtonmethodsforthevariationalinequalityarisingfromtwomembranesproblem
AT ruishengran pathfollowingandsemismoothnewtonmethodsforthevariationalinequalityarisingfromtwomembranesproblem