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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Format: | Article |
Language: | English |
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SpringerOpen
2019-01-01
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Series: | Journal of Inequalities and Applications |
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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. |
first_indexed | 2024-12-11T06:07:39Z |
format | Article |
id | doaj.art-29efaad47e0a416d82d1ca3e2b28a2a2 |
institution | Directory Open Access Journal |
issn | 1029-242X |
language | English |
last_indexed | 2024-12-11T06:07:39Z |
publishDate | 2019-01-01 |
publisher | SpringerOpen |
record_format | Article |
series | Journal of Inequalities and Applications |
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 |
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