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On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method
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SYSNO ASEP 0563211 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method Author(s) Gfrerer, H. (AT)
Outrata, Jiří (UTIA-B) RID, ORCID
Valdman, Jan (UTIA-B) RID, ORCIDSource Title Large-Scale Scientific Computing. - Cham : Springer, 2022 / Lirkov I. ; Margenov S. - ISSN 0302-9743 - ISBN 978-3-030-97548-7 Pages s. 515-523 Number of pages 9 s. Publication form Print - P Action International Conference on Large-Scale Scientific Computing /13./ Event date 07.06.2021 - 11.06.2021 VEvent location Sozopol Country BG - Bulgaria Event type WRD Language eng - English Country CH - Switzerland Keywords Contact problems ; Tresca friction ; Semismooth* Newton method ; Finite elements ; Matlab implementation Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GF19-29646L GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000893681300059 EID SCOPUS 85127132123 DOI 10.1007/978-3-030-97549-4_59 Annotation An equilibrium of a linear elastic body subject to loading and satisfying the friction and contact conditions can be described by a variational inequality of the second kind and the respective discrete model attains the form of a generalized equation. To its numerical solution we apply the semismooth* Newton method by Gfrerer and Outrata (2019) in which, in contrast to most available Newton-type methods for inclusions, one approximates not only the single-valued but also the multi-valued part. This is performed on the basis of limiting (Morduchovich) coderivative. In our case of the Tresca friction, the multi-valued part amounts to the subdifferential of a convex function generated by the friction and contact conditions. The full 3D discrete problem is then reduced to the contact boundary. Implementation details of the semismooth* Newton method are provided and numerical tests demonstrate its superlinear convergence and mesh independence. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2023
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