On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12310%2F22%3A43904870" target="_blank" >RIV/60076658:12310/22:43904870 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007/978-3-030-97549-4_59" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-030-97549-4_59</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-97549-4_59" target="_blank" >10.1007/978-3-030-97549-4_59</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

LARGE-SCALE SCIENTIFIC COMPUTING (LSSC 2021)

ISBN

978-3-030-97549-4

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

9

Strana od-do

515-523

Název nakladatele

SPRINGER INTERNATIONAL PUBLISHING AG

Místo vydání

CHAM

Místo konání akce

Sozopol

Datum konání akce

7. 6. 2021

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000893681300059