Interior point method for 3D contact problems with fiction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F12%3A33142073" target="_blank" >RIV/61989592:15310/12:33142073 - isvavai.cz</a>

Výsledek na webu

<a href="http://kmd.fp.tul.cz/sna/sna-sbornik2012-final_OPR.pdf" target="_blank" >http://kmd.fp.tul.cz/sna/sna-sbornik2012-final_OPR.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Interior point method for 3D contact problems with fiction

Popis výsledku v původním jazyce

We consider the problem of minimization of convex quadratic function subject to linear and quadratic constraints. Such minimizations arise from the finite element approximation of contact problems of linear elasticity with friction in 3D. We generalize the path-following (PF) variant of the interior point method that was proposed for solving linear programming problems. The main idea consists in applying the Newton iterations to solve equations in the (modified) system of the KKT conditions. The most expensive part of each iteration is the solution of an indefinite linear system. As the matrices are typically ill-conditioned, preconditioners are needed. Our preconditioners are optimal in the sense that condition numbers of the preconditioned matrices are bounded by a constant multiple of the condition number of the Hessian matrix of the given quadratic function.

Název v anglickém jazyce

Interior point method for 3D contact problems with fiction

Popis výsledku anglicky

We consider the problem of minimization of convex quadratic function subject to linear and quadratic constraints. Such minimizations arise from the finite element approximation of contact problems of linear elasticity with friction in 3D. We generalize the path-following (PF) variant of the interior point method that was proposed for solving linear programming problems. The main idea consists in applying the Newton iterations to solve equations in the (modified) system of the KKT conditions. The most expensive part of each iteration is the solution of an indefinite linear system. As the matrices are typically ill-conditioned, preconditioners are needed. Our preconditioners are optimal in the sense that condition numbers of the preconditioned matrices are bounded by a constant multiple of the condition number of the Hessian matrix of the given quadratic function.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název statě ve sborníku

SNA'12. Seminar on Numerical Analysis. Winter School.

ISBN

978-80-7372-821-2

ISSN

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e-ISSN

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Počet stran výsledku

4

Strana od-do

108-112

Název nakladatele

Technická univerzita v Liberci

Místo vydání

Liberec

Místo konání akce

Liberec

Datum konání akce

23. 1. 2012

Typ akce podle státní příslušnosti

CST - Celostátní akce

Kód UT WoS článku

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