Non-Monotone Projected Gradient Method in Linear Elasticity Contact Problems with Given Friction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00559266" target="_blank" >RIV/68145535:_____/20:00559266 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27120/20:10245722 RIV/61989100:27240/20:10245722 RIV/61989100:27730/20:10245722

Výsledek na webu

<a href="https://www.mdpi.com/2071-1050/12/20/8674" target="_blank" >https://www.mdpi.com/2071-1050/12/20/8674</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/su12208674" target="_blank" >10.3390/su12208674</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Non-Monotone Projected Gradient Method in Linear Elasticity Contact Problems with Given Friction

Popis výsledku v původním jazyce

We are focusing on the algorithms for solving the large-scale convex optimization problem in linear elasticity contact problems discretized by Finite Element method (FEM). The unknowns of the problem are the displacements of the FEM nodes, the corresponding objective function is defined as a convex quadratic function with symmetric positive definite stiffness matrix and additional non-linear term representing the friction in contact. The feasible set constraints the displacement subject to non-penetration conditions. The dual formulation of this optimization problem is well-known as a Quadratic Programming (QP) problem and can be considered as a most basic non-linear optimization problem. Understanding these problems and the development of efficient algorithms for solving them play the crucial role in the large-scale problems in practical applications. We shortly review the theory and examine the behavior and the efficiency of Spectral Projected Gradient method modified for QP problems (SPG-QP) on the solution of a toy example in MATLAB environment.

Název v anglickém jazyce

Non-Monotone Projected Gradient Method in Linear Elasticity Contact Problems with Given Friction

Popis výsledku anglicky

We are focusing on the algorithms for solving the large-scale convex optimization problem in linear elasticity contact problems discretized by Finite Element method (FEM). The unknowns of the problem are the displacements of the FEM nodes, the corresponding objective function is defined as a convex quadratic function with symmetric positive definite stiffness matrix and additional non-linear term representing the friction in contact. The feasible set constraints the displacement subject to non-penetration conditions. The dual formulation of this optimization problem is well-known as a Quadratic Programming (QP) problem and can be considered as a most basic non-linear optimization problem. Understanding these problems and the development of efficient algorithms for solving them play the crucial role in the large-scale problems in practical applications. We shortly review the theory and examine the behavior and the efficiency of Spectral Projected Gradient method modified for QP problems (SPG-QP) on the solution of a toy example in MATLAB environment.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Sustainability

ISSN

2071-1050

e-ISSN

2071-1050

Svazek periodika

12

Číslo periodika v rámci svazku

20

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

11

Strana od-do

8674

Kód UT WoS článku

000583086900001

EID výsledku v databázi Scopus

2-s2.0-85093122217