On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00532969" target="_blank" >RIV/67985556:_____/20:00532969 - isvavai.cz</a>

Výsledek na webu

<a href="https://epubs.siam.org/doi/abs/10.1137/19M1254490" target="_blank" >https://epubs.siam.org/doi/abs/10.1137/19M1254490</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/19M1254490" target="_blank" >10.1137/19M1254490</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization

Popis výsledku v původním jazyce

One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum compliance formulation of the variable thickness sheet (VTS) problem, which is equivalent to a convex problem. We propose to solve the VTS problem by the penalty-barrier multiplier (PBM) method, introduced by R. Polyak and later studied by Ben-Tal and Zibulevsky and others. The most computationally expensive part of the algorithm is the solution of linear systems arising from the Newton method used to minimize a generalized augmented Lagrangian. We use a special structure of the Hessian of this Lagrangian to reduce the size of the linear system and to convert it to a form suitable for a standard multigrid method. This converted system is solved approximately by a multigrid

Název v anglickém jazyce

On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization

Popis výsledku anglicky

One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum compliance formulation of the variable thickness sheet (VTS) problem, which is equivalent to a convex problem. We propose to solve the VTS problem by the penalty-barrier multiplier (PBM) method, introduced by R. Polyak and later studied by Ben-Tal and Zibulevsky and others. The most computationally expensive part of the algorithm is the solution of linear systems arising from the Newton method used to minimize a generalized augmented Lagrangian. We use a special structure of the Hessian of this Lagrangian to reduce the size of the linear system and to convert it to a form suitable for a standard multigrid method. This converted system is solved approximately by a multigrid

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure 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

SIAM Journal on Scientific Computing

ISSN

1064-8275

e-ISSN

—

Svazek periodika

42

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

"A28"-"A53"

Kód UT WoS článku

000551241700029

EID výsledku v databázi Scopus

2-s2.0-85083763340