Počet záznamů: 1
On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization
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SYSNO ASEP 0532969 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization Tvůrce(i) Brune, A. (GB)
Kočvara, Michal (UTIA-B) RID, ORCIDCelkový počet autorů 2 Zdroj.dok. SIAM Journal on Scientific Computing. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1064-8275
Roč. 42, č. 1 (2020), A28-A53Poč.str. 26 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova topology optimization ; multigrid methods ; interior point methods ; preconditioners for iterative methods ; augmented Lagrangian methods Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Způsob publikování Omezený přístup Institucionální podpora UTIA-B - RVO:67985556 UT WOS 000551241700029 EID SCOPUS 85083763340 DOI 10.1137/19M1254490 Anotace 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 Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2021 Elektronická adresa https://epubs.siam.org/doi/abs/10.1137/19M1254490
Počet záznamů: 1