Number of the records: 1
On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization
- 1.
SYSNO ASEP 0532969 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization Author(s) Brune, A. (GB)
Kočvara, Michal (UTIA-B) RID, ORCIDNumber of authors 2 Source Title SIAM Journal on Scientific Computing. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1064-8275
Roč. 42, č. 1 (2020), A28-A53Number of pages 26 s. Publication form Print - P Language eng - English Country US - United States Keywords topology optimization ; multigrid methods ; interior point methods ; preconditioners for iterative methods ; augmented Lagrangian methods Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support UTIA-B - RVO:67985556 UT WOS 000551241700029 EID SCOPUS 85083763340 DOI 10.1137/19M1254490 Annotation 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 Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2021 Electronic address https://epubs.siam.org/doi/abs/10.1137/19M1254490
Number of the records: 1