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

0532969 - ÚTIA 2021 RIV US eng J - Journal Article
Brune, A. - Kočvara, Michal
On Barrier and Modified Barrier Multigrid Methods for Three-Dimensional Topology Optimization.
SIAM Journal on Scientific Computing. Roč. 42, č. 1 (2020), A28-A53. ISSN 1064-8275. E-ISSN 1095-7197
Institutional support: RVO:67985556
Keywords : topology optimization * multigrid methods * interior point methods * preconditioners for iterative methods * augmented Lagrangian methods
OECD category: Pure mathematics
Impact factor: 2.373, year: 2020
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2020/MTR/kocvara-0532969.pdf https://epubs.siam.org/doi/abs/10.1137/19M1254490

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
Permanent Link: http://hdl.handle.net/11104/0311788