Newton-type method for the variational discretization of topology optimization problems

Anton Evgrafov

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Abstract

We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, which we achieve by inverting a part of perturbed optimality conditions for the problem. In this way, the computational bottleneck is conveniently shifted from evaluating the merit function to a direction finding subproblem. The latter involves solving certain linearized PDEs, and the computational effort is similar to that of finding a gradient of the merit function in the traditional nested approach. We illustrate the performance of the algorithm on benchmark topology optimized problems in fluid mechanics.
Original languageEnglish
Title of host publicationProceedings of the 26th Nordic Seminar on Computational Mechanics
EditorsAnders Logg, André Massing, Kent-Andre Mardel
Publication date2013
Pages135-138
ISBN (Print)978-82-92593-12-7
Publication statusPublished - 2013
Event26th Nordic Seminar on Computational Mechanics - Oslo, Norway
Duration: 23 Oct 201325 Oct 2013
Conference number: 26
http://noacm.no/vpage/1/0/NSCM

Conference

Conference26th Nordic Seminar on Computational Mechanics
Number26
CountryNorway
CityOslo
Period23/10/201325/10/2013
Internet address

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