Volume 52, Number 1, January–February 2018
|Page(s)||275 - 303|
|Published online||04 May 2018|
Total variation regularization of multi-material topology optimization
Faculty of Mathematics, University Duisburg-Essen,
2 Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria
3 Radon Institute, Austrian Academy of Sciences, Linz, Austria
* Corresponding author: firstname.lastname@example.org
Accepted: 28 November 2017
This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is proposed which involves total variation regularization combined with a suitably chosen cost functional that promotes the diffusion coefficient assuming prespecified values at each point of the domain. The main difficulty lies in the delicate functional-analytic structure of the resulting nondifferentiable optimization problem with pointwise constraints for functions of bounded variation, which makes the derivation of useful pointwise optimality conditions challenging. To cope with this difficulty, a novel reparametrization technique is introduced. Numerical examples using a regularized semismooth Newton method illustrate the structure of the obtained diffusion coefficient.
Mathematics Subject Classification: 49Q10 / 49K20 / 49M15
Key words: Topology optimization / total variation / convex analysis / non-smooth optimization / semi-smooth Newton method
© EDP Sciences, SMAI 2018
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