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Title
A convex analysis approach to multi-material topology optimization.
AuthorClason, Christian ; Kunisch, Karl
Published in
ESAIM: Mathematical Modelling and Numerical Analysis, 2016, Vol. 50, Issue 6, page 1917-1936
PublishedEDP Sciences, 2016
Edition
Accepted version
LanguageEnglish
Document typeJournal Article
Keywords (EN)Topology optimization / convex analysis / convexification / semi-smooth Newton method
ISSN1290-3841
URNurn:nbn:at:at-ubg:3-3530 Persistent Identifier (URN)
DOI10.1051/m2an/2016012 
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 The work is publicly available
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Abstract (English)

This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available materials. A "multibang" framework based on convex analysis is proposed where the desired piecewise constant structure is incorporated using a convex penalty term. Together with a suitable tracking term, this allows formulating the problemof optimizing the topology of the distribution of material parameters as minimizing a convex functional subject to a (nonlinear) equality constraint. The applicability of this approach is validated for two model problems where the control enters as a potential and a diffusion coefficient, respectively. This is illustrated in both cases by numerical results based on a semismooth Newton method.

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