On Shape Optimization for an Evolution Coupled System

Leugering G, Novotny AA, Menzala GP, Sokolowski J (2011)

Publication Type: Journal article

Publication year: 2011

Journal

Applied Mathematics and Optimization Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 64

Pages Range: 441--466

Volume: 64

Issue: 3

Journal Issue: 3

DOI: 10.1007/s00245-011-9148-7

Abstract

A shape optimization problem in three spatial dimensions for an elasto-dynamic piezoelectric body coupled to an acoustic chamber is introduced. Well-posedness of the problem is established and first order necessary optimality conditions are derived in the framework of the boundary variation technique. In particular, the existence of the shape gradient for an integral shape functional is obtained, as well as its regularity, sufficient for applications e.g. in modern loudspeaker technologies. The shape gradients are given by functions supported on the moving boundaries. The paper extends results obtained by the authors in (Math. Methods Appl. Sci. 33(17):2118–2131, 2010) where a similar problem was treated without acoustic coupling.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Additional Organisation(s)

Exzellenz-Cluster Engineering of Advanced Materials

Involved external institutions

National Laboratory of Scientific Computing / Laboratório Nacional de Computação Científica (LNCC) BR Brazil (BR) Université de Lorraine FR France (FR)

How to cite

APA:

Leugering, G., Novotny, A.A., Menzala, G.P., & Sokolowski, J. (2011). On Shape Optimization for an Evolution Coupled System. Applied Mathematics and Optimization, 64(3), 441--466. https://dx.doi.org/10.1007/s00245-011-9148-7

MLA:

Leugering, Günter, et al. "On Shape Optimization for an Evolution Coupled System." Applied Mathematics and Optimization 64.3 (2011): 441--466.

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