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Domain expression of the shape derivative and application to electrical impedance tomography

Please always quote using this URN:urn:nbn:de:0296-matheon-12703
  • The well-known structure theorem of Hadamard-Zol\'esio states that the derivative of a shape functional is a distribution on the boundary of the domain depending only on the normal perturbations of a smooth enough boundary. However a volume representation (distributed shape derivative) is more general than the boundary form and allows to work with shapes having a lower regularity. It is customary in the shape optimization literature to assume regularity of the domains and use the boundary expression of the shape derivative for numerical algorithm. In this paper we describe the numerous advantages of the distributed shape derivative in terms of generality, easiness of computation and numerical implementation. We give several examples of numerical applications such as the inverse conductivity problem and the level set method.

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Metadaten
Author:Antoine Laurain
URN:urn:nbn:de:0296-matheon-12703
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/12/18
Release Date:2013/12/18
Tag:Shape optimization; electrical impedance tomography; level set method
Institute:Technische Universität Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Project:C Energy and Materials (Production) / C37 Shape/Topology optimization methods for inverse problems
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q93 PDEs in connection with control and optimization
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Qxx Manifolds [See also 58Exx] / 49Q10 Optimization of shapes other than minimal surfaces [See also 90C90]
Preprint Number:1047
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