Volume 35, Issue 5
Construction of GPT-Vanishing Structures Using Shape Derivative

Tingting Feng ,  Hyeonbae Kang and Hyundae Lee

10.4208/jcm.1605-m2016-0540

J. Comp. Math., 35 (2017), pp. 569-585.

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  • Abstract

The Generalized Polarization Tensors (GPT) is a series of tensors which contain informations on the shape of a domain and its material parameters. The aim of this paper is to provide a method of constructing GPT-vanishing structures using shape derivative for two-dimensional conductivity or anti-plane elasticity problem. We assume a multi-coating geometry as a candidate of GPT-vanishing structure. We define a cost functional to minimize GPT and compute the shape derivative of this functional deriving an asymptotic expansion of the perturbations of the GPTs due to a small deformation of interfaces of the structure. We present some numerical examples of GPT-vanishing structures for several different shaped inclusions.

  • History

Published online: 2017-10

  • AMS Subject Headings

65N06, 65B99.

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