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Construction of GPT-Vanishing Structures Using Shape Derivative

Construction of GPT-Vanishing Structures Using Shape Derivative
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Year:    2017

Author:    Tingting Feng, Hyeonbae Kang, Hyundae Lee

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 5 : pp. 569–585

Abstract

The Generalized Polarization Tensors (GPT) are a series of tensors which contain information 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1605-m2016-0540

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 5 : pp. 569–585

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Generalized polarization tensor Asymptotic expansions Shape derivative.

Author Details

Tingting Feng

Hyeonbae Kang

Hyundae Lee

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