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.