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

Tingting Feng, Hyeonbae Kang & Hyundae Lee

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

Published online: 2017-10

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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.

  • Keywords

Generalized polarization tensor Asymptotic expansions Shape derivative

  • AMS Subject Headings

65N06 65B99.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

passionting@163.com (Tingting Feng)

hbkang@inha.ac.kr (Hyeonbae Kang)

hdlee@inha.ac.kr (Hyundae Lee)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-569, author = {Feng , Tingting and Kang , Hyeonbae and Lee , Hyundae }, title = {Construction of GPT-Vanishing Structures Using Shape Derivative}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {5}, pages = {569--585}, 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.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1605-m2016-0540}, url = {http://global-sci.org/intro/article_detail/jcm/10032.html} }
TY - JOUR T1 - Construction of GPT-Vanishing Structures Using Shape Derivative AU - Feng , Tingting AU - Kang , Hyeonbae AU - Lee , Hyundae JO - Journal of Computational Mathematics VL - 5 SP - 569 EP - 585 PY - 2017 DA - 2017/10 SN - 35 DO - http://dor.org/10.4208/jcm.1605-m2016-0540 UR - https://global-sci.org/intro/article_detail/jcm/10032.html KW - Generalized polarization tensor KW - Asymptotic expansions KW - Shape derivative AB - 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.
Tingting Feng , Hyeonbae Kang & Hyundae Lee . (2020). Construction of GPT-Vanishing Structures Using Shape Derivative. Journal of Computational Mathematics. 35 (5). 569-585. doi:10.4208/jcm.1605-m2016-0540
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