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://doi.org/10.4208/jcm.1605-m2016-0540
UR - https://global-sci.org/intro/article_detail/jcm/10032.html
KW - Generalized polarization tensor, Asymptotic expansions, Shape derivative.
AB - <p style="text-align: justify;">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.</p>