@Article{JCM-35-569, author = {Feng , TingtingKang , 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) 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1605-m2016-0540}, url = {http://global-sci.org/intro/article_detail/jcm/10032.html} }