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Isaac Newton Institute for Mathematical Sciences

Free boundary problem for GPT-vanishing structure

Presenter: Tingting Feng (Inha University)

Co-authors: Hyeonbae Kang (Inha University), Hyundae Lee (Inha University)


The Generalized Polarization Tensors (GPTs) contain significant information on the shape of the domain and its material parameter. The aim of our efforts is to provide a method of constructing GPT-vanishing structures using shape derivative for two-dimensional conductivity or anti-plane elasticity problem. We design an optimization approach which solves the problem by minimizing a cost functional. In order to compute the shape derivative of this functional, we rigorously derive an asymptotic expansion of the perturbations of the GPTs that are due to small deformations of the boundaries of the coatings. We also present some numerical examples of GPT-vanishing structures for several different shaped inclusions.