CONSTRUCTION OF GPT-VANISHING STRUCTURES USING SHAPE DERIVATIVE

• 来源期刊: 计算数学（英文版）
• 关键词: Generalized polarization tensor Asymptotic expansions Shape derivative
• 年，卷（期）: 2017,（5）
• 页码范围: 569-585
• 页数: 17页
• 语种: 英文
• DOI: 10.4208/jcm.1605-m2016-0540

摘要

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.