The Generalized Polarization Tensors （GPT） is a series of tensors which contain infor- mations on the shape of a domain and its material parameters. The aim of this paper is to provide a method of constructing GPT-v...The Generalized Polarization Tensors （GPT） is a series of tensors which contain infor- mations 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 min- imize 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.展开更多
文摘The Generalized Polarization Tensors （GPT） is a series of tensors which contain infor- mations 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 min- imize 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.
