Enhancement of Near Cloaking Using Generalized Polarization Tensors Vanishing Structures. Part I: The Conductivity Problem

TL;DR

This paper introduces a novel method for constructing near-cloaking structures in conductivity problems by ensuring their first Generalized Polarization Tensors vanish, significantly improving cloaking effectiveness.

Contribution

It presents a new approach to design structures with vanishing Generalized Polarization Tensors, enhancing near-cloaking in conductivity applications.

Findings

Vanishing of the first Generalized Polarization Tensors improves cloaking.

Numerical examples demonstrate the effectiveness of the proposed structures.

Abstract

The aim of this paper is to provide an original method of constructing very effective near-cloaking structures for the conductivity problem. These new structures are such that their first Generalized Polarization Tensors vanish. We show that this in particular significantly enhances the cloaking effect. We then present some numerical examples of Generalized Polarization Tensors vanishing structures.