Two-Dimensional Elastic Scattering Coefficients and Enhancement of Nearly Elastic Cloaking

TL;DR

This paper introduces elastic scattering coefficients for inclusions, develops a reconstruction algorithm for inverse scattering, and demonstrates their use in enhancing nearly elastic cloaking with stability and resolution analyses.

Contribution

It presents a new framework for elastic scattering coefficients, a reconstruction method from multi-static data, and designs structures to improve cloaking performance.

Findings

Reconstruction algorithm effectively extracts scattering coefficients.

Scattering-coefficients-vanishing structures enhance cloaking.

Analysis of decay, stability, and resolution limits.

Abstract

The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to mathematical imaging and elastic cloaking, the notion of elastic scattering coefficients of an inclusion is presented from the perspective of boundary layer potentials and a few properties are discussed. A reconstruction algorithm is developed and analyzed for extracting the elastic scattering coefficients from multi-static response measurements of the scattered field in order to cater to inverse scattering problems. The decay rate, stability and error analyses, and the estimate of maximal resolving order in terms of the signal-to-noise ratio are discussed. Moreover, scattering-coefficients-vanishing structures are designed and their utility for enhancement of nearly elastic cloaking is elucidated.