Live load matrix recovery from scattering data in linear elasticity

TL;DR

This paper presents new iterative algorithms for approximating unknown linear loads in 2D linear elasticity inverse scattering problems, demonstrating convergence for moderate loads through numerical experiments.

Contribution

It introduces novel iterative methods for recovering linear loads from scattering data and provides numerical evidence of their convergence.

Findings

Effective approximation of linear loads from scattering data.

Convergence demonstrated for moderate load magnitudes.

New algorithms outperform existing methods in specific scenarios.

Abstract

We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown linear load given by a square matrix. For both backscattering data and fixed-angle scattering data, we show how to obtain numerical approximations of the so-called Born approximations and propose new iterative algorithms that provide sequences of approximations to the unknown load. Numerical evidences of the convergence for not too large loads are also given.