Fast inverse elastic scattering of multiple particles in three dimensions

TL;DR

This paper presents a fast and efficient method for inverse elastic scattering in three dimensions, capable of accurately recovering the shape and location of multiple particles using far field data and advanced computational techniques.

Contribution

It introduces a novel combination of asymptotic analysis and a fast multipole-based algorithm for inverse elastic scattering of multiple particles.

Findings

The method accurately determines particle locations and shapes.

It efficiently handles multiple scattering problems.

Numerical experiments validate the instant determination of particles.

Abstract

Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three dimensions. We measure the far field information and apply the time reversal method to recover the unknown elastic particles. Two regimes are considered depending on the size and distance among particles. First, an asymptotic analysis for the imaging of small and distant particles is given based on the scattering property of a single particle, which can be used for selective focusing. Second, when particles are not small but well-separated, a fast algorithm, based on the combination of multiple scattering theory and fast multipole method, is proposed to efficiently simulate the forward multiple scattering problem and applied in the inverse elastic scattering. Numerical experiments demonstrate the proposed method can determine the locations and shapes of multiple particles instantly.