Factorization method for inverse time-harmonic elastic scattering with a single plane wave

Guanqiu Ma; Guanghui Hu

doi:10.3934/dcdsb.2022050

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2022, Volume 27, Issue 12: 7469-7492. Doi: 10.3934/dcdsb.2022050

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$ \varphi $

-attracting sets and estimate of their attractive velocity for infinite-dimensional dynamical systems

Factorization method for inverse time-harmonic elastic scattering with a single plane wave

Guanqiu Ma^1, and
Guanghui Hu^2, ,

1.
Department of Applied Mathematics, Beijing Computational Science Research Center, Beijing, 100193, China
2.
School of Mathematical Sciences and LPMC, Nankai Universtiy, Tianjin, 300071, China

^*Corresponding author: Guanghui Hu
^*Corresponding author: Guanghui Hu

Received: September 2021

Revised: January 2022

Early access: March 2022

Published: December 2022

This work is supported by NSFC 12071236 and NSAF U1930402

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Abstract

This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source in linear elasticity. The approach also applies to the compressional (resp. shear) part of the far-field pattern excited by a single compressional (resp. shear) plane wave. The one-wave factorization is based on the scattering data for a priori given testing scatterers. It can be regarded as a domain-defined sampling method and does not require forward solvers. We derive the spectral system of the far-field operator for rigid disks and show that, using testing disks, the one-wave factorization method can be justified independently of the classical factorization method.

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Figure 4.1. Illustration of a convex polygonal source term where $ O $ is corner point of $ D $

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