A novel Newton method for inverse elastic scattering problems

Yan Chang; Yukun Guo; Hongyu Liu; Deyue Zhang

doi:10.1088/1361-6420/ad4dda

A novel Newton method for inverse elastic scattering problems

Yan Chang, Yukun Guo^*, Hongyu Liu, Deyue Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

Abstract

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method. © 2024 IOP Publishing Ltd.

Original language	English
Article number	075009
Journal	Inverse Problems
Volume	40
Issue number	7
Online published	12 Jun 2024
DOIs	https://doi.org/10.1088/1361-6420/ad4dda
Publication status	Published - Jul 2024

Funding

Y Chang and Y Guo were supported by the NSFC grant 11971133. H Liu was supported by the NSFC/RGC Joint Research Scheme, N_CityU101/21; ANR/RGC Joint Research Scheme, A-CityU203/19; and the Hong Kong RGC General Research Funds (projects 11311122, 12301420 and 11300821). D Zhang was supported by the NSFC grant 12171200.

Research Keywords

convergence
elastic wave
inverse scattering
Newton method

RGC Funding Information

RGC-funded

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10.1088/1361-6420/ad4dda

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title = "A novel Newton method for inverse elastic scattering problems",

abstract = "This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method. {\textcopyright} 2024 IOP Publishing Ltd.",

keywords = "convergence, elastic wave, inverse scattering, Newton method",

author = "Yan Chang and Yukun Guo and Hongyu Liu and Deyue Zhang",

year = "2024",

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doi = "10.1088/1361-6420/ad4dda",

language = "English",

volume = "40",

journal = "Inverse Problems",

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TY - JOUR

T1 - A novel Newton method for inverse elastic scattering problems

AU - Chang, Yan

AU - Guo, Yukun

AU - Liu, Hongyu

AU - Zhang, Deyue

PY - 2024/7

Y1 - 2024/7

N2 - This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method. © 2024 IOP Publishing Ltd.

AB - This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method. © 2024 IOP Publishing Ltd.

KW - convergence

KW - elastic wave

KW - inverse scattering

KW - Newton method

UR - http://www.scopus.com/inward/record.url?scp=85196027610&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85196027610&origin=recordpage

U2 - 10.1088/1361-6420/ad4dda

DO - 10.1088/1361-6420/ad4dda

M3 - RGC 21 - Publication in refereed journal

SN - 0266-5611

VL - 40

JO - Inverse Problems

JF - Inverse Problems

IS - 7

M1 - 075009

ER -

A novel Newton method for inverse elastic scattering problems

Abstract

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GRF: Mathematical Study of Fields Concentration and Gradient Estimates with Applications

NSFC: A Mathematical Theory of Subwavelength Resonances in Elasticity with Applications and Beyond

GRF: Mathematical Studies of Surface-localized Transmission Eigenstates and Applications

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A novel Newton method for inverse elastic scattering problems

Abstract

Funding

Research Keywords

RGC Funding Information

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Projects

GRF: Mathematical Study of Fields Concentration and Gradient Estimates with Applications

NSFC: A Mathematical Theory of Subwavelength Resonances in Elasticity with Applications and Beyond

GRF: Mathematical Studies of Surface-localized Transmission Eigenstates and Applications

Cite this