EFFECTIVE MEDIUM THEORY FOR EMBEDDED OBSTACLES IN ELASTICITY WITH APPLICATIONS TO INVERSE PROBLEMS

Qingle MENG; Zhengjian BAI; Huaian DIAO; Hongyu LIU

doi:10.1137/21M1431369

EFFECTIVE MEDIUM THEORY FOR EMBEDDED OBSTACLES IN ELASTICITY WITH APPLICATIONS TO INVERSE PROBLEMS

Qingle MENG, Zhengjian BAI, Huaian DIAO^*, Hongyu LIU

^*Corresponding author for this work

Department of Mathematics

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

12 Citations (Scopus)

44 Downloads (CityUHK Scholars)

Abstract

We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic elastic medium with a particular choice of material parameters. We derive sharp estimates to rigorously verify such an effective approximation. Our study is strongly motivated by the related studies of two challenging inverse elastic problems including the inverse boundary problem with partial data and the inverse scattering problem of recovering mediums with buried obstacles. The proposed effective medium theory readily yields some interesting applications of practical significance to these inverse problems.

Original language	English
Pages (from-to)	720-749
Journal	SIAM Journal on Applied Mathematics
Volume	82
Issue number	2
Online published	27 Apr 2022
DOIs	https://doi.org/10.1137/21M1431369
Publication status	Published - 2022

Funding

The work of the second author was partially supported by the National Natural Sci-ence Foundation of China under grant 11671337 and the Natural Science Foundation of Fujian Prov-ince of China under grant 2021J01033. The work of the third author was partially supported by JilinUniversity and the National Science Foudation of China under grant 1211101002 and NSFC/RGCJoint Research Fund (project 12161160314). The fourth author was supported by City Universityof Hong Kong, the Hong Kong RGC General Research Fund (projects 12301420, 12302919, and12301218), and the NSFC/RGC Joint Research Fund (project NCityU101/21).

Research Keywords

asymptotic analysis
effective medium theory
elastic scattering
embedded obstacle
inverse elastic problems
variational analysis

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2022, Society for Industrial and Applied Mathematics. MENG, Q., BAI, Z., DIAO, H., & LIU, H. (2022). EFFECTIVE MEDIUM THEORY FOR EMBEDDED OBSTACLES IN ELASTICITY WITH APPLICATIONS TO INVERSE PROBLEMS. SIAM Journal on Applied Mathematics, 82(2), 720-749. https://doi.org/10.1137/21M1431369.

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title = "EFFECTIVE MEDIUM THEORY FOR EMBEDDED OBSTACLES IN ELASTICITY WITH APPLICATIONS TO INVERSE PROBLEMS",

abstract = "We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic elastic medium with a particular choice of material parameters. We derive sharp estimates to rigorously verify such an effective approximation. Our study is strongly motivated by the related studies of two challenging inverse elastic problems including the inverse boundary problem with partial data and the inverse scattering problem of recovering mediums with buried obstacles. The proposed effective medium theory readily yields some interesting applications of practical significance to these inverse problems.",

keywords = "asymptotic analysis, effective medium theory, elastic scattering, embedded obstacle, inverse elastic problems, variational analysis",

author = "Qingle MENG and Zhengjian BAI and Huaian DIAO and Hongyu LIU",

year = "2022",

doi = "10.1137/21M1431369",

language = "English",

volume = "82",

pages = "720--749",

journal = "SIAM Journal on Applied Mathematics",

issn = "0036-1399",

publisher = "Society for Industrial and Applied Mathematics",

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T1 - EFFECTIVE MEDIUM THEORY FOR EMBEDDED OBSTACLES IN ELASTICITY WITH APPLICATIONS TO INVERSE PROBLEMS

AU - MENG, Qingle

AU - BAI, Zhengjian

AU - DIAO, Huaian

AU - LIU, Hongyu

PY - 2022

Y1 - 2022

N2 - We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic elastic medium with a particular choice of material parameters. We derive sharp estimates to rigorously verify such an effective approximation. Our study is strongly motivated by the related studies of two challenging inverse elastic problems including the inverse boundary problem with partial data and the inverse scattering problem of recovering mediums with buried obstacles. The proposed effective medium theory readily yields some interesting applications of practical significance to these inverse problems.

AB - We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic elastic medium with a particular choice of material parameters. We derive sharp estimates to rigorously verify such an effective approximation. Our study is strongly motivated by the related studies of two challenging inverse elastic problems including the inverse boundary problem with partial data and the inverse scattering problem of recovering mediums with buried obstacles. The proposed effective medium theory readily yields some interesting applications of practical significance to these inverse problems.

KW - asymptotic analysis

KW - effective medium theory

KW - elastic scattering

KW - embedded obstacle

KW - inverse elastic problems

KW - variational analysis

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U2 - 10.1137/21M1431369

DO - 10.1137/21M1431369

M3 - RGC 21 - Publication in refereed journal

SN - 0036-1399

VL - 82

SP - 720

EP - 749

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 2

ER -

EFFECTIVE MEDIUM THEORY FOR EMBEDDED OBSTACLES IN ELASTICITY WITH APPLICATIONS TO INVERSE PROBLEMS

Abstract

Funding

Research Keywords

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

GRF: Geometric Properties of Three Classes of Spectral Problems with Applications to Inverse Problems and Material Sciences

GRF: Mathematical and Computational Studies of Geomagnetic Anomaly Detections

Cite this

EFFECTIVE MEDIUM THEORY FOR EMBEDDED OBSTACLES IN ELASTICITY WITH APPLICATIONS TO INVERSE PROBLEMS

Abstract

Funding

Research Keywords

Publisher's Copyright Statement

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Permanent Link

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Projects

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

GRF: Geometric Properties of Three Classes of Spectral Problems with Applications to Inverse Problems and Material Sciences

GRF: Mathematical and Computational Studies of Geomagnetic Anomaly Detections

Cite this