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

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

12 Citations (Scopus)
34 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 languageEnglish
Pages (from-to)720-749
JournalSIAM Journal on Applied Mathematics
Volume82
Issue number2
Online published27 Apr 2022
DOIs
Publication statusPublished - 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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