TY - JOUR
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
UR - http://www.scopus.com/inward/record.url?scp=85126940745&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85126940745&origin=recordpage
U2 - 10.1137/21M1431369
DO - 10.1137/21M1431369
M3 - RGC 21 - Publication in refereed journal
VL - 82
SP - 720
EP - 749
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 2
ER -