TY - JOUR
T1 - Numerical Solution of an Inverse Obstacle Scattering Problem for Elastic Waves via the Helmholtz Decomposition
AU - Junhong Yue, Ming Li, Peijun Li & Xiaokai Yuan
JO - Communications in Computational Physics
VL - 3
SP - 809
EP - 837
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0194
UR - https://global-sci.org/intro/article_detail/cicp/13148.html
KW - The elastic wave equation, inverse obstacle scattering, domain derivative, the Helmholtz decomposition.
AB - <p style="text-align: justify;">Consider an inverse obstacle scattering problem in an open space which
is filled with a homogeneous and isotropic elastic medium. The inverse problem is
to determine the obstacle&#39;s surface from the measurement of the displacement on an
artificial boundary enclosing the obstacle. In this paper, a new approach is proposed
for numerical solution of the inverse problem. By introducing two scalar potential
functions, the method uses the Helmholtz decomposition to split the displacement of
the elastic wave equation into the compressional and shear waves, which satisfy a
coupled boundary value problem of the Helmholtz equations. The domain derivative
is studied for the coupled Helmholtz system. In particular, we show that the domain
derivative of the potentials is the Helmholtz decomposition of the domain derivative
of the displacement for the elastic wave equation. Numerical results are presented to
demonstrate the effectiveness of the proposed method.</p>