TY - JOUR
T1 - Perfectly Matched Layer Method for Acoustic Scattering Problem by a Locally Perturbed Line with Impedance Boundary Condition
AU - Jiang , Xue
AU - Li , Xujing
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 101
EP - 140
PY - 2019
DA - 2019/12
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0047
UR - https://global-sci.org/intro/article_detail/aamm/13421.html
KW - Uniaxial perfectly matched layer, Helmholtz equation, locally perturbed half-plane, impedance condition.
AB - <p style="text-align: justify;">In this paper, we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition. Different from the problem with Dirichlet boundary condition, the Green function of the Helmholtz equation with impedance boundary condition becomes very complicated and comprises surface waves along the locally perturbed line. A uniaxial perfectly matched layer (UPML) method is proposed to truncate the half plane into a bounded computational domain.&nbsp; The main contribution of this paper is to prove the well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution as either the thickness or the medium parameter of PML increases.</p>