TY - JOUR
T1 - An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems
AU - Zhiming Chen & Xinming Wu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 113
EP - 137
PY - 2008
DA - 2008/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6044.html
KW - Adaptivity, uniaxial perfectly matched layer, a posteriori error analysis, acoustic scattering problems.
AB - <p style="text-align: justify;">The uniaxial perfectly matched layer (PML) method uses rectangular domain
to define the PML problem and thus provides greater flexibility and efficiency in dealing with problems involving anisotropic scatterers. In this paper an adaptive uniaxial
PML technique for solving the time harmonic Helmholtz scattering problem is developed. The PML parameters such as the thickness of the layer and the fictitious medium
property are determined through sharp a posteriori error estimates. The adaptive finite
element method based on a posteriori error estimate is proposed to solve the PML equation which produces automatically a coarse mesh size away from the fixed domain and
thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. Numerical experiments are included to illustrate the competitive behavior of
the proposed adaptive method. In particular, it is demonstrated that the PML layer can
be chosen as close to one wave-length from the scatterer and still yields good accuracy
and efficiency in approximating the far fields.</p>