TY - JOUR
T1 - An Optimal 9-Point Finite Difference Scheme for the Helmholtz Equation with PML
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 389
EP - 410
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/574.html
KW - Helmholtz equation, PML, 9-point finite difference scheme, numerical dispersion.
AB - <p style="text-align: justify;">In this paper, we analyze the defect of the rotated 9-point finite difference scheme,
and present an optimal 9-point finite difference scheme for the Helmholtz equation with perfectly
matched layer (PML) in two dimensional domain. For this method, we give an error analysis
for the numerical wavenumber’s approximation of the exact wavenumber. Moreover, based on
minimizing the numerical dispersion, we propose global and refined choice strategies for choosing
optimal parameters of the 9-point finite difference scheme. Numerical experiments are given to
illustrate the improvement of the accuracy and the reduction of the numerical dispersion.</p>