TY - JOUR
T1 - Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates
AU - Su , Xiaolu
AU - Feng , Xiufang
AU - Li , Zhilin
JO - Journal of Computational Mathematics
VL - 5
SP - 499
EP - 510
PY - 2016
DA - 2016/10
SN - 34
DO - http://doi.org/10.4208/jcm.1604-m2015-0290
UR - https://global-sci.org/intro/article_detail/jcm/9809.html
KW - Helmholtz equation, Compact finite difference schemes, Polar coordinate, The immersed interface method, High order method.
AB - <p style="text-align: justify;">In this paper, fourth-order compact finite difference schemes are proposed for solving Helmholtz equation with piecewise wave numbers in polar coordinates with axis-symmetric and in some cases that the solution depends both of independent variables. The idea of the immersed interface method is applied to deal with the discontinuities in the wave number and certain derivatives of the solution. Numerical experiments are included to confirm the accuracy and efficiency of the proposed method.</p>