TY - JOUR
T1 - High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients
AU - Xiufang Feng, Zhilin Li, & Zhonghua Qiao
JO - Journal of Computational Mathematics
VL - 3
SP - 324
EP - 340
PY - 2011
DA - 2011/06
SN - 29
DO - http://doi.org/10.4208/jcm.1010-m3204
UR - https://global-sci.org/intro/article_detail/jcm/8481.html
KW - Helmholtz equation, Compact finite difference scheme, Discontinuous media,
Immersed interface method, Nine-point stencil.
AB - <p style="text-align: justify;">In this paper, third- and fourth-order compact finite difference schemes are proposed for solving Helmholtz equations with discontinuous media along straight interfaces in two space dimensions. To keep the compactness of the finite difference schemes and get global high order schemes, even at the interface where the wave number is discontinuous, the idea of the immersed interface method is employed. Numerical experiments are included to confirm the efficiency and accuracy of the proposed methods.</p>