@article{a7a08e07f770474dad05792e6ef2d3e7,
title = "High order compact finite difference schemes for the Helmholtz equation with discontinuous coefficients",
abstract = "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.",
keywords = "Compact finite difference scheme, Discontinuous media, Helmholtz equation, Immersed interface method, Nine-point stencil",
author = "Xiufang Feng and Zhilin Li and Zhonghua Qiao",
note = "Funding information: We would like to thank Dr. Semyon Tsynkov for useful discussions. The first author was partially supported by the Key Project of Chinese Ministry of Education Grant No. 209134. Part of the work was done when the first author visited NC State University. The second author was partialy supported by the US ARO grants 56349MA-MA, and 550694-MA, and the AFSOR grant FA9550-09-1-0520, and the US NSF grant DMS-0911434. The third author was partially supported by Hong Kong Baptist University grant FRG/08-09/II-35. Publisher copyright: {\textcopyright} Global Science Press",
year = "2011",
month = may,
doi = "10.4208/jcm.1010-m3204",
language = "English",
volume = "29",
pages = "324--340",
journal = "Journal of Computational Mathematics",
issn = "0254-9409",
publisher = "Global Science Press",
number = "3",
}