High order compact finite difference schemes for the Helmholtz equation with discontinuous coefficients

Xiufang Feng; Zhilin Li; Zhonghua Qiao

doi:10.4208/jcm.1010-m3204

High order compact finite difference schemes for the Helmholtz equation with discontinuous coefficients

Xiufang Feng^*
, Zhilin Li
, Zhonghua Qiao

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

45 Citations (Scopus)

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.

Original language	English
Pages (from-to)	324-340
Number of pages	17
Journal	Journal of Computational Mathematics
Volume	29
Issue number	3
DOIs	https://doi.org/10.4208/jcm.1010-m3204
Publication status	Published - May 2011

User-Defined Keywords

Compact finite difference scheme
Discontinuous media
Helmholtz equation
Immersed interface method
Nine-point stencil

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10.4208/jcm.1010-m3204

Cite this

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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",

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AU - Feng, Xiufang

AU - Li, Zhilin

AU - Qiao, Zhonghua

N1 - 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: © Global Science Press

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N2 - 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.

AB - 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.

KW - Compact finite difference scheme

KW - Discontinuous media

KW - Helmholtz equation

KW - Immersed interface method

KW - Nine-point stencil

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DO - 10.4208/jcm.1010-m3204

M3 - Journal article

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SP - 324

EP - 340

JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

IS - 3

ER -

High order compact finite difference schemes for the Helmholtz equation with discontinuous coefficients

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