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Volume 29, Issue 3
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

J. Comp. Math., 29 (2011), pp. 324-340.

Published online: 2011-06

[An open-access article; the PDF is free to any online user.]

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  • 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

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

  • AMS Subject Headings

65N06.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-29-324, author = {Xiufang Feng, Zhilin Li, and Zhonghua Qiao}, title = {High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {3}, pages = {324--340}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1010-m3204}, url = {http://global-sci.org/intro/article_detail/jcm/8481.html} }
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 -

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.

Xiufang Feng, Zhilin Li, and Zhonghua Qiao. (2011). High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients. Journal of Computational Mathematics. 29 (3). 324-340. doi:10.4208/jcm.1010-m3204
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