Volume 34, Issue 5
Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates

Xiaolu Su, Xiufang Feng & Zhilin Li

DOI: 10.4208/jcm.1604-m2015-0290

J. Comp. Math., 34 (2016), pp. 499-510.

Published online: 2016-10

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  • Abstract

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.

  • Keywords

Helmholtz equation Compact finite difference schemes Polar coordinate The immersed interface method High order method

  • AMS Subject Headings

65M06 65N06.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

614590197@qq.com (Xiaolu Su)

xf_feng@nxu.edu.cn (Xiufang Feng)

zhilin.li@gmail.com (Zhilin Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-499, author = {Su , Xiaolu and Feng , Xiufang and Li , Zhilin }, title = {Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {5}, pages = {499--510}, abstract = { 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.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1604-m2015-0290}, url = {http://global-sci.org/intro/article_detail/jcm/9809.html} }
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 KW - Compact finite difference schemes KW - Polar coordinate KW - The immersed interface method KW - High order method AB - 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.
Xiaolu Su , Xiufang Feng & Zhilin Li . (2020). Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates. Journal of Computational Mathematics. 34 (5). 499-510. doi:10.4208/jcm.1604-m2015-0290
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