Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates

Authors

  • Xiaolu Su School of Mathematics and Computer Science, NingXia University, YinChuan, 750021, China
  • Xiufang Feng School of Mathematics and Computer Science, NingXia University, YinChuan, 750021, China
  • Zhilin Li Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA Nanjing Normal University, Nanjing, China

DOI:

https://doi.org/10.4208/jcm.1604-m2015-0290

Keywords:

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

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.

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Published

2018-08-22

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Issue

Vol. 34 No. 5 (2016)

Section

Articles

How to Cite

Fourth-Order Compact Schemes for Helmholtz Equations with Piecewise Wave Numbers in the Polar Coordinates. (2018). Journal of Computational Mathematics, 34(5), 499-510. https://doi.org/10.4208/jcm.1604-m2015-0290