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Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates

Published online by Cambridge University Press:  24 March 2015

Kun Wang ,
Yau Shu Wong  and
Jian Deng
Kun Wang*
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P.R. China Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G 2G1, Canada
Yau Shu Wong
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G 2G1, Canada
Jian Deng
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G 2G1, Canada
*
*Corresponding author. Email addresses: wk580@163.com (K. Wang), yauwong@ualberta.ca (Y. S. Wong), deng2@ualberta.ca (J. Deng)
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Abstract

This paper presents new finite difference schemes for solving the Helmholtz equation in the polar and spherical coordinates. The most important result presented in this study is that the developed difference schemes are pollution free, and their convergence orders are independent of the wave number k. Let h denote the step size, it will be demonstrated that when solving the Helmholtz equation at large wave numbers and considering kh is fixed, the errors of the proposed new schemes decrease as h decreases even when k is increasing and kh > 1.

Keywords

65N0665N1565N22Helmholtz equationhigh wave numberpolar coordinatespherical coordinatepollution freehigh order difference scheme

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Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 3 , March 2015 , pp. 779 - 807
Copyright
Copyright © Global-Science Press 2015 

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