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Volume 17, Issue 3
Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates

Kun Wang, Yau Shu Wong & Jian Deng

DOI: 10.4208/cicp.110214.101014a

Commun. Comput. Phys., 17 (2015), pp. 779-807.

Published online: 2018-04

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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.

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@Article{CiCP-17-779, author = {Kun Wang, Yau Shu Wong and Jian Deng}, title = {Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {3}, pages = {779--807}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.110214.101014a}, url = {http://global-sci.org/intro/article_detail/cicp/10977.html} }
TY - JOUR T1 - Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates AU - Kun Wang, Yau Shu Wong & Jian Deng JO - Communications in Computational Physics VL - 3 SP - 779 EP - 807 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.110214.101014a UR - https://global-sci.org/intro/article_detail/cicp/10977.html KW - AB -

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.

Kun Wang, Yau Shu Wong and Jian Deng. (2018). Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates. Communications in Computational Physics. 17 (3). 779-807. doi:10.4208/cicp.110214.101014a
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