Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates
Year: 2015
Communications in Computational Physics, Vol. 17 (2015), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.110214.101014a
Communications in Computational Physics, Vol. 17 (2015), Iss. 3 : pp. 779–807
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
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