Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates. (24th March 2015)

• Record Type: Journal Article
• Authors: Wang, Kun; Wong, Yau Shu; Deng, Jian
• Is Part Of: Communications in computational physics. Volume 17:Number 3(2015:Mar.)
• Page Start: 779
• Page End: 807
• Publication Date: 2015-03-24
• Subjects: 65N06, -- 65N15, -- 65N22; Helmholtz equation, -- high wave number, -- polar coordinate, -- spherical coordinate, -- pollution free, -- high order difference scheme; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.110214.101014a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.