Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 6 : pp. 986–1002
Abstract
We consider efficient finite difference methods for solving the three-dimensional (3D) acoustic scattering by an impenetrable circular cylindrical obstacle. By using the separation of variable and other techniques, we first transform the 3D problem into a series of one-dimensional (1D) problems in this paper, and then construct some efficient and accuracy finite difference methods to solve these 1D problems instead of the 3D one. There are mainly two advantages for these methods: one is that they are pollution free for the problem to be considered in this paper; and the other is that the linear systems generated from these schemes have tri-diagonal structures. These features lead to easy implementation and much less computational cost. Numerical examples are presented to verify the efficiency and accuracy of the numerical methods, even with the wave number greater than 100.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-475
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 6 : pp. 986–1002
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Helmholtz equation circular cylindrical coordinate finite difference method pollution free 3D ocean waveguide.