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Volume 13, Issue 6
Efficient Finite Difference Methods for Acoustic Scattering from Circular Cylindrical Obstacle

R. Guo, K. Wang & L.-W. Xu

Int. J. Numer. Anal. Mod., 13 (2016), pp. 986-1002.

Published online: 2016-11

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  • 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.

  • Keywords

Helmholtz equation, circular cylindrical coordinate, finite difference method, pollution free, 3D ocean waveguide.

  • AMS Subject Headings

65N06, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-986, author = {R. Guo, K. Wang and L.-W. Xu}, title = {Efficient Finite Difference Methods for Acoustic Scattering from Circular Cylindrical Obstacle}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {6}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/475.html} }
TY - JOUR T1 - Efficient Finite Difference Methods for Acoustic Scattering from Circular Cylindrical Obstacle AU - R. Guo, K. Wang & L.-W. Xu JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 986 EP - 1002 PY - 2016 DA - 2016/11 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/475.html KW - Helmholtz equation, circular cylindrical coordinate, finite difference method, pollution free, 3D ocean waveguide. AB -

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.

R. Guo, K. Wang and L.-W. Xu. (2016). Efficient Finite Difference Methods for Acoustic Scattering from Circular Cylindrical Obstacle. International Journal of Numerical Analysis and Modeling. 13 (6). 986-1002. doi:
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