scholarly journals Efficient computation of the 2D Green's function for 1D periodic layered structures using the Ewald method

2003 ◽  
Author(s):  
F. Capolino ◽  
D.R. Wilton ◽  
W.A. Johnson
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Layered Structures ◽  
Efficient Computation ◽  
Ewald Method

Efficient computation of the 2D periodic Green’s function using the Ewald method

2006 ◽  
Vol 219 (2) ◽  
pp. 899-911 ◽  
Author(s):  
Siddharth Oroskar ◽  
David R. Jackson ◽  
Donald R. Wilton
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Efficient Computation ◽  
Ewald Method

scholarly journals A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

2021 ◽  
Vol 11 (6) ◽  
pp. 2722
Author(s):  
Zhiwen Qian ◽  
Dejiang Shang ◽  
Yuan Hu ◽  
Xinyang Xu ◽  
Haihan Zhao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Shallow Water ◽  
Green's Function ◽  
Plane Waves ◽  
Spherical Wave ◽  
Sound Field ◽  
Efficient Computation ◽  
Image Source ◽  
Source Method ◽  
Pekeris Waveguide

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

Efficient computation of the two-dimensional periodic Green's function

1999 ◽  
Vol 47 (5) ◽  
pp. 895-897 ◽  
Author(s):  
G.S. Wallinga ◽  
E.J. Rothwell ◽  
K.M. Chen ◽  
D.P. Nyquist
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Two Dimensional ◽  
Efficient Computation
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