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

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.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

scholarly journals Chemical Source Inversion Using Assimilated Constituent Observations in an Idealized Two-Dimensional System

2009 ◽  
Vol 137 (9) ◽  
pp. 3013-3025
Author(s):  
Andrew Tangborn ◽  
Robert Cooper ◽  
Steven Pawson ◽  
Zhibin Sun
Keyword(s):  
Kalman Filter ◽  
Green’S Function ◽  
Green's Function ◽  
Transport Model ◽  
Chemical Constituents ◽  
Gaussian Model ◽  
Satellite Observation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Source Inversion

Abstract A source inversion technique for chemical constituents is presented that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier–Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green’s function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral model but differs by an unbiased Gaussian model error and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out either by directly using synthetically generated observations with added noise or by first assimilating the observations and using the analyses to extract observations. Twenty identical twin experiments were conducted for each set of source and observation configurations, and it was found that in the limiting cases of a very few localized observations or an extremely large observation network there is little advantage to carrying out assimilation first. For intermediate observation densities, the source inversion error standard deviation is decreased by 50% to 90% when the observations are assimilated with the Kalman filter before carrying out the Green’s function inversion.

scholarly journals Evaluating the exfoliation of two-dimensional materials with a Green's function surface model

2020 ◽  
Vol 101 (7) ◽  
Author(s):  
Yipeng An ◽  
Yusheng Hou ◽  
Shijing Gong ◽  
Ruqian Wu ◽  
Chuanxi Zhao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Surface Model ◽  
Two Dimensional ◽  
Two Dimensional Materials
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