scholarly journals A flow-through Hankel transform technique for rapid, accurate Green's function computation

Radio Science ◽  
1999 ◽  
Vol 34 (2) ◽  
pp. 549-555 ◽  
Author(s):  
Art Raiche
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Hankel Transform ◽  
Function Computation ◽  
Flow Through

Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed

2007 ◽  
Vol 14 (1) ◽  
pp. 109-123
Author(s):  
Robert Gilbert ◽  
Miao-Jung Ou
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Near Field ◽  
Sound Field ◽  
Hankel Transform ◽  
Field Approximation ◽  
Construction Scheme ◽  
Stratified Ocean ◽  
Asymptotic Representations ◽  
Layer Waveguide

Abstract In this paper, the near-field approximation of the acoustic Green's function in a two-layer waveguide is constructed by using a variation of the method of Ahluwalia and Keller [Exact and asymptotic representations of the sound field in a stratified ocean, Springer, 1977]. The relation between the constructed multiple-scattering representation (suitable for near-field) and the Hankel transform representation (suitable for mid-range) is also discussed in this paper. The construction scheme presented in this paper can be generalized for an N-layer waveguide.

An Improved Technique for Elastodynamic Green's Function Computation for Transversely Isotropic Solids

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Samaneh Fooladi ◽  
Tribikram Kundu
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Composite Structures ◽  
Transversely Isotropic ◽  
Computational Effort ◽  
Computational Time ◽  
Function Computation ◽  
Time Harmonic ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

Elastodynamic Green's function for anisotropic solids is required for wave propagation modeling in composites. Such modeling is needed for the interpretation of experimental results generated by ultrasonic excitation or mechanical vibration-based nondestructive evaluation tests of composite structures. For isotropic materials, the elastodynamic Green’s function can be obtained analytically. However, for anisotropic solids, numerical integration is required for the elastodynamic Green's function computation. It can be expressed as a summation of two integrals—a singular integral and a nonsingular (or regular) integral. The regular integral over the surface of a unit hemisphere needs to be evaluated numerically and is responsible for the majority of the computational time for the elastodynamic Green's function calculation. In this paper, it is shown that for transversely isotropic solids, which form a major portion of anisotropic materials, the integration domain of the regular part of the elastodynamic time-harmonic Green's function can be reduced from a hemisphere to a quarter-sphere. The analysis is performed in the frequency domain by considering time-harmonic Green's function. This improvement is then applied to a numerical example where it is shown that it nearly halves the computational time. This reduction in computational effort is important for a boundary element method and a distributed point source method whose computational efficiencies heavily depend on Green's function computational time.

scholarly journals RENORMALIZATION GROUP APPROACH TO THE PROBLEM OF FLOW THROUGH IRREGULAR PACKED BEDS

2000 ◽  
Vol 14 (09) ◽  
pp. 963-981
Author(s):  
DMITRI VOLCHENKOV ◽  
RICARDO LIMA
Keyword(s):  
Differential Equation ◽  
Renormalization Group ◽  
Green’S Function ◽  
Green's Function ◽  
Nonlinear Diffusion ◽  
Arbitrary Dimension ◽  
Packed Beds ◽  
Group Approach ◽  
Renormalization Group Approach ◽  
Flow Through

We have calculated the asymptotics of Green's function of the differential equation of nonlinear diffusion in the microscopic range with strong porosity fluctuations in the problem of flow through irregular packed beds for the arbitrary dimension of space and arbitrary porosity fluctuations covariance.

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