Study of the comparison of the methods of equivalent sources and boundary element methods for near-field acoustic holography

2006 ◽  
Vol 120 (6) ◽  
pp. 3694-3705 ◽  
Author(s):  
Nicolas P. Valdivia ◽  
Earl G. Williams
Keyword(s):  
Boundary Element ◽  
Near Field ◽  
Boundary Element Methods ◽  
Acoustic Holography ◽  
Equivalent Sources

scholarly journals A New Method for Determining Optimal Regularization Parameter in Near-Field Acoustic Holography

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yue Xiao
Keyword(s):  
Point Source ◽  
Regularization Parameter ◽  
Near Field ◽  
New Method ◽  
Tikhonov Regularization Method ◽  
Acoustic Holography ◽  
Reconstruction Process ◽  
Curve Method ◽  
Univariate Optimization ◽  
Equivalent Sources

Tikhonov regularization method is effective in stabilizing reconstruction process of the near-field acoustic holography (NAH) based on the equivalent source method (ESM), and the selection of the optimal regularization parameter is a key problem that determines the regularization effect. In this work, a new method for determining the optimal regularization parameter is proposed. The transfer matrix relating the source strengths of the equivalent sources to the measured pressures on the hologram surface is augmented by adding a fictitious point source with zero strength. The minimization of the norm of this fictitious point source strength is as the criterion for choosing the optimal regularization parameter since the reconstructed value should tend to zero. The original inverse problem in calculating the source strengths is converted into a univariate optimization problem which is solved by a one-dimensional search technique. Two numerical simulations with a point driven simply supported plate and a pulsating sphere are investigated to validate the performance of the proposed method by comparison with the L-curve method. The results demonstrate that the proposed method can determine the regularization parameter correctly and effectively for the reconstruction in NAH.

THEORY AND BOUNDARY ELEMENT METHODS FOR NEAR-FIELD ACOUSTIC HOLOGRAPHY

2005 ◽  
Vol 13 (01) ◽  
pp. 163-185 ◽  
Author(s):  
THOMAS DELILLO ◽  
TOMASZ HRYCAK ◽  
VICTOR ISAKOV
Keyword(s):  
Boundary Element ◽  
Measurement Errors ◽  
Acoustic Pressure ◽  
Near Field ◽  
Boundary Element Methods ◽  
Gradient Algorithm ◽  
Pressure Measurements ◽  
Layer Potentials ◽  
Equation Boundary ◽  
Surface Vibrations

We consider the problem of recovering surface vibrations from acoustic pressure measurements taken in the interior or the exterior of a region. We give two formulations of the problem. One is based on a representation of the pressure as layer potentials and the other is based on approximation by a class of specific solutions to the Helmholtz equation. Boundary element methods are developed to approximate the integral operators. A conjugate gradient algorithm based on Lanczos bidiagonalization is applied to compute regularized solutions to the ill-conditioned equations in the presence of measurement errors. Numerical examples which compare the two formulations are presented.

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

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