INVERSE ACOUSTIC SCATTERING PROBLEMS IN OCEAN ENVIRONMENTS

1999 ◽  
Vol 07 (02) ◽  
pp. 111-132 ◽  
Author(s):  
YONGZHI XU
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Stratified Medium ◽  
Computational Results ◽  
Scattering Problems ◽  
Numerical Examples ◽  
Layered Waveguide ◽  
Shape Determination

This paper presents theoretical and computational results from our research on inverse scattering problems for acoustic waves in ocean environments. In particular, we discuss the determination of a three-dimensional (3-D) distributed inhomogeneity in a two-layered waveguide from scattered sound and the shape determination of an object in a stratified medium. Numerical examples are presented.

Adaptivity and Three Dimensional Hierarchical Boundary Elements for Rigid Acoustic Scattering Problems

1995 ◽  
Author(s):  
Steven J. Newhouse ◽  
Ian C. Mathews
Keyword(s):  
Boundary Element ◽  
Acoustic Analysis ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Error Estimator ◽  
Infinite Domain ◽  
Scattering Problems ◽  
Effective Form ◽  
Mesh Density ◽  
Acoustic Scattering Problems

Abstract The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited. This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.

Band Gap Formation by Cylinder Arrays in an Acoustic Waveguide

2007 ◽  
Author(s):  
Liang-Wu Cai ◽  
David C. Calvo ◽  
Dalcio K. Dacol ◽  
Gregory J. Orris
Keyword(s):  
Acoustic Waves ◽  
Stop Band ◽  
Three Dimensional ◽  
Wave Number ◽  
Pass Band ◽  
Gap Formation ◽  
Numerical Examples ◽  
Cylinder Arrays ◽  
Horizontal Wave ◽  
Special Case

Scattering of acoustic waves by arrays of identical circular cylindrical scatterers in a horizontal waveguide is studied. Although three-dimensional in its geometry, the waveguide permits only a finite number of modes of acoustic wave propagating in different directions with respect to horizontal, and the number of these propagating modes increases as the frequency increases. The horizontal wave numbers of these modes span a range of frequency limited by the total wave number. Numerical examples are used to explore a special case in which the cylinder height equals the depth of the waveguide and in which the cylinders and the waveguide have pressure-release boundaries at both top and bottom surfaces. In such a special case, there is no coupling among the modes permitted by the waveguide and hence is the simplest case for such problems. It is observed that the combination of the modes generally decreases the wave-blocking effects of a stop band; and it is likely that a stop band in one waveguide mode might correspond to a pass band in a different mode. However, numerical examples also show that the main characteristics of a stop band are maintained, despite the multiple modes; and it is possible to extend the stop band by cascading cylinders arrays of different arrangement.

Axisymmetric acoustic scattering by vortices

2002 ◽  
Vol 473 ◽  
pp. 275-294 ◽  
Author(s):  
Y. HATTORI ◽  
STEFAN G. LLEWELLYN SMITH
Keyword(s):  
Mach Number ◽  
Born Approximation ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Order Effects ◽  
Incoming Wave ◽  
Spherical Vortex ◽  
The Difference ◽  
Higher Order Effects

The scattering of acoustic waves by compact three-dimensional axisymmetric vortices is studied using direct numerical simulation in the case where the incoming wave is aligned with the symmetry axis and the direction of propagation of the vortices. The cases of scattering by Hill’s spherical vortex and Gaussian vortex rings are examined, and results are compared with predictions obtained by matched asymptotic expansions and the Born approximation. Good agreement is obtained for long waves, with the Born approximation usually giving better predictions, especially as the difference in scale between vortex and incoming waves decreases and as the Mach number of the flow increases. An improved version of the Born approximation which takes into account higher-order effects in Mach number gives the best agreement.

scholarly journals Three-dimensional acoustic scattering by layered media: a novel surface formulation with operator expansions implementation

2011 ◽  
Vol 468 (2139) ◽  
pp. 731-758 ◽  
Author(s):  
David P. Nicholls
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Boundary Integral ◽  
Helmholtz Equations ◽  
Irregular Structures ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Boundary Integral Operators ◽  
Operator Expansions

The scattering of acoustic waves by irregular structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses on the rapid and highly accurate numerical approximation of solutions of Helmholtz equations coupled across irregular periodic interfaces meant to model acoustic waves incident upon a multi-layered medium. We describe not only a novel surface formulation for the problem in terms of boundary integral operators (Dirichlet–Neumann operators), but also a Boundary Perturbation methodology (the Method of Operator Expansions) for its numerical simulation. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than volumetric approaches), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of Boundary Integral/Element Methods. The approach is a generalization to multiple layers of Malcolm & Nicholls' Operator Expansions algorithm for dielectric structures with two layers. As with this precursor, this approach is efficient and spectrally accurate.

scholarly journals Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170242 ◽  
Author(s):  
Oscar P. Bruno ◽  
Stephen P. Shipman ◽  
Catalin Turc ◽  
Venakides Stephanos
Keyword(s):  
Green Function ◽  
Blow Up ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Three Dimensions ◽  
Scattering Problems ◽  
Periodic Surfaces ◽  
Lattice Sum ◽  
The Green Function ◽  
First Time

This work, part II in a series, presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near what are commonly called ‘Wood anomaly frequencies’. At these frequencies, there is a grazing Rayleigh wave, and the quasi-periodic Green function ceases to exist. We present a modification of the Green function by adding two types of terms to its lattice sum. The first type are transversely shifted Green functions with coefficients that annihilate the growth in the original lattice sum and yield algebraic convergence. The second type are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on this new Green function for scattering by doubly periodic surfaces at and around Wood frequencies. We believe this is the first solver able to handle Wood frequencies for doubly periodic scattering problems in three dimensions. We demonstrate the method by applying it to acoustic scattering.

scholarly journals The determination of the surface impedance of an obstacle

1993 ◽  
Vol 36 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Andrzej W. Kȩdzierawski
Keyword(s):  
Acoustic Waves ◽  
Surface Impedance ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Far Field ◽  
Field Patterns ◽  
Time Harmonic ◽  
Scattered Fields

The inverse scattering problem we consider is to determine the surface impedance of a three-dimensional obstacle of known shape from a knowledge of the far-field patterns of the scattered fields corresponding to many incident time-harmonic plane acoustic waves. We solve this problem by using both the methods of Kirsch-Kress and Colton-Monk.

FICTITIOUS DOMAIN METHODS FOR THE NUMERICAL SOLUTION OF THREE-DIMENSIONAL ACOUSTIC SCATTERING PROBLEMS

1999 ◽  
Vol 07 (03) ◽  
pp. 161-183 ◽  
Author(s):  
ERKKI HEIKKOLA ◽  
YURI A. KUZNETSOV ◽  
KONSTANTIN N. LIPNIKOV
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Fictitious Domain ◽  
Scattering Problems ◽  
Element Discretization ◽  
Fictitious Domain Methods ◽  
Acoustic Scattering Problems

Efficient iterative methods for the numerical solution of three-dimensional acoustic scattering problems are considered. The underlying exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a non-reflecting boundary condition on the artificial boundary. The finite element discretization of the approximate boundary value problem is performed using locally fitted meshes, and algebraic fictitious domain methods with separable preconditioners are applied to the solution of the resultant mesh equations. These methods are based on imbedding the original domain into a larger one with a simple geometry (for example, a sphere or a parallelepiped). The iterative solution method is realized in a low-dimensional subspace, and partial solution methods are applied to the linear systems with the preconditioner. The results of numerical experiments demonstrate the efficiency and accuracy of the approach.

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