An Iterative Method for the Solution of Three-Dimensional Inverse Acoustic Scattering Problems

2002 ◽  
Author(s):  
Charbel Farhat ◽  
Radek Tezaur ◽  
Rabia Djellouli
Keyword(s):  
Domain Decomposition Method ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Field Pattern ◽  
Far Field ◽  
Computationally Efficient ◽  
Scattering Problems ◽  
Multi Stage ◽  
Computational Methodology ◽  
Acoustic Scattering Problems

We present a computational methodology for retrieving the shape of an impenetrable obstacle from the knowledge of some acoustic far-field patterns. This methodology is based on the well-known regularized Newton algorithm, but distinguishes itself from similar optimization procedures by (a) a frequency-aware multi-stage solution strategy, (b) a computationally efficient usage of the exact sensitivities of the far-field pattern to the specified shape parameters, and (c) a numerically scalable domain decomposition method for the fast solution of three-dimensional direct acoustic scattering problems. We illustrate the salient features and highlight the performance characteristics of the proposed computational methodology with the solution on a parallel processor of various inverse mockup submarine problems.

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.

Newton-Like Method for Solving Inverse Obstacle Acoustic Scattering Problems

2000 ◽  
Author(s):  
Rabia Djellouli ◽  
Charbel Farhat ◽  
Radek Tezaur
Keyword(s):  
Acoustic Scattering ◽  
Numerical Procedure ◽  
Decomposition Methods ◽  
Computationally Efficient ◽  
Scattering Problems ◽  
Absorbing Boundary ◽  
Element Discretization ◽  
Jacobian Matrices ◽  
Fast Solution ◽  
Acoustic Scattering Problems

Abstract A Newton-like method is designed for determining the shape or sought-after shape modifications of a scatterer from the knowledge of acoustic far-field patterns at a given number of observation points. This method distinguishes itself from existing numerical procedures by the following features: (a) exact Jacobian matrices for the linearized problems rather than approximate ones, (b) a fast numerical procedure for computing these Jacobian matrices, (c) a computationally efficient absorbing boundary condition for the finite element discretization, and (d) a numerically scalable domain decomposition methods for the fast solution of high-frequency direct acoustic scattering problems.

Full Aperture Reconstruction of the Acoustic Far-Field Pattern from Few Measurements

2012 ◽  
Vol 11 (2) ◽  
pp. 647-659 ◽  
Author(s):  
Hélène Barucq ◽  
Chokri Bekkey ◽  
Rabia Djellouli
Keyword(s):  
Total Variation ◽  
Acoustic Scattering ◽  
Numerical Procedure ◽  
Field Pattern ◽  
Far Field ◽  
Exact Representation ◽  
Scattering Problems ◽  
Reconstruction Procedure ◽  
The Stability ◽  
Far Field Pattern

AbstractWe propose a numerical procedure to extend to full aperture the acoustic far-field pattern (FFP) when measured in only few observation angles. The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion. The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms. We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.

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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