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.

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.

Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems

2020 ◽  
Vol 28 (4) ◽  
pp. 223-245
Author(s):  
Gabriel N. Gatica ◽  
Salim Meddahi
Keyword(s):  
Boundary Element ◽  
Acoustic Scattering ◽  
Rates Of Convergence ◽  
Boundary Element Methods ◽  
Scattering Problems ◽  
Combined Use ◽  
Virtual Element ◽  
2D And 3D ◽  
Element Method ◽  
Acoustic Scattering Problems

AbstractThis paper extends the applicability of the combined use of the virtual element method (VEM) and the boundary element method (BEM), recently introduced to solve the coupling of linear elliptic equations in divergence form with the Laplace equation, to the case of acoustic scattering problems in 2D and 3D. The well-posedness of the continuous and discrete formulations are established, and then Cea-type estimates and consequent rates of convergence are derived.

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.

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