scholarly journals Asymptotic convergence in finite and boundary element methods: part 2: The LBB constant for rigid and elastic scattering problems

1994 ◽  
Vol 28 (6) ◽  
pp. 93-109 ◽  
Author(s):  
L. Demkowicz
Keyword(s):  
Elastic Scattering ◽  
Boundary Element ◽  
Boundary Element Methods ◽  
Asymptotic Convergence ◽  
Scattering Problems

scholarly journals Nodal and Divergence-Conforming Boundary-Element Methods Applied to Electromagnetic Scattering Problems

2004 ◽  
Vol 40 (2) ◽  
pp. 1053-1056
Author(s):  
M.M. Afonso ◽  
J.A. Vasconcelos ◽  
R.C. Mesquita ◽  
C. Vollaire ◽  
L. Nicolas
Keyword(s):  
Boundary Element ◽  
Electromagnetic Scattering ◽  
Boundary Element Methods ◽  
Scattering Problems

scholarly journals Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation

2021 ◽  
Author(s):  
Daniel Seibel
Keyword(s):  
Wave Equation ◽  
Boundary Element ◽  
Domain Boundary ◽  
Boundary Element Methods ◽  
Scattering Problems ◽  
Computational Costs ◽  
Adaptive Cross Approximation ◽  
Transient Problems ◽  
Matrix Compression ◽  
Convolution Quadrature Method

AbstractTime-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices have to be computed for a large number of time steps or frequencies. In this article, we propose a new approximation scheme for the Convolution Quadrature Method powered BEM, which we apply to scattering problems governed by the wave equation. We use $${\mathscr {H}}^2$$ H 2 -matrix compression in the spatial domain and employ an adaptive cross approximation algorithm in the frequency domain. In this way, the storage and computational costs are reduced significantly, while the accuracy of the method is preserved.

Boundary Element Methods in Probabilistic Acoustic Radiation Problems

1990 ◽  
Vol 112 (4) ◽  
pp. 556-560 ◽  
Author(s):  
R. P. Daddazio ◽  
M. M. Ettouney
Keyword(s):  
Boundary Element ◽  
Acoustic Radiation ◽  
Probabilistic Approach ◽  
Boundary Element Methods ◽  
Fluid Structure Interactions ◽  
Scattering Problems ◽  
Fluid Structure ◽  
Wide Range ◽  
System Properties ◽  
Engineering Practices

Boundary Element Methods (BEM) are suited to a wide range of engineering problems, especially those of a semi-infinite nature. Examples of such problems can be found in the fluid-structure interactions of acoustic radiation and scattering problems and in the soil-structure interactions of earthquake and machine foundation problems. The required input parameters, dynamic loads, and system properties for such problems are not in general well-defined and can be considered random variables. Probabilistic structural analysis through the use of the BEM has been introduced by Ettouney et al. (1989a, 1989b) for the solution of plane elastic systems with uncertain material properties. The method was applied to solution of problems in the fields of structural and geotechnical engineering. In this work, we extend the use of this probabilistic approach to area of fluid-structure interaction by applying this technique to the problem of acoustic radiation from structures. The advantages of the probabilistic viewpoint are discussed with regard to current engineering practices. The importance of confidence estimates for criteria of nonexceedance response is emphasized.

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