Efficient absorbing boundary conditions for the finite element solution of 3D scattering problems

1995 ◽  
Vol 31 (3) ◽  
pp. 1534-1537 ◽  
Author(s):  
A.K. Belhora ◽  
L. Pichon
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Finite Element Solution ◽  
Element Solution ◽  
Scattering Problems ◽  
Absorbing Boundary

On Transient Three-Dimensional Absorbing Boundary Conditions for the Modeling of Acoustic Scattering from Near-Surface Obstacles

1997 ◽  
Vol 05 (01) ◽  
pp. 117-136 ◽  
Author(s):  
Loukas F. Kallivokas ◽  
Aggelos Tsikas ◽  
Jacobo Bielak
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Half Space ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Absorbing Boundary Conditions ◽  
Scattering Problems ◽  
Absorbing Boundary ◽  
Near Surface ◽  
Stiffness Matrices

We have recently developed absorbing boundary conditions for the three-dimensional scalar wave equation in full-space. Their applicability has been extended to half-space scattering problems where the scatterer is located near a pressure-free surface. A variational scheme was also proposed for coupling the structural acoustics equations with the absorbing boundary conditions. It was shown that the application of a Galerkin method on the variational form results in an attractive finite element scheme that, in a natural way, gives rise to a surface-only absorbing boundary element on the truncation boundary. The element — the finite element embodiment of a second-order absorbing boundary condition — is completely characterized by a pair of symmetric, frequency-independent damping and stiffness matrices, and is equally applicable to the transient and harmonic steady-state regimes. Previously, we had applied the methodology to problems involving scatterers of arbitrary geometry. In this paper, we validate our approach by comparing numerical results for rigid spherical scatterers submerged in a half-space, against a recently developed analytic solution.

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