scholarly journals Asymptotic and Absorbing Boundary Conditions for Finite Element Analysis of Digital Circuit and Scattering Problems

1990 ◽  
Author(s):  
Ahmed Khebir ◽  
Raj Mittra
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Digital Circuit ◽  
Absorbing Boundary Conditions ◽  
Scattering Problems ◽  
Absorbing Boundary ◽  
Element Analysis

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.

Rayleigh-Ritz Analysis of Vibrating Plates Based on a Class of Eigenfunctions

2009 ◽  
Author(s):  
Giuseppe Catania ◽  
Silvio Sorrentino
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Linear Combination ◽  
Equation Of Motion ◽  
Extensive Literature ◽  
Shape Functions ◽  
Element Analysis ◽  
Vibrating Plates ◽  
General Basis

In the Rayleigh-Ritz condensation method the solution of the equation of motion is approximated by a linear combination of shape-functions selected among appropriate sets. Extensive literature dealing with the choice of appropriate basis of shape functions exists, the selection depending on the particular boundary conditions of the structure considered. This paper is aimed at investigating the possibility of adopting a set of eigenfunctions evaluated from a simple stucture as a general basis for the analysis of arbitrary-shaped plates. The results are compared to those available in the literature and using standard finite element analysis.

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