Stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions

2012 ◽  
Vol 131 (4) ◽  
pp. 2742-2752 ◽  
Author(s):  
Hae-Won Jang ◽  
Jeong-Guon Ih
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Time Domain ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Interior Problem ◽  
Acoustic Boundary Element ◽  
Element Method

A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions

2012 ◽  
Vol 11 (2) ◽  
pp. 573-593 ◽  
Author(s):  
S. N. Chandler-Wilde ◽  
S. Langdon ◽  
M. Mokgolele
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Incident Wave ◽  
Degrees Of Freedom ◽  
Boundary Element Methods ◽  
Convex Polygons ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Element Method

AbstractWe consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

scholarly journals Nonlinear Modal Analysis of a One-Dimensional Bar Undergoing Unilateral Contact via the Time-Domain Boundary Element Method

2017 ◽  
Author(s):  
Jayantheeswar Venkatesh ◽  
Anders Thorin ◽  
Mathias Legrand
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
Unilateral Contact ◽  
Dimensional System ◽  
One Dimensional ◽  
The Time Domain ◽  
Element Method

Finite elements in space with time-stepping numerical schemes, even though versatile, face theoretical and numerical difficulties when dealing with unilateral contact conditions. In most cases, an impact law has to be introduced to ensure the uniqueness of the solution: total energy is either not preserved or spurious high-frequency oscillations arise. In this work, the Time Domain Boundary Element Method (TD-BEM) is shown to overcome these issues on a one-dimensional system undergoing a unilateral Signorini contact condition. Unilateral contact is implemented by switching between free boundary conditions (open gap) and fixed boundary conditions (closed gap). The solution method does not numerically dissipate energy unlike the Finite Element Method and properly captures wave fronts, allowing for the search of periodic solutions. Indeed, TD-BEM relies on fundamental solutions which are travelling Heaviside functions in the considered one-dimensional setting. The proposed formulation is capable of capturing main, subharmonic as well as internal resonance backbone curves useful to the vibration analyst. For the system of interest, the nonlinear modeshapes are piecewise-linear unseparated functions of space and time, as opposed to the linear modeshapes that are separated half sine waves in space and full sine waves in time.

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