Improving the performance of the boundary element method with time-dependent fundamental solutions by the use of a wavelet expansion in the time domain

2007 ◽  
Vol 71 (3) ◽  
pp. 363-378 ◽  
Author(s):  
Sami Barmada
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Fundamental Solutions ◽  
Time Dependent ◽  
Wavelet Expansion ◽  
The Time Domain ◽  
Element Method

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

Horn effect prediction based on the time domain boundary element method

2017 ◽  
Vol 82 ◽  
pp. 79-84 ◽  
Author(s):  
Yang Zhang ◽  
Chuan-Xing Bi ◽  
Yong-Bin Zhang ◽  
Xiao-Zheng Zhang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
The Time Domain ◽  
Element Method

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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