Padé approximation in time-domain boundary conditions of porous surfaces

2007 ◽  
Vol 122 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Vladimir E. Ostashev ◽  
Sandra L. Collier ◽  
D. Keith Wilson ◽  
David F. Aldridge ◽  
Neill P. Symons ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Domain Boundary ◽  
Padé Approximation ◽  
Pade Approximation ◽  
Porous Surfaces

scholarly journals Time‐domain boundary conditions in atmospheric acoustics

2007 ◽  
Vol 121 (5) ◽  
pp. 3064-3064
Author(s):  
Vladimir E. Ostashev ◽  
Sandra L. Collier ◽  
David H. Marlin ◽  
D. Keith Wilson ◽  
David F. Aldridge ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Domain Boundary ◽  
Atmospheric Acoustics

scholarly journals Padé approximation for time-domain plane wave reflected from a lossy earth

2018 ◽  
Vol 2 (10) ◽  
pp. 105001
Author(s):  
Ayoub Lahmidi ◽  
Abderrahman Maaouni ◽  
Zeyneb Belganche
Keyword(s):  
Plane Wave ◽  
Time Domain ◽  
Padé Approximation ◽  
Pade Approximation

scholarly journals A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Nwaf Al-Armani
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Padé Approximation ◽  
Current Approach ◽  
Pade Approximation ◽  
Flow Problems ◽  
Blasius Problem ◽  
Classical Boundary ◽  
Layer Flow ◽  
Conditions At Infinity

The main feature of the boundary layer flow problems is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such problems. To the best of the authors’ knowledge, two procedures were used extensively in the past two decades to deal with the boundary conditions at infinity, either the Padé approximation or the direct numerical codes. However, an intensive work is needed to perform the calculations using the Padé technique. Regarding this point, a new idea is proposed in this paper. The idea is based on transforming the unbounded domain into a bounded one by the help of a transformation. Accordingly, the original differential equation is transformed into a singular differential equation with classical boundary conditions. The current approach is applied to solve a class of the Blasius problem and a special class of the Falkner-Skan problem via an improved version of Adomian’s method (Ebaid, 2011). In addition, the numerical results obtained by using the proposed technique are compared with the other published solutions, where good agreement has been achieved. The main characteristic of the present approach is the avoidance of the Padé approximation to deal with the infinity boundary conditions.

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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