scholarly journals A time domain Galerkin boundary element method for a heat conduction interface problem

2009 ◽  
Author(s):  
R. Vodička
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Interface Problem ◽  
Galerkin Boundary Element Method ◽  
Element Method

Relationship Among Coefficient Matrices in Symmetric Galerkin Boundary Element Method for Two-Dimensional Scalar Problems

2003 ◽  
Vol 70 (4) ◽  
pp. 479-486 ◽  
Author(s):  
G. Y. Yu
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Current Method ◽  
Present Formulation ◽  
Weakly Singular ◽  
Potential Problems ◽  
Galerkin Boundary Element Method ◽  
The Relationship ◽  
Element Method

Based on the assumption that solutions from different methods should be the same, the relationship among weakly singular, strongly singular and hypersingular matrices associated with symmetric Galerkin boundary element method (SGBEM) is derived in this paper. Hypersingularity is avoided through matrix manipulations so that only weakly and strongly singularities need to be solved. Compared with the advantages brought about by symmetry, the additional computation caused by matrix manipulations is not so important in many cases, especially for time-domain problems or when one wants to couple BEM with other symmetric schemes. Simplicity is the advantage of the current method over the traditional SGBEM. Both steady-state and time-domain potential problems have been studied, and two numerical examples are included to show the effectiveness and accuracy of the present formulation.

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.

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