scholarly journals Coupled boundary element method and finite difference method for the heat conduction in laser processing

2008 ◽  
Vol 32 (11) ◽  
pp. 2429-2458 ◽  
Author(s):  
Sirilath J. DeSilva ◽  
Cho Lik Chan
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Laser Processing ◽  
Element Method

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

Mould cooling simulation for injection moulding using a fast boundary element method approach

2009 ◽  
Vol 224 (4) ◽  
pp. 653-662 ◽  
Author(s):  
H Zhou ◽  
Y Zhang ◽  
J Wen ◽  
S Cui
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Injection Moulding ◽  
Heat Conduction Problem ◽  
Solution Time ◽  
Combination Method ◽  
Dynamic Allocation ◽  
Actual Problem ◽  
Element Method

The existing cooling simulations for injection moulding are mostly based on the boundary element method (BEM). In this paper, a fast BEM approach for mould cooling analysis is developed. The actual problem is decoupled into a one-dimensional transient heat conduction problem within the thin part and a cycle-averaged steady state three-dimensional heat conduction problem of the mould. The BEM is formulated for the solution of the mould heat transfer problem. A dynamic allocation strategy of integral points is proposed when using the Gaussian integral formula to generate the BEM matrix. Considering that the full and unsymmetrical influence matrix of the BEM may lead to great storage space and solution time, this matrix is transformed into a sparse matrix by two methods: the direct rounding method or the combination method. This approximated sparsification approach can reduce the storage memory and solution time significantly. For validation, six typical cases with different element numbers are presented. The results show that the error of the direct rounding method is too large while that of the combination method is acceptable.

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