Direct and indirect boundary element methods for solving the heat conduction problem

1985 ◽  
Vol 49 (1) ◽  
pp. 37-54 ◽  
Author(s):  
G. Athanasiadis
Keyword(s):  
Heat Conduction ◽  
Boundary Element ◽  
Heat Conduction Problem ◽  
Boundary Element Methods

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.

BEM Solution With Minimal Energy Technique for the Geometrical Inverse Heat Conduction Problem in a Doubly Connected Domain

2003 ◽  
Vol 125 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Chang-Yong Choi ◽  
Jong Chull Jo
Keyword(s):  
Heat Conduction ◽  
Boundary Element ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Boundary Surface ◽  
Inverse Heat Conduction Problem ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Minimal Energy ◽  
Element Analysis

This article addresses the use of boundary element method in conjunction with minimal energy technique for solving a geometrical inverse heat conduction problem. The problem considered in this study is to estimate the unknown inner boundary position in an irregular-shaped hollow body of which the inner boundary surface is subjected to a specified temperature condition. For solving the problem, first boundary element equations are converted into the quadratic programming problem by minimizing the energy functional with a constraint, next a hypothetical inner boundary is defined such that the actual inner boundary is located interior of the hypothetical solution domain, then temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error in inner surface temperatures, and finally boundary element analysis is performed for the position of an unknown boundary. Based on these main solution procedures, an effective detection algorithm is provided. In addition, the solution method is numerically tested to investigate the effects of measurement errors on the accuracy of estimation.

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