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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >Virtual boundary element method in conjunction with conjugate gradient algorithm for three-dimensional inverse heat conduction problems
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Virtual boundary element method in conjunction with conjugate gradient algorithm for three-dimensional inverse heat conduction problems

机译：虚拟边界元方法与共轭梯度算法结合三维逆热导电问题

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摘要

In this article, the virtual boundary element method (VBEM) in conjunction with conjugate gradient algorithm (CGA) is employed to treat three-dimensional inverse problems of steady-state heat conduction. On the one hand, the VBEM may face numerical instability if a virtual boundary is improperly selected. The numerical accuracy is very sensitive to the choice of the virtual boundary. The condition number of the system matrix is high for the larger distance between the physical boundary and the fictitious boundary. On the contrary, it is difficult to remove the source singularity. On the other hand, the VBEM will encounter ill-conditioned problem when this method is used to analyze inverse problems. This study combines the VBEM and the CGA to model three-dimensional heat conduction inverse problem. The introduction of the CGA effectively overcomes the above shortcomings, and makes the location of the virtual boundary more free. Furthermore, the CGA, as a regularization method, successfully solves the ill-conditioned equation of three-dimensional heat conduction inverse problem. Numerical examples demonstrate the validity and accuracy of the proposed method.
机译：在本文中，采用与共轭梯度算法（CGA）结合的虚拟边界元方法（VBEM）来处理稳态导热的三维逆问题。一方面，如果选择虚拟边界不正确地，VBEM可能面临数值不稳定性。数值准确性对虚拟边界的选择非常敏感。系统矩阵的条件数量高，用于物理边界和虚拟边界之间的较大距离。相反，难以消除源奇点。另一方面，当该方法用于分析逆问题时，VBEM将遇到不良状态问题。本研究结合了VBEM和CGA来模拟三维导热逆问题。 CGA的引入有效地克服了上述缺点，并使虚拟边界的位置更自由。此外，CGA作为正则化方法，成功地解决了三维导热逆问题的不良条件方程。数值示例展示了所提出的方法的有效性和准确性。

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