基于双倒易边界元法的非稳态导热几何边界识别

采用基于双倒易边界元法和共轭梯度法的反演算法求解二维非稳态导热边界识别问题。正问题采用双倒易边界元法求解，该法避免了传统边界元法需进行区域积分的缺点，仅需纯边界积分计算。反问题的解在正问题的基础上通过共轭梯度法最小化目标函数得到。考虑了管道和空腔未知边界为正弦曲线、偏心圆、椭圆等形状时的识别情况，讨论了初值、测量误差和加热热流大小等因素对反演解精度的影响。结果表明，该方法能将各种不规则边界识别出来，对初值和测量误差不敏感，加热热流增大时反演解精度有所提高。

Geometry Boundary Identification of Unsteady Heat Conduction Based on Dual Reciprocity Boundary Element Method

A boundary identification problem of two-dimensional unsteady heat conduction was solved by using dual reciprocity boundary element method (DRBEM) and conjugate gradient method (CGM)-based inverse algorithm. The direct problem was solved by DRBEM, which eliminated the drawback of domain integral for classical boundary element method and resulted in pure boundary integral calculation. The inverse solution was obtained through minimizing the object function using CGM based on the direct problem. Unknown boundaries with eccentric cycle, sinusoidal curve and ellipse were considered for pipeline and cavity. The effects of the initial guesses, the measured errors and the magnitude of heat flux on the accuracy of inverse solutions were discussed. The results show that the proposed method can identify different kind of irregular boundaries, and is not sensitivity to initial guesses and measured errors. The accuracy of inverse solutions increases with the heat flux imposed on the known boundary.