中文摘要：

文章采用边界元法分析二维瞬态热传导问题；建立热扩散系数和导热系数反演问题的目标函数，利用共轭梯度法对该目标函数进行优化，引入复变量求导法求解目标函数梯度矩阵，该方法的求导精度优于常规差分法；探讨了迭代初值、测量数据随机偏差对计算结果的影响。迭代初值不同，反演结果都能收敛到精确解；随机偏差越大，迭代步数越多；随机偏差越小，计算结果越趋近于精确解。算例验证了方法的有效性和稳定性。

英文摘要：

T he boundary element method（BEM ） is used to analyze 2‐D transient heat conduction prob‐lem .T he objective function is established for determining the thermal diffusivity and the thermal con‐ductivity .The conjugate gradient method is developed to optimize the objective function .The complex variable differentiation method is employed to compute the gradient matrix of the objective function . The method is more accurate than the traditional finite difference method .The effect of the initial iter‐ative values and random noises on numerical results is discussed .For different certain initial iterative values ,the results can converge to the exact ones .With the increase of the noises ,the iterative num‐ber correspondingly increases .With the decrease of the noises ,the numerical results are in better a‐greement with the analytical ones .The numerical examples demonstrate the effectiveness and stability of the presented method .