中文摘要：

给出了一类二维热传导方程反问题中边界温度场的重建算法。首先将反问题归结为一泛函极小化问题;然后通过对未知边界的有限维逼近,将反问题分解成一系适定的热传导方程正问题;最后根据偏微分方程线性问题的叠加原理,将泛函极小化问题离散为线性代数方程组,再应用Tikhonov正则化方法求解线性代数方程组,从而获得边界温度场的数值解。数值算例表明了本文的算法是有效的,且具有较强的稳定性。

英文摘要：

An algorithm is presented for reconstructing the boundary temperature of a two - dimensional inverse heat conduction problem. The inverse problem is formulated to a functional minimization problem ; and it is transformed into a series of direct problems of heat conduct equation that are well -posed by a finite approximation of the unknown boundary temperature. Finally, according to partial differential equations the superposition principle of linear problem, the functional minimization problem is discretized into linear algebraic equations, then, we obtain the approximate solution of the unknown boundary temperature by applying Tikhonov regularization method for solving linear algebraic equations. Numerical example shows that the presented algorithm is efficient and it has a strong stability.