用光滑化正则化方法数值求解含热源参数识别问题

摘要

针对求解含热源参数识别问题,本文利用微分方程初边值问题的一个特殊结构,推导了一个简化形式,通过光滑化正则化方法比较容易地获得它的数值解,从而得到了具有较好稳定性,计算量较小,并且快速收敛的数值算法.同时进行了数值模拟实验,结果表明,该算法是可行且有效的.%To numerically solve the conductive coefficient of thermal conductive equation including source term, the special construction of the partial differential equation is used, and a simple integral formula is deduced. With the use of the smoothing regularization means, the numerical solution of this ill-posed inverse problem can be easily gained. This method has good numerical stability, less computing cost and rapid convergence. Meanwhile, numerical experiments show its feasibility and effectiveness.