逆热传导方程的一个正则化方法

A Regularization for Solving the Sideways Heat Equation

考虑了标准的一维逆热传导方程.问题是不适定的,即解不连续地依赖于数据.通过Fourier逼近的方法进行正则化处理,提出了一个新的算法,理论分析和数值实验均表明该算法是稳定的;该算法不仅保留了测量数据的部分高频成份,同时还具有相同的精度和计算复杂性.

This paper considers an inverse heat conduction problem, the sideways heat equation. The problem is ill-posed, in the sense that the solution （if it exists） does not depend continuously on the data. A new algorithm is proposed to regularize this problem by a Fourierbased approximation. The theory analysis and numerical experiments prove it is stable. ＇This algorithm not only keeps parts of high-frequency components of the data, but also presents the same accurate and computing complexity.