一类热传导问题源项识别的快速稳定算法

Stable and Fast Algorithm for Identification of Source in Heat Conduction Problems

利用正算子的性质和Lax-Milgram定理,将一维热传导方程源项识别问题转化为适定的、第二类Volterra方程的求解,给出一个新的快速稳定算法,并进行理论分析.采用两种实现后验准则的新途径,在输入数据的误差水平已知和未知的情况下,快速地决定正则参数.数值实验证实了算法的有效性.

With properties of non-negative operator and Lax-Milgram theorem, we transform an ill-posed 1D heat conduction problem into a well-posed second kind Volterra equation, and introduce a stable and fast algorithm. Related theoretical analysis is shown. For the determination of regularization parameter, the algorithm employs two posterior strategies, which can be realized quickly whether the error level of input data are known or unknown. Numerical tests demonstrate merit of the algorithm.