热传导方程源项反演问题的指数型正则化方法

An Exponential Regularization Method for the Source Term Inversion Problem of Heat Conduction Equations

研究了有界域中热传导方程源项反演问题。通过热传导方程的特征值和特征函数,利用分离变量法重建源项,并给出了源项反演的条件稳定性,依据构造的指数型正则化方法,给出了先验选取和后验选取正则化参数下指数型正则化方法的正则化解的收敛性和误差估计。数值模拟的计算结果验证了算法的有效性。

The source term inversion of heat conduction equations in bounded domains is studied.Through the eigenvalues and eigenfunctions of the heat conduction equation,the source term is reconstructed by the separated variable method,and the conditional stability of the source term inversion is given,and the convergence and error estimation of the regularization method under the exponential regularization method under the prior selection and posterior selection regularization parameters are given according to the constructed exponential regularization method.The calculation results of numerical simulation verify the effectiveness of the algorithm.