求解一类热源反演问题的光滑化方法及实现

The Mollification Method and Its Implementations for Solving the Inverse Heat Source Problem

考虑求解一类抛物方程热源反演问题的光滑化方法,给出卷积核函数的一般取法,讨论正则化参数的选取策略,证明无论正则化参数是先验还是后验选取时,正则化解均可达到最优的收敛速度.数值实验说明了该光滑化方法的数值有效性.

The mollification method for solving the inverse heat source problem of parabolic equation is considered in this paper.The general definition of the convolution kernel function is given,and the selection strategy of the regularization parameter is discussed.The convergence rate of regularization solution is order-optimal for both the a-priori and a-posteriori selection strategies of the regularization parameter.Numerical experiments show the numerical validity of the mollification method.