基于离散特征系统的抛物方程源项反演方法

Source Term Inversion of Parabolic Equation Based on Discretecharacteristic System

主要研究离散特征系统下抛物方程源项反演的对数型正则化方法。首先,用有限差分法离散椭圆算子,利用分块矩阵的特点计算出椭圆算子的离散特征值和相应的特征向量;然后,将它们应用到抛物型方程源项反演的对数型正则化方法中。通过数值实验表明,对数型正则化方法可以通过离散特征值及其对应的特征向量成功实现。

This paper mainly studies the logarithmic regularization method for source term inversion of parabolic equations in discrete characteristic systems. Firstly, the finite difference method is used to discretize the elliptic operator, and the discrete eigenvalues and corresponding eigenvectors of the elliptic operator are calculated by using the characteristics of the block matrix;Then, they are applied to the logarithmic regularization method for source term inversion of parabolic equations. Numerical experiments show that the logarithmic regularization method can be successfully implemented through discrete eigenvalues and their corresponding eigenvectors.