用同伦方法反演非饱和土中溶质迁移参数

非饱和土中溶质迁移参数反演问题可以归结为非线性算子方程的求解问题. 将同伦方法 引入该问题的求解，通过构造线性同伦将原问题转化为求解同伦函数最小值的无约束优化问 题. 同时在分析了同伦参数正则化效应的基础上，提出一种两段同伦参数修正方法. 即在求 解的初始阶段，根据拟Sigmoid函数调整同伦参数，以追踪同伦路径，保证计算稳定地进行； 在迭代的后期，采用与残差相关的同伦参数修正方法，以抵抗观测噪声对求解的影响. 数值 算例为求解带有平衡及非平衡吸附效应的一维非饱和土中溶质迁移模型参数反演问题，计算 结果表明了该方法的大范围收敛性及较强的抵抗观测噪声的能力.

A homotopy method for parameter inversion of solute transport through unsaturated soils

Parameter inversion of solute transport inside unsaturated soils was generally solved through a nonlinear operator equation. In this paper, we propose a homotopy method to deal with this problem. The original problem is finally transformed into an unconstrained optimization problem of minimizing the homotopy function. Considering the regularization effect of homotopy parameter, we adopt a two-step update scheme of homotopy parameter. In the early stage, a quasi-sigmoid method is used to assure the stability of computation, while in the later stage, the calibration of the homotopy parameter is governed by the computational residuals in order to compensate the error of observed data. Problems of parameter inversion of solute transport coupled with equilibrium and non-equilibrium effects through one-dimensional unsaturated soils are carried out as numerical examples and the computational results clearly demonstrate the feature of global convergence of the homotopy method. Moreover, even though experimental quantities are contaminated heavily by noise, a favorable solution is still obtained.