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

Parameter inversion of solute transport insideunsaturated soils was generally solved through a nonlinear operatorequation. In this paper, we propose a homotopy method to deal with thisproblem. The original problem is finally transformed into an unconstrainedoptimization problem of minimizing the homotopy function. Considering theregularization effect of homotopy parameter, we adopt a two-step updatescheme of homotopy parameter. In the early stage, a quasi-sigmoid method isused to assure the stability of computation, while in the later stage, thecalibration of the homotopy parameter is governed by the computationalresiduals in order to compensate the error of observed data. Problems ofparameter inversion of solute transport coupled with equilibrium andnon-equilibrium effects through one-dimensional unsaturated soils arecarried out as numerical examples and the computational results clearlydemonstrate the feature of global convergence of the homotopy method.Moreover, even though experimental quantities are contaminated heavily bynoise, a favorable solution is still obtained.