This paper considers the constrained inverse problem based on the nonlinear convection-diffusion equation in the multiphase porous media flow. To solve this problem, a widely convergent homotopy method is introduced and proposed. To evaluate the performance of the mentioned method, two numerical examples are presented. This method turns out to have wide convergence region and strong anti-noise ability.

In this paper, we consider the parameter identification problem of partial differential equations with constraints. A nonlinear multigrid method is introduced to the process of parameter inversion. By keeping the objective functions on coarse grids consistent with those on fine grids, the proposed method reduces the dimensions of objective functions enormously and mitigates the risk of trapping in local minima effectively. Furthermore, constraints significantly improve the convergence ability of the method. We performed the numerical simulation based on the porosity identification of elastic wave equations in the fluid-saturated porous media, which suggests that the nonlinear multigrid method with constraints decreases the computational expenditure, suppresses the noise, and improves the inversion results.

In this study, we developed a vehicle allocation model that can meet the requirements and cost best, the data related to the number of calls in each zone, and the variability required to respond to different types of calls. First, several indicators are extracted to quantify the advantages of station construction in each zone, and the hierarchical analysis method and TOPSIS are used to score each zone, and then select the stations that need to be built according to the score. Subsequently, according to the call requirements of each zone, its distance from the site, the amount of resources owned, etc, we develop a vehicle allocation model based on integer programming.

In this paper, in order to improve traditional TOPSIS water weight distribution model, the analytic hierarchy process combined with coefficient of variation method is used to calculate the weight. In the improved model, vertical distance is adopted to calculate the result, which avoids some defects caused by Euclidean distance. In the process of practical application, improved TOPSIS method selected 12 evaluation indicators with water resources development, social benefits, economic benefits, ecological environmental benefits and other aspects of evaluation, making the model more fit the reality. The results show that when the method is applied to water right allocation in Arizona, the calculated results are in agreement with the practice.