The problem for determining the exchange rate function of 2D CCPF model by measurements on the partial boundary is considered and solved as one PDE-constraint optimization problem. The optimal variant is the minimum o...The problem for determining the exchange rate function of 2D CCPF model by measurements on the partial boundary is considered and solved as one PDE-constraint optimization problem. The optimal variant is the minimum of a cost functional that quantifies the difference between the measurements and the exact solutions. Gradientbased algorithm is used to solve this optimization problem. At each step, the derivative of the cost functional with respect to the exchange rate function is calculated and only one forward solution and one adjoint solution are needed. One method based on the adjoint equation is developed and implemented. Numerical examples show the efficiency of the adjoint method.展开更多
Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a c...Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow(CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume(matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely,the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.展开更多
基金supported by the Key Project National Science Foundation of China(No.91130004)the Natural Science Foundation of China(Nos.11171077,11331004)the National Talents Training Base for Basic Research and Teaching of Natural Science of China(No.J1103105)
文摘The problem for determining the exchange rate function of 2D CCPF model by measurements on the partial boundary is considered and solved as one PDE-constraint optimization problem. The optimal variant is the minimum of a cost functional that quantifies the difference between the measurements and the exact solutions. Gradientbased algorithm is used to solve this optimization problem. At each step, the derivative of the cost functional with respect to the exchange rate function is calculated and only one forward solution and one adjoint solution are needed. One method based on the adjoint equation is developed and implemented. Numerical examples show the efficiency of the adjoint method.
基金supported by the National Natural Science Foundation of China(Nos.91330202,11301089,91130004)Chinese Ministry of Education(No.20110071120001)the Programme of Introducing Talents of Discipline to Universities of China(No.B08018)
文摘Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow(CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume(matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely,the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.
