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
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.
