Adjoint Method for an Inverse Problem of CCPF Model

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...

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Bibliographic Details
Published in:Chinese annals of mathematics. Serie B 2014-05, Vol.35 (3), p.337-354
Main Authors: Chen, Zhenhua, An, Kaiqi, Liu, Yuan, Chen, Wenbin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
伴随方法
伴随方程
偏微分方程
反演问题
成本函数
最优化问题
模型
测量值
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Summary: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.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-014-0837-9