关于二阶伴随模型的理论研究

基金项目: 国家自然科学基金(49876001);国家“九五”攀登项目“现代地壳运动和地球动力学研究”(C95-04-05)

A study on the theory of second order adjoint model

1.
National Marine Data and Information Service, State Oceanic Administration, Tianjin 300171;Institute of Oceanology, Academy Sinica, Qngdao 266071
2.
College of Mathematical Science, Nankai University, Tianjin 300171
3.
National Marine Data and Information Service, State Oceanic Administration, Tianjin 300171

摘要: Hesse矩阵-目标函数关于控制变量的二阶偏导数形成的矩阵,在变分数据同化过程中以及敏感性分析等方面起着重要的作用;它可以通过建立数学模型的一阶和二阶伴随模型求得.以浅水方程模型为例,利用泛函的Gâteaux微分和Hilbert空间上伴随算子的概念,导出了一阶和二阶伴随模型并由此得到Hesse矩阵.改进了Zhi Wang等(1992)建立的二阶伴随模型理论.
- Hesse矩阵 /
- 二阶伴随模型 /
- 浅水方程模型
Abstract: The Hessian matrix, which is formed by the second order partial derivatives of the cost function with respect to control variables, plays an important role in the procedure of variational data assimilation(VDA), sensitivity analysis, etc.,and it can be obtained by establishing the first order adjoint(FOA) and second order adjoint (SOA) models for direct model.The derivations of the FOA and SOA models of shallow water equations model are given in detail, which is based upon the Gateaux differential of functional and the concepts of the adjoint operators in Hilbert space.We obtain the result for SOA model of the shallow water equations model, which improves the theory established in the paper of Zhi Wang et al.(1992).
- Hessian matrix /
- SOA model /
- shallow water equations model