This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown t...This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, Inverse Problems 13（1997）, pp.253-282] is established for solving the acoustic inverse scattering problem.展开更多
The variational method of data assimilation is used to solve an inverse problem in the transport of sediment in river, which plays an important role in the change of natural environment. The cost function is defined t...The variational method of data assimilation is used to solve an inverse problem in the transport of sediment in river, which plays an important role in the change of natural environment. The cost function is defined to measure the error between model predictions and field observations. The adjoint model of IAP river sedimentation model is created to obtain the gradient of the cost function with respect to control variables. The initial conditions are taken as the control variables; their optimal values can be retrieved by minimizing the cost function with limited memory quasi Newton method (LMQN). The results show that the adjoint method approach can successfully make the model prediction well fit the simulated observations. And it is expected to use this method to solve other inverse problems of river sedimentation. But some numerical problems need to be discussed before applying to real river data.展开更多
文摘This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, Inverse Problems 13（1997）, pp.253-282] is established for solving the acoustic inverse scattering problem.
基金Project partially supported by the State Key Laboratory of Numerical Modelling for Atmospheric Sciences and Geoplysical Fluid Dynmics,Institute of Atmosphenic Physics,Chinese Academy of Sciences.
文摘The variational method of data assimilation is used to solve an inverse problem in the transport of sediment in river, which plays an important role in the change of natural environment. The cost function is defined to measure the error between model predictions and field observations. The adjoint model of IAP river sedimentation model is created to obtain the gradient of the cost function with respect to control variables. The initial conditions are taken as the control variables; their optimal values can be retrieved by minimizing the cost function with limited memory quasi Newton method (LMQN). The results show that the adjoint method approach can successfully make the model prediction well fit the simulated observations. And it is expected to use this method to solve other inverse problems of river sedimentation. But some numerical problems need to be discussed before applying to real river data.
