Analysis of an adjoint problem approach to the identification of an unknown diffusion coefficient
نویسندگان
چکیده
Abstract. An inverse problem for the identification of an unknown coefficient in a quasilinear parabolic partial differential equation is considered. We present an approach based on utilizing adjoint versions of the direct problem in order to derive equations explicitly relating changes in inputs (coefficients) to changes in outputs (measured data). Using these equations it is possible to show that the coefficient to data mappings are continuous, strictly monotone and injective. The equations are further exploited to construct an approximate solution to the inverse problem and to analyze the error in the approximation. Finally, results of some numerical experiments are displayed.
منابع مشابه
Optimal Control of Light Propagation Governed by Eikonal Equation within Inhomogeneous Media Using Computational Adjoint Approach
A mathematical model is presented in the present study to control the light propagation in an inhomogeneous media. The method is based on the identification of the optimal materials distribution in the media such that the trajectories of light rays follow the desired path. The problem is formulated as a distributed parameter identification problem and it is solved by a numerical met...
متن کاملIncremental Identification of Transport Phenomena in Convection-diffusion Systems
In this paper an incremental approach for the identification of transport phenomena in convection-diffusion systems on the basis of high-resolution measurement data is presented. The transport is represented by a convection term with known convective velocity and by a diffusion term with an unknown, generally state-dependent transport coefficient. The reconstruction of this transport coefficien...
متن کاملEstimating the Parameters in Photovoltaic Modules: A Constrained Optimization Approach
This paper presents a novel identification technique for estimation of unknown parameters in photovoltaic (PV) systems. A single diode model is considered for the PV system, which consists of five unknown parameters. Using information of standard test condition (STC), three unknown parameters are written as functions of the other two parameters in a reduced model. An objective function and ...
متن کاملDamage Assessment using an Inverse Fracture Mechanics approach
This paper studies the application of an inverse methodology for problem solving in fracture mechanics using the finite element analysis. The method was applied to both detection of subsurface cracks and the study of propagating cracks. The procedure for detection of subsurface cracks uses a first order optimization analysis coupled with a penalty function to solve for the unknown geometric par...
متن کاملImplementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary condition
The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...
متن کامل