Parameter Identification in a Two-Dimensional Parabolic Equation Using an ADI Based Solver

Abstract

In this work we consider the identification of spatially varying diffusivity in the diffusion-convection-reaction equation from point observations of the state variable. A least-squares approach is used for the parameter identification problem. In order to overcome the ill-posedness for identifying the spatially dependent parameter, the cost functional associated to identification problem is regularized. We studied both the effect of the regularization parameter and the effect of the level of discretization on the parameter estimates. The alternating direction implicit (ADI) method is considered for solving the linear systems of equations. The results of some numerical experiments are presented.