Parameter Identification Using Quasi-Linearization

Abstract

Identification problems are fundamental to science, engineering, and medicine. In such problems the characteristics of a system must be determined from observations. For example, in managing water re sources, we must determine the transmissivity of an aquifer from measurements of the underground water level at a number of wells.

In this paper we describe the quasi-linearization method for solving the identification problem associated with a set of parabolic differential equa tions. For problems in two spatial dimensions, we discuss the computational aspects of the method, pay ing special attention to the case in which the para bolic equations have widely varying coefficients (i.e., they exhibit numerical dispersion). We apply this method to the problem of identifying transmis sivity for an underground water reservoir. This parameter identification problem is improperly posed. Finally, we present the results of numerical experi ments performed on some test problems.