A proposed algorithm for the solution of the large‐scale inverse problem in groundwater

This paper introduces a new algorithm for the solution of the problem of parameter identification associated with a two‐dimensional unsteady state groundwater flow. The parameters to be identified are functions of the space variables. It is assumed that some observations on the dependent variable of the governing equation are available. The unknown parameters are directly identified from observations. An implicit finite difference scheme is used to approximate the original partial differential equation. A least squares criterion function is employed. The identification problem is then formulated as a standard quadratic programing representation by quasi‐linearization. The formulation is further modified by a simple matrix operation which drastically reduces the dimension of the constraint set. The new algorithm is shown to be very effective in solving the large‐scale inverse problem, and it is easily implemented, rapidly convergent, and able to handle any inequality constraints, a feature that is essential for such a problem.