Efficient Computational Algorithm in Groundwater Management

Abstract

In this paper an efficient computational algorithm of the finite element and dynamic linear programming method (the FE&DLP method) for transient groundwater management in confined aquifers is studied in order to save computer time and memory due to its special structures. The FE&DLP method has been developed by the combined use of the finite element method with dynamic linear programming to optimize transient distributed parameter systems with both equality or inequality constraints and an objective function. Such systems are frequently encountered in various engineering and scientific problems of control and optimization and, especially are of interest in groundwater management. The finite element method is powerful numerical method for the solution of differential equation systems because of its generality with respect to geometry and material properties. Dynamic linear programming is the extension of linear programming to the time domain. The proposed efficient computational algorithm (the simplified simplex algorithm) makes it possible to obtain an initial basic feasible solution of the simplex method for linear programming without the introduction of artificial variables and to omit the troublesome Phase I of the simplex method. Therefore, the proposed algorithm allows us to solve large-scale optimal control problems in transient groundwater management.