UTILIZING SPARSITY IN TIME-VARYING OPTIMAL-CONTROL OF AQUIFER CLEANUP

A method for exploiting the sparsity structure of a finite-element sim ulation model in a linked dynamic optimal control model is developed. The linked optimization/simulation model has been used for the computa tion of time-varying optimal pumping rates for the pump-and-treat reme diation of contaminated ground water. The methodology presented reduce s the computational effort involved in the determination of time-varyi ng optimal pumping rates by an order of n, from n(3) to n(2), where n is the number of non-Dirichlet nodes used in the simulation of the aqu ifer. The method presented uses the characteristic banded structure of finite element model matrices in derivative computations used by the optimal control algorithm, and also within the algorithmic computation s of the optimization method itself. Timing results demonstrating the improvement of this method for problems having n = 100 to n = 1,575 (s tate dimension 2n = 200 to 2n = 3,150) ate presented. It is shown that the efficiency of the sparse algorithm is highest when the length of management periods equals the length of simulation time periods. The r esults indicate that for a problem with 2n = 1,000, the sparse algorit hm is as much as 98% faster than an algorithm neglecting sparsity.